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http://www.ams.org/mathscinet-getitem?mr=93g:35100	MathSciNet bibliographic data MR1152231 (93g:35100) 35P05 (35J05 58G25) Melas, Antonios D. On the nodal line of the second eigenfunction of the Laplacian in ${\bf R}\sp 2$${\bf R}\sp 2$. J. Differential Geom. 35 (1992), no. 1, 255–263. Article For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.	{"extraction_info": {"found_math": true, "script_math_tex": 1, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9926114678382874, "perplexity": 3644.177371540143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163047545/warc/CC-MAIN-20131204131727-00071-ip-10-33-133-15.ec2.internal.warc.gz"}
http://mystonline.info/adding-mixed-fractions-worksheets/kindergarten-adding-and-subtracting-mixed-fractions-worksheet-year-6-medium-to-large-size-of-proper-improper/	# Kindergarten Adding And Subtracting Mixed Fractions Worksheet Year 6 Medium To Large Size Of Proper Improper kindergarten adding and subtracting mixed fractions worksheet year 6 medium to large size of proper improper. add subtract multiply divide mixed fractions worksheet adding worksheets ks2 3 with answers how to,gallery for adding mixed fractions worksheets subtracting numbers and with like denominators pdf 5th grade simple,adding simple mixed fractions worksheets practice 5th grade how to add with the same denominator a,adding mixed fractions with like denominators worksheets pdf 6th grade 5th math download them and try to solve,adding mixed fractions worksheets 5th grade subtracting multiplying dividing subtract numbers regrouping add multiply divide worksheet,adding and subtracting mixed fractions printable worksheets fraction worksheet with year 6 tes,adding mixed fractions worksheets pdf subtracting multiplying dividing add subtract numbers worksheet like,adding mixed fractions worksheets the best image 5th grade practice simple,adding mixed fractions worksheets pdf with like denominators subtracting and best solutions of add subtract multiply divide worksheet,adding and subtracting mixed fractions worksheets pdf with unlike denominators like math drills to decimals dividing worksheet equivalent.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9097135066986084, "perplexity": 17388.819300352687}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039741192.34/warc/CC-MAIN-20181113020909-20181113042909-00064.warc.gz"}
https://rd.springer.com/article/10.3103/S106345411801003X	Vestnik St. Petersburg University, Mathematics , Volume 51, Issue 1, pp 31–35 # On the Stability of the Zero Solution of a Second-Order Differential Equation under a Periodic Perturbation of the Center • A. A. Dorodenkov Mathematics ## Abstract Small periodic perturbations of the oscillator $$\ddot x + {x^{2n}}$$ sgn x = Y(t, x, $$\dot x$$) are considered, where n < 1 is a positive integer and the right-hand side is a small perturbation periodic in t, which is an analytic function in $$\dot x$$ and x in a neighborhood of the origin. New Lyapunov-type periodic functions are introduced and used to investigate the stability of the equilibrium position of the given equation. Sufficient conditions for asymptotic stability and instability are given. ## Keywords asymptotic stability small periodic perturbation oscillator ## References 1. 1. A. M. Lyapunov, “A study of one of the special cases of the motion stability problem,” in Collected Works (Akad. Nauk SSSR, Moscow, 1956), Vol. 2, pp. 272–331 [in Russian].Google Scholar 2. 2. Yu. N. Bibikov, “Stability and bifurcation for periodic perturbations of the equilibrium of an oscillator with infinite or infinitesimal oscillation frequency,” Math. Notes 65, 269–279 (1999). 3. 3. Yu. N. Bibikov and A. G. Savelyeva, “Periodic perturbations of a nonlinear oscillator,” Differ. Equations 52, 405–412 (2016). 4. 4. A. A. Dorodenkov, “Stability and bifurcation of the birth of invariant tori for an equilibrium state of an essentially nonlinear second-order differential equation,” Vestn. S.-Petersburg Univ.: Math. 42, 262–268 (2009).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8363864421844482, "perplexity": 1305.8907826690415}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159561.37/warc/CC-MAIN-20180923153915-20180923174315-00060.warc.gz"}
https://scipost.org/submissions/1911.06720v2/	# Algebraic structure of classical integrability for complex sine-Gordon ### Submission summary As Contributors: Luc FRAPPAT Arxiv Link: https://arxiv.org/abs/1911.06720v2 (pdf) Date accepted: 2020-02-11 Date submitted: 2020-01-30 01:00 Submitted by: FRAPPAT, Luc Submitted to: SciPost Physics Discipline: Physics Subject area: Mathematical Physics Approach: Theoretical ### Abstract The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed. Published as SciPost Phys. 8, 033 (2020) ### List of changes Dear Editor, We have revised our manuscript according to the requested changes of the referee. Here are the major modifications: - page 2, the sentence has been modified to clarify the point. - we added three paragraphs in section 3 : a/ page 8, a comment on an alternative procedure of quantizing the complex sine-Gordon model (with refs 23 and 24 added); b/ page 8, a comment on the potential existence of discrete quantum systems related to CSG (with ref. 26). c/ page 9, a final paragraph about the feasibility of the quantization itself. In addition, the grammar and the punctuation have been revised. Best regards, The authors	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.719235897064209, "perplexity": 2329.662045936939}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400187899.11/warc/CC-MAIN-20200918124116-20200918154116-00146.warc.gz"}
http://sci-gems.math.bas.bg/jspui/handle/10525/586	Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/586 Title: Functionally Countable Spaces and Baire Functions Authors: Choban, M. Keywords: FunctionallCountable SpaceBaire SetDistinguished SetBaire FunctionMeasurable Mapping Issue Date: 1997 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 233p-242p Abstract: The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice. URI: http://hdl.handle.net/10525/586 ISSN: 1310-6600 Appears in Collections: Volume 23 Number 3-4 Files in This Item: File Description SizeFormat	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5154390931129456, "perplexity": 4990.769037178764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542712.49/warc/CC-MAIN-20161202170902-00025-ip-10-31-129-80.ec2.internal.warc.gz"}
https://biomch-l.isbweb.org/search?searchJSON=%7B%22tag%22%3A%5B%22dynamometry%22%5D%7D	Hi All, I am using a Biodex system 3 dynamometer and Bipac but unfortunately they do not communicate when it comes to gravity correction...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8468731641769409, "perplexity": 2447.4958474764235}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057733.53/warc/CC-MAIN-20210925172649-20210925202649-00130.warc.gz"}
https://discuss.codechef.com/questions/29659/lowsum-editorial	× # LOWSUM - Editorial Author: Vineet Paliwal Tester: Roman Rubanenko Editorialist: Jingbo Shang EASY # PREREQUISITES: Sort, Priority Queue, Binary Search # PROBLEM: Given two arrays A[1..K], B[1..K], deal with Q queries of finding the n-th smallest pair sum in all K^2 pair sums (A[i] + B[j]). # EXPLANATION: A brute force enumeration can give us an O(K^2 logK) - O(1) algorithm: just simply store all possible sums and use the some sorting algorithm such as quick sort. And then, for each query, return the n-th number of the stored sorted array. This brute force algortihm’s time complexity is O(K^2 + Q). Also, it needs O(K^2) space. Both time and memory are exceeded. There are 2 ways to improve this brute force algorithm. The common key point to improve this brute force algorithm is as following: Suppose A[] and B[] are sorted ascendingly, A[i] + B[j] is smaller than or equal to any A[i] + B[k] if k > j. For instance, we use quick sort to sort A[] and B[] in O(K logK) time. And then, 2 possible solutions are here. The first solution is that we can find the smallest sum among at most K candidates (one for each A[i]) and remove it. After n removes, the n-th smallest sum is found. More specifically, we can maintain K pointers for each A[i]. Let’s say ptr[1..K] (equals 1 initially). First, we can use a binary heap (or other priority queues, balanced binary search trees, etc...) to find the smallest sum among A[i] + B[ptr[i]]. Second, suppose the smallest is A[p] + B[ptr[p]]. We remove it from the heap, then increase the pointer ptr[p] by 1 and insert a new element A[p] + B[ptr[p]] if it exists. Repeat this process n times, the n-th smallest sum is got. This algorithm’s time complexity is O(n log K) for each query, and thus O(K logK + Q n logK) in total. The second solution is more tricky and useful. Consider the dual problem: given a number X, find how many pair sums are smaller than or equal to X (The answer of the original problem is that the smallest X such that there are at least n pair sums smaller than or equal to X). To solve the dual problem, based on the previous observation, there exists limit[i] such that A[i] + B[1..limit[i]] are all smaller than or equal to X while A[i] + B[limit[i] + 1 … K] are all greater than X. Furthermore, limit[i] >= limit[i + 1] since A[i] <= A[i + 1]. Using these two properties, we can simply get the rank of X in O(K) time. Through binary search, we can get the answer of original problem in O(K logAnswer), and thus O(K logK + Q K logAnswer) in total. # AUTHOR'S AND TESTER'S SOLUTIONS: Author's solution can be found here. Tester's solution can be found here. This question is marked "community wiki". 13.8k347483500 accept rate: 35% 161446072 2 I solved this after the contest and used a very simple approach. First sort both the arrays. Since the limit on q is 10000, this can be done with the following code. for(j=1;j<=n;++j) { k=10001/j; ind=min(k,n); num=a[j]; for(k=1;k<=ind;++k) v.pb(num+b[k]); } This will ensure that atleast the first 10000 sums will be stored in v. Then we just have to sort the vector v and print the answer of every query. answered 21 Nov '13, 02:08 1.5k●8●21●30 accept rate: 0% can u please explain me ur approach? (12 Dec '13, 10:32) @sikander_nsit please explain your solution more. It would be great for us to get a solution which is very simple and sweet. Thanks, (14 Mar '14, 00:13) your trick is great .. can you give proof of correctness of your algo..please?? (21 Aug '15, 00:58) 1 @arcturus I used binary search to search for X and then binary search to count the pairs, but also a trick (when count exceeds 10.000 break, since qi is maximum 10.000). Without the trick it gave TLE. answered 18 Nov '13, 14:17 4★lazzrov 136●1●1●8 accept rate: 0% Ah, I see. But I guess if the testcase was really evil, the second solution will also get TLE even with that trick. Probably it was not the intended way, as both tester and setter used the first approach. (18 Nov '13, 22:25) arcturus5★ 1 can anybody please explain me the first approach? not getting it :( answered 12 Dec '13, 10:24 296●8●21●22 accept rate: 11% 1 though editorial has been provided for this problem but still i am not able to understand it. it would be great if someone explain me the correct approach to solve this problem.......... answered 28 Dec '13, 14:40 4★zealf 1.1k●6●11●26 accept rate: 3% well,i am requesting again especially to the editorialist of this problem to explain his solution given above... (29 Dec '13, 18:12) zealf4★ 0 Hmm, I tried both approach in the contest. However, only the first one get AC (http://www.codechef.com/viewsolution/2998337 ). The second solution gave me TLE (http://www.codechef.com/viewsolution/2997409 ). Is the time limit too strict for the second solution or it is just me that didn't implement the algorithm efficiently? answered 18 Nov '13, 08:14 5★arcturus 1●2 accept rate: 0% 0 I'm getting wrong answer for this solution. Can someone help me out? http://www.codechef.com/viewsolution/3718821 answered 08 Apr '14, 04:43 3★anndr31 16●1 accept rate: 16% 0 Though editorial has been delivered for this tricky but quiet i am not competent to comprehend it. it would be good if somebody clarify me the exact method to resolve this problem pay to get a research paper done answered 21 Jun '16, 11:35 1 accept rate: 0% 0 Despite the fact that publication has been conveyed for this dubious however calm i am not capable to grasp it. somebody should illuminate me the precise strategy to determine this issue. startup demo video answered 15 Jul '16, 11:47 1 accept rate: 0% toggle preview community wiki By Email: Markdown Basics • italic or _italic_ • bold or __bold__ • image?![alt text](/path/img.jpg "title") • numbered list: 1. Foo 2. Bar • to add a line break simply add two spaces to where you would like the new line to be. • basic HTML tags are also supported • mathemetical formulas in Latex between \$ symbol Tags: ×9,473 ×2,119 ×431 ×397 ×10 ×6	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8689684271812439, "perplexity": 2461.403195065529}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189031.88/warc/CC-MAIN-20170322212949-00018-ip-10-233-31-227.ec2.internal.warc.gz"}
http://math.stackexchange.com/users/18124/daniel?tab=activity&sort=comments	daniel Reputation Top tag Next privilege 5,000 Rep. Approve tag wiki edits 11h comment Why are very large prime numbers important in cryptography? If you have a question the site functions best if you post it as a question rather than an answer. Feb 7 comment Using the Brun Sieve to show very weak approximation to twin prime conjecture Halberstam and Richert in Sieve Methods (Dover, 2011) prove using Brun's sieve that there are infinitely many p such that p+2 has at most 8 prime factors. Including some introductory material the exposition takes 67 pages. The key is their definition of the characteristic function on p. 58. The basic idea is simple enough but doesn't look like it lends itself to anything one could describe as a "straightforward exercise." Jan 18 comment Proof of inequality involving multiplicative function? Terms in the binomial expressions on the left with m factors are all covered by terms in mth powers of the expression on the right. Once we see the LHS can be written as a product of binomials we can compare the two sides. Your hint prompted me to look at the LHS again. The key (which I forgot or didn't know) is that $n=p_k\#,~\binom{k}{m}$ is the number of squarefree divisors of n having $\nu(d)=m.$ Jan 14 comment Proof of inequality involving multiplicative function? @user1952009: edited to reflect that. Jan 10 comment English wording for “first level of asymptotic expansion” You can say $f$ is asymptotically equivalent to $g.$ Jan 9 comment “The PNT obtained by statistical methods” @ErickWong: In that case I will vote to reopen. Jan 8 comment “The PNT obtained by statistical methods” Maybe asking about Erdos-Kac theorem? Jan 1 comment Prove $\| \sum_{i \leq n} \frac{\mu(i)}{i} \| \leq 1$ This result was not relegated to exercises in Apostol and OP say s/he is new to number theory. So I wonder if this is enough. Dec 31 comment Prove $\| \sum_{i \leq n} \frac{\mu(i)}{i} \| \leq 1$ This is proved at pp. 66-67 of Apostol (Intro. to Analytic Number Thy.) Different approach. Dec 24 comment Equidistribution theorem of Weyl Perhaps OP is asking if equidistribution of a sequence $a\cdot n$ can be used to show that $a$ is irrational? I don't think Weyl works in that direction but at least it's a question. Vote to reopen. Dec 12 comment What is the effective lower bound on gaps between zeta zeros? jstor.org/stable/pdf/2372402.pdf?seq=1#page_scan_tab_contents. See paragraph below formula (2). There are a lot of questions here on lim inf with good answers BTW. Nov 25 comment Zeros of the prime zeta function @mixedmath: Minimally, is it possible to show $P(s) =\zeta(s)$ implies $s$ is a zero of $C(s)$ without direct reference to $C(s).$ The argument begins, "Suppose the two integrals are equal for some value of s," and concludes, for example, "s is thus a zero of this series on the right, which with some work is seen to be $C(s).$" Nov 15 comment What is the proportion of primes that can be written as $a^2 + b^2$? See Ingham, The Distribution of Prime Numbers, pp. 106-107. Nov 8 comment What is your idea about this conjecture? @Dylan: Using Eric N's reformulation my claim is $j(2\cdot 3\cdot...\cdot13)\leq 30.$ In the table in the paper $n$ is the index of the largest prime. If $n=6$ then $h(n)$ is 22. According to this paper my claim is true, but the paper gives a stronger result. Nov 7 comment What is your idea about this conjecture? @SimonS: Good question either way, but the numerical work in this case might be misleading. Suppose it is true for some but not all n? Oct 28 comment Proof of Prime Number Theorem The Prime Number Theorem by Jameson is also good. Oct 19 comment Which progressions and sequences are guaranteed to contain infinitely many primes? You can construct infinitely many such sequences. OEIS contains some of the interesting ones. Sep 23 comment What are all of the possible fractional forms an offspring's genetic makeup? Maybe you should post this at the Bio SE site. Sep 10 comment Approximate zeros of a (hypothetical) analog of $\zeta(s)$ @draks: I looked at that question and the very nice answers there (and long ago upvoted). The r.h.s. of (1) in Ray M's answer is quite different from (1) above. Sep 5 comment A (possibly) easier version of Bertrand's Postulate Bertrand implies a prime on p, 2p. Choose p(n) max less than a non-prime n. Then there is a prime on n, 2p(n) which implies a prime on n,2n (Bertrand). So I think the two are equivalent. You don't need case 1, for the reason you give.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9339137077331543, "perplexity": 522.3934481105608}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701162648.4/warc/CC-MAIN-20160205193922-00235-ip-10-236-182-209.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/109548/x-compact-metric-space-fx-rightarrow-mathbbr-continuous-attains-max-min	# $X$ compact metric space, $f:X\rightarrow\mathbb{R}$ continuous attains max/min Let $X$ be a compact metric space, show that a continuous function $f:X\rightarrow\mathbb{R}$ attains a maximum and a minimum value on $X$. Attempt: So the important thing is that I have previously shown that such a function is bounded and that for compact $X$, $f(X)$ is compact given $f$ continuous. In $\mathbb{R}$, compact $\implies$ closed and bounded. So $f(X)$ is closed and contains its accumulation points, and it is bounded so $\exists \sup(A),\inf(A)$ and since closed $\implies \sup(A)\in A, \inf(A)\in A$. Did I miss anything/make an unwarranted leap of logic? - The ideas are all there, and they’re connected properly, but it’s not really a well-written proof as it stands. – Brian M. Scott Feb 15 '12 at 7:24 By the way, $\sup$ and $\inf$ are predefined: use \sup, \inf. – Brian M. Scott Feb 15 '12 at 7:25 It is better to avoid $\exists$ and $\implies$ symbols when writing math. Just write "there exist" and "then". After all, you write math in english not in other strange symbolic language. – leo Jun 9 '12 at 3:15 Here’s an example of how the same argument could be written up nicely. Since $X$ is compact and $f$ is continuous, $f[X]$ is a compact subset of $\mathbb{R}$ and therefore closed and bounded. Since $f[X]$ is bounded, it has both a supremum and an infimum, and since it is closed, $\sup f[X]\in f[X]$ and $\inf f[X]\in f[X]$. Thus, there are $x_0,x_1\in X$ such that $f(x_0)=\inf f[X]$ and $f(x_1)=\sup f[X]$; that is, $f$ attains its minimum and maximum values at $x_0$ and $x_1$, respectively. - +1 Textbook proof. – user38268 Feb 15 '12 at 9:44 Your argument is fundamentally sound, but you have to assume that your metric space is nonempty. Here is a direct proof that requires no other results (the proof generalizes, like yours, to arbitrary topological spaces): Let $X$ be a nonempty metric space and $f:X\to\mathbb{R}$ a continuous function without a maximum. Then $X$ has an open cover without a finite subcover. Proof: 1. Suppose $f(X)$ is unbounded. Then $\big\{f^{-1}\big((-\infty, n)\big):n\in\mathbb{N}\big\}$ is an open cover without finite subcover. 2. Suppose $f(X)$ is bounded, with supremum $s$. Since $f$ has no maximum, $s\notin f(X)$ and $\big\{f^{-1}\big((-\infty, s-1/n)\big):n\in\mathbb{N}\big\}$ is an open cover without finite subcover. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9656176567077637, "perplexity": 211.04115382324284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997895170.20/warc/CC-MAIN-20140722025815-00233-ip-10-33-131-23.ec2.internal.warc.gz"}
http://openstudy.com/updates/50d1e938e4b069abbb70fda2	Here's the question you clicked on: 55 members online • 0 viewing • This Question is Closed 1. anonymous • 3 years ago Best Response You've already chosen the best response. 0 0k 2. anonymous • 3 years ago Best Response You've already chosen the best response. 0 $\frac{6+x}{3}=1$ multiply by LCD (3) $3\frac{6+x}{3}=31$ $6+x=3$ subtract 6 from both sides and you should get the answer 3. anonymous • 3 years ago Best Response You've already chosen the best response. 0 -3... 4. anonymous • 3 years ago Best Response You've already chosen the best response. 0 \|dw:1355934285826:dw\| 5. anonymous • 3 years ago Best Response You've already chosen the best response. 0 \|dw:1355934391619:dw\| 6. anonymous • 3 years ago Best Response You've already chosen the best response. 0 how is it negative? 7. anonymous • 3 years ago Best Response You've already chosen the best response. 0 when u subtract 6 1-6=-5 8. anonymous • 3 years ago Best Response You've already chosen the best response. 0 6+x/3=1 multiply both sides by 3 18+x=3 18+x-3 9. anonymous • 3 years ago Best Response You've already chosen the best response. 0 but how does that make it a negative??? if ur just subtracting and there is no negatives in this problem?? 10. anonymous • 3 years ago Best Response You've already chosen the best response. 0 who is greater the 6 or the 1? 11. anonymous • 3 years ago Best Response You've already chosen the best response. 0 its too easy, its general arithmetics.. 12. anonymous • 3 years ago Best Response You've already chosen the best response. 0 6 duh sorry i thought i posted it 13. anonymous • 3 years ago Best Response You've already chosen the best response. 0 That is the answer that is my book ##### 1 Attachment 14. anonymous • 3 years ago Best Response You've already chosen the best response. 0 thats what i did hehe 15. anonymous • 3 years ago Best Response You've already chosen the best response. 0 its correct @chevygirl Well Done 16. anonymous • 3 years ago Best Response You've already chosen the best response. 0 why did you say -3? @soty2013 17. anonymous • 3 years ago Best Response You've already chosen the best response. 0 we thought its was $\frac{6+x}{3}$ 18. anonymous • 3 years ago Best Response You've already chosen the best response. 0 19. anonymous • 3 years ago Best Response You've already chosen the best response. 0 yes so we said that , now we all are correct lol :) 20. anonymous • 3 years ago Best Response You've already chosen the best response. 0 ok well thanks 21. Not the answer you are looking for? Search for more explanations. • Attachments: Find more explanations on OpenStudy ##### spraguer (Moderator) 5→ View Detailed Profile 23 • Teamwork 19 Teammate • Problem Solving 19 Hero • You have blocked this person. • ✔ You're a fan Checking fan status... Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000035762786865, "perplexity": 20529.313355378268}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719045.47/warc/CC-MAIN-20161020183839-00367-ip-10-171-6-4.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1788075/proof-of-an-equality-norm	# proof of an equality norm Let the mapping $T:\ell^{2}\rightarrow \ell^{2}$ is defined as follow. $$T(x_1,x_2,\ldots,x_n,\ldots)=(x_1,\dfrac{1}{2}x_2,\ldots,\dfrac{1}{n}x_n,\ldots)$$ In this case, i've easily earned: $$\sigma(T)=\{0\}\cup\{\dfrac{1}{n}:n\in\mathbb{N}\}$$ Now, if $\lambda=x+iy\in\mathbb{C}$ and $\lambda\notin\sigma(T)$, i should prove $$\Vert(\lambda I-T)^{-1}\Vert=\dfrac{1}{\displaystyle\inf_{n\in\mathbb{N}}\,\left\vert\lambda-\dfrac{1}{n}\right\vert}$$ can you help me for starting of prove? Thanks. You have $$(\lambda I-T)(x_1,x_2,\ldots)=((\lambda-1)x_1, (\lambda-\frac12)x_2,\ldots).$$ Define an operator $S$ by $$S (x_1,x_2,\ldots)=(\frac{x_1} {\lambda -1},\frac {x_2}{\lambda -\frac12},\ldots).$$ By the choice of $\lambda$ the linear operator $S$ is well-defined and bounded: by construction, $S (\lambda I-T)=(\lambda I-T)S=I$. So $S=(\lambda I-T)^{-1}$ (bounded, because $\lambda\not\in\sigma (T)$. And $$\tag{1}\\|S\\|=\sup\left\{\frac1 {\left\|\lambda-\frac1n\right\|}:\ n\in\mathbb N\right\}=\frac1 {\inf\left\{\left\|\lambda-\frac1n\right \|:\ n\in\mathbb N\right\}}.$$ $\\ \$ The only piece left hanging, to justify the first equality in $(1)$, is to show that if $$R (x_1,x_2,\ldots)=(r_1x_1,r_2x_2,\ldots)$$ then $\\|R\\|=\sup\{\|r_n\|:\ n\}$. This follows, if we write $c=\sup\{\|r_n\|:\ n\}$: $$\\|Rx\\|^2=\sum_j\|r_jx_j\|^2\leq c^2\sum_j\|x_j\|^2=c^2\,\\|x\\|^2,$$ so $\\|R\\|\leq c$. Let $j$ such that $\|r_j\|>r-\frac1j$. If $e_j\in\ell^2$ is the sequence with a $1$ in the $j^{\rm th}$ position and zeroes elsewhere, then $\\|e_j\\|=1$ and $$\\|Re_j\\|=\|r_j\|>r-\frac1j.$$ So $\\|R\\|=c=\sup\{\|r_n\|:\ n\}$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9917354583740234, "perplexity": 115.13234288126687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371624083.66/warc/CC-MAIN-20200406102322-20200406132822-00140.warc.gz"}
http://moodle.dbit.in/mod/forum/discuss.php?d=115	## Site news ### IEEE-DBIT STUDENTS CHAPTER is organizing "LINFOMATRIX" IEEE-DBIT STUDENTS CHAPTER is organizing "LINFOMATRIX" A 2-Day Line Follower Robotic workshop followed by a MAZE SOLVING Robotic Competition on July 26-27, 2014. For the details of the workshop click on the attached documents.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39493268728256226, "perplexity": 24970.836451138468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813818.15/warc/CC-MAIN-20180221222354-20180222002354-00346.warc.gz"}
https://community.wolfram.com/groups/-/m/t/1638221	# Message Boards GROUPS: Posted 1 month ago 255 Views \| 2 Replies \| 0 Total Likes \| This may be a dumb question, but I often need to solve expressions for something other than a variable. As a trivial example, say we have a common-emitter amplifier:Vout = Vsupply - (Vin - Vbe)((hfe + 1)/hfe) * RC/REAnd I want to solve it for the DC transfer function Vout/Vin. Can Mathematica do this, at all?Now, I understand there is actually no solution here, but a small change makes it solvable (and still easy to reason around):Vout = - (Vin - Vbe)((hfe + 1)/hfe)RC/RENow, this simple example I can solve easily. But there are complex expression created in cascades of stages and ladders that get a bit more complex in hurry... But even being to solve the simple problems would be nice as a "calculator" function. I can calculate square roots and look up logarithms in tables myself also, but I sure prefer to work with a calculator.Any ideas? Maybe I just missed something obvious? 2 Replies Sort By: Posted 1 month ago A replacement can do something like that, unless I misunderstand you: In[7]:= Vout == Simplify[Vsupply - (Vin - Vbe) ((hfe + 1)/hfe)RC/RE /. Vin -> Vout/DCTransferFunction] Out[7]= Vout == ((1 + hfe) RC (DCTransferFunction Vbe - Vout))/( DCTransferFunction hfe RE) + Vsupply You can leave it to Mathematica to find the replacement with Solve: Vout == Simplify[ Vsupply - (Vin - Vbe) ((hfe + 1)/hfe)*RC/RE /. Solve[Vout/Vin == DCTransferFunction, Vin][[1]]] Is the intent to eliminate the variables of interest i.e. Vout/Vin->?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.414665162563324, "perplexity": 3753.2243937048606}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578727587.83/warc/CC-MAIN-20190425154024-20190425180024-00178.warc.gz"}
https://www.physicsforums.com/threads/does-time-translational-symmetry-imply-h-0-or-e-0.839007/	# Does time translational symmetry imply H'=0 or E'=0? 1. Oct 21, 2015 ### davidbenari The Hamiltonian is not always equal to the total energy. In fact the Hamiltonian for a system of particles could be defined as $H=L-\sum \dot{q_i}\frac{\partial L}{\partial \dot{q_i}}$ Which is the total energy only if the potential energy is a function of $q_i$ and if the kinetic energy is a homogeneous quadratic function of $\dot{q_i}$. I know how to show that the condition $\frac{\partial L}{\partial t}=0$ implies $\frac{d}{dt}H=0$. But I was left wondering: People always say time-translational symmetry implies conservation of energy, but I don't think this is the case. Time translational symmetry implies the conservation of the Hamiltonian, which may or may not be the total energy. So which one is true? Does time translational symmetry imply conservation of the Hamiltonian or of the Energy? In my opinion it could imply the energy too, given a good set of coordinates that aren't flying around in space w.r.t to an inertial frame such that it would involve time in your Lagrangian... Thanks. Last edited: Oct 21, 2015 2. Oct 22, 2015 ### Staff: Mentor You can always write the total energy as Hamiltonian. It might be possible to write down a proper Hamiltonian for things that are not the total energy (not sure), but that doesn't change the result of energy conservation. 3. Oct 22, 2015 ### davidbenari Hmm. My book derives $\frac{d}{dt}(L-\sum \dot{q}_i \frac{\partial L}{\partial \dot{q}_i})=0$ from time translational symmetry. Where the quantity in parenthesis is $-H$. In order to show $H=K+U$ you would need $U=U(q_i)$ and $\sum \dot{q}_i\frac{\partial K}{\partial \dot{q}_i}=2K$ (which is Eulers theorem for homogeneous functions). Also you need that the transformation equations between generalized coordinates and rectangular coordinates don't contain time. Which makes sense once you verify those statements (I could post some of this work in case its not too clear). I don't see why total energy would always be the Hamiltonian given the restrictions above. Is there a theorem you could point me to? Something to ponder? Thanks. 4. Oct 22, 2015 ### davidbenari Is there a way to circumvent the Hamiltonian expression to derive $\frac{d}{dt} E =0$ from $\frac{\partial L}{\partial t}=0$? 5. Oct 22, 2015 ### davidbenari Also I've noticed many proofs of the typical statements of Noether's theorem aren't quite that general as people try to say. For example, "space translational symmetry implies conservation of linear momentum". Well, that requires that the potential be velocity independent. So its not as general as the sentence in quotations tries to imply. I guess most potentials are velocity independent though...	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9164883494377136, "perplexity": 351.8831870555308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590443.0/warc/CC-MAIN-20180719012155-20180719032155-00608.warc.gz"}
http://web.eecs.utk.edu/~dongarra/etemplates/node145.html	Next: Software Availability Up: Jacobi-Davidson Methods G. Sleijpen Previous: An Algorithm Template. Contents Index Computing Interior Eigenvalues If one is searching for the eigenpair with the smallest or largest eigenvalue only, then the obvious restart approach works quite well, but often it does not do very well if one is interested in an interior eigenvalue. The problem is that the Ritz values converge monotonically towards exterior eigenvalues, and a Ritz value that is close to a target value in the interior of the spectrum may be well on its way to some other exterior eigenvalue. It may even be the case that the corresponding Ritz vector has only a small component in the direction of the desired eigenvector. It will be clear that such a Ritz vector represents a poor candidate for restart and the question is, What is a better vector for restart? One answer is given by the so-called harmonic Ritz vectors, discussed in §3.2; see also [331,349,411]. As we have seen, the Jacobi-Davidson methods generate basis vectors for a subspace . For the projection of onto this subspace we compute the vectors . The harmonic Ritz values are inverses of the Ritz values of , with respect to the subspace spanned by the . They can be computed without inverting , since a harmonic Ritz pair satisfies (60) for and . This implies that the harmonic Ritz values are the eigenvalues of the pencil , or, since : For stability reasons we orthonormalize the columns of and transform the columns of accordingly. This also further simplifies the equation: we see that the harmonic Ritz values are the inverses of the eigenvalues of the symmetric matrix . In [349] it is shown that for Hermitian the harmonic Ritz values converge monotonically towards the smallest nonzero eigenvalues in absolute value. Note that the harmonic Ritz values are unable to identify a zero eigenvalue of , since that would correspond to an infinite eigenvalue of . Likewise, the harmonic Ritz values for the shifted matrix converge monotonically towards eigenvalues closest to the target value . Fortunately, the search subspace for the shifted matrix and the unshifted matrix coincide, which facilitates the computation of harmonic Ritz pairs for any shift. The harmonic Ritz vector for the shifted matrix, corresponding to the harmonic Ritz value closest to , can be interpreted as maximizing a Rayleigh quotient for . It represents asymptotically the best information that is available for the wanted eigenvalue, and hence it represents asymptotically the best candidate as a starting vector after restart, provided that . For harmonic Ritz values, the correction equation has to take into account the orthogonality with respect to , and this leads to skew projections. We can use orthogonal projections in the following way. If is the selected approximation of an eigenvector, the Rayleigh quotient leads to the residual with smallest norm; that is, with , we have that for any scalar , including the harmonic Ritz value . Moreover, the residual for the Rayleigh quotient is orthogonal to . This makes compatible'' with the operator in the correction equation. Here . An algorithm for the Jacobi-Davidson method based on harmonic Ritz values and vectors, combined with restart and deflation, is given in Algorithm 4.19. The algorithm can be used for the computation of a number of successive eigenvalues immediately to the right of the target value . To apply this algorithm we need to specify a starting vector , a tolerance , a target value , and a number that specifies how many eigenpairs near should be computed. The value of denotes the maximum dimension of the search subspace. If it is exceeded, a restart takes place with a subspace of specified dimension . On completion, the eigenvalues at the right side nearest to are delivered. The computed eigenpairs , , satisfy , where denotes the th column of . For exterior eigenvalues a simpler algorithm has been described in §4.7.3. We will now comment on some parts of the algorithm in view of our discussions in previous subsections. (1) Initialization phase. (3)-(7) The vector is made orthogonal with respect to the current test subspace by means of modified Gram-Schmidt. This can be replaced, for improved numerical stability, by an adoption (for the vector ) of the template given in Algorithm 4.14. (8)-(10) The values represent elements of the square by matrix , where denotes the by matrix with columns , and likewise . Because is Hermitian, only the upper triangular part of this matrix is computed. (11)-(13) At this point the eigenpairs for the problem should be computed. This can be done with a suitable routine for Hermitian dense matrices from LAPACK. Note that the harmonic Ritz values are the inverses of the eigenvalues of . We have to compute the Rayleigh quotient for , and next normalize , in order to compute a proper residual . We have used that . The vectors are the columns of by matrix and . (14) The stopping criterion is to accept an eigenvector approximation as soon as the norm of the residual (for the normalized eigenvector approximation) is below . This means that we accept inaccuracies in the order of in the computed eigenvalues, and inaccuracies (in angle) in the eigenvectors of , provided that the associated eigenvalue is simple and well separated from the others; see (4.4). Detection of all wanted eigenvalues cannot be guaranteed; see note (14) for Algorithm 4.13 and note (13) for Algorithm 4.17. (17) This is a restart after acceptance of an approximate eigenpair. The restart is slightly more complicated since two subspaces are involved. Recomputation of the spanning vectors from these subspaces is done in (18)-(21). (24) At this point we have a restart when the dimension of the subspace exceeds . After a restart, the Jacobi-Davidson iterations are resumed with a subspace of dimension . The selection of this subspace is based on the harmonic Ritz values nearest to the target . (31)-(32) The deflation with computed eigenvectors is represented by the factors with . The matrix has the computed eigenvectors as its columns. If a left preconditioner is available for the operator , then with a Krylov solver similar reductions are realizable, as in the situation for exterior eigenvalues. A template for the efficient handling of the left-preconditioned operator is given in Algorithm 4.18. Next: Software Availability Up: Jacobi-Davidson Methods G. Sleijpen Previous: An Algorithm Template. Contents Index Susan Blackford 2000-11-20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9120842814445496, "perplexity": 502.99966576387254}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500826322.0/warc/CC-MAIN-20140820021346-00017-ip-10-180-136-8.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/speed-of-electron.217436/	# Homework Help: Speed of electron 1. Feb 23, 2008 ### tony873004 ** Edit: Nevermind. I figured it out using the Work Energy theorem. An electron is released from rest 1.0 cim above a uniformly charged infinite plane with a charge density of 10-9C/m2. What is the speed of the electron when it hits the plane? my attempt: Potential energy when it is released= kinetic energy when it hits. kqQ/r = 0.5 mv2 isolate v: $$v = \sqrt {\frac{{2kqQ}}{{m \cdot r}}}$$ This would work if I was given 2 point charges, but how do I do this with a charge density and a point charge? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution Last edited: Feb 23, 2008	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9648508429527283, "perplexity": 913.7835017461068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221219469.90/warc/CC-MAIN-20180822030004-20180822050004-00500.warc.gz"}
http://en.wikipedia.org/wiki/Bit_shifting	# Bitwise operation (Redirected from Bit shifting) In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits. It is a fast, primitive action directly supported by the processor, and is used to manipulate values for comparisons and calculations. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. ## Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least significant) side, advancing left. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first one. ### NOT The bitwise NOT, or complement, is a unary operation that performs logical negation on each bit, forming the ones' complement of the given binary value. Bits that are 0 become 1, and those that are 1 become 0. For example: NOT 0111 (decimal 7) = 1000 (decimal 8) The bitwise complement is equal to the two's complement of the value minus one. If two's complement arithmetic is used, then NOT x = −x − 1. For unsigned integers, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. For example, for 8-bit unsigned integers, NOT x = 255 - x, which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a decreasing range from 255 to 0. A simple but illustrative example use is to invert a grayscale image where each pixel is stored as an unsigned integer. ### AND A bitwise AND takes two binary representations of equal length and performs the logical AND operation on each pair of corresponding bits. The result in each position is 1 if the first bit is 1 and the second bit is 1; otherwise, the result is 0. In this, we perform the multiplication of two bits; i.e., 1 × 0 = 0 and 1 × 1 = 1. For example: 0101 (decimal 5) AND 0011 (decimal 3) = 0001 (decimal 1) The operation may be used to determine whether a particular bit is set (1) or clear (0). For example, given a bit pattern 0011 (decimal 3), to determine whether the second bit is set we use a bitwise AND with a bit pattern containing 1 only in the second bit: 0011 (decimal 3) AND 0010 (decimal 2) = 0010 (decimal 2) Because the result 0010 is non-zero, we know the second bit in the original pattern was set. This is often called bit masking. (By analogy, the use of masking tape covers, or masks, portions that should not be altered or portions that are not of interest. In this case, the 0 values mask the bits that are not of interest.) If we store the result, this may be used to clear selected bits in a register. Given the example 0110 (decimal 6), the second bit may be cleared by using a bitwise AND with the pattern that has a zero only in the second bit: 0110 (decimal 6) AND 1101 (decimal 13) = 0100 (decimal 4) Because of this property, it becomes easy to check the parity of a binary number by checking the value of the lowest valued bit. Using the example above: 0110 (decimal 6) AND 0001 (decimal 1) = 0000 (decimal 0) Therefore 6 is divisible by two and even. ### OR A bitwise OR takes two bit patterns of equal length and performs the logical inclusive OR operation on each pair of corresponding bits. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1; otherwise, the result is 0. For example: 0101 (decimal 5) OR 0011 (decimal 3) = 0111 (decimal 7) The bitwise OR may be used to set selected bits, such as a specific bit (or flag) in a register where each bit represents an individual Boolean state. For example 0010 (decimal 2) can be considered a set of four flags, where the first, third, and fourth flags are clear (0) and the second flag is set (1). The fourth flag may be set by performing a bitwise OR between this value and a bit pattern with only the fourth bit set: 0010 (decimal 2) OR 1000 (decimal 8) = 1010 (decimal 10) This technique is an efficient way to store a number of Boolean values using as little memory as possible. ### XOR A bitwise XOR takes two bit patterns of equal length and performs the logical exclusive OR operation on each pair of corresponding bits. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1. In this we perform the comparison of two bits, being 1 if the two bits are different, and 0 if they are the same. For example: 0101 (decimal 5) XOR 0011 (decimal 3) = 0110 (decimal 6) The bitwise XOR may be used to invert selected bits in a register (also called toggle or flip). Any bit may be toggled by XORing it with 1. For example, given the bit pattern 0010 (decimal 2) the second and fourth bits may be toggled by a bitwise XOR with a bit pattern containing 1 in the second and fourth positions: 0010 (decimal 2) XOR 1010 (decimal 10) = 1000 (decimal 8) This technique may be used to manipulate bit patterns representing sets of Boolean states. Assembly language programmers sometimes use XOR as a short-cut to setting the value of a register to zero. Performing XOR on a value against itself always yields zero, and on many architectures this operation requires fewer clock cycles and/or memory than loading a zero value and saving it to the register. ### Mathematical equivalents Assuming x > y, for the non-negative integers, the bitwise operations can be written as follows: $\text{NOT }x = \sum_{n=0}^{b}2^n\left[\left(\left\lfloor\frac{x}{2^n}\right\rfloor \bmod 2 + 1\right) \bmod 2\right]$ $x\text{ AND }y = \sum_{n=0}^{b}2^n\left(\left\lfloor\frac{x}{2^n}\right\rfloor \bmod 2\right)\left(\left\lfloor\frac{y}{2^n}\right\rfloor \bmod 2\right)$ $x\text{ OR }y = \sum_{n=0}^{b}2^n\left[\left[\left(\left\lfloor\frac{x}{2^n}\right\rfloor \bmod 2\right) + \left(\left\lfloor\frac{y}{2^n}\right\rfloor \bmod 2\right) + \left(\left\lfloor\frac{x}{2^n}\right\rfloor \bmod 2\right)\left(\left\lfloor\frac{y}{2^n}\right\rfloor \bmod 2\right)\bmod 2\right]\bmod 2\right]$ $x\text{ XOR }y = \sum_{n=0}^{b}2^n\left[\left[\left(\left\lfloor\frac{x}{2^n}\right\rfloor \bmod 2\right) + \left(\left\lfloor\frac{y}{2^n}\right\rfloor \bmod 2\right)\right]\bmod 2\right]$ Where $b$ is the number of bits in $x$ ($= \lfloor\log_2 x\rfloor$ for all $x \neq 0$). ### Atomic inputs For the examples above often 3 and 5 (binary 0011 and 0101) are used as inputs. They correspond to the unchanged statements among the 2-ary logical connectives. For the 3-ary case 15, 51 and 85 would be used. These numbers are found in the number triangle : 1 01 3 5 0011 0101 15 51 85 00001111 00110011 01010101 ## Bit shifts The bit shifts are sometimes considered bitwise operations, because they operate on the binary representation of an integer instead of its numerical value; however, the bit shifts do not operate on pairs of corresponding bits, and therefore cannot properly be called bit-wise. In these operations the digits are moved, or shifted, to the left or right. Registers in a computer processor have a fixed width, so some bits will be "shifted out" of the register at one end, while the same number of bits are "shifted in" from the other end; the differences between bit shift operators lie in how they determine the values of the shifted-in bits. ### Arithmetic shift Left arithmetic shift Right arithmetic shift In an arithmetic shift, the bits that are shifted out of either end are discarded. In a left arithmetic shift, zeros are shifted in on the right; in a right arithmetic shift, the sign bit (the MSB in two's complement) is shifted in on the left, thus preserving the sign of the operand. This example uses an 8-bit register: 00010111 (decimal +23) LEFT-SHIFT = 00101110 (decimal +46) 10010111 (decimal −105) RIGHT-SHIFT = 11001011 (decimal −53) In the first case, the leftmost digit was shifted past the end of the register, and a new 0 was shifted into the rightmost position. In the second case, the rightmost 1 was shifted out (perhaps into the carry flag), and a new 1 was copied into the leftmost position, preserving the sign of the number. Multiple shifts are sometimes shortened to a single shift by some number of digits. For example: 00010111 (decimal +23) LEFT-SHIFT-BY-TWO = 01011100 (decimal +92) A left arithmetic shift by n is equivalent to multiplying by 2n (provided the value does not overflow), while a right arithmetic shift by n of a two's complement value is equivalent to dividing by 2n and rounding toward negative infinity. If the binary number is treated as ones' complement, then the same right-shift operation results in division by 2n and rounding toward zero. ### Logical shift Left logical shift Right logical shift In a logical shift, zeros are shifted in to replace the discarded bits. Therefore the logical and arithmetic left-shifts are exactly the same. However, as the logical right-shift inserts value 0 bits into the most significant bit, instead of copying the sign bit, it is ideal for unsigned binary numbers, while the arithmetic right-shift is ideal for signed two's complement binary numbers. ### Rotate no carry Left circular shift or rotate Right circular shift or rotate Another form of shift is the circular shift or bit rotation. In this operation, the bits are "rotated" as if the left and right ends of the register were joined. The value that is shifted in on the right during a left-shift is whatever value was shifted out on the left, and vice versa. This operation is useful if it is necessary to retain all the existing bits, and is frequently used in digital cryptography. ### Rotate through carry Left rotate through carry Right rotate through carry Rotate through carry is similar to the rotate no carry operation, but the two ends of the register are separated by the carry flag. The bit that is shifted in (on either end) is the old value of the carry flag, and the bit that is shifted out (on the other end) becomes the new value of the carry flag. A single rotate through carry can simulate a logical or arithmetic shift of one position by setting up the carry flag beforehand. For example, if the carry flag contains 0, then x RIGHT-ROTATE-THROUGH-CARRY-BY-ONE is a logical right-shift, and if the carry flag contains a copy of the sign bit, then x RIGHT-ROTATE-THROUGH-CARRY-BY-ONE is an arithmetic right-shift. For this reason, some microcontrollers such as low end PICs just have rotate and rotate through carry, and don't bother with arithmetic or logical shift instructions. Rotate through carry is especially useful when performing shifts on numbers larger than the processor's native word size, because if a large number is stored in two registers, the bit that is shifted off the end of the first register must come in at the other end of the second. With rotate-through-carry, that bit is "saved" in the carry flag during the first shift, ready to shift in during the second shift without any extra preparation. ### Shifts in C, C++, C#, Python In C-inspired languages, the left and right shift operators are "<<" and ">>", respectively. The number of places to shift is given as the second argument to the shift operators. For example, x = y << 2; assigns x the result of shifting y to the left by two bits. In C, the result of right-shifting a negative value is implementation-defined, and the result of left-shifting a signed value is undefined if the result cannot be represented in the result type.[1] In C#, the right-shift is an arithmetic shift when the first operand is an int or long. If the first operand is of type uint or ulong, the right-shift is a logical shift.[2] There are also compiler-specific intrinsics implementing circular shifts, like _rotl8, _rotl16, _rotr8, _rotr16 in Microsoft Visual C++. ### Shifts in Java In Java, all integer types are signed, and the "<<" and ">>" operators perform arithmetic shifts. Java adds the operator ">>>" to perform logical right shifts, but because the logical and arithmetic left-shift operations are identical, there is no "<<<" operator in Java. More details of Java shift operators:[3] • The operators << (left shift), >> (signed right shift), and >>> (unsigned right shift) are called the shift operators. • The type of the shift expression is the promoted type of the left-hand operand. For example, aByte >>> 2 is equivalent to ((int) aByte) >>> 2. • If the promoted type of the left-hand operand is int, only the five lowest-order bits of the right-hand operand are used as the shift distance. It is as if the right-hand operand were subjected to a bitwise logical AND operator & with the mask value 0x1f (0b11111).[4] The shift distance actually used is therefore always in the range 0 to 31, inclusive. • If the promoted type of the left-hand operand is long, then only the six lowest-order bits of the right-hand operand are used as the shift distance. It is as if the right-hand operand were subjected to a bitwise logical AND operator & with the mask value 0x3f (0b111111).[4] The shift distance actually used is therefore always in the range 0 to 63, inclusive. • The value of n >>> s is n right-shifted s bit positions with zero-extension. ### Shifts in Pascal In Pascal, as well as in all its dialects (such as Object Pascal and Standard Pascal), the left and right shift operators are "shl" and "shr", respectively. The number of places to shift is given as the second argument. For example, the following assigns x the result of shifting y to the left by two bits: x := y shl 2; ## Applications Bitwise operations are necessary particularly in lower-level programming such as writing device drivers, low-level graphics, communications protocol packet assembly, and decoding. Although machines often have efficient built-in instructions for performing arithmetic and logical operations, in fact, all these operations can be performed by combining the bitwise operators and zero-testing in various ways.[5] For example, here is a pseudocode example showing how to multiply two arbitrary integers a and b (a greater than b) using only bitshifts and addition: c = 0 while b ≠ 0 if (b and 1) ≠ 0 c = c + a left shift a by 1 right shift b by 1 return c This implementation of ancient Egyptian multiplication, like most multiplication algorithms, involves bitshifts: while a ≠ 0 c = b and a b = b xor a left shift c by 1 a = c return b As a note, in these code samples "=" is the assignment operator, not the equality operator.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4798150658607483, "perplexity": 1251.3320212294816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678702045/warc/CC-MAIN-20140313024502-00075-ip-10-183-142-35.ec2.internal.warc.gz"}
https://web2.0calc.com/questions/help-please-find-the-residue-of-182-cdot-12-15-cdot-7-3-pmod-14	+0 # Help Please! Find the residue of $182\cdot 12 - 15\cdot 7 + 3\pmod{14}$. 0 36 4 Please Help! Mar 15, 2020 ### 4+0 Answers #1 +2847 0 please help your latex rendering Mar 15, 2020 #2 0 The answer was ten Guest Mar 15, 2020 #3 0 the answer was ten? What is the answer now? Did it change? Guest Mar 16, 2020 #4 +24366 +1 Help Please! Find the residue of $$182\cdot 12 - 15\cdot 7 + 3\pmod{14}$$. $$\begin{array}{\|rcll\|} \hline && \mathbf{182\cdot 12 - 15\cdot 7 + 3\pmod{14}} \\ &=& 2082 \pmod{14} \\ &=& 148*14 + 10 \pmod{14} \\ &=& 0 + 10 \pmod{14} \\ &=& \mathbf{ 10 \pmod{14} } \\ \hline \end{array}$$ Mar 16, 2020	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9989268779754639, "perplexity": 19886.603242120455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370505366.8/warc/CC-MAIN-20200401034127-20200401064127-00389.warc.gz"}
http://tex.stackexchange.com/questions/51192/how-to-use-underscores-with-pgfplotstable	# How to use underscores with pgfplotstable? I have an input file like this: ``````some_entry 123 another_entry 456 yet_another_entry 789 `````` and I want to typeset it as a table with: ``````\pgfplotstabletypeset[col sep=space]{FILENAME} `````` Problem is that LaTeX seems to interpret the underscores as a command to typeset subscript. Escaping the underscores in the input file does not work. - `\begingroup\makeatletter\@makeother\_\pgfplotstabletypeset[col sep=space]{FILENAME}\endgroup` might work – egreg Apr 8 '12 at 16:09 ``````\pgfplotstabletypeset[col sep=space,columns/colname1/.style={string type}]{FILENAME} ``````colname1 colname2	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.988874077796936, "perplexity": 11012.454454372557}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699186520/warc/CC-MAIN-20130516101306-00015-ip-10-60-113-184.ec2.internal.warc.gz"}
http://math.tutornext.com/calculus/limits-at-infinity.html	# Limits at Infinity Sub Topics Limits at infinity is an important topic in calculus. It deals with the maximization of any application that has to be dealt with in physics, chemistry and engineering applications. Example : A particle inside a potential well varies from x $\rightarrow$ 0 to $\infty$. ## Finding Limits at Infinity Finding limits at infinity is an important concept as it helps us understand the behavior of a function. A function can have a domain from +$\infty$ to -$\infty$ or can have a range from +$\infty$ to -$\infty$. Limits at infinity has a broad meaning. It may refer to the limit of the function when the variable approaches $\pm \infty$ , the function approaches $\pm \infty$ for some values of the variable or when the variable approaches $\pm \infty$ , the function also approaches $\pm \infty$ . In the first case it would be referred to as the limits at infinity, in the second case it is called as the infinite limits and in the third case it is referred to as infinite limits at infinity. ## Limits at Infinity Rules To make the evaluation of the limits at infinity, a closer study has revealed certain interesting facts and helped mathematicians to frame the limits at infinity rules. Before we proceed, we would like to remind you that limits at infinity are relevant only in case of rational functions. For polynomial functions, the quick answer is the limit would either be $\infty$ or -$\infty$. Let f(x) is a rational function expressed in the form f(x) = $\frac{g(x)}{h(x)}$ $h(x)\neq 0$. The order of the functions play an important role. The limit at infinity rules state that, 1) If the order of g(x) is higher than that of h(x) then the limit at infinity is $\infty$ , if the sign of the ratio of the leading coefficients is positive and -$\infty$ if the sign of the ratio of the leading coefficients is negative. 2) If the order of g(x) is same as that of h(x) then the limit at infinity is the ratio of the leading coefficients. 3) If the order of g(x) is lower than that of h(x) then the limit at infinity is 0. ## Evaluating Limits at Infinity Evaluating limits at infinity for rational functions is easily done by the rules we have already stated. These rules are framed by just simple algebraic operations. As an example, let us illustrate one case. Let f(x) = $\left [ \frac{6x^{2}}{(3x^{2}+2x)} \right ]$, dividing both the numerator and the denominator by x2, f(x) = $\frac{6}{[3+(\frac{2}{x})]}$. As x ->$\infty$, the term $\frac{2}{x}$ becomes 0 and hence the limit is $\frac{6}{3}$ = 2, which is the ratio of the leading coefficients. In case of polynomial functions the limit at infinity is $\infty$ or -$\infty$, depends on the sign of the leading coefficient. In case of logarithmic functions, the limit at infinity is $\infty$ . In case of exponential functions, the limit at infinity is $\infty$or 0, depending on the sign of the exponent variable. For example, the limit at infinity of ex is $\infty$ and of e-x is 0.The limit at infinity of trigonometric functions are interesting. Since the range of sine and cosine functions are restricted to [-1,1], the limit is indefinite but it is bounded only between -1 and 1. For the remaining four trigonometric functions the limit at infinity is undefined because all have a range of (- $\infty$,$\infty$). ## Limits at Infinity Examples Let us see few examples of limits at infinity, Let f(x) = x4 - 5x2 + 6. This is a polynomial function and the leading coefficient is positive. Hence the limit at infinity of this function is $\infty$ . Let f(x) = -2x3 - 4x2 + 8. This is a polynomial function and the leading coefficient is negative. Hence the limit at infinity of this function is -$\infty$. Let f(x) = $\left [ \frac{3x}{(4x^{2}+5x)} \right ]$. This is a rational function and the order of the numerator function is less than that of the denominator function. As per the limits at infinity rules, the limit at infinity for this function is 0. We have already explained about the limits at infinity for logarithmic, exponential and trigonometric functions. We will see another important example, probably, the definition of e, the exponential constant. Consider the function f(x)= $[1+(\frac{1}{x})]^{x}$. Let us evaluate the limit at infinity of this function. Taking the natural logarithm on both sides, In f(x) = In F(x) = $[1+(\frac{1}{x})]^{x}$ = $xf(x)$ = $[1+(\frac{1}{x})]$ = $x[(\frac{1}{x})-(\frac{1}{2x^{2}})+(\frac{1}{3x^{3}})-.....]$ =$[(1)-(\frac{1}{2x})+(\frac{1}{3x^{2}})]$ or, f(x) = $e^{[(1)-(\frac{1}{2x})+(\frac{1}{3x^{2}})-.....]}$ Now the limit at infinity of f(x) = limit at infinity of $e^{[(1)-(\frac{1}{2x})+(\frac{1}{3x^{2}})-.....]}$ = e Therefore, limit at infinity of $[1+(\frac{1}{x})]^{x}$ = e. ## Infinite Limits Infinite limits means the limit of the function is $\infty$ or -$\infty$ for one or more values of the variable. Obvious examples are logarithmic functions and trigonometric functions, other than sine and cosine functions. For rational functions, infinite limits occur at points where the denominator function becomes 0. A logarithmic function has infinite limit of - $\infty$ for logarithm of a term approaches 0. Trigonometric functions, other than sine and cosine functions have infinite limits of $\infty$ or -$\infty$ for some values of the variable. For example, for f(x) = tan (x) the left hand side limit at odd multiples of $\frac{\pi }{2}$ is $\infty$ and the right hand side limit at odd multiples of $\frac{\pi }{2}$ is -$\infty$. ## Finding Infinite Limits There are different methods of finding infinite limits of functions, depending on the types of functions. The infinite limits of rational functions occur at the zeroes of the denominator function. Hence the method to find infinite limits is to find the zeroes of the function. It may be noted that if there are common factor terms between the numerator and the denominator functions, the limit is not infinite for the solution of the common factor. The rational function has only a hole there. For example if $f(x)$ = $\frac{(x^{2}-1)}{[(x-1)(x+2)]}$, the limit at x = 1 is not infinite. On the other hand, it has an infinite limit at x = -2.The infinite limits of other functions can be found by solving for the value of the variable which would make the function approach $\infty$ or - $\infty$. We will discuss more with examples in the next section. ## Evaluating Infinite Limits Evaluating infinite limits or solving infinite limits involve more of algebraic techniques based on the concept of infinite limits. Let us illustrate with a few examples. ## Infinite Limits at Infinity Functions which tend to $\infty$ or -$\infty$ when the variable approaches $\infty$ or -$\infty$, they are said to have infinite limits at infinity. All polynomial functions, logarithmic function and exponential functions with positive exponents have infinite limits at infinity. A rational function in which the numerator function is of higher order than that of the denominator function has infinite limits at infinity. Because the rational function can be simplified by long division and the quotient will contain the variable or its higher powers, For example, the limit at infinity for the function f(x) = $\frac{(x^{2}+2x-4)}{(x)}$ is $\infty$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9967238903045654, "perplexity": 232.73916037751692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645330816.69/warc/CC-MAIN-20150827031530-00069-ip-10-171-96-226.ec2.internal.warc.gz"}
https://math.stackexchange.com/questions/1950206/understanding-low-rank-approximation-from-the-svd	# Understanding low-rank approximation, from the SVD I've been on a couple Wikipedia pages today reading up on the SVD and the use of low rank approximation, and I have a couple of basic questions: if $$A = U\Sigma V^*$$ $$= [U_1 U_2] \begin{bmatrix} \Sigma_1 & 0 \\ 0 & \Sigma_2 \\ \end{bmatrix}[V_1 V_2]$$ then $A'=U_1\Sigma_1V_1$, called a "reduced SVD", is a rank $r$ matrix such that the Frobenius norm $\|\|A-A'\|\|_F$ is minimized. So, does this mean that for some large data matrix -- let's say all the columns of $A$ represent lung cancer patients, and the rows represent variables such as the patients' age, height, weight, marital status, smoker / non-smoker, has or doesn't have family history of cancer, etc. -- with the lower rank $r$ matrix, we essentially "delete" all of the rows that are insignificant, in the sense that those rows of variables showed no variance and so isn't helpful? E.g. maybe the vast majority of patients are married, and so we delete the row corresponding to marital status. And so we keep all the rows of the matrix that have the most variance. Intuitively, this seems wrong: based on the above, I could wrongly throw out the row variable of smoker status, if the vast majority of the patients were smokers and so there is little variance. But that would be throwing out pretty essential data that shows that most lung cancer patients were smokers. So, where have I gone wrong in my thinking of low-rank approximation / the SVD? Also, concerning the data matrix $A$: does it ever act on vectors via ? That would seem silly...what would its "action" even be? It's just an enormous array of the patients' data. It's not some...rotation...or dilation...or reflection....or projection... whereas, in contrast, a stochastic matrix acting on probability vectors has the effect of 'updating' the probability vector of some Markov chain. Thanks, • – dantopa Jun 5 '17 at 22:38 Also remember that when you do low rank approximation you basically remove the contribution of the singular vectors that correspond to the smallest singular values. These do not necessarily correspond to the rows of the matrix $A$ but could correspond to some linear combination of them. I hope this helps. • Glad I could help. As far as I know Matlab doesn't do any qualitative stuff on its own. Matlab will perform SVD on the Matrix as you say and will give the researcher 3 matrices. The $U$,$V$ matrices contain singular vectors and the $\Sigma$ matrix will have the singular values. The researcher can then decide how many principal components he wants to use. He can keep the singular vectors (these correspond to the directions of maximum variance as we have pointed out). He may then project onto the space of the principal components to get a new feature description – MrHat Oct 3 '16 at 13:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8072715401649475, "perplexity": 471.359562481911}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540488870.33/warc/CC-MAIN-20191206145958-20191206173958-00388.warc.gz"}
http://mathoverflow.net/questions/115207/finite-order-arithmetic-and-etcs?answertab=oldest	# Finite order arithmetic and ETCS I'm looking for a reference to the statement that Lawvere's Elementary Theory of the Category of Sets (ETCS) is equal in proof-theoretic strength to finite order arithmetic. The person who informed me of this said it was well-known in certain circles, but he couldn't think of a reference. Actually, all I need is a reference to one half of the equivalence: that anything provable in finite order arithmetic is provable in ETCS. The story: I've been looking at Colin McLarty's paper A finite order arithemetic foundation for cohomology, which shows that nothing stronger than finite order arithmetic is needed anywhere in EGA or SGA. I want to state that nothing stronger than ETCS is needed anywhere in EGA or SGA. To back that up with references, I therefore need something that relates ETCS to finite order arithmetic. Edit This question has generated lots of discussion about McLarty's paper. I'm genuinely interested in that discussion, but I'd also like to emphasize that it's peripheral to my question, which is simply a reference request: where can I find it stated/proved that ETCS is equal in strength to finite order arithmetic? Further edit Maybe I can make this question more transparent to experts in non-categorical set theory. ETCS is well-known to have the same strength as the membership-based theory known as "bounded Zermelo with choice" or "restricted Zermelo with choice". (One reference: Mac Lane and Moerdijk, Sheaves in Geometry and Logic, Section VI.10.) The axioms are extensionality, empty set, pairing, union, power set, foundation, restricted comprehension, infinity, and choice. Here "restricted comprehension" means that we only consider formulas that are restricted in the sense that all quantifiers are of the form "$\forall x \in y$" or "$\exists x \in y$". - David: I don't know. I simply want a reference! – Tom Leinster Dec 2 '12 at 22:14 @xuhan: I guess I'm not sure 26 letters suffice to write every word in English since I haven't read the entire OED... – François G. Dorais Dec 2 '12 at 23:15 @Xuhan. The fact is that little of EGA or SGA raises any set theoretic issues. Much of it is commutative algebra transparently formalizable in second order arithmetic. While crystalline cohomology does go beyond that, it may not go beyond third order arithmetic, and clearly is far short of arithmetic of all finite orders. The stronger claims in "arxiv.org/abs/1102.1773" are supported by arguments in the paper. – Colin McLarty Dec 3 '12 at 0:23 As Tom knows, ETCS in the original published form is proof theoretically equivalent to Zermelo set theory with the separation axiom restricted to formulas with all quantifiers bounded. That proof is published in several places. Both those theories are equivalent to the arithmetic of all finite orders. The result does follow from the result I address in arxiv.org/abs/1207.6357 but that draft is defective and I have a repair in progress. I first said the fact about finite order arithmetic is simpler than that paper, but actually I do not know it is, and anyway I do not know a reference for it. – Colin McLarty Dec 3 '12 at 0:27 @Joel David Hamkins. The place to go for intuition on set theoretic issues in ETCS is A.R.D. Mathias, 1992: "What is Mac Lane missing", in W.J.H. Judah and H.Woodin (eds), `Set Theory of the Continuum', although that paper puts ETCS into a membership-based form. The title is a joke as Adrien uses "MacLane" as the name of a set theory. In short, you cannot use induction on the natural numbers in unbounded set theoretic constructions so you can prove each transfinite cardinal has a successor but not that there are unboundedly many of them. – Colin McLarty Dec 3 '12 at 0:41 Ah, Thomas Forster's 1998 paper "Weak systems of set theory related to HOL" is available on-line at various places including https://www.dpmms.cam.ac.uk/~tf/maltapaper.ps He says it is proved in Jensen RB "On the consistency of a slight (?) modification of Quine's NF" Synthese 19 1969 pp 25--63. Lake J "Comparing Type theory and Set theory" Zeitschrift fur Matematische Logik 21 1975 pp 355-56. For a fanatically detailed proof and discussion see Mathias at https://www.dpmms.cam.ac.uk/~ardm/maclane.pdf - Thanks a lot, Colin, but I'm pretty confused. None of Forster, Jensen or Mathias seem to mention finite order arithmetic (or $n$th order arithmetic) by name. I haven't been able to get hold of Lake yet. Forster says that Jensen and Lake prove the equivalence of ETCS (or rather, what he calls Mac Lane set theory) with something he calls TST. But then, neither of the strings "TST" or "theory of simple types" appear in Jensen. – Tom Leinster Dec 3 '12 at 13:57 So here's my understanding. We know that ETCS is equivalent to bounded Zermelo with choice, also called Mac Lane set theory: there are plenty of references for that. Forster says that Jensen and Lake prove that Mac Lane set theory is equivalent to something that Forster calls TST (Theory of Simple Types). Jensen doesn't mention anything by this name, nor finite order arithmetic. – Tom Leinster Dec 3 '12 at 14:01 Yes. More than knowing ETCS has the strength of bounded Zermelo (which equals the strength of bounded Zermelo with choice) we have many published proofs. I did not look at Jensen or Lake. I could not get Jensen here at home. And I always like to read Mathias. ETCS is actually bi-interpretable with certain variants of bounded Z with choice, meaning they not only have the same strength but prove exactly the same theorems. The main issue there seems to be existence of transitive closures. – Colin McLarty Dec 3 '12 at 15:47 Ok, so I notice you (Colin) say "It has the proof theoretic strength of finite order arithmetic, in the sense of the simple theory of types with infinity (see Takeuti (1987, Part II))." (For others, Takeuti's book is reviewed in Zentralblatt here zentralblatt-math.org/zmath/… (first edition) and here zentralblatt-math.org/zbmath/search/?q=an%3A0609.03019 (second edition)). Where in Takeuti is it shown that TST is equivalent to finite-order arithmetic? – David Roberts Dec 4 '12 at 0:24 For Takeuti, "simple type theory" is synonymous with "higher (finite) order predicate logic," and does not include an axiom of infinity (though I think for most people simple type theory does include infinity). this is my favorite reference on simple type theory. So I call simple type theory with infinity "finite order arithmetic." – Colin McLarty Dec 4 '12 at 2:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8019448518753052, "perplexity": 1177.6712017929417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936465456.40/warc/CC-MAIN-20150226074105-00139-ip-10-28-5-156.ec2.internal.warc.gz"}
http://bayeconsoft.com/html_documentationse14.html	### 2.10 User-deﬁned functions BayES supports user-deﬁned functions. These functions are deﬁned in BayES script ﬁles and can take multiple arguments and return multiple values. User-deﬁned functions are called from script ﬁles or other functions and can be used to perform a particular task that may require many lines of code, helping to keep the code in the main script tidy. Also, in cases where a task needs to be performed repeatedly, it is easier to describe the task in a user-deﬁned function and to call this function at the appropriate places in the script ﬁle. Each user-deﬁned function must be declared and implemented in its own BayES script ﬁle. These special ﬁles have a speciﬁc form. For example, suppose that we want to deﬁne a function named myFunction that takes a list of arguments, ar1, ar2, ..., uses these argument to do some calculations and deﬁnes a list of return values, rv1, rv2, ..., which will be available after the function completes its job. The following code should be put in a BayES script ﬁle called myFunction.bsf and this ﬁle saved in the current working directory: function [rv1, rv2, ... ] = @myFunction(ar1, ar2, ...) <list of statements> // these statements will use ar1, ar2, ..., and define // rv1, rv2, ..., which will be available in the calling // workspace once the function completes its job end Functions are not meant to be executed independently, but to be called from other scripts (or other functions). A statement like: [y1, y2, ... ] = @myFunction(x1, x2, ...); placed within a BayES script represents a call to the user-deﬁned function myFunction. When such a calling statement is encountered the following process takes place: 1. the arguments x1, x2, ... passed to myFunction in the calling statement are copied and made available in the function’s workspace as ar1, ar2, ...6 2. program control jumps to the user-deﬁned function myFunction, where the listed statements are executed and the return values, rv1, rv2, ..., are assigned 3. program control jumps back to the calling script and the function’s return values are made available to the workspace that contains the calling statement as y1, y2, ... The directory "\$BayESHOME/Samples/4$-$Functions" contains samples of simple and not-so-simple functions. Here we will describe how to deﬁne and use a simple function called SimpleFunction, which takes a single argument x and returns 2x. Suppose the ﬁle SimpleFunction.bsf is located in the current working directory and it contains the following code: function [y] = @SimpleFunction(x) // Print a message on the console print("program control is now in @SimpleFunction"); // Print the value of x on the console print(x); // Assign the value 2x to y y = 2x; // Print a message on the console print("program control is about to leave @SimpleFunction"); end The ﬁrst statement in the function simply notiﬁes the user that program control has passed to @SimpleFunction by printing a message on the BayES console. The next statement prints the value of x, as it is deﬁned in the workspace of @SimpleFunction. The third statement assigns the value 2x to y and the last statement, again, prints information on the BayES console that program control leaves @SimpleFunction. The code in SimpleFunction.bsf cannot be executed simply by hitting Ctrl+R on the script editor window: the function needs to be called from another script. This is demonstrated in Example 2.10. Example 2.10 ▼ Input // Define a 1x2 matrix z using draws from an exponential distribution z = exprnd(2.5, 1, 2); // Call "@SimpleFunction" and assign its return value to w w = @SimpleFunction(z); // Print a message on the console to indicate that @SimpleFunction finished print("nnControl is back to the calling script"); // Print the value of w from the calling script print(w); ▼ Output Program control is now in @SimpleFunction x = 0.5597008 0.23834727 Program control is about to leave @SimpleFunction Control is back to the calling script w = 1.1194016 0.47669454 #### 2.10.1 Rules for deﬁning and calling functions The following rules apply when deﬁning and calling functions: 1. each function must be deﬁned in its own BayES script ﬁle 2. the keyword function must be the ﬁrst word in the script ﬁle that deﬁnes the function 3. the function name must be the same as the ﬁle name of the BayES script ﬁle that contains its deﬁnition, prepended by ‘@ 4. the function deﬁnition ends with the end keyword; everything that follows this keyword in the script ﬁle that deﬁnes the function is ignored 5. when calling a function the BayES script ﬁle that contains its deﬁnition must be in the current working directory 6. functions can have zero, one, or multiple arguments of diﬀerent types (matrices, datasets, strings, etc.) 7. the order in which arguments are passed to a function matters 8. functions can have zero, one, or multiple return values of diﬀerent types (matrices, datasets, strings, etc.); if the function returns only one value then the square brackets in the deﬁnition and calling statements can be omitted 9. the order in which return values are assigned to elements in the workspace of the calling script matters 10. functions have their own workspace and arguments are passed by making copies: functions are aware only of items that have been passed to them as arguments and cannot access items in the workspace of the calling script7 6Each function has its own workspace and it cannot access any elements deﬁned in the workspace of the calling script (see also Section 2.10.1). 7If the workspace of the calling script has an item with id value x and a function is called, which deﬁnes another item with id value x, these two items are distinct: altering the value of x deﬁned inside the function will not aﬀect the value of x in the calling script.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36586835980415344, "perplexity": 533.4747860467988}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487611320.18/warc/CC-MAIN-20210614013350-20210614043350-00338.warc.gz"}
http://mathhelpforum.com/advanced-algebra/198385-gaussian-elimination-3-simultaneous-equations.html	# Math Help - Gaussian Elimination - 3 Simultaneous equations 1. ## Gaussian Elimination - 3 Simultaneous equations Hi all, Really, really struggling with this question. I've tried using a few examples but I cant seem to get narrow down 3 terms to just 1. I always end up with 2 letters/terms remaining. The 3 equations I have are: 7i + 8ii + 7iii = 2 (Equation 1) 6i + 7ii + 5iii = 8 (Equation 2) 6i + 9ii + 6iii = 2 (Equation 3) So I need to work out the values for i, ii and iii. I tried using the 3 step procedure as described in a text book I have. But it doesn't seem to work. I hope someone can help. 2. ## Re: Gaussian Elimination - 3 Simultaneous equations instead of i, ii and iii i will use a,b, and c. so our 3 equations become: 7a + 8b + 7c = 2 6a + 7b + 5c = 8 6a + 9b + 6c = 2. subtract equation 2 from equation 3 to obtain: 2b + c = -6 () now, we need another equation with just b and c in it, to see if we can eliminate another variable. since we want the "a" terms to cancel, multiply equation 1 by 6, and equation 2 by 7: 42a + 48b + 42c = 12 (equation 1a) 42a + 49b + 35c = 56 (equation 2a) then subtract equation 1a from equation 2a to get: b - 7c = 44 (), and now we multiply () by 2 to get: 2b - 14c = 88. subtract () from this, and we have: -15c = 94, so c = -94/15. using (*) we have: 2b - 94/15 = -6 b - 47/15 = -3 b = -3 + 47/15 = -45/15 + 47/15 = 2/15 and finally, using equation 1, we have: 7a + 8(2/15) + 7(-94/15) = 2, so: a + 16/105 - 94/15 = 2/7 thus: a = 2/7 - 16/105 + 94/15 = 30/105 - 16/105 + 658/105 = 672/105 = 96/15 = 32/5. now let's see if our solution is correct (the first two times i did this, i made errors, so don't feel bad if you did, too): 7(32/5) + 8(2/15) + 7(-94/15) = 224/5 + 16/15 - 658/15 = 4704/105 + 112/105 - 4606/105 = 210/105 = 2 (so equation 1 checks out). 6(32/5) + 7(2/15) + 5(-94/15) = 192/5 + 14/15 - 94/3 = 576/15 + 14/15 - 470/15 = 120/15 = 8 (so equation 2 checks out). 6(32/5) + 9(2/15) + 6(-94/15) = 192/5 + 6/5 - 188/5 = 10/5 = 2 (all three equations check out). so a = 32/5, b = 2/15, c = -94/15 is indeed the correct solution (with some rather ugly arithmetic attached). 3. ## Re: Gaussian Elimination - 3 Simultaneous equations Thanks Deveno! That is perfect!! Going back over my original attempts I realise that NOT using fractions was a mistake! The decimal numbers got VERY messy. Thanks again, for taking the time to write it all out. I actually understand the process better now. Chris 4. ## Re: Gaussian Elimination - 3 Simultaneous equations Hello, chrisa112! Didn't you say Gaussian elimination? $\begin{array}{ccc\|c}7a + 8b + 7c &=& 2 \\ 6a + 7b + 5c &=& 8 \\ 6a + 9b + 6c &=& 2 \end{array}$ We have: . $\left\|\begin{array}{ccc\|c}7&8&7&2 \\ 6&7&5&8 \\ 6&9&6&2 \end{array}\right\|$ $\begin{array}{c}R_1-R_2 \\ \\ R_3-R_2 \end{array}\left\|\begin{array}{ccc\|c}1&1&2&\text{-}6 \\ 6&7&5&8 \\ 0&2&1&\text{-}6 \end{array}\right\|$ $\begin{array}{c} \\ R_2-6R_1 \\ \\ \end{array}\left\|\begin{array}{ccc\|c}1&1&2&\text{-}6 \\ 0&1&\text{-}7&44 \\ 0&2&1&\text{-}6 \end{array}\right\|$ $\begin{array}{c}R_1-R_2\ \\ R_3-2R_2 \end{array}\left\|\begin{array}{ccc\|c}1&0&9&\text{-}50 \\ 0&1&\text{-}7&44 \\ 0&0&15&\text{-}94 \end{array}\right\|$ . . $\begin{array}{c}\\ \\ \frac{1}{15}R_3 \end{array}\left\|\begin{array}{ccc\|c}1&0&9&\text{-}50 \\ 0&1&\text{-}7&44 \\ 0&0&1&\text{-}\frac{94}{15}\end{array}\right\|$ $\begin{array}{c}R_1 - 9R_3 \\ R_2 + 7R_3 \\ \\ \end{array}\left\|\begin{array}{ccc\|c}1&0&0&\frac{3 2}{5} \\ 0&1&0&\frac{2}{15} \\ 0&0&1&\text{-}\frac{94}{15} \end{array}\right\|$ 5. ## Re: Gaussian Elimination - 3 Simultaneous equations What Deveno did is also "Gaussian Elimination" as well as your row-reduction. 6. ## Re: Gaussian Elimination - 3 Simultaneous equations Yes Deveno had solved it very smartly and this is a “Gaussian Elimination” even I got agreed with Hallsoflvy. Good job done by Deveno.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8042813539505005, "perplexity": 1879.6887529545984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049274191.57/warc/CC-MAIN-20160524002114-00139-ip-10-185-217-139.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/205446/norm-of-complex-matrix-with-euclidean-norm	# Norm of complex Matrix with euclidean norm Would you help me to prove the norm of 2 by 2 matrix $$A=\begin{bmatrix} a & b \\ c & d% \end{bmatrix}$$ is $$\def\trc{\operatorname{tr}}\frac{\trc(A^A)+\sqrt{\trc(A^A)^2-4\det(A^A)}}{2}.$$ I just try by maximizing $h(x,y)=\|\|A\begin{bmatrix} x \\ y% \end{bmatrix}\|\|$ where $x^2+y^2=1$ but not get this result. - As I mentioned in my answer, your formula does not give a norm. You need to take the square root of that. For example, if you let $a=2$, $b=c=0$, $d=1$, then for $A+A$ your formula gives $16$, while for $A$ it gives $4$: so it doesn't satisfy the triangle inequality. – Martin Argerami Oct 3 '12 at 1:36 I think you are talking about the operator norm induced by the euclidean norm, and not the euclidean norm per se. In that case, the norm will be the square root of the number you mention. The operator norm of $A$ can be characterized as the square root of the biggest eigenvalue of $A^A$. The eigenvalues of $A^A$ are the roots of its characteristic polynomial. As $A^A$ is $2\times 2$, its characteristic polynomial is $p(t)=t^2-\mbox{tr}(A^A)\,t+\det(A^A)$. So its biggest eigenvalue is $$\frac{\mbox{tr}(A^A)+\sqrt{\mbox{tr}(A^A)^2-4\det(A^A)}}2$$ (the polynomial $p$ has always non-negative roots, so the formula above certainly gives the biggest eigenvalue). So the norm of $A$ is $$\left(\frac{\mbox{tr}(A^A)+\sqrt{\mbox{tr}(A^A)^2-4\det(A^A)}}2\right)^{1/2}.$$ - Couldnt be solve by calculus only? – beginner Oct 1 '12 at 15:04 Probably. It will be certainly more convoluted, because if you try to do Lagrange multipliers to your $h$, what you are really doing is first finding a vector where the maximum occurs, and then evaluating $h$ at that vector. – Martin Argerami Oct 1 '12 at 15:19 It's the spectral radius of $A^A$, that is, the largest modulus of the eigenvalues of $A^A$. We can express them with a second degree equation satisfied by the eigenvalues, and knowing they are non-negative, we can see that the given expression is the norm of the matrix. - The problem cant be solved only by multivariable calculus (using Lagrange Multiplier)? – beginner Oct 1 '12 at 14:50 It's possible, but I don't know whether it is simpler. You could include your attempt with this method in the OP, then we will try to see where you think there is a problem. – Davide Giraudo Oct 1 '12 at 14:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9735608696937561, "perplexity": 145.54791552576475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398464253.80/warc/CC-MAIN-20151124205424-00075-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.biostars.org/p/226666/	error will using transdecoder.predict 1 0 Entering edit mode 5.7 years ago najibveto ▴ 70 hello i am using transdecoder to get the longest orf after that i blasted them against zebrafish proteins database and while i wanted to integrate the blast results i got this error: najib@najib-VirtualBox:~/Downloads/TransDecoder-3.0.1$perl TransDecoder.Predict -t fatheadminnow.fasta --retain_blastp_hits blastp.outfmt6 ##################### Counts of kept entries according to attributes: BLASTP\|FRAMESCORE\|LONGORF 22069 BLASTP\|FRAMESCORE 15283 FRAMESCORE 3298 BLASTP 946 LONGORF 444 FRAMESCORE\|LONGORF 321 BLASTP\|LONGORF 149 ######################## Command: /home/najib/Downloads/TransDecoder-3.0.1/util/index_gff3_files_by_isoform.pl fatheadminnow.fasta.transdecoder_dir/longest_orfs.gff3 Can't load '/home/najib/miniconda3/lib/perl5/5.22.0/x86_64-linux-thread-multi/auto/DB_File/DB_File.so' for module DB_File: libdb-4.3.so: cannot open shared object file: No such file or directory at /home/najib/miniconda3/lib/perl5/5.22.0/XSLoader.pm line 70. at /home/najib/miniconda3/lib/perl5/5.22.0/x86_64-linux-thread-multi/DB_File.pm line 255. Compilation failed in require at /home/najib/Downloads/TransDecoder-3.0.1/util/../PerlLib/TiedHash.pm line 6. BEGIN failed--compilation aborted at /home/najib/Downloads/TransDecoder-3.0.1/util/../PerlLib/TiedHash.pm line 6. Compilation failed in require at /home/najib/miniconda3/lib/perl5/5.22.0/base.pm line 99. ...propagated at /home/najib/miniconda3/lib/perl5/5.22.0/base.pm line 108. BEGIN failed--compilation aborted at /home/najib/Downloads/TransDecoder-3.0.1/util/../PerlLib/Gene_obj_indexer.pm line 6. Compilation failed in require at /home/najib/Downloads/TransDecoder-3.0.1/util/index_gff3_files_by_isoform.pl line 8. BEGIN failed--compilation aborted at /home/najib/Downloads/TransDecoder-3.0.1/util/index_gff3_files_by_isoform.pl line 8. Error, cmd: /home/najib/Downloads/TransDecoder-3.0.1/util/index_gff3_files_by_isoform.pl fatheadminnow.fasta.transdecoder_dir/longest_orfs.gff3 died with ret 512 at TransDecoder.Predict line 379. najib@najib-VirtualBox:~/Downloads/TransDecoder-3.0.1$ can someone tell me what is missing and what is the solution for it? thanks for your help. transcriptome transdecoder • 2.3k views 0 Entering edit mode 5.7 years ago EVR ▴ 590 Hi, Kindly check whether yyou have installed all the rpel mdules required by Transdecoder. It seems that library "XSLoader.pm " is totlally missing. Kindly re install and re-run the programm	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20402805507183075, "perplexity": 12873.257042156105}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571987.60/warc/CC-MAIN-20220813202507-20220813232507-00407.warc.gz"}
http://mathhelpforum.com/calculus/82879-second-order-differential-equations.html	# Thread: Second order differential equations! 1. ## Second order differential equations! Find y in terms of x given that d2y/dx2 - 4(dy/dx) + 4y = e^2x and that dy/dx=1 and y=0 at x=0 I've worked out that the complementary function is (A+Bx)e^2x However, i don't understand why I should be using y=k(x^2)e^2x as the particular integral and not y=ke^2x Can anyone explain? 2. Originally Posted by Erghhh Find y in terms of x given that d2y/dx2 - 4(dy/dx) + 4y = e^2x and that dy/dx=1 and y=0 at x=0 I've worked out that the complementary function is (A+Bx)e^2x However, i don't understand why I should be using y=k(x^2)e^2x as the particular integral and not y=ke^2x Can anyone explain? Since your complimentary solution contains a $xe^{2x}$ term, then by reduction of order, your particular solution must contain a $x^2e^{2x}$ term. Thus, I believe your particular solution must take on the form $y_p=\left(A_1+A_2x+A_3x^2\right)e^{2x}$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8717824220657349, "perplexity": 1318.592883699985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738662698.85/warc/CC-MAIN-20160924173742-00085-ip-10-143-35-109.ec2.internal.warc.gz"}
http://slideplayer.com/slide/1405129/	# Oxidation-Reduction: A Reaction ## Presentation on theme: "Oxidation-Reduction: A Reaction"— Presentation transcript: Oxidation Reduction Redox An introduction to electron transfer reactions Oxidation-Reduction: A Reaction Oxidation: When a substances loses electrons. Reduction: When a substance gains electrons. Consider: Ca(s) + 2H+(aq)  Ca2+(aq) + H2(g). The neutral Ca(s) has lost two e- to 2 H+ to become Ca2+. We say Ca has been oxidized to Ca2+ At the same time 2 electrons are gained by 2 H+ to form H2 . We say H+ is reduced to H2 . Redox Reaction with Air Consider the reaction of Ca with O2: 2Ca(s) + O2(g)  2CaO(s) Ca is easily oxidized in air. On the left there is shiny Ca metal. On the right we see a white powder – Calcium oxide. Again, Ca(s) loses electrons and is oxidized to Ca+2 And the neutral O2 has gained electrons from the Ca to become O2- in CaO. We say O2 has been reduced to O2-. Electron Transfer and Terminology Lose electrons: Oxidation Gain electrons: Reduction. GER Leo It Takes Two: Oxidation-Reduction In all reduction-oxidation (redox) reactions, one species is reduced at the same time as another is oxidized. Oxidizing Agent: The species which causes oxidation is called the oxidizing agent. The substance which is oxidized loses electrons to the other. The oxidizing agent is always reduced Reducing Agent: The species which causes reduction is called the reducing agent. The substance which is reduces gains electrons from the other. The Reducing agent is always oxidized Oxidation of Metals with Acids It is common for metal to produce hydrogen gas when they react with acids. For example, the reaction between Mg and HCl: Mg(s) + 2HCI(aq)  MgCl2(aq) + H2(g) . In this reaction, Mg is oxidized and H in HCl is reduced. Note the change in oxidation state for these species: Mg0  Mg+2 in MgCl2 & H+ in HCl  H0 in H2 Redox reaction with Acid It is possible for metals to be oxidized with salt: Fe(s) + Ni(NO3)2 (aq)  Fe(NO3)2 (aq) + Ni (s) . Molecular Equation The net ionic equation shows the redox chemistry well: Fe(s) + Ni+2(aq)  Fe2+(aq) + Ni (s) Net ionic Equation In this reaction iron has been oxidized to Fe2+ while the Ni+2 has been reduced to Ni0. What determines whether the reaction occurs ? The Activity Series Metals can be placed in order of their tendencies for losing electrons. This is called the activity series. Competition For e- Transfer Consider: Na, Mg, Al, Metallic character decreases left to right. Metal tend to give up electrons. Now consider the reaction: Na + AlCl3  ??? (NaCl + Al) To determine if the reaction occurs, the question is to determine which metal has a greater affinity for electrons (or which is willing to lose e- ). Na is more willing to lose e- than Al Al is more willing to accept e- (less metallic) Conclude: The reaction occurs. 3Na + AlCl3  3NaCl + Al A metal in the activity series can only be oxidized by a metal ion below it. In our example, Na is oxidized by Al. The metals at the top of the activity series are called active metals. The metals at the bottom of the activity series are called noble metals. Example: Silver and Copper If we place Cu into a solution of Ag+ ions, will copper plate out of solution ? Cu(s) + 2AgNO3(aq)  ? [Cu(NO3)2(aq) + 2Ag (s)] or Cu (s) + 2Ag+ (aq)  ? [Cu2+(aq) + 2Ag (s)] Which metal is active? Which is noble ? g Cu g Ag \ Therefore, Cu 2+ ions is be formed because Cu is above Ag in the activity series. Copper Cu g Cu e-Silver Ag g Ag e- Example: Redox Reaction B&L 4.47: Based on the activity series, what is the outcome of the following reaction ? b) Ag(s) + PbNO3 (aq)  ? c) Cr (s) + NiSO4 (aq)  ? e) H2 (g) + CuCl2 (aq)  ? f) Ba (s) + H2O (l)  ? b) Ag vs. Pb , Pb is more active, no reaction occurs c) Cr vs. Ni , Cr is more active, reaction occurs Cr (s) + NiSO4 (aq)  Ni (s) + CrSO4 (aq) d) H2 vs. Cu , H2 is more active, reaction occurs H2 (g) + CuCl2 (aq)  2HCl (aq) + Cu (s) e) Ba vs. H2 , Ba is more active, reaction occurs Ba (s) + H2O (l)  H2 (g) + Ba(OH)2 (aq) Summary Redox - Oxidation/Reduction reaction Oxidation- Lose electron (LEO) Reduction- Gain electron (GER) Activity Series- Table showing elements’ relative ease of oxidation. Active Metal Metal which prefers to lose e- and therefore prefers the oxidized form. Noble Metal Metal which do not lose e- and therefore prefers the zero state.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8310226202011108, "perplexity": 12949.742910015562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687702.11/warc/CC-MAIN-20170921063415-20170921083415-00520.warc.gz"}
https://www.physicsforums.com/threads/e-mc-2-do-i-have-this-right.65805/	# E=MC^2 - Do I have this right? 1. Mar 3, 2005 OK first let me explain, I have NO formal physics background, not even high school, so please don't flame me if these are dumb questions 1. What unit of measure is E? If it were distance we could say miles or kilometers. 2. I understand that this formula is for mass at rest. If the mass were moving at 50% light speed, would the answer to E=MC^2 be half of what it would be for the same mass at rest? 3. In nuclear fusion I understand the energy is based on applying this formula to the mass left over when 2 atoms fuse. So looking at a Hydrogen atom, if .00794 atomic mass were converted into energy during the fusion, does that mean the energy gained from this fusion is Energy = .00794 x c^2? I don't know if that is the right number but I needed to apply one for the purpose of this question. Thanks 2. Mar 3, 2005 ### dextercioby Energy,and it is measured in Joules. Not exactly in that form.$$E=m_{0}c^{2}$$ is for mass at rest.Notice the fact that the subscript "0" indicates that thing... No.It would be more.It's really easy to compute the energy,once you know the connection between rest mass $m_{0}$,movement mass $m$ (or "M",as you denoted it) and the velocity $v=\|\vec{v}\|$.Just arithmetics. EXACTLY...Einstein's formula tells us how much enegy is involved in nuclear reactions...Pay attention with the units,though.That 0.00794 a.m.u.needs to be converted to Kg and then the final result (the energy) would be in Joules,energy's unit. Daniel. 3. Mar 3, 2005 ### James R 1. Any unit of energy will do. The standard SI unit is the Joule. If m is in kilograms and c is in metres per second, then E works out in Joules. 2. The complete formula is: $$E = \frac{mc^2}{\sqrt{1-(v/c)^2}}$$ where $v$ is the speed of the object. If you plug in $v=c/2$, you get: $$E = \frac{mc^2}{\sqrt{1-(1/2)^2}} = \frac{2}{\sqrt{3}}mc^2 \approx (1.15)mc^2$$ When an object is moving, the energy is greater than $mc^2$. In fact, $mc^2$ is the rest energy only. The "extra" energy is kinetic energy. 3. Essentially, you are right, but you need the mass in kilograms rather than atomic mass units. The conversion factor is: $1$ amu = $1.66 \times 10^{-24}[/tex] kilograms. Hope this helps. 4. Mar 3, 2005 ### TsunamiJoe also, not to sound stupid, but what exactly is E=mc^2 solving, the energy at rest? and if that is the case would that be more commonly known as potential energy? 5. Mar 4, 2005 ### dextercioby No.In the form where that "m" is the rest mass,it is just the rest energy of the particle.If that "m" is not the rest mass,it is the TOTAL ENERGY OF THE PARTICLE,rest+kinetic... Daniel. 6. Mar 4, 2005 ### SpaceTiger Staff Emeritus Physicist - Joules Astrophysicist - Ergs Particle Physicist - eV Nutritionist - Calories Electrician - Kilowatt-hours King of England - Foot-pounds Oil Tycoon - Barrels Enron Executive - Dollars Mars Spacecraft Operator - Joules, no....foot-pounds, wait, no... 7. Mar 4, 2005 ### pmb_phy The unit is Jopules. This a derived unit and as such can be exressed in term of basic units, i.e. [joules] = [N = Newton's][L = distance] where [joules] = [kg][m2]/[s2] If you intend m to mean rest mass then your equation leaves something to be desired. The actuall expression is [itex]E = \gamma mc^2$. You should have written E0 = mc2. The expression for energy for a particle in motion is $$E = \gamma m c^2$$ recall that $$\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$$ Its rather simple to get the energy you're speaking of. Merely replace v by v/2. Pete 8. Mar 4, 2005 ### Moose352 He meant to write c/2, not v/2. 9. Mar 5, 2005 Thanks! I understand it better now. Similar Discussions: E=MC^2 - Do I have this right?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9721924066543579, "perplexity": 974.5456832917555}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423809.62/warc/CC-MAIN-20170721202430-20170721222430-00233.warc.gz"}
http://rcd.ics.org.ru/authors/detail/1602-alexandr_kirillov	0 2013 Impact Factor # Alexandr Kirillov ## Publications: Kirillov A. A. Modification of gravity and Dark Matter 2006, vol. 11, no. 2, pp. 269-280 Abstract Upon a phenomenological consideration of possible modifications of gravity we introduce a bias operator $ρ_{DM} =\hat{K}ρ_{vis}$. We show that the empirical definition of a single bias function $K_{emp}(r,t)$ (i.e., of the kernel for the bias operator) allows to account for all the variety of Dark Matter halos in astrophysical systems. For every discrete source such a bias produces a specific correction to the Newton's potential $\phi=-GM(1/r+F(r,t))$ and therefore all DM effects can be explained as a modification of the gravity law. We also demonstrate that a specific choice of the bias $K \sim 1/r^2$ (which produces a logarithmic correction to the Newton's law $F \sim -\ln r$) shows quite a good qualitative agreement with the observed picture of the modern Universe Keywords: galaxy formation, clusters, dark matter Citation: Kirillov A. A., Modification of gravity and Dark Matter , Regular and Chaotic Dynamics, 2006, vol. 11, no. 2, pp. 269-280 DOI: 10.1070/RD2006v011n02ABEH000350 Kirillov A. A. Billiards in Cosmological Models 1996, vol. 1, no. 2, pp. 13-22 Abstract Recently the billiards, forming an important part in theory of dynamical systems with singularities [1,2], found their unexpected application in cosmological problems. It turnes out that a wide class of cosmological models near a singular point, corresponding to the origin of development of our Universe, admits its representation as billiards on the space of constant negative curvature [4,5]. A problem of similar model randomness is reduced to a problem of properties of corresponding billiards. The aim of the present paper is to show the way in which such representation is reached and to present the results obtained within the limits of those models. Citation: Kirillov A. A., Billiards in Cosmological Models, Regular and Chaotic Dynamics, 1996, vol. 1, no. 2, pp. 13-22 DOI:10.1070/RD1996v001n02ABEH000011	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8541853427886963, "perplexity": 586.5855480210655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156471.4/warc/CC-MAIN-20180920120835-20180920141235-00402.warc.gz"}
http://tex.stackexchange.com/questions/61043/objects-in-commutative-diagram-dcpic/76414	Objects in Commutative Diagram DCpic I have the diagram of the folllowing form: \begindc \obj(1,1){$A$} \obj(3,1){$B$} \obj(3,3){$C$} \mor(1,1)(3,1) {$f$ }[\atright,\solidarrow] \mor(1,1)(3,3) {$g$ } \mor(3,1)(3,3) {$h$ }[\atright,\solidarrow] \enddc I wonder if the "objects" A,B,C must be in normal math font only, i.e. we can't replace such A with \mathsf{A} or \mathfrak{A} or \mathbf{A}. If this is really a restriction, is there any other package that allows special math fonts as "objects"? - Welcome to TeX.SE. It is always best to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. As well, I took the liberty to format your post a little. See this link for more details on available formatting. – yo' Jun 24 '12 at 15:25 You can use \obj(1,1)[A]{$\mathsf{A}$}, but I strongly advise you to use a more modern and powerful package such as tikz-cd or xy. – egreg Jun 24 '12 at 15:38 Thank you very much for both comments. – Pachara Jun 24 '12 at 15:47 @egreg It seems that your comment answers the question, or at least comes close to doing so. Please consider adding it as an answer. – Andrew Uzzell Oct 12 '12 at 8:50 You can use \obj(1,1)[A]{$\mathsf{A}$} so that the optional argument sets the node name. However, there are more modern and powerful packages than dcpic for any sort of commutative diagram. I've used XY-pic (\usepackage[all,cmtip]{xypic}), but the more recent tikz-cd seems very promising and easy to use. - As proposed by egreg, a more modern package would much easier for such things. The currently best package to learn should be tikz-cd (my recommendation). Here is your diagram using this. % arara: pdflatex \documentclass{article} \usepackage{tikz-cd} \usepackage{amsfonts} \begin{document} \begin{tikzcd} & C \\ A\mathsf{A}\mathfrak{A}\mathbf{A} \arrow{r}[swap]{f} \arrow{ur}{g} & B \arrow{u}[swap]{h} \end{tikzcd} \end{document} -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7491691708564758, "perplexity": 2217.98376505835}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447552650.71/warc/CC-MAIN-20141224185912-00090-ip-10-231-17-201.ec2.internal.warc.gz"}
https://codeforces.com/blog/entry/50614	### Errichto's blog By Errichto, 3 years ago, , Hello Codeforces! Did you miss Limak? I’d like you to invite for CodeChef February Lunchtime that will start at 19:35 IST / 17:05 MSK of 25-th February 2017 (check your time zone here) and will last 3 hours. The contest starts 5 minutes later than usually to allow you to catch a breath after the AtCoder Mujin Contest that ends at 17:00 MSK. I am an author of problems and editorials, while niyaznigmatul is a tester. I want to thank PraveenDhinwa (who is a contest admin) and suraj_sharma for their technical help. Translators: CherryTree (Russian), huzecong (Mandarin) and VNOI team (Vietnamese). Language verification: arjunarul. There is no registration required, anybody with a CodeChef handle can participate. Top school participants can win CodeChef laddus (details on the contest page). You will be provided 4 problems with subtasks (IOI-style grading). Ties are broken by time of reaching your final score. The contest should be a bit easier than a Div1 Codeforces round. I honestly think that all problems are interesting and valuable — some for beginners and some for experiences competitors (IMO one particular problem is so new and beautiful). Remember about subtasks if you can't solve a problem for the full score, and read the editorial after the contest. I wish you great fun and no frustrating bugs. Hope to see a lot of you in the leaderboard! EDIT: The time of start corrected to "19:35 IST / 17:05 MSK". EDIT2: Bump, the contest starts in 24 hours. EDIT3: The contest is over. I hope you enjoyed problems. You can find editorials here. And congratulations to Petr, uwi and savinov for getting the top 3 places! • +61 » 3 years ago, # \| +49 "I honestly think that all problems are interesting and valuable — some for beginners and some for experiences competitors (IMO one particular problem is so new and beautiful)."Most probably joining based on this sentence. » 3 years ago, # \| +17 bump, 3 minutes » 3 years ago, # \| ← Rev. 2 → +10 I have noticed that: Those who achieve the score first will be placed higher in the ranklist in case of a tie. So, in case someone got 400, his rank should not be changed anymore as those who got 400 after him should rank lower than him.However, when the ranklist first show my score was 400, my rank was 10. And just now when i refreshed the ranklist, I found out that my rank dropped to 14. Isn't this behavior impossible to happen?Did I misunderstand the rules of ranking or there is something wrong with the ranklist?UPD Some of the contestants ranked higher than me achieved 400 later than me. • » » 3 years ago, # ^ \| +5 Thanks for letting us know. Indeed something is broken with the leaderboard. We'll investigate that. • » » 3 years ago, # ^ \| -10 I think Codechef IOI style leaderboards take into account penalties. So maybe you have better solving time but more penalties. • » » » 3 years ago, # ^ \| +5 But the rules stated that: You can submit solutions as many times as you'd like, there are no penalties for incorrect submissions. Only your best correct submission will be considered. So there should not be any penalties to wrong submissions. • » » 3 years ago, # ^ \| 0 The problem is fixed. You can check your place now. » 3 years ago, # \| 0 Can anybody give some edge cases/tricky test cases for Bear and Bribing Tree? I can't find the mistake in my logic. • » » 3 years ago, # ^ \| +2 Your submission wrong on this case: 2 3 9 6 10 3 15 1 13 16 19 3 10 1 8 9 15 10 4 13 20 The correct answer should be: 4 5 • » » » 3 years ago, # ^ \| 0 If you don't mind providing the testcase for my solution, I'd be glad, the same nickname. • » » » » 3 years ago, # ^ \| ← Rev. 2 → 0 1 4 9 6 10 13 5 9 18 3 1 11 12 7 19 8 20 16 14 The answer should be 7 instead of 8.BTW, it is harder to generate a counter case for you:) • » » » 3 years ago, # ^ \| 0 Alright, thanks! » 3 years ago, # \| +20 From your codechef blog: "IMO one particular problem is so new and beautiful"So which one was it? • » » 3 years ago, # ^ \| ← Rev. 2 → +1 overflow-points problem — I've never seen something similar and the solution is just cute. • » » » 3 years ago, # ^ \| 0 I believe, it's very sad that this problem can be solved with a purely random algorithm. • » » » » 3 years ago, # ^ \| +6 How? • » » » » » 3 years ago, # ^ \| 0 I also want to know how! I didn't see any AC solution that is a "purely randomized algorithm", though I agree that one part of the solution can be done with randomization. • » » » » » » 3 years ago, # ^ \| 0 Here is my solution. I think it's purely random algorithm. • » » » » » » » 3 years ago, # ^ \| 0 Can you show me how to run the randomized part of your solution? It doesn't seem to finish in minutes on my machine, even for k = 2, what I guess tries to find 3 points. • » » » » » » » » 3 years ago, # ^ \| 0 Actually, there's no magic, I just waited. I think 2-3 minutes for one new point. • » » » » » » » » » 3 years ago, # ^ \| +6 You are right, it found the next point. Apparently I didn't try hard enough during the problem preparation.Are you able to explain why it works? I have no idea why this program is able to find more than 3-4 points. • » » » » » » » » » 3 years ago, # ^ \| +1 Of course I can't. During the contest I understood that I'm stupid enough to solve more than 2 problems and the only hope to get a better rank was to try this random algo... And I'm not very proud right now • » » » » » » » » » 3 years ago, # ^ \| +6 But trying this algo turned out be a great idea. You solved a problem so there is nothing be ashamed of. The question is: why it works? I will try to figure that out. • » » » » » » 3 years ago, # ^ \| ← Rev. 2 → +3 I believe the main difficulty was to find ten non-collinear points with small (<=15) coordinates (after that just multiply each coordinate with 216)? I just did this: add the points with both coordinates ≤ 15 in a vector. At each step consider the current element in the vector and if it is not in the same line as any two chosen points choose it (otherwise ignore it). This gave me 19 points which was more than enough. Code • » » » » » » » 3 years ago, # ^ \| ← Rev. 2 → +18 This is intended. Still, what BlueOptimizedOurWay described is completely different.Also, I don't agree with you about the main difficulty. Finding such non-collinear points is easy even without computer. I still think that the hardest part was to get the idea about coordinates divisible by 216. • » » » » » 3 years ago, # ^ \| 0 Just generating random points and checking if the new point is ok to be taken. • » » » 3 years ago, # ^ \| 0 but this particular problem is not IOI-style, is it? but it's interesting anyway • » » » » 3 years ago, # ^ \| +3 Why not? • » » » 3 years ago, # ^ \| +15 Thought I couldn't solve this problem, I enjoyed solving the other three very much. Thanks for preparing such nice problemset. » 3 years ago, # \| +3 Will there be an editorial?Is there a way to see the tests on codechef? • » » 3 years ago, # ^ \| 0 All editorials can be found here.You can't see tests. Likely stress testing your solution locally will help you to find a counter-test.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4346764087677002, "perplexity": 1479.003735926144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987803441.95/warc/CC-MAIN-20191022053647-20191022081147-00363.warc.gz"}
https://brilliant.org/problems/thats-tricky-2/	# That's Tricky #2 Discrete Mathematics Level pending How many number of terms are in the expansion of: $$( x^{2} + 1 + \frac{1} {x^{2}} )^{n}$$ Assumptions : Terms are for powers of x. ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20568986237049103, "perplexity": 6841.8450401692835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560281084.84/warc/CC-MAIN-20170116095121-00456-ip-10-171-10-70.ec2.internal.warc.gz"}
https://scribesoftimbuktu.com/convert-to-a-fraction-7-826/	# Convert to a Fraction 7.826 7.826 Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are 3 numbers to the right of the decimal point, place the decimal number over 103 (1000). Next, add the whole number to the left of the decimal. 78261000 Reduce the fractional part of the mixed number. 7413500 Convert 7413500 to an improper fraction. A mixed number is an addition of its whole and fractional parts. 7+413500 To write 7 as a fraction with a common denominator, multiply by 500500. 7⋅500500+413500 Combine 7 and 500500. 7⋅500500+413500 Combine the numerators over the common denominator. 7⋅500+413500 Simplify the numerator. Multiply 7 by 500. 3500+413500	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8266333341598511, "perplexity": 720.4248157979507}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337404.30/warc/CC-MAIN-20221003070342-20221003100342-00379.warc.gz"}
https://everything.explained.today/Generalized_continued_fraction/	# Generalized continued fraction explained In complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary complex values. A generalized continued fraction is an expression of the form x=b0+\cfrac{a1}{b1+\cfrac{a2}{b2+\cfrac{a3}{b3+\cfrac{a4}{b4+\ddots}}}} where the are the partial numerators, the are the partial denominators, and the leading term is called the integer part of the continued fraction. The successive convergents of the continued fraction are formed by applying the fundamental recurrence formulas: \begin{align} x0&= A0 B0 =b0,\\[4px] x1&= A1 B1 = b1b0+a1 b1 ,\\[4px] x2&= A2 B2 = b2(b1b0+a1)+a2b0 b2b1+a2 , ... \end{align} where is the numerator and is the denominator, called continuants, of the th convergent. They are given by the recursion \begin{align} An&=bnAn-1+anAn-2,\\ Bn&=bnBn-1+anBn-2 forn\ge1\end{align} with initial values \begin{align} A-1&=1,&A0&=b0,\B-1&=0,&B0&=1. \end{align} If the sequence of convergents approaches a limit the continued fraction is convergent and has a definite value. If the sequence of convergents never approaches a limit the continued fraction is divergent. It may diverge by oscillation (for example, the odd and even convergents may approach two different limits), or it may produce an infinite number of zero denominators . ## History The story of continued fractions begins with the Euclidean algorithm,[1] a procedure for finding the greatest common divisor of two natural numbers and . That algorithm introduced the idea of dividing to extract a new remainder - and then dividing by the new remainder repeatedly. Nearly two thousand years passed before devised a technique for approximating the roots of quadratic equations with continued fractions in the mid-sixteenth century. Now the pace of development quickened. Just 24 years later, in 1613, Pietro Cataldi introduced the first formal notation for the generalized continued fraction. Cataldi represented a continued fraction as {a0 ⋅ }\& n1 d1 ⋅ \& n2 d2 ⋅ \& n3 d3 with the dots indicating where the next fraction goes, and each representing a modern plus sign. Late in the seventeenth century John Wallis introduced the term "continued fraction" into mathematical literature. New techniques for mathematical analysis (Newton's and Leibniz's calculus) had recently come onto the scene, and a generation of Wallis' contemporaries put the new phrase to use. In 1748 Euler published a theorem showing that a particular kind of continued fraction is equivalent to a certain very general infinite series. Euler's continued fraction formula is still the basis of many modern proofs of convergence of continued fractions. In 1761, Johann Heinrich Lambert gave the first proof that is irrational, by using the following continued fraction for : \tan(x)=\cfrac{x}{1+\cfrac{-x2}{3+\cfrac{-x2}{5+\cfrac{-x2}{7+{}\ddots}}}} Continued fractions can also be applied to problems in number theory, and are especially useful in the study of Diophantine equations. In the late eighteenth century Lagrange used continued fractions to construct the general solution of Pell's equation, thus answering a question that had fascinated mathematicians for more than a thousand years.[2] Amazingly, Lagrange's discovery implies that the canonical continued fraction expansion of the square root of every non-square integer is periodic and that, if the period is of length, it contains a palindromic string of length . In 1813 Gauss derived from complex-valued hypergeometric functions what is now called Gauss's continued fractions. They can be used to express many elementary functions and some more advanced functions (such as the Bessel functions), as continued fractions that are rapidly convergent almost everywhere in the complex plane. ## Notation The long continued fraction expression displayed in the introduction is probably the most intuitive form for the reader. Unfortunately, it takes up a lot of space in a book (and is not easy for the typesetter, either). So mathematicians have devised several alternative notations. One convenient way to express a generalized continued fraction looks like this: x= b 0+ a1 b1+ a2 b2+ a3 b3+ Pringsheim wrote a generalized continued fraction this way: x=b0+ a1\mid \midb1 + a2\mid \midb2 + a3\mid \midb3 + … . Carl Friedrich Gauss evoked the more familiar infinite product when he devised this notation: x=b0+\underset{i=1}\overset{infty}\operatorname{K} ai bi . Here the "" stands for Kettenbruch, the German word for "continued fraction". This is probably the most compact and convenient way to express continued fractions; however, it is not widely used by English typesetters. ## Some elementary considerations Here are some elementary results that are of fundamental importance in the further development of the analytic theory of continued fractions. ### Partial numerators and denominators If one of the partial numerators is zero, the infinite continued fraction b0+\underset{i=1}\overset{infty}\operatorname{K} ai bi is really just a finite continued fraction with fractional terms, and therefore a rational function of to and to . Such an object is of little interest from the point of view adopted in mathematical analysis, so it is usually assumed that all . There is no need to place this restriction on the partial denominators . ### The determinant formula When the th convergent of a continued fraction xn=b0+\underset{i=1}\overset{n}\operatorname{K} ai bi is expressed as a simple fraction we can use the determinant formula to relate the numerators and denominators of successive convergents and to one another. The proof for this can be easily seen by induction. Base case The case results from a very simple computation. Inductive step Assume that holds for . Then we need to see the same relation holding true for . Substituting the value of and in we obtain: \begin{align} &=bnAn-1Bn-1+anAn-1Bn-2-bnAn-1Bn-1-anAn-2Bn-1\\ &=an(An-1Bn-2-An-2Bn-1) \end{align} which is true because of our induction hypothesis. An-1Bn-AnBn-1= na \left(-1\right) 1a 2 … an= n \prod i=1 (-ai) Specifically, if neither nor is zero we can express the difference between the th and th convergents like this: xn-1-xn= An-1 Bn-1 - An Bn =\left(-1\right)n a1a2 … an BnBn-1 = n \prod (-ai) i=1 BnBn-1 . ### The equivalence transformation If is any infinite sequence of non-zero complex numbers we can prove, by induction, that b0+\cfrac{a1}{b1+\cfrac{a2}{b2+\cfrac{a3}{b3+\cfrac{a4}{b4+\ddots}}}}= b0+\cfrac{c1a1}{c1b1+\cfrac{c1c2a2}{c2b2+\cfrac{c2c3a3}{c3b3+\cfrac{c3c4a4}{c4b4+\ddots}}}} where equality is understood as equivalence, which is to say that the successive convergents of the continued fraction on the left are exactly the same as the convergents of the fraction on the right. The equivalence transformation is perfectly general, but two particular cases deserve special mention. First, if none of the are zero a sequence can be chosen to make each partial numerator a 1: b0+\underset{i=1}\overset{infty}\operatorname{K} ai bi =b0+\underset{i=1}\overset{infty}\operatorname{K} 1 cibi where,,, and in general . Second, if none of the partial denominators are zero we can use a similar procedure to choose another sequence to make each partial denominator a 1: b0+\underset{i=1}\overset{infty}\operatorname{K} ai bi =b0+\underset{i=1}\overset{infty}\operatorname{K} diai 1 where and otherwise . These two special cases of the equivalence transformation are enormously useful when the general convergence problem is analyzed. ### Notions of convergence As mentioned in the introduction, the continued fraction x=b0+\underset{i=1}\overset{infty}\operatorname{K} ai bi converges if the sequence of convergents tends to a finite limit. This notion of convergence is very natural, but it is sometimes too restrictive. It is therefore useful to introduce the notion of general convergence of a continued fraction. Roughly speaking, this consists in replacing the infty \operatorname{K} i=n \tfrac{ai}{bi} part of the fraction by, instead of by 0, to compute the convergents. The convergents thus obtained are called modified convergents. We say that the continued fraction converges generally if there exists a sequence \} \{w n such that the sequence of modified convergents converges for all \{wn\} sufficiently distinct from \} \{w n . The sequence *\} \{w n is then called an exceptional sequence for the continued fraction. See Chapter 2 of for a rigorous definition. There also exists a notion of absolute convergence for continued fractions, which is based on the notion of absolute convergence of a series: a continued fraction is said to be absolutely convergent when the series f=\sumn\left(fn-fn-1\right), where fn= n \operatorname{K} i=1 \tfrac{ai}{bi} are the convergents of the continued fraction, converges absolutely. The Śleszyński–Pringsheim theorem provides a sufficient condition for absolute convergence. Finally, a continued fraction of one or more complex variables is uniformly convergent in an open neighborhood when its convergents converge uniformly on ; that is, when for every there exists such that for all, for all z\in\Omega , \|f(z)-fn(z)\|<\varepsilon. ### Even and odd convergents It is sometimes necessary to separate a continued fraction into its even and odd parts. For example, if the continued fraction diverges by oscillation between two distinct limit points and, then the sequence must converge to one of these, and must converge to the other. In such a situation it may be convenient to express the original continued fraction as two different continued fractions, one of them converging to, and the other converging to . The formulas for the even and odd parts of a continued fraction can be written most compactly if the fraction has already been transformed so that all its partial denominators are unity. Specifically, if x=\underset{i=1}\overset{infty}\operatorname{K} ai 1 is a continued fraction, then the even part and the odd part are given by xeven=\cfrac{a1}{1+a2-\cfrac{a2a3}{1+a3+a4-\cfrac{a4a5}{1+a5+a6-\cfrac{a6a7}{1+a7+a8-\ddots}}}} and xodd=a1-\cfrac{a1a2}{1+a2+a3-\cfrac{a3a4}{1+a4+a5-\cfrac{a5a6}{1+a6+a7-\cfrac{a7a8}{1+a8+a9-\ddots}}}} respectively. More precisely, if the successive convergents of the continued fraction are, then the successive convergents of as written above are, and the successive convergents of are .[3] ### Conditions for irrationality If and are positive integers with for all sufficiently large, then x=b0+\underset{i=1}\overset{infty}\operatorname{K} ai bi converges to an irrational limit. ### Fundamental recurrence formulas The partial numerators and denominators of the fraction's successive convergents are related by the fundamental recurrence formulas: \begin{align} A-1&=1&B-1&=0\\ A0&=b0&B0&=1\\ An+1&=bn+1An+an+1An-1&Bn+1&=bn+1Bn+an+1Bn-1 \end{align} The continued fraction's successive convergents are then given by x n= An Bn . These recurrence relations are due to John Wallis (1616–1703) and Leonhard Euler (1707–1783). As an example, consider the regular continued fraction in canonical form that represents the golden ratio : x=1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\ddots}}}} Applying the fundamental recurrence formulas we find that the successive numerators are and the successive denominators are, the Fibonacci numbers. Since all the partial numerators in this example are equal to one, the determinant formula assures us that the absolute value of the difference between successive convergents approaches zero quite rapidly. ## Linear fractional transformations A linear fractional transformation (LFT) is a complex function of the form w=f(z)= a+bz c+dz , where is a complex variable, and are arbitrary complex constants such that . An additional restriction that is customarily imposed, to rule out the cases in which is a constant. The linear fractional transformation, also known as a Möbius transformation, has many fascinating properties. Four of these are of primary importance in developing the analytic theory of continued fractions. • If the LFT has one or two fixed points. This can be seen by considering the equation f(z)=zdz2+cz=a+bz which is clearly a quadratic equation in . The roots of this equation are the fixed points of . If the discriminant is zero the LFT fixes a single point; otherwise it has two fixed points. z=g(w)= -a+cw b-dw such that for every point in the extended complex plane, and both and preserve angles and shapes at vanishingly small scales. From the form of we see that is also an LFT. • The composition of two different LFTs for which is itself an LFT for which . In other words, the set of all LFTs for which is closed under composition of functions. The collection of all such LFTs, together with the "group operation" composition of functions, is known as the automorphism group of the extended complex plane. • If the LFT reduces to w=f(z)= a c+dz , which is a very simple meromorphic function of with one simple pole (at) and a residue equal to . (See also Laurent series.) ### The continued fraction as a composition of LFTs Consider a sequence of simple linear fractional transformations \begin{align} \tau0(z)&=b0+z,\\[4px]\tau1(z)&= a1 b1+z ,\\[4px] \tau2(z)&= a2 b2+z ,\\[4px]\tau3(z)&= a3 b3+z ,\\&\vdots \end{align} Here we use to represent each simple LFT, and we adopt the conventional circle notation for composition of functions. We also introduce a new symbol to represent the composition of transformations ; that is, \begin{align} \boldsymbol{\Tau}\boldsymbol{1}(z)&=\tau0\circ\tau1(z)=\tau0(\tau1(z)),\\ \boldsymbol{\Tau}\boldsymbol{2}(z)&=\tau0\circ\tau1\circ\tau2(z)=\tau0(\tau1(\tau2(z))), \end{align} and so forth. By direct substitution from the first set of expressions into the second we see that \begin{align} \boldsymbol{\Tau}\boldsymbol{1}(z)&=\tau0\circ\tau1(z)&=&b0+\cfrac{a1}{b1+z}\\[4px] \boldsymbol{\Tau}\boldsymbol{2}(z)&=\tau0\circ\tau1\circ\tau2(z)&=&b0+\cfrac{a1}{b1+\cfrac{a2}{b2+z}} \end{align} and, in general, \boldsymbol{\Tau}\boldsymbol{n}(z)=\tau0\circ\tau1\circ\tau2\circ\circ\taun(z)= b0+\underset{i=1}\overset{n}\operatorname{K} ai bi where the last partial denominator in the finite continued fraction is understood to be . And, since, the image of the point under the iterated LFT is indeed the value of the finite continued fraction with partial numerators: \boldsymbol{\Tau}\boldsymbol{n}(0)=\boldsymbol{\Tau}\boldsymbol{n+1}(infty)=b0+\underset{i=1}\overset{n}\operatorname{K} ai bi . ### A geometric interpretation Defining a finite continued fraction as the image of a point under the iterated linear functional transformation leads to an intuitively appealing geometric interpretation of infinite continued fractions. The relationship xn=b0+\underset{i=1}\overset{n}\operatorname{K} ai bi = An Bn =\boldsymbol{\Tau}\boldsymbol{n }(0) = \boldsymbol_(\infty)\, can be understood by rewriting and in terms of the fundamental recurrence formulas: \begin{align} \boldsymbol{\Tau}\boldsymbol{n }(z)& = \frac& \boldsymbol_(z)& = \frac;\\[6px]\boldsymbol_(z)& = \frac& \boldsymbol_(z)& = \frac .\,\end In the first of these equations the ratio tends toward as tends toward zero. In the second, the ratio tends toward as tends to infinity. This leads us to our first geometric interpretation. If the continued fraction converges, the successive convergents are eventually arbitrarily close together. Since the linear fractional transformation is a continuous mapping, there must be a neighborhood of that is mapped into an arbitrarily small neighborhood of . Similarly, there must be a neighborhood of the point at infinity which is mapped into an arbitrarily small neighborhood of . So if the continued fraction converges the transformation maps both very small and very large into an arbitrarily small neighborhood of, the value of the continued fraction, as gets larger and larger. For intermediate values of, since the successive convergents are getting closer together we must have An-1 Bn-1 An Bn ⇒ An-1 An Bn-1 Bn =k where is a constant, introduced for convenience. But then, by substituting in the expression for we obtain \boldsymbol{\Tau}\boldsymbol{n }(z) = \frac= \frac \left(\frac\right)\approx \frac \left(\frac\right) = \frac\, so that even the intermediate values of (except when) are mapped into an arbitrarily small neighborhood of, the value of the continued fraction, as gets larger and larger. Intuitively, it is almost as if the convergent continued fraction maps the entire extended complex plane into a single point.[4] Notice that the sequence lies within the automorphism group of the extended complex plane, since each is a linear fractional transformation for which . And every member of that automorphism group maps the extended complex plane into itself: not one of the can possibly map the plane into a single point. Yet in the limit the sequence defines an infinite continued fraction which (if it converges) represents a single point in the complex plane. When an infinite continued fraction converges, the corresponding sequence of LFTs "focuses" the plane in the direction of, the value of the continued fraction. At each stage of the process a larger and larger region of the plane is mapped into a neighborhood of, and the smaller and smaller region of the plane that's left over is stretched out ever more thinly to cover everything outside that neighborhood.[5] For divergent continued fractions, we can distinguish three cases: 1. The two sequences and might themselves define two convergent continued fractions that have two different values, and . In this case the continued fraction defined by the sequence diverges by oscillation between two distinct limit points. And in fact this idea can be generalized: sequences can be constructed that oscillate among three, or four, or indeed any number of limit points. Interesting instances of this case arise when the sequence constitutes a subgroup of finite order within the group of automorphisms over the extended complex plane. 2. The sequence may produce an infinite number of zero denominators while also producing a subsequence of finite convergents. These finite convergents may not repeat themselves or fall into a recognizable oscillating pattern. Or they may converge to a finite limit, or even oscillate among multiple finite limits. No matter how the finite convergents behave, the continued fraction defined by the sequence diverges by oscillation with the point at infinity in this case.[6] 3. The sequence may produce no more than a finite number of zero denominators . while the subsequence of finite convergents dances wildly around the plane in a pattern that never repeats itself and never approaches any finite limit either. Interesting examples of cases 1 and 3 can be constructed by studying the simple continued fraction x=1+\cfrac{z}{1+\cfrac{z}{1+\cfrac{z}{1+\cfrac{z}{1+\ddots}}}} where is any real number such that .[7] ## Euler's continued fraction formula See main article: Euler's continued fraction formula. Euler proved the following identity: a0+a0a1+a0a1a2++a0a1a2 … an= a0 1- a1 1+a1- a2 … 1+a2- an 1+an . From this many other results can be derived, such as 1 + u1 1 + u2 1 + … + u3 1 = un 1 u1- 2 u 1 u1+u2- 2 u 2 u2+u3- 2 u n-1 un-1+un , and 1 a0 + x a0a1 + x2 a0a1a2 + … + xn = a0a1a2\ldotsan 1 a0- a0x a1+x- a1x … a2+x- an-1x an+x . Euler's formula connecting continued fractions and series is the motivation for the, and also the basis of elementary approaches to the convergence problem. ## Examples ### Transcendental functions and numbers Here are two continued fractions that can be built via Euler's identity. ex= x0 0! + x1 1! + x2 2! + x3 3! + x4 4! +=1+\cfrac{x}{1-\cfrac{1x}{2+x-\cfrac{2x}{3+x-\cfrac{3x}{4+x-\ddots}}}} log(1+x)= x1 1 - x2 2 + x3 3 - x4 4 +=\cfrac{x}{1-0x+\cfrac{12x}{2-1x+\cfrac{22x}{3-2x+\cfrac{32x}{4-3x+\ddots}}}} Here are additional generalized continued fractions: \arctan\cfrac{x}{y}=\cfrac{xy}{1y2+\cfrac{(1xy)2}{3y2-1x2+\cfrac{(3xy)2}{5y2-3x2+\cfrac{(5xy)2}{7y2-5x2+\ddots}}}} =\cfrac{x}{1y+\cfrac{(1x)2}{3y+\cfrac{(2x)2}{5y+\cfrac{(3x)2}{7y+\ddots}}}} x y e =1+\cfrac{2x}{2y-x+\cfrac{x2}{6y+\cfrac{x2}{10y+\cfrac{x2}{14y+\cfrac{x2}{18y+\ddots}}}}} ⇒ e2=7+\cfrac{2}{5+\cfrac{1}{7+\cfrac{1}{9+\cfrac{1}{11+\ddots}}}} log\left(1+ x y \right)=\cfrac{x}{y+\cfrac{1x}{2+\cfrac{1x}{3y+\cfrac{2x}{2+\cfrac{2x}{5y+\cfrac{3x}{2+\ddots}}}}}}=\cfrac{2x}{2y+x-\cfrac{(1x)2}{3(2y+x)-\cfrac{(2x)2}{5(2y+x)-\cfrac{(3x)2}{7(2y+x)-\ddots}}}} This last is based on an algorithm derived by Aleksei Nikolaevich Khovansky in the 1970s.[8] Example: the natural logarithm of 2 (= ≈ 0.693147...): log2=log(1+1)=\cfrac{1}{1+\cfrac{1}{2+\cfrac{1}{3+\cfrac{2}{2+\cfrac{2}{5+\cfrac{3}{2+\ddots}}}}}}=\cfrac{2}{3-\cfrac{12}{9-\cfrac{22}{15-\cfrac{32}{21-\ddots}}}} Here are three of 's best-known generalized continued fractions, the first and third of which are derived from their respective arctangent formulas above by setting and multiplying by 4. The Leibniz formula for : \pi=\cfrac{4}{1+\cfrac{12}{2+\cfrac{32}{2+\cfrac{52}{2+\ddots}}}} = infty \sum n=0 4(-1)n 2n+1 = 4 1 - 4 3 + 4 5 - 4 7 +- converges too slowly, requiring roughly terms to achieve correct decimal places. The series derived by Nilakantha Somayaji: \pi=3+\cfrac{12}{6+\cfrac{32}{6+\cfrac{52}{6+\ddots}}} =3- infty \sum n=1 (-1)n n(n+1)(2n+1) =3+ 1 1 ⋅ 2 ⋅ 3 - 1 2 ⋅ 3 ⋅ 5 + 1 3 ⋅ 4 ⋅ 7 -+ is a much more obvious expression but still converges quite slowly, requiring nearly 50 terms for five decimals and nearly 120 for six. Both converge sublinearly to . On the other hand: \pi=\cfrac{4}{1+\cfrac{12}{3+\cfrac{22}{5+\cfrac{32}{7+\ddots}}}} =4-1+ 1 6 - 1 34 + 16 3145 - 4 4551 + 1 6601 - 1 38341 +- converges linearly to, adding at least three digits of precision per four terms, a pace slightly faster than the arcsine formula for : \pi=6\sin-1\left( 1 2 \right)= infty \sum n=0 3 ⋅ \binom{2n n } = \frac + \frac + \frac + \frac + \cdots\! which adds at least three decimal digits per five terms. • Note: this continued fraction's rate of convergence tends to, hence tends to, whose common logarithm is . The same (the silver ratio squared) also is observed in the unfolded general continued fractions of both the natural logarithm of 2 and the th root of 2 (which works for any integer) if calculated using . For the folded general continued fractions of both expressions, the rate convergence, hence, whose common logarithm is, thus adding at least three digits per two terms. This is because the folded GCF folds each pair of fractions from the unfolded GCF into one fraction, thus doubling the convergence pace. The Manny Sardina reference further explains "folded" continued fractions. • Note: Using the continued fraction for cited above with the best-known Machin-like formula provides an even more rapidly, although still linearly, converging expression: \pi=16\tan-1\cfrac{1}{5}-4\tan-1\cfrac{1}{239}=\cfrac{16}{u+\cfrac{12}{3u+\cfrac{22}{5u+\cfrac{32}{7u+\ddots}}}} -\cfrac{4}{v+\cfrac{12}{3v+\cfrac{22}{5v+\cfrac{32}{7v+\ddots}}}}. with and . ### Roots of positive numbers The th root of any positive number can be expressed by restating, resulting in \sqrt[n]{zm}=\sqrt[n]{\left(xn+y\right)m}=xm+\cfrac{my}{nxn-m+\cfrac{(n-m)y}{2xm+\cfrac{(n+m)y}{3nxn-m+\cfrac{(2n-m)y}{2xm+\cfrac{(2n+m)y}{5nxn-m+\cfrac{(3n-m)y}{2xm+\ddots}}}}}} which can be simplified, by folding each pair of fractions into one fraction, to \sqrt[n]{zm}=xm+\cfrac{2xmmy}{n(2xn+y)-my-\cfrac{(12n2-m2)y2}{3n(2xn+y)-\cfrac{(22n2-m2)y2}{5n(2xn+y)-\cfrac{(32n2-m2)y2}{7n(2xn+y)-\cfrac{(42n2-m2)y2}{9n(2xn+y)-\ddots}}}}}. The square root of is a special case with and : \sqrt{z}=\sqrt{x2+y}=x+\cfrac{y}{2x+\cfrac{y}{2x+\cfrac{3y}{6x+\cfrac{3y}{2x+\ddots}}}}=x+\cfrac{2xy}{2(2x2+y)-y-\cfrac{1 ⋅ 3y2}{6(2x2+y)-\cfrac{3 ⋅ 5y2}{10(2x2+y)-\ddots}}} which can be simplified by noting that : \sqrt{z}=\sqrt{x2+y}=x+\cfrac{y}{2x+\cfrac{y}{2x+\cfrac{y}{2x+\cfrac{y}{2x+\ddots}}}}=x+\cfrac{2xy}{2(2x2+y)-y-\cfrac{y2}{2(2x2+y)-\cfrac{y2}{2(2x2+y)-\ddots}}}. The square root can also be expressed by a periodic continued fraction, but the above form converges more quickly with the proper and . #### Example 1 The cube root of two (21/3 or ≈ 1.259921...) can be calculated in two ways: Firstly, "standard notation" of,, and : \sqrt[3]2=1+\cfrac{1}{3+\cfrac{2}{2+\cfrac{4}{9+\cfrac{5}{2+\cfrac{7}{15+\cfrac{8}{2+\cfrac{10}{21+\cfrac{11}{2+\ddots}}}}}}}}=1+\cfrac{21}{9-1-\cfrac{24}{27-\cfrac{57}{45-\cfrac{810}{63-\cfrac{1113}{81-\ddots}}}}}. Secondly, a rapid convergence with, and : \sqrt[3]2=\cfrac{5}{4}+\cfrac{0.5}{50+\cfrac{2}{5+\cfrac{4}{150+\cfrac{5}{5+\cfrac{7}{250+\cfrac{8}{5+\cfrac{10}{350+\cfrac{11}{5+\ddots}}}}}}}}=\cfrac{5}{4}+\cfrac{2.51}{253-1-\cfrac{24}{759-\cfrac{57}{1265-\cfrac{810}{1771-\ddots}}}}. #### Example 2 Pogson's ratio (1001/5 or ≈ 2.511886...), with, and : \sqrt[5]{100}=\cfrac{5}{2}+\cfrac{3}{250+\cfrac{12}{5+\cfrac{18}{750+\cfrac{27}{5+\cfrac{33}{1250+\cfrac{42}{5+\ddots}}}}}}=\cfrac{5}{2}+\cfrac{5 ⋅ 3}{1265-3-\cfrac{1218}{3795-\cfrac{2733}{6325-\cfrac{4248}{8855-\ddots}}}}. #### Example 3 The twelfth root of two (21/12 or ≈ 1.059463...), using "standard notation": \sqrt[12]2=1+\cfrac{1}{12+\cfrac{11}{2+\cfrac{13}{36+\cfrac{23}{2+\cfrac{25}{60+\cfrac{35}{2+\cfrac{37}{84+\cfrac{47}{2+\ddots}}}}}}}}=1+\cfrac{21}{36-1-\cfrac{1113}{108-\cfrac{2325}{180-\cfrac{3537}{252-\cfrac{4749}{324-\ddots}}}}}. #### Example 4 Equal temperament's perfect fifth (27/12 or ≈ 1.498307...), with : With "standard notation": \sqrt[12]{27}=1+\cfrac{7}{12+\cfrac{5}{2+\cfrac{19}{36+\cfrac{17}{2+\cfrac{31}{60+\cfrac{29}{2+\cfrac{43}{84+\cfrac{41}{2+\ddots}}}}}}}}=1+\cfrac{27}{36-7-\cfrac{519}{108-\cfrac{1731}{180-\cfrac{2943}{252-\cfrac{4155}{324-\ddots}}}}}. A rapid convergence with,, and : \sqrt[12]{27}=\cfrac{1}{2}\sqrt[12]{312-7153}=\cfrac{3}{2}-\cfrac{0.57153}{4 ⋅ 312-\cfrac{11 ⋅ 7153}{6-\cfrac{13 ⋅ 7153}{12 ⋅ 312-\cfrac{23 ⋅ 7153}{6-\cfrac{25 ⋅ 7153}{20 ⋅ 312-\cfrac{35 ⋅ 7153}{6-\cfrac{37 ⋅ 7153}{28 ⋅ 312-\cfrac{47 ⋅ 7153}{6-\ddots}}}}}}}} \sqrt[12]{27}=\cfrac{3}{2}-\cfrac{3 ⋅ 7153}{12(219+312)+7153-\cfrac{11 ⋅ 13 ⋅ 71532}{36(219+312)-\cfrac{23 ⋅ 25 ⋅ 71532}{60(219+312)-\cfrac{35 ⋅ 37 ⋅ 71532}{84(219+312)-\ddots}}}}. More details on this technique can be found in General Method for Extracting Roots using (Folded) Continued Fractions. ## Higher dimensions Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number, and the way lattice points in two dimensions lie to either side of the line . Generalizing this idea, one might ask about something related to lattice points in three or more dimensions. One reason to study this area is to quantify the mathematical coincidence idea; for example, for monomials in several real numbers, take the logarithmic form and consider how small it can be. Another reason is to find a possible solution to Hermite's problem. There have been numerous attempts to construct a generalized theory. Notable efforts in this direction were made by Felix Klein (the Klein polyhedron), Georges Poitou and George Szekeres. ## References • Angell. David. 2010. A family of continued fractions. Journal of Number Theory. Elsevier. 130. 4. 904–911. 10.1016/j.jnt.2009.12.003. • Book: Angell , David . 2021. Irrationality and Transcendence in Number Theory. Chapman and Hall/CRC. 9780367628376. • Book: Beckmann , Petr . 1971. A History of Pi. St. Martin's Press, Inc.. 131–133, 140–143. 0-88029-418-3. registration. • Book: Bombelli , Rafael . Rafael Bombelli. 1579. L'algebra. • Borwein. Jonathan Michael. Jonathan Borwein. Crandall. Richard E.. Richard Crandall. Fee. Greg. Greg Fee. 2004. On the Ramanujan AGM Fraction, I: The Real-Parameter Case. Experimental Mathematics. 13. 3. 275–285. 10.1080/10586458.2004.10504540. 17758274. • Book: Cataldi , Pietro Antonio . Pietro Cataldi. 1613. Trattato del modo brevissimo di trovar la radice quadra delli numeri. A treatise on a quick way to find square roots of numbers. • Book: Chrystal , George . George Chrystal. 1999. Algebra, an Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges: Pt. 1. American Mathematical Society. 0-8218-1649-7. 500. • Book: Cusick. Thomas W.. Flahive. Mary E.. 1989. The Markoff and Lagrange Spectra. limited. American Mathematical Society. 0-8218-1531-8. 89. • Web site: Euclid. Euclid. 2008. 300 BC. Clay Mathematics Institute. Elements. • Web site: Euler. Leonhard. Leonhard Euler. 1748. E101 – Introductio in analysin infinitorum, volume 1. The Euler Archive. 2 May 2022. • Book: Gauss , Carl Friedrich . Carl Friedrich Gauss. 1813. Disquisitiones generales circa seriem infinitam. • Book: Havil , Julian . 2012. The Irrationals: A Story of the Numbers You Can't Count On. Princeton University Press. j.ctt7smdw. 280. 978-0691143422 . • Book: Jones. William B.. Thron. W.J.. 1980. Continued fractions. Analytic theory and applications. Encyclopedia of Mathematics and its Applications. 11. Reading, MA. Addison-Wesley. 0-201-13510-8. 0445.30003. registration. (Covers both analytic theory and history.) • Book: Lorentzen. Lisa. Lisa Lorentzen. Waadeland. Haakon. 1992. Continued Fractions with Applications. Reading, MA. North Holland. 978-0-444-89265-2. (Covers primarily analytic theory and some arithmetic theory.) • Book: Perron , Oskar . Oskar Perron. 1977a. 1954. Die Lehre von den Kettenbrüchen. Band I: Elementare Kettenbrüche. 3. Vieweg + Teubner Verlag. 9783519020219. • Book: Perron , Oskar . Oskar Perron. 1977b. 1954. Die Lehre von den Kettenbrüchen. Band II: Analytisch-funktionentheoretische Kettenbrüche. 3. Vieweg + Teubner Verlag. 9783519020226. • Web site: Porubský. Štefan. Basic definitions for continued fractions. 2008. Interactive Information Portal for Algorithmic Mathematics. Institute of Computer Science of the Czech Academy of Sciences. Prague, Czech Republic. 2 May 2022. • Book: Press. WH. Teukolsky. SA. Vetterling. WT. Flannery. BP. 2007. Numerical Recipes: The Art of Scientific Computing. 3rd. Cambridge University Press. New York. 978-0-521-88068-8. Section 5.2. Evaluation of Continued Fractions. http://apps.nrbook.com/empanel/index.html?pg=206. • Web site: Sardina. Manny. 2007. General Method for Extracting Roots using (Folded) Continued Fractions. Surrey (UK). • Szekeres. George. George Szekeres. 1970. Multidimensional continued fractions. Ann. Univ. Sci. Budapest. Eötvös Sect. Math.. 13. 113–140. • Von Koch. Helge. Helge von Koch. 1895. Sur un théorème de Stieltjes et sur les fonctions définies par des fractions continues. Bulletin de la Société Mathématique de France. 23. 33–40. 10.24033/bsmf.508. 26.0233.01. • Book: Wall , Hubert Stanley . Hubert Stanley Wall. 1967. Analytic Theory of Continued Fractions. Reprint. Chelsea Pub Co. 0-8284-0207-8. (This reprint of the D. Van Nostrand edition of 1948 covers both history and analytic theory.) • Book: Wallis , John . John Wallis. 1699. Opera mathematica. Mathematical Works.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9694328904151917, "perplexity": 1542.5484848221258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00307.warc.gz"}
https://makarandtapaswi.wordpress.com/2009/11/13/from-real-to-complex-to-vector-gaussian-distributions/	# From Real to Complex to Vector Gaussians Gaussian distributions are probably the most widely used distributions in mathematics and engineering. Though one strange aspect of them is that they have slightly different equations for the real and complex cases. This is an interesting problem, and has a really nice reasoning, which generally is not taught in classes. In an attempt to answer the why here goes… All of us have definitely at some point of time seen this familiar real Gaussian distribution $p_x(x) = \frac{1}{\sqrt{2\pi \sigma^2}} e^{-\frac{x^2}{2\sigma^2}}$ which changes to a real vector form as $p_x(\mathbf{x}) = \frac{1}{\sqrt{(2\pi)^N \|\mathbf{C_x}\|}} e^{-\frac{1}{2}\mathbf{x}^T \mathbf{C_x}^{-1}\mathbf{x}}$ where $x$ is a vector of Gaussian distributions $x_1, x_2, \ldots, x_N$ with 0 mean and covariance matrix $\mathbf{C_x}$. This can be written directly under the assumption that the individual $x_i$ are uncorrelated, and since uncorrelated gaussians are independent, a multiplication of the individual gaussian distributions can be carried out. Further, there is a change when referring to complex distributions. This is due to the difference in the definition of the Covariance matrix itself, which can be now written as a covariance matrix of the real and imaginary parts $\mathbf{C_z}$ or the covariance matrix generated by using the complex number directly as $\mathbf{C_s}$ where $\mathbf{z} = [\mathbf{x y}]^T$ and $\mathbf{u} = [\mathbf{u u^*}]^T$ are both column vectors of 2N size. This gives a relation between $\mathbf{C_z} = \frac{1}{2} \mathbf{T}^H \mathbf{C_s} \mathbf{T}$ where $\mathbf{T}$ is a 2-D unitary matrix. This half factor is responsible for the disappearance of the 2 in the fraction, and $\|\mathbf{C_s}\| = \|\mathbf{C_u}\|^2$ is responsible for the removal of the square root. Thus the final Complex Guassian Multivariate distribution ends up (different from the real one) as $p_u(\mathbf{u}) = \frac{1}{(\pi)^N \|\mathbf{C_u}\|} e^{-\mathbf{u}^T \mathbf{C_u}^{-1}\mathbf{u}}$ when $\mathbf{u}$ is circulant complex random variable, i.e. the covariance of real and imaginary parts is same, and they are uncorrelated (generally satisfied in applications). One last point, its important to note that independence implies uncorrelation, but uncorrelation need not imply independence except for the nice and widely used Gaussian case 🙂	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 15, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9575178027153015, "perplexity": 203.899802924897}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590295.61/warc/CC-MAIN-20180718154631-20180718174631-00084.warc.gz"}
http://mathhelpforum.com/discrete-math/52594-iternation-definition.html	# Math Help - Iternation definition 1. ## Iternation definition How do I work out an iterative definition (difference equation) for the sequences: (i). {1, 1/4, 1/9, 1/16...} (ii). {3, -6, 12, -24...} Thanks. 2. Originally Posted by tkexer How do I work out an iterative definition (difference equation) for the sequences: (i). {1, 1/4, 1/9, 1/16...} (ii). {3, -6, 12, -24...} Thanks. i. The $n$-the term is $1/n^2$ so: $\frac{1}{(n+1)^2} = \frac{1}{(1+\frac{1}{\sqrt{1/n^2}})^2}$ so: $ a_{n+1}=\frac{1}{(1+\frac{1}{\sqrt{a_n}})^2},\ \ \ a_1=1 $ RonL	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7406797409057617, "perplexity": 8389.394633929121}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00426-ip-10-147-4-33.ec2.internal.warc.gz"}
http://mathhelpforum.com/discrete-math/26349-proving-disproving-print.html	# Proving and Disproving • January 18th 2008, 06:30 AM TheRekz Proving and Disproving 1. [tex] \forall m,n \in Z, if m + n is even then either m and n are both even or they are both odd [\math] 2. Prove or disprove using contradiction. Every integer > 11 is the sum of two composite integers. For the first number, is it the same if I prove that if m and n are both even then m +n is even and if m and n are both odd then m + n is even? • January 18th 2008, 07:06 AM ThePerfectHacker Quote: Originally Posted by TheRekz 1. $\forall m,n \in Z, if m + n$ is even then either m and n are both even or they are both odd By division algorithm we can write $m=2a+r_1$ where $r_1=0,1$ and $n=2b+r_2$ then $n+m = 2(a + b) + (r_1+r_2)$ for this to be even we require that $(r_1,r_2)=(0,0)$ or $(r_1,r_2)=(1,1)$, i.e. both even or both odd. Quote: 2. Prove or disprove using contradiction. Every integer > 11 is the sum of two composite integers. If $n>11$ is even then $n - 4 > 2$ is even and these are composite, thus, $n=4+(n-4)$. If $n>11$ and is odd then we $n-9>2$ is even and so composite which means we can write $n = 9 + (n-9)$. • January 18th 2008, 07:39 AM TheRekz is there any other way to proof this?? your explanation seems complicated although it makes sense. I don't quite understand where did you get the m = 2a + r from?? so you mean r can be either 0 or 1 here depends whether m is odd or even? if m is even then r is 0?? r can therefore also be 2 right? • January 18th 2008, 08:17 AM CaptainBlack Quote: Originally Posted by TheRekz 1. [tex] \forall m,n \in Z, if m + n is even then either m and n are both even or they are both odd [\math] (all number refered to are in $\mathbb{Z}$) Supose there are $n$ and $m$ such that $n$ is odd and $m$ even and $n+m$ is even. By supposition there exist $k_1$ and $k_2$ such that $n=2k_1+1,\ m=2k_2$. Then $n+m=2(k_1+k_2)+1$ which is odd, which contradicts our supposition. Hence if $n+m$ is even either $m$ and $n$ are both even or they are both odd RonL • January 18th 2008, 08:20 AM CaptainBlack Quote: Originally Posted by TheRekz 1 For the first number, is it the same if I prove that if m and n are both even then m +n is even and if m and n are both odd then m + n is even? No you have to show that if n+m is even both n and m are even or both are odd, and that you will not have done. RonL • January 18th 2008, 08:40 AM TheRekz Quote: Originally Posted by CaptainBlack No you have to show that if n+m is even both n and m are even or both are odd, and that you will not have done. RonL can you help me to do number 2?? Cause I don't really get it on the post no.2 answer • January 18th 2008, 10:16 AM CaptainBlack Quote: Originally Posted by TheRekz can you help me to do number 2?? Cause I don't really get it on the post no.2 answer ImPerfectHackers proof is quite simple (and neat): Suppose that there is an integer $N> 11$ not the sum of two composite integers. Then $N$ is even or odd. Case 1: $N$ even, put $n_1=4,\ n_2=N-4$, then both $n_1$ and $n_2$ are even and greater than $2$ and hence composite, but this contradicts our assumption so $N$ cannot be composite. Case 2: $N$ odd, put $n_1=9,\ n_2=N-9$, then both $n_1$ is composite and $n_2$ is even and greater than $2$ and hence composite, but this contradicts our assumption so $N$ cannot be composite. Case 1 and Case 2 together contradict the original assumption and so the theorem: Every integer > 11 is the sum of two composite integers; is proven by contradiction. RonL • January 23rd 2008, 03:19 PM TheRekz Quote: Originally Posted by CaptainBlack ImPerfectHackers proof is quite simple (and neat): Suppose that there is an integer $N> 11$ not the sum of two composite integers. Then $N$ is even or odd. Case 1: $N$ even, put $n_1=4,\ n_2=N-4$, then both $n_1$ and $n_2$ are even and greater than $2$ and hence composite, but this contradicts our assumption so $N$ cannot be composite. Case 2: $N$ odd, put $n_1=9,\ n_2=N-9$, then both $n_1$ is composite and $n_2$ is even and greater than $2$ and hence composite, but this contradicts our assumption so $N$ cannot be composite. Case 1 and Case 2 together contradict the original assumption and so the theorem: Every integer > 11 is the sum of two composite integers; is proven by contradiction. RonL just one more question, how do we know that n2 is even here?? thanks?? • January 23rd 2008, 08:13 PM CaptainBlack Quote: Originally Posted by TheRekz just one more question, how do we know that n2 is even here?? thanks?? In Case 1:By hypothesis N is even, and > 11, so N-4 is even (and >7) In Case 2:By hypothesis N is odd, and > 11, so N-9 is even (and >2) (even-even is even, and odd-odd is also even) RonL	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 54, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9753541350364685, "perplexity": 384.42897487389234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988458.74/warc/CC-MAIN-20150728002308-00342-ip-10-236-191-2.ec2.internal.warc.gz"}
https://chet-aero.com/2018/10/02/consistency-convergence-and-stability-of-lax-wendroff-scheme-applied-to-convection-equation/	The purpose of this project is to examine the Lax-Wendroff scheme to solve the convection (or one-way wave) equation and to determine its consistency, convergence and stability. ## Overview of Taylor Series Expansions The case examined utilized a Taylor Series expansion, so some explanation common to both is in order. The general expression for a Taylor series is found in A Course in Mathematical Analysis Volume 1: Derivatives and Differentials; Definite Integrals; Expansion in Series; Applications to Geometry (Dover Books on Mathematics) and is given as As a general rule, $h$ will represent a time or distance step, i.e. $\Delta_{x},\,\Delta_{t}$, although the second case will require a more versatile application of $h$. In any event, the forward spatial Taylor series expansion from a single point is given as $u(x_{{k+1}},t_{{n}})=u(x_{{k}},t_{{n}})+D_{{1}}(u)(x_{{k}},t_{{n}})\Delta_{{x}}+1/2\,\left(D_{{1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{2}+1/6\,\left(D_{{1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{3}\\ +1/24\,\left(D_{{1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{4}+{\frac{1}{120}}\,\left(D_{{1,1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{5}\\+{\frac{1}{720}}\,\left(D_{{1,1,1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{6}+O(1){\Delta_{{x}}}^{7}$ For our analysis $u\left(x,t\right)$ is the function of the finite difference approximation, contrasted with the exact function $v\left(x,t\right)$. The subscripts $k,n$ and indices for space and time respectively. The backward spatial expansion is given as $u(x_{{k-1}},t_{{n}})=u(x_{{k}},t_{{n}})-D_{{1}}(u)(x_{{k}},t_{{n}})\Delta_{{x}}+1/2\,\left(D_{{1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{2}\\-1/6\,\left(D_{{1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{3}+1/24\,\left(D_{{1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{4}\\-{\frac{1}{120}}\,\left(D_{{1,1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{5}+{\frac{1}{720}}\,\left(D_{{1,1,1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{6}-O(1){\Delta_{{x}}}^{7}$ In like fashion the expansion for time is as follows: $u(x_{{k}},t_{{n+1}})u(x_{{k}},t_{{n}})+D_{{2}}(u)(x_{{k}},t_{{n}})\Delta_{{t}}+1/2\,\left(D_{{2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{2}\\+1/6\,\left(D_{{2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{3}+1/24\,\left(D_{{2,2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{4}\\+{\frac{1}{120}}\,\left(D_{{2,2,2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{5}+{\frac{1}{720}}\,\left(D_{{2,2,2,2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{6}+O(1){\Delta_{{t}}}^{7}$ ## Convection Equation Now let us turn to the convection equation. Although CFD aficionados refer to this equation in this way, in solid mechanics this is the “one-way” wave equation, i.e., without reflections. The derivation and solution of this equation is detailed here. In either case the governing equation is ${\frac{\partial}{\partial t}}v(x,t)+a{\frac{\partial}{\partial x}}v(x,t)=0$ When solved using the Lax-Wendroff scheme, it is expressed as $u(x_{{k}},t_{{n+1}})=u(x_{{k}},t_{{n}})-1/2\, R\left(u(x_{{k+1}},t_{{n}})-u(x_{{k-1}},t_{{n}})\right)\\+1/2\,{R}^{2}\left(u(x_{{k+1}},t_{{n}})-2\, u(x_{{k}},t_{{n}})+u(x_{{k-1}},t_{{n}})\right)$ where $R=a\frac{\Delta_{t}}{\Delta_{x}}$ The solution for this problem is given in Numerical Methods for Engineers and Scientists, Second Edition. ### Application of Taylor Series Expansions for Consistency If we apply the results of the Taylor series expansions to the Lax-Wendroff scheme and perform a good deal of algebra (including substituting for $R$,) the result is $u(x_{{k}},t_{{n}})+D_{{2}}(u)(x_{{k}},t_{{n}})\Delta_{{t}}+1/2\,\left(D_{{2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{2}+1/6\,\left(D_{{2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{3}\\+1/24\,\left(D_{{2,2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{4}+{\frac{1}{120}}\,\left(D_{{2,2,2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{5}+{\frac{1}{720}}\,\left(D_{{2,2,2,2,2,2}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{t}}}^{6}+O(1){\Delta_{{t}}}^{7}\\=\\u(x_{{k}},t_{{n}})+r\left(D_{{1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{2}-1/12\, r\left(D_{{1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{4}-1/40\, r\left(D_{{1,1,1,1,1,1}}\right)(u)(x_{{k}},t_{{n}}){\Delta_{{x}}}^{6}$ Rearranging, making a change in notation and dropping the $\mathcal{O}$ terms as well, On the left hand side is the exact equation, which is strictly speaking equal to zero. On the right hand side is the residual for consistency of the finite difference scheme. If the scheme is consistent with the original equation, it too should approach zero as $\Delta_{x},\,\Delta_{t}\rightarrow0$. Based on this we note the following: • All of the right hand side terms contain $\Delta_{x},\,\Delta_{t}$ or both. Thus, as these approach zero, the entire right hand side will approach zero. Thus the scheme is consistent with the original differential equation. • The lowest order terms for the time and spatial steps on the right hand side are $\Delta_{t}$ and $\Delta_{x}^{2}$ respectively. Thus we can conclude that the truncation error is $\mathcal{O}\left(t\right)+\mathcal{O}\left(x^{2}\right)$. Or is it? Let us assume that the solution is twice differentiable. By this we mean that the function has second derivatives in both space and time. (Another way of interpreting this is to say that “twice differentiable” means that the solution has no derivatives beyond the second, in which case many of the terms in the Taylor Series expansion would go to zero.) Then we differentiate the original equation once temporally, thus ${\frac{\partial^{2}}{\partial{t}^{2}}}v(x,t)+a{\frac{\partial^{2}}{\partial t\partial x}}v(x,t)=0$ Now let us do the same thing but spatially, and (with a little additional algebra) we obtain $-a{\frac{\partial^{2}}{\partial t\partial x}}v(x,t)-{a}^{2}{\frac{\partial^{2}}{\partial{x}^{2}}}v(x,t)=0$ ${\frac{\partial^{2}}{\partial{t}^{2}}}v(x,t)-{a}^{2}{\frac{\partial^{2}}{\partial{x}^{2}}}v(x,t)=0$ which is, mirabile visu, the wave equation. Applying this solution for the original equation to the finite difference residual results in Now we see that the lowest order terms are $\Delta_{t}^{2}$ and $\Delta_{x}^{2}$, which means that the truncation error is $\mathcal{O}\left(t^{2}\right)+\mathcal{O}\left(x^{2}\right)$. We duly note that the fourth order spatial derivative is multiplied by $\Delta_{{t}}{\Delta_{{x}}}^{2}$. However, the squared term will be the predominant one as $\Delta_{x},\,\Delta_{t}\rightarrow0$, so this does not change our conclusion. Also, if “twice differentiable” means that the function has no further derivatives beyond the second, then all of the terms go to zero, and the numerical solution, within machine accuracy, is exact. This also applies to the next section as well; the vector described there would be the zero vector under these conditions. ### Consistency in a Norm The Taylor Series expansion is only valid at the point at which it is taken. For most differential equations, we are interested in solutions along a broader region. This is in part the purpose for considering consistency in a norm. Let us consider the result we just obtained, thus The right hand side represents the residual for consistency of the finite difference scheme. If we were to consider a Taylor Series expansion for all of the points in space and time under consideration, what we would end up with is an infinite set of residuals, i.e., the right hand side of the above equation, which could then be arranged in a vector. If we designate this vector as$R$, then each entry can be designated as follows: Now let us consider the nature of the differential equation. The following is adapted from Numerical Solution of Differential Equations: Finite Difference and Finite Element Solution of the Initial, Boundary and Eigenvalue Problem in the… (Computer Science and Applied Mathematics). We can consider the differential equation as a linear transformation. Since we have defined the results as an vector, we can express this as follows for the exact solution: $Av\left(x,t\right)=F$ and for the finite difference solution $Au\left(x,t\right)=F+R$ The result difference between the two is the residual we defined earlier. The finite difference representation is the same as the original if and only if $A$ is the same in both cases. Combining both equations, $A\left(v\left(x,t\right)-u\left(x,t\right)\right)=R$ and rearranging $v\left(x,t\right)-u\left(x,t\right)=A^{-1}R$ Now let us consider the norm. Given the infinite number of entries in this vector, the most convenient norm to take would be the infinity norm, where the norm would be the largest absolute value in the set. For an inner product space, $\|\|v\left(x,t\right)-u\left(x,t\right)\|\|_{\infty}=\|\|A^{-1}\|\|_{\infty}\,\|\|R\|\|_{\infty}$ We have shown that each and every $r_{n}\rightarrow0$ as $\Delta_{x},\,\Delta_{t}\rightarrow0$. (Additionally the function would have to be bounded, continuous and at least twice differentiable at all points.) From this, $R\rightarrow0$ and $\|\|R\|\|_{\infty}\rightarrow0$. If $A$ and $A^{-1}$ are bounded (as they are in a linear transformation,) then $\|\|v\left(x,t\right)-u\left(x,t\right)\|\|_{\infty}\rightarrow0$ and thus the exact solution and its finite difference counterpart become the same. This is consistency by definition. (The most serious obstacle to actually constructing such a vector–a necessary prerequisite to a norm–is evaluating the derivatives. One “solution” would be to used the exact solution of the original differential equation, but that assumes we can arrive at an exact solution. In many cases, the whole point of a numerical solution is because the exact, “closed form” solution is unavailable. Thus we would end up with numerical evaluations for the derivatives.) As for other norms such as the Euclidean norm, if the entries in the vector approach zero as $\Delta_{x},\,\Delta_{t}\rightarrow0$, we would expect the norm to do so as well, as discussed above. It should be noted that the infinity norm would be best to pick up a point slowly converging on zero than a Euclidean norm. ### von Neumann Stability Analysis Turning to the issue of stability, we will perform a von Neumann analysis. In this type of analysis we will analyze a stability factor $\|G\|$ defined as follows: $1\geq\|G\|=\frac{u(x_{{k}},t_{{n+1}})}{u(x_{{k}},t_{{n}})}$ The idea behind this is to determine “whether or not the calculation can be rendered useless by unfavourable error propagation” (from The Numerical Treatment of Differential Equations.) In other methods, such as perturbation methods, an error is introduced into the scheme and its propagation is explicitly analysed. The von Neumann analysis does the same thing but in a more compact form. The heart of the von Neumann method is to substitute a Fourier series expression into the difference scheme. Thus, for our difference scheme $u(x_{{k}},t_{{n+1}})=u(x_{{k}},t_{{n}})-1/2\, R\left(u(x_{{k+1}},t_{{n}})-u(x_{{k-1}},t_{{n}})\right)+1/2\,{R}^{2}\left(u(x_{{k+1}},t_{{n}})-2\, u(x_{{k}},t_{{n}})+u(x_{{k-1}},t_{{n}})\right)$ we substitute $u(x_{{k}},t_{{n+1}})={e^{p_{{m}}\left(t+\Delta_{{t}}\right)+\sqrt{-1}k_{{m}}x}}\\u(x_{{k}},t_{{n}})={e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}\\u(x_{{k+1}},t_{{n}})={e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x+\Delta_{{x}}\right)}}\\u(x_{{k-1}},t_{{n}})= {e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x-\Delta_{{x}}\right)}}$ to yield ${e^{p_{{m}}\left(t+\Delta_{{t}}\right)+\sqrt{-1}k_{{m}}x}}={e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}\\-1/2\, R\left({e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x+\Delta_{{x}}\right)}}-{e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x-\Delta_{{x}}\right)}}\right)\\+1/2\,{R}^{2}\left({e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x+\Delta_{{x}}\right)}}-2\,{e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}+{e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x-\Delta_{{x}}\right)}}\right)$ As an aside, When most people think of “Fourier series” they think of a real series of sines, cosines and coefficients. This was certainly in evidence in the presentation of the method in The Numerical Treatment of Differential Equations. However, it has been the author’s experience that the best way to treat these is to do so in a “real-complex continuum,” i.e., to express these exponentially and to convert them to circular (or in some cases hyperbolic) functions as the complex analysis would admit. An example of that is here. Solving for the amplification factor defined above, $\|G\|={\frac{{e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}-1/2\, R\left({e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x+\Delta_{{x}}\right)}}-{e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x-\Delta_{{x}}\right)}}\right)}{{e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}}}\\+{\frac{1/2\,{R}^{2}\left({e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x+\Delta_{{x}}\right)}}-2\,{e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}+{e^{p_{{m}}t+\sqrt{-1}k_{{m}}\left(x-\Delta_{{x}}\right)}}\right)}{{e^{p_{{m}}t+\sqrt{-1}k_{{m}}x}}}}$ Simplifying, $\|G\|=1-1/2\, R{e^{\sqrt{-1}k_{{m}}\Delta_{{x}}}}+1/2\, R{e^{-\sqrt{-1}k_{{m}}\Delta_{{x}}}}+1/2\,{R}^{2}{e^{\sqrt{-1}k_{{m}}\Delta_{{x}}}}-{R}^{2}+1/2\,{R}^{2}{e^{-\sqrt{-1}k_{{m}}\Delta_{{x}}}}$ or $\|G\|=1+{R}^{2}\cos(k_{{m}}\Delta_{{x}})-{R}^{2}-\sqrt{-1}R\sin(k_{{m}}\Delta_{{x}})$ and then $1\geq G=\sqrt{\left(1+{R}^{2}\cos(k_{{m}}\Delta_{{x}})-{R}^{2}\right)^{2}+{R}^{2}\left(\sin(k_{{m}}\Delta_{{x}})\right)^{2}}$ Solving for $R$ at the points of equality yields three results: $R=-1,0,1$. Since negative values for $R$ have no physical meaning, we conclude that $0\leq R\leq1$ for this method to be stable. Thus we can say that the method is conditionally unstable. ### Convergence The Lax Equivalence Theorem posits that, if the problem is properly posed and the finite difference scheme used is consistent and stable, the necessary and consistent conditions for convergence have been met (see Numerical Methods for Engineers and Scientists, Second Edition.) We have shown that, with the assumptions stated above, the scheme is consistent with the original differential equation, with or without the provision of twice differentiability. The method is thus convergent within the conditions stated above for stability; outside of those conditions the method is neither stable nor convergent.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 56, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9658638834953308, "perplexity": 228.9743793592161}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662543797.61/warc/CC-MAIN-20220522032543-20220522062543-00354.warc.gz"}
https://socratic.org/questions/a-nitrogen-gas-occupies-a-volume-of-500-ml-at-a-pressure-of-0-971-atm-what-volum#113715	Physics Topics # A nitrogen gas occupies a volume of 500 ml at a pressure of 0.971 atm. What volume will the gas occupy at a pressure of 1.50 atm, assuming the temperature remains constant? Dec 7, 2014 The answer is $324 m L$. This is a simple application of Boyle's law ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$, which states that a gas' pressure and volume are proportional to eachother. It can be derived from the combined gas law, $P V = n R T$, by keeping $T$ constant. So, we have ${V}_{2} = {P}_{1} / {P}_{2} \cdot {V}_{1} = \frac{0.971}{1.50} \cdot 500 m L = 324 m L$ -> pressure increases, volume decreases and vice versa. ##### Impact of this question 21403 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8828670382499695, "perplexity": 1293.2734305870433}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499744.74/warc/CC-MAIN-20230129144110-20230129174110-00394.warc.gz"}
https://www.physicsforums.com/threads/pressure-vessel-and-resulting-flow-through-a-pipe.239952/	# Pressure vessel and resulting flow through a pipe • Start date • #1 354 0 Hi everybody, I've been going around in circles with this problem and not sure if I'm approaching it correctly. I have a vessel filled with a fluid and connected to a pipe (circular cross section) with a tap on the end. The pressure on the vessel is not atmospheric, it is about 1 bar absolute (adjustable). The pressure on the pipe is atmospheric and the tap opens to atmospheric. I need a flow of about 2l/s from the fully open tap. How do I go about finding the exact pressure required on the vessel in order to get this flow rate? I was thinking of bernoulli's, but that is only good for inviscid, laminar flow. I think that my flow will have changing viscosities with temperature changes and possibly be in the turbulent region. Am I right in assuming, that if I apply a pressure of 1 bar absolute (so the pressure on the outside of the vessel is 1 bar greater than the pressure in the vessel) to the vessel, that the pressure drop experienced from the vessel through the pipe, to atmospheric, will be 1 bar? Say for example the pressure in the vessel was 10 bar absolute and I applied a pressure of 11 bar absolute to the outside of the vessel. The pressure difference over the vessel wall would be 1 bar, right? then if I attach a pipe to that vessel and the pipe is open to atmospheric, then the pressure drop to atmosphere would be 1 bar, right? Man, for some reason I can't get this through my head. I'm sure the pressure drop through the pipe to atmospheric would actually be 10 bar. any help to ease my fundamental ignorance would be much appreciated. One step at a time... Thanks. • #2 FredGarvin 5,066 9 First things first: Bernoulli does not stipulate laminar vs. turbulent flow. That is not one of the restrictions of its derivation. The three main assumptions of the Bernoulli equation are steady state, incompressible, inviscid (no friction) flow along a streamline. I can think of many problems in which the turbulent regime has to be considered. For instance, have you never done a pipe friction factor calculation? If Bernoulli were limited to the laminar regime only, we could always use $$f=\frac{Re}{64}$$ and go about our business. We would never need a Moody diagram. If your fluid is a liquid, then at lower pressures, the incompressible assumption is quite valid. The frictionless assumption can be acceptable as well, depending on the layout of your system. If you're not going through a lot of valves, orifices and long line lengths, the frictionless assumption may not be too bad also. The steady state assumption is sometimes a tough one to validate because you will, most likely, have an ever changing system. However, it can be a very good starting point to calculate this scenario under that assumption. redargon said: I think that my flow will have changing viscosities with temperature changes That is an issue if you have changing temperatures and viscosities. If that is the case then I would first break the system up into multiple small segments and solve for the end conditions at a segment and then fold those into the input for the next segment in line. It's analogous to calculating the area under a curve by calculating the areas of a bunch of rectangles. redargon said: Am I right in assuming, that if I apply a pressure of 1 bar absolute (so the pressure on the outside of the vessel is 1 bar greater than the pressure in the vessel) to the vessel, that the pressure drop experienced from the vessel through the pipe, to atmospheric, will be 1 bar? Close. If you apply a pressure of 1 bar GAUGE to the vessel it will be 1 bar above atmospheric.If you apply 1 bar absolute to the tank, you are actually a bit lower that 1 standard atmosphere in pressure. A vessel pressure of 1 bar gauge would indeed result in an overall delta P of 1 bar. Last edited: • #3 russ_watters Mentor 20,276 6,858 You didn't say how big the pipe is. 1 L/s would be a lot of air for a small pipe and though you can use Bernoulli's as a good approximation, you may get a velocity big enough to choke the flow. So first calculate the velocity you need, based on the pipe size. From that we can decide what assumptions are valid (ie, things like temperature drop due to pressure drop). • #4 stewartcs 2,177 3 Hi everybody, I have a vessel filled with a fluid and connected to a pipe (circular cross section) with a tap on the end. The pressure on the vessel is not atmospheric, it is about 1 bar absolute (adjustable). The pressure on the pipe is atmospheric and the tap opens to atmospheric. I need a flow of about 2l/s from the fully open tap. How do I go about finding the exact pressure required on the vessel in order to get this flow rate? What is the vessel made of (i.e. is it rigid)? Is the vessel sealed (other than the pipe)? Is the fluid liquid or gas? Is fluid entering the system or is it a fixed amount? Do you have a schematic for clarity? CS • #5 354 0 First off, thanks Fred, I was going insane trying to get guage and absolute right in my head, I haven't done this stuff since varsity, so I'm a little rusty. I think I had been staring at the problem so long that I just wasn't understanding it any more. This morning I'm feeling a little fresher and ready to keep on tackling it. • #6 354 0 You didn't say how big the pipe is. 1 L/s would be a lot of air for a small pipe and though you can use Bernoulli's as a good approximation, you may get a velocity big enough to choke the flow. So first calculate the velocity you need, based on the pipe size. From that we can decide what assumptions are valid (ie, things like temperature drop due to pressure drop). Thanks for your input Russ, the fluid is actually a liquid and I have a feeling the pipe inner diameter will be in the range of 2mm to 5mm. I did some velocity calcs yesterday and looking to try a fresh approach today after clarity of a few fundamentals from Fred (above) • #7 354 0 What is the vessel made of (i.e. is it rigid)? Is the vessel sealed (other than the pipe)? Is the fluid liquid or gas? Is fluid entering the system or is it a fixed amount? Do you have a schematic for clarity? CS Stewart, most of the stuff is confidential information as it pertains to a competitive design, that's why I have to be a little vague. Also, not everything has been specified because it is still in a concept phase. I can't attach a schematic (as an engineer I am a believer of free information and improvement of systems/designs by any means necessary for the benefit of all, but my company sees the world in a different light, so I will have to conform on this one), but I can try to offer some clarity. I'm not asking for a complete solution, just checking my fundamentals to insure I don't go down the wrong path for a week and waste everybody's time and money (oh, and look like a buffoon along the way). I think I can get enough information with general questions without pissing people on the forum off (I personally loathe problems with vagueness) and without breaking any contractual requirements. Like I said, I don't need a total solution from the forum (the solution part is what I get paid to do ) just a few pointers to approve my throries. The vessel is sealed except for the pipe (which has a tap/valve at the end). The vessel is not rigid and is expected to reduce it's volume with the fluid inside. The fluid is a liquid. The fulid is a fixed amount (obviously decreasing in volume with the vessel as the valve/tap at the end of the pipe is opened) I wanted to keep the flow laminar to keep things simple (as an aero engineer, I know turbulence is complicated and never behaves nicely ) but management decided that turbulence (no, they have never seen a moody diagram or the implicit colebrook equation and they think D'Arcy is that chick that played guitar for the smashing pumpkins) would be a great way to slow the flow down. So a thin, rough pipe is what I get to work with and I'm expecting higher than laminar Re numbers (probably Re>8000). An aero has to do what everyone expects an aero can do. Thanks for all the help so far, I found this forum the other day and totally dig it ! My family and friends are going to see a lot less of me as i explore all the interesting problems and solutions. • #8 stewartcs 2,177 3 Stewart, most of the stuff is confidential information as it pertains to a competitive design, that's why I have to be a little vague. Also, not everything has been specified because it is still in a concept phase. I can't attach a schematic (as an engineer I am a believer of free information and improvement of systems/designs by any means necessary for the benefit of all, but my company sees the world in a different light, so I will have to conform on this one), but I can try to offer some clarity. I'm not asking for a complete solution, just checking my fundamentals to insure I don't go down the wrong path for a week and waste everybody's time and money (oh, and look like a buffoon along the way). I think I can get enough information with general questions without pissing people on the forum off (I personally loathe problems with vagueness) and without breaking any contractual requirements. Like I said, I don't need a total solution from the forum (the solution part is what I get paid to do ) just a few pointers to approve my throries. The vessel is sealed except for the pipe (which has a tap/valve at the end). The vessel is not rigid and is expected to reduce it's volume with the fluid inside. The fluid is a liquid. The fulid is a fixed amount (obviously decreasing in volume with the vessel as the valve/tap at the end of the pipe is opened) I wanted to keep the flow laminar to keep things simple (as an aero engineer, I know turbulence is complicated and never behaves nicely ) but management decided that turbulence (no, they have never seen a moody diagram or the implicit colebrook equation and they think D'Arcy is that chick that played guitar for the smashing pumpkins) would be a great way to slow the flow down. So a thin, rough pipe is what I get to work with and I'm expecting higher than laminar Re numbers (probably Re>8000). An aero has to do what everyone expects an aero can do. Thanks for all the help so far, I found this forum the other day and totally dig it ! My family and friends are going to see a lot less of me as i explore all the interesting problems and solutions. That sounds basically like a bladder type accumulator except that the fluid and gas are swapped (i.e. the gas is not inside the bladder, the fluid is). Is that correct? CS • #9 354 0 That sounds basically like a bladder type accumulator except that the fluid and gas are swapped (i.e. the gas is not inside the bladder, the fluid is). Is that correct? CS Yip, that's it. We apply a pressure to the bladder/vessel. This causes the fluid in the vessel to flow through the connected pipe. Then we model this flow in order to calculate what sort of pressure we need to obtain a certain flowrate. How would you go about modelling this? I am planning to use D'Arcy-Weisbach in the turbulent region (so using a friction factor calculated using the colebrook equation) to calculate the pressure drop over the pipe. Correlate this pressure drop to the flowrate. Could I use Hagen Poiseuille or are there restrictions? • #10 stewartcs 2,177 3 Yip, that's it. We apply a pressure to the bladder/vessel. This causes the fluid in the vessel to flow through the connected pipe. Then we model this flow in order to calculate what sort of pressure we need to obtain a certain flowrate. How would you go about modelling this? I am planning to use D'Arcy-Weisbach in the turbulent region (so using a friction factor calculated using the colebrook equation) to calculate the pressure drop over the pipe. Correlate this pressure drop to the flowrate. Could I use Hagen Poiseuille or are there restrictions? I'd model it like an accumulator, since that is what you have (just inverted which doesn't make any difference), up to the outlet in order to get the flow rate at that point. Then I'd use Bernoulli with Darcy (and the Swamee-Jain equation for the friction factor) from that point on. Caveat: For a rapid discharge make sure to use real gas equations of state (or NIST data) for gas properties. API Specification 16D has the equations for all of this if you need them. CS • #11 354 0 the next step Ok, so did some work on this problem and modelled it (basically, to get the fundamentals correct) according to what is in the attached pdf file. I'm not sure if this is correct or not, it just doesn't look right and I can't figure out why. Any help or ideas are much appreciated. Thanks. #### Attachments • 31.9 KB Views: 530 • #12 354 0 nobody have any ideas? after thinking a little more about it, the pressure that the inner chamber "sees" is it's own internal pressure plus the pressure applied to it by the chamber around it, right? So if I had 4 bar in the outer chamber and 2 bar in the inner chamber and atmosphere was 1 bar, then when I opened the valve the pressure would drop from 6 bar to 1 bar atmospheric. right? I really feel like i'm not getting something here. • #13 stewartcs 2,177 3 Ok, so did some work on this problem and modelled it (basically, to get the fundamentals correct) according to what is in the attached pdf file. I'm not sure if this is correct or not, it just doesn't look right and I can't figure out why. Any help or ideas are much appreciated. Thanks. Just took a quick look at your calcs and didn't check the math but.... Based on what you have drawn, you seem to be on the right track with a few exceptions. In your drawing if P1 is the gas pressure then (until the valve is opened) P2 (as you have shown it) will equal P1 since it is in equilibrium. So you don't need to have P2 represented there. Represent P2 at the outlet of the accumulator instead. Since you've stated that the outlet is atmospheric then P2 = Patm. Your equation therefore accounts for it already. Typically accumulators do not have the gas on the bottom and the fluid on top. Is there a particular reason for that? I would make gravity work on my side personally. Also, the calculation you have (once corrected) will give you the initial velocity at the exit unless the charge pressure (P1) is constant. If it is constant you'll have a constant flow rate at the outlet. If the charge pressure is not constant, but rather "precharged" to a certain value, then you'll have to account for the polytropic expansion of the gas as the fluid exits. Also, I wouldn't necessarily exclude v1. Just relate it in terms of areas and v2 and then substitute it into your equation. Finally, I would break the problem down into two parts. Model the flow rate out of the accumulator as discussed above (just lose the Darcy term and then include a discharge coefficient to correct the outlet flow rate). Then you can find the pressure drop in the pipe using Darcy and the normal flow equations. Hope that helps. CS • #14 354 0 That's great and it helps, thanks CS, I'm glad I'm on the right track. So you say P2 will equal P1 if it is in equilibrium before the valve is opened. What if the liquid in the inner vessel is stored with an internal pressure, like if it was soda water or any pressurised liquid? I agree that gravity would be a big help if the whole system was upside down. I suppose one could gain the same benefits of gravity by lowering the pipe exit below the liquid level or lower. Not including v1 would make things slightly easier, but like you say it is just a ratio of the areas of v2, so easy to apply later if it is needed, or even right at the start. I'm going to try the two part approach, will try to find a suitable discharge coefficient. Seeing that dimensions haven't been specified yet (still in the concept phase) it's difficult to get coefficients that apply, but I'll just put a Cd variable in there for now. • #15 stewartcs 2,177 3 That's great and it helps, thanks CS, I'm glad I'm on the right track. So you say P2 will equal P1 if it is in equilibrium before the valve is opened. What if the liquid in the inner vessel is stored with an internal pressure, like if it was soda water or any pressurised liquid? Referring to the drawing you provided, the vessel is sealed and rigid with a moveable partition (piston or whatever) separating the gas at pressure P1 from the liquid at pressure P2 with the valve at the outlet of the liquid section closed. If that is a true representation of your design, then the pressures P1 and P2 must be in equilibrium since nothing is moving (the valve is closed initially). Just like in a can of soda, until you open the top, the carbonated gas and liquid pressures are in equilibrium. Hope that helps. CS • #16 354 0 Referring to the drawing you provided, the vessel is sealed and rigid with a moveable partition (piston or whatever) separating the gas at pressure P1 from the liquid at pressure P2 with the valve at the outlet of the liquid section closed. If that is a true representation of your design, then the pressures P1 and P2 must be in equilibrium since nothing is moving (the valve is closed initially). Just like in a can of soda, until you open the top, the carbonated gas and liquid pressures are in equilibrium. Hope that helps. CS yeah, that makes sense. • Last Post Replies 8 Views 587 • Last Post Replies 3 Views 5K • Last Post Replies 2 Views 3K • Last Post Replies 4 Views 1K • Last Post Replies 1 Views 4K • Last Post Replies 1 Views 575 • Last Post Replies 1 Views 5K • Last Post Replies 1 Views 1K • Last Post Replies 8 Views 4K • Last Post Replies 4 Views 2K	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6324701309204102, "perplexity": 724.9729567322853}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369553.75/warc/CC-MAIN-20210304235759-20210305025759-00359.warc.gz"}
https://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C1/Appendix_A:_Formulae	# A-level Mathematics/OCR/C1/Appendix A: Formulae < A-level Mathematics‎ \| OCR‎ \| C1 By the end of this module you will be expected to have learned the following formulae: ## The Laws of Indices 1. $x^ax^b = x^{a+b}\,$ 2. $\frac{x^a}{x^b} = x^{a-b}$ 3. $x^{-n}=\frac{1}{x^n}$ 4. $\left(x^a\right)^b = x^{ab}$ 5. $\left(xy \right)^n = x^n y^n$ 6. $\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$ 7. $x^\frac{a}{b} = \sqrt[b]{x^a}$ 8. $x^0 = 1\,$ 9. $x^1 = x\,$ ## The Laws of Surds 1. $\sqrt{xy} = \sqrt{x} \times \sqrt{y}$ 2. $\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}$ 3. $\frac{a}{b+\sqrt{c}} = \frac{a}{b+\sqrt{c}} \times \frac{b-\sqrt{c}}{b-\sqrt{c}} = \frac{a(b-\sqrt{c})}{b^2-c}$ ## Polynomials ### Parabolas If f(x) is in the form $a(x + b)^2 + c$ 1. -b is the axis of symmetry 2. c is the maximum or minimum y value Axis of Symmetry = $\frac{-b}{2a}$ ### Completing the Square $ax^2+bx+c=0\,$ becomes $a\left(x + \frac{b}{2a}\right)^2 -\frac{b^2}{4a} + c$ • The solutions of the quadratic $ax^2+bx+c=0$ are: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ • The discriminant of the quadratic $ax^2+bx+c=0$ is $b^2 - 4ac$ ## Errors 1. $Absolute\ error = value\ obtained - true\ value$ 2. $Relative\ error = \frac{absolute\ error}{true\ value}$ 3. $Percentage\ error = relative\ error \times 100$ ## Coordinate Geometry $m=\frac {y_2-y_1}{x_2-x_1}$ The equation of a line passing through the point $\left (x_1 , y_1 \right )$ and having a slope m is $y - y_1 = m \left ( x - x_1 \right)$. ### Perpendicular lines Lines are perpendicular if $m_1 \times m_2=-1$ ### Distance between two points $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ ### Mid-point of a line $\left(\frac {{x_1} + {x_2}}{2} ; \frac {{y_1} + {y_2}}{2}\right)$ ### General Circle Formulae $Area = \pi r^2\,$ $Circumference = 2 \pi r\,$ ### Equation of a Circle $\left (x - h \right )^2 + \left (y - k \right )^2 = r^2$, where (h,k) is the center and r is the radius. ## Differentiation ### Differentiation Rules 1. Derivative of a constant function: $\frac{dy}{dx} \left (c \right) = 0$ 2. The Power Rule: $\frac{dy}{dx} \left (x^n \right) = nx^{n - 1}$ 3. The Constant Multiple Rule: $\frac{dy}{dx} c f \left ( x \right ) = c \frac{dy}{dx} f \left ( x \right )$ 4. The Sum Rule: $\frac{dy}{dx} \begin{bmatrix} f \left ( x \right ) + g \left ( x \right ) \end{bmatrix} = \frac{dy}{dx} f \left ( x \right ) + \frac{dy}{dx} g \left ( x \right )$ 5. The Difference Rule: $\frac{dy}{dx} \begin{bmatrix} f \left ( x \right ) - g \left ( x \right ) \end{bmatrix} = \frac{dy}{dx} f \left ( x \right ) - \frac{dy}{dx} g \left ( x \right )$ ### Rules of Stationary Points • If $f' \left ( c \right ) = 0$ and $f'' \left ( c \right ) <0$, then c is a local maximum point of f(x). The graph of f(x) will be concave down on the interval. • If $f' \left ( c \right ) = 0$ and $f'' \left ( c \right ) >0$, then c is a local minimum point of f(x). The graph of f(x) will be concave up on the interval. • If $f' \left ( c \right ) = 0$ and $f'' \left ( c \right ) = 0$ and $f''' \left ( c \right ) \ne 0$, then c is a local inflection point of f(x). This is part of the C1 (Core Mathematics 1) module of the A-level Mathematics text.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 44, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9362976551055908, "perplexity": 1480.611662947972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430453921765.84/warc/CC-MAIN-20150501041841-00076-ip-10-235-10-82.ec2.internal.warc.gz"}
http://tex.stackexchange.com/questions/74308/isolated-coloring-of-math-symbols-and-boxes-in-equations	# Isolated coloring of math symbols and boxes in equations I know that by using a package like xcolor I can use $\color{<color>} <math symbols>$ to typeset math symbols in my preferred color. But how can I isolate the color to specific symbols only? Say for instance the illustrations of commented equations in Howard Anton's Calculus book have colors for underbraces and the bounding text boxes but have none for the included text. Consider the following MWE \documentclass[]{article} \usepackage{amsmath} \usepackage{xcolor} \begin{document} $$\dfrac{d}{dx}[\sin(3x^2+2)]=\underbrace{\cos(3x^2+2)}_{\text{ \fbox{\parbox[b][]{2cm}{ Derivative of the outise evaluated at the inside} }}} \cdot \underbrace{6x}_{\text{ \color{blue}{\fbox{\parbox[b][]{1.25cm}{ Derivative of the inside} }}}}$$ \end{document} which outputs How can I isolate the coloring to the underbraces and the bounding box to blue without affecting the other symbols/text? - \documentclass{article} \usepackage{amsmath} \usepackage{xcolor} \makeatletter \renewcommand\underbrace[2][olive]{% \mathop{\vtop{\m@th\ialign{##\crcr $\hfil\displaystyle{#2}\hfil$\crcr \noalign{\kern3\p@\nointerlineskip}% \textcolor{#1}{\upbracefill}\crcr\noalign{\kern3\p@}}}}\limits} \makeatother \newcommand\ColorBox[3][olive]{\text{\fcolorbox{#1}{white}{\parbox[b][]{#2}{\raggedright#3}}}} \begin{document} $$\frac{d}{dx}[\sin(3x^2+2)]=\underbrace{\cos(3x^2+2)}_{\ColorBox{2cm}{Derivative of the outise evaluated at the inside}} \cdot \underbrace[red!60!black]{6x}_{\ColorBox[red!60!black]{1.25cm}{Derivative of the inside}}$$ \end{document} The syntax: \underbrace[<color>]{<text>} \ColorBox[<color>]{<width>}{<text>} The default color: olive. - That was fast. Where can I find the definition for \underbraces and other such commands? – hpesoj626 Sep 27 '12 at 8:27 @hpesoj626 For LaTeX kernel commands, such as \underbrace, you can open a terminal a run texdox source2e or in CTAN: source2e. – Gonzalo Medina Sep 27 '12 at 12:57 Here are some minor alternatives to Gonzalo's answer, provided by the abraces package. More specifically, it allows for inserting arbitrary code within the brace construction using @{<stuff>}: \documentclass{article} $$\dfrac{\mathrm{d}}{\mathrm{d}x}\big[\sin(3x^2+2)\big]= \underbrace[@{\color{olive}}l1D1r]{\cos(3x^2+2)}_{\color{olive} \text{\fbox{\parbox[b]{2cm}{\raggedright% \color{black}Derivative of the outside evaluated at the inside} }}} \cdot \underbrace[@{\color{red!60!black}}l1D1r]{\vphantom{()}6x}_{\color{red!60!black} \text{\fbox{\parbox[b]{1.25cm}{\raggedright% \color{black}Derivative of the inside} }}}$$ • Using \mathrm{d} for d/dx; • Enlarging the brackets around the LHS using \big[ and \big]; and • Inserting \vphantom to lower the \underbrace for both components of the chain rule to the same depth.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 3, "x-ck12": 0, "texerror": 0, "math_score": 0.8235992193222046, "perplexity": 3012.0904234140053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464053209501.44/warc/CC-MAIN-20160524012649-00041-ip-10-185-217-139.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/24685/question-on-impulse-momentum-theory	# Question on Impulse-Momentum theory A 5kg stone kicked by a student undergoes a velocity change from 6m/s to 10m/s in 4 seconds; ---- What is the momentum change of the stone within the time interval? ---- What impulse was impacted on the body during this time interval? For the first question : $$p_2-p_1= M V_1 - MV_2 = M(V_1-V_2)= 5\textrm{ kg}(10-6)\textrm{m s}^{-1} = 20 \textrm{ kg m s}^{-1}$$ Is that correct for the first question? As for the second : I'm stuck. Help. $$\textrm{impulse}=I = F\cdot t$$ $$F = (mv-mu)/t$$ $$F = m(v-u)/t$$ $$F\cdot t = m(v-u)$$ $$\Rightarrow I = 5\textrm{ kg}(10-6)\textrm{ m s}^{-1} = 20 \textrm{ kg m s}^{-1}$$ is that correct? Because there has been no need to use time (4 seconds)...... or : $$F = ma = 5 \textrm{ kg} \frac{(10-6)\textrm{ m s}^{-1}}{4\textrm{s}}= 5\textrm{ N}$$ $$\textrm{impulse}= I = F\cdot T= 5\textrm{ N}\cdot 4 \textrm{ s} = 20\textrm{ N s},$$ still the same 20. Thanks - Yes, your thinking is correct. The impulse imparted is equal to both the applied force times the time and to the change in momentum, $$I=F\Delta t=\Delta p.$$ (This is exactly Newton's second law.) The time taken by the kick is superfluous in your question.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7532821297645569, "perplexity": 775.6475461652884}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207932737.93/warc/CC-MAIN-20150521113212-00112-ip-10-180-206-219.ec2.internal.warc.gz"}
https://www.arxiv-vanity.com/papers/2003.14228/	# Mobility Changes in Response to COVID-19 Michael S. Warren, Samuel W. Skillman v1.0-4-ga6898c6 Descartes Labs Santa Fe, NM 87501, USA ###### Abstract In response to the COVID-19 pandemic, both voluntary changes in behavior and administrative restrictions on human interactions have occurred. These actions are intended to reduce the transmission rate of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). We use anonymized and/or de-identified mobile device locations to measure mobility, a statistic representing the distance a typical member of a given population moves in a day. Results indicate that a large reduction in mobility has taken place, both in the United States and globally. In the US, large mobility reductions have been detected associated with the onset of the COVID-19 threat and specific government directives. Mobility data at the US admin1 (state) and admin2 (county) level have been made freely available under a Creative Commons Attribution (CC BY 4.0) license via the GitHub repository github.com/descarteslabs/DL-COVID-19. ## I Introduction As of March 28, 2020, the coronavirus pandemic COVID-19 is affecting 200 countries and over 600,000 individuals [1, 2]. Efforts to prevent spread of the virus include travel and work restrictions, quarantines, curfews, cancellations and postponements of events, and facility closures. These policies aim to reduce the probability of contact between infected and non-infected persons to minimize disease transmission [3]. We hypothesize that the effect of these interventions are measurable in the aggregate geospatial statistics of people’s daily movement. Measuring changes in mobility is a critical input for forecasting disease spread and assessing the effectiveness of containment strategies [4]. Geolocation reports from smartphones and other mobile devices offer a mechanism to sample the movement of individuals. There are significant privacy concerns related to the availability of such data [5]. Standard practice is to make such traces anonymous, where the true identities of nodes are replaced by random identifiers. However, the privacy concern remains. Nodes are open to observations in public spaces, and they may voluntarily or inadvertently disclose partial knowledge of their whereabouts [6]. Some studies have shown that sharing anonymized location data can lead to privacy risks and that, at a minimum, the data needs to be coarse in either the time domain or the space domain [7]. We do not and will not use mobile device location data to identify individuals. All analysis we perform is statistically aggregated, removing the ability to characterize the behavior of any single device. ## Ii Method Cloud computing with associated high-bandwidth storage capacity, combined with recent advances in machine learning, is enabling understanding of the world at a scale and level of granularity never before possible [8]. Mobile devices exemplified by the smartphone are an obvious result of this technological advance. In this work, we analyze a commercially available mobile device location dataset using cloud computing resources. We heavily leverage our festivus virtual file system layer [9] for this analysis, reading over 50 TB of input data and utilizing about 50,000 CPU hours of computation. Raw location data from commercial data providers is generally provided in a compressed, comma-delimited text format, with one position report per line. Reports contain, at a minimum, an anonymized node id, epoch time (seconds elapsed since 00:00:00 UTC on January 1, 1970), latitude, longitude and an estimate of position accuracy. Data is obtained in multiple files to facilitate parallel processing, and a typical volume of compressed data is 100 GB per day. Data is delivered once per day. Our analysis algorithm is implemented with the Python programming language [10, 11] in a parallel task-based execution environment. The first step in analysis is to eliminate reports with estimated position accuracy that exceeds some threshold. We use a threshold of 50 meters. Median reported accuracy across all position reports is in the range of 15-20 meters. In order to make daily statistics more interpretable, the reported timestamp is converted to local time. If a time conversion is not performed, then the statistics in each area would be analyzed in UTC, and would not correspond to a “day” in the local timezone. For instance, a day in UTC from 00:00 to 23:59 would correctly correspond to a local day (midnight to midnight) in the UK, but would be noon to noon in New Zealand. This would lead to analysis artifacts (e.g. a day that combines Sunday afternoon with Monday morning in New Zealand cannot be consistently compared to midnight Sunday through midnight Monday in the UK). Our initial conversion to local time uses an approximate local solar time with a time zone offset of, tzhours=⌊longitude15⌉ when processing individual position reports, but later determines the precise local timezone once for each device. To facilitate the computation of statistics for each node, the reports for each node are collated. Device reports are typically not delivered in a form that can be easily processed per node, so we perform the equivalent of a parallel bucket sort [12]. Our previous work developing algorithms for computational cosmology demonstrated the utility of abstracting the most challenging aspect of a parallel algorithm into a sort [13]. We eliminate nodes that have fewer than 10 reports in a day. We also eliminate nodes that report over a short part of the day (less than 8 hours) to avoid biasing the mobility stastistic downward with transient reports. We calculate a number of statistics intended to capture the mobility of a population (Figure 1). The max-distance mobility is the maximum Haversine (great circle) distance (in units of ) from the initial location report of the day. Outliers (which can occur with bad position reports caused by poor GPS fixes or other errors) are trimmed by eliminating the top 10% of the distribution. The bounding box mobility is computed by determining the area of the bounding box of the reports , and then converting to an equivalent linear distance in , . The convex hull mobility is computed by determining the area of the convex hull of the reported positions, and then converting it to an equivalent linear distance in via . For a canonical position of each processed node (such as the first or last report of the day in local time, or a derived location such as the centroid of node locations) we reverse geocode the location to a country and administrative region. We use ISO 3166-1 alpha-2 codes for the country_code and GeoNames feature names and codes for subcategories. Admin1 is the first-order administrative division, being a primary administrative division of a country, such as a state in the United States. Admin2 is a second-order administrative division, such as a county or borough in the United States. Name is a populated place feature, representing a city, town, village, or other agglomeration of buildings where people live and work. For each area of interest found by the reverse geocoding procedure above, we compute a variety of statistics across the mobility measures . These statistics include the mean, median and quartiles. For the results reported here, we focus on the median of the max-distance mobility , which we designate . We further define a normalized mobility index, m50_index=100m50m50norm, where is a “normal” value of in a region, defined as the median in that region during a designated earlier time period. We use the median weekday value of between the dates of 2020-02-17 and 2020-03-07 as to investigate COVID-19 related changes in the US. Note that has dimensions of kilometers, while is dimensionless. is easily transformed to a percentage change from baseline behavior via pct change=m50_index−100. Output of our analysis is stored in two formats. The first is newline-delimited JavaScript Object Notation (NDJSON) (also known as JSON lines format) which is a convenient format for storing structured data that may be processed one record at a time [14]. It works well with unix-style text processing tools and shell pipelines, and can be read into a python dictionary data structure with a simple motif for line in file: Using a format such as the GeoJSON FeatureCollection object is problematic for very large datasets, because the file must be parsed as a whole, and records cannot be processed one-at-a-time in a streaming fashion. We also store the data in a comma-seperated values (CSV) format which may be more familiar to users of traditional geographic information systems or mapping tools. One significant caveat to the accuracy of the statistics we present here is related to systematic sampling errors. We assume that the sampling of devices is “fair” and represents the behavior of the population as a whole. Since data is available for only a small fraction of the total number of devices (a few percent at most), it is possible that those position reports that are selected for inclusion in the raw location data we use as input have a correlation with behavior that is not representative of the average. For instance, if the data vendor includes position reports from a transportation “app”, we expect those reports to show considerably more distance traveled than an app that would be used while at home. As long as the data from both sets of apps is consistently included, the systematic sampling error would be expected to be small. However, if the data vendor loses access to one type of app, that would skew the mobility statistics, and not represent a change in actual behavior. Similar types of error would be expected if there was a correlation between changes in mobility, and the probability of appearing in the location dataset (e.g. if people who travel long distances are more likely to disable location reporting). We mitigate the effects of these sampling errors to the extent possible by analysis of multiple datasets, and we seek to validate the statistics through independent observations. ## Iii Results On January 23, 2020 the city of Wuhan was closed by canceling planes and trains leaving the city, and suspending buses, subways and ferries within it. By this date at least 17 people had died and more than 570 others had been infected, including in Taiwan, Japan, Thailand, South Korea and the United States. Ideally, we could analyze mobility around the epicenter of the outbreak in China, but we do not have access to data from that country. A recent study from researchers in Beijing was able to access aggregated statistics provided by the two largest telecommunications operators in China [15]. Between January 24 and 27, there is a dramatic drop in mobility observed in Hong Kong and Singapore 2. On Friday, Jan. 24 in Singapore was 3.6 km. By Monday, Jan. 27 it had fallen more than 50% to 1.5 km. The change was even more pronounced in Hong Kong, dropping to 180 meters from 2.3 km. The weekend of January 25 also corresponded to the Chinese New Year holiday, so the change in mobility in that time period could have been independently influenced by the holiday. The behavior of the these graphs for some countries between January 29 and February 27 is subject to the systematic sampling error we described previously, which shows an anomalous drop in mobility during the month of February. Using an alternate input dataset, the behavior in Singapore and Malaysia is much more consistent over that time period 3. Other notable features from that graph are the weekly cycles, with Friday having the highest mobility, particularly in the US, a lower value on Jan. 20 (the Martin Luther King Jr. Day holiday in the US) and the dip on Feb. 25 in Indonesia, which corresponds to a day of heavy rain which flooded Jakarta, the capital. Figures 2-3 also show the significant response in the US beginning March 14, and corresponding drops in the rest of the world as a new wave of mobility restrictions were put into place. Note that we do not plot values on Saturday and Sunday for clarity, since mobility on Sunday is usually much lower than weekdays. In Figure 4 we show mobility in six selected US states beginning March 2. We detect that more rural states (with presumably longer travel distances) normally have a higher than more urban states, specifically values of 9-11 km for Texas vs 5 km for New York for the first week in March. Reductions in mobility are detected across all six states March 13-16, with New York falling from 5.2 km on Monday, March 2 to only 31 meters on Monday, March 23. This implies that half of the individuals in the entire state of New York spent most of their day within less than 100 feet of their initial position. To better understand the change from “normal” mobility and compare states with each other, Figure 5 plots the normalized , demonstating that Florida and Texas have dropped to about 30% of normal, and California, Illinois, New York and Washington to less than 20% of normal. We can also look at smaller geographic regions by plotting the change in mobility within counties. In Figure 6 we show the 10 most highly sampled counties in California. The inital reduction seen on Mar. 17 in Alameda, Contra Costa and Santa Clara counties can be attributed to the shelter-in-place order for the six Bay Area counties which took effect at 12:01am. The order expanded statewide the evening of Mar. 19. Counties in Illinois are illustrated in Figure 7. The spike in mobility on March 13 in Champaign County we believe is associated with a large number of students leaving the University of Illinois Urbana-Champaign after the on-campus classes were cancelled. A similar jump is seen in Figure 9 on March 13 in Monongalia County, associated with students leaving West Virginia University (enrollment of 30,000 students in a county with about 100,000 people). West Virgina was the last state in the US to report a coronovirus infection. ## Iv Conclusion We have detected dramatic changes in mobility due to COVID-19, both within the US and globally. Mobility data at the US admin1 (state) and admin2 (county) level have been made freely available under a Creative Commons Attribution (CC BY 4.0) license via the GitHub repository github.com/descarteslabs/DL-COVID-19. As the situation develops, combining information such as that we derive here with pandemic growth rates in various geographies will allow more accurate models of the interventions being made, and help save lives.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3119519054889679, "perplexity": 1379.062845561806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00400.warc.gz"}
http://mathhelpforum.com/algebra/125779-mathematical-induction-proof.html	# Math Help - mathematical induction proof 1. ## mathematical induction proof f(n) = 2, for n=0. f(n) = 2f(n-1)-n+1, for n>=1. prove f(n)=(2^n)+n+1 for n=0 -> f(n)=2. for n=k -> f(n)=(2^k)-k+1. for n=k+1 -> f(n)=(2^k+1)+k+2. Thats where i'm stuck. What am I supposed to do next? 2. Hi Your notation does not seem to be really appropriate I suggest $u_0=2$ $u_{n+1}=2 \:u_n - n$ You need to prove that $u_n = 2^n+n+1$ $2^0+0+1 = 2 = u_0$ therefore it is true for n=0 Suppose that it is true for n=k. This means that $u_k = 2^k+k+1$. You need to prove that $u_{k+1} = 2^{k+1}+k+2$ You know that $u_{k+1} = 2 \:u_k - k$ and that $u_k = 2^k+k+1$ Substitute $u_k = 2^k+k+1$ in the expression of $u_{k+1}$ to prove that $u_{k+1} = 2^{k+1}+k+2$ 3. Originally Posted by blank f(n) = 2, for n=0. f(n) = 2f(n-1)-n+1, for n>=1. prove f(n)=(2^n)+n+1 for n=0 -> f(n)=2. for n=k -> f(n)=(2^k)-k+1. for n=k+1 -> f(n)=(2^k+1)+k+2. Thats where i'm stuck. What am I supposed to do next? $f(0)=2$ $f(n)=2f(n-1)-n+1,\ for\ n\ge1$ If you write a few terms, it appears $f(n)=2^n+n+1$ Prove using induction that this is so. $f(n)=2^n+n+1$ If this is true, then the following will also be true... $f(n+1)=2^{n+1}+(n+1)+1=(2)2^n+(n+1)+1=2^n+2^n+(n+1 )+1$ $=[2^n+n+1]+2^n+1=f(n)+2^n+1$ Therefore, if we can prove that $f(n+1)$ really equals $f(n)+2^n+1$ then we only need to prove it works for the first term, since a mathematical chain reaction has been set up.. We attempt to prove it from f(n)=2f(n-1)-n+1. f(n+1)=2f(n)-(n+1)+1=2f(n)-n. The question is.... Is $2f(n)-n=f(n)+2^n+1$ ? Is $2f(n)-f(n)=2^n+n+1$ ? $f(n)=2^n+n+1$ true f(0)=1+0+1=2 f(1)=2+1+1=4=2(2)-1+1 true	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.934083104133606, "perplexity": 1249.0545011913835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119647884.33/warc/CC-MAIN-20141024030047-00110-ip-10-16-133-185.ec2.internal.warc.gz"}
https://mathtuition88.com/category/maths-tuition/page/7/	The scandal at the University of North Carolina at Chapel Hill is principally about academic dishonesty. But it highlights an institutional failure at almost all American colleges that dissuades students from pursuing the best career possible. Some academic departments systematically inflate students’ grades. And many of those departments give students the least rigorous preparation for the labor market. Part of college is learning what you’re good at. Students use freshman-year courses to gauge their interest and aptitude in different majors. A student who receives an A in writing and a B in calculus might conclude that she’s a better writer than mathematician. But what if she actually earned the average grade in both courses? Plenty of students who start in difficult fields such as math decide to scale back their ambitions. That’s fine if it’s a personal choice–but not if they’re doing so because they got deceptive messages from their graders. The latest research also suggests that there could be more subtle problems at work, like the proliferation of grade inflation in the humanities and social sciences, which provides another incentive for students to leave STEM majors. It is no surprise that grades are lower in math and science, where the answers are clear-cut and there are no bonus points for flair. Professors also say they are strict because science and engineering courses build on one another, and a student who fails to absorb the key lessons in one class will flounder in the next. After studying nearly a decade of transcripts at one college, Kevin Rask, then a professor at Wake Forest University, concluded last year that the grades in the introductory math and science classes were among the lowest on campus. The chemistry department gave the lowest grades over all, averaging 2.78 out of 4, followed by mathematics at 2.90. Education, language and English courses had the highest averages, ranging from 3.33 to 3.36. Ben Ost, a doctoral student at Cornell, found in a similar study that STEM students are both “pulled away” by high grades in their courses in other fields and “pushed out” by lower grades in their majors. How to join 9 Dots using 4 Lines? (Advanced Version) This is a humorous math comic based on the popular brainteaser: How do we join 9 dots using 4 lines? (Hint: Think out of the box. See the solution here: Answer) However, Spiked Math has added a new twist to the riddle. Enjoy the comic! Credit: http://spikedmath.com/ Math + Comics = Learning That’s Fun! Help students build essential math skills and meet math standards with 80 laugh-out-loud comic strips and companion mini-story problems. Each reproducible comic and problem set reinforces a key math skill: multiplication, division, fractions, decimals, measurement, geometry, and more. Great to use for small-group or independent class work and for homework! For use with Grades 3-6. The Math of Ebola Source: http://www.npr.org/blogs/goatsandsoda/2014/09/18/349341606/why-the-math-of-the-ebola-epidemic-is-so-scary In the past week, world leaders have started using a mathematical term when they talk about the Ebola epidemic in West Africa. “It’s spreading and growing exponentially,” President Obama said Tuesday. “This is a disease outbreak that is advancing in an exponential fashion,” said Dr. David Nabarro, who is heading the U.N.’s effort against Ebola. Students who have learnt how the exponential graph looks like will know that the exponential function grows extremely quickly. In fact, for large enough x, the exponential function $e^x$ will be larger than any polynomial function, say $x^{100}$. For example, when x=700, $e^{700}=1.01\times 10^{304}$, while $700^{100}=3.23 \times 10^{284}$. Fortunately, there is some good news: Before we all start panicking (which I have been working hard not to do, myself), the world did get some welcome news this week. On Tuesday, President Obama announced plans for the U.S. military to provide 1,700 hospital beds in West Africa. It will also help set up training facilities for health care workers. This introductory text offers a clear exposition of the algorithmic principles driving advances in bioinformatics. Accessible to students in both biology and computer science, it strikes a unique balance between rigorous mathematics and practical techniques, emphasizing the ideas underlying algorithms rather than offering a collection of apparently unrelated problems.The book introduces biological and algorithmic ideas together, linking issues in computer science to biology and thus capturing the interest of students in both subjects. It demonstrates that relatively few design techniques can be used to solve a large number of practical problems in biology, and presents this material intuitively.An Introduction to Bioinformatics Algorithms is one of the first books on bioinformatics that can be used by students at an undergraduate level. It includes a dual table of contents, organized by algorithmic idea and biological idea; discussions of biologically relevant problems, including a detailed problem formulation and one or more solutions for each; and brief biographical sketches of leading figures in the field. These interesting vignettes offer students a glimpse of the inspirations and motivations for real work in bioinformatics, making the concepts presented in the text more concrete and the techniques more approachable.PowerPoint presentations, practical bioinformatics problems, sample code, diagrams, demonstrations, and other materials can be found at the Author’s website. The Making of a Mile of Pi – Numberphile This guy (from the Youtube channel Numberphile) actually printed a million digits of Pi! Check out how long the piece of paper actually is! Longer Version (30 minutes): Featured book: Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing This book provides a fun, hands-on approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie’s opening weekend? How can you use mathematics to find your celebrity look-alike? What is Homer Simpson’s method for disproving Fermat’s Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or result–such as Google’s PageRank and the traveling salesman problem–and the applications grow more challenging as you progress through the chapters. But don’t worry, helpful solutions are provided each step of the way. Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Bird–and much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pace–a bit and a byte at a time. Topics coming out for A Maths Paper 2 Recently, the A Maths Paper 2 just finished (today), and the A Maths Paper 2 is hot on its heels, coming tomorrow! Usually, topics tested in Paper 1 will most likely not come out again in Paper 2, so students doing their last minute revision can use this fact to focus their revision. Topics that came out in Paper 1: 1. Binomial Theorem 2. Trigonometry (Addition Formula, find exact value) 3. Rate of change 4. Partial Fractions 5. Linear Law 6. Prove Trigonometry 7. Coordinate Geometry 8. Integrate & Differentiate Trigonometric Functions 9. Discriminant (b^2-4ac) 10. Stationary Points 11. Tangent/Normal Topics likely to come out in Paper 2: 1. Indices/Surds 2. Polynomials 3. Exponential / Logarithmic Equations 4. R-formula 5. Sketching of Trigonometric Graphs 6. Circles 7. Proofs in plane geometry 8. Integration as the reverse of differentiation 9. Area under curve 10. Kinematics All the best for those who are taking the A Maths Paper 2 exam tomorrow. 🙂 What is tested for A Maths (Additional Maths) Exam Just to share an A Maths question that is likely to come out for 2014 A Maths Exam. It is the brand new topic just added this year: Sum and difference of cubes. $\boxed{\alpha^3+\beta^3=(\alpha+\beta)(\alpha^2-\alpha\beta+\beta^2)}$ $\boxed{\alpha^3-\beta^3=(\alpha-\beta)(\alpha^2+\alpha\beta+\beta^2)}$ Attached below is a practice question on Alpha Cube+Beta Cube question that may be likely to come out this year! After all, if it is just added in the syllabus it is highly likely that they will test it. Alpha Beta Cube Question Good luck for the exam! Maths Tuition For Mathematics Tuition, contact Mr Wu at: Email: mathtuition88@gmail.com Highly Recommended Math Books for University Self Study Recently, a viewer of my website asked if I was able to suggest any undergraduate level university textbooks for self study that follows the university curriculum. Self-study is challenging but not impossible. Choosing a good and appropriate book of the right level is of crucial importance. For instance, for beginners to Calculus, I wouldn’t recommend Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) by Rudin. It is simply too difficult for beginners or even intermediate students. Any book by Bourbaki is also not suitable for beginners, for instance. Update: I recently found a book that is a better alternative to Rudin: Mathematical Analysis, Second Edition by Apostol! Many online sources have very positive reviews on Apostol’s Analysis book. I have read it and found it much more readable than Rudin. I would like to suggest the following books (mainly for Pure Mathematics). Ideally, the motivated student is able to self study and obtain the knowledge equivalent to a 4 Year course at a university. The recommendations are divided into Year 1, Year 2, Year 3 and Year 4. If you have any other recommendations, please feel free to comment below! Year 1 Introduction to Pure Math and Proofs: How to Prove It: A Structured Approach Calculus: Thomas’ Calculus (12th Edition) Linear Algebra: Linear Algebra and Its Applications, 4th Edition Multivariable Calculus: Thomas’ Calculus, Multivariable (13th Edition) Year 2 Linear Algebra II (Second Year Course): Linear Algebra, 4th Edition Analysis I: Introduction to Real Analysis Abstract Algebra I: A First Course in Abstract Algebra (3rd Edition) This book will be an introduction to Group Theory. Probability: Introduction to Probability, 2nd Edition Analysis II: Calculus, 4th edition (Note: Despite the title “Calculus”, this book is actually a rather rigorous book on Analysis, suitable as a second course textbook) Complex Analysis I: Complex Variables and Applications (Brown and Churchill) Year 3 ODE (Ordinary Differential Equations): Ordinary Differential Equations (Dover Books on Mathematics) Algebra II: Abstract Algebra, 3rd Edition Algebra II will usually be a course on Rings, Modules. (Note: You can use this book for learning Galois Theory too) Differential Geometry: Differential Geometry of Curves and Surfaces Year 4 Number Theory: An Introduction to the Theory of Numbers Galois Theory: Abstract Algebra, 3rd Edition (Note: Same textbook as for Algebra II) PDE (Partial Differential Equations): A First Course in Partial Differential Equations: with Complex Variables and Transform Methods (Dover Books on Mathematics) Functional Analysis: Introductory Functional Analysis with Applications Topology: Topology (2nd Edition) Measure and Integration: The Elements of Integration and Lebesgue Measure Congratulations for reaching the bottom of this long list! All the best for your studies in Mathematics. 🙂 Python Math Programming Recently, I am thinking of learning the Python language for Math programming. An advantage for using Python for Math Programming (e.g. testing out some hypothesis about numbers), is that the Python programming language theoretically has no largest integer value that it can handle. It can handle integers as large as your computer memory can handle. (Read more at: http://userpages.umbc.edu/~rcampbel/Computers/Python/numbthy.html) Other programming languages, for example Java, may have a maximum integer value beyond which the program starts to fail. Java integers can only have a maximum value of $2^{31}-1 \approx 2.15 \times 10^9$, which is pretty limited if you are doing programming with large numbers (for example over a trillion). For instance, the seventh Fermat number is already 18446744073709551617. I was using Java personally until recently I needed to program larger integers to test out some hypothesis. How to install Python (free): Hope this is a good introduction for anyone interested in programming! Featured book: Learning Python, 5th Edition Get a comprehensive, in-depth introduction to the core Python language with this hands-on book. Based on author Mark Lutz’s popular training course, this updated fifth edition will help you quickly write efficient, high-quality code with Python. It’s an ideal way to begin, whether you’re new to programming or a professional developer versed in other languages. Complete with quizzes, exercises, and helpful illustrations, this easy-to-follow, self-paced tutorial gets you started with both Python 2.7 and 3.3— the latest releases in the 3.X and 2.X lines—plus all other releases in common use today. You’ll also learn some advanced language features that recently have become more common in Python code. • Explore Python’s major built-in object types such as numbers, lists, and dictionaries • Create and process objects with Python statements, and learn Python’s general syntax model • Use functions to avoid code redundancy and package code for reuse • Organize statements, functions, and other tools into larger components with modules • Dive into classes: Python’s object-oriented programming tool for structuring code • Write large programs with Python’s exception-handling model and development tools • Learn advanced Python tools, including decorators, descriptors, metaclasses, and Unicode processing Pick’s Theorem Proof (Video) This is an excellent video I found on Youtube by Professor Wildberger on the proof of Pick’s Theorem. It is easy enough for a high school student to understand! Pick’s Theorem is a formula $A=I+\frac{B}{2}-1$ which gives the area of a simple polygon whose vertices lie on points with integer coordinates. Surprisingly, it is a relatively modern theorem, the result was first described by Georg Alexander Pick in 1899. Using Pick’s Formula, the area of the above polygon is $A=I+\frac{B}{2}-1=7+\frac{8}{2}-1=10$. We can also see that it is the sum of two triangles $A=\frac{1}{2}(4)(2)+\frac{1}{2}(4)(3)=10$. Amazing Formula! Source: http://en.wikipedia.org/wiki/Pick’s_theorem A recent visitor to my website bought this book. Highly interesting and suitable for parents of young children. Three to seven is a critical period where the brain develops, hence learning about how to teach math to preschoolers is of great significance for young parents. This book is a captivating account of a professional mathematician’s experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn first? How hard should they work? Should they even “work” at all? Should we push them, or just let them be? There are no correct answers to these questions, and the author deals with them in classic math-circle style: he doesn’t ask and then answer a question, but shows us a problem–be it mathematical or pedagogical–and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced. This book does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. Mathematicians, psychologists, educators, parents, and everybody interested in the intellectual development in young children will find this book to be an invaluable, inspiring resource. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). Educational Math Cartoons at whyu.org Are you looking for Educational Math Cartoon Videos? Recently I came upon this site http://www.whyu.org/, which is funded by the Goldman Charitable Foundation in partnership with the University of Central Florida. These videos are designed to be used as collateral material for mathematics courses on the K-12 and college levels, and to be a resource for informal independent study. Rather than focusing on procedural problem solving, the objective is to give insight into theconcepts on which the rules of mathematics are based. Once a student has gained a strong conceptual foundation, the material presented in math textbooks is much easier to digest and retain An example of their Math cartoon on Infinite Series: Hope you enjoy their videos! “Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You’ll never forget the Pythagorean theorem again!”—Scientific American Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations. Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you’d had. Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x. Check out this interesting Math Olympiad Integer Sequence Question! (September 2014 Math Problem of the Month) While the books in this series are primarily designed for AMC competitors, they contain the most essential and indispensable concepts used throughout middle and high school mathematics. Some featured topics include key concepts such as equations, polynomials, exponential and logarithmic functions in Algebra, various synthetic and analytic methods used in Geometry, and important facts in Number Theory. The topics are grouped in lessons focusing on fundamental concepts. Each lesson starts with a few solved examples followed by a problem set meant to illustrate the content presented. At the end, the solutions to the problems are discussed with many containing multiple methods of approach. I recommend these books to not only contest participants, but also to young, aspiring mathletes in middle school who wish to consolidate their mathematical knowledge. I have personally used a few of the books in this collection to prepare some of my students for the AMC contests or to form a foundation for others. By Dr. Titu Andreescu US IMO Team Leader (1995 – 2002) Director, MAA American Mathematics Competitions (1998 – 2003) Director, Mathematical Olympiad Summer Program (1995 – 2002) Coach of the US IMO Team (1993 – 2006) Member of the IMO Advisory Board (2002 – 2006) Chair of the USAMO Committee (1996 – 2004) I love this book! I love the style, the selection of topics and the choice of problems to illustrate the ideas discussed. The topics are typical contest problem topics: divisors, absolute value, radical expressions, Veita’s Theorem, squares, divisibility, lots of geometry, and some trigonometry. And the problems are delicious. Although the book is intended for high school students aiming to do well in national and state math contests like the American Mathematics Competitions, the problems are accessible to very strong middle school students. The book is well-suited for the teacher-coach interested in sets of problems on a given topic. Each section begins with several substantial solved examples followed by a varied list of problems ranging from easily accessible to very challenging. Solutions are provided for all the problems. In many cases, several solutions are provided. By Professor Harold Reiter Chair of MATHCOUNTS Question Writing Committee. Chair of SAT II Mathematics committee of the Educational Testing Service Chair of the AMC 12 Committee (and AMC 10) 1993 to 2000. Thanks for reading our blog Mathtuition88.com. We are also on: If you are a subscriber, thanks for your support! We will continue our mission of blogging interesting articles on Mathematics! Google’s signature ranking algorithm “PageRank” is heavily based on linear algebra! Read the above book to find out more! An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google’s ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics. Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis,Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program Gmail iOS update adds iPhone 6 support and a math joke Just to share, interesting Math Joke by Google Gmail! You may need to brush up on your math if it seems odd to you that Google just updated the iOS Gmail app to version 3.1415926. But Google is definitely not the type of company that turns down an opportunity to make a math joke, even when that joke is as simple as naming an app update after pi. Besides that, the Gmail for iOS update has a single improvement: support for the iPhone 6 and iPhone 6 Plus. Featured: You may want to buy this Spigen Tough Armor Case if you are buying the new “flexible” iPhone 6 / 6 plus! iPhone 6 Plus Case, Spigen® [KICK-STAND] iPhone 6 Plus (5.5) Case Protective [Tough Armor] [Gunmetal] Dual Layer EXTREME Protection Cover Heavy Duty Kick-Stand Feature Case for iPhone 6 Plus (5.5) (2014) – Gunmetal (SGP11053) • TPU + Polycarbonate = Dual Protection • Advanced Shock Absorption Technology: Web Pattern TPU case • Drop Protection with AIR CUSHION Corners • Built in Kick-Stand for Hands-Free Viewing • Compatible with Apple iPhone 6 Plus (5.5″) Only – 2014 Lunes (Mathematics) What are Lunes? Check out this absolutely interesting video: Source: http://en.wikipedia.org/wiki/Hippocrates_of_Chios “As it is, the book is indispensable; it has, indeed, no serious English rival.” — Times Literary Supplement “Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century.” — Prof. W. H. Stahl “Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry.” Education Info Confused About What to Do After 12th Standard? So, your +2 level exams are over, and you are looking forward to join a college, but you do not really know which stream to choose. You, inevitably, have different people in your life, suggesting different streams to you, leaving you even more confused. While one stream brings you more money, the other one gives you a much stress-free life. Do not worry. Here is a guide through the tricky path. Following are some fine points of the streams available for graduation. Arts or Humanities If you are someone who has completed your schooling with an Arts background, you need to choose a course that suits your talent profile. It does not matter if you choose an academic course or a professional one; you need to be sure about your career goals. The stream of Arts offers you a wide array of courses which must be analysed properly before taking admission in any one of them. These courses include plain and simple B.A. or Bachelor of Arts, Hotel Management, Event Management, Fashion Designing, Mass Communication, and many more. All these courses offer lucrative career opportunities in the best industries worldwide. Besides, you can also go for Foreign Language Courses; these are high in demand, and help you get a job in multinational companies. The most frequently opted for foreign language courses are Spanish, French, Russian, Korean and Japanese. Science Science happens to offer the widest number of courses after 12th. If you have had a science background at school, your first two preferences would likely be Medicine and Engineering. Besides these, you can also opt for B.Sc degree in Physics, Chemistry, Biology or Mathematics; a degree in Agriculture, Forensic Science, Bio Technology, Geology, etc. As Medicine and Engineering happen to be popular choices, we are going to elaborate on these two courses. If you choose Medicine, you can opt for any one of the following- Bachelor of Medicine and Bachelor of Surgery (MBBS), Bachelor of Physiotherapy, Bachelor of Ayurveda Medicine and Surgery (BAMS), Bachelor of Science in Optometry, Bachelor of Dental Surgery (BDS) and Bachelor of Pharmacy. As far as Engineering is concerned, there is wide array of options, which include Aeronautical Engineering, Automobile Engineering, Civil Engineering, Electrical and Electronics Engineering, Computer and Communication Engineering, Information Technology Engineering, Mechanical Engineering, Chemical Engineering, Biomedical Engineering, etc. Commerce In case you are a Commerce student, it is quite likely that ‘Chartered Accountancy’ is what strikes your head. However, you need to begin with graduation. Courses such as BCom, BBA, BBS, BMS, etc., are some of the options Commerce students choose for their graduation. Besides, you can also opt for a diploma or certificate course in Taxation, Accounting, Applied Managerial Economics, Micro Finance, Banking and Insurance, Stock Market, Micro Finance, etc. Specialising in Commerce makes you eligible for jobs like that of Account Analyst, Account Assistant, Accounting Coordinator, Financial Consultant, Accounting Coordinator, Financial Auditor, Accounting Clerk, etc. Think before you choose There is no harm in taking others’ suggestions, but the ultimate decision must be yours. Nobody, but you know what you are comfortable at. It does not matter how much your parents coax you to take up Engineering, if you find Literature more interesting, go for it. After all, it is you who have to study the subject for the next three or four years, and build a future on the same. So, nobody but you can decide which course is best for you. Also keep in mind that the course you choose gives you a good scope as far as career options are concerned. What you choose now will decide the shape of your future. So, please choose wisely. Author’s bio: Jeff Traven is a professor at a well-known university is California. During his spare time, he likes to blog on various kinds topics that help young students choose the right courses after 12th, so that they can have a bright and prosperous future. Why do Exterior Angles add up to 360 degrees? Source: http://www.fromquarkstoquasars.com/20-gifs-that-teach-you-science-concepts-better-than-your-teacher-probably-can/ This is the real reason why exterior angles of a polygon add up to 360 degrees! If you shrink the polygon (which doesn’t affect the sum of exterior angles), the exterior angles eventually meet at a point, and the sum of angles at a point is 360 degrees. This is some cool math to think about! Featured book: Math Appeal: Mind-Stretching Math Riddles NEW YORK TIMES bestselling author Greg Tang challenges kids to solve problems creatively in this follow-up to MATH FOR ALL SEASONS. In this book you’ll learn to see How very clever you can be. Holder’s Inequality for Lp Spaces These are two excellent videos explaining Holder’s Inequality for Lp Spaces: This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included. Love Math Graphs! How to remember graphs? Many students have a hard time remembering how graphs look like. Here is a humorous cartoon (suitable for Valentine’s Day) on how some graphs look like! Remember, Maths is not just about exams, homework, or getting A1/A2. Maths, above all, is about the LOVE of learning and thinking. Featured book: Love and Math: The Heart of Hidden Reality A New York Times Science Bestseller What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics. Fire HD Kids Edition Tablet: Educational Review As an Amazon Affiliate, Mathtuition88 is proud to introduce the Fire HD Kids Edition: All-new Fire HD tablet—with 1 year of Amazon FreeTime Unlimited, Kid-Proof Case, and a 2-year worry-free guarantee—up to $95 in savings A real tablet, not a toy—A quad-core processor for great performance, a vivid HD display, front and rear-facing cameras, and Dolby Digital Audio Built for even the toughest kids—Enjoy the peace of mind with an unprecedented 2-year worry-free guarantee—if they break it, we’ll replace it for free. No questions asked Don’t worry about the bill—The Kids Edition includes a year of Amazon FreeTime Unlimited so kids get unlimited access to 5,000 books, movies, TV shows, educational apps, and games—at no additional cost. Best-in-class parental controls—Create individual profiles for each of your children. Personalize screen time limits, educational goals, and age-appropriate content Kid-Proof Case—Durable, lightweight case to protect against drops and bumps caused by kids at play. This is a potential good alternative to the Ipad. Ipad is more for games, while the Fire HD Kids Edition Tablet is more educational, with a hand-curated subscription of over 5,000 kid-friendly books, movies, TV shows, educational apps, and games. It will be out soon this October 2014! Pre-order now by clicking this link: Click here to Pre-order. AlgTop1: One-dimensional objects This is a continuation of the series of Algebraic Topology videos. Previous post was AlgTop 0. Professor Wildberger is an interesting speaker. He holds some unorthodox views, for instance he doesn’t believe in “real numbers” or “infinite sets”. Nevertheless, his videos are excellent and educational. Highly recommended to watch! The basic topological objects, the line and the circle are viewed in a new light. This is the full first lecture of this beginner’s course in Algebraic Topology, given by N J Wildberger at UNSW. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways. Author: NJ Wildberger This revolutionary book establishes new foundations for trigonometry and Euclidean geometry. It shows how to replace transcendental trig functions with high school arithmetic and algebra to dramatically simplify the subject, increase accuracy in practical problems, and allow metrical geometry to be systematically developed over a general field. This new theory brings together geometry, algebra and number theory and sets out new directions for algebraic geometry, combinatorics, special functions and computer graphics. The treatment is careful and precise, with over one hundred theorems and 170 diagrams, and is meant for a mathematically mature audience. Gifted high school students will find most of the material accessible, although a few chapters require calculus. Applications include surveying and engineering problems, Platonic solids, spherical and cylindrical coordinate systems, and selected physics problems, such as projectile motion and Snell’s law. Examples over finite fields are also included. Books for Gifted Children Featured book: This is the #1 Top-Selling book recommended on my website! It includes Mathematical Logic Puzzles from Mensa. Highly recommended for gifted children. Parents, if your child is gifted and you want to stretch his or her learning potential, you may want to buy this book as it is the most complete quiz book on the market. It doesn’t matter whether you are in the Gifted Education Programme, as long as you have an interest in logic puzzles this book is for you. Maths and Science is essentially about logical thinking, so logic puzzles will directly benefit studies in maths and science. Above all, logic puzzles are meant to be fun and a good and healthy pastime. Puzzle fans have bought more than 650,000 copies of the Mensa Genius Quiz series—the only books that let readers “match wits with Mensa,” comparing how well they do against members of the famous high-IQ society. Here, in a giant omnibus edition, are four best-selling titles: The Mensa Genius Quiz Books 1 & 2, The Mensa Genius Quiz-A-Day Book, and The Mensa Genius ABC Book. Here are more than 800 fun mindbenders to exercise every part of your brain—word games, trivia, logic riddles, number challenges, visual puzzles—plus tips on how to improve your thinking skills. All the puzzles have been tested by members of American Mensa, Ltd., and include the percentage of Mensa testers who could solve each one, so that you can score yourself against some of the nation’s fittest mental athletes. Start Maths Revision Early for the Best Results! O Level Group Tuition @ Bishan starting in 2014! Maths is a subject that requires students to start revision / practice early! It needs consistent practice and last minute studying is not going to work well! Many students have the wrong concept that they can start practising questions one or two months before the O Levels. The problem is, without constant practice, the questions from the Ten Year Series would be too difficult for students to even begin attempting the questions! This is especially true for Additional Mathematics. This leads to panic and is not the desired study strategy. This is the main reason why it is possible to score very low (less than 20 marks out of 100) in Maths, if the student does not have solid foundation or has lack of practice. To avoid this scenario, start practicing and revising Maths now! Many students already start studying / learning in advance during the December holidays. January is still a good time to start! As the Chinese proverb states: “一年之计在于春一日之计在于晨”, the best time to begin planning for a task is in Spring. Also, the current O Level Maths is not like the O Level of the past! Due to higher education standards nowadays, and competition from foreigners (especially China students whose pet subjects are Maths and Chinese), the bell curve for E Maths has shifted very very high. Rumours have it that 90 marks is necessary for a guaranteed A1 in E Maths. On the bright side, it is very possible to improve in Maths with practice. Look at the Mathematics questions in O Levels, one long question is around 10 marks. Answering that one question correctly will already boost your score by 10 marks. (2 grades). Answering two long questions correctly will boost score by a whopping 20 marks! Hesitate no longer! Start revising for your Maths now! O Level Group Tuition @ Bishan starting in 2014! Maths Challenge Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty): Source: Anderson E Maths Prelim 2011 If you have solved the problem, please email your solution to mathtuition88@gmail.com . (Include your name and school if you wish to be listed in the hall of fame below.) Students who answer correctly (with workings) will be listed in the hall of fame. 🙂 Hall of Fame (Correct Solutions): 1) Ex Moe Sec Sch Maths teacher Mr Paul Siew 2) Queenstown Secondary School, Maths teacher Mr Desmond Tay 3) Tay Yong Qiang (Waiting to enter University) Mr Heng, however, noted that how well a child does in school depends on how motivated he is. Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose. Minister for Education Heng Swee Keat (Photo: MOE) SINGAPORE: Minister for Education Heng Swee Keat has said parents should consider other factors apart from a school’s previous year cut-off point (COP) when helping their P6 children decide on which secondary school to choose. Writing on his Facebook page, Mr Heng said it would be good for parents to have an open talk with their children to know what type of secondary school they are interested in. Mr Heng, however, noted that how well a child does in school depends on how motivated he is. So he encourages parents to carefully consider the kind of environment that will best motivate their children, and enable them to develop themselves fully in the next four to five years. Some children, he said, are late developers and the right environment helps them thrive. Mr Heng urged parents to think of how best they can help their children develop confidence and enjoy the space to discover his talents and passions. Recommended Maths Olympiad Books for Self Learning / Domain Test Math Olympiad Books are useful for GEP/DSA preparation. It is also useful for the latest type of test called Domain Tests, which is basically a subject test (Math included) for entry into top secondary schools like the Raffles / Hwa Chong family. There are different subject domains (depending on the school), ranging from General domain / Academic domain / CCA domain. A First Step to Mathematical Olympiad Problems (Mathematical Olympiad Series) The Art of Problem Solving, Vol. 1: The Basics The first book is written by Professor Derek Holton. Prof Holton writes a nice column for a Math magazine, which gives out books as prizes to correct solutions. GEP Math Olympiad Books If you are searching for GEP Math Olympiad Books to prepare for the GEP Selection Test, you may search for Math Olympiad Books for Elementary School. Note that Math Olympiad Books for IMO (International Mathematics Olympiad) are too difficult even for a gifted 9 year old kid! A suitable book would be The Original Collection of Math Contest Problems: Elementary and Middle School Math Contest problems. It covers the areas of Algebra, Geometry, Counting and Probability, and Number Sense, over 500 examples and problems with fully explained solutions. Other Suitable Math Olympiad Books for GEP These are some books that are very popular and highly rated on Amazon. Math, Science, Reading Scores Show U.S. Schools Slipping Behind Math, Science, Reading Scores Show U.S. Schools Slipping Behind Posted: December 10, 2010 PRINTER FRIENDLY VERSION: PDF The United States received a stark wake-up call this week with the release of international test results showing students in other countries are surpassing American students when it comes to math, science and reading. China and Australia outperformed the U.S. in each of the three subject areas tested. The results of a major international education assessment show that American students are lagging behind many other countries in crucial skills like reading, math and science. “The United States came in 23rd or 24th in most subjects. We can quibble, or we can face the brutal truth that we’re being out-educated,” said U.S. Education Secretary Arne Duncan. Test compares U.S. to other countries The PISA tests how advanced students are in science, math and reading compared to their peers around the world. The test, known as the Program for International Student Assessment (PISA), directly assesses how prepared teenagers are in math, science and reading compared to their peers in other countries. The test is translated into each country’s language, and officials from the participating countries are able to review questions before students take the exam to make sure each test is fair and unbiased. In the U.S., the participating schools and students are randomly selected. On average, about 4,500 students are tested in each of the participating countries. China and Finland lead the way Chinese and Finnish students scored highest on the PISA test. Each PISA subject area is scored on a scale where 500 points is the average. The results announced this week show many countries outperforming the U.S. Here’s a sample: Math: China 600, Germany 513, United States 487 (31st place) Reading: China 556, Korea 539, United States 500 (17th place) Science: China 575, Finland 554, United States 502 (23rd place) The results of a major international education assessment show that American students are lagging behind many other countries in crucial skills like reading, math and science. In China, all parents know that maths is the number one subject in schools ‘Above all, it is a cultural thing.” Professor Lianghuo Fan is reflecting on the differences he has noticed between maths education in China and Singapore, where he lived and taught for 40 years, and in Britain, where he is now based. “In China, all parents know that maths is the number one subject in schools, and they expect that in a modern society everyone must be comfortable with maths, even if that means they have to work hard at it.“That attitude is passed on to their children. But here in Britain, you can feel students’ attitude about mathematics is different. They feel all right if they say they don’t like mathematics.” Professor Fan is not alone in highlighting this national phobia of ours about maths. The government has this week shown itself determined to tackle the problem head on with the unveiling of a new “back-to-basics” primary school maths curriculum, with a renewed emphasis on times-tables, mental arithmetic, fractions and rote learning. Most people over 40 will see the proposals as a return to the classroom practice of their childhood – but in its introductory remarks the Department for Education claimed inspiration from Asian model that Professor Fan knows so well: “I never heard a child in China or Singapore say that they don’t like maths’,” he stresses, “without a sense of embarrassment.” We are sitting in a café near Southampton University – where 50-year-old Professor Fan has been head of the Mathematics and Science Education Research Centre since 2010 – as we try to decide if anything lies behind the popular stereotype that Asian children are “naturally” better at maths than those in the West. It is, for example, in the core storyline of Safe, the recent Hollywood blockbuster, starring Jason Statham. An 11-year-old girl, Mei (played by Chinese-born actress Catherine Chan), is a maths prodigy who can decode number sequences at a glance – and therefore has to be protected from the baddies. Formula to guess Month of Birthday from Singapore NRIC Latest Update: We have created a JavaScript App to Guess Birthday Month from NRIC Here is a Math Formula trick to have fun with your friends, to guess their Month of Birthday given their NRIC, within two tries. (only works for Singapore citizens born after 1970) The formula is: take the 3rd and 4th digit of the NRIC, put them together, divide by 10, and multiply by 3. For an example, if a person’s NRIC is S8804xxxx, we take 04, divide by 10 to get 0.4 Then, 0.4 multiplied by 3 gives 1.2 Then, guess that the person is either born in January (round down 1.2 to 1) or February (round up 1.2 to 2). There is a high chance that you are right! Usually, round up for the first six months (Jan to Jun), and round down for the last six months (Jul to Dec). This formula was developed and tested by me. There are some exceptions to the rule, but generally it works fine especially for people born from 1980 to 2000. Hope you have fun with maths, and impress your friends! Maths Skills to be a Doctor Doctor and Lawyer are the top two favourite careers in Singapore. Do doctors need to use Maths? Read the below to find out. Even if Maths is not directly needed, the logical thinking skills learnt in Mathematics will definitely be of great use. 🙂 I am not a medical doctor, but my two younger siblings are medical students, and the Mathematical knowledge and thinking skills have definitely helped them in their medical studies. Functional numeracy is as essential to an aspiring medical professional as functional literacy. As a physician, perhaps the most important mathematical skills you will need are: 1. Basic mathematical knowledge sufficient to calculate drug doses, concentrations, etc. 2. An understanding of the core statistical concepts most commonly represented in the medical literature. 3. Knowledge of algebra to understand calculations of acid–base status, etc. 4. Ability to appreciate whether or not results are mathematically plausible. (Nusbaum, 2006) The careful logical reasoning that is necessary for the study of mathematics is an essential element of clinical reasoning. Although you do not need higher mathematics to get through medical school, you will need the ability to manipulate numbers, including fractions, ratios, powers of 10 and logarithms. You will also need a basic understanding of probability, graphs and simple algebra. You will need to rearrange equations and convert between units of measure. It’s often unclear from your interactions with a doctor how much math she is using in order to treat you. While not all doctors have to use math as directly and frequently as engineers do, all of them must understand the complex mathematical equations that inform different medical treatments in order to administer treatments correctly. Dosages and Half-Life One of the most common ways in which doctors use mathematics is in the determination of medicine prescriptions and dosages. Doctors not only have to use basic arithmetic to calculate what dosage of a particular drug will be effective for your height and body type over a specific period of time, they will also have to be aware of the medicine’s cycle through the body and how the dosage of one drug compares with the dosage of a similar type of drug. Sometimes doctors have to use calculus to figure out the right dosage of a drug. Calculus is the study of how changing variables affect a system. In the human body, the kidney processes medicine. However, people’s kidneys are at varying levels of health. Doctors can designate the kidney as a changing function in a calculus equation known as the Cockroft-Gault equation. This equation uses the level of creatine in a patient’s blood to find the level of the kidney’s functioning, which allows the doctor to determine the appropriate dose. Cancer Treatment When a doctor administers radiation therapy to a cancer patient, the radiation beams have to cross each other at specific angles, so that they harm the cancerous tumor without harming the surrounding healthy tissue. The precise numbers for these angles must be calculated mathematically. Cancer tends to respond to any drug by mutating so that its DNA is no longer affected by that drug. Oncologists and medical scientists have decided to target cancerous tumors with many different kinds of drugs at once so that the cancer is unable to respond adequately. They use complex mathematical models that plot the speed and timing of the cancer’s different mutations to figure out what combinations and dosages of different drugs should be used. Medical Images and Tests Doctors in medical imaging use two-dimensional images of a patient’s body taken from thousands of angles to create a three-dimensional image for analysis. Determining what angles should be used and how they will fit together requires mathematics. Medical researchers who study disease will analyze the mathematical dimensions of these images. Neurologists who run EEGs on patients to measure their brain waves must add and subtract different voltages and use Fourier transforms to filter out signal static. Fourier transforms are used to alter functions in calculus. Treatment Research Medical scientists working with cardiologists use differential equations to describe blood flow dynamics. They also build sophisticated computer models to find the ideal size of an artificial aorta and where to place it in an infant pending a heart transplant. Doctors have to read medical journals to keep up on the latest scientific findings for the benefit of their patients. In addition to describing the calculus used to model health conditions, medical journal studies also make heavy use of statistics and probability to describe the health conditions of whole populations and the likelihood that different treatments will be effective. Maths Skills to be a Good Lawyer Doctor and Lawyer are the top two favourite careers in Singapore. On the surface, Lawyers seem not to need much maths, but recent research shows that Mathematics skills and thinking may be crucial to becoming a better Lawyer. There is a “highly significant relationship” between law students’ math skills and the substance of their legal analysis, according to research from Arden Rowell, a professor of law and the Richard W. and Marie L. Corman Scholar at Illinois. CHAMPAIGN, Ill. — The stereotype of lawyers being bad with numbers may persist, but new research by two University of Illinois legal scholars suggests that law students are surprisingly good at math, although those with low levels of numeracy analyze some legal questions differently. According to research from Arden Rowell and Jessica Bregant, there is a “highly significant relationship” between law students’ math skills and the substance of their legal analysis, suggesting that legal analysis – and by extension, legal advice – may vary with a lawyer’s native math skills. What the research shows is that math matters to lawyers more – and for different reasons – than people have realized,” said Rowell, a professor of law and the Richard W. and Marie L. Corman Scholar at Illinois. “People are only now starting to pay attention to the fact that lawyers and judges who are bad at math can make mistakes that ruin people’s lives. That implicates numeracy as a neglected but potentially critical aspect of legal education, because it’s not something that law schools have traditionally focused on when selecting students.” JC Cut Off Points JC Cut Off Points (COP) To sign up for JC Tuition (subjects other than Math, e.g. GP Tuition): Check out this recommended tuition agency: StarTutor! Aggregate Scores of Junior Colleges (JC) Outliers: The Story of Success This is a very inspirational book on why do some people succeed, and what makes high-achievers different? Famous author Malcolm Gladwell reveals the secret and how it is possible for average ordinary people to achieve the same results. (Best Seller on Amazon.com) Check out our post on Recommended Graphical Calculator for JC. Also check out our post on: Which JC is Good? 1. RJC Cut Off Points: Arts 3, Science 3 2. HCI Cut Off Points: Arts 3, Science 3 3. VJC Cut Off Points: Arts 5, Science 4 4. NJC Cut Off Points: Arts 5, Science 5 5. ACS(I) Cut Off Points: Science 5 6. ACJC Cut Off Points: Arts 7, Science 6 7. TJC Cut Off Points: Arts 7, Science 6 8. AJC Cut Off Points: Arts 10, Science 8 9. MJC Cut Off Points: Arts 9, Science 9 10. NYJC Cut Off Points: Arts 9, Science 9 11. SAJC Cut Off Points: Arts 9, Science 9 12. CJC Cut Off Points: Arts 10, Science 10 13. SRJC Cut Off Points: Arts 13, Science 13 14. TPJC Cut Off Points: Arts 13, Science 14 15. JJC Cut Off Points: Arts 13, Science 16 16. PJC Cut Off Points: Arts 16, Science 16 17. YJC Cut Off Points: Arts 20, Science 20 18. IJC Cut Off Points: Arts 20, Science 20 L1R5 aggregate scores/ Cut Off Points (with bonus points) of students admitted to JCs in the 2012 Joint Admissions Exercise (JAE). Junior College Arts Science/IB Anderson JC 10 8 Anglo-Chinese JC 7 6 Anglo-Chinese School (Independent) – 5 Catholic JC 10 10 Hwa Chong Institution 3 3 Innova JC 20 20 Jurong JC 13 16 Meridian JC 9 9 Nanyang JC 9 9 National JC 5 5 Pioneer JC 16 16 Raffles Institution 3 3 Serangoon JC 13 13 St. Andrew’s JC 9 9 St. Joseph Institution – – Tampines JC 13 14 Temasek JC 7 6 Victoria JC 5 4 Yishun JC 20 20 JC Cut Off Points (Bonus Points) For students seeking admission to JC/Poly/ITE and with the following CCA grades:a. Grades of A1 – A2 (2 points)b. Grades of B3 – C6 (1 point) For students seeking admission to JC/MI courses and with grades of A1 to C6 in both their first languages (i.e. English and a Higher Mother Tongue). This is provided that these choices come before any Poly/ITE choices.(2 points) For students seeking admission to JC/MI courses and with grades of A1 to C6 in Malay/Chinese (Special Programme) (MSP/CSP) or Bahasa Indonesia (BI) as their third language. This is provided that these choices come before any Poly/ITE choices.(2 points) For students from feeder schools if they choose their affiliated Junior College course(s) as their:a. 1st choice, or b. 1st and 2nd choices. (2 points) The bonus points can be deducted from their total points, and will be helpful to enter the JC (depending on the JC’s Cut Off Points). Theoretical Minimum Score is 0 points (if under CLEP or MLEP programme), otherwise minimum score is 2 points. Teachers have profound effect on students, says Heng Swee Keat Education Minister Heng Swee Keat said teachers “grow knowledge, instill beliefs, inculcate values, nurture passion, and in so doing, they shape the future” of students. File photo: Minister for Education Heng Swee Keat SINGAPORE: Education Minister Heng Swee Keat said on Thursday “teachers affect all of us more deeply” than one can know. In a Facebook post ahead of Teachers’ Day on Friday, Mr Heng sent his warmest thoughts and admiration to all teachers who dedicate themselves to bringing out the best in children. In the tribute to all teachers, Mr Heng said they “grow knowledge, instill beliefs, inculcate values, nurture passion, and in so doing, they shape the future” of their students. He added that every child who grows up confident and compassionate has been affected by a caring teacher in some way. Mr Heng said in order to give every child a profound educational experience, every teacher must be a caring educator. O Level E Maths and A Maths Tuition starting next year at Bishan O Level E Maths and A Maths Tuition starting next year at Bishan ————————– View Mr Wu’s GEP Testimonial at https://mathtuition88.com/group-tuition/ Despite being in the Gifted Education Programme (GEP), Mr Wu is just an ordinary Singaporean. His secret to academic success is hard work and the Maths Techniques he has discovered by himself while navigating through the education system. He would like to teach these techniques to students, hence choosing to become a full-time Mathematics tutor. Mr Wu has developed his own methods to check the answer, remember formulas (with understanding), which has helped a lot of students. Many Math questions can be checked easily, leading to the student being 100% confident of his or her answer even before the teacher marks his answer, and reducing the rates of careless mistakes. Mr Wu’s friendly and humble nature makes him well-liked by students. Many of his students actually request for more tuition by themselves! (not the parents) O Level E Maths and A Maths Tuition starting next year at Bishan, the best location in Central Singapore. Timings are Monday 7-9pm, Thursday 7-9pm. Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free. Register with us now by email (mathtuition88@gmail.com). Vacancies will be allocated on a first-come-first-serve basis. Thanks and wishing all a nice day. Additional Maths — from Fail to Top in Class Really glad to hear good news from one of my students. From failing Additional Maths all the way, he is now the top in his entire class. Really huge improvement, and I am really happy for him. 🙂 To other students who may be reading this, remember not to give up! As long as you persevere, it is always possible to improve. Understanding the Birthday Paradox 23 people. In a room of just 23 people there’s a 50-50 chance of two people having the same birthday. In a room of 75 there’s a 99.9% chance of two people matching. Put down the calculator and pitchfork, I don’t speak heresy. The birthday paradox is strange, counter-intuitive, and completely true. It’s only a “paradox” because our brains can’t handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenarios we’re involved in (both faulty assumptions, by the way). Let’s see why the paradox happens and how it works. Continue reading at http://betterexplained.com/articles/understanding-the-birthday-paradox/ Missing dollar riddle; Maths Group Tuition 2014 Ad: Maths Group Tuition starting in 2014 Maths can be fun too! Build up interest in Mathematics by trying out some of these interesting Maths Riddles. The riddle Three guests check into a hotel room. The clerk says the bill is$30, so each guest pays $10. Later the clerk realizes the bill should only be$25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn’t know the total of the revised bill, the bellhop decides to just give each guest$1 and keep $2 for himself. Each guest got$1 back: so now each guest only paid $9; bringing the total paid to$27. The bellhop has $2. And$27 + $2 =$29 so, if the guests originally handed over $30, what happened to the remaining$1? Try it out before looking at the answer! Maths Group Tuition starting in 2014 SINGAPORE – Five government scholarship recipients, including a missionaries’ child who grew up in Papua New Guinea and a Youth Olympic Games triathlete, have been awarded the prestigious President’s Scholarships this year, at a ceremony at the Istana on Friday evening. Get the full story from The Straits Times. Here is the full speech by President Tony Tan: Deputy Prime Minister Teo Chee Hean and Mrs Teo Minister for Education Heng Swee Keat Excellencies Chairman and Members of the Public Service Commission Good evening. Each year, the Public Service Commission awards scholarships to outstanding young men and women who want to serve Singapore and Singaporeans through a career in the Public Service. The most prestigious undergraduate scholarship awarded by the Commission is the President’s Scholarship. It is awarded to young Singaporeans who have the integrity and commitment to work for Singapore’s continued success. To be awarded a President’s Scholarship, one must demonstrate more than just excellence in academic and non-academic pursuits. One must also show a strong ethos for public service, impeccable character, remarkable leadership and dedication towards improving the lives of Singaporeans. 2013 President’s Scholars This evening, the President’s Scholarship is awarded to five exceptional young individuals who have distinguished themselves based on their leadership capabilities and calibre, and their passion to bring the nation forward. Counting on her mind 1,248 words 24 May 2005 Digital Life English (c) 2005 Singapore Press Holdings Limited You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN Given that multiple degrees are common today, the fact that Miss Yeo Sze Ling has two degrees in mathematics, and is working on her doctorate in the same field, is probably not news. Until you find out that she is blind. The 27-year-old who earned her Bachelor’s degree (Honours) and a Master’s degree from National University of Singapore (NUS) is now into research on coding mathematics theories and cryptography. These are used in computing algorithms to protect passwords or data from being stolen when they are zipped from computer to computer. The field is an interest she shares with John Nash Jr, a mathematical genius who won a Nobel Prize, portrayed in the Oscar-winning movie, A Beautiful Mind. Certainly, like Nash, her achievements should mean a lot. He was a schizophrenic who thought he was doing secret cryptography work for the American government. She has been blind from the age of about four when glaucoma struck. Glaucoma is a condition that increases pressure within the eyeball causing sight loss. Technology has come in handy. On campus, she totes a laptop. At home in a four-room HDB flat in Bishan, her desktop Compaq PC holds today’s tech staples – e-mail and MSN Messenger for exchanging notes with friends. The Internet is her source for research as well as for online newspapers or electronic books like A Beautiful Mind. Rote learning has to make way for digital literacy: Heng Swee Keat Education Minister Heng Swee Keat has said that with information readily available, rote learning has to make way for digital literacy. SINGAPORE: Education Minister Heng Swee Keat has said that with information readily available, rote learning has to make way for digital literacy. Speaking at the Second International Summit of the Book on Friday, Mr Heng said there is a need to place greater emphasis on critical and inventive thinking. Whether it is a papyrus, print or the iPad, it seems that books are here to stay. Professor Tommy Koh, chairman of the Organising Committee of the Second International Summit of the Book, and Ambassador-at-Large, said: “I think the book will endure to the end of time. “But the form of the book has changed and will change. The container will change, the platform on which we read the book will also change. “My children, for example, prefer to read the book either on the computer, on the iPad, on the tablet and other electronic forms. I still prefer the printed book. But in one form or another, the book will endure. There can be no human civilisation without books.” But the question is whether readers are able to discern truths from untruths, especially in an era that is inundated with information. Mr Heng said: “Some fear that the technologically sophisticated books of the future will dull the mind, as we no longer bother to use our imagination to render words into sounds and images. “They worry too that we will forget to think for ourselves after we close the book because social media offers such an array of ready-made opinions that we will just pick one off the virtual shelf rather than form our own. “We need to place greater emphasis on critical and inventive thinking, so that we may go on to imagine and create new insights. “At the workplace, as the information revolution transforms the nature of work, our ability to move from theory to practice, to apply learning imaginatively in different contexts, and to create new knowledge, will become increasing valuable.” Maths Group Tuition to start in 2014! Sergey Mikhaylovich Brin (Russian: Сергей Михайлович Брин; born August 21, 1973) is an American computer scientist and Internet entrepreneur who, with Larry Page, co-founded Google, one of the most profitable Internet companies.[4] As of 2013, his personal wealth was estimated to be \$22.8billion.[2] Together, Brin and Page own about 16 percent of the company. Brin immigrated to the United States with his family from the Soviet Union at the age of six. He earned his undergraduate degree at the University of Maryland, following in his father’s and grandfather’s footsteps by studying mathematics, as well as computer science. After graduation, he moved to Stanford University to acquire a Ph.D. in computer science. There he met Larry Page, with whom he later became friends. They crammed their dormitory room with inexpensive computers and applied Brin’s data mining system to build a superior search engine. The program became popular at Stanford and they suspended their PhD studies to start up Google in a rented garage. The Economist newspaper referred to Brin as an “Enlightenment Man“, and someone who believes that “knowledge is always good, and certainly always better than ignorance”, a philosophy that is summed up by Google’s motto “Organize the world’s information and make it universally accessible and useful”[5][6] and “Don’t be evil“. Education in the United States Brin attended grade school at Paint Branch Montessori School in Adelphi, Maryland, but he received further education at home; his father, a professor in the department of mathematics at the University of Maryland, encouraged him to learn mathematics and his family helped him retain his Russian-language skills. In September 1990 Brin enrolled in the University of Maryland to study computer science and mathematics, where he received his Bachelor of Science in May 1993 with honors.[14] Maths Group Tuition to start in 2014! Source: http://ww1.math.nus.edu.sg/ The history of the Department of Mathematics at NUS traces back to 1929, when science education began in Singapore with the opening of Raffles College with less than five students enrolled in mathematics. Today it is one of the largest departments in NUS, with about 70 faculty members and teaching staff supported by 13 administrative and IT staff. The Department offers a wide selection of courses (called modules) covering wide areas of mathematical sciences with about 6,000 students enrolling in each semester. Apart from offering B.Sc. programmes in Mathematics, Applied Mathematics and Quantitative Finance, the Department also participates actively in major interdisciplinary programs, including the double degree programme in Mathematics/Applied Mathematics and Computer Science, the double major programmes in Mathematics and Economics as well as with other subjects, and the Computational Biology programme. Another example of the Department’s student centric educational philosophy is the Special Programme in Mathematics (SPM), which is specially designed for a select group of students who have a strong passion and aptitude for mathematics. The aim is to enable these students to build a solid foundation for a future career in mathematical research or state-of-the-art applications of mathematics in industry. The Department is ranked among the best in Asia in mathematical research. It offers a diverse and vibrant program in graduate studies, in fundamental as well as applied mathematics. It promotes interdisciplinary applications of mathematics in science, engineering and commerce. Faculty members’ research covers all major areas of contemporary mathematics. For more information, please see research overview, selected publications, and research awards. Maths Group Tuition Singapore‘s grading system in schools is differentiated by the existence of many types of institutions with different education foci and systems. The grading systems that are used at Primary, Secondary, and Junior College levels are the most fundamental to the local system used. Featured book: “If you’ve ever said ‘I’m no good at numbers,’ this book can change your life.” (Gloria Steinem) Primary 5 to 6 standard stream • A*: 91% and above • A: 75% to 90% • B: 60% to 74% • C: 50% to 59% • D: 35% to 49% • E: 20% to 34% • U: Below 20% • A1: 75% and above • A2: 70% to 74% • B3: 65% to 69% • B4: 60% to 64% • C5: 55% to 59% • C6: 50% to 54% • D7: 45% to 49% • E8: 40% to 44% • F9: Below 40% The GPA table for Raffles Girls’ School and Raffles Institution (Secondary) is as below: A+ 80-100 4.0 A 70-79 3.6 B+ 65-69 3.2 B 60-64 2.8 C+ 55-59 2.4 C 50-54 2.0 D 45-49 1.6 E 40-44 1.2 F <40 0.8 The GPA table differs from school to school, with schools like Dunman High School excluding the grades “C+” and “B+”(meaning grades 50-59 is counted a C, vice-versa) However, in other secondary schools like Hwa Chong Institution and Victoria School, there is also a system called MSG (mean subject grade) which is similar to GPA that is used. A1 75-100 1 A2 70-74 2 B3 65-69 3 B4 60-64 4 C5 55-59 5 C6 50-54 6 D7 45-49 7 E8 40-44 8 F9 <40 9 The mean subject grade is calculated by adding the points together, then divided by the number of subjects. For example, if a student got A1 for math and B3 for English, his MSG would be (1+3)/2 = 2. • A1: 75% and above • A2: 70% to 74% • B3: 65% to 69% • B4: 60% to 64% • C5: 55% to 59% • C6: 50% to 54% • D7: 45% to 49% • E8: 40% to 44% • F9: Below 40% The results also depends on the bell curve. Junior college level (GCE A and AO levels) • A: 70% and above • B: 60% to 69% • C: 55% to 59% • D: 50% to 54% • E: 45% to 49% (passing grade) • S: 40% to 44% (denotes standard is at AO level only), grade N in the British A Levels. • U: Below 39% Maths Group Tuition starting in 2014! Shing-Tung Yau (Chinese: 丘成桐; pinyin: Qiū Chéngtóng; Cantonese Yale: Yāu Sìngtùng; born April 4, 1949) is a Chinese-born American mathematician. He won the Fields Medal in 1982. Yau’s work is mainly in differential geometry, especially in geometric analysis. His contributions have had an influence on both physics and mathematics and he has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein‘s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using Calabi–Yau compactification—to show that string theory is a viable candidate for a unified theory of nature. Calabi–Yau manifolds are among the ‘standard toolkit’ for string theorists today. Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hong Kong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father Chiou Chenying, a philosophy professor, died. After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to the University of California, Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of Shiing-Shen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University. Since 1987, he has been at Harvard University,[1] where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K-12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 10, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1874944120645523, "perplexity": 2856.781262238847}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153729.44/warc/CC-MAIN-20210728123318-20210728153318-00266.warc.gz"}
https://socratic.org/questions/how-do-you-solve-z-2-8-6-2	Algebra Topics # How do you solve z/2.8 = -6.2? Jun 20, 2015 Multiply both sides of the equation by $2.8$ to get: $z = - 6.2 \cdot 2.8 = - 17.36$ #### Explanation: The truth of an equation is preserved by any of the following operations: (1) Add or subtract the same value on both sides. (2) Multiply or divide both sides by the same non-zero value. Note that you can also do things like square both sides of an equation, but this can introduce spurious solutions: that is the new equation may have solutions that the old one does not. ##### Impact of this question 357 views around the world You can reuse this answer	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9301924109458923, "perplexity": 567.3822333148275}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738595.30/warc/CC-MAIN-20200809222112-20200810012112-00098.warc.gz"}
http://math.stackexchange.com/questions/367726/help-doubt-about-uniqueness-in-mathematics	# Help! Doubt About Uniqueness in Mathematics Many times in mathematics, as for example when we find the solution of an ODE, we can not claim uniqueness just by construction, instead we have to use a theorem. The reasoning behind this is that even if we found a solution and the solution appears to be unique from the point of view of the method used, how can we be sure there is no another method which provides another solution? Now my question: sometimes the following type of argument is accepted as valid. For example, a simple differential equation like this one $y'(x)=x^2$ with $y(0)=0$, we say that $y(x)=\frac{1}{3}x^3$ is the only solution (without the use of an uniqueness theorem, I think is because of the Fundamental Theorem of Calculus). How can be sure now that there is not another way to solve the equation that provides another solution (without using the uniqueness theorem of course)? When is this type of argument valid and when not? Down in some of the answers some people say that the reason in the previous example for uniqueness is because the anti-derivative is unique, which sounds reasonable. But the Laplace transform of a function that satisfies certain conditions is also unique. And we can't say that the solution of an ODE is unique only beause it was calculated through the Laplace transform method. - When is what argument valid? I see no arguments above to validate. – Math Gems Apr 20 '13 at 22:54 @MathGems uniqueness without using an uniqueness theorem as in the example. – Ambesh Apr 20 '13 at 22:54 Without knowing the uniqueness theorem, what logical basis do you have for believing that the solution should be unique? Does the same reasoning tell you that prime factorizations of integers is unique? – Math Gems Apr 20 '13 at 22:57 @MathGems Well, I'm not using my intuition. I have seen teachers do that. I have a very reputed teacher that claims uniqueness on construction basis sometimes. And that is driving me nuts. – Ambesh Apr 20 '13 at 22:59 For the specific case you are asking, and similar questions, we do use a uniqueness theorem all the time: If two functions $f$ and $g$ have the same derivative, their difference is constant. We may not bother to mention it all the time, just as we do not bother to mention that arithmetic is commutative every time we have integers $a,b$, and rewrite $ab$ as $ba$. Anyway, the result that if $f'=g'$ then $f,g$ differ by a constant tells you that if you find any function, by any method whatsoever, such that $f'(x)=x^2$, then any other $y$ with $y'=x^2$ will be $f(x)+c$. – Andrés E. Caicedo Apr 20 '13 at 23:05 It's unique because it is a ODE with separable variables, and its solution is found via separation of the variables and integration. The function obtained via integration is unique except for the arbitrary constant, which is uniquely determined by the initial condition. EDIT: I must correct this: let's suppose you have an ODE which is variable-separable that is defined by $$h(y)y'=g(x)$$ You can find a solution via integration as usual: $$\int h(y)dy=\int g(x)dx$$ The function is given inplicitly by the above equation. Let's suppose that $y(a)=b$ is the initial condition. If $y'(a)\neq 0$ then $y$ is locally invertible (as per the Inverse Function theorem) and you can find a local unique solution $y(x)$ which can be extended to a maximal conected domain; in this case it is correct to say that the solution obtained via the separation method is unique without recurring to the Existence & Uniqueness of solutions. An important remark: the Existence and Uniqueness Theorem for ODEs works fine for equations defined as $y'(x)=f(y,x)$, where $\|f\|$ is limited on a neighbourhood of the initial condition $(a,y(a))$. In the example cited on the comments, $f$ is something like $$f(x,y)=\dfrac{\hat{f}(x)}{y}$$ for some $\hat{f}$ so if $y(0)=0$, $\|f\|$ is not limited around $(0,0)$ and uniqueness cannot be guaranteed. - @Gustavo_Marra But how do we know that is really unique? Why integration is different than another method? For example using the Laplace transform to find the solution of an ODE. – Ambesh Apr 20 '13 at 23:00 Comes from the uniqueness of the primitive (antiderivative) of a function modulo an adding constant. Also see the Fundamental Theorem of Calculus. – Marra Apr 20 '13 at 23:03 @MykeArya uniqueness can be proven by the mean value theorem, which shows that a function defined on an interval with derivative zero is a constant. Then you take the difference of any solution to an ODE with the solution you solve for and use linearity of the derivative to show that that difference has derivative zero. The initial condition identifies the constant. – Chris Janjigian Apr 20 '13 at 23:42 I must be missing something: the equation $2y\frac{dy}{dx}=4x^3$, $y(0)=0$ is separable and has four solutions on $\mathbb{R}$ (two possibilities each side of the origin). – Shane O Rourke Apr 21 '13 at 9:13 As well as $y_1=x^2$ and $y_2=-x^2$, there is $y_3=\left\{\begin{array}{rl}x^2 & x<0\\ -x^2 & x\geq 0\end{array}\right.$ and $y_4=-y_3$. – Shane O Rourke Apr 21 '13 at 9:36 Although they may not be explicitly mentioned, there are in fact uniqueness theorems that are at the foundation of such "unique by construction" arguments. Let's consider your specific example of solutions of a nonhomogenous differential equation. It is simply a special case of the ubiquitous linear principle that the general solution of a nonhomogeneous linear equation is given by adding any particular solution to the general solution of the associated homogeneous equation. More explicitly, if $\rm\:D\:$ is a linear map then one easily proves Lemma $\ \$ If $\rm\ D\:f_1\ =\ g\$ then $\rm\ D\:f_2\ =\ g\ \iff\ 0\ =\ D\:f_1 - D\:f_2\ =\ D\:(f_1-f_2)$ Therefore $\rm\ D^{-1}(g)\ =\ f_1 +\ ker\ D\ =\:\:$ particular + homogeneous solution, as in linear algebra. In particular $\rm\ \ \int g\ =\ f_1 +\ c,\$ for $\rm\ c\in ker\ \dfrac{d}{d\:x}\: =\:\:$ constants w.r.t. the derivation $\rm\ D\: =\: \dfrac{d}{d\:x}\:.$ Compare this to $\rm \ x\, =\, 3\, +\, 5\, \mathbb Z,\:$ the solution of $\rm\ 2\: x\ \equiv\ 6\pmod{10}\:,\:$ with particular solution $\rm x \equiv 3\:,\:$ and homogeneous solution: $\rm\ 2\: x\:\equiv 0\pmod{10}\iff 10\:\|\:2\:x\iff 5\:\|\:x\iff x\in 5\ \mathbb Z\:.$ - Based on your reactions to the other answers, I think your problem might be with the form of such arguments. The general idea is this: we want to prove the uniqueness of a particular gadget satisfying certain properties. From those properties, we deduce that it has other properties, and eventually we show that an any gadget which satisfies all of these properties must be our particular gadget. Maybe there are other ways to approach the problem or other properties of the gadget which we haven't used, but in any case the gadget is unique. Analogously (?), a detective might determine that a master thief acted alone before determining the thief's identity. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9152416586875916, "perplexity": 189.48606447617627}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824319.59/warc/CC-MAIN-20160723071024-00275-ip-10-185-27-174.ec2.internal.warc.gz"}
https://jpmccarthymaths.com/2010/12/02/ms-2001-week-11/?replytocom=43	On Monday we completed our introduction to horizontal asymptotes and vertical asymptotes. On Wednesday we did some examples of curve sketching and applied max/ min problems. Problems You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial: Wills’ Exercise Sheets Stationary Points are points $a\in\mathbb{R}$ where the derivative of a differentiable function $f:\mathbb{R}\rightarrow\mathbb{R}$, $f'(a)=0$. When asked to find the critical points of a function defined on the entire real line (rather than just on a closed interval $[a,b]$), the ‘endpoints’, $\pm\infty$ are not considered critical points. Convex is concave up and concave is concave down. Other Exercise Sheets – Questions on Asymptotes From section 4 Q. 5 from Problems, find the vertical asymptotes of the the functions 5(b) [(7-10), (13), (15-16), (23)] and Q. 5(c) [except (30-31)] Past Exam Papers Q. 2(a), 6(b) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf All of this except Q. 1(d) [this is the Autumn 2010 paper which wasn’t on the library website earlier in the year] http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/Autumn/MS2001Aut2010.pdf	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8223809003829956, "perplexity": 1474.2795499395666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00641.warc.gz"}
https://en.wikibooks.org/wiki/Proteomics/Protein_Identification_-_Mass_Spectrometry/Instrumentation	# Proteomics/Protein Identification - Mass Spectrometry/Instrumentation « Protein Identification - Mass SpectrometryInstrumentation » Introduction Types of Mass Spectrometry This Section: ## How does a Mass Spectrometer work? A mass spectrometer is made up of three components: an ion source, mass analyzer, and a detector. The unknown sample which may originate as solid, liquid, solution or vapor, is presented to the ionization source. After ionizing the sample, the ions of the sample are passed to the mass analyzer region where separation based on the mass-to-charge ratio occurs. Once separated by the analyzer, the ions then enter the detector portion of the mass spectrometer. At this point, the machine calculates the mass-to-charge ratio and the relative abundance of each of the different ions. From this information, a spectrum graph can be created such as the one to the right. Most mass spectrometers are maintained under a vacuum to improve the chances of ions traveling from ionization source to detector without interference by collision with air molecules. ## Ion Source The ion source is the mass spectrometer component which ionizes the sample to be analyzed. Ionization mainly serves to present the sample as vaporized ions which can be acted upon by the mass analyzer and measured by the ion detector. There are many different methods available to ionize samples, such as positive or negative ion modes. The ionization method chosen should depend on the type of sample and the type of mass spectrometer. Ionization Methods: File:ES-MassSpec.jpeg Electronspray ionization MALDI There are three types of ionization methods, electron ionization, chemical ionization and photo-induced ionization. Electron ionization involves application of an electrical current to the sample to induce ionization. Chemical ionization involves interaction of the sample with reagent molecules to induce ionization. Ions produced are often denoted with symbols that indicate the nature of the ionization, eg. [M+H]+ is used to represent a molecule which is protonated. • Electron ionization • Chemical Ionization The methods commonly used in proteomics are ‘Matrix Assisted Laser Desorption Ionization’ or MALDI and ‘Electrospray Ionization’ also known as ESI. Atmospheric pressure chemical ionization and Atmospheric pressure photo-ionization are two other forms as well. MALDI uses a solid support target plate where a UV active matrix (solid or liquid) is spotted on the plate followed by the sample over the matrix. The laser hits the spot on the crystallized matrix and transfers energy from the matrix molecule to the sample. This energy transfer vaporizes the sample, sending a plume of ions into the MALDI source. This plume of ions is then collected and held in the source until a pulse sends them all out simultaneously. If the MALDI is attached to a Time of Flight(TOF) mass analyzer these ions are then sent down the TOF tube (typically ~2m) and are separated according to their velocity (light ions hitting first). MALDI is the preferred instrumentation for proteomics due to ease of reading the spectrum; most ions are found in the +1 charge state [M+H]. Electrospray, on the other hand, is done by injecting the sample dissolved in a slightly acidic solution through a heated capillary that has a voltage around 10v. This allows for highly charged particles to be formed at the tip of the capillary. As the particles evaporate, their charge/volume increases to a point where charge repulsion forces take over and the particle will explode. A small drop will form which continues the process until individual molecules are in the gas phase and charged. These ions will then travel into the analyzer, typically a quadrupole, to be scanned one mass at a time. The molecules in electrospray tend to be multiply charged and even though the upper mass limit of a quadrupole is 2000 m/z, the multiple charges allow for high mass ions or proteins to be identified. Proteins will have a charge envelope in which each peak has a different amount of charges on them. Special software is needed to deconvolve the multiple charge species peaks into a single mass peak, such as MassLynx from Waters. This form of ionization is good for most compounds, although is not best with neutral or low polarity molecules. Atmospheric pressure chemical ionization involves interaction of the sample with reagent molecules to induce ionization. As in electrospray ionization, liquid is pumped through a capillary. At the tip it is nebulized and a corona discharge takes place ionizing the molecules. The molecules interact with the analyte and transfer their charge. This form of ionization is good for small thermally stable molecules. Atmospheric pressure photo-ionization uses photons to excite and ionize the molecules after they have been nebulized. This form of ionization is good for neutral compounds. ## Mass Analyzers The mass analyzer is the component that separates the ions created from the ion source by their mass-to-charge ratios. Mass analyzers are based on the principles of charged particles in an electric or magnetic field. By using Lorentz force law and Newton’s second law of motion you can generate the following equation: ${\displaystyle ({\frac {m}{q}})\mathbf {a} =\mathbf {E} +\mathbf {v} \times \mathbf {B} }$ Where m is the mass, the ionic charge is q , a the acceleration, E is the electric field, and the vector cross product of the ion velocity and the magnetic field is v x B. This equation says that two particles with the same mass to charge ratio (m/q) will behave exactly the same. So what this equation is basically saying is that the mass to charge ratio acts as a determinant of acceleration of the ion, which can also be represented as the addition of the electric field plus the cross product of the ion velocity and magnetic field. ### Scanning Mass Analyzers Scanning mass analyzers need to separate the ions based on their relative abundances and mass to charge ratios. Electromagnetic fields are used to separate the ions based on their mass to charge ratios, by using a slit they are able to regulate which mass to charge ratio ions get to the detector. Once selected for a particular mass to charge ratio, the ion current is then recorded as a function of time which is analagous to mass. ### Sector Mass Spectrometer Mass spectrometer that uses a mass analyzer using magnetic, electric or static sector in it is called a sector instrument. This also works in combination of sectors like BEB, magnetic-electric-magnetic. In the present days, these sector instruments are mostly double focusing i.e, the ion beams are focused in both direction and velocity. Here is how a magnetic sector mass spectrometer works, imagine a tube like thing between two electromagnets. When the electrons are passed through the tube from one end to another the magnetic field bends the electron stream by exerting turning force on it. Then m/z ratio is determined. ### Orbitrap Mass spectrometer Orbitrap Mass spectrometer is the one in which ions are subjected to an electric field produced by electrodes tangentially. Also these ions are trapped between outer electrodes, where as ions are attracted with an electrostatic attraction to the inner electrode which is balanced by centrifugal force. Therefore these ions move in a circular manner around the inner electrode also back and forth with a particular m/z ratio. By using this ion oscillation based on the m/z ratio, the trap can act as a mass analyzer. You can think of this method as a filter or funnel which only allows certain ion masses to pass through. The "funnel" is actually a combination of positively and negatively charged metal rods which together form a channel through which the ions travel. The theory is that only selected masses will be able to pass through the channel, as all other ions won't have a stable trajectory though it and will hit the quadrupole rods, stopping the ion from reaching the detector. A quadrupole ion trap mass spectrometer consists of hyperbolic electrodes with a ring and two endcaps, which is the core of this instrument. In this method, ions are trapped and then sequentially ejected into a conventional electron multiplier detector from the ion trap. That way all ions can be stored during the process of mass analysis. Recent findings showed that using 1 mtorr of helium gas in the trapping volume substantially improved the resolution of the instrument with the kinetic energy of the ions reducing and the ion trajectories contracted to the center of the trap. A packet can be formed with a given m/z ions. This spectrometer is used widely for commercial purposes because of the high resolution and it is inexpensive. In the linear ion trap mass spectrometer the ions are trapped within a set of quadrupole rods to hold the ions radially and end electrodes to maintain the ions axially with a static electrical potential. It is simply said that unlike Quadrupole Ion Trap, which uses a 3-D field, Linear Quadrupole Ion Trap uses a 2-D field. It has a selective mass filter that detects the ions of particular m/z ratio. This method has advantages like higher ion storage capacity and faster scanning technique. ### Time of Flight Mass Analysers The TOF (Time of Flight) is a mass analyzer that allows ions to flow down a field free region; which allows the ions with a greater velocity, lighter ions, to hit the detector first. This is especially compatible with MALDI due to the fact that the TOF needs a pulsed instrument for its source. In this way ions are generated in the MALDI source and held there for a brief time and all are pulsed into the TOF at the same exact time. In this way, If all ions have the same kinetic energy, the ions with the lower mass will have a higher velocity and reach the detector first; whereas the ions with the higher mass will have a lower velocity and hit the detector last. The kinetic energy of an ion leaving a source if given by: ${\displaystyle T=eV={\frac {mv^{2}}{2}}}$ Where velocity v is defined by the Length of the path L divided by time t. ${\displaystyle v={\frac {L}{t}}}$ By substituting this equation into the first and solving for time you arrive at. ${\displaystyle t=L{\sqrt {({\frac {m}{e}})({\frac {1}{2V}})}}}$ From this equation you can easily see how mass directly affects travel time. Mass is directly proportional to time. Using the m/e portion of the equation you can clearly see how a larger mass means a longer time, and likewise how a lower mass would mean a smaller m/e and thus shorter travel time. ### Ion Cyclotron Resonance Spectrometer ICR is a form of trapped Ion mass analyzer, that specifically is defined as a static trap. It is basically a box with three parallel metal sides. Trapped ion analyzers work by keeping the ions in the trap and controlling the ions by using positive and negatively charged electrical fields in a carefully series of timed events. ICR specifically works on the principle that in a magnetic field, ions move in a circular path whose frequency is mass dependent. So using the cyclotron frequency you can surmise the mass. Equating the Lorentz force in a magnetic field to the equation for centripetal force yields. ${\displaystyle evB={\frac {mv^{2}}{r}}}$ You can then easily solve the above equation for the frequency F or ${\displaystyle F={\frac {v}{r}}}$ Groups of ions with the same mass to charge ratios will have the same cyclotron frequency but may be moving out of synch with one another, this is why an excitation pulse is needed to bring the resonant ions into phase with one another and the excitation pulse. Next the ions which will be passing close to the ICR cell receiver plates cause "image currents" which can be collected and amplified and analyzed. This signal registered in the receiver plates depends both on the number of ions and their distances from the receiver plates. ### Fourier transformation This mass spectrometry includes a mass analyzer that uses cyclotron frequency of the ions to determine their m/z ratio. Here a magnetic field with electric trapping plates known as penning trap is used to hold the ions. An oscillating electric field with the magnetic field at right angle to it is used to excite the trapped ions to a larger cyclotron radius. This results in packets of oscillating ions. The trapping plates detects the signal as a image current and results in a interferogram with sine waves called free induction decay (FID). By performing a Fourier transform to this data, a mass spectrum can be generated with useful signal. ## Detector Those ions which pass through analyzer are now separated by the desired methods. This mass spectrometry component records the charge induced by an ion passing by a surface or current produced when an ion hits a surface. From these charges or currents, a mass spectrum can be produced as well as measure the total number of ions at each each m/z which are present. Due to the fact that the number of ions entering the detector at any given moment is minuscule, signal amplification is often necessary. Next section: Types of Mass Spectrometry ## Articles Summarized ### Principles and Applications of Liquid Chromatography-Mass Spectrometry in Clinical Biochemistry #### Main Focus One benefit of Liquid Chromatography - Mass Spectrometry is there are different configurations to allow for results more geared toward the experiment. #### Summary LC-MS was slow to take off due to inefficient technologies. However, in the mid 1990’s, after new technologies were developed, it became more popular. This was in part due to its high specificity and ability to handle more complex mixtures than the other options available at the time, such as GC-MS. Mass spectrometry starts by ionizing samples to generate charged molecule fragments then analyzing their mass to charge-ratio. There are different technologies used to perform the mass spectrometry part of LC-MS to obtain different results, some being more versatile than others, such as changing the ion source, changing the mass analyzer, changing the ion suppression as well as changing the direct injection method. Different ion sources that can be used clinically would be an electrospray ionization source, an atmospheric pressure chemical ionization source or an atmospheric pressure photo-ionization source. Electrospray ionization, also known as ESI, works well on polar molecules; metabolites, xenobiotics and peptides are some examples. Atmospheric pressure chemical ionization source, also known as APCI, is great analyzer for small thermally stable molecules and neutral non-polar molecules such as free steroids. Atmospheric pressure photo-ionization, also known as APPI, works well with neutral compounds such as steroids. There are four different types of mass analyzers that can be used; these are the quadrupole analyzers, time-of-flight analyzers, ion trap analyzers, and hybrid analyzers. Quadrupole analyzers are are widely used because their ease of scanning and good quality quantitative data. Time-of-flight analyzers are used for small molecules because of its high sensitivity. Ion trap analyzers have the ability to fragment an ionize ions several times giving so-called MSn capabilities. Hybrid analyzers can be switched between ion trap mode and conventional quadrupole mode. There are also different steps that can be changed in the Liquid Chromatography part of LC-MS to make the procedure more versatile such as changing the flow rate, the mobile phase, the resolution and through-put and the quanitation (calibration). The parameters and conditions involved in LC-MS can be changed to optimize the assay. However, these conditions are specific to the particular analyte and the LC separation. Therefore there are no general conditions. Some of these conditions include using a dilute solution of the analyte and using single MS or tandem MS. It is also important to make sure the LC-MS system is working properly with protocols to detect deviations from normal performance. LC-MS is used in the Biochemical screening for genetic disorders as well as therapeutic drug monitoring and steroid hormones. #### New Terms GC-MS Gas chromatography-mass spectrometry (GC-MS) is a method that combines the features of gas-liquid chromatography and mass spectrometry to identify different substances within a test sample. ( http://en.wikipedia.org/wiki/GC-MS) Ion source A device in which gas ions are produced, focused, accelerated, and emitted as a narrow beam. Also known as ion gun; ionization source. ( http://www.answers.com/topic/ion-source ) Calibration a set of graduations to indicate values or positions —usually used in plural ( http://www.merriam-webster.com/dictionary/calibration ) Deviation noticeable or marked departure from accepted norms of behavior ( http://www.merriam-webster.com/dictionary/deviation ) Xenobiotics a chemical compound (as a drug, pesticide, or carcinogen) that is foreign to a living organism ( http://www.merriam-webster.com/dictionary/xenobiotics ) #### Course Relevance How is this applicable to the proteomics class? It is important to be able to analyze what makes up a protein so that we can understand the affects of that protein on an organism. Being able to see the differences between a given protein and its normal counterpart could help in the understanding of genetic diseases. LC-MS gives scientists the ability do protein separation. ## Websites Summarized ### What is Mass Spectrometry? Chiu CM, Muddiman DC. http://www.asms.org/whatisms/index.html (3/28/09) #### Main Focus This website discusses what mass spectrometry is, the history behind it, and how it works. #### Summary Mass spectrometry is a powerful analytical technique that is used to identify unknown compounds, to quantify known compounds, and to elucidate the structure and chemical properties of molecules. Compounds can be identified at very low concentrations. Mass spectrometry is used by a wide range of professionals such as physicians, astonomers, and biologists. For example it can monitor the breath of patients by anesthesiologists during surgery and determine the composition of molecular species found in space. It can be used to identify structures of biomolecules as well sequence them. It is also used to identify and quantitate compounds of complex organic mixtures. Mass spectrometry was invented by J.J. Thomson in a vacuum tube. His invention was used to discover a number of isotopes, to determine the relative abundance of the isotopes, and to measure their "exact masses" which are important in the foundation for later developments in diverse fields ranging from geochronology to biochemical research. A mass spectrometer is an instrument that measures the masses of individual molecules that have been converted into ions by becoming electrically charged. A mass spectrometer does not actually measure the molecular mass directly, but rather the mass-to-charge ratio of the ions formed from the molecules. The charge on an ion is denoted by the integer number of the fundamental unit of charge, and the mass-to-charge ratio. It represents daltons per fundamental unit of charge. Results are in a generated mass spectrum. A mass spectrum is a graph of ion intensity as a function of mass-to-charge ratio. #### New Terms dalton a unit of mass for expressing masses of atoms, molecules, or nuclear particles equal to 1⁄12 of the atomic mass of the most abundant carbon isotope ( http://www.merriam-webster.com/medical/dalton ) corona a faint glow adjacent to the surface of an electrical conductor at high voltage ( http://www.merriam-webster.com/dictionary/corona ) mass spectrum the spectrum of a stream of gaseous ions separated according to their differing mass and charge ( http://www.merriam-webster.com/dictionary/mass%20spectrum ) elucidate to make lucid especially by explanation or analysis ( http://www.merriam-webster.com/dictionary/elucidate ) isotopes any of two or more species of atoms of a chemical element with the same atomic number and nearly identical chemical behavior but with differing atomic mass or mass number and different physical properties ( http://www.merriam-webster.com/dictionary/isotopes ) #### Course Relevance How is this applicable to the proteomics class? Proteomics is the study of the protein and is defined as the qualitative and quantitative comparison of proteomes under different conditions to further unravel biological processes. Mass spectrometry allows for the study of the components of an organism and how they create their individual functions.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8731256723403931, "perplexity": 1265.1706837225202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250608062.57/warc/CC-MAIN-20200123011418-20200123040418-00327.warc.gz"}
https://hal.in2p3.fr/in2p3-00998925	# Origin of atmospheric aerosols at the Pierre Auger Observatory using studies of air mass trajectories in South America Abstract : The Pierre Auger Observatory is making significant contributions towards understanding the nature and origin of ultra-high energy cosmic rays. One of its main challenges is the monitoring of the atmosphere, both in terms of its state variables and its optical properties. The aim of this work is to analyze aerosol optical depth $\tau_{\rm a}(z)$ values measured from 2004 to 2012 at the observatory, which is located in a remote and relatively unstudied area of the Pampa Amarilla, Argentina. The aerosol optical depth is in average quite low - annual mean $\tau_{\rm a}(3.5~{\rm km})\sim 0.04$ - and shows a seasonal trend with a winter minimum - $\tau_{\rm a}(3.5~{\rm km})\sim 0.03$ -, and a summer maximum - $\tau_{\rm a}(3.5~{\rm km})\sim 0.06$ -, and an unexpected increase from August to September - $\tau_{\rm a}(3.5~{\rm km})\sim 0.055$). We computed backward trajectories for the years 2005 to 2012 to interpret the air mass origin. Winter nights with low aerosol concentrations show air masses originating from the Pacific Ocean. Average concentrations are affected by continental sources (wind-blown dust and urban pollution), while the peak observed in September and October could be linked to biomass burning in the northern part of Argentina or air pollution coming from surrounding urban areas. Document type : Journal articles Domain : http://hal.in2p3.fr/in2p3-00998925 Contributor : Sylvie Flores Connect in order to contact the contributor Submitted on : Tuesday, June 3, 2014 - 8:45:05 AM Last modification on : Sunday, June 26, 2022 - 12:01:27 PM ### Citation A. Aab, J. Aublin, P. Billoir, M. Blanco, L. Caccianiga, et al.. Origin of atmospheric aerosols at the Pierre Auger Observatory using studies of air mass trajectories in South America. Atmospheric Research, Elsevier, 2014, 149, pp.120-135. ⟨10.1016/j.atmosres.2014.05.021⟩. ⟨in2p3-00998925⟩ Record views	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6266319155693054, "perplexity": 2752.486426345159}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335304.71/warc/CC-MAIN-20220929034214-20220929064214-00219.warc.gz"}
https://atcoder.jp/contests/arc096/tasks/arc096_b	D - Static Sushi Time Limit: 2 sec / Memory Limit: 256 MB ### 制約 • 1 ≤ N ≤ 10^5 • 2 ≤ C ≤ 10^{14} • 1 ≤ x_1 < x_2 < ... < x_N < C • 1 ≤ v_i ≤ 10^9 • 入力中のすべての値は整数である。 ### 部分点 • N ≤ 100 を満たすテストセットに正解すると、300 点が与えられる。 ### 入力 N C x_1 v_1 x_2 v_2 : x_N v_N ### 入力例 1 3 20 2 80 9 120 16 1 ### 出力例 1 191 ### 入力例 2 3 20 2 80 9 1 16 120 ### 出力例 2 192 2 貫目と 3 貫目の寿司の位置が入れ替わりました。再び、中橋くんの始めの位置から時計回りに 2 メートル歩くと、80 キロカロリーの寿司を食べることができます。今回はここで向きを変え、反時計回りに 6 メートル歩くと、120 キロカロリーの寿司を食べることができます。ここで退店すると、摂取した栄養価の合計は 200 キロカロリー、消費したエネルギーの合計は 8 キロカロリーで、差し引き 192 キロカロリーを摂取することができ、これが最大の値です。 ### 入力例 3 1 100000000000000 50000000000000 1 ### 出力例 3 0 ### 入力例 4 15 10000000000 400000000 1000000000 800000000 1000000000 1900000000 1000000000 2400000000 1000000000 2900000000 1000000000 3300000000 1000000000 3700000000 1000000000 3800000000 1000000000 4000000000 1000000000 4100000000 1000000000 5200000000 1000000000 6600000000 1000000000 8000000000 1000000000 9300000000 1000000000 9700000000 1000000000 ### 出力例 4 6500000000 Score : 500 points ### Problem Statement "Teishi-zushi", a Japanese restaurant, is a plain restaurant with only one round counter. The outer circumference of the counter is C meters. Customers cannot go inside the counter. Nakahashi entered Teishi-zushi, and he was guided to the counter. Now, there are N pieces of sushi (vinegared rice with seafood and so on) on the counter. The distance measured clockwise from the point where Nakahashi is standing to the point where the i-th sushi is placed, is x_i meters. Also, the i-th sushi has a nutritive value of v_i kilocalories. Nakahashi can freely walk around the circumference of the counter. When he reach a point where a sushi is placed, he can eat that sushi and take in its nutrition (naturally, the sushi disappears). However, while walking, he consumes 1 kilocalories per meter. Whenever he is satisfied, he can leave the restaurant from any place (he does not have to return to the initial place). On balance, at most how much nutrition can he take in before he leaves? That is, what is the maximum possible value of the total nutrition taken in minus the total energy consumed? Assume that there are no other customers, and no new sushi will be added to the counter. Also, since Nakahashi has plenty of nutrition in his body, assume that no matter how much he walks and consumes energy, he never dies from hunger. ### Constraints • 1 ≤ N ≤ 10^5 • 2 ≤ C ≤ 10^{14} • 1 ≤ x_1 < x_2 < ... < x_N < C • 1 ≤ v_i ≤ 10^9 • All values in input are integers. ### Subscores • 300 points will be awarded for passing the test set satisfying N ≤ 100. ### Input Input is given from Standard Input in the following format: N C x_1 v_1 x_2 v_2 : x_N v_N ### Output If Nakahashi can take in at most c kilocalories on balance before he leaves the restaurant, print c. ### Sample Input 1 3 20 2 80 9 120 16 1 ### Sample Output 1 191 There are three sushi on the counter with a circumference of 20 meters. If he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks seven more meters clockwise, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 9 kilocalories, thus he can take in 191 kilocalories on balance, which is the largest possible value. ### Sample Input 2 3 20 2 80 9 1 16 120 ### Sample Output 2 192 The second and third sushi have been swapped. Again, if he walks two meters clockwise from the initial place, he can eat a sushi of 80 kilocalories. If he walks six more meters counterclockwise this time, he can eat a sushi of 120 kilocalories. If he leaves now, the total nutrition taken in is 200 kilocalories, and the total energy consumed is 8 kilocalories, thus he can take in 192 kilocalories on balance, which is the largest possible value. ### Sample Input 3 1 100000000000000 50000000000000 1 ### Sample Output 3 0 Even though the only sushi is so far that it does not fit into a 32-bit integer, its nutritive value is low, thus he should immediately leave without doing anything. ### Sample Input 4 15 10000000000 400000000 1000000000 800000000 1000000000 1900000000 1000000000 2400000000 1000000000 2900000000 1000000000 3300000000 1000000000 3700000000 1000000000 3800000000 1000000000 4000000000 1000000000 4100000000 1000000000 5200000000 1000000000 6600000000 1000000000 8000000000 1000000000 9300000000 1000000000 9700000000 1000000000 ### Sample Output 4 6500000000 All these sample inputs above are included in the test set for the partial score.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5545585751533508, "perplexity": 5695.666380747455}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658844.27/warc/CC-MAIN-20190117062012-20190117084012-00480.warc.gz"}
https://worldwidescience.org/topicpages/0-9/15n+backbone+chemical.html	#### Sample records for 15n backbone chemical 1. Combining ambiguous chemical shift mapping with structure-based backbone and NOE assignment from 15N-NOESY KAUST Repository Jang, Richard 2011-01-01 Chemical shift mapping is an important technique in NMRbased drug screening for identifying the atoms of a target protein that potentially bind to a drug molecule upon the molecule\\'s introduction in increasing concentrations. The goal is to obtain a mapping of peaks with known residue assignment from the reference spectrum of the unbound protein to peaks with unknown assignment in the target spectrum of the bound protein. Although a series of perturbed spectra help to trace a path from reference peaks to target peaks, a one-to-one mapping generally is not possible, especially for large proteins, due to errors, such as noise peaks, missing peaks, missing but then reappearing, overlapped, and new peaks not associated with any peaks in the reference. Due to these difficulties, the mapping is typically done manually or semi-automatically. However, automated methods are necessary for high-throughput drug screening. We present PeakWalker, a novel peak walking algorithm for fast-exchange systems that models the errors explicitly and performs many-to-one mapping. On the proteins: hBclXL, UbcH5B, and histone H1, it achieves an average accuracy of over 95% with less than 1.5 residues predicted per target peak. Given these mappings as input, we present PeakAssigner, a novel combined structure-based backbone resonance and NOE assignment algorithm that uses just 15N-NOESY, while avoiding TOCSY experiments and 13C- labeling, to resolve the ambiguities for a one-toone mapping. On the three proteins, it achieves an average accuracy of 94% or better. Copyright © 2011 ACM. 2. Site-specific protein backbone and side-chain NMR chemical shift and relaxation analysis of human vinexin SH3 domain using a genetically encoded {sup 15}N/{sup 19}F-labeled unnatural amino acid Energy Technology Data Exchange (ETDEWEB) Shi, Pan [National Laboratory for Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China); School of Life Science, University of Science and Technology of China, Hefei, Anhui 230026 (China); Xi, Zhaoyong; Wang, Hu [School of Chemistry, University of Science and Technology of China, Hefei, Anhui 230026 (China); Shi, Chaowei [National Laboratory for Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China); School of Life Science, University of Science and Technology of China, Hefei, Anhui 230026 (China); Xiong, Ying, E-mail: yxiong73@ustc.edu.cn [School of Life Science, University of Science and Technology of China, Hefei, Anhui 230026 (China); Tian, Changlin, E-mail: cltian@ustc.edu.cn [National Laboratory for Physical Science at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China) 2010-11-19 Research highlights: {yields} Chemical synthesis of {sup 15}N/{sup 19}F-trifluomethyl phenylalanine. {yields} Site-specific incorporation of {sup 15}N/{sup 19}F-trifluomethyl phenylalanine to SH3. {yields} Site-specific backbone and side chain chemical shift and relaxation analysis. {yields} Different internal motions at different sites of SH3 domain upon ligand binding. -- Abstract: SH3 is a ubiquitous domain mediating protein-protein interactions. Recent solution NMR structural studies have shown that a proline-rich peptide is capable of binding to the human vinexin SH3 domain. Here, an orthogonal amber tRNA/tRNA synthetase pair for {sup 15}N/{sup 19}F-trifluoromethyl-phenylalanine ({sup 15}N/{sup 19}F-tfmF) has been applied to achieve site-specific labeling of SH3 at three different sites. One-dimensional solution NMR spectra of backbone amide ({sup 15}N){sup 1}H and side-chain {sup 19}F were obtained for SH3 with three different site-specific labels. Site-specific backbone amide ({sup 15}N){sup 1}H and side-chain {sup 19}F chemical shift and relaxation analysis of SH3 in the absence or presence of a peptide ligand demonstrated different internal motions upon ligand binding at the three different sites. This site-specific NMR analysis might be very useful for studying large-sized proteins or protein complexes. 3. Backbone and Ile-δ1, Leu, Val Methyl 1H, 13C and 15N NMR chemical shift assignments for human interferon-stimulated gene 15 protein Energy Technology Data Exchange (ETDEWEB) Yin, Cuifeng; Aramini, James M.; Ma, LiChung; Cort, John R.; Swapna, G.V.T.; Krug, R. M.; Montelione, Gaetano 2011-10-01 Human interferon-stimulated gene 15 protein (ISG15), also called ubiquitin cross-reactive protein (UCRP), is the first identified ubiquitin-like protein containing two ubiquitin-like domains fused in tandem. The active form of ISG15 is conjugated to target proteins via the C-terminal glycine residue through an isopeptide bond in a manner similar to ubiquitin. The biological role of ISG15 is strongly associated with the modulation of cell immune function, and there is mounting evidence suggesting that many viral pathogens evade the host innate immune response by interfering with ISG15 conjugation to both host and viral proteins in a variety of ways. Here we report nearly complete backbone 1HN, 15N, 13CO, and 13Ca, as well as side chain 13Cb, methyl (Ile-d1, Leu, Val), amide (Asn, Gln), and indole NH (Trp) NMR resonance assignments for the 157-residue human ISG15 protein. These resonance assignments provide the basis for future structural and functional solution NMR studies of the biologically important human ISG15 protein. 4. Easy and unambiguous sequential assignments of intrinsically disordered proteins by correlating the backbone {sup 15}N or {sup 13}C′ chemical shifts of multiple contiguous residues in highly resolved 3D spectra Energy Technology Data Exchange (ETDEWEB) Yoshimura, Yuichi; Kulminskaya, Natalia V.; Mulder, Frans A. A., E-mail: fmulder@chem.au.dk [Aarhus University, Department of Chemistry and Interdisciplinary Nanoscience Center (iNANO) (Denmark) 2015-02-15 Sequential resonance assignment strategies are typically based on matching one or two chemical shifts of adjacent residues. However, resonance overlap often leads to ambiguity in resonance assignments in particular for intrinsically disordered proteins. We investigated the potential of establishing connectivity through the three-bond couplings between sequentially adjoining backbone carbonyl carbon nuclei, combined with semi-constant time chemical shift evolution, for resonance assignments of small folded and larger unfolded proteins. Extended sequential connectivity strongly lifts chemical shift degeneracy of the backbone nuclei in disordered proteins. We show here that 3D (H)N(COCO)NH and (HN)CO(CO)NH experiments with relaxation-optimized multiple pulse mixing correlate up to seven adjacent backbone amide nitrogen or carbonyl carbon nuclei, respectively, and connections across proline residues are also obtained straightforwardly. Multiple, recurrent long-range correlations with ultra-high resolution allow backbone {sup 1}H{sup N}, {sup 15}N{sup H}, and {sup 13}C′ resonance assignments to be completed from a single pair of 3D experiments. 5. (H)N(COCA)NH and HN(COCA)NH experiments for 1H-15N backbone assignments in 13C/15N-labeled proteins Energy Technology Data Exchange (ETDEWEB) Bracken, Clay; Palmer, Arthur G. III [Columbia University, Department of Biochemistry and Molecular Biophysics (United States); Cavanagh, John [New York State Department of Health, NMR Structural Biology Facility, Wadsworth Center (United States) 1997-01-15 Triple resonance HN(COCA)NH pulse sequences for correlating 1H(i), 15N(i),1H(i-1), and 15N(i-1) spins that utilize overlapping coherence transfer periods provide increased sensitivity relative to pulse sequences that utilize sequential coherence transfer periods. Although the overlapping sequence elements reduce the overall duration of the pulse sequences, the principal benefit derives from a reduction in the number of 180 deg. pulses. Two versions of the technique are presented: a 3D (H)N(COCA)NH experiment that correlates 15N(i),1H(i-1), and 15N(i-1) spins, and a 3D HN(COCA)NH experiment that correlates 1H(i), 15N(i),1H(i-1), and 15N(i-1) spins by simultaneously encoding the 1H(i) and 15N(i) chemical shifts during the t1 evolution period. The methods are demonstrated on a 13C/15N-enriched sample of the protein ubiquitin and are easily adapted for application to 2H/13C/15N-enriched proteins. 6. (15)N Heteronuclear Chemical Exchange Saturation Transfer MRI. Science.gov (United States) Zeng, Haifeng; Xu, Jiadi; Yadav, Nirbhay N; McMahon, Michael T; Harden, Bradley; Frueh, Dominique; van Zijl, Peter C M 2016-09-01 A two-step heteronuclear enhancement approach was combined with chemical exchange saturation transfer (CEST) to magnify (15)N MRI signal of molecules through indirect detection via water protons. Previous CEST studies have been limited to radiofrequency (rf) saturation transfer or excitation transfer employing protons. Here, the signal of (15)N is detected indirectly through the water signal by first inverting selectively protons that are scalar-coupled to (15)N in the urea molecule, followed by chemical exchange of the amide proton to bulk water. In addition to providing a small sensitivity enhancement, this approach can be used to monitor the exchange rates and thus the pH sensitivity of the participating (15)N-bound protons. PMID:27548755 7. Combining automated peak tracking in SAR by NMR with structure-based backbone assignment from 15N-NOESY KAUST Repository Jang, Richard 2012-03-21 Background: Chemical shift mapping is an important technique in NMR-based drug screening for identifying the atoms of a target protein that potentially bind to a drug molecule upon the molecule\\'s introduction in increasing concentrations. The goal is to obtain a mapping of peaks with known residue assignment from the reference spectrum of the unbound protein to peaks with unknown assignment in the target spectrum of the bound protein. Although a series of perturbed spectra help to trace a path from reference peaks to target peaks, a one-to-one mapping generally is not possible, especially for large proteins, due to errors, such as noise peaks, missing peaks, missing but then reappearing, overlapped, and new peaks not associated with any peaks in the reference. Due to these difficulties, the mapping is typically done manually or semi-automatically, which is not efficient for high-throughput drug screening.Results: We present PeakWalker, a novel peak walking algorithm for fast-exchange systems that models the errors explicitly and performs many-to-one mapping. On the proteins: hBclXL, UbcH5B, and histone H1, it achieves an average accuracy of over 95% with less than 1.5 residues predicted per target peak. Given these mappings as input, we present PeakAssigner, a novel combined structure-based backbone resonance and NOE assignment algorithm that uses just 15N-NOESY, while avoiding TOCSY experiments and 13C-labeling, to resolve the ambiguities for a one-to-one mapping. On the three proteins, it achieves an average accuracy of 94% or better.Conclusions: Our mathematical programming approach for modeling chemical shift mapping as a graph problem, while modeling the errors directly, is potentially a time- and cost-effective first step for high-throughput drug screening based on limited NMR data and homologous 3D structures. 2012 Jang et al.; licensee BioMed Central Ltd. 8. Backbone dynamics of free barnase and its complex with barstar determined by 15N NMR relaxation study International Nuclear Information System (INIS) Backbone dynamics of uniformly 15N-labeled free barnase and its complex with unlabelled barstar have been studied at 40 deg. C, pH 6.6, using 15N relaxation data obtained from proton-detected 2D {1H}-15N NMR spectroscopy. 15N spin-lattice relaxation rate constants (R1), spin-spin relaxation rate constants (R2), and steady-state heteronuclear {1H}-15N NOEs have been measured at a magnetic field strength of 14.1 Tesla for 91 residues of free barnase and for 90 residues out of a total of 106 in the complex (excluding three prolines and the N-terminal residue) backbone amide 15N sites of barnase. The primary relaxation data for both the cases have been analyzed in the framework of the model-free formalism using both isotropic and axially symmetric models of the rotational diffusion tensor. As per the latter, the overall rotational correlation times (τm) are 5.0 and 9.5 ns for the free and complexed barnase, respectively. The average order parameter is found to be 0.80 for free barnase and 0.86 for the complex. However, the changes are not uniform along the backbone and for about 5 residues near the binding interface there is actually a significant decrease in the order parameters on complex formation. These residues are not involved in the actual binding. For the residues where the order parameter increases, the magnitudes vary significantly. It is observed that the complex has much less internal mobility, compared to free barnase. From the changes in the order parameters, the entropic contribution of NH bond vector motion to the free energy of complex formation has been calculated. It is apparent that these motions cause significant unfavorable contributions and therefore must be compensated by many other favorable contributions to effect tight complex formation. The observed variations in the motion and their different locations with regard to the binding interface may have important implications for remote effects and regulation of the enzyme action 9. Backbone dynamics of free barnase and its complex with barstar determined by 15N NMR relaxation study Energy Technology Data Exchange (ETDEWEB) Sahu, Sarata C. [Tata Institute of Fundamental Research, Department of Chemical Sciences (India); Bhuyan, Abani K.; Udgaonkar, Jayant B. [University of Agricultural Sciences (UAS), National Centre for Biological Sciences, Tata Institute of Fundamental Research (India); Hosur, R.V. [Tata Institute of Fundamental Research, Department of Chemical Sciences (India) 2000-10-15 Backbone dynamics of uniformly {sup 15}N-labeled free barnase and its complex with unlabelled barstar have been studied at 40 deg. C, pH 6.6, using {sup 15}N relaxation data obtained from proton-detected 2D {l_brace}{sup 1}H{r_brace}-{sup 15}N NMR spectroscopy. {sup 15}N spin-lattice relaxation rate constants (R{sub 1}), spin-spin relaxation rate constants (R{sub 2}), and steady-state heteronuclear {l_brace}{sup 1}H{r_brace}-{sup 15}N NOEs have been measured at a magnetic field strength of 14.1 Tesla for 91 residues of free barnase and for 90 residues out of a total of 106 in the complex (excluding three prolines and the N-terminal residue) backbone amide {sup 15}N sites of barnase. The primary relaxation data for both the cases have been analyzed in the framework of the model-free formalism using both isotropic and axially symmetric models of the rotational diffusion tensor. As per the latter, the overall rotational correlation times ({tau}{sub m}) are 5.0 and 9.5 ns for the free and complexed barnase, respectively. The average order parameter is found to be 0.80 for free barnase and 0.86 for the complex. However, the changes are not uniform along the backbone and for about 5 residues near the binding interface there is actually a significant decrease in the order parameters on complex formation. These residues are not involved in the actual binding. For the residues where the order parameter increases, the magnitudes vary significantly. It is observed that the complex has much less internal mobility, compared to free barnase. From the changes in the order parameters, the entropic contribution of NH bond vector motion to the free energy of complex formation has been calculated. It is apparent that these motions cause significant unfavorable contributions and therefore must be compensated by many other favorable contributions to effect tight complex formation. The observed variations in the motion and their different locations with regard to the binding interface 10. Sequence-specific 1H, 13C and 15N backbone resonance assignments of the plakin repeat domain of human envoplakin. Science.gov (United States) Jeeves, Mark; Fogl, Claudia; Al-Jassar, Caezar; Chidgey, Martyn; Overduin, Michael 2016-04-01 The plakin repeat domain is a distinctive hallmark of the plakin superfamily of proteins, which are found within all epithelial tissues. Plakin repeat domains mediate the interactions of these proteins with the cell cytoskeleton and are critical for the maintenance of tissue integrity. Despite their biological importance, no solution state resonance assignments are available for any homologue. Here we report the essentially complete (1)H, (13)C and (15)N backbone chemical shift assignments of the singular 22 kDa plakin repeat domain of human envoplakin, providing the means to investigate its interactions with ligands including intermediate filaments. PMID:26590577 11. Unraveling the complexity of protein backbone dynamics with combined (13)C and (15)N solid-state NMR relaxation measurements. Science.gov (United States) Lamley, Jonathan M; Lougher, Matthew J; Sass, Hans Juergen; Rogowski, Marco; Grzesiek, Stephan; Lewandowski, Józef R 2015-09-14 Typically, protein dynamics involve a complex hierarchy of motions occurring on different time scales between conformations separated by a range of different energy barriers. NMR relaxation can in principle provide a site-specific picture of both the time scales and amplitudes of these motions, but independent relaxation rates sensitive to fluctuations in different time scale ranges are required to obtain a faithful representation of the underlying dynamic complexity. This is especially pertinent for relaxation measurements in the solid state, which report on dynamics in a broader window of time scales by more than 3 orders of magnitudes compared to solution NMR relaxation. To aid in unraveling the intricacies of biomolecular dynamics we introduce (13)C spin-lattice relaxation in the rotating frame (R1ρ) as a probe of backbone nanosecond-microsecond motions in proteins in the solid state. We present measurements of (13)C'R1ρ rates in fully protonated crystalline protein GB1 at 600 and 850 MHz (1)H Larmor frequencies and compare them to (13)C'R1, (15)N R1 and R1ρ measured under the same conditions. The addition of carbon relaxation data to the model free analysis of nitrogen relaxation data leads to greatly improved characterization of time scales of protein backbone motions, minimizing the occurrence of fitting artifacts that may be present when (15)N data is used alone. We also discuss how internal motions characterized by different time scales contribute to (15)N and (13)C relaxation rates in the solid state and solution state, leading to fundamental differences between them, as well as phenomena such as underestimation of picosecond-range motions in the solid state and nanosecond-range motions in solution. 12. Effects of ion binding on the backbone dynamics of calbindin D9k determined by 15N NMR relaxation. Science.gov (United States) Akke, M; Skelton, N J; Kördel, J; Palmer, A G; Chazin, W J 1993-09-21 The backbone dynamics of apo- and (Cd2+)1-calbindin D9k have been characterized by 15N nuclear magnetic resonance spectroscopy. Spin-lattice and spin-spin relaxation rate constants and steady-state [1H]-15N nuclear Overhauser effects were measured at a magnetic field strength of 11.74 T by two-dimensional, proton-detected heteronuclear NMR experiments using 15N-enriched samples. The relaxation parameters were analyzed using a model-free formalism that characterizes the dynamics of the N-H bond vectors in terms of generalized order parameters and effective correlation times. The data for the apo and (Cd2+)1 states were compared to those for the (Ca2+)2 state [Kördel, J., Skelton, N. J., Akke, M., Palmer, A. G., & Chazin, W. J. (1992) Biochemistry 31, 4856-4866] to ascertain the effects on ion ligation on the backbone dynamics of calbindin D9k. The two binding loops respond differently to ligation by metal ions: high-frequency (10(9)-10(12) s-1) fluctuations of the N-terminal ion-binding loop are not affected by ion binding, whereas residues G57, D58, G59, and E60 in the C-terminal ion-binding loop have significantly lower order parameters in the apo state than in the metal-bound states. The dynamical responses of the four helices to binding of ions are much smaller than that for the C-terminal binding loop, with the strongest effect on helix III, which is located between the linker loop and binding site II. Significant fluctuations on slower time scales also were detected in the unoccupied N-terminal ion-binding loop of the apo and (Cd2+)1 states; the apparent rates were greater for the (Cd2+)1 state. These results on the dynamical response to ion binding in calbindin D9k provide insights into the molecular details of the binding process and qualitative evidence for entropic contributions to the cooperative phenomenon of calcium binding for the pathway in which the ion binds first in the C-terminal site. PMID:8373781 13. Backbone and sidechain 1H, 15N and 13C assignments of Tyrosine Phosphatase related to Biofilm formation A (TpbA) of Pseudomonas aeruginosa OpenAIRE Koveal, Dorothy; Jayasundera, Thusitha B.; Wood, Thomas K.; Peti, Wolfgang; Page, Rebecca 2012-01-01 The backbone and side chain resonance assignments of the Tyrosine Phosphatase related to Biofilm formation A (TpbA) of Pseudomonas aeruginosa have been determined based on triple-resonance experiments using uniformly [13C,15N]-labeled protein. This assignment is the first step towards the determination of the 3-dimensional structure of TpbA. 14. Predicting 15N chemical shifts in proteins using the preceding residue-specific individual shielding surfaces from φ, ψi-1, and χ1torsion angles International Nuclear Information System (INIS) Empirical shielding surfaces are most commonly used to predict chemical shifts in proteins from known backbone torsion angles, φ and ψ. However, the prediction of 15N chemical shifts using this technique is significantly poorer, compared to that for the other nuclei such as 1Hα, 13Cα, and 13Cβ. In this study, we investigated the effects from the preceding residue and the side-chain geometry, χ1, on 15N chemical shifts by statistical methods. For an amino acid sequence XY, the 15N chemical shift of Y is expressed as a function of the amino acid types of X and Y, as well as the backbone torsion angles, φ and ψi-1. Accordingly, 380 empirical 'Preceding Residue Specific Individual (PRSI)' 15N chemical shift shielding surfaces, representing all the combinations of X and Y (except for Y=Pro), were built and used to predict 15N chemical shift from φ and ψi-1. We further investigated the χ1 effects, which were found to account for differences in 15N chemical shifts by ∼5 ppm for amino acids Val, Ile, Thr, Phe, His, Tyr, and Trp. Taking the χ1 effects into account, the χ1-calibrated PRSI shielding surfaces (XPRSI) were built and used to predict 15N chemical shifts for these amino acids. We demonstrated that 15N chemical shift predictions are significantly improved by incorporating the preceding residue and χ1 effects. The present PRSI and XPRSI shielding surfaces were extensively compared with three recently published programs, SHIFTX (Neal et al., 2003), SHIFTS (Xu and Case, 2001 and 2002), and PROSHIFT (Meiler, 2003) on a set of ten randomly selected proteins. A set of Java programs using XPRSI shielding surfaces to predict 15N chemical shifts in proteins were developed and are freely available for academic users at http://www.pronmr.com or by sending email to one of the authors Yunjun Wang 15. CO{sub H}(N)CACB experiments for assigning backbone resonances in {sup 13}C/{sup 15}N-labeled proteins Energy Technology Data Exchange (ETDEWEB) Astrof, Nathan; Bracken, Clay; Cavanagh, John; Palmer, Arthur G 1998-05-15 A triple resonance NMR experiment, denoted CO{sub H}(N)CACB, correlates{sup 1}H{sup N} and {sup 13}CO spins with the{sup 13}C{sup {alpha}} and{sup 13}C{sup {beta}} spins of adjacent amino acids. The pulse sequence is an 'out-and-back' design that starts with{sup 1}H{sup N} magnetization and transfers coherence via the {sup 15}N spin simultaneously to the {sup 13}CO and{sup 13}C{sup {alpha}} spins, followed by transfer to the{sup 13}C{sup {beta}} spin. Two versions of the sequence are presented: one in which the {sup 13}CO spins are frequency labeled during an incremented t{sub 1} evolution period prior to transfer of magnetization from the {sup 13}C{sup {alpha}} to the{sup 13}C{sup {beta}} resonances, and one in which the{sup 13}CO spins are frequency labeled in a constant-time manner during the coherence transfer to and from the{sup 13}C{sup {beta}} resonances. Because {sup 13}COand {sup 15}N chemical shifts are largely uncorrelated, the technique will be especially useful when degeneracy in the{sup 1}H{sup N}-{sup 15}N chemical shifts hinders resonance assignment. The CO{sub H}(N)CACB experiment is demonstrated using uniformly {sup 13}C/{sup 15}N-labeled ubiquitin. 16. Protein backbone chemical shifts predicted from searching a database for torsion angle and sequence homology International Nuclear Information System (INIS) Chemical shifts of nuclei in or attached to a protein backbone are exquisitely sensitive to their local environment. A computer program, SPARTA, is described that uses this correlation with local structure to predict protein backbone chemical shifts, given an input three-dimensional structure, by searching a newly generated database for triplets of adjacent residues that provide the best match in φ/ψ/χ1 torsion angles and sequence similarity to the query triplet of interest. The database contains 15N, 1HN, 1Hα, 13Cα, 13Cβ and 13C' chemical shifts for 200 proteins for which a high resolution X-ray (≤2.4 A) structure is available. The relative importance of the weighting factors for the φ/ψ/χ1 angles and sequence similarity was optimized empirically. The weighted, average secondary shifts of the central residues in the 20 best-matching triplets, after inclusion of nearest neighbor, ring current, and hydrogen bonding effects, are used to predict chemical shifts for the protein of known structure. Validation shows good agreement between the SPARTA-predicted and experimental shifts, with standard deviations of 2.52, 0.51, 0.27, 0.98, 1.07 and 1.08 ppm for 15N, 1HN, 1Hα, 13Cα, 13Cβ and 13C', respectively, including outliers 17. Proton-detected 3D (15)N/(1)H/(1)H isotropic/anisotropic/isotropic chemical shift correlation solid-state NMR at 70kHz MAS. Science.gov (United States) Pandey, Manoj Kumar; Yarava, Jayasubba Reddy; Zhang, Rongchun; Ramamoorthy, Ayyalusamy; Nishiyama, Yusuke 2016-01-01 Chemical shift anisotropy (CSA) tensors offer a wealth of information for structural and dynamics studies of a variety of chemical and biological systems. In particular, CSA of amide protons can provide piercing insights into hydrogen-bonding interactions that vary with the backbone conformation of a protein and dynamics. However, the narrow span of amide proton resonances makes it very difficult to measure (1)H CSAs of proteins even by using the recently proposed 2D (1)H/(1)H anisotropic/isotropic chemical shift (CSA/CS) correlation technique. Such difficulties due to overlapping proton resonances can in general be overcome by utilizing the broad span of isotropic chemical shifts of low-gamma nuclei like (15)N. In this context, we demonstrate a proton-detected 3D (15)N/(1)H/(1)H CS/CSA/CS correlation experiment at fast MAS frequency (70kHz) to measure (1)H CSA values of unresolved amide protons of N-acetyl-(15)N-l-valyl-(15)N-l-leucine (NAVL). 18. Post-translational heterocyclic backbone modifications in the 43-peptide antibiotic microcin B17. Structure elucidation and NMR study of a 13C,15N-labelled gyrase inhibitor. Science.gov (United States) Bayer, A; Freund, S; Jung, G 1995-12-01 Microcin B17 (McB17), the first known gyrase inhibitor of peptidic nature, is produced by ribosomal synthesis and post-translational modification of the 69-residue precursor protein by an Escherichia coli strain. To elucidate the chemical structure of the mature 43-residue peptide antibiotic, fermentation and purification protocols were established and optimized which allowed the isolation and purification of substantial amounts of highly pure McB17 (non-labelled, 15N-labelled and 13C/15N-labelled peptide. By ultraviolet-absorption spectroscopy. HPLC-electrospray mass spectrometry and GC-mass spectrometry, amino acid analysis, protein sequencing, and, in particular, multidimensional NMR, we could demonstrate and unequivocally prove that the enzymic modification of the precursor backbone at Gly-Cys and Gly-Ser segments leads to the formation of 2-aminomethylthiazole-4-carboxylic acid and 2-aminomethyloxazole-4-carboxylic acid, respectively. In addition, two bicyclic modifications 2-(2-aminomethyloxazolyl)thiazole-4-carboxylic acid and 2-(2-aminomethylthiazolyl)oxazole-4-carboxylic acid were found that consist of directly linked thiazole and oxazole rings derived from one Gly-Ser-Cys and one Gly-Cys-Ser segment. Analogous to the thiazole and oxazole rings found in antitumor peptides of microbial and marine origin, these heteroaromatic ring systems of McB17 presumably play an important role in its gyrase-inhibiting activity, e.g. interacting with the DNA to trap the covalent protein-DNA intermediate of the breakage-reunion reaction of the gyrase. 19. Backbone dynamics of a biologically active human FGF-1 monomer, complexed to a hexasaccharide heparin-analogue, by {sup 15}N NMR relaxation methods Energy Technology Data Exchange (ETDEWEB) Canales-Mayordomo, Angeles; Fayos, Rosa [Centro de Investigaciones Biologicas, CSIC, Departamento de Estructura y Funcion de Proteinas (Spain); Angulo, Jesus; Ojeda, Rafael [Instituto de Investigaciones Quimicas, CSIC, Grupo de Carbohidratos (Spain); Martin-Pastor, Manuel [Unidad de RM y Unidad de RMN de Biomoleculas Asociada al CSIC, Laboratorio de Estructura e Estructura de Biomoleculas Jose Carracido (Spain); Nieto, Pedro M.; Martin-Lomas, Manuel [Instituto de Investigaciones Quimicas, CSIC, Grupo de Carbohidratos (Spain); Lozano, Rosa; Gimenez-Gallego, Guillermo; Jimenez-Barbero, Jesus [Centro de Investigaciones Biologicas, CSIC, Departamento de Estructura y Funcion de Proteinas (Spain)], E-mail: jjbarbero@cib.csic.es 2006-08-15 The binding site and backbone dynamics of a bioactive complex formed by the acidic fibroblast growth factor (FGF-1) and a specifically designed heparin hexasaccharide has been investigated by HSQC and relaxation NMR methods. The comparison of the relaxation data for the free and bound states has allowed showing that the complex is monomeric, and still induces mutagenesis, and that the protein backbone presents reduced motion in different timescale in its bound state, except in certain points that are involved in the interaction with the fibroblast growth factor receptor (FGFR) 20. 1H, 15N and 13C backbone assignments of GDP-bound human H-Ras mutant G12V. Science.gov (United States) Amin, Nader; Chiarparin, Elisabetta; Coyle, Joe; Nietlispach, Daniel; Williams, Glyn 2016-04-01 Harvey Ras (H-Ras) is a membrane-associated GTPase with critical functions in cell proliferation and differentiation. The G12V mutant of H-Ras is one of the most commonly encountered oncoproteins in human cancer. This mutation disrupts the GTPase activity of H-Ras, leading to constitutive activation and aberrant downstream signalling. Here we report the backbone resonance assignments of human H-Ras mutant G12V lacking the C-terminal membrane attachment domain. 1. Qualitative Study of Substituent Effects on NMR 15N and 17O Chemical Shifts Science.gov (United States) Contreras, Rubén H.; Llorente, Tomás; Pagola, Gabriel I.; Bustamante, Manuel G.; Pasqualini, Enrique E.; Melo, Juan I.; Tormena, Cláudio F. 2009-08-01 A qualitative approach to analyze the electronic origin of substituent effects on the paramagnetic part of chemical shifts is described and applied to few model systems, where its potentiality can be appreciated. The formulation of this approach is based on the following grounds. The influence of different inter- or intramolecular interactions on a second-order property can be qualitatively predicted if it can be known how they affect the main virtual excitations entering into that second-order property. A set of consistent approximations are introduced in order to analyze the behavior of occupied and virtual orbitals that define some experimental trends of magnetic shielding constants. This approach is applied first to study the electronic origin of methyl-β substituent effects on both 15N and 17O chemical shifts, and afterward it is applied to a couple of examples of long-range substituent effects originated in charge transfer interactions such as the conjugative effect in aromatic compounds and σ-hyperconjugative interactions in saturated multicyclic compounds. 2. Qualitative study of substituent effects on NMR (15)N and (17)O chemical shifts. Science.gov (United States) Contreras, Rubén H; Llorente, Tomás; Pagola, Gabriel I; Bustamante, Manuel G; Pasqualini, Enrique E; Melo, Juan I; Tormena, Cláudio F 2009-09-10 A qualitative approach to analyze the electronic origin of substituent effects on the paramagnetic part of chemical shifts is described and applied to few model systems, where its potentiality can be appreciated. The formulation of this approach is based on the following grounds. The influence of different inter- or intramolecular interactions on a second-order property can be qualitatively predicted if it can be known how they affect the main virtual excitations entering into that second-order property. A set of consistent approximations are introduced in order to analyze the behavior of occupied and virtual orbitals that define some experimental trends of magnetic shielding constants. This approach is applied first to study the electronic origin of methyl-beta substituent effects on both (15)N and (17)O chemical shifts, and afterward it is applied to a couple of examples of long-range substituent effects originated in charge transfer interactions such as the conjugative effect in aromatic compounds and sigma-hyperconjugative interactions in saturated multicyclic compounds. PMID:19685922 3. The HSP90 binding mode of a radicicol-like E-oxime from docking, binding free energy estimations, and NMR 15N chemical shifts Science.gov (United States) Spichty, Martin; Taly, Antoine; Hagn, Franz; Kessler, Horst; Barluenga, Sofia; Winssinger, Nicolas; Karplus, Martin 2009-01-01 We determine the binding mode of a macrocyclic radicicol-like oxime to yeast HSP90 by combining computer simulations and experimental measurements. We sample the macrocyclic scaffold of the unbound ligand by parallel tempering simulations and dock the most populated conformations to yeast HSP90. Docking poses are then evaluated by the use of binding free energy estimations with the linear interaction energy method. Comparison of QM/MM-calculated NMR chemical shifts with experimental shift data for a selective subset of back-bone 15N provides an additional evaluation criteria. As a last test we check the binding modes against available structure-activity-relationships. We find that the most likely binding mode of the oxime to yeast HSP90 is very similar to the known structure of the radicicol-HSP90 complex. PMID:19482409 4. Detection of closed influenza virus hemagglutinin fusion peptide structures in membranes by backbone {sup 13}CO-{sup 15}N rotational-echo double-resonance solid-state NMR Energy Technology Data Exchange (ETDEWEB) Ghosh, Ujjayini; Xie Li; Weliky, David P., E-mail: weliky@chemistry.msu.edu [Michigan State University, Department of Chemistry (United States) 2013-02-15 The influenza virus fusion peptide is the N-terminal {approx}20 residues of the HA2 subunit of the hemagglutinin protein and this peptide plays a key role in the fusion of the viral and endosomal membranes during initial infection of a cell. The fusion peptide adopts N-helix/turn/C-helix structure in both detergent and membranes with reports of both open and closed interhelical topologies. In the present study, backbone {sup 13}CO-{sup 15}N REDOR solid-state NMR was applied to the membrane-associated fusion peptide to detect the distribution of interhelical distances. The data clearly showed a large fraction of closed and semi-closed topologies and were best-fitted to a mixture of two structures that do not exchange. One of the earlier open structural models may have incorrect G13 dihedral angles derived from TALOS analysis of experimentally correct {sup 13}C shifts. 5. (1)H, (13)C, (15)N backbone and side-chain resonance assignment of Nostoc sp. C139A variant of the heme-nitric oxide/oxygen binding (H-NOX) domain. Science.gov (United States) Alexandropoulos, Ioannis I; Argyriou, Aikaterini I; Marousis, Kostas D; Topouzis, Stavros; Papapetropoulos, Andreas; Spyroulias, Georgios A 2016-10-01 The H-NOX (Heme-nitric oxide/oxygen binding) domain is conserved across eukaryotes and bacteria. In human soluble guanylyl cyclase (sGC) the H-NOX domain functions as a sensor for the gaseous signaling agent nitric oxide (NO). sGC contains the heme-binding H-NOX domain at its N-terminus, which regulates the catalytic site contained within the C-terminal end of the enzyme catalyzing the conversion of GTP (guanosine 5'-triphosphate) to GMP (guanylyl monophosphate). Here, we present the backbone and side-chain assignments of the (1)H, (13)C and (15)N resonances of the 183-residue H-NOX domain from Nostoc sp. through solution NMR. 6. (1)H, (13)C, and (15)N backbone resonance assignments of the full-length 40 kDa S. acidocaldarius Y-family DNA polymerase, dinB homolog. Science.gov (United States) Moro, Sean L; Cocco, Melanie J 2015-10-01 The dinB homolog (Dbh) is a member of the Y-family of translesion DNA polymerases, which are specialized to accurately replicate DNA across from a wide variety of lesions in living cells. Lesioned bases block the progression of high-fidelity polymerases and cause detrimental replication fork stalling; Y-family polymerases can bypass these lesions. The active site of the translesion synthesis polymerase is more open than that of a replicative polymerase; consequently Dbh polymerizes with low fidelity. Bypass polymerases also have low processivity. Short extension past the lesion allows the high-fidelity polymerase to switch back onto the site of replication. Dbh and the other Y-family polymerases have been used as structural models to investigate the mechanisms of DNA polymerization and lesion bypass. Many high-resolution crystal structures of Y-family polymerases have been reported. NMR dynamics studies can complement these structures by providing a measure of protein motions. Here we report the (15)N, (1)H, and (13)C backbone resonance assignments at two temperatures (35 and 50 °C) for Sulfolobus acidocaldarius Dbh polymerase. Backbone resonance assignments have been obtained for 86 % of the residues. The polymerase active site is assigned as well as the majority of residues in each of the four domains. PMID:26154586 7. Automated prediction of 15N, 13Cα, 13Cβ and 13C' chemical shifts in proteins using a density functional database International Nuclear Information System (INIS) A database of peptide chemical shifts, computed at the density functional level, has been used to develop an algorithm for prediction of 15N and 13C shifts in proteins from their structure; the method is incorporated into a program called SHIFTS (version 4.0). The database was built from the calculated chemical shift patterns of 1335 peptides whose backbone torsion angles are limited to areas of the Ramachandran map around helical and sheet configurations. For each tripeptide in these regions of regular secondary structure (which constitute about 40% of residues in globular proteins) SHIFTS also consults the database for information about sidechain torsion angle effects for the residue of interest and for the preceding residue, and estimates hydrogen bonding effects through an empirical formula that is also based on density functional calculations on peptides. The program optionally searches for alternate side-chain torsion angles that could significantly improve agreement between calculated and observed shifts. The application of the program on 20 proteins shows good consistency with experimental data, with correlation coefficients of 0.92, 0.98, 0.99 and 0.90 and r.m.s. deviations of 1.94, 0.97, 1.05, and 1.08 ppm for 15N, 13Cα, 13Cβ and 13C', respectively. Reference shifts fit to protein data are in good agreement with 'random-coil' values derived from experimental measurements on peptides. This prediction algorithm should be helpful in NMR assignment, crystal and solution structure comparison, and structure refinement 8. Inferential protein structure determination and refinement using fast, electronic structure based backbone amide chemical shift predictions CERN Document Server Christensen, Anders S 2015-01-01 This report covers the development of a new, fast method for calculating the backbone amide proton chemical shifts in proteins. Through quantum chemical calculations, structure-based forudsiglese the chemical shift for amidprotonen in protein has been parameterized. The parameters are then implemented in a computer program called Padawan. The program has since been implemented in protein folding program Phaistos, wherein the method andvendes to de novo folding of the protein structures and to refine the existing protein structures. 9. Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks Energy Technology Data Exchange (ETDEWEB) Shen Yang; Bax, Ad, E-mail: bax@nih.gov [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States) 2013-07-15 A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, {>=}90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed ({phi}, {psi}) torsion angles of ca 12 Masculine-Ordinal-Indicator . TALOS-N also reports sidechain {chi}{sup 1} rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts. 10. Essential roles of four-carbon backbone chemicals in the control of metabolism Institute of Scientific and Technical Information of China (English) Sabrina; Chriett; Luciano; Pirola 2015-01-01 The increasing incidence of obesity worldwide and its related cardiometabolic complications is an urgent public health problem. While weight gain results from a negative balance between the energy expenditure and calorie intake, recent research has demonstrated that several small organic molecules containing a four-carbon backbone can modulate this balance by favoring energy expenditure, and alleviating endoplasmic reticulum stress and oxidative stress. Such small molecules include the bacterially produced short chain fatty acid butyric acid, its chemically produced derivative 4-phenylbutyric acid, the main ketone body D-β-hydroxybutyrate- synthesized by the liver- and the recently discovered myokine β-aminoisobutyric acid. Conversely, another butyraterelated molecule, α-hydroxybutyrate, has been found to be an early predictor of insulin resistance and glucose intolerance. In this minireview, we summarize recent advances in the understanding of the mechanism of action of these molecules, and discuss their use as therapeutics to improve metabolic homeostasis or their detection as early biomarkers of incipient insulin resistance. 11. Quantum chemical benchmark study on 46 RNA backbone families using a dinucleotide unit. Science.gov (United States) Kruse, Holger; Mladek, Arnost; Gkionis, Konstantinos; Hansen, Andreas; Grimme, Stefan; Sponer, Jiri 2015-10-13 We have created a benchmark set of quantum chemical structure-energy data denoted as UpU46, which consists of 46 uracil dinucleotides (UpU), representing all known 46 RNA backbone conformational families. Penalty-function-based restrained optimizations with COSMO TPSS-D3/def2-TZVP ensure a balance between keeping the target conformation and geometry relaxation. The backbone geometries are close to the clustering-means of their respective RNA bioinformatics family classification. High-level wave function methods (DLPNO-CCSD(T) as reference) and a wide-range of dispersion-corrected or inclusive DFT methods (DFT-D3, VV10, LC-BOP-LRD, M06-2X, M11, and more) are used to evaluate the conformational energies. The results are compared to the Amber RNA bsc0χOL3 force field. Most dispersion-corrected DFT methods surpass the Amber force field significantly in accuracy and yield mean absolute deviations (MADs) for relative conformational energies of ∼0.4-0.6 kcal/mol. Double-hybrid density functionals represent the most accurate class of density functionals. Low-cost quantum chemical methods such as PM6-D3H+, HF-3c, DFTB3-D3, as well as small basis set calculations corrected for basis set superposition errors (BSSEs) by the gCP procedure are also tested. Unfortunately, the presently available low-cost methods are struggling to describe the UpU conformational energies with satisfactory accuracy. The UpU46 benchmark is an ideal test for benchmarking and development of fast methods to describe nucleic acids, including force fields. PMID:26574283 12. ¹H and (15)N NMR Analyses on Heparin, Heparan Sulfates and Related Monosaccharides Concerning the Chemical Exchange Regime of the N-Sulfo-Glucosamine Sulfamate Proton. Science.gov (United States) Pomin, Vitor H 2016-01-01 Heparin and heparan sulfate are structurally related glycosaminoglycans (GAGs). Both GAGs present, although in different concentrations, N-sulfo-glucosamine (GlcNS) as one of their various composing units. The conditional fast exchange property of the GlcNS sulfamate proton in these GAGs has been pointed as the main barrier to its signal detection via NMR experiments, especially ¹H-(15)N HSQC. Here, a series of NMR spectra is collected on heparin, heparan sulfate and related monosaccharides. The N-acetyl glucosamine-linked uronic acid types of these GAGs were properly assigned in the ¹H-(15)N HSQC spectra. Dynamic nuclear polarization (DNP) was employed in order to facilitate 1D spectral acquisition of the sulfamate (15)N signal of free GlcNS. Analyses on the multiplet pattern of scalar couplings of GlcNS (15)N has helped to understand the chemical properties of the sulfamate proton in solution. The singlet peak observed for GlcNS happens due to fast chemical exchange of the GlcNS sulfamate proton in solution. Analyses on kinetics of alpha-beta anomeric mutarotation via ¹H NMR spectra have been performed in GlcNS as well as other glucose-based monosaccharides. 1D ¹H and 2D ¹H-(15)N HSQC spectra recorded at low temperature for free GlcNS dissolved in a proton-rich solution showed signals from all exchangeable protons, including those belonging to the sulfamate group. This work suits well to the current grand celebration of one-century-anniversary of the discovery of heparin. PMID:27618066 13. ¹H and (15)N NMR Analyses on Heparin, Heparan Sulfates and Related Monosaccharides Concerning the Chemical Exchange Regime of the N-Sulfo-Glucosamine Sulfamate Proton. Science.gov (United States) Pomin, Vitor H 2016-09-07 Heparin and heparan sulfate are structurally related glycosaminoglycans (GAGs). Both GAGs present, although in different concentrations, N-sulfo-glucosamine (GlcNS) as one of their various composing units. The conditional fast exchange property of the GlcNS sulfamate proton in these GAGs has been pointed as the main barrier to its signal detection via NMR experiments, especially ¹H-(15)N HSQC. Here, a series of NMR spectra is collected on heparin, heparan sulfate and related monosaccharides. The N-acetyl glucosamine-linked uronic acid types of these GAGs were properly assigned in the ¹H-(15)N HSQC spectra. Dynamic nuclear polarization (DNP) was employed in order to facilitate 1D spectral acquisition of the sulfamate (15)N signal of free GlcNS. Analyses on the multiplet pattern of scalar couplings of GlcNS (15)N has helped to understand the chemical properties of the sulfamate proton in solution. The singlet peak observed for GlcNS happens due to fast chemical exchange of the GlcNS sulfamate proton in solution. Analyses on kinetics of alpha-beta anomeric mutarotation via ¹H NMR spectra have been performed in GlcNS as well as other glucose-based monosaccharides. 1D ¹H and 2D ¹H-(15)N HSQC spectra recorded at low temperature for free GlcNS dissolved in a proton-rich solution showed signals from all exchangeable protons, including those belonging to the sulfamate group. This work suits well to the current grand celebration of one-century-anniversary of the discovery of heparin. 14. Natural-abundance 15N NMR studies of Turkey ovomucoid third domain. Assignment of peptide 15N resonances to the residues at the reactive site region via proton-detected multiple-quantum coherence Science.gov (United States) Ortiz-Polo, Gilberto; Krishnamoorthi, R.; Markley, John L.; Live, David H.; Davis, Donald G.; Cowburn, David Heteronuclear two-dimensional 1H{ 15N} multiple-quantum (MQ) spectroscopy has been applied to a protein sample at natural abundance: ovomucoid third domain from turkey ( Meleagris gallopavo), a serine proteinase inhibitor of 56 amino acid residues. Peptide amide 1H NMR assignments obtained by two-dimensional 1H{ 1H} NMR methods (R. Krishnamoorthi and J. L. Markley, unpublished data) led to identification of the corresponding 1H{ 15N} MQ coherence cross peaks. From these, 15N NMR chemical shifts were determined for several specific backbone amide groups of amino acid residues located around the reactive site region of the inhibitor. The results suggest that amide 15N chemical shifts, which are readily obtained in this way, may serve as sensitive probes for conformational studies of proteins. 15. Quantification of protein backbone hydrogen-deuterium exchange rates by solid state NMR spectroscopy Energy Technology Data Exchange (ETDEWEB) Lopez del Amo, Juan-Miguel; Fink, Uwe; Reif, Bernd, E-mail: reif@tum.d [Leibniz-Institut fuer Molekulare Pharmakologie (FMP) (Germany) 2010-12-15 We present the quantification of backbone amide hydrogen-deuterium exchange rates (HDX) for immobilized proteins. The experiments make use of the deuterium isotope effect on the amide nitrogen chemical shift, as well as on proton dilution by deuteration. We find that backbone amides in the microcrystalline {alpha}-spectrin SH3 domain exchange rather slowly with the solvent (with exchange rates negligible within the individual {sup 15}N-T{sub 1} timescales). We observed chemical exchange for 6 residues with HDX exchange rates in the range from 0.2 to 5 s{sup -1}. Backbone amide {sup 15}N longitudinal relaxation times that we determined previously are not significantly affected for most residues, yielding no systematic artifacts upon quantification of backbone dynamics (Chevelkov et al. 2008b). Significant exchange was observed for the backbone amides of R21, S36 and K60, as well as for the sidechain amides of N38, N35 and for W41{epsilon}. These residues could not be fit in our previous motional analysis, demonstrating that amide proton chemical exchange needs to be considered in the analysis of protein dynamics in the solid-state, in case D{sub 2}O is employed as a solvent for sample preparation. Due to the intrinsically long {sup 15}N relaxation times in the solid-state, the approach proposed here can expand the range of accessible HDX rates in the intermediate regime that is not accessible so far with exchange quench and MEXICO type experiments. 16. Chemical weathering and the role of sulfuric and nitric acids in carbonate weathering: Isotopes (13C, 15N, 34S, and 18O) and chemical constraints Science.gov (United States) Li, Cai; Ji, Hongbing 2016-05-01 Multiple isotopes (13C-DIC, 34S and 18O-SO42-, 15N and 18O-NO3-) and water chemistry were used to evaluate weathering rates and associated CO2 consumption by carbonic acid and strong acids (H2SO4 and HNO3) in a typical karst watershed (Wujiang River, Southwest China). The dual sulfate isotopes indicate that sulfate is mainly derived from sulfide oxidation in coal stratum and sulfide-containing minerals, and dual nitrate isotopes indicate that nitrate is mainly derived from soil N and nitrification. The correlation between isotopic compositions and water chemistry suggests that sulfuric and nitric acids, in addition to carbonic acid, are involved in carbonate weathering. The silicate and carbonate weathering rates are 7.2 t km-2 yr-1 and 76 t km-2 yr-1, respectively. In comparison with carbonate weathering rates (43 t km-2 yr-1) by carbonic acid alone, the subsequent increase in rates indicates significant enhancement of weathering when combined with sulfuric and nitric acids. Therefore, the role of sulfuric and nitric acids in the rock weathering should be considered in the global carbon cycle. 17. Synthesis of Gemcitabine-13C, 15N2 and Gemcitabine-13C, 15N2 Metabolites Directory of Open Access Journals (Sweden) ZHU Cheng-gu;YANG Shao-zu;YAN Sheng-wang;FANG Ning-jing;CAI Ding-long;LI Gang 2014-02-01 Full Text Available Homemade urea-13C, 15N2 was used to react with 3-methyl acrylonitrile closure to form cytosine-13C, 15N2 (2,which was protected by trimethylsilylation with BSA and condensed with 2-deoxy-2,2-difluoro-D-erythro-pentofuranose-3,5-dibenzoate-1-methanesulfonate at 120 ℃ to afford blocked gemcitabine-13C, 15N2. Hydrolytic removal of the blocking groups of gemcitabine-13C, 15N2 with NaOH gave gemcitabine-13C, 15N2, and its metabolite was obtained by further hydrolytic deamination of gemcitabine-13C, 15N2. The final products were characterized and detected by HPLC, LC-MS and NMR, and confirmed that the chemical purities were higher than 98%, isotopic abundances were 99% 13C, 98% 15N, and they were suitable for drug metabolism studies. 18. Pseudo 5D HN(C)N Experiment to Facilitate the Assignment of Backbone Resonances in Proteins Exhibiting High Backbone Shift Degeneracy CERN Document Server Kumar, Dinesh; Shukla, Vaibhav Kumar; Pandey, Himanshu; Arora, Ashish; Guleria, Anupam 2014-01-01 Assignment of protein backbone resonances is most routinely carried out using triple resonance three dimensional NMR experiments involving amide 1H and 15N resonances. However for intrinsically unstructured proteins, alpha-helical proteins or proteins containing several disordered fragments, the assignment becomes problematic because of high degree of backbone shift degeneracy. In this backdrop, a novel reduced dimensionality (RD) experiment -(5,3)D-hNCO-CANH- is presented to facilitate (and/or to validate) the sequential backbone resonance assignment in such proteins. The proposed 3D NMR experiment makes use of the modulated amide 15N chemical shifts (resulting from the joint sampling along both its indirect dimensions) to resolve the ambiguity involved in connecting the neighboring amide resonances (i.e. HiNi and Hi-1Ni-1) for overlapping amide NH peaks. The experiment -encoding 5D spectral information- leads to a conventional 3D spectrum with significantly reduced spectral crowding and complexity. The impr... 19. Backbone and stereospecific (13)C methyl Ile (δ1), Leu and Val side-chain chemical shift assignments of Crc. Science.gov (United States) Sharma, Rakhi; Sahu, Bhubanananda; Ray, Malay K; Deshmukh, Mandar V 2015-04-01 Carbon catabolite repression (CCR) allows bacteria to selectively assimilate a preferred compound among a mixture of several potential carbon sources, thus boosting growth and economizing the cost of adaptability to variable nutrients in the environment. The RNA-binding catabolite repression control (Crc) protein acts as a global post-transcriptional regulator of CCR in Pseudomonas species. Crc triggers repression by inhibiting the expression of genes involved in transport and catabolism of non-preferred substrates, thus indirectly favoring assimilation of preferred one. We report here a nearly complete backbone and stereospecific (13)C methyl side-chain chemical shift assignments of Ile (δ1), Leu and Val of Crc (~ 31 kDa) from Pseudomonas syringae Lz4W. PMID:24496608 20. Pressure dependence of backbone chemical shifts in the model peptides Ac-Gly-Gly-Xxx-Ala-NH2. Science.gov (United States) Erlach, Markus Beck; Koehler, Joerg; Crusca, Edson; Kremer, Werner; Munte, Claudia E; Kalbitzer, Hans Robert 2016-06-01 For a better understanding of nuclear magnetic resonance (NMR) detected pressure responses of folded as well as unstructured proteins the availability of data from well-defined model systems are indispensable. In this work we report the pressure dependence of chemical shifts of the backbone atoms (1)H(α), (13)C(α) and (13)C' in the protected tetrapeptides Ac-Gly-Gly-Xxx-Ala-NH2 (Xxx one of the 20 canonical amino acids). Contrary to expectation the chemical shifts of these nuclei have a nonlinear dependence on pressure in the range from 0.1 to 200 MPa. The polynomial pressure coefficients B 1 and B 2 are dependent on the type of amino acid studied. The coefficients of a given nucleus show significant linear correlations suggesting that the NMR observable pressure effects in the different amino acids have at least partly the same physical cause. In line with this observation the magnitude of the second order coefficients of nuclei being direct neighbors in the chemical structure are also weakly correlated. PMID:27335085 1. Pressure dependence of backbone chemical shifts in the model peptides Ac-Gly-Gly-Xxx-Ala-NH2. Science.gov (United States) Erlach, Markus Beck; Koehler, Joerg; Crusca, Edson; Kremer, Werner; Munte, Claudia E; Kalbitzer, Hans Robert 2016-06-01 For a better understanding of nuclear magnetic resonance (NMR) detected pressure responses of folded as well as unstructured proteins the availability of data from well-defined model systems are indispensable. In this work we report the pressure dependence of chemical shifts of the backbone atoms (1)H(α), (13)C(α) and (13)C' in the protected tetrapeptides Ac-Gly-Gly-Xxx-Ala-NH2 (Xxx one of the 20 canonical amino acids). Contrary to expectation the chemical shifts of these nuclei have a nonlinear dependence on pressure in the range from 0.1 to 200 MPa. The polynomial pressure coefficients B 1 and B 2 are dependent on the type of amino acid studied. The coefficients of a given nucleus show significant linear correlations suggesting that the NMR observable pressure effects in the different amino acids have at least partly the same physical cause. In line with this observation the magnitude of the second order coefficients of nuclei being direct neighbors in the chemical structure are also weakly correlated. 2. Pseudo 5D HN(C)N experiment to facilitate the assignment of backbone resonances in proteins exhibiting high backbone shift degeneracy Energy Technology Data Exchange (ETDEWEB) Kumar, Dinesh, E-mail: dineshcbmr@gmail.com [Centre of Biomedical Research (CBMR), SGPGIMS Campus, Raibareli Road, Lucknow 226014 (India); Raikwal, Nisha [Centre of Biomedical Research (CBMR), SGPGIMS Campus, Raibareli Road, Lucknow 226014 (India); Shukla, Vaibhav Kumar; Pandey, Himanshu; Arora, Ashish [Molecular and Structural Biology Division, CSIR, Central Drug Research Institute, Lucknow 226031 (India); Guleria, Anupam, E-mail: anuguleriaphy@gmail.com [Centre of Biomedical Research (CBMR), SGPGIMS Campus, Raibareli Road, Lucknow 226014 (India) 2014-09-30 Graphical abstract: - Highlights: • A reduced dimensionality experiment – referred as pseudo 5D HN(C)N- is presented. • Encodes highly resolved 5D spectral information in a 3D spectrum. • Superior in terms of peak dispersion. • Facilitates assignment of crowded HSQC spectra of moderately sized proteins. • Modulated {sup 15}N chemical shifts are used to break the amide shift degeneracy. - Abstract: Assignment of protein backbone resonances is most routinely carried out using triple resonance three-dimensional NMR experiments involving amide {sup 1}H/{sup 15}N resonances. However for intrinsically unstructured proteins, alpha-helical proteins or proteins containing several disordered fragments, the assignment becomes problematic because of high-degree of backbone shift degeneracy. In this backdrop, a novel reduced-dimensionality (RD) experiment –(5, 3)D-hNCO-CANH- is presented to facilitate/validate the sequential backbone resonance assignment in such proteins. The proposed 3D NMR experiment makes use of the modulated amide {sup 15}N chemical shifts (resulting from the joint sampling along both its indirect dimensions) to resolve the ambiguity involved in connecting the neighboring amide resonances (i.e. H{sub i}N{sub i} and H{sub i−1}N{sub i−1}) for overlapping amide-NH peaks. The experiment -in combination with routine triple resonance 3D-NMR experiments involving backbone amide ({sup 1}H/{sup 15}N) and carbon ({sup 13}C{sup α}/{sup 13}C′) chemical shifts- will serve as a powerful complementary tool to achieve the nearly complete assignment of protein backbone resonances in a time efficient manner. 3. Evolution of the chemical (NH4) and isotopic (δ15N-NH4) composition of pig manure stored in an experimental deep pit International Nuclear Information System (INIS) during eight months, from November 2001 to July 2002 at atmospheric conditions. Ammonium concentration and its nitrogen isotopic composition were analysed weekly during the first six months and every ten days during the last two months. Ammonium concentration oscillates between 3000 and 4000 ppm, with no progressive decrease in time as it would be expected in a volatilisation process. This is caused by the loss of manure volume due to evaporation (50 % in eight months) which compensates the ammonia volatilisation and keeps the ammonium concentration stable. The nitrogen isotopic composition of the ammonium is controlled by the volatilisation process. During the first ten days, the pig manure has an isotopic composition between +8 and +10 per mille, and after eight months, it raises up to +25 per mille. However, the pig manure is not stored in the deep pits more than six months; consequently, the range of δ15NNH4 values to be considered for pig manure as an input of nitrogen contamination should be from +8 to +15 per mille. Still, this isotopic composition can be higher if manure is stored during the summer time since the higher temperatures may increase the volatilisation rate and raise the ammonium isotopic composition in a shorter period of time. Unlike synthetic fertilisers, which are characterised by a δ15N close to the 0 per mille, the organic fertilisers (pig manure) are enriched in 15N15N from +8 to +15 per mille). Therefore the nitrogen isotopic composition is a valuable tool to evaluate the origin of nitrate agricultural contaminations. As an example, nitrate nitrogen isotopic composition has been used in some areas in Catalonia to confirm that pig manure is the main contributor to the nitrate pollution in groundwaters 4. Backbone and sidechain 1H, 13C and 15N resonance assignments of the human brain-type fatty acid binding protein (FABP7) in its apo form and the holo forms binding to DHA, oleic acid, linoleic acid and elaidic acid DEFF Research Database (Denmark) Oeemig, Jesper S; Jørgensen, Mathilde L; Hansen, Mikka S; 2009-01-01 In this manuscript, we present the backbone and side chain assignments of human brain-type fatty acid binding protein, also known as FABP7, in its apo form and in four different holo forms, bound to DHA, oleic acid, linoleic acid and elaidic acid.......In this manuscript, we present the backbone and side chain assignments of human brain-type fatty acid binding protein, also known as FABP7, in its apo form and in four different holo forms, bound to DHA, oleic acid, linoleic acid and elaidic acid.... 5. Accurate determination of order parameters from 1H,15N dipolar couplings in MAS solid-state NMR experiments. Science.gov (United States) Chevelkov, Veniamin; Fink, Uwe; Reif, Bernd 2009-10-01 A reliable site-specific estimate of the individual N-H bond lengths in the protein backbone is the fundamental basis of any relaxation experiment in solution and in the solid-state NMR. The N-H bond length can in principle be influenced by hydrogen bonding, which would result in an increased N-H distance. At the same time, dynamics in the backbone induces a reduction of the experimental dipolar coupling due to motional averaging. We present a 3D dipolar recoupling experiment in which the (1)H,(15)N dipolar coupling is reintroduced in the indirect dimension using phase-inverted CP to eliminate effects from rf inhomogeneity. We find no variation of the N-H dipolar coupling as a function of hydrogen bonding. Instead, variations in the (1)H,(15)N dipolar coupling seem to be due to dynamics of the protein backbone. This is supported by the observed correlation between the H(N)-N dipolar coupling and the amide proton chemical shift. The experiment is demonstrated for a perdeuterated sample of the alpha-spectrin SH3 domain. Perdeuteration is a prerequisite to achieve high accuracy. The average error in the analysis of the H-N dipolar couplings is on the order of +/-370 Hz (+/-0.012 A) and can be as small as 150 Hz, corresponding to a variation of the bond length of +/-0.005 A. 6. Methods of 15N tracer research in biological systems International Nuclear Information System (INIS) The application of the stable isotope 15N is of increasing importance in different scientific disciplines, especially in medicine, agriculture, and the biosciences. The close correlation between the growing interest and improvements of analytical procedures resulted in remarkable advances in the 15N tracer technique. On the basis of the latest results of 15N tracer research in life sciences and agriculture methods of 15N tracer research in biological systems are compiled. The 15N methodology is considered under three headings: Chemical analysis with a description of methods of sample preparation (including different separation and isolation methods for N-containing substances of biological and agricultural origin) and special procedures converting ammonia to molecular nitrogen. Isotopic analysis with a review on the most important methods of isotopic analysis of nitrogen: mass spectrometry (including the GC-MS technique), emission spectrometry, NMR spectroscopy, and other analytical procedures. 15N-tracer techniques with a consideration of the role of the isotope dilution analysis as well as different labelling techniques and the mathematical interpretation of tracer data (modelling, N turnover experiments). In these chapters also sources of errors in chemical and isotopic analysis, the accuracy of the different methods and its importance on tracer experiments are discussed. Procedures for micro scale 15N analysis and aspects of 15N analysis on the level of natural abundance are considered. Furthermore some remarks on isotope effects in 15N tracer experiments are made. (author) 7. Orientation Preferences of Backbone Secondary Amide Functional Groups in Peptide Nucleic Acid Complexes: Quantum Chemical Calculations Reveal an Intrinsic Preference of Cationic D-Amino Acid-Based Chiral PNA Analogues for the P-form OpenAIRE Topham, Christopher M.; Smith, Jeremy C. 2006-01-01 Geometric descriptions of nonideal interresidue hydrogen bonding and backbone-base water bridging in the minor groove are established in terms of polyamide backbone carbonyl group orientation from analyses of residue junction conformers in experimentally determined peptide nucleic acid (PNA) complexes. Two types of interresidue hydrogen bonding are identified in PNA conformers in heteroduplexes with nucleic acids that adopt A-like basepair stacking. Quantum chemical calculations on the bindin... 8. Synthesis of 15N labeled glyphosate International Nuclear Information System (INIS) Amongst the actually commercialized herbicides the Glyphosate is the most used in Brazil. Its efficiency as well as the others herbicides against undesirable weeds is harmed by its final composts left at the environment. Although studies has being carried out to improve the knowledge about the herbicides behavior at the environment its complexity has led them towards innumerous to new significant research work where the use of radiolabeled composts (radiative tracers) are recommended to evaluate their bio-availability in the soil. However is the use, the manipulation and the storage of radiolabeled composts is requires an extra care under chemical safety point of view. The use of non radiolabeled composts is a world tendency especially for field researches. Under this context the presented work describes a method for the synthesis of 15N labeled glyphosate. The 15N-herbicide was undertaken by phosphometilation with the phosphit dialquil and 15N-glycine. The tests where carried out through a micro scale production plant and of equimolars amounts. At these conditions it's was possible to reach approximately a 20% of yield. At the conclusion of a best operational condition its expected to offer another important toll that shall be used in glyphosate behavior at the environment and undesirably weeds. (author) 9. Testing Backbone.js CERN Document Server Roemer, Ryan 2013-01-01 This book is packed with the step by step tutorial and instructions in recipe format helping you setup test infrastructure and gradually advance your skills to plan, develop, and test your backbone applications.If you are a JavaScript developer looking for recipes to create and implement test support for your backbone application, then this book is ideal for you. 10. Synthesis of {sup 15}N labeled glyphosate; Sintese do glifosato enriquecido com {sup 15}N Energy Technology Data Exchange (ETDEWEB) Oliveira, Claudineia R. de; Bendassolli, Jose Albertino; Tavares, Glauco Arnold; Rossete, Alexssandra L.R.M.; Tagliassachi, Romulo Barbieri; Prestes, Cleuber Vieira [Centro de Energia Nuclear na Agricultura (CENA), Piracicaba, SP (Brazil). Dept. de Isotopos Estaveis]. E-mail: crolivei@cena.usp.br 2005-07-01 Amongst the actually commercialized herbicides the Glyphosate is the most used in Brazil. Its efficiency as well as the others herbicides against undesirable weeds is harmed by its final composts left at the environment. Although studies has being carried out to improve the knowledge about the herbicides behavior at the environment its complexity has led them towards innumerous to new significant research work where the use of radiolabeled composts (radiative tracers) are recommended to evaluate their bio-availability in the soil. However is the use, the manipulation and the storage of radiolabeled composts is requires an extra care under chemical safety point of view. The use of non radiolabeled composts is a world tendency especially for field researches. Under this context the presented work describes a method for the synthesis of {sup 15}N labeled glyphosate. The {sup 15}N-herbicide was undertaken by phosphometilation with the phosphit dialquil and {sup 15}N-glycine. The tests where carried out through a micro scale production plant and of equimolars amounts. At these conditions it's was possible to reach approximately a 20% of yield. At the conclusion of a best operational condition its expected to offer another important toll that shall be used in glyphosate behavior at the environment and undesirably weeds. (author) 11. Orientation Preferences of Backbone Secondary Amide Functional Groups in Peptide Nucleic Acid Complexes: Quantum Chemical Calculations Reveal an Intrinsic Preference of Cationic D-Amino Acid-Based Chiral PNA Analogues for the P-form Energy Technology Data Exchange (ETDEWEB) Smith, Jeremy C [ORNL; Topham, Christopher [University of Heidelberg 2007-01-01 Geometric descriptions of nonideal interresidue hydrogen bonding and backbone-base water bridging in the minor groove are established in terms of polyamide backbone carbonyl group orientation from analyses of residue junction conformers in experimentally determined peptide nucleic acid (PNA) complexes. Two types of interresidue hydrogen bonding are identified in PNA conformers in heteroduplexes with nucleic acids that adopt A-like base pair stacking. Quantum chemical calculations on the binding of a water molecule to an O2 base atom in glycine-based PNA thymine dimers indicate that junctions modeled with P-form backbone conformations are lower in energy than a dimer comprising the predominant conformation observed in A-like helices. It is further shown in model systems that PNA analogs based on D-lysine are better able to preorganize in a conformation exclusive to P-form helices than is glycine-based PNA. An intrinsic preference for this conformation is also exhibited by positively charged chiral PNA dimers carrying 3-amino-D-alanine or 4-aza-D-leucine residue units that provide for additional rigidity by side-chain hydrogen bonding to the backbone carbonyl oxygen. Structural modifications stabilizing P-form helices may obviate the need for large heterocycles to target DNA pyrimidine bases via PNADNA-PNA triplex formation. Quantum chemical modeling methods are used to propose candidate PNA Hoogsteen strand designs. 12. Orientation preferences of backbone secondary amide functional groups in peptide nucleic acid complexes: quantum chemical calculations reveal an intrinsic preference of cationic D-amino acid-based chiral PNA analogues for the P-form. Science.gov (United States) Topham, Christopher M; Smith, Jeremy C 2007-02-01 Geometric descriptions of nonideal interresidue hydrogen bonding and backbone-base water bridging in the minor groove are established in terms of polyamide backbone carbonyl group orientation from analyses of residue junction conformers in experimentally determined peptide nucleic acid (PNA) complexes. Two types of interresidue hydrogen bonding are identified in PNA conformers in heteroduplexes with nucleic acids that adopt A-like basepair stacking. Quantum chemical calculations on the binding of a water molecule to an O2 base atom in glycine-based PNA thymine dimers indicate that junctions modeled with P-form backbone conformations are lower in energy than a dimer comprising the predominant conformation observed in A-like helices. It is further shown in model systems that PNA analogs based on D-lysine are better able to preorganize in a conformation exclusive to P-form helices than is glycine-based PNA. An intrinsic preference for this conformation is also exhibited by positively charged chiral PNA dimers carrying 3-amino-D-alanine or 4-aza-D-leucine residue units that provide for additional rigidity by side-chain hydrogen bonding to the backbone carbonyl oxygen. Structural modifications stabilizing P-form helices may obviate the need for large heterocycles to target DNA pyrimidine bases via PNA.DNA-PNA triplex formation. Quantum chemical modeling methods are used to propose candidate PNA Hoogsteen strand designs. PMID:17071666 13. Reduced Dimensionality (4,3)D-hnCOCANH Experiment: An Efficient Backbone Assignment tool for NMR studies of Proteins CERN Document Server Kumar, Dinesh 2013-01-01 Sequence specific resonance assignment and secondary structure determination of proteins form the basis for variety of structural and functional proteomics studies by NMR. In this context, an efficient standalone method for rapid assignment of backbone (1H, 15N, 13Ca and 13C') resonances and secondary structure determination of proteins has been presented here. Compared to currently available strategies used for the purpose, the method employs only a single reduced dimensionality (RD) experiment -(4,3)D-hnCOCANH and exploits the linear combinations of backbone (13Ca and 13C') chemical shifts to achieve a dispersion relatively better compared to those of individual chemical shifts (see the text) for efficient and rapid data analysis. Further, the experiment leads to the spectrum with direct distinction of self (intra-residue) and sequential (inter-residue) carbon correlation peaks; these appear opposite in signs and therefore can easily be discriminated without using an additional complementary experiment. On ... 14. Simultaneous acquisition of {sup 13}C{sup {alpha}}-{sup 15}N and {sup 1}H-{sup 15}N-{sup 15}N sequential correlations in proteins: application of dual receivers in 3D HNN Energy Technology Data Exchange (ETDEWEB) Chakraborty, Swagata; Paul, Subhradip; Hosur, Ramakrishna V., E-mail: hosur@tifr.res.in [Tata Institute of Fundamental Research, Department of Chemical Sciences (India) 2012-01-15 We describe here, adaptation of the HNN pulse sequence for multiple nuclei detection using two independent receivers by utilizing the detectable {sup 13}C{sup {alpha}} transverse magnetization which was otherwise dephased out in the conventional HNN experiment. It enables acquisition of 2D {sup 13}C{sup {alpha}}-{sup 15}N sequential correlations along with the standard 3D {sup 15}N-{sup 15}N-{sup 1}H correlations, which provides directionality to sequential walk in HNN, on one hand, and enhances the speed of backbone assignment, on the other. We foresee that the implementation of dual direct detection opens up new avenues for a wide variety of modifications that would further enhance the value and applications of the experiment, and enable derivation of hitherto impossible information. 15. Biosynthetic uniform 13C,15N-labelling of zervamicin IIB. Complete 13C and 15N NMR assignment. Science.gov (United States) Ovchinnikova, Tatyana V; Shenkarev, Zakhar O; Yakimenko, Zoya A; Svishcheva, Natalia V; Tagaev, Andrey A; Skladnev, Dmitry A; Arseniev, Alexander S 2003-01-01 Zervamicin IIB is a member of the alpha-aminoisobutyric acid containing peptaibol antibiotics. A new procedure for the biosynthetic preparation of the uniformly 13C- and 15N-enriched peptaibol is described This compound was isolated from the biomass of the fungus-producer Emericellopsis salmosynnemata strain 336 IMI 58330 obtained upon cultivation in the totally 13C, 15N-labelled complete medium. To prepare such a medium the autolysed biomass and the exopolysaccharides of the obligate methylotrophic bacterium Methylobacillus flagellatus KT were used. This microorganism was grown in totally 13C, 15N-labelled minimal medium containing 13C-methanol and 15N-ammonium chloride as the only carbon and nitrogen sources. Preliminary NMR spectroscopic analysis indicated a high extent of isotope incorporation (> 90%) and led to the complete 13C- and 15N-NMR assignment including the stereospecific assignment of Aib residues methyl groups. The observed pattern of the structurally important secondary chemical shifts of 1H(alpha), 13C=O and 13C(alpha) agrees well with the previously determined structure of zervamicin IIB in methanol solution. PMID:14658801 16. Benchmark quantum-chemical calculations on a complete set of rotameric families of the DNA sugar-phosphate backbone and their comparison with modern density functional theory. Science.gov (United States) Mládek, Arnošt; Krepl, Miroslav; Svozil, Daniel; Cech, Petr; Otyepka, Michal; Banáš, Pavel; Zgarbová, Marie; Jurečka, Petr; Sponer, Jiří 2013-05-21 The DNA sugar-phosphate backbone has a substantial influence on the DNA structural dynamics. Structural biology and bioinformatics studies revealed that the DNA backbone in experimental structures samples a wide range of distinct conformational substates, known as rotameric DNA backbone conformational families. Their correct description is essential for methods used to model nucleic acids and is known to be the Achilles heel of force field computations. In this study we report the benchmark database of MP2 calculations extrapolated to the complete basis set of atomic orbitals with aug-cc-pVTZ and aug-cc-pVQZ basis sets, MP2(T,Q), augmented by ΔCCSD(T)/aug-cc-pVDZ corrections. The calculations are performed in the gas phase as well as using a COSMO solvent model. This study includes a complete set of 18 established and biochemically most important families of DNA backbone conformations and several other salient conformations that we identified in experimental structures. We utilize an electronically sufficiently complete DNA sugar-phosphate-sugar (SPS) backbone model system truncated to prevent undesired intramolecular interactions. The calculations are then compared with other QM methods. The BLYP and TPSS functionals supplemented with Grimme's D3(BJ) dispersion term provide the best tradeoff between computational demands and accuracy and can be recommended for preliminary conformational searches as well as calculations on large model systems. Among the tested methods, the best agreement with the benchmark database has been obtained for the double-hybrid DSD-BLYP functional in combination with a quadruple-ζ basis set, which is, however, computationally very demanding. The new hybrid density functionals PW6B95-D3 and MPW1B95-D3 yield outstanding results and even slightly outperform the computationally more demanding PWPB95 double-hybrid functional. B3LYP-D3 is somewhat less accurate compared to the other hybrids. Extrapolated MP2(D,T) calculations are not as 17. HN-NCA heteronuclear TOCSY-NH experiment for {sup 1}H{sup N} and {sup 15}N sequential correlations in ({sup 13}C, {sup 15}N) labelled intrinsically disordered proteins Energy Technology Data Exchange (ETDEWEB) Wiedemann, Christoph; Goradia, Nishit; Häfner, Sabine [Leibniz Institute for Age Research, Fritz Lipmann Institute, Research Group Biomolecular NMR Spectroscopy (Germany); Herbst, Christian [Ubon Ratchathani University, Department of Physics, Faculty of Science (Thailand); Görlach, Matthias; Ohlenschläger, Oliver; Ramachandran, Ramadurai, E-mail: raman@fli-leibniz.de [Leibniz Institute for Age Research, Fritz Lipmann Institute, Research Group Biomolecular NMR Spectroscopy (Germany) 2015-10-15 A simple triple resonance NMR experiment that leads to the correlation of the backbone amide resonances of each amino acid residue ‘i’ with that of residues ‘i−1’ and ‘i+1’ in ({sup 13}C, {sup 15}N) labelled intrinsically disordered proteins (IDPs) is presented. The experimental scheme, {HN-NCA heteronuclear TOCSY-NH}, exploits the favourable relaxation properties of IDPs and the presence of {sup 1}J{sub CαN} and {sup 2}J{sub CαN} couplings to transfer the {sup 15}N{sub x} magnetisation from amino acid residue ‘i’ to adjacent residues via the application of a band-selective {sup 15}N–{sup 13}C{sup α} heteronuclear cross-polarisation sequence of ∼100 ms duration. Employing non-uniform sampling in the indirect dimensions, the efficacy of the approach has been demonstrated by the acquisition of 3D HNN chemical shift correlation spectra of α-synuclein. The experimental performance of the RF pulse sequence has been compared with that of the conventional INEPT-based HN(CA)NH pulse scheme. As the availability of data from both the HCCNH and HNN experiments will make it possible to use the information extracted from one experiment to simplify the analysis of the data of the other and lead to a robust approach for unambiguous backbone and side-chain resonance assignments, a time-saving strategy for the simultaneous collection of HCCNH and HNN data is also described. 18. Complete resonance assignment for the polypeptide backbone of interleukin 1β using three-dimensional heteronuclear NMR spectroscopy International Nuclear Information System (INIS) The complete sequence-specific assignment of the 15N and 1H backbone resonances of the NMR spectrum of recombinant human interleukin 1β has been obtained by using primarily 15N-1H heteronuclear three-dimensional (3D) NMR techniques in combination with 15N-1H heteronuclear and 1H homonuclear two-dimensional NMR. The fingerprint region of the spectrum was analyzed by using a combination of 3D heteronuclear 1H Hartmann-Hahn 15N-1H multiple quantum coherence (3D HOHAHA-HMQC) and 3D heteronuclear 1H nuclear Overhauser 15N-1H multiple quantum coherence (3D NOESY-HMQC) spectroscopies. The authors show that the problems of amide NH and CαH chemical shift degeneracy that are prevalent for proteins of the size are readily overcome by using the 3D heteronuclear NMR technique. A doubling of some peaks in the spectrum was found to be due to N-terminal heterogeneity of the 15N-labeled protein, corresponding to a mixture of wild-type and des-Ala-1-interleukin 1β. The complete list of 15N and 1H assignments is given for all the amide NH and CαH resonances of all non-proline residues, as well as the 1H assignments for some of the amino acid side chains. This first example of the sequence-specific assignment of a protein using heteronuclear 3D NMR provides a basis for further conformational and dynamic studies of interleukin 1β 19. Backbone colorings for graphs: Tree and path backbones NARCIS (Netherlands) Broersma, Hajo; Fomin, Fedor V.; Golovach, Petr A.; Woeginger, Gerhard J. 2007-01-01 We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph $G = (V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V \\to {1,2,\\ldots}$ of $G$ in which the colors assigned to adjace 20. Backbone colorings for networks: tree and path backbones NARCIS (Netherlands) Broersma, H.J.; Fomin, F.V.; Golovach, P.A.; Woeginger, G.J. 2003-01-01 We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V\\rightarrow \\{1,2,\\ldots\\}$ of $G$ in which the colors assigned to 1. Backbone amide linker strategy DEFF Research Database (Denmark) Shelton, Anne Pernille Tofteng; Jensen, Knud Jørgen 2013-01-01 In the backbone amide linker (BAL) strategy, the peptide is anchored not at the C-terminus but through a backbone amide, which leaves the C-terminal available for various modifications. This is thus a very general strategy for the introduction of C-terminal modifications. The BAL strategy...... to assemble the final peptide. One useful application of this strategy is in the synthesis of C-terminal peptide aldehydes. The C-terminal aldehyde is masked as an acetal during synthesis and then conveniently demasked in the final cleavage step to generate the free aldehyde. Another application...... amino acid residue by reductive amination. This can be used as a general approach for the introduction of other C-terminal modifications as well as functionalities, such as fluorophors. The second step is an acylation of a secondary amine, followed by standard Fmoc-based solid-phase synthesis... 2. Geometry motivated alternative view on local protein backbone structures OpenAIRE Zacharias, Jan; Knapp, Ernst Walter 2013-01-01 We present an alternative to the classical Ramachandran plot (R-plot) to display local protein backbone structure. Instead of the (ϕ, ψ)-backbone angles relating to the chemical architecture of polypeptides generic helical parameters are used. These are the rotation or twist angle ϑ and the helical rise parameter d. Plots with these parameters provide a different view on the nature of local protein backbone structures. It allows to display the local structures in polar (d, ϑ)-coordinates, whi... 3. Backbone colorings along perfect matchings NARCIS (Netherlands) Broersma, H.J.; Fujisawa, J.; Yoshimoto, K. 2003-01-01 Given a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a backbone coloring for $G$ and $H$ is a proper vertex coloring $V\\rightarrow \\{1,2,\\ldots\\}$ of $G$ in which the colors assigned to adjacent vertices in $H$ differ by at least two. In a recent paper, backbone coloring 4. The effect of organic matter and nitrification inhibitor on 15 N H4 and 15 N O3 absorption by the maize International Nuclear Information System (INIS) The effect of the forms 15 N H4 and 15 N O3 in presence or absence of organic matter and of the nitrification inhibitor AM (2-amino-4-chloro-6-methyl-pyrimidine) in dry matter weight and nitrogen content of the plant derived from soil and form fertilizer is studied. The experiment was carried out in greenhouse and the test plant was the hybrid Maize Centralmex . The fertilizers (15 N H4)2 S O4 and Na15 N O3, were added in two levels: 40 and 120 Kg N/ha, with 1,02% of N and 1,4% of 15 N in excess, respectively. Three soils of different physical and chemical characteristics were used; Regosol intergrade, Latosol Roxo and Podzolized de Lins e Marilia var. Marilia. (M.A.C.) 5. 15N in biological nitrogen fixation studies International Nuclear Information System (INIS) A bibliography with 298 references on the use of the stable nitrogen isotope 15N in the research on the biological fixation of dinitrogen is presented. The literature pertaining to this bibliography covers the period from 1975 to the middle of 1985. (author) 6. 15N2 incorporation by rhizosphere soil International Nuclear Information System (INIS) Heterotrophic nitrogen fixation by rhizosphere soil samples from 20 rice cultivars grown under uniform field conditions was estimated employing 15N-tracer technique. Rhizosphere soil samples from different rice cultivars showed striking differences with regard to their ability to incorporate 15N2. Rhizosphere samples from rice straw-amended (3 and 6 tons/ha) soil exhibited more pronounced nitrogen-fixing activity than the samples form unamended soil; while the activity of the rhizosphere samples from soil receiving combined nitrogen (40 and 80 kg N/ha) was relatively low. However, the inhibitory effect of combined nitrogen was not expressed in the presence of rice straw at 6 tons/ha. Results suggest that plant variety, application of combined nitrogen and organic matter influence the rhizosphere nitrogen fixation. (orig.) 7. Reduced dimensionality tailored HN(C)N experiments for facile backbone resonance assignment of proteins through unambiguous identification of sequential HSQC peaks Science.gov (United States) Kumar, Dinesh 2013-12-01 Two novel reduced dimensionality (RD) tailored HN(C)N [S.C. Panchal, N.S. Bhavesh, R.V. Hosur, Improved 3D triple resonance experiments, HNN and HN(C)N, for HN and 15N sequential correlations in (13C, 15N) labeled proteins: application to unfolded proteins, J. Biomol. NMR 20 (2001) 135-147] experiments are proposed to facilitate the backbone resonance assignment of proteins both in terms of its accuracy and speed. These experiments - referred here as (4,3)D-hNCOcaNH and (4,3)D-hNcoCANH - exploit the linear combination of backbone 15N and 13C‧/13Cα chemical shifts simultaneously to achieve higher peak dispersion and randomness along their respective F1 dimensions. Simply, this has been achieved by modulating the backbone 15N(i) chemical shifts with that of 13C‧ (i - 1)/13Cα (i - 1) spins following the established reduced dimensionality NMR approach [T. Szyperski, D.C. Yeh, D.K. Sukumaran, H.N. Moseley, G.T. Montelione, Reduced-dimensionality NMR spectroscopy for high-throughput protein resonance assignment, Proc. Natl. Acad. Sci. USA 99 (2002) 8009-8014]. Though the modification is simple it has resulted an ingenious improvement of HN(C)N both in terms of peak dispersion and easiness of establishing the sequential connectivities. The increased dispersion along F1 dimension solves two purposes here: (i) resolves the ambiguities arising because of degenerate 15N chemical shifts and (ii) reduces the signal overlap in F2(15N)-F3(1H) planes (an important requisite in HN(C)N based assignment protocol for facile and unambiguous identification of sequentially connected HSQC peaks). The performance of both these experiments and the assignment protocol has been demonstrated using bovine apo Calbindin-d9k (75 aa) and urea denatured UNC60B (a 152 amino acid ADF/cofilin family protein of Caenorhabditis elegans), as representatives of folded and unfolded protein systems, respectively. 8. CPMG sequences with enhanced sensitivity to chemical exchange International Nuclear Information System (INIS) Improved relaxation-compensated Carr-Purcell-Meiboom-Gill pulse sequences are reported for studying chemical exchange of backbone 15N nuclei. In contrast to the original methods [J. P. Loria, M. Rance, and A. G. Palmer, J. Am. Chem. Soc.121, 2331-2332 (1999)], phenomenological relaxation rate constants obtained using the new sequences do not contain contributions from 1H-1H dipole-dipole interactions. Consequently, detection and quantification of chemical exchange processes are facilitated because the relaxation rate constant in the limit of fast pulsing can be obtained independently from conventional 15N spin relaxation measurements. The advantages of the experiments are demonstrated using basic pancreatic trypsin inhibitor 9. 15N-labed glycine synthesis OpenAIRE Claudinéia R. O. Tavares; José A. Bendassolli; Fernando Coelho; Carlos R. Sant Ana Filho; Clelber V. Prestes 2006-01-01 This work describes a method for 15N-isotope-labeled glycine synthesis, as well as details about a recovery line for nitrogen residues. To that effect, amination of alpha-haloacids was performed, using carboxylic chloroacetic acid and labeled aqueous ammonia (15NH3). Special care was taken to avoid possible 15NH3 losses, since its production cost is high. In that respect, although the purchase cost of the 13N-labeled compound (radioactive) is lower, the stable tracer produced constitutes an i... 10. Cross-Correlated Relaxation of Dipolar Coupling and Chemical-Shift Anisotropy in Magic-Angle Spinning R1ρ NMR Measurements: Application to Protein Backbone Dynamics Measurements. Science.gov (United States) Kurauskas, Vilius; Weber, Emmanuelle; Hessel, Audrey; Ayala, Isabel; Marion, Dominique; Schanda, Paul 2016-09-01 Transverse relaxation rate measurements in magic-angle spinning solid-state nuclear magnetic resonance provide information about molecular motions occurring on nanosecond-to-millisecond (ns-ms) time scales. The measurement of heteronuclear ((13)C, (15)N) relaxation rate constants in the presence of a spin-lock radiofrequency field (R1ρ relaxation) provides access to such motions, and an increasing number of studies involving R1ρ relaxation in proteins have been reported. However, two factors that influence the observed relaxation rate constants have so far been neglected, namely, (1) the role of CSA/dipolar cross-correlated relaxation (CCR) and (2) the impact of fast proton spin flips (i.e., proton spin diffusion and relaxation). We show that CSA/D CCR in R1ρ experiments is measurable and that the CCR rate constant depends on ns-ms motions; it can thus provide insight into dynamics. We find that proton spin diffusion attenuates this CCR due to its decoupling effect on the doublet components. For measurements of dynamics, the use of R1ρ rate constants has practical advantages over the use of CCR rates, and this article reveals factors that have so far been disregarded and which are important for accurate measurements and interpretation. 11. Change of 15N natural abundance (δ15N) in a forest soil receiving elevated N deposition International Nuclear Information System (INIS) Natural abundance of 15N15N) has been used to interpret N mineralization in forest ecosystems. Forest litter typically has depleted δ15N values ranging from -8 to 0 per mille and δ15N values of organic N in forest soil profiles become more enriched with depth. This study investigated (1) the change of δ15N and total N with depth, and (2) the relation between the change of δ15N within the 0 to 10, 10 to 20 and 20 to 30 cm intervals of the mineral layer and the N mineralization rates in these layers 12. Orientational constraints as three-dimensional structural constraints from chemical shift anisotropy: the polypeptide backbone of gramicidin A in a lipid bilayer. OpenAIRE Mai, W.; Hu, W; Wang, C; Cross, T A 1993-01-01 Chemical shifts observed from samples that are uniformly aligned with respect to the magnetic field can be used as very high-resolution structural constraints. This constraint takes the form of an orientational constraint rather than the more familiar distance constraint. The accuracy of these constraints is dependent upon the quality of the tensor characterization. Both tensor element magnitudes and tensor orientations with respect to the molecular frame need to be considered. Here these con... 13. The 15N-enrichment in dark clouds and Solar System objects CERN Document Server Hily-Blant, Pierre; Faure, Alexandre; Quirico, Eric 2013-01-01 The line intensities of the fundamental rotational transitions of H13CN and HC15N were observed towards two prestellar cores, L183 and L1544, and lead to molecular isotopic ratios 140 6 14N/15N 6 250 and 140 6 14N/15N 6 360, respectively. The range of values reflect genuine spatial variations within the cores. A comprehensive analysis of the available measurements of the nitrogen isotopic ratio in prestellar cores show that molecules carrying the nitrile functional group appear to be systematically 15N-enriched com- pared to those carrying the amine functional group. A chemical origin for the differential 15N-enhance- ment between nitrile- and amine-bearing interstellar molecules is proposed. This sheds new light on several observations of Solar System objects: (i) the similar N isotopic fractionation in Jupiter's NH3 and solar wind N+; (ii) the 15N-enrichments in cometary HCN and CN (that might represent a direct inter- stellar inheritance); and (iii) 15N-enrichments observed in organics in primitive cosmoma... 14. 15N NMR spectroscopy of Pseudomonas cytochrome c-551 International Nuclear Information System (INIS) 15N-1H correlation spectroscopy with detection at the 1H frequency has been used at natural abundance to detect nitrogen nuclei bonded to protons in the ferrocytochrome c-551 from Pseudomonas aeruginosa (ATCC 19429). Side-chain aromatic nitrogen, main-chain amides, and side-chain amides have been assigned to specific residues by comparison to previous proton assignments. Assignment ambiguities arising from overlap in the proton dimension have been resolved by examining spectra as a function of temperature and pH. Nitrogen chemical shifts are reported at pH 4.6 and 9.4 and three temperatures, 32, 50, and 60 degree C. Significant differences arise from the observed protein shifts and expected shifts in the random coil polypeptide 15. Simultaneous acquisition of 13Cα–15N and 1H–15N–15N sequential correlations in proteins: application of dual receivers in 3D HNN International Nuclear Information System (INIS) We describe here, adaptation of the HNN pulse sequence for multiple nuclei detection using two independent receivers by utilizing the detectable 13Cα transverse magnetization which was otherwise dephased out in the conventional HNN experiment. It enables acquisition of 2D 13Cα–15N sequential correlations along with the standard 3D 15N–15N–1H correlations, which provides directionality to sequential walk in HNN, on one hand, and enhances the speed of backbone assignment, on the other. We foresee that the implementation of dual direct detection opens up new avenues for a wide variety of modifications that would further enhance the value and applications of the experiment, and enable derivation of hitherto impossible information. 16. Nitrogen cycling in an extreme hyperarid environment inferred from δ15N analyses of plants, soils and herbivore diet Science.gov (United States) Díaz, Francisca P.; Frugone, Matías; Gutiérrez, Rodrigo A.; Latorre, Claudio 2016-03-01 Climate controls on the nitrogen cycle are suggested by the negative correlation between precipitation and δ15N values across different ecosystems. For arid ecosystems this is unclear, as water limitation among other factors can confound this relationship. We measured herbivore feces, foliar and soil δ15N and δ13C values and chemically characterized soils (pH and elemental composition) along an elevational/climatic gradient in the Atacama Desert, northern Chile. Although very positive δ15N values span the entire gradient, soil δ15N values show a positive correlation with aridity as expected. In contrast, foliar δ15N values and herbivore feces show a hump-shaped relationship with elevation, suggesting that plants are using a different N source, possibly of biotic origin. Thus at the extreme limits of plant life, biotic interactions may be just as important as abiotic processes, such as climate in explaining ecosystem δ15N values. 17. Nitrogen cycling in an extreme hyperarid environment inferred from δ(15)N analyses of plants, soils and herbivore diet. Science.gov (United States) Díaz, Francisca P; Frugone, Matías; Gutiérrez, Rodrigo A; Latorre, Claudio 2016-01-01 Climate controls on the nitrogen cycle are suggested by the negative correlation between precipitation and δ(15)N values across different ecosystems. For arid ecosystems this is unclear, as water limitation among other factors can confound this relationship. We measured herbivore feces, foliar and soil δ(15)N and δ(13)C values and chemically characterized soils (pH and elemental composition) along an elevational/climatic gradient in the Atacama Desert, northern Chile. Although very positive δ(15)N values span the entire gradient, soil δ(15)N values show a positive correlation with aridity as expected. In contrast, foliar δ(15)N values and herbivore feces show a hump-shaped relationship with elevation, suggesting that plants are using a different N source, possibly of biotic origin. Thus at the extreme limits of plant life, biotic interactions may be just as important as abiotic processes, such as climate in explaining ecosystem δ(15)N values. PMID:26956399 18. Binding of oxytocin and 8-arginine-vasopressin to neurophysin studied by /sup 15/N NMR using magnetization transfer and indirect detection via protons Energy Technology Data Exchange (ETDEWEB) Live, D.H.; Cowburn, D. 1987-10-06 NMR was used to monitor the binding to neurophysin of oxytocin and 8-arginine-vasopressin, /sup 15/N labeling being used to identify specific backbone /sup 15/N and /sup 1/H signals. The most significant effects of binding were large downfield shifts in the amino nitrogen resonance of Phe-3 of vasopressin and in its associated proton, providing evidence that the peptide bond between residues 2 and 3 of the hormones is hydrogen-bonded to the protein within hormone-neurophysin complexes. Suggestive evidence for hydrogen bonding of the amino nitrogen of Tyr-2 was also obtained in the form of decreased proton exchange rates on binding; however, the chemical shift changes of this nitrogen and its associated proton indicated that such hydrogen bonding, if present, is probably weak. Shifts in the amino nitrogen of Asn-5 and in the -NH protons of both Asn-5 and Cys-6 demonstrated that these residues are significantly perturbed by binding, suggesting conformational changes of the ring on binding and/or the presence of binding sites on the hormone outside the 1-3 region. No support was obtained for the thesis that there is a significant second binding site for vasopressin on each neutrophysin chain. The behavior of both oxytocin and vasopressin on binding was consistent with formation of 1:1 complexes in slow exchange with the free state under most pH conditions. At low pH there was evidence of an increased exchange rate. Additionally, broadening of /sup 15/N resonances in the bound state at low pH occurred without a corresponding change in the resonances of equilibrating free hormone. The results suggest significant conformational alteration in neurophysin-hormone complexes at low pH possibly associated with protonation of the carboxyl group of the hormone-protein salt bridge. 19. The C$^{14}$N/C$^{15}$N Ratio in Diffuse Molecular Clouds CERN Document Server Ritchey, Adam M; Lambert, David L 2015-01-01 We report the first detection of C$^{15}$N in diffuse molecular gas from a detailed examination of CN absorption lines in archival VLT/UVES spectra of stars probing local diffuse clouds. Absorption from the C$^{15}$N isotopologue is confidently detected (at $\\gtrsim4\\sigma$) in three out of the four directions studied and appears as a very weak feature between the main $^{12}$CN and $^{13}$CN absorption components. Column densities for each CN isotopologue are determined through profile fitting, after accounting for weak additional line-of-sight components of $^{12}$CN, which are seen in the absorption profiles of CH and CH$^+$ as well. The weighted mean value of C$^{14}$N/C$^{15}$N for the three sight lines with detections of C$^{15}$N is $274\\pm18$. Since the diffuse molecular clouds toward our target stars have relatively high gas kinetic temperatures and relatively low visual extinctions, their C$^{14}$N/C$^{15}$N ratios should not be affected by chemical fractionation. The mean C$^{14}$N/C$^{15}$N ratio ... 20. Synthesis and NMR of {sup 15}N-labeled DNA fragments Energy Technology Data Exchange (ETDEWEB) Jones, R.A. [Rutgers, The State Univ. of New Jersey, Piscataway, NJ (United States) 1994-12-01 DNA fragments labeled with {sup 15}N at the ring nitrogens and at the exocyclic amino groups can be used to obtain novel insight into interactions such as base pairing, hydration, drug binding, and protein binding. A number of synthetic routes to {sup 15}N-labeled pyrimidine nucleosides, purines, and purine nucleosides have been reported. Moreover, many of these labeled bases or monomers have been incorporated into nucleic acids, either by chemical synthesis or by biosynthetic procedures. The focus of this chapter will be on the preparation of {sup 15}N-labeled purine 2{prime}-deoxynucleosides, their incorporation into DNA fragments by chemical synthesis, and the results of NMR studies using these labeled DNA fragments. 1. Mechanism of the bisphosphatase reaction of 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase probed by (1)H-(15)N NMR spectroscopy. Science.gov (United States) Okar, D A; Live, D H; Devany, M H; Lange, A J 2000-08-15 The histidines in the bisphosphatase domain of rat liver 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase were labeled with (15)N, both specifically at N1' and globally, for use in heteronuclear single quantum correlation (HSQC) NMR spectroscopic analyses. The histidine-associated (15)N resonances were assigned by correlation to the C2' protons which had been assigned previously [Okar et al., Biochemistry 38, 1999, 4471-79]. Acquisition of the (1)H-(15)N HSQC from a phosphate-free sample demonstrated that the existence of His-258 in the rare N1' tautomeric state is dependent upon occupation of the phosphate binding site filled by the O2 phosphate of the substrate, fructose-2,6-bisphosphate, and subsequently, the phosphohistidine intermediate. The phosphohistidine intermediate is characterized by two hydrogen bonds involving the catalytic histidines, His-258 and His-392, which are directly observed at the N1' positions of the imidazole rings. The N1' of phospho-His-258 is protonated ((1)H chemical shift, 14.0 ppm) and hydrogen bonded to the backbone carbonyl of Gly-259. The N1' of cationic His-392 is hydrogen bonded ((1)H chemical shift, 13.5 ppm) to the phosphoryl moiety of the phosphohistidine. The existence of a protonated phospho-His-258 intermediate and the observation of a fairly strong hydrogen bond to the same phosphohistidine implies that hydrolysis of the covalent intermediate proceeds without any requirement for an "activated" water. Using the labeled histidines as probes of the catalytic site mutation of Glu-327 to alanine revealed that, in addition to its function as the proton donor to fructose-6-phosphate during formation of the transient phosphohistidine intermediate at the N3' of His-258, this residue has a significant role in maintaining the structural integrity of the catalytic site. The (1)H-(15)N HSQC data also provide clear evidence that despite being a surface residue, His-446 has a very acidic pK(a), much less than 6.0. On the basis of 2. 1H, 13C, and 15N backbone and side chain resonance assignments of thermophilic Geobacillus kaustophilus cyclophilin-A Energy Technology Data Exchange (ETDEWEB) Holliday, Michael; Zhang, Fengli; Isern, Nancy G.; Armstrong, Geoffrey S.; Eisenmesser, Elan Z. 2014-04-01 Cyclophilins catalyze the reversible peptidyl-prolyl isomerization of their substrates and are present across all kingdoms of life from humans to bacteria. Although numerous biological roles have now been discovered for cyclophilins, their function was initially ascribed to their chaperone-like activity in protein folding where they catalyze the often rate-limiting step of proline isomerization. This chaperone-like activity may be especially important under extreme conditions where cyclophilins are often over expressed, such as in tumors for human cyclophilins {Lee, 2010 #1167}, but also in organisms that thrive under extreme conditions, such as theromophilic bacteria. Moreover, the reversible nature of the peptidyl-prolyl isomerization reaction catalyzed by cyclophilins has allowed these enzymes to serve as model systems for probing the role of conformational changes during catalytic turnover {Eisenmesser, 2002 #20;Eisenmesser, 2005 #203}. Thus, we present here the resonance assignments of a thermophilic cyclophilin from Geobacillus kaustophilus derived from deep-sea sediment {Takami, 2004 #1384}. This thermophilic cyclophilin may now be studied at a variety of temperatures to provide insight into the comparative structure, dynamics, and catalytic mechanism of cyclophilins. 3. 1H, 13C, and 15N backbone and side chain resonance assignments of thermophilic Geobacillus kaustophilus cyclophilin-A. Science.gov (United States) Holliday, Michael J; Zhang, Fengli; Isern, Nancy G; Armstrong, Geoffrey S; Eisenmesser, Elan Z 2014-04-01 Cyclophilins catalyze the reversible peptidyl-prolyl isomerization of their substrates and are present across all kingdoms of life from humans to bacteria. Although numerous biological roles have now been discovered for cyclophilins, their function was initially ascribed to their chaperone-like activity in protein folding where they catalyze the often rate-limiting step of proline isomerization. This chaperone-like activity may be especially important under extreme conditions where cyclophilins are often over expressed, such as in tumors for human cyclophilins (Lee Archiv Pharm Res 33(2): 181-187, 2010), but also in organisms that thrive under extreme conditions, such as theromophilic bacteria. Moreover, the reversible nature of the peptidyl-prolyl isomerization reaction catalyzed by cyclophilins has allowed these enzymes to serve as model systems for probing the role of conformational changes during catalytic turnover (Eisenmesser et al. Science 295(5559): 1520-1523, 2002; Eisenmesser et al. Nature 438(7064): 117-121, 2005). Thus, we present here the resonance assignments of a thermophilic cyclophilin from Geobacillus kaustophilus derived from deep-sea sediment (Takami et al. Extremophiles 8(5): 351-356, 2004). This thermophilic cyclophilin may now be studied at a variety of temperatures to provide insight into the comparative structure, dynamics, and catalytic mechanism of cyclophilins. 4. Multinuclear NMR of 15 N labelled organic molecules International Nuclear Information System (INIS) The paper presents the application of multinuclear NMR techniques to the study of 15 N labeled organic molecules. There are some important points of great interest in such type of research, namely, structure determination, i.e. location of the 15 N in molecule and determination of 15 N concentration in order to obtain quantitative results about the intramolecular short and long range interaction. Different NMR techniques were used in the study of 13 C, 1 H and 15 N. Obtaining the 15 N NMR signal imposes some special preparation of the spectrometer. First, we had to manage a very large spectral window (-400 to +1200 ppm) which makes difficult finding the signal. Secondly, in the condition of proton decoupling, in a very large band, a decrease of the signal can occur due to the NOE negative effect. To avoid this effect, other decoupling method, called 'inverse gated 1 H decoupling' was used. As a reference, for 15 N, we used CH3NO2, fixed at 0 ppm. In order to find the suitable spectral window we used the formamide (15 N). The results of obtaining the 15 N-labeled procaine are presented. (author) 5. Comparison of {sup 15}N- and {sup 13}C-determined parameters of mobility in melittin Energy Technology Data Exchange (ETDEWEB) Zhu Lingyang [University Indianapolis, Department of Physics, Indiana University Purdue (United States); Prendergast, Franklyn G. [Mayo Foundation, Department of Pharmacology (United States); Kemple, Marvin D. [University Indianapolis, Department of Physics, Indiana University Purdue (United States) 1998-07-15 Backbone and tryptophan side-chain mobilities in the 26-residue, cytolytic peptide melittin (MLT) were investigated by {sup 15}N and {sup 13}C NMR. Specifically, inverse-detected {sup 15}N T{sub 1} and steady-state NOE measurements were made at 30 and 51 MHz on MLT at 22 deg. C enriched with {sup 15}N at six amide positions and in the Trp{sup 19} side chain. Both the disordered MLT monomer (1.2 mM peptide at pH 3.6 in neat water) and {alpha}-helical MLT tetramer (4.0 mM peptide at pH 5.2 in 150 mM phosphate buffer) were examined. The relaxation data were analyzed in terms of the Lipari and Szabo model-free formalism with three parameters: {tau}{sub m}, the correlation time for the overall rotation; S{sup 2}, a site-specific order parameter which is a measure of the amplitude of the internal motion; and {tau}{sub e}, a local, effective correlation time of the internal motion. A comparison was made of motional parameters from the {sup 15}N measurements and from {sup 13}C measurements on MLT, the latter having been made here and previously [Kemple et al. (1997) Biochemistry, 36, 1678-1688]. {tau}{sub m} and {tau}{sub e} values were consistent from data on the two nuclei. In the MLT monomer, S{sup 2} values for the backbone N-H and C{alpha}-H vectors in the same residue were similar in value but in the tetramer the N-H order parameters were about 0.2 units larger than the C{alpha}-H order parameters. The Trp side-chain N-H and C-H order parameters, and {tau}{sub e} values were generally similar in both the monomer and tetramer. Implications of these results regarding the dynamics of MLT are examined. 6. ANSS Backbone Station Quality Assessment Science.gov (United States) Leeds, A.; McNamara, D.; Benz, H.; Gee, L. 2006-12-01 In this study we assess the ambient noise levels of the broadband seismic stations within the United States Geological Survey's (USGS) Advanced National Seismic System (ANSS) backbone network. The backbone consists of stations operated by the USGS as well as several regional network stations operated by universities. We also assess the improved detection capability of the network due to the installation of 13 additional backbone stations and the upgrade of 26 existing stations funded by the Earthscope initiative. This assessment makes use of probability density functions (PDF) of power spectral densities (PSD) (after McNamara and Buland, 2004) computed by a continuous noise monitoring system developed by the USGS- ANSS and the Incorporated Research Institutions in Seismology (IRIS) Data Management Center (DMC). We compute the median and mode of the PDF distribution and rank the stations relative to the Peterson Low noise model (LNM) (Peterson, 1993) for 11 different period bands. The power of the method lies in the fact that there is no need to screen the data for system transients, earthquakes or general data artifacts since they map into a background probability level. Previous studies have shown that most regional stations, instrumented with short period or extended short period instruments, have a higher noise level in all period bands while stations in the US network have lower noise levels at short periods (0.0625-8.0 seconds), high frequencies (8.0- 0.125Hz). The overall network is evaluated with respect to accomplishing the design goals set for the USArray/ANSS backbone project which were intended to increase broadband performance for the national monitoring network. 7. 15N Fractionation in Star-Forming Regions and Solar System Objects Science.gov (United States) Wirstrom, Eva; Milam, Stefanie; Adande, GIlles; Charnley, Steven; Cordiner, Martin 2015-01-01 A central issue for understanding the formation and evolution of matter in the early Solar System is the relationship between the chemical composition of star-forming interstellar clouds and that of primitive Solar System materials. The pristinemolecular content of comets, interplanetary dust particles and carbonaceous chondrites show significant bulk nitrogen isotopic fractionation relative to the solar value, 14N15N 440. In addition, high spatial resolution measurements in primitive materials locally show even more extreme enhancements of 14N15N 100. 8. Backbone dynamics of the human CC-chemokine eotaxin Energy Technology Data Exchange (ETDEWEB) Ye Jiqing; Mayer, Kristen L.; Stone, Martin J. [Indiana University, Department of Chemistry (United States) 1999-10-15 Eotaxin is a CC chemokine with potent chemoattractant activity towards eosinophils. {sup 15}N NMR relaxation data have been used to characterize the backbone dynamics of recombinant human eotaxin. {sup 15}N longitudinal (R{sub 1}) and transverse (R{sub 2}) auto relaxation rates, heteronuclear {sup 1}H-{sup 15}N steady-state NOEs, and transverse cross-relaxation rates ({eta}{sub xy}) were obtained at 30 deg. C for all resolved backbone secondary amide groups using {sup 1} H-detected two-dimensional NMR experiments. Ratios of transverse auto and cross relaxation rates were used to identify NH groups influenced by slow conformational rearrangement. Relaxation data were fit to the extended model free dynamics formalism, yielding parameters describing axially symmetric molecular rotational diffusion and the internal dynamics of each NH group. The molecular rotational correlation time ({tau}{sub m}) is 5.09{+-}0.02 ns, indicating that eotaxin exists predominantly as a monomer under the conditions of the NMR study. The ratio of diffusion rates about unique and perpendicular axes (D{sub parallel}/D{sub perpendicular}) is 0.81{+-}0.02. Residues with large amplitudes of subnanosecond motion are clustered in the N-terminal region (residues 1-19), the C-terminus (residues 68-73) and the loop connecting the first two {beta}-strands (residues 30-37). N-terminal flexibility appears to be conserved throughout the chemokine family and may have implications for the mechanism of chemokine receptor activation. Residues exhibiting significant dynamics on the microsecond-millisecond time scale are located close to the two conserved disulfide bonds, suggesting that these motions may be coupled to disulfide bond isomerization. 9. MERA: a webserver for evaluating backbone torsion angle distributions in dynamic and disordered proteins from NMR data Energy Technology Data Exchange (ETDEWEB) Mantsyzov, Alexey B. [M.V. Lomonosov Moscow State University, Faculty of Fundamental Medicine (Russian Federation); Shen, Yang; Lee, Jung Ho [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States); Hummer, Gerhard [Max Planck Institute of Biophysics (Germany); Bax, Ad, E-mail: bax@nih.gov [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States) 2015-09-15 MERA (Maximum Entropy Ramachandran map Analysis from NMR data) is a new webserver that generates residue-by-residue Ramachandran map distributions for disordered proteins or disordered regions in proteins on the basis of experimental NMR parameters. As input data, the program currently utilizes up to 12 different parameters. These include three different types of short-range NOEs, three types of backbone chemical shifts ({sup 15}N, {sup 13}C{sup α}, and {sup 13}C′), six types of J couplings ({sup 3}J{sub HNHα}, {sup 3}J{sub C′C′}, {sup 3}J{sub C′Hα}, {sup 1}J{sub HαCα}, {sup 2}J{sub CαN} and {sup 1}J{sub CαN}), as well as the {sup 15}N-relaxation derived J(0) spectral density. The Ramachandran map distributions are reported in terms of populations of their 15° × 15° voxels, and an adjustable maximum entropy weight factor is available to ensure that the obtained distributions will not deviate more from a newly derived coil library distribution than required to account for the experimental data. MERA output includes the agreement between each input parameter and its distribution-derived value. As an application, we demonstrate performance of the program for several residues in the intrinsically disordered protein α-synuclein, as well as for several static and dynamic residues in the folded protein GB3. 10. 1H, 15N and 13C NMR resonance assignment, secondary structure and global fold of the FMN-binding domain of human cytochrome P450 International Nuclear Information System (INIS) The FMN-binding domain of human NADPH-cytochrome P450 reductase,corresponding to exons 3-;7, has been expressed at high level in an active form and labelled with 13C and 15N. Most of the backbone and aliphatic side-chain 1H, 15Nand 13C resonances have been assigned using heteronuclear double- and triple-resonance methods, together with a semiautomatic assignment strategy. The secondary structure as estimated from the chemical shift index and NOE connectivities consists of six α-helices and fiveβ-strands. The global fold was deduced from the long-range NOE sun ambiguously assigned in a 4D 13C-resolved HMQC-NOESY-HMQC spectrum. The fold is of the alternating α/β type, with the fiveβ-strands arranged into a parallel β-sheet. The secondary structure and global fold are very similar to those of the bacterial flavodoxins, but the FMN-binding domain has an extra short helix in place of a loop, and an extra helix at the N-terminus (leading to the membrane anchordomain in the intact P450 reductase). The experimental constraints were combined with homology modelling to obtain a structure of the FMN-bindingdomain satisfying the observed NOE constraints. Chemical shift comparisons showed that the effects of FMN binding and of FMN reduction are largely localised at the binding site 11. Study on synthesis of 15N-hydrazine hydrate International Nuclear Information System (INIS) The 15N labeled hydrazine hydrate is a strong reducing agent in the synthesis procedure of stable isotope labeled compounds, and it has been widely used in the isotope-labeled pharmaceutical synthesis. The reaction conditions of 15N labeled hydrazine hydrate were mainly investigated by single-factor design, and the following optimized conditions were obtained: the concentration of available chlorine was 115-120 g/L, the chlorination re- action time was 30∼40 min, the reflux time was 7 min, and the mass ratio of material was m(catalyst) : m (urea) = 1.0 : 10.0, and the yield of 15N labeled hydrazine hydrate was 76.1%, the abundance of 15N was 99.20%. (authors) 12. Stereospecific assignments of glycine in proteins by stereospecific deuteration and {sup 15}N labeling Energy Technology Data Exchange (ETDEWEB) Hansen, A.P.; Curley, R.W. Jr.; Panigot, M.J.; Fesik, S.W. [Ohio State Univ., Columbus, OH (United States) 1994-12-01 Stereospecific assignments are important for accurately determining the three-dimensional structures of proteins through the use of multidimensional NMR techniques. It is especially important to stereospecifically assign the glycine {alpha}-protons in proteins because of the potential for different backbone conformations of this residue. These stereospecific assignments are critical for interpreting the {sup 3}J{sub NH,{alpha}H} coupling constants and NOEs involving the glycine {alpha}-protons that determine the conformation of this part of the protein. However, it is often difficult to unambiguously obtain the stereospecific assignments for glycine residues by using only NOE data. In this poster, we present a method for unambiguous, stereospecific assignment of the {alpha}-protons of glycine residues. This method involves synthesis of stereo-specifically deuterated and {sup 15}N-labeled Gly using a slightly modified procedure originally described by Woodard and coworkers for the stereoselective deuteration of glycine. The stereospecifically deuterated and {sup 15}N-labeled Gy has been incorporated into recombinant proteins expressed in both bacterial systems (FKBP) and mammalian cells (u-PA). Two- and three-dimensional isotope-filtered and isotope-edited NMR experiments were used to obtain the stereospecific assignments of the glycine {alpha}-protons for these proteins. 13. 1H, 13C, and 15N resonance assignment of the ubiquitin-like domain from Dsk2p OpenAIRE Chen, Tony; Zhang, Daoning; Matiuhin, Yulia; Glickman, Michael; Fushman, David 2008-01-01 The ubiquitin-like domain (UBL) of yeast protein Dsk2p is widely believed to recognize and bind to ubiquitin receptors on the proteasome and, as part of Dsk2p, to bridge polyubiquitinated substrates and proteasomal degradation machinery. Here we report NMR resonance assignment for 1H, 15N, and 13C nuclei in the backbone and side chains of the UBL domain of Dsk2p. This assignment will aid in NMR studies focused on understanding of Dsk2’s interactions with proteasomal receptors and its role as ... 14. Phenylalanine δ15N in Paleo Archives as a New Proxy for δ15N of Exported Primary Production Science.gov (United States) McCarthy, M.; Batista, F. C.; Vokhshoori, N. L.; Brown, J. T.; Guilderson, T. P.; Ravelo, A. C.; Sherwood, O. 2012-12-01 Compound-specific isotope analysis of individual amino acids (CSI-AA) is emerging as a powerful new tool for studying the paleo nitrogen cycle. Because most detrital organic nitrogen is composed of amino acids, CSI-AA can reveal the mechanistic basis for organic nitrogen diagenesis, preserve a record of past food web structure, and potentially reconstruct the δ15N values of past nitrate and primary production. Within the commonly measured amino acids, the δ15N value of phenylalanine (Phe) appears uniquely promising as a new proxy that reflects the nitrogen isotopic value of the original source. Phe δ15N values remain almost unchanged with trophic transfer through food webs, and also during at least the initial stages of organic matter degradation. Here we synthesize results from both bio-archives and recent sediments, which together suggest that at least in Holocene archives the Phe δ15N value does in fact record the average inorganic nitrogen δ15N value at the base of planktonic food webs. However, several important unknowns also remain. These include the extent of variation in amino acid isotopic fractionation patterns in phylogenetically distinct algal groups. The stability of Phe δ15N values in older sediments where organic matter has undergone extensive diagenesis is also an important research area, which may ultimately establish the temporal limit for application of this approach to study past geological epochs. Together, however, results to date suggest that of Phe δ15N values in paleo archives represent a novel molecular-level proxy which is not tied to any specific organism or group, but rather can provide an integrated estimate of δ15N value of exported primary production. 15. Balance study of the fate of 15N fertilizer International Nuclear Information System (INIS) An interim report is presented on a series of experiments with wooden box-type lysimeters (60 cm x 60 cm x 70 cm) loaded with a sandy soil, a loess soil and straw-amended soil. The lysimeters support crops rotated over a five-year period to be studied - potato, barley, sugar-beet, barley (with winter rape) and finally (1979) potato. Each lysimeter received split applications of urea at total rates of 0, 50 or 100 kg.ha-1. The effects of soil residues of the herbicide monolinuron were also studied. The report deals with data collected during the first three years of the planned experiments (1975 - 1977 inclusive). 15N-labelled urea (47 atom 15N% excess) was initially used but in some experiments this was followed by applications of unlabelled urea in order to study the fate of the residual 15N in the subsequent years. The results to date indicated that in the first year highest recoveries in the plant of the applied 15N obtained on the sandy soil. The low recoveries of 15N in the subsequent years when unlabelled urea was supplied also indicated significant storage by soil or root organic matter of the applied 15N. Compared with the control (zero application of urea nitrogen), potato took up more total nitrogen in the presence of fertilizer including more of the unlabelled soil pool nitrogen. Analyses of the soil profiles in terms of total soil nitrogen and fertilizer-derived nitrogen (on the basis of 15N assays) indicated leaching of the labelled nitrogen down the soil profile in all cases during the three-year period. Analysis of NO3-N in leachates confirmed the presence of labelled urea-derived nitrogen. (author) 16. Utilization of 15N-urea in laying hens. 3 International Nuclear Information System (INIS) In 3 colostomized laying hens the incorporation of heavy nitrogen from urea into the amino acids of the 21 eggs laid during the 8-day experiment was determined. In these eggs the content of 15 amino acids was ascertained separately in white and yolk of the eggs and their atom-% 15N excess (15N') was determined. The heavy nitrogen could be detected in all amino acids investigated. The incorporation of 15N' into the essential amino acids of the white and yolk of eggs is very low. Of the 15N' amount of the urea applied 0.18% could be detected in the 9 essential amino acids of the white of egg and 0.12% in those of the yolk. For the 6 analyzed nonessential amino acids the rediscovery quota of 15N' in the white of egg was 0.50% and in the yolk 0.81% is that the NPN-source urea is insignificant for egg protein synthesis. (author) 17. Future High Capacity Backbone Networks DEFF Research Database (Denmark) Wang, Jiayuan This thesis - Future High Capacity Backbone Networks - deals with the energy efficiency problems associated with the development of future optical networks. In the first half of the thesis, novel approaches for using multiple/single alternative energy sources for improving energy efficiency...... is studied in details with dynamic network simulations using OPNET. Dynamic routing optimization methods are proposed. The influences of re-routing and load-balancing factors on the algorithm are evaluated with a focus on different re-routing thresholds. Results from dynamic network simulations show that re...... aiming for reducing the dynamic part of the energy consumption of the network may increase the fixed part of the energy consumption meanwhile. In the second half of the thesis, the conflict between energy efficiency and Quality of Service (QoS) is addressed by introducing a novel software defined... 18. 3D-TROSY-based backbone and ILV-methyl resonance assignments of a 319-residue homodimer from a single protein sample Energy Technology Data Exchange (ETDEWEB) Krejcirikova, Anna; Tugarinov, Vitali, E-mail: vitali@umd.edu [University of Maryland, Department of Chemistry and Biochemistry (United States) 2012-10-15 The feasibility of practically complete backbone and ILV methyl chemical shift assignments from a single [U-{sup 2}H,{sup 15}N,{sup 13}C; Ile{delta}1-{l_brace}{sup 13}CH{sub 3}{r_brace}; Leu,Val-{l_brace}{sup 13}CH{sub 3}/{sup 12}CD{sub 3}{r_brace}]-labeled protein sample of the truncated form of ligand-free Bst-Tyrosyl tRNA Synthetase (Bst-{Delta}YRS), a 319-residue predominantly helical homodimer, is established. Protonation of ILV residues at methyl positions does not appreciably detract from the quality of TROSY triple resonance data. The assignments are performed at 40 Degree-Sign C to improve the sensitivity of the measurements and alleviate the overlap of {sup 1}H-{sup 15}N correlations in the abundant {alpha}-helical segments of the protein. A number of auxiliary approaches are used to assist in the assignment process: (1) selection of {sup 1}H-{sup 15}N amide correlations of certain residue types (Ala, Thr/Ser) that simplifies 2D {sup 1}H-{sup 15}N TROSY spectra, (2) straightforward identification of ILV residue types from the methyl-detected 'out-and-back' HMCM(CG)CBCA experiment, and (3) strong sequential HN-HN NOE connectivities in the helical regions. The two subunits of Bst-YRS were predicted earlier to exist in two different conformations in the absence of ligands. In agreement with our earlier findings (Godoy-Ruiz in J Am Chem Soc 133:19578-195781, 2011), no evidence of dimer asymmetry has been observed in either amide- or methyl-detected experiments. 19. ~(15)N Isotope Used for Study of Groundwater Nitrogen Pollution in Shijiazhuang City, China Institute of Scientific and Technical Information of China (English) 2004-01-01 Shijiazhuang City is the capital of Hebei province, China. Groundwater is the major water supply source for living and industry need of the city. Due to a rapid increase of population and development of industry and agriculture, a series of groundwater environmental problems are created. In the paper, the situation of groundwater pollution in Shijiazhuang city is reported. Based on the groundwater chemical data and ~(15)N measurement results both on groundwater and soils, the reason of groundwater nitra... 20. Reduced Dimensionality tailored HN(C)N Pulse Sequences for Efficient Backbone Resonance Assignment of Proteins through Rapid Identification of Sequential HSQC peaks CERN Document Server Kumar, Dinesh 2013-01-01 Two novel reduced dimensionality (RD) experiments -(4,3)D-hNCOcaNH and (4,3)D-hNcoCANH- have been presented here to facilitate the backbone resonance assignment of proteins both in terms of its accuracy and speed. The experiments basically represent an improvisation of previously reported HN(C)N experiment [Panchal et. al., J. Biomol. NMR. (2002), 20 (2), 135-147] and exploit the simple reduced dimensionality NMR concept [Szyperski et. al. (2002), Proc. Natl. Acad. Sci. U.S.A. 99(12), 8009-8014] to achieve (a) higher dispersion and resolution along the co-evolved F1 dimension and (b) rapid identification of sequential HSQC peaks on its F2(15N)- F3(1H) planes. The current implementation is based on the fact that the linear combination of 15N and 13CO/13Ca chemical shifts offers relatively better dispersion and randomness compared to the individual chemical shifts; thus enables the assignment of crowded HSQC spectra by resolving the ambiguities generally encountered in HNCN based assignment protocol because of ... 1. Ner protein of phage Mu: Assignments using {sup 13}C/{sup 15}N-labeled protein Energy Technology Data Exchange (ETDEWEB) Strzelecka, T.; Gronenborn, A.M.; Clore, G.M. [National Institutes of Health, Bethesda, MD (United States) 1994-12-01 The Ner protein is a small (74-amino acid) DNA-binding protein that regulates a switch between the lysogenic and lytic stages of phage Mu. It inhibits expression of the C repressor gene and down-regulates its own expression. Two-dimensional NMR experiments on uniformly {sup 15}N-labeled protein provided most of the backbone and some of the sidechain proton assignments. The secondary structure determination using two-dimensional NOESY experiments showed that Ner consists of five {alpha}-helices. However, because most of the sidechain protons could not be assigned, the full structure was not determined. Using uniformly {sup 13}C/{sup 15}N-labeled Ner and a set of three-dimensional experiments, we were able to assign all of the backbone and 98% of the sidechain protons. In particular, the CBCANH and CBCA(CO)NH experiments were used to sequentially assign the C{alpha} and C{beta} resonances; the HCCH-CTOCSY and HCCH-COSY were used to assign sidechain carbon and proton resonances. 2. Vertical δ13C and δ15N changes during pedogenesis Science.gov (United States) Brunn, Melanie; Spielvogel, Sandra; Wells, Andrew; Condron, Leo; Oelmann, Yvonne 2015-04-01 The natural abundance of soil organic matter (SOM) stable C and N isotope ratios are subjected to vertical changes throughout the soil profile. This vertical distribution is a widely reported phenomenon across varieties of ecosystems and constitutes important insights of soil carbon cycling. In most ecosystems, SOM becomes enriched in heavy isotopes by several per mill in the first few centimeters of the topsoil. The enrichment of 13C in SOM with soil depth is attributed to biological and physical-chemical processes in soil e.g., plant physiological impacts, microbial decomposition, sorption and transport processes. Such vertical trends in 13C and 15N abundance have rarely been related to SOM composition during pedogenesis. The aims of our study were to investigate short and long-term δ13C and δ15N depth changes and their interrelations under progressing pedogenesis and ecosystem development. We sampled soils across the well studied fordune progradation Haast-chronosequence, a dune ridge system under super-humid climate at the West Coast of New Zealand's South Island (43° 53' S, 169° 3' E). Soils from 11 sites with five replicates each covered a time span of around 2870 yr of soil development (from Arenosol to Podzol). Vertical changes of δ13C and δ15N values of SOM were investigated in the organic layers and in 1-cm depth intervals of the upper 10 cm of the mineral soil. With increasing soil depth SOM became enriched in δ13C by 1.9 ± SE 0.1 o and in δ15N by 6.0 ± 0.4 ‰˙Litter δ13C values slightly decreased with increasing soil age (r = -0.61; p = 0.00) likely due to less efficient assimilation linked to nutrient limitations. Fractionation processes during mycorrhizal transfer appeared to affect δ15N values in the litter. We found a strong decrease of δ15N in the early succession stages ≤ 300 yr B.P. (r = -0.95; p = 0.00). Positive relations of vertical 13C and 15N enrichment with soil age might be related to decomposition and appeared to be 3. Protein-Backbone Thermodynamics across the Membrane Interface. Science.gov (United States) Bereau, Tristan; Kremer, Kurt 2016-07-01 The thermodynamics of insertion of a protein in a membrane depends on the fine interplay between backbone and side-chain contributions interacting with the lipid environment. Using computer simulations, we probe how different descriptions of the backbone glycyl unit affect the thermodynamics of insertion of individual residues, dipeptides, and entire transmembrane helices. Due to the lack of reference data, we first introduce an efficient methodology to estimate atomistic potential of mean force (PMF) curves from a series of representative and uncorrelated coarse-grained (CG) snapshots. We find strong discrepancies between two CG models, Martini and PLUM, against reference atomistic PMFs and experiments. Atomistic simulations suggest a weak free energy of insertion between water and a POPC membrane for the glycyl unit, in overall agreement with experimental results despite severe assumptions in our calculations. We show that refining the backbone contribution in PLUM significantly improves the PMF of insertion of the WALP16 transmembrane peptide. An improper balance between the glycyl backbone and the attached side chain will lead to energetic artifacts, rationalizing Martini's overstabilization of WALP's adsorbed interfacial state. It illustrates difficulties associated with free-energy-based parametrizations of single-residue models, as the relevant free energy of partitioning used for force-field parametrization does not arise from the entire residue but rather the solvent-accessible chemical groups. PMID:27138459 4. Preparation of double labeled 13C, 15N3-nitrofurantoin%双标记13C,15N3-呋喃妥因的制备 Institute of Scientific and Technical Information of China (English) 徐建飞; 杜晓宁; 王伟; 张彰 2012-01-01 以双标记13C,15N3 -氨基脲为原料,先与苯甲醛缩合,继而与氯乙酸乙酯取代、环化,再经盐酸水解反应后与5-硝基糠醛二乙酯反应,最终制得双标记13C,15N3-呋喃妥因.产物经红外光谱、高效液相色谱及质谱表征.结果表明,所选用的合成路线反应条件温和,产物总收率高于60％,且同位素丰度不下降；目标产物的化学纯度＞99.0％,13C同位素丰度＞98％,15N同位素丰度＞99％.%A novel method was established to synthesize double labeled 13C,15N3-nitrofurantoin. Starting material 13C,15 N3-semicarbazide was firstly converted to benzaldehyde semicarbazone (II) by condensation with benzaldehyde. Compound (II) was then allowed to react with ethyl a-chloroacetate in the presence of sodium ethoxide, forming 1-benzylideneaminohydratoin (III). Compound (III) was hydrolyzed with hydrochloric acid and condensed with 5-nitro furfural diacetate, generating the target compound) nitrofurantoin-13C,l5N3) (V). As-synthesized target product was characterized by infrared spectrometry, high-performance liquid chromatog-raphy, and mass spectrometry. It has been found that the established synthetic route is dominated by mild reaction conditions and gives rise to the final product in a yield of above 60%, while the abundance of the isotopes does not tend to decline. Namely, the chemical purity of the target product is above 99. 0%, and the abundances of 13C and 15N are above 98% and 99%, respectively. 5. The contamination of commercial 15N2 gas stocks with 15N-labeled nitrate and ammonium and consequences for nitrogen fixation measurements. Directory of Open Access Journals (Sweden) Richard Dabundo Full Text Available We report on the contamination of commercial 15-nitrogen (15N N2 gas stocks with 15N-enriched ammonium, nitrate and/or nitrite, and nitrous oxide. 15N2 gas is used to estimate N2 fixation rates from incubations of environmental samples by monitoring the incorporation of isotopically labeled 15N2 into organic matter. However, the microbial assimilation of bioavailable 15N-labeled N2 gas contaminants, nitrate, nitrite, and ammonium, is liable to lead to the inflation or false detection of N2 fixation rates. 15N2 gas procured from three major suppliers was analyzed for the presence of these 15N-contaminants. Substantial concentrations of 15N-contaminants were detected in four Sigma-Aldrich 15N2 lecture bottles from two discrete batch syntheses. Per mole of 15N2 gas, 34 to 1900 µmoles of 15N-ammonium, 1.8 to 420 µmoles of 15N-nitrate/nitrite, and ≥21 µmoles of 15N-nitrous oxide were detected. One 15N2 lecture bottle from Campro Scientific contained ≥11 µmoles of 15N-nitrous oxide per mole of 15N2 gas, and no detected 15N-nitrate/nitrite at the given experimental 15N2 tracer dilutions. Two Cambridge Isotopes lecture bottles from discrete batch syntheses contained ≥0.81 µmoles 15N-nitrous oxide per mole 15N2, and trace concentrations of 15N-ammonium and 15N-nitrate/nitrite. 15N2 gas equilibrated cultures of the green algae Dunaliella tertiolecta confirmed that the 15N-contaminants are assimilable. A finite-differencing model parameterized using oceanic field conditions typical of N2 fixation assays suggests that the degree of detected 15N-ammonium contamination could yield inferred N2 fixation rates ranging from undetectable, <0.01 nmoles N L(-1 d(-1, to 530 nmoles N L(-1 d(-1, contingent on experimental conditions. These rates are comparable to, or greater than, N2 fixation rates commonly detected in field assays. These results indicate that past reports of N2 fixation should be interpreted with caution, and demonstrate that the purity of 6. 15N Solid-State NMR as a Probe of Flavin H-bonding OpenAIRE Cui, Dongtao; Koder, Ronald L.; Dutton, P. Leslie; Miller, Anne-Frances 2011-01-01 Flavins mediate a wide variety of different chemical reactions in biology. To learn how one cofactor can be made to execute different reactions in different enzymes, we are developing solid-state NMR (SSNMR) to probe the flavin electronic structure, via the 15N chemical shift tensor principal values (δii). We find that SSNMR has superior responsiveness to H-bonds, compared to solution NMR. H-bonding to a model of the flavodoxin active site produced an increase of 10 ppm in the δ11 of N5 altho... 7. Detection of organic sulfur by [sup 15]N and [sup 19]F NMR via formation of iminosulfuranes Energy Technology Data Exchange (ETDEWEB) Franz, J.A.; Linehan, J.C.; Lamb, C.N. 1992-08-01 We have synthesized new iminosulfuranes from a variety of diaryl-and dialkyl sulfides and dibenzothiophene. The pattern of [sup 15]N chemical shifts indicates that functional groups attached to sulfur are not simply resolved into aryl and alkyl groups. Thus, resolution of sulfur functional groups using [sup 15]N NMR via iminosulfurane does not appear practicable. However, iminosulfurane formation, together with the N-haloamide reaction and the Pummerer rearrangement, provides pathways for chemical discrimination of different sulfur substituents using unique [sup 15]N- or, [sup 19]F-labelled fragments for different categories of sulfur functional groups. In efforts currently underway, we are applying these reactions to methylated extracts and conversion products of the high-organic-sulfur containing Yugoslavian Rasa and Spanish Mequinenza lignites. 1 tab, 14 refs. 8. Detection of organic sulfur by {sup 15}N and {sup 19}F NMR via formation of iminosulfuranes Energy Technology Data Exchange (ETDEWEB) Franz, J.A.; Linehan, J.C.; Lamb, C.N. 1992-08-01 We have synthesized new iminosulfuranes from a variety of diaryl-and dialkyl sulfides and dibenzothiophene. The pattern of {sup 15}N chemical shifts indicates that functional groups attached to sulfur are not simply resolved into aryl and alkyl groups. Thus, resolution of sulfur functional groups using {sup 15}N NMR via iminosulfurane does not appear practicable. However, iminosulfurane formation, together with the N-haloamide reaction and the Pummerer rearrangement, provides pathways for chemical discrimination of different sulfur substituents using unique {sup 15}N- or, {sup 19}F-labelled fragments for different categories of sulfur functional groups. In efforts currently underway, we are applying these reactions to methylated extracts and conversion products of the high-organic-sulfur containing Yugoslavian Rasa and Spanish Mequinenza lignites. 1 tab, 14 refs. 9. Isotopic enrichment of 15N by ionic exchange cromatography International Nuclear Information System (INIS) The ionic exchange chromatographic method in columns of resin which is employed in the study of isotopic enrichment of 15N is presented. Determinations are made of the isotopic separation constant for the exchange of isotopes 15N and 14N in the equilibrium involving ammonium hidroxide in the solution phase and ions NH4+ adsorbed in cationic resins: Dowex 50W-X8 and X12, 100-200 mesh. Experiments are also conducted for determination of height of theoretical plates for situations of equilibrium of the NH4+ band in two systems of resin's columns aimed at estimating the experimental conditions used. The isotopic analyses of nitrogen are carried out by mass spectrometry 10. Synthesis of 15 alpha-hydroxyestrogen 15-N-acetylglucosaminides. Science.gov (United States) Suzuki, E; Namba, S; Kurihara, H; Goto, J; Matsuki, Y; Nambara, T 1995-03-01 The synthesis of 15-N-acetylglucosaminides of 15 alpha-hydroxyesterone, 15 alpha-hydroxyestradiol, and 15 alpha-hydroxyestriol (estetrol) is described. The latter two were prepared by condensation of 2-acetamido-1 alpha-chloro-1,2-dideoxy-3,4,6-trio-O-acetyl-D-glucopyranose with appropriately protected 15 alpha-hydroxyestrogens by the Koenigs-Knorr reaction employing cadmium carbonate as a catalyst. Subsequent removal of protecting groups with methanolic potassium hydroxide provided the desired conjugates. 15 alpha-Hydroxyestrone 15-N-acetylglucosaminide was synthesized from the corresponding 15 alpha-hydroxyestradiol derivative by Jones oxidation followed by brief alkaline hydrolysis. These conjugates underwent enzymatic hydrolysis with beta-N-acetylglucosaminidase from Jack beans to produce 15 alpha-hydroxyestrogens. PMID:7792832 11. Geomorphic control on the δ15N of mountain forests Directory of Open Access Journals (Sweden) R. G. Hilton 2013-03-01 Full Text Available Mountain forests are subject to high rates of physical erosion which can export particulate nitrogen from ecosystems. However, the impact of geomorphic processes on nitrogen budgets remains poorly constrained. We have used the elemental and isotopic composition of soil and plant organic matter to investigate nitrogen cycling in the mountain forest of Taiwan, from 24 sites with distinct geomorphic (topographic slope and climatic (precipitation, temperature characteristics. The organic carbon to nitrogen ratio of soil organic matter decreased with soil 14C age, providing constraint on average rates of nitrogen loss using a mass balance model. Model predictions suggest that present day estimates of nitrogen deposition exceed contemporary and historic nitrogen losses. We found ∼6‰ variability in the stable isotopic composition (δ15N of soil and plants which was not related to soil 14C age or climatic conditions. Instead, δ15N was significantly, negatively correlated with topographic slope. Using the mass balance model, we demonstrate that the correlation can be explained by an increase in nitrogen loss by non-fractioning pathways on steeper slopes, where physical erosion most effectively removes particulate nitrogen. Published data from forests on steep slopes are consistent with the correlation. Based on our dataset and these observations, we hypothesise that variable physical erosion rates can significantly influence soil δ15N, and suggest particulate nitrogen export is a major, yet underappreciated, loss term in the nitrogen budget of mountain forests. 12. Nitrogen input 15N-signatures are reflected in plant 15N natural abundances of N-rich tropical forest in China Science.gov (United States) Abdisa Gurmesa, Geshere; Lu, Xiankai; Gundersen, Per; Yunting, Fang; Mo, Jiangming 2016-04-01 In this study, we tested the measurement of natural abundance of 15N15N) for its ability to assess changes in N cycling due to increased N deposition in two forest types; namely, an old-growth broadleaved forest and a pine forest, in southern China. We measured δ15N values of inorganic N in input and output fluxes under ambient N deposition, and N concentration and δ15N of major ecosystem compartments under ambient and increased N deposition. Our results showed that N deposition to the forests was 15N-depleted, and was dominated by NH4-N. Plants were 15N-depleted due to imprint from the 15N-depleted atmospheric N deposition. The old-growth forest had larger N concentration and was more 15N-enriched than the pine forest. Nitrogen addition did not significantly affect N concentration, but it significantly increased δ15N values of plants, and slightly more so in the pine forest, toward the 15N signature of the added N in both forests. The result indicates that the pine forest may rely more on the 15N-depleted deposition N. Soil δ15N values were slightly decreased by the N addition. Our result suggests that ecosystem δ15N is more sensitive to the changes in ecosystem N status and N cycling than N concentration in N-saturated sub-tropical forests. 13. Comparison of the backbone dynamics of wild-type Hydrogenobacter thermophilus cytochrome c{sub 552} and its b-type variant Energy Technology Data Exchange (ETDEWEB) Tozawa, Kaeko; Ferguson, Stuart J.; Redfield, Christina, E-mail: christina.redfield@bioch.ox.ac.uk [University of Oxford, Department of Biochemistry (United Kingdom); Smith, Lorna J., E-mail: lorna.smith@chem.ox.ac.uk [University of Oxford, Department of Chemistry (United Kingdom) 2015-06-15 Cytochrome c{sub 552} from the thermophilic bacterium Hydrogenobacter thermophilus is a typical c-type cytochrome which binds heme covalently via two thioether bonds between the two heme vinyl groups and two cysteine thiol groups in a CXXCH sequence motif. This protein was converted to a b-type cytochrome by substitution of the two cysteine residues by alanines (Tomlinson and Ferguson in Proc Natl Acad Sci USA 97:5156–5160, 2000a). To probe the significance of the covalent attachment of the heme in the c-type protein, {sup 15}N relaxation and hydrogen exchange studies have been performed for the wild-type and b-type proteins. The two variants share very similar backbone dynamic properties, both proteins showing high {sup 15}N order parameters in the four main helices, with reduced values in an exposed loop region (residues 18–21), and at the C-terminal residue Lys80. Some subtle changes in chemical shift and hydrogen exchange protection are seen between the wild-type and b-type variant proteins, not only for residues at and neighbouring the mutation sites, but also for some residues in the heme binding pocket. Overall, the results suggest that the main role of the covalent linkages between the heme group and the protein chain must be to increase the stability of the protein. 14. COVALENT BINDING OF REDUCED METABOLITES OF [15N3] TNT TO SOIL ORGANIC MATTER DURING A BIOREMEDIATION PROCESS ANALYZED BY 15N NMR SPECTROSCOPY. (R826646) Science.gov (United States) Evidence is presented for the covalent binding ofbiologically reduced metabolites of 2,4,6-15N3-trinitrotoluene(TNT) to different soil fractions (humic acids, fulvicacids, and humin) using liquid 15N NMR spectroscopy. Asilylation p... 15. Exercise: The Backbone of Spine Treatment Science.gov (United States) Exercise: The Backbone of Spine Treatment \| View Video Back Purchase Video Struggling with Low Back Pain? Many people are surprised to learn that carefully selected exercise can actually reduce back pain. Some exercises can ... 16. Exercise: The Backbone of Spine Treatment Medline Plus Full Text Available Exercise: The Backbone of Spine Treatment \| View Video Back Purchase Video Struggling with Low Back Pain? Many people are surprised to learn that carefully selected exercise can actually reduce back pain. Some exercises can ... 17. Exercise: The Backbone of Spine Treatment Medline Plus Full Text Available Exercise: The Backbone of Spine Treatment \| View Video Back Purchase Video Struggling with Low Back Pain? Many people are surprised to learn that carefully selected exercise can ... 18. Dynamic of N fertilizers: urea (15 N) and aqua ammonia (15 N) incorporated to the sugar cane soil. Final report International Nuclear Information System (INIS) The dynamic of N fertilizers, urea and aqua ammonia, in the soil of sugar cane crops are studied with an emphasis on the horizontal and vertical moving. The nitrogen routing from urea and aqua ammonia sources, by isotopic technique with 15 N in relation to the leaching, volatilization and extraction by the cultivation and residue of N immobilized manure in the soil with sugar cane plantation is also analysed. (C.G.C.) 19. A novel method for trapping and analyzing 15N in NO for tracing NO sources Science.gov (United States) Kang, Ronghua; Mulder, Jan; Dörsch, Peter 2016-04-01 15N isotope tracing is an effective and direct approach to investigate the biological and chemical sources of nitric oxide (NO) in soil. However, NO is highly reactive and rapidly converted to nitrogen dioxide (NO2) in the presence of ozone. Various chemical conversions of NO to the more stable solutes nitrite (NO2-) and nitrate (NO3-) have been proposed, which allow analysing the 15N abundance without major fractionation. However, NO emissions from soils are usually small, posing major challenges to conversion efficiency and background contamination. Here we present a novel method in which NO is oxidized to NO2- by chromium trioxide (CrO3) prior to conversion to NO2- and NO3- in an alkaline hydrogen peroxide (H2O2) solution. Immediately following trapping, manganese dioxide (MnO2) and 5M HCl are added to remove excess H2O2, and to adjust the pH to around 6.0-7.0, respectively. The resulting solution can be stored until analysis and is none-toxic, allowing to use a modified denitrifier method (Zhu et al., submitted), where NO2- and NO3- are reduced quantitatively to nitrous oxide (N2O). Optimum NO conversion rates of > 90% even at extremely low initial NO concentration were obtained with 4% H2O2, 0.5 M NaOH, and 0.5 L min-1 gas flow rate. In a laboratory test, using NO gas with different 15N signals produced from unlabelled and labelled NO2-, we found an overall precision of 0.4‰ for unlabelled and 49.7‰ for NO enriched with 1.0 atom% 15N, respectively. This indicates that this method can be used for both natural abundance studies of NO, as well as in labelling studies tracing NO sources. Zhu J, Yu L, Bakken LR, Mørkved PT, Mulder J, Dörsch P. Controlled induction of denitrification in Pseudomonas aureofaciens: a modified denitrifier method for 15N and 18O analysis in NO3- from natural water samples by IRMS. Submitted. 20. Toward structural dynamics: protein motions viewed by chemical shift modulations and direct detection of C'N multiple-quantum relaxation. Science.gov (United States) Mori, Mirko; Kateb, Fatiha; Bodenhausen, Geoffrey; Piccioli, Mario; Abergel, Daniel 2010-03-17 Multiple quantum relaxation in proteins reveals unexpected relationships between correlated or anti-correlated conformational backbone dynamics in alpha-helices or beta-sheets. The contributions of conformational exchange to the relaxation rates of C'N coherences (i.e., double- and zero-quantum coherences involving backbone carbonyl (13)C' and neighboring amide (15)N nuclei) depend on the kinetics of slow exchange processes, as well as on the populations of the conformations and chemical shift differences of (13)C' and (15)N nuclei. The relaxation rates of C'N coherences, which reflect concerted fluctuations due to slow chemical shift modulations (CSMs), were determined by direct (13)C detection in diamagnetic and paramagnetic proteins. In well-folded proteins such as lanthanide-substituted calbindin (CaLnCb), copper,zinc superoxide dismutase (Cu,Zn SOD), and matrix metalloproteinase (MMP12), slow conformational exchange occurs along the entire backbone. Our observations demonstrate that relaxation rates of C'N coherences arising from slow backbone dynamics have positive signs (characteristic of correlated fluctuations) in beta-sheets and negative signs (characteristic of anti-correlated fluctuations) in alpha-helices. This extends the prospects of structure-dynamics relationships to slow time scales that are relevant for protein function and enzymatic activity. 1. Natural abundance (14)N and (15)N solid-state NMR of pharmaceuticals and their polymorphs. Science.gov (United States) Veinberg, Stanislav L; Johnston, Karen E; Jaroszewicz, Michael J; Kispal, Brianna M; Mireault, Christopher R; Kobayashi, Takeshi; Pruski, Marek; Schurko, Robert W 2016-06-29 (14)N ultra-wideline (UW), (1)H{(15)N} indirectly-detected HETCOR (idHETCOR) and (15)N dynamic nuclear polarization (DNP) solid-state NMR (SSNMR) experiments, in combination with plane-wave density functional theory (DFT) calculations of (14)N EFG tensors, were utilized to characterize a series of nitrogen-containing active pharmaceutical ingredients (APIs), including HCl salts of scopolamine, alprenolol, isoprenaline, acebutolol, dibucaine, nicardipine, and ranitidine. A case study applying these methods for the differentiation of polymorphs of bupivacaine HCl is also presented. All experiments were conducted upon samples with naturally-abundant nitrogen isotopes. For most of the APIs, it was possible to acquire frequency-stepped UW (14)N SSNMR spectra of stationary samples, which display powder patterns corresponding to pseudo-tetrahedral (i.e., RR'R''NH(+) and RR'NH2(+)) or other (i.e., RNH2 and RNO2) nitrogen environments. Directly-excited (14)N NMR spectra were acquired using the WURST-CPMG pulse sequence, which incorporates WURST (wideband, uniform rate, and smooth truncation) pulses and a CPMG (Carr-Purcell Meiboom-Gill) refocusing protocol. In certain cases, spectra were acquired using (1)H → (14)N broadband cross-polarization, via the BRAIN-CP (broadband adiabatic inversion - cross polarization) pulse sequence. These spectra provide (14)N electric field gradient (EFG) tensor parameters and orientations that are particularly sensitive to variations in local structure and intermolecular hydrogen-bonding interactions. The (1)H{(15)N} idHETCOR spectra, acquired under conditions of fast magic-angle spinning (MAS), used CP transfers to provide (1)H-(15)N chemical shift correlations for all nitrogen environments, except for two sites in acebutolol and nicardipine. One of these two sites (RR'NH2(+) in acebutolol) was successfully detected using the DNP-enhanced (15)N{(1)H} CP/MAS measurement, and one (RNO2 in nicardipine) remained elusive due to the absence of 2. Heteronuclear 2D-correlations in a uniformly [13C, 15N] labeled membrane-protein complex at ultra-high magnetic fields Energy Technology Data Exchange (ETDEWEB) Egorova-Zachernyuk, T.A.; Hollander, J. [Gorlaeus Laboratories (Netherlands); Fraser, N. [University of Glasgow, Division of Biochemistry and Molecular Biology (United Kingdom); Gast, P.; Hoff, A.J. [Leiden University, Huygens Laboratories (Netherlands); Cogdell, R. [University of Glasgow, Division of Biochemistry and Molecular Biology (United Kingdom); Groot, H.J.M. de; Baldus, M. [Gorlaeus Laboratories (Netherlands) 2001-03-15 One- and two-dimensional solid-state NMR experiments on a uniformly labeled intrinsic membrane-protein complex at ultra-high magnetic fields are presented. Two-dimensional backbone and side-chain correlations for a [U-{sup 13}C,{sup 15}N] labeled version of the LH2 light-harvesting complex indicate significant resolution at low temperatures and under Magic Angle Spinning. Tentative assignments of some of the observed correlations are presented and attributed to the {alpha}-helical segments of the protein, mostly found in the membrane interior. 3. Application of δ13C and δ15N isotopic signatures of organic matter fractions sequentially separated from adjacent arable and forest soils to identify carbon stabilization mechanisms OpenAIRE Kayler, Z.E.; Kaiser, M; Gessler, A.; Ellerbrock, R. H.; M. Sommer 2011-01-01 Identifying the chemical mechanisms behind soil carbon bound in organo-mineral complexes is necessary to determine the degree to which soil organic carbon is stabilized belowground. Analysis of δ13C and δ15N isotopic signatures of stabilized OM fractions along with soil mineral characteristics may yield important information about OM-mineral associations and their processing history. We anlayzed the δ13C and δ15N isotopic signatures from two organic matter (OM) fractio... 4. Fate of orally administered {sup 15}N-labeled polyamines in rats bearing solid tumors Energy Technology Data Exchange (ETDEWEB) Kobayashi, Masaki; Samejima, Keijiro; Goda, Hitomi; Niitsu, Masaru [Josai Univ., Sakado, Saitama (Japan). Faculty of Pharmaceutical Sciences; Xu Yongji [Qingdao Univ. of Science and Technology (China). Inst. of Chemical and Molecular Technology; Takahashi, Masakazu [Sasaki Inst., Tokyo (Japan); Hashimoto, Yoshiyuki [Kyoritsu Coll. of Pharmacy, Tokyo (Japan) 2003-03-01 We studied absorption, distribution, metabolism, and excretion of polyamines (putrescine, spermidine, and spermine) in the gastrointestinal tract using {sup 15}N-labeled polyamines as tracers and ionspray ionization mass spectrometry (IS-MS). The relatively simple protocol using rats bearing solid tumors provided useful information. Three {sup 15}N-labeled polyamines that were simultaneously administered were absorbed equally from gastrointestinal tract, and distributed within tissues at various concentrations. The uptake of {sup 15}N-spermidine seemed preferential to that of {sup 15}N-spermine since the concentrations of {sup 15}N-spermidine in the liver and tumors were higher, whereas those of {sup 15}N-spermine were higher in the kidney, probably due to the excretion of excess extracellular spermine. Most of the absorbed {sup 15}N-putrescine seemed to be lost, suggesting blood and tissue diamine oxidase degradation. Concentrations of {sup 15}N-spermidine and {sup 15}N-spermine in the tumor were low. We also describe the findings from two rats that were administered with {sup 15}N-spermine. The tissue concentrations of {sup 15}N-spermine were unusually high, and significant levels of {sup 15}N-spermidine were derived from {sup 15}N-spermine in these animals. (author) 5. Investigation of the metabolism of colostomized laying hens with 15N-labelled wheat. 6 International Nuclear Information System (INIS) Three colostomized laving hens received 40 g 15N-labelled wheat with 20.13 atom-% 15N excess (15N'), 19.18 atom-% 15N'-lysine, 18.17 atom-% 15N'-histidine and 20.43 atom-% 15N'-arginine per day over a period of four days. After having received the same non-labelled feed ration on the following four days, the hens were slaughtered. The incorporation and distribution of 15N' in the total nitrogen and the nitrogen of the basic amino acids was determined in liver, kidneys, muscles, bones and the remaining carcass (excluding blood, digestive tract and genital organs). The quota of nitrogen of natural isotope frequency (14N) of the total 14N of the hens' carcasses was 47% in the muscles, 14% in the bones and 20% in the feathers; the relative 15N' values were 37%, 8% and 1%, resp. The atom-% 15N' in the kidneys was twice as much as in the liver four days after the last 15N' application. The average percentage of the nitrogen in the three basic amino acids of the total nitrogen in the tissues and organs (excluding feathers) is 25% concerning both 14N and 15N'. The 15N' balance revealed that in hen 1 100%, in hen 2 102% and in hen 3 101% of the consumed wheat 15N' were found. (author) 6. Microsoft Operations Framework implementation for The Backbone NARCIS (Netherlands) Kienhuis, G.H. 2007-01-01 Doel The Backbone ontwerpt, implementeert en beheert IT infrastructuren voor bedrijven en instellingen. Beheer wordt proactief uitgevoerd met behulp van Microsoft Operation Manager (MOM) 2005. MOM is een applicatie die de status en gebeurtenissen van systemen zichtbaar maakt vanuit één locatie. Om 7. Green Network Planning Model for Optical Backbones DEFF Research Database (Denmark) Gutierrez Lopez, Jose Manuel; Riaz, M. Tahir; Jensen, Michael; 2010-01-01 Communication networks are becoming more essential for our daily lives and critically important for industry and governments. The intense growth in the backbone traffic implies an increment of the power demands of the transmission systems. This power usage might have a significant negative effect... 8. Determination of 15N nitrates in water samples using mass spectrometry International Nuclear Information System (INIS) The nitrogen element (Z = 7) has two stable isotopes, whose relative quantities are 99.64% for 14N and 0.36% for 15N. Nitrogen is part of many processes and reactions that are important to life and that affect the quality of the water. Within the nitrogen cycle there are kinetic and thermodynamic fractionation processes, which are potentially important for tracing its sources and demands. Water contamination due to nitrates is a serious problem that is affecting large parts of the biosphere. Surface water contamination can be remedied by prevention and control measures, but the problem becomes acute when the contamination penetrates to groundwater water. Contaminated groundwater can remain in the aquifers for centuries, even milleniums, and decontamination is very difficult, if not impossible. Isotopic techniques can help to evaluate how vulnerable the groundwater is to contamination from the surface when its displacement speed and extra load area are determined. Then the sources of surface contamination (natural, industrial, agricultural, domestic) can be identified. Isotopic techniques can also describe an incipient contamination, and they can provide an early alert when chemical or biological indicators do not reveal any signs for concern. The isotopic fractionation of several nitrogen compounds provide the basis for using 15N as a hydrological isotope tool. There are three main sources of nitrogen contamination in water, these are: organic nitrogen in the soil, nitrogenized fertilizers, domestic, industrial and animal wastes. The following technical procedure describes the method for determining the isotopic ration 15N/14N in nitrates in water. The nitrate is separated from the water using ion exchange columns through a resin, which is eluded with HCI and with the addition of silver oxide becomes silver nitrate. This solution is freeze-dried and submitted to combustion at 850 in a sealed quartz tube, using copper/copper oxide for the nitrogen reduction and 9. Study on Nitrogen Forms in Phenolic Polymers Incorporating Protien by 15N CP—MAS NMR Institute of Scientific and Technical Information of China (English) CHENGLILI; WENQIXIAO; 等 1996-01-01 Phenolic polymers synthesized by reactions by reactions of p-benzoquinone with 15N-labelled protein or (15NH4)2SO4 were studied by using 15N CP-MAS NMR technique in combination with chemical approaches.Results showed that more than 80% of nitrogen in quinone-protein polymers was in the form of amide with some present as aromatic and /or aliphatic amine and less than 10% of nitrogen occurred as heterocyclic N.The nitrogen distribution in the non-hydrolyzable residue of the quinone-protein polymers was basically similar to that of soil humic acid reported in literature with the exception that a higher proportion of N as heterocyclic N and aromatic amine and a lower proportion of N as amide and aliphatic amine were found in the former than in the latter,More than 70% of total nitrogen in quinone-(NH4)2OS4 polymer was acid resistant ,of which about 53% occurred as pyrrole,nitrile and imion type N.The possible roles of the reactions of phenols or quinones with proteins in the formation of humic acid.especially the non-hydrolyzable nitrogen in humicacid,are discussed. 10. Metabolic studies in colostomized laying hens using 15N-labelled wheat. 4 International Nuclear Information System (INIS) 3 colostomized laying hybrids received over 4 days a dosage of 672 mg 15N excess (15N'), 20.3 mg lysine 15N', 23.0 mg histidine 15N' and 66.7 mg arginine 15N' with a ration customary in production. After feeding the same unlabelled ration for another 4 days the hens were killed and the N content of the blood as well as of its fractions (cells, plasma, free amino acids of the plasma) was determined. The 15N' was determined in the total blood, the corpuscles, the plasma, the nonprotein-N (NPN) fraction as well as in the amino acids lysine, histidine and arginine. The average amount of the blood cell N in the total blood N was 58.5% and that of the plasma 40.3%; the corresponding 15N' values amounted to 66.1% and 33.9%, respectively. The sum of the 15N' of the basic amino acids of the blood cells, on an average, amounted to 39.7% of the total cell 15N'; the corresponding average value for the total 15N' in lysine, histidine and arginine of the blood plasma 15N' was 23.6.% and the quota of the three free amino acids of the total NP15N' of the plasma was 6.2%. (author) 11. Orientation-dependent backbone-only residue pair scoring functions for fixed backbone protein design Directory of Open Access Journals (Sweden) Bordner Andrew J 2010-04-01 Full Text Available Abstract Background Empirical scoring functions have proven useful in protein structure modeling. Most such scoring functions depend on protein side chain conformations. However, backbone-only scoring functions do not require computationally intensive structure optimization and so are well suited to protein design, which requires fast score evaluation. Furthermore, scoring functions that account for the distinctive relative position and orientation preferences of residue pairs are expected to be more accurate than those that depend only on the separation distance. Results Residue pair scoring functions for fixed backbone protein design were derived using only backbone geometry. Unlike previous studies that used spherical harmonics to fit 2D angular distributions, Gaussian Mixture Models were used to fit the full 3D (position only and 6D (position and orientation distributions of residue pairs. The performance of the 1D (residue separation only, 3D, and 6D scoring functions were compared by their ability to identify correct threading solutions for a non-redundant benchmark set of protein backbone structures. The threading accuracy was found to steadily increase with increasing dimension, with the 6D scoring function achieving the highest accuracy. Furthermore, the 3D and 6D scoring functions were shown to outperform side chain-dependent empirical potentials from three other studies. Next, two computational methods that take advantage of the speed and pairwise form of these new backbone-only scoring functions were investigated. The first is a procedure that exploits available sequence data by averaging scores over threading solutions for homologs. This was evaluated by applying it to the challenging problem of identifying interacting transmembrane alpha-helices and found to further improve prediction accuracy. The second is a protein design method for determining the optimal sequence for a backbone structure by applying Belief Propagation 12. Characterization of mu s-ms dynamics of proteins using a combined analysis of N-15 NMR relaxation and chemical shift: Conformational exchange in plastocyanin induced by histidine protonations DEFF Research Database (Denmark) Hass, M. A. S.; Thuesen, Marianne Hallberg; Christensen, Hans Erik Mølager; 2004-01-01 An approach is presented that allows a detailed, quantitative characterization of conformational exchange processes in proteins on the mus-ms time scale. The approach relies on a combined analysis of NMR relaxation rates and chemical shift changes and requires that the chemical shift...... variabilis (A.v. PCu) (Ma, L.; Hass, M. A. S.; Vierick, N.; Kristensen, S. M.; Ulstrup, J.; Led, J. J. Biochemistry 2003, 42, 320-330). The R-1 and R-2 relaxation rates of the backbone N-15 nuclei were measured at a series of pH and temperatures on an 15N labeled sample of A.v. PCu, and the 15 N chemical...... quantitatively by the correlation between the R-ex terms and the corresponding chemical shift differences of the exchanging species. By this approach, the R-ex terms of N-15 nuclei belonging to contiguous regions in the protein could be assigned to the same exchange process. Furthermore, the analysis... 13. 15N isotope fractionation in an aquatic food chain: Bellamya aeruginosa (Reeve) as an algal control agent. Science.gov (United States) Han, Shiqun; Yan, Shaohua; Chen, Kaining; Zhang, Zhenhua; Zed, Rengel; Zhang, Jianqiu; Song, Wei; Liu, Haiqin 2010-01-01 15N isotope tracer techniques and ecological modeling were adopted to investigate the fractionation of nitrogen, its uptake and transformation in algae and snail (Bellamya aeruginosa Reeve). Different algal species were found to differ in their uptake of nitrogen isotopes. Microcystis aeruginisa Kütz. demonstrated the greatest 15N accumulation capacity, with the natural variation in isotopic ratio (delta 15N) and the isotope fractionation factor (epsilon, % per hundred) being the highest among the species investigated. The transformation and utilization of 15N by snails differed depending on the specific algae consumed (highest for Chlorella pyrenoidosa Chick., lowest for M. aeruginisa). When snails was seeded in the experimental pond, the algae population structure changed significantly, and total algal biomass as well as the concentration of all nitrogen species decreased, causing an increase in water transparency. A model, incorporating several chemical and biological parameters, was developed to predict algal biomass in an aquatic system when snails was present. The data collected during this investigation indicated that the gastropods such as snails could significantly impact biological community and water quality of small water bodies, suggesting a role for biological control of noxious algal blooms associated with eutrophication. PMID:20397413 14. FAO/IAEA - interregional training course on the use of 15N in soil science and plant nutrition International Nuclear Information System (INIS) This training manual provides an introduction for the basic methodology and principles of application of the stable isotope 15N. After preliminary remarks on stable isotope terminology fundamentals, experimental problems and methods of quantitative nitrogen determination in soil and plant studies are reported in the main part of the manual. An appendix with a compilation of different parameters such as natural abundance of stable isotopes, selected atomic weights and multiples of them conversion factors of chemical compounds, and much more concludes the manual 15. Utilization of 15N-labelled urea in laying hens. 4 International Nuclear Information System (INIS) In order to study the utilization of urea in poultry, 3 colostomized laying hybrids were orally supplied with a traditional ration supplemented with 1% 15N'-labelled urea with a 15N excess (15N') of 96.06 atom-% over a period of 6 days. After another 2 days on which the hens received the same ration with unlabelled urea, they were killed. The atom-% 15N' of the blood on an average of the 3 hens was 0.64, of the plasma 1.40 and of the corpuscles 0.47. The TCA-soluble fraction of the blood had an average 15N' of 1.14 atom-%; the 15N amount was 9.7% of the total amount of 15N in the blood. The amount of 15N' in the urea in the blood was 6.8 atom-%. This shows that the absorbed urea is decomposed very slowly. The quota of 15N' in the basic amino acids from the total 15N' of the blood plasma was only 0.3% and that of the corpuscles 2.2%. The average 15N' of the mature follicles was 2.39 atom-% whereas the smallest and the remaining ovary contain 1.12 atom-%. The labelling level of lysine in mature egg cells was, in contrast to this, only 0.08 atom-% 15N' and in infantile follicles 0.04 atom-% 15N'. 1% of the 15N' quota was in the follicles and the remaining ovary. Of the basic amino acids, histidine is most strongly labelled. The lower incorporation of the 15N' from urea into the basic amino acids shows that the nitrogen of this compound can be used for the synthesis of the essential amino acids to a low degree only. (author) 16. Transforming plastic surfaces with electrophilic backbones from hydrophobic to hydrophilic. Science.gov (United States) Kim, Samuel; Bowen, Raffick A R; Zare, Richard N 2015-01-28 We demonstrate a simple nonaqueous reaction scheme for transforming the surface of plastics from hydrophobic to hydrophilic. The chemical modification is achieved by base-catalyzed trans-esterification with polyols. It is permanent, does not release contaminants, and causes no optical or mechanical distortion of the plastic. We present contact angle measurements to show successful modification of several types of plastics including poly(ethylene terephthalate) (PET) and polycarbonate (PC). Its applicability to blood analysis is explored using chemically modified PET blood collection tubes and found to be quite satisfactory. We expect this approach will reduce the cost of manufacturing plastic devices with optimized wettability and can be generalized to other types of plastic materials having an electrophilic linkage as its backbone. 17. Hash: a program to accurately predict protein H{sup {alpha}} shifts from neighboring backbone shifts Energy Technology Data Exchange (ETDEWEB) Zeng Jianyang, E-mail: zengjy@gmail.com [Tsinghua University, Institute for Interdisciplinary Information Sciences (China); Zhou Pei [Duke University Medical Center, Department of Biochemistry (United States); Donald, Bruce Randall [Duke University, Department of Computer Science (United States) 2013-01-15 Chemical shifts provide not only peak identities for analyzing nuclear magnetic resonance (NMR) data, but also an important source of conformational information for studying protein structures. Current structural studies requiring H{sup {alpha}} chemical shifts suffer from the following limitations. (1) For large proteins, the H{sup {alpha}} chemical shifts can be difficult to assign using conventional NMR triple-resonance experiments, mainly due to the fast transverse relaxation rate of C{sup {alpha}} that restricts the signal sensitivity. (2) Previous chemical shift prediction approaches either require homologous models with high sequence similarity or rely heavily on accurate backbone and side-chain structural coordinates. When neither sequence homologues nor structural coordinates are available, we must resort to other information to predict H{sup {alpha}} chemical shifts. Predicting accurate H{sup {alpha}} chemical shifts using other obtainable information, such as the chemical shifts of nearby backbone atoms (i.e., adjacent atoms in the sequence), can remedy the above dilemmas, and hence advance NMR-based structural studies of proteins. By specifically exploiting the dependencies on chemical shifts of nearby backbone atoms, we propose a novel machine learning algorithm, called Hash, to predict H{sup {alpha}} chemical shifts. Hash combines a new fragment-based chemical shift search approach with a non-parametric regression model, called the generalized additive model, to effectively solve the prediction problem. We demonstrate that the chemical shifts of nearby backbone atoms provide a reliable source of information for predicting accurate H{sup {alpha}} chemical shifts. Our testing results on different possible combinations of input data indicate that Hash has a wide rage of potential NMR applications in structural and biological studies of proteins. 18. (13)C, (15)N CPMAS NMR and GIAO DFT calculations of stereoisomeric oxindole alkaloids from Cat's Claw (Uncaria tomentosa). Science.gov (United States) Paradowska, Katarzyna; Wolniak, Michał; Pisklak, Maciej; Gliński, Jan A; Davey, Matthew H; Wawer, Iwona 2008-11-01 Oxindole alkaloids, isolated from the bark of Uncaria tomentosa [Willd. ex Schult.] Rubiaceae, are considered to be responsible for the biological activity of this herb. Five pentacyclic and two tetracyclic alkaloids were studied by solid-state NMR and theoretical GIAO DFT methods. The (13)C and (15)N CPMAS NMR spectra were recorded for mitraphylline, isomitraphylline, pteropodine (uncarine C), isopteropodine (uncarine E), speciophylline (uncarine D), rhynchophylline and isorhynchophylline. Theoretical GIAO DFT calculations of shielding constants provide arguments for identification of asymmetric centers and proper assignment of NMR spectra. These alkaloids are 7R/7S and 20R/20S stereoisomeric pairs. Based on the (13)C CP MAS chemical shifts the 7S alkaloids (delta C3 70-71ppm) can be easily and conveniently distinguished from 7R (deltaC3 74.5-74.9ppm), also 20R (deltaC20 41.3-41.7ppm) from the 20S (deltaC20 36.3-38.3ppm). The epiallo-type isomer (3R, 20S) of speciophylline is characterized by a larger (15)N MAS chemical shift of N4 (64.6ppm) than the allo-type (3S, 20S) of isopteropodine (deltaN4 53.3ppm). (15)N MAS chemical shifts of N1-H in pentacyclic alkaloids are within 131.9-140.4ppm. 19. Mimicking floodplain reconnection and disconnection using 15N mesocosm incubations Directory of Open Access Journals (Sweden) W. Wanek 2012-04-01 Full Text Available Floodplain restoration changes the nitrate delivery pattern and dissolved organic matter pool in backwaters but other effects are not yet well known. We performed two mesocosm experiments to quantify the nitrate metabolism in two types of floodplains. Rates of denitrification, dissimilatory nitrate reduction to ammonium (DNRA and anammox were measured using 15N tracer additions in mesocosms containing undisturbed floodplain sediments originating from (1 restored and (2 disconnected sites in the Alluvial Zone National Park on the Danube River downstream of Vienna, Austria. DNRA rates were an order of magnitude lower than denitrification and neither rate was affected by changes in nitrate delivery pattern or organic matter quality. Anammox was not detected at any of the sites. Denitrification was out-competed by assimilation which was estimated to use up to 70% of the available nitrate. Overall, denitrification was higher in the restored sites, with mean rates of 5.7±2.8 mmol N m−2 h−1 compared to the disconnected site (0.6±0.5 mmol N m−1 h−1. In addition, ratios of N2O : N2 were lower in the restored site indicating a more complete denitrification. Nitrate addition did not have any effect on denitrification, nor on the N2O : N2 ratio. However, DOM quality significantly changed the N2O : N2 ratio in both sites. Addition of riverine derived organic matter lowered the N2O : N2 ratio in the disconnected site, whereas addition of floodplain derived organic matter increased the N2O : N2 ratio in the restored site. These results demonstrate that increasing floodplains hydrological connection to the main river channel increases nitrogen retention and decreases nitrous oxide emissions. 20. Mechanism of Solid-State Thermolysis of Ammonia Boraine: 15N NMR Study Using Fast Magic-Angle Spinning and Dynamic Nuclear Polarization Energy Technology Data Exchange (ETDEWEB) Kobayashi, Takeshi [Ames Laboratory; Gupta, Shalabh [Ames Laboratory; Caporini, Marc A [Bruker BioSpin Corporation; Pecharsky, Vitalij K [Ames Laboratory; Pruski, Marek [Ames Laboratory 2014-08-28 The solid-state thermolysis of ammonia borane (NH3BH3, AB) was explored using state-of-the-art 15N solid-state NMR spectroscopy, including 2D indirectly detected 1H{15N} heteronuclear correlation and dynamic nuclear polarization (DNP)-enhanced 15N{1H} cross-polarization experiments as well as 11B NMR. The complementary use of 15N and 11B NMR experiments, supported by density functional theory calculations of the chemical shift tensors, provided insights into the dehydrogenation mechanism of AB—insights that have not been available by 11B NMR alone. Specifically, highly branched polyaminoborane derivatives were shown to form from AB via oligomerization in the “head-to-tail” manner, which then transform directly into hexagonal boron nitride analog through the dehydrocyclization reaction, bypassing the formation of polyiminoborane. 1. Precision and sensitivity of the measurement of 15N enrichment in D-alanine from bacterial cell walls using positive/negative ion mass spectrometry Science.gov (United States) Tunlid, A.; Odham, G.; Findlay, R. H.; White, D. C. 1985-01-01 Sensitive detection of cellular components from specific groups of microbes can be utilized as 'signatures' in the examination of microbial consortia from soils, sediments or biofilms. Utilizing capillary gas chromatography/mass spectrometry and stereospecific derivatizing agents, D-alanine, a component localized in the prokaryotic (bacterial) cell wall, can be detected reproducibly. Enrichments of D-[15N]alanine determined in E. coli grown with [15N]ammonia can be determined with precision at 1.0 atom%. Chemical ionization with methane gas and the detection of negative ions (M - HF)- and (M - F or M + H - HF)- formed from the heptafluorobutyryl D-2 butanol ester of D-alanine allowed as little as 8 pg (90 fmol) to be detected reproducibly. This method can be utilized to define the metabolic activity in terms of 15N incorporation at the level of 10(3)-10(4) cells, as a function of the 15N-14N ratio. 2. Net neutrality at internet backbone provider level OpenAIRE Baglioni, Laura; Calabrese, Armando; Ghiron, Nathan Levialdi 2013-01-01 This paper analysis the Internet interconnection market and combine the main technical (i.e. service quality) and economic aspects (i.e. profits and utility) characterizing relations between market players (end users, EUs; Internet Service Providers, ISPs; Internet Backbone Providers, IBPs) in order to determine possible economic outcomes in the strategic interaction between them. The proposed model enables a comparison to be made between expected values of social welfare (i.e. EU utility and... 3. SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network Energy Technology Data Exchange (ETDEWEB) Shen Yang; Bax, Ad, E-mail: bax@nih.go [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States) 2010-09-15 NMR chemical shifts provide important local structural information for proteins and are key in recently described protein structure generation protocols. We describe a new chemical shift prediction program, SPARTA+, which is based on artificial neural networking. The neural network is trained on a large carefully pruned database, containing 580 proteins for which high-resolution X-ray structures and nearly complete backbone and {sup 13}C{sup {beta}} chemical shifts are available. The neural network is trained to establish quantitative relations between chemical shifts and protein structures, including backbone and side-chain conformation, H-bonding, electric fields and ring-current effects. The trained neural network yields rapid chemical shift prediction for backbone and {sup 13}C{sup {beta}} atoms, with standard deviations of 2.45, 1.09, 0.94, 1.14, 0.25 and 0.49 ppm for {delta}{sup 15}N, {delta}{sup 13}C', {delta}{sup 13}C{sup {alpha}}, {delta}{sup 13}C{sup {beta}}, {delta}{sup 1}H{sup {alpha}} and {delta}{sup 1}H{sup N}, respectively, between the SPARTA+ predicted and experimental shifts for a set of eleven validation proteins. These results represent a modest but consistent improvement (2-10%) over the best programs available to date, and appear to be approaching the limit at which empirical approaches can predict chemical shifts. 4. Backbone Dynamics of Triple-helical Collagen-like Structure OpenAIRE Lazarev, Yu.A.; Lazareva, A.V.; Komarov, V.M. 1999-01-01 Some details of the backbone dynamics in the collagen-like triple helix is discussed and the role of backbone dynamics in functioning collagen proteins is illustrated. On a series of oligotripeptides synthetic analogs of collagen formation of high-frequency vibrational backbone dynamics and low-frequency nonlinear backbone dynamics upon stepwise elongation of peptide chain have been described using infrared spectroscopy and hydrogen-exchange method. In the fully completed triple helix the lev... 5. Studies with 15N-labelled lysine in colostomized laying hens. 5 International Nuclear Information System (INIS) 3 colostomized laying hens received, together with a commercial ration of 120 g, 0.2 % 15N-labelled L-lysine with an atom-% 15N excess (15N') of 48 %; subsequently the same ration was fed over a period od 4 days with 0.2 % unlabelled L-lysine. After the end of the experiment the hens were slaughtered. The atom-% 15N' was determined in total, in the lysine, histidine and arginine N of blood cells, plasma, NPN fraction of the blood, stomach, small intestine, cecum and rectum. 15N' in the blood cells was 0.11 atom-% in the blood plasma 0.17 atom-%, in the NPN fraction of the blood 0.09 atom-%, in the tissues of the gastrointestinal tract 0.11 atom-% and in its contents 0.12 atom-%. On the average the blood contained per hen 77.9 % lysine-15N', 16.4 % arginine-15N' and 5.7 % histidine-15N' of the basic amino acid-15N'. For the gastrointestinal tract 78.7 % lysine-15N', 19.0 % arginine-15N' and 2.3 % histidine-15N' of the 15N' of the basic amino acids were ascertained. In comparison to histidine the α-amino-N of lysine is incorporated to a considerably higher degree into arginine. For lysine and arginine the atom-% 15N' in the contents of the gastrointestinal tract is 4 days after the end of the supplementation of labelled lysine 8 to 10 times higher than in the feces of the last day of the experiment. This indicates a considerable secretion of the 2 amino acids in the gastrointestinal tract and their reabsorption to a large extent. (author) 6. 15N tracer kinetic studies on the validity of various 15N tracer substances for determining whole-body protein parameters in very small preterm infants International Nuclear Information System (INIS) Reliable 15N tracer substances for tracer kinetic determination of whole-body protein parameters in very small preterm infants are still a matter of intensive research, especially after some doubts have been raised about the validity of [15N]glycine, a commonly used 15N tracer. Protein turnover, synthesis, breakdown, and further protein metabolism data were determined by a paired comparison in four preterm infants. Their post-conceptual age was 32.2 +/- 0.8 weeks, and their body weight was 1670 +/- 181 g. Tracer substances applied in this study were a [15N]amino acid mixture (Ia) and [15N]glycine (Ib). In a second group of three infants with a post conceptual age of 15N-labeled 32.0 +/- 1.0 weeks and a body weight of 1,907 +/- 137 g, yeast protein hydrolysate (II) was used as a tracer substance. A three-pool model was employed for the analysis of the data. This model takes into account renal and fecal 15N losses after a single 15N pulse. Protein turnovers were as follows: 11.9 +/- 3.1 g kg-1 d-1 (Ia), 16.2 +/- 2.5 g kg-1 d-1 (Ib), and 10.8 +/- 3.0 g kg-1 d-1 (II). We were able to demonstrate an overestimation of the protein turnover when Ib was used. There was an expected correspondence in the results obtained from Ia and II. The 15N-labeled yeast protein hydrolysate is a relatively cheap tracer that allows reliable determination of whole-body protein parameters in very small preterm infants 7. 1H, 13C and 15N backbone resonance assignment of the arsenate reductase from Staphylococcus aureus in its reduced state NARCIS (Netherlands) Jacobs, D.M.; Messens, J.; Wechselberger, R.W.; Brosens, E.; Willem, R.; Wyns, L.; Martins, J.C. 2001-01-01 In S. aureus, resistance to the metal(III)oxyanions arsenite As(III)O− 2 and antimonite Sb(III)O− 2 is mediated by two proteins, ArsB and ArsR, encoded in the ars operon of plasmid pI258 (Silver, 1999). ArsR acts as the transcription repressor, which is de-repressed in the presence of intracellular 8. Improved 3D triple resonance experiments, HNN and HN(C)N, for HN and 15N sequential correlations in (13C, 15N) labeled proteins: Application to unfolded proteins Energy Technology Data Exchange (ETDEWEB) Panchal, Sanjay C.; Bhavesh, Neel S.; Hosur, Ramakrishna V. [Tata Institute of Fundamental Research, Department of Chemical Sciences (India) 2001-06-15 Two triple resonance experiments, HNN and HN(C)N, are presented which correlate H{sup N} and {sup 15}N resonances sequentially along the polypeptide chain of a doubly ({sup 13}C, {sup 15}N) labeled protein. These incorporate several improvements over the previously published sequences for a similar purpose and have several novel features. The spectral characteristics enable direct identification of certain triplets of residues, which provide many starting points for the sequential assignment procedure. The experiments are sensitive and their utility has been demonstrated with a 22 kDa protein under unfolding conditions where most of the standard triple resonance experiments such as HNCA, CBCANH etc. have limited success because of poor amide, C{sup {alpha}} and C{sup {beta}} chemical shift dispersions. 9. Improved 3D triple resonance experiments, HNN and HN(C)N, for HN and 15N sequential correlations in (13C, 15N) labeled proteins: Application to unfolded proteins International Nuclear Information System (INIS) Two triple resonance experiments, HNN and HN(C)N, are presented which correlate HN and 15N resonances sequentially along the polypeptide chain of a doubly (13C, 15N) labeled protein. These incorporate several improvements over the previously published sequences for a similar purpose and have several novel features. The spectral characteristics enable direct identification of certain triplets of residues, which provide many starting points for the sequential assignment procedure. The experiments are sensitive and their utility has been demonstrated with a 22 kDa protein under unfolding conditions where most of the standard triple resonance experiments such as HNCA, CBCANH etc. have limited success because of poor amide, Cα and Cβ chemical shift dispersions 10. Regulation of [15N]urea synthesis from [5-15N]glutamine. Role of pH, hormones, and pyruvate. Science.gov (United States) Nissim, I; Yudkoff, M; Brosnan, J T 1996-12-01 We have utilized both [5-15N]glutamine and [3-13C] pyruvate as metabolic tracers in order to: (i) examine the effect of pH, glucagon (GLU), or insulin on the precursor-product relationship between 15NH3, [15N]citrulline, and, thereby, [15N]urea synthesis and (ii) elucidate the mechanism(s) by which pyruvate stimulates [15N] urea synthesis. Hepatocytes isolated from rat were incubated at pH 6.8, 7.4, or 7.6 with 1 mM [5-15N]glutamine and 0.1 mM 14NH4Cl in the presence or the absence of [3-13C] pyruvate (2 mM). A separate series of experiments was performed at pH 7.4 in the presence of insulin or GLU. 15NH3 enrichment exceeded or was equal to that of [15N]citrulline under all conditions except for pH 7.6, when the 15N enrichment in citrulline exceeded that in ammonia. The formation of [15N]citrulline (atom % excess) was increased with higher pH. Flux through phosphate-dependent glutaminase (PDG) and [15N]urea synthesis were stimulated (p < 0.05) at pH 7.6 or with GLU and decreased (p < 0.05) at pH 6.8. Insulin had no significant effect on flux through PDG or on [15N]urea synthesis. Decreased [15N]urea production at pH 6.8 was associated with depleted aspartate and glutamate levels. Pyruvate attenuated this decrease in the aspartate and glutamate pools and stimulated [15N]urea synthesis. Production of Asp from pyruvate was increased with increasing medium pH. Approximately 80% of Asp was derived from [3-13C]pyruvate regardless of incubation pH or addition of hormone. Furthermore, approximately 20, 40, and 50% of the mitochondrial N-acetylglutamate (NAG) pool was derived from [3-13C]pyruvate at pH 6.8, 7.4, and 7.6, respectively. Both the concentration and formation of [13C]NAG from [3-13C]pyruvate were increased (p < 0.05) with glucagon and decreased (p < 0.05) with insulin or at pH 6.8. The data suggest a correlation between changes in [15N]urea synthesis and alterations in the level and synthesis of [13C]NAG from pyruvate. The current observations suggest that the 11. Porous solid backbone impregnation for electrochemical energy conversion systems KAUST Repository 2013-09-19 An apparatus and method for impregnating a porous solid backbone. The apparatus may include a platform for holding a porous solid backbone, an ink jet nozzle configured to dispense a liquid solution onto the porous solid backbone, a positioning mechanism configured to position the ink jet nozzle proximate to a plurality of locations of the porous solid backbone, and a control unit configured to control the positioning mechanism to position the ink jet nozzle proximate to the plurality of locations and cause the ink jet nozzle to dispense the liquid solution onto the porous solid backbone. 12. Alanine flux in obese and healthy humans as evaluated by 15N- and 2H3-labeled alanines International Nuclear Information System (INIS) Estimates of plasma alanine flux as measured in humans using L-[15N]-alanine or L-[3,3,3-2H3]alanine were compared by simultaneous intravenous infusion of both tracers. Plasma isotope enrichments were measured by chemical ionization gas chromatography-mass spectrometry. In 16 obese women before and during a hypocaloric diet and in 4 normal men in the postabsorptive and fed states, the fluxes were highly correlated (r2 = 0.93) although plasma alanine flux with the 2H tracer was two to three times greater than that obtained with [15N]alanine. The fluxes decreased with the hypocaloric diet in obese subjects and increased during the fed state in healthy adults. Thus, although the estimates of alanine flux differed according to the tracer used, both appear to give equivalent information about changes in alanine kinetics induced by the nutritional conditions examined 13. Acetylene inhibition of N2O reduction in laboratory soil and groundwater denitrification assays: evaluation by 15N tracer and 15N site preference of N2O OpenAIRE Weymann, Daniel; Well, Reinhard; Lewicka-Szczebak, Dominika; Rohe, Lena 2013-01-01 Acetylene inhibition of N2O reduction in laboratory soil and groundwaterdenitrification assays: evaluation by 15N tracer and 15N site preference ofN2ODaniel Weymann (1), Reinhard Well (2), Dominika Lewicka-Szczebak (2,3), and Rohe Lena (2)(1) Forschungszentrum Juelich, Agrosphere Institute (IBG-3), Juelich, Germany (), (2)Thünen-Institute of Climate-Smart Agriculture, Braunschweig, Germany, (3) University of Wroclaw, PolandThe measurement of denitrification in soils and... 14. Impact of Backbone Fluorination on π-Conjugated Polymers in Organic Photovoltaic Devices: A Review Directory of Open Access Journals (Sweden) Nicolas Leclerc 2016-01-01 Full Text Available Solution-processed bulk heterojunction solar cells have experienced a remarkable acceleration in performances in the last two decades, reaching power conversion efficiencies above 10%. This impressive progress is the outcome of a simultaneous development of more advanced device architectures and of optimized semiconducting polymers. Several chemical approaches have been developed to fine-tune the optoelectronics and structural polymer parameters required to reach high efficiencies. Fluorination of the conjugated polymer backbone has appeared recently to be an especially promising approach for the development of efficient semiconducting polymers. As a matter of fact, most currently best-performing semiconducting polymers are using fluorine atoms in their conjugated backbone. In this review, we attempt to give an up-to-date overview of the latest results achieved on fluorinated polymers for solar cells and to highlight general polymer properties’ evolution trends related to the fluorination of their conjugated backbone. 15. Peptoid-Peptide hybrid backbone architectures DEFF Research Database (Denmark) 2010-01-01 -amino acids (alpha/beta-peptides) have been investigated in some detail as well. The present Minireview is a survey of the literature concerning hybrid structures of alpha-amino acids and peptoids, including beta-peptoids (N-alkyl-beta-alanine oligomers), and is intended to give an overview of this area......Peptidomimetic oligomers and foldamers have received considerable attention for over a decade, with beta-peptides and the so-called peptoids (N-alkylglycine oligomers) representing prominent examples of such architectures. Lately, hybrid or mixed backbones consisting of both alpha- and beta... 16. Understanding VoIP from Backbone Measurements OpenAIRE Birke, Robert Rene' Maria; Petracca, Michele; Mellia, Marco 2007-01-01 VoIP has widely been addressed as the technology that will change the Telecommunication model opening the path for convergence. Still today this revolution is far from being complete, since the majority of telephone calls are originated by circuit-oriented networks. In this paper for the first time to the best of our knowledge, we present a large dataset of measurements collected from the FastWeb backbone, which is one of the first worldwide Telecom operator to offer VoIP and high-speed data ... 17. Instant Backbone.js application development CERN Document Server Hunter, Thomas 2013-01-01 Get to grips with a new technology, understand what it is and what it can do for you, and then get to work with the most important features and tasks. This book is a practical, step-by-step tutorial that will teach you to build Backbone.js applications quickly and efficiently.This book is targeted towards developers. It is assumed that you have at least a basic understanding of JavaScript and jQuery selectors. If you are interested in building dynamic Single Page Applications that interact heavily with a backend server, then this is the book for you. 18. A Native to Amyloidogenic Transition Regulated by a Backbone Trigger Energy Technology Data Exchange (ETDEWEB) Eakin,C.; Berman, A.; Miranker, A. 2006-01-01 Many polypeptides can self-associate into linear, aggregated assemblies termed amyloid fibers. High-resolution structural insights into the mechanism of fibrillogenesis are elusive owing to the transient and mixed oligomeric nature of assembly intermediates. Here, we report the conformational changes that initiate fiber formation by beta-2-microglobulin (beta2m) in dialysis-related amyloidosis. Access of beta2m to amyloidogenic conformations is catalyzed by selective binding of divalent cations. The chemical basis of this process was determined to be backbone isomerization of a conserved proline. On the basis of this finding, we designed a beta2m variant that closely adopts this intermediate state. The variant has kinetic, thermodynamic and catalytic properties consistent with its being a fibrillogenic intermediate of wild-type beta2m. Furthermore, it is stable and folded, enabling us to unambiguously determine the initiating conformational changes for amyloid assembly at atomic resolution. 19. Investigation into endogenous N metabolism in 15N-labelled pigs. 1 International Nuclear Information System (INIS) 4 male castrated pigs (55-65 kg) either received a wheat-fish meal diet (1 and 2) or a wheat-horse bean diet (3 and 4) without straw meal supplement (1 and 3) or with a supplement of 20% dry matter (2 and 4). In order to investigate whether a 15N labelling of the pigs is also possible with a protein excess in the ration, the animals received 24.8 g (1 and 2) and 11.6 g crude protein/kg/sup 0.75/ live weight (3 and 4). During a 10-day 15N-labelling 385 mg 15N excess (15N') per kg/sup 0.75/ were applied with 15N labelling the following quotas of the applied 15N amount were incorporated: 1 = 10.2%, 2 = 7.2%, 3 = 18.7%, 4 = 14.4%. 15N excretion in both TCA fractions of feces showed a highly significant positive correlation to the increasing content of crude fibre in the 4 diets. The immediate 15N incorporation into the TCA-precipitable fraction of feces proves that 15N enters the large intestine endogenously and serves bacterial protein synthesis. 3 days after the last 15 application the pigs were killed. The values of atom-% 15N' were determined in the TCA-precipitable blood plasma and in the TCA-precipitable fraction of the liver. The other examined organs and tissues showed smaller differences between the test animals. The results show that the 15N labelling of tissues and organs of pigs is also possible at a high level of protein supply by means of an oral application of [15N] ammonia salts. (author) 20. Nitrogen (15N) recovery from ammonium and nitrate applied to the soil by sugar cane International Nuclear Information System (INIS) An experiment was developed in a field aimed to compare the recovery of the ammonium-15 N and nitrate-15 N by the sugar cane plants harvested mechanically without burning. A rate of 70 kg ha-1 of N was applied as ammonium nitrate, in strip, onto cultural residues. Two lineal meters micropots were used. They received the fertilizer labeled with 15 N. Two treatments were established using labeled ammonium (NH4+-15 N) or nitrate (NO3-15 N). Two months after fertilization, four samples of the aerial part (two lineal meters) for treatment in the portions that did not receive the fertilizer-15 N, were taken in order to evaluated the fitomass production (Mg ha-1) and N-total accumulated (kg ha-1). This evaluation was repeated every two months up to complete five of them. Two leaves (leaves with 3 deg C visible auricle) were collected from plants that were in a middle of the micropots (15 N) and in corresponding positions in the adjacent rows, to evaluated the concentration of 15 N. There was a larger absorption of the nitrate-N (30.5%) than of the ammonium-N (21.2%). On the other hand, in the soil the results showed larger ammonium-15 N residual effect concentration, probably due to microorganism immobilization. (author) 1. Effects of growth and change of food on the δ15N in marine fishes International Nuclear Information System (INIS) Information is limited concerning variation of the δ15N with growth in marine organisms and consequently the effect of growth of marine biota on the δ15N is not yet well understood. The δ15N in 26 species of marine fishes taken from Japanese coastal waters together with 4664 stomach contents of these fishes were examined to investigate the effects of food habits and growth on the δ15N. The mean δ15N for two species that fed mainly on large-size fishes and six species that fed mainly on small-size fishes were 14.5±1.0per mille and 12.8±0.7per mille, respectively. For five species that fed mainly on decapod crustaceans, two species that fed mainly on zooplankton, and three species that fed mainly on benthos (mainly Polychaeta), the δ15N were 13.0±0.7, 9.7±0.9, and 12.2±1.2per mille, respectively. The mean δ15N in the species whose prey were mainly fish or decapod crustaceans was about 3-5per mille higher than the species whose prey was mainly zooplankton. Within the four species that shift their food habits with growth to higher trophic level, the δ15N significantly increased with growth in one species (Pacific cod), while not significant increase in the δ15N with growth in the remaining species. (author) 2. Binding of thiocyanate to lactoperoxidase: 1H and 15N nuclear magnetic resonance studies Energy Technology Data Exchange (ETDEWEB) Modi, S.; Behere, D.V.; Mitra, S. (Tata Institute of Fundamental Research, Bombay (India)) 1989-05-30 The binding of thiocyanate to lactoperoxidase (LPO) has been investigated by 1H and 15N NMR spectroscopy. 1H NMR of LPO shows that the major broad heme methyl proton resonance at about 61 ppm is shifted upfield by addition of the thiocyanate, indicating binding of the thiocyanate to the enzyme. The pH dependence of line width of 15N resonance of SC15N- in the presence of the enzyme has revealed that the binding of the thiocyanate to the enzyme is facilitated by protonation of an ionizable group (with pKa of 6.4), which is presumably distal histidine. Dissociation constants (KD) of SC15N-/LPO, SC15N-/LPO/I-, and SC15N-/LPO/CN- equilibria have been determined by 15N T1 measurements and found to be 90 +/- 5, 173 +/- 20, and 83 +/- 6 mM, respectively. On the basis of these values of KD, it is suggested that the iodide ion inhibits the binding of the thiocyanate but cyanide ion does not. The thiocyanate is shown to bind at the same site of LPO as iodide does, but the binding is considerably weaker and is away from the ferric ion. The distance of 15N of the bound thiocyanate ion from the iron is determined to be 7.2 +/- 0.2 A from the 15N T1 measurements. 3. Investigation of the metabolism of colostomized laying hens with 15N-labelled wheat. 5 International Nuclear Information System (INIS) In an experiment with 3 colostomized laying hybrids each animal received 80 g pelleted mixed feed and 40 g 15N-labelled wheat with 20.13 atom-% 15N excess (15N') over a period of four days. On the following four days the hens received rations composed in the same way with unlabelled wheat, however in the tissues and organs of the slaughtered hens 15N' was determined in the total N and the amino acids lysine, histidine and arginine in both the segments of the gastro intestinal tract and in its content. The amount of 15N' stomach, small intestine and colon was 43.7%, 27.2% and 29.1%, respectively. The tissue of the small intestine contained, on an average, the highest 15N' in lysine of all the basic amino acids. It was 0.82 atom-% 15N' for lysine, 0.55% for histidine and 0.63% for arginine. The percentage of the 15N' of the basic amino acids from the corresponding total 15N' amount of the charges was 20.5% in the contents of the gastrointestinal tract, 28.0% in the stomach tissue and in the tissues of the small intestine 24.4% of the cecum 21.5% and of the rectum 25.7%. (author) 4. Utilization of 15N-labelled urea in laying hens. 6 International Nuclear Information System (INIS) 3 colostomized laying hybrids received a normal ration containing 1% 15N-labelled urea with 96.06% atom-% 15N excess (15N') over six days. Subsequently the same ration with unlabelled urea was given over 2 days, after which the animals were butchered. In the kidneys the 15N' amounted to 1.1 atom-% and 1.8 atom-% in the liver. The TCA soluble N fraction and the ammonia were more highly labelled than the total N. Lysine, histidine and arginine were lowly labelled in the kidneys. This also applies to the liver with the exception of histidine. In the branch-chained and aromatic amino acids of the liver the 15N' was between 0.2 and 0.3 atom-%. The highest labelling of non-essential amino acids was found in glutamic acid with 0.9 atom-% 15N' and aspartic acid with 1.1 atom-% 15 N'. The evaluation of the amino acid in the liver showed that the 6 non-essential amino acids account for two thirds of the total amino acid 15N' whereas the 9 essential ones account for one third of the amino acid 15N' only. (author) 5. The influence of DNA binding on the backbone dynamics of the yeast cell-cycle protein Mbp1 International Nuclear Information System (INIS) Mbp1 is a transcription factor involved in the regulation of the cell cycle in yeast. The N-terminus of this protein contains a DNA binding domain that includes a winged helix-turn-helix motif. The C-terminal 24 residues of this domain (the 'tail') are disordered in the crystal state, but are important for DNA binding. We have measured 15N NMR relaxation rates at 11.75 and 14.1 T to determine the dynamics of the free protein and in its complex with a specific DNA duplex. The dynamics data were quantitatively analysed using both spectral density mapping and the Lipari-Szabo formalism including the effects of chemical exchange and rotational anisotropy. A detailed analysis has been made of the effect of anisotropy, exchange and experimental precision on the recovered motional parameters. The backbone NH relaxation is affected by motions on a variety of time scales from millisecond to tens of picoseconds. The relaxation data show a structured core of 100 residues corresponding to that observed in the crystal state. Within the core of the protein, two regions on either side of the putative recognition helix (helix B) show slow (ca. 0.2 ms) conformational exchange dynamics that are quenched upon DNA binding. The C-terminal 24 residues are generally more dynamic than in the core. However, in the free protein, a stretch of ∼8 residues in the middle of the tail show relaxation behaviour similar to that in the core, indicating a structured region. NOEs between Ala 114 in this structured part of the tail and residues in the N-terminal beta strand of the core of the protein demonstrate that the tail folds back onto the core of the protein. In the complex with DNA, the structured part of the tail extends by ca. 3 residues. These data provide a framework for understanding the biochemical data on the mechanism and specificity of DNA binding 6. δ(15) N from soil to wine in bulk samples and proline. Science.gov (United States) Paolini, Mauro; Ziller, Luca; Bertoldi, Daniela; Bontempo, Luana; Larcher, Roberto; Nicolini, Giorgio; Camin, Federica 2016-09-01 7. Disturbance and topography shape nitrogen availability and δ15N over long-term forest succession Science.gov (United States) Forest disturbance and long-term succession can promote open N cycling that increases N loss and soil δ15N values. We examined soil and foliar patterns in N and δ15N, and soil N mineralization, across a topographically complex montane forest landscape influenced by human logging ... 8. Human dietary δ(15)N intake: representative data for principle food items. Science.gov (United States) Huelsemann, F; Koehler, K; Braun, H; Schaenzer, W; Flenker, U 2013-09-01 Dietary analysis using δ(15)N values of human remains such as bone and hair is usually based on general principles and limited data sets. Even for modern humans, the direct ascertainment of dietary δ(15)N is difficult and laborious, due to the complexity of metabolism and nitrogen fractionation, differing dietary habits and variation of δ(15)N values of food items. The objective of this study was to summarize contemporary regional experimental and global literature data to ascertain mean representative δ(15)N values for distinct food categories. A comprehensive data set of more than 12,000 analyzed food samples was summarized from the literature. Data originated from studies dealing with (1) authenticity tracing or origin control of food items, and (2) effects of fertilization or nutrition on δ(15)N values of plants or animals. Regional German food δ(15)N values revealed no major differences compared with the mean global values derived from the literature. We found that, in contrast to other food categories, historical faunal remains of pig and poultry are significantly enriched in (15)N compared to modern samples. This difference may be due to modern industrialized breeding practices. In some food categories variations in agricultural and feeding regimens cause significant differences in δ(15)N values that may lead to misinterpretations when only limited information is available. 9. δ(15) N from soil to wine in bulk samples and proline. Science.gov (United States) Paolini, Mauro; Ziller, Luca; Bertoldi, Daniela; Bontempo, Luana; Larcher, Roberto; Nicolini, Giorgio; Camin, Federica 2016-09-01 10. A fast method to prepare water samples for 15N analysis Institute of Scientific and Technical Information of China (English) 肖化云; 刘丛强 2001-01-01 Automatic element analyser is often used to prepare organic matters tor 15N analysis. It is seldom used to prepare water samples. Water samples are conventionally dealt with by Kjeldahl-Rittenberg technique. But it requires tedious and labor-intensive sample preparation. A fast and reliable method is proposed in this paper to prepare water samples for 15N analysis. 11. Utilization of 15N-labelled urea in laying hens. 8 International Nuclear Information System (INIS) 3 colostomized laying hybrids received orally with a conventional ration 1% urea with 96.06 atom-% 15N excess (15N') over a period of 6 days. In the period of the experiment every hen consumed 2.87 g 15N'. After another 2 days, on which they received conventional feed urea, the animals were butchered. 15N' was determined in the total N and in 15 amino acids of the oviduct. Of the 15 amino acids the labelling of glutamic acid, glycine and serine was highest and on average amounted to 0.80, 0.66 and 0.67 atom-% 15N', resp. In lysine and arginine only 0.10 and 0.11 atom-% 15N' could be detected. The amino acid N with natural isotopic frequency amounted to a quarter for the basic amino acids, a tenth for the branched chain ones and for the non-essential ones (glutamic acid, aspartic acid, serine, glycine, alanine, proline) a third of the total oviduct 14N. The average quota of 15N' is only 3.6%, that of the branched chain amino acids 4.5 and that of the non-essential ones 21.1%. Consequently, the 15N' of the urea is mainly used for the synthesis of the non-essential amino acids of the oviduct. (author) 12. Utilization of 15N-labelled urea in laying hens. 2 International Nuclear Information System (INIS) In an N metabolism experiment 3 colostomized laying hybrids received 2870 mg 15N excess (15N') per animal in 6 days in the form of urea with their conventional feed rations. During the 8-day experiment the 21 eggs laid were separated into egg-shell, white of egg and yolk. Weight, N content and 15N' of the individual fractions of the eggs were determined. On an average 4.6% of the heavy nitrogen was in the egg-shells, 50% in the white of egg and 45.5% in the yolk. 2.8%, 4.5% and 5.5% (hens 1 - 3) of the 15N' consumed were detected in the eggs. The maximum 15N' output in the white of egg was reached on the 6th day, whereas 15N' output in the yolk showed a nearly linear increase in the time of the experiment. The results show that labelled nitrogen from urea is incorporated into the egg to a lower degree than after the feeding of 15N-labelled proteins and that the development of its incorporation into the white of egg and the yolk differ from that after the feeding of 15N-labelled native proteins. (author) 13. Labelling of sewage with 13C and 15N isotopes International Nuclear Information System (INIS) Treatment of sewage water varies with the type and level of technology applied. As a result, sewage sludges vary in composition. In Western Europe, a combination of mechanical, biological, and chemical treatments is commonly applied. The biological treatment of sewage water - the activated sludge process - results in removal of carbon and nitrogen through immobilization in microbes. With strong aeration of the wastewater, energy-rich substrates and nutrients are assimilated by aerobic microbes and a large microbial biomass results. The biomass consists mainly of living microbial cells and components of dying and dead cells, but also of colloidal particles and metal ions bound to the surfaces of the microbes. The organic matter produced during aeration - the biological sludge - is removed by settlement. The biological treatment of wastewater was the starting point for the labelling procedure of sewage sludge. Labelling of waste products with stable tracer isotopes can be done in two ways: (i) labelling of the original material from which wastes are generated, e.g. by labelling of the diet fed to animals; and (ii) labelling during the biological turnover through addition of nitrogen or carbon compounds to wastes. In this study, tracers were added to wastewater during biological treatment 14. Extracting the information backbone in online system CERN Document Server Zhang, Qian-Ming; Shang, Ming-Sheng 2013-01-01 Information overload is a serious problem in modern society and many solutions such as recommender system have been proposed to filter out irrelevant information. In the literature, researchers mainly dedicated to improve the recommendation performance (accuracy and diversity) of the algorithms while overlooked the influence of topology of the online user-object bipartite networks. In this paper, we find that some information provided by the bipartite networks is not only redundant but also misleading. With such "less can be more" feature, we design some algorithms to improve the recommendation performance by eliminating some links from the original networks. Moreover, we propose a hybrid method combining the time-aware and topology-aware link removal algorithms to extract the backbone which contains the essential information for the recommender systems. From the practical point of view, our method can improve the performance and reduce the computational time of the recommendation system, thus improve both of... 15. Sofosbuvir as backbone of interferon free treatments. Science.gov (United States) Bourlière, Marc; Oules, Valèrie; Ansaldi, Christelle; Adhoute, Xavier; Castellani, Paul 2014-12-15 Sofosbuvir is the first-in-class NS5B nucleotide analogues to be launched for hepatitis C virus (HCV) treatment. Its viral potency, pangenotypic activity and high barrier to resistance make it the ideal candidate to become a backbone for several IFN-free regimens. Recent data demonstrated that sofosbuvir either with ribavirin alone or in combination with other direct-acting antivirals (DAAs) as daclatasvir, ledipasvir or simeprevir are able to cure HCV in at least 90% or over of patients. Treatment experienced genotype 3 population may remain the most difficult to treat population, but ongoing DAA combination studies will help to fill this gap. Safety profile of sofosbuvir or combination with other DAAs is good. Resistance to sofosbuvir did not appear as a significant issue. The rationale for using this class of drug and the available clinical data are reviewed. 16. 1H and 15N Dynamic Nuclear Polarization Studies of Carbazole Energy Technology Data Exchange (ETDEWEB) Hu, Jian Zhi; Solum, Mark S.; Wind, Robert A.; Nilsson, Brad L.; Peterson, Matt A.; Pugmire, Ronald J.; Grant, David M. 2000-01-01 15N NMR experiments, combined with dynamic nuclear polarization (DNP), are reported on carbazole doped with the stable free radical 1,3 bisdiphenylene-2 phenylally1 (BDPA). Doping shortens the nuclear relaxation times and provides paramagnetic centers that can be used to enhance the nuclear signal by means of DNP so that 15 N NMR experiments can be done in minutes. The factors were measured in a 1.4 T external field, using both unlabeled and 98% 15N labeled carbazole with doping levels varying between 0.65 and 5.0 wt % BDPA. A doping level of approximately 1 wt % produced optimal results. DNP enhancement factors of 35 and 930 were obtained for 1H and 15N, respectively making it possible to perform 15N DNP NMR experiments at the natural abundance level. 17. Syntheses of 15N-labeled pre-queuosine nucleobase derivatives Directory of Open Access Journals (Sweden) Jasmin Levic 2014-08-01 Full Text Available Pre-queuosine or queuine (preQ1 is a guanine derivative that is involved in the biosynthetic pathway of the hypermodified tRNA nucleoside queuosine (Que. The core structure of preQ1 is represented by 7-(aminomethyl-7-deazaguanine (preQ1 base. Here, we report the synthesis of three preQ1 base derivatives with complementary 15N-labeling patterns, utilizing [15N]-KCN, [15N]-phthalimide, and [15N3]-guanidine as cost-affordable 15N sources. Such derivatives are required to explore the binding process of the preQ1 base to RNA targets using advanced NMR spectroscopic methods. PreQ1 base specifically binds to bacterial mRNA domains and thereby regulates genes that are required for queuosine biosynthesis. 18. Using a macroalgal δ15N bioassay to detect cruise ship waste water effluent inputs International Nuclear Information System (INIS) Highlights: → Green macroalgae exposed to nutrient solutions exhibited changes in tissue 15N signatures. → Macroalgae exhibited no fractionation with NO3 and slight fractionation with NH4. → Algae exposed to cruise ship waste water had increased tissue δ15N indicating a heavy N source. → Field bioassays exhibited decreased δ15N indicating isotopically light riverine δ15N-NO3 was likely the dominant N source. → Algal bioassays could not detect a δ15N cruise ship waste water signal in this system. - Abstract: Green macroalgae bioassays were used to determine if the δ15N signature of cruise ship waste water effluent (CSWWE) could be detected in a small harbor. Opportunistic green macroalgae (Ulva spp.) were collected, cultured under nutrient depleted conditions and characterized with regard to N content and δ15N. Samples of algae were used in controlled incubations to evaluate the direction of isotope shift from exposure to CSWWE. Algae samples exposed to CSWWE exhibited an increase of 1-2.5 per mille in δ15N values indicating that the CSWWE had an enriched isotope signature. In contrast, algae samples exposed to field conditions exhibited a significant decrease in the observed δ15N indicating that a light N source was used. Isotopically light, riverine nitrogen derived from N2-fixing trees in the watershed may be a N source utilized by algae. These experiments indicate that the δ15N CSWWE signature was not detectable under the CSWWE loading conditions of this experiment. 19. Utilization of 15N-labelled urea in laying hens. 9 International Nuclear Information System (INIS) For studying the incorporation of the 15N labelled urea into individual organs and tissues 3 colostomized laying hens were butchered after they had received 1% urea (96.06 atom-% 15N excess) with a high quality ration over a period of six days and after receiving conventional urea for another two days. Nitrogen and atom-% 15N excess (15N') were determined in the bones, the feathers and the remaining body (skin, lungs and windpipe, head with comb and wattle, lower leg without bones and with skin, pancreas and fatty tissue). In the remaining body the atom-% 15N' was determined in 15 amino acids. The labelling in the remaining body and the bones was approximately the same and averaged 0.37 atom-% 15N'. A significantly lower relative frequency could be detected in the feathers. The lysine of the remaining body contained only 0.04 atom-% 15N', tyrosine 0.06, histidine and arginine 0.07. The phenylalanine and proline molecules were labelled with 0.11 atom-% 15N'. Most 15N' was incorporated in serine and glutamic acid with over 0.30 atom-%. In the six non-essential amino acids out of the 15 amino acids studied, 48.6 of the non-isotopic nitrogen of the total N of the remaining body and 70.7% of the isotopic nitrogen of total 15N' could be detected. Consequently the urea N is mainly used for the synthesis of the non-essential amino acids, with its utilization being very low. (author) 20. Global Fold of Human Cannabinoid Type 2 Receptor Probed by Solid-State 13C-, 15N-MAS NMR and Molecular Dynamics Simulations OpenAIRE Kimura, Tomohiro; Vukoti, Krishna; Lynch, Diane L.; Hurst, Dow P.; Grossfield, Alan; Pitman, Michael C.; Reggio, Patricia H.; Yeliseev, Alexei A.; Gawrisch, Klaus 2013-01-01 The global fold of human cannabinoid type 2 (CB2) receptor in the agonist-bound active state in lipid bilayers was investigated by solid-state 13C- and 15N magic-angle spinning (MAS) NMR, in combination with chemical-shift prediction from a structural model of the receptor obtained by microsecond-long molecular dynamics (MD) simulations. Uniformly 13C-, and 15N-labeled CB2 receptor was expressed in milligram quantities by bacterial fermentation, purified, and functionally reconstituted into l... 1. Backbone analysis and algorithm design for the quadratic assignment problem Institute of Scientific and Technical Information of China (English) JIANG He; ZHANG XianChao; CHEN GuoLiang; LI MingChu 2008-01-01 As the hot line in NP-hard problems research in recent years, backbone analysis is crucial for phase transition, hardness, and algorithm design. Whereas theoretical analysis of backbone and its applications in algorithm design are still at a begin-ning state yet, this paper took the quadratic assignment problem (QAP) as a case study and proved by theoretical analysis that it is NP-hard to find the backbone, l.e., no algorithm exists to obtain the backbone of a QAP in polynomial time. Results of this paper showed that it is reasonable to acquire approximate backbone by inter-section of local optimal solutions. Furthermore, with the method of constructing biased instances, this paper proposed a new meta-heuristic - biased instance based approximate backbone (BI-AB), whose basic idea is as follows: firstly, con-struct a new biased instance for every QAP instance (the optimal solution of the new instance is also optimal for the original one); secondly, the approximate backbone is obtained by intersection of multiple local optimal solutions computed by some existing algorithm; finally, search for the optimal solutions in the reduced space by fixing the approximate backbone. Work of the paper enhanced the re-search area of theoretical analysis of backbone. The meta-heuristic proposed in this paper provided a new way for general algorithm design of NP-hard problems as well. 2. Standardized 15N tracer methods for the evaluation of the plasma protein turnover in clinical practice. 1 International Nuclear Information System (INIS) Methods for quantitative isolation of plasma proteins or groups of proteins (total plasma or serum proteins, fibrin, total globulines, α, β, γ-globolines, albumin) are described based on combination of chromatography with precipitation and extraction techniques. These methods are adapted to the special requirements of 15N analysis. They can be performed in clinic-chemical standard laboratories without special apparatuses or devices. The described procedures are the biochemico-analytical basis for the quantitative evaluation of tracer kinetics data by means of mathematic modelling. (author) 3. FIRST MEASUREMENTS OF {sup 15}N FRACTIONATION IN N{sub 2}H{sup +} TOWARD HIGH-MASS STAR-FORMING CORES Energy Technology Data Exchange (ETDEWEB) Fontani, F. [INAF-Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze (Italy); Caselli, P.; Bizzocchi, L. [Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse 1, D-85748 Garching (Germany); Palau, A. [Centro de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, P.O. Box 3-72, 58090 Morelia, Michoacán, México (Mexico); Ceccarelli, C. [Univ. Grenoble Alpes, IPAG, F-38000 Grenoble (France) 2015-08-01 We report on the first measurements of the isotopic ratio {sup 14}N/{sup 15}N in N{sub 2}H{sup +} toward a statistically significant sample of high-mass star-forming cores. The sources belong to the three main evolutionary categories of the high-mass star formation process: high-mass starless cores, high-mass protostellar objects, and ultracompact H ii regions. Simultaneous measurements of the {sup 14}N/{sup 15}N ratio in CN have been made. The {sup 14}N/{sup 15}N ratios derived from N{sub 2}H{sup +} show a large spread (from ∼180 up to ∼1300), while those derived from CN are in between the value measured in the terrestrial atmosphere (∼270) and that of the proto-solar nebula (∼440) for the large majority of the sources within the errors. However, this different spread might be due to the fact that the sources detected in the N{sub 2}H{sup +} isotopologues are more than those detected in the CN ones. The {sup 14}N/{sup 15}N ratio does not change significantly with the source evolutionary stage, which indicates that time seems to be irrelevant for the fractionation of nitrogen. We also find a possible anticorrelation between the {sup 14}N/{sup 15}N (as derived from N{sub 2}H{sup +}) and the H/D isotopic ratios. This suggests that {sup 15}N enrichment could not be linked to the parameters that cause D enrichment, in agreement with the prediction by recent chemical models. These models, however, are not able to reproduce the observed large spread in {sup 14}N/{sup 15}N, pointing out that some important routes of nitrogen fractionation could be still missing in the models. 4. Variable δ15N Diet-Tissue Discrimination Factors among Sharks: Implications for Trophic Position, Diet and Food Web Models OpenAIRE Olin, Jill A.; Hussey, Nigel E.; Alice Grgicak-Mannion; Mark W Fritts; Wintner, Sabine P.; Fisk, Aaron T. 2013-01-01 The application of stable isotopes to characterize the complexities of a species foraging behavior and trophic relationships is dependent on assumptions of δ(15)N diet-tissue discrimination factors (∆(15)N). As ∆(15)N values have been experimentally shown to vary amongst consumers, tissues and diet composition, resolving appropriate species-specific ∆(15)N values can be complex. Given the logistical and ethical challenges of controlled feeding experiments for determining ∆(15)N values for lar... 5. Bromine recovery in residual solutions generated in the 15 N isotopic determination methodology (Rittenberg, 1946) International Nuclear Information System (INIS) The isotopic determination of 15 N (Rittenberg, 1946) is a methodology used in the Laboratory of Isotope Stable (CENA/USP). In this procedure, in the oxidation of nitrogen species for N2, solution of Li Br O is used, generating as residue 50 L y-1 of solution contends Li Br and Li Br O. Seeking to recover the bromine contained in that residue, very toxic substance, a special line was built composed by reaction balloons (1 and 2 liters), addition funnel, gas flow regulator and connections in glass. In the system proposed, after the acidification (sulfuric acid) of the alkaline residual solution, the liberated bromine (Br2) it was then dragged by flow of nitrogen and reacted with solution of LiOH. That reaction facilitated the production of Li Br O in solution (Efficiency = 82±2%), that was reused later on same analytic procedure. The high cost of the liquid bromine is another attractiveness that corroborates the employment of the developed procedure. They took place isotopic determinations using the recovered solutions and prepared, and the observed values didn't show statistical difference (T test of Student). The presented procedure is part of the Management Program of Chemical Residues of CENA/USP, which seeks to destine the residues of responsibility of the institution appropriately, forming professionals to the practices of environmental management. (author) 6. Nitrogen fertilizer (15N leaching in a central pivot fertigated coffee crop Directory of Open Access Journals (Sweden) Rafael Pivotto Bortolotto 2012-08-01 Full Text Available Nitrogen has a complex dynamics in the soil-plant-atmosphere system. N fertilizers are subject to chemical and microbial transformations in soils that can result in significant losses. Considering the cost of fertilizers, the adoption of good management practices like fertigation could improve the N use efficiency by crops. Water balances (WB were applied to evaluate fertilizer N leaching using 15N labeled urea in west Bahia, Brazil. Three scenarios (2008/2009 were established: i rainfall + irrigation the full year, ii rainfall only; and iii rainfall + irrigation only in the dry season. The water excess was considered equal to the deep drainage for the very flat area (runoff = 0 with a water table located several meters below soil surface (capillary rise = 0. The control volume for water balance calculations was the 0 - 1 m soil layer, considering that it involves the active root system. The water drained below 1 m was used to estimate fertilizer N leaching losses. WB calculations used the mathematic model of Penman-Monteith for evapotranspiration, considering the crop coefficient equal to unity. The high N application rate associated to the high rainfall plus irrigation was found to be the main cause for leaching, which values were 14.7 and 104.5 kg ha-1 for the rates 400 and 800 kg ha-1 of N, corresponding to 3.7 and 13.1 % of the applied fertilizer, respectively. 7. NMR experiments for resonance assignments of 13C, 15N doubly-labeled flexible polypeptides: Application to the human prion protein hPrP(23-230) International Nuclear Information System (INIS) A combination of three heteronuclear three-dimensional NMR experiments tailored for sequential resonance assignments in uniformly 15N, 13C-labeled flexible polypeptide chains is described. The 3D (H)N(CO-TOCSY)NH, 3D (H)CA(CO-TOCSY)NH and 3D (H)CBCA(CO-TOCSY)NH schemes make use of the favorable 15N chemical shift dispersion in unfolded polypeptides, exploit the slow transverse 15N relaxation rates of unfolded polypeptides in high resolution constant-time [1H, 15N]-correlation experiments, and use carbonyl carbon homonuclear isotropic mixing to transfer magnetization sequentially along the amino acid sequence. Practical applications are demonstrated with the 100-residue flexible tail of the recombinant human prion protein, making use of spectral resolution up to 0.6 Hz in the 15N dimension, simultaneous correlation with the two adjacent amino acid residues to overcome problems associated with spectral overlap, and the potential of the presently described experiments to establish nearest-neighbor correlations across proline residues in the amino acid sequence 8. 15N-labeled nitrogen from green manure and ammonium sulfate utilization by the sugarcane ratoon International Nuclear Information System (INIS) Legumes as green manure are alternative sources of nitrogen (N) for crops and can supplement or even replace mineral nitrogen fertilization due to their potential for biological nitrogen fixation (BNF). The utilization of nitrogen by sugarcane (Saccharum spp.) fertilized with sunn hemp (Crotalaria juncea L.) and ammonium sulfate (AS) was evaluated using the 15N tracer technique. N was added at the rate of 196 and 70 kg ha-1 as 15N-labeled sunn hemp green manure (SH) and as ammonium sulfate (AS), respectively. Treatments were: (I) Control; (II) AS15N; (III) SH15N + AS; (IV) SH15N; and (V) AS15N + SH. Sugarcane was cultivated for five years and was harvested three times. 15N recovery was evaluated in the two first harvests. In the sum of the three harvests, the highest stalk yields were obtained with a combination of green manure and inorganic N fertilizer; however, in the second cutting the yields were higher where SH was used than in plots with AS. The recovery of N by the first two consecutive harvests accounted for 19 to 21% of the N applied as leguminous green manure and 46 to 49% of the N applied as AS. The amounts of inorganic N, derived from both N sources, present in the 0-0.4 m layer of soil in the first season after N application and were below 1 kg ha-1. (author) 9. Steroselective synthesis and application of L-( sup 15 N) amino acids Energy Technology Data Exchange (ETDEWEB) Unkefer, C.J. (Los Alamos National Lab., NM (United States)); Lodwig, S.N. (Centralia Coll., WA (United States). Div. of Science) 1991-01-01 We have developed two general approaches to the stereoselective synthesis of {sup 15}N- and {sup 13}C-labeled amino acids. First, labeled serine, biosynthesized using the methylotrophic bacterium M. extorquens AM1, serves as a chiral precursor for the synthesis of other amino acids. For example, pyridoxal phosphate enzymes can be used for the conversion of L-({alpha}-{sup 15}N)serine to L-({alpha}-{sup 15}N)tyrosine, L-({alpha}-{sup 15}N)tryptophan, and L-({alpha}-{sup 15}N)cysteine. In the second approach, developed by Oppolzer and Tamura, an electrophilic amination'' reagent, 1-chloro-1-nitrosocyclohexane, was used to convert chiral enolates into L-{alpha}-amino acids. We prepared 1-chloro-1-({sup 15}N) nitrosocyclohexane and used it to aminate chiral enolates to produce L-({alpha}-{sup 15}N)amino acids. The stereoselectivity of this scheme using the Oppolzer sultam chiral auxiliary is remarkable, producing enantiomer ratios of 200 to 1. 22 refs., 4 figs. 10. Alkaline Hydrolysis/Polymerization of 2,4,6-Trinitrotoluene: Characterization of Products by 13C and 15N NMR Science.gov (United States) Thorn, K.A.; Thorne, P.G.; Cox, L.G. 2004-01-01 Alkaline hydrolysis has been investigated as a nonbiological procedure for the destruction of 2,4,6-trinitrotoluene (TNT) in explosives contaminated soils and munitions scrap. Nucleophilic substitutions of the nitro and methyl groups of TNT by hydroxide ion are the initial steps in the alkaline degradation of TNT. Potential applications of the technique include both in situ surface liming and ex situ alkaline treatment of contaminated soils. A number of laboratory studies have reported the formation of an uncharacterized polymeric material upon prolonged treatment of TNT in base. As part of an overall assessment of alkaline hydrolysis as a remediation technique, and to gain a better understanding of the chemical reactions underlying the hydrolysis/polymerization process, the soluble and precipitate fractions of polymeric material produced from the calcium hydroxide hydrolysis of unlabeled and 15N-labeled TNT were analyzed by elemental analysis and 13C and 15N nuclear magnetic resonance spectroscopy. Spectra indicated that reactions leading to polymerization included nucleophilic displacement of nitro groups by hydroxide ion, formation of ketone, carboxyl, alcohol, ether, and other aliphatic carbons, conversion of methyl groups to diphenyl methylene carbons, and recondensation of aromatic amines and reduced forms of nitrite, including ammonia and possibly hydroxylamine, into the polymer. Compared to the distribution of carbons in TNT as 14% sp 3- and 86% sp2-hybridized, the precipitate fraction from hydrolysis of unlabeled TNT contained 33% sp3- and 67% sp 2-hybridized carbons. The concentration of nitrogen in the precipitate was 64% of that in TNT. The 15N NMR spectra showed that, in addition to residual nitro groups, forms of nitrogen present in the filtrate and precipitate fractions include aminohydroquinone, primary amide, indole, imine, and azoxy, among others. Unreacted nitrite was recovered in the filtrate fraction. The toxicities and susceptibilities to 11. Quantitative Proteomics: Measuring Protein Synthesis Using 15N Amino Acids Labeling in Pancreas Cancer Cells OpenAIRE Zhao, Yingchun; Lee, Wai-Nang Paul; Lim, Shu; Go, Vay Liang; Xiao, Jing; Cao, Rui; Zhang, Hengwei; Recker, Robert; Xiao, Gary Guishan 2009-01-01 Pancreatic cancer MIA PaCa cells were cultured in the presence and absence of 15N amino acids mixture for 72 hours. During protein synthesis, the incorporation of 15N amino acids results in a new mass isotopomer distribution in protein, which is approximated by the concatenation of two binomial distributions of 13C and 15N. Fraction of protein synthesis (FSR) can thus be determined from the relative intensities of the ‘labeled’ (new) and the ‘unlabeled” (old) spectra. Six prominent spots were... 12. Radiative p 15N Capture in the Region of Astrophysical Energies Science.gov (United States) Dubovichenko, S. B.; Burtebaev, N.; Dzhazairov-Kakhramanov, A. V.; Alimov, D. K. 2016-06-01 Within the framework of the modified potential cluster model with classification of orbital states according to the Young schemes, the possibility of describing experimental data for the astrophysical S-factor of p 15N radiative capture at energies from 50 to 1500 keV is considered. It is shown that on the basis of M1 and E1 transitions from various p 15N scattering states to the ground state of the 16O nucleus in the p 15N channel it is entirely possible to successfully explain the overall behavior of the S-factor in the considered energy region in the presence of two resonances. 13. Nitrogen distribution a 15 N fertilizer in different soil fractions of a barley cultivation International Nuclear Information System (INIS) A culture of barley in the open fields has been fertilized on 9 m2 with Ca(NO3)2 containing 20,8% 15N excess. At the crop, 15 N distribution shows that half of the fertilized nitrogen which is exported by the crop has become organic in the Ap horizon. The use of different methods of fractionation of the soil, shows the biological character of this reorganization, in which the biomass appears to be the main 15 N nitrogen stock 14. NHC Backbone Configuration in Ruthenium-Catalyzed Olefin Metathesis. Science.gov (United States) Paradiso, Veronica; Costabile, Chiara; Grisi, Fabia 2016-01-01 The catalytic properties of olefin metathesis ruthenium complexes bearing N-heterocyclic carbene ligands with stereogenic centers on the backbone are described. Differences in catalytic behavior depending on the backbone configurations of symmetrical and unsymmetrical NHCs are discussed. In addition, an overview on asymmetric olefin metathesis promoted by chiral catalysts bearing C₂-symmetric and C₁-symmetric NHCs is provided. PMID:26805793 15. λ-backbone colorings along pairwise disjoint stars and matchings NARCIS (Netherlands) Broersma, H.J.; Fujisawa, J.; Marchal, L.; Paulusma, D.; Salman, A.N.M.; Yoshimoto, K. 2009-01-01 Given an integer $\\lambda \\ge 2$, a graph $G=(V,E)$ and a spanning subgraph $H$ of $G$ (the backbone of $G$), a $\\lambda$-backbone coloring of $(G,H)$ is a proper vertex coloring $V\\to\\{1,2,\\ldots\\}$ of $G$, in which the colors assigned to adjacent vertices in $H$ differ by at least $\\lambda$. We st 16. NHC Backbone Configuration in Ruthenium-Catalyzed Olefin Metathesis Directory of Open Access Journals (Sweden) 2016-01-01 Full Text Available The catalytic properties of olefin metathesis ruthenium complexes bearing N-heterocyclic carbene ligands with stereogenic centers on the backbone are described. Differences in catalytic behavior depending on the backbone configurations of symmetrical and unsymmetrical NHCs are discussed. In addition, an overview on asymmetric olefin metathesis promoted by chiral catalysts bearing C2-symmetric and C1-symmetric NHCs is provided. 17. NHC Backbone Configuration in Ruthenium-Catalyzed Olefin Metathesis. Science.gov (United States) Paradiso, Veronica; Costabile, Chiara; Grisi, Fabia 2016-01-20 The catalytic properties of olefin metathesis ruthenium complexes bearing N-heterocyclic carbene ligands with stereogenic centers on the backbone are described. Differences in catalytic behavior depending on the backbone configurations of symmetrical and unsymmetrical NHCs are discussed. In addition, an overview on asymmetric olefin metathesis promoted by chiral catalysts bearing C₂-symmetric and C₁-symmetric NHCs is provided. 18. Free backbone carbonyls mediate rhodopsin activation. Science.gov (United States) Kimata, Naoki; Pope, Andreyah; Sanchez-Reyes, Omar B; Eilers, Markus; Opefi, Chikwado A; Ziliox, Martine; Reeves, Philip J; Smith, Steven O 2016-08-01 Conserved prolines in the transmembrane helices of G-protein-coupled receptors (GPCRs) are often considered to function as hinges that divide the helix into two segments capable of independent motion. Depending on their potential to hydrogen-bond, the free C=O groups associated with these prolines can facilitate conformational flexibility, conformational switching or stabilization of the receptor structure. To address the role of conserved prolines in family A GPCRs through solid-state NMR spectroscopy, we focus on bovine rhodopsin, a GPCR in the visual receptor subfamily. The free backbone C=O groups on helices H5 and H7 stabilize the inactive rhodopsin structure through hydrogen-bonds to residues on adjacent helices. In response to light-induced isomerization of the retinal chromophore, hydrogen-bonding interactions involving these C=O groups are released, thus facilitating repacking of H5 and H7 onto the transmembrane core of the receptor. These results provide insights into the multiple structural and functional roles of prolines in membrane proteins. PMID:27376589 19. A data acquisition backbone core library International Nuclear Information System (INIS) For the new experiments at FAIR new concepts of data acquisition systems have to be developed like the distribution of self-triggered, time stamped data streams over high performance networks for event building. The data acquisition backbone core (DABC) is a general purpose software framework designed for the implementation of such data acquisition systems. It provides the event building over networks like InfiniBand or Gigabit Ethernet. All kinds of data channels (front-end systems) are supported by program plug-ins into functional components of DABC like data input, combiner, scheduler, event builder, analysis and storage components. Commands and parameters of DABC and its application plug-ins are published by DIM servers. A Java based Graphical User Interface provides the dynamic control and visualization of these components. Application specific GUIs can be added. After a testing phase, DABC can be used to develop high performance data acquisition systems. Besides that DABC will be used for the implementation of various test beds needed for the final design of data acquisition systems at FAIR like detector tests, readout components test, and data flow investigations 20. Extracting the information backbone in online system. Directory of Open Access Journals (Sweden) Qian-Ming Zhang Full Text Available Information overload is a serious problem in modern society and many solutions such as recommender system have been proposed to filter out irrelevant information. In the literature, researchers have been mainly dedicated to improving the recommendation performance (accuracy and diversity of the algorithms while they have overlooked the influence of topology of the online user-object bipartite networks. In this paper, we find that some information provided by the bipartite networks is not only redundant but also misleading. With such "less can be more" feature, we design some algorithms to improve the recommendation performance by eliminating some links from the original networks. Moreover, we propose a hybrid method combining the time-aware and topology-aware link removal algorithms to extract the backbone which contains the essential information for the recommender systems. From the practical point of view, our method can improve the performance and reduce the computational time of the recommendation system, thus improving both of their effectiveness and efficiency. 1. Extracting Backbones from Weighted Complex Networks with Incomplete Information Directory of Open Access Journals (Sweden) Liqiang Qian 2015-01-01 Full Text Available The backbone is the natural abstraction of a complex network, which can help people understand a networked system in a more simplified form. Traditional backbone extraction methods tend to include many outliers into the backbone. What is more, they often suffer from the computational inefficiency—the exhaustive search of all nodes or edges is often prohibitively expensive. In this paper, we propose a backbone extraction heuristic with incomplete information (BEHwII to find the backbone in a complex weighted network. First, a strict filtering rule is carefully designed to determine edges to be preserved or discarded. Second, we present a local search model to examine part of edges in an iterative way, which only relies on the local/incomplete knowledge rather than the global view of the network. Experimental results on four real-life networks demonstrate the advantage of BEHwII over the classic disparity filter method by either effectiveness or efficiency validity. 2. 13C and 15N fractionation of CH4/N2 mixtures during photochemical aerosol formation: Relevance to Titan Science.gov (United States) Sebree, Joshua A.; Stern, Jennifer C.; Mandt, Kathleen E.; Domagal-Goldman, Shawn D.; Trainer, Melissa G. 2016-05-01 The ratios of the stable isotopes that comprise each chemical species in Titan's atmosphere provide critical information towards understanding the processes taking place within its modern and ancient atmosphere. Several stable isotope pairs, including 12C/13C and 14N/15N, have been measured in situ or probed spectroscopically by Cassini-borne instruments, space telescopes, or through ground-based observations. Current attempts to model the observed isotope ratios incorporate fractionation resulting from atmospheric diffusion, hydrodynamic escape, and primary photochemical processes. However, the effect of a potentially critical pathway for isotopic fractionation - organic aerosol formation and subsequent deposition onto the surface of Titan - has not been considered due to insufficient data regarding fractionation during aerosol formation. To better understand the nature of this process, we have conducted a laboratory study to measure the isotopic fractionation associated with the formation of Titan aerosol analogs, commonly referred to as 'tholins', via far-UV irradiation of several methane (CH4) and dinitrogen (N2) mixtures. Analysis of the δ13C and δ15N isotopic signatures of the photochemical aerosol products using an isotope ratio mass spectrometer (IRMS) show that fractionation direction and magnitude are dependent on the initial bulk composition of the gas mixture. In general, the aerosols showed enrichment in 13C and 14N, and the observed fractionation trends can provide insight into the chemical mechanisms controlling photochemical aerosol formation. 3. Sequence-specific {sup 1}H, {sup 13}C, and {sup 15}N resonance assignments for intestinal fatty-acid-binding protein complexed with palmitate (15.4 kDA) Energy Technology Data Exchange (ETDEWEB) Hodsdon, M.E.; Toner, J.J.; Cistola, D.P. [Washington Univ. School of Medicine, St. Louis, MO (United States) 1994-12-01 Intestinal fatty-acid-binding protein (I-FABP) belongs to a family of soluble, cytoplasmic proteins that are thought to function in the intracellular transport and trafficking of polar lipids. Individual members of this protein family have distinct specificities and affinities for fatty acids, cholesterol, bile salts, and retinoids. We are comparing several retinol- and fatty-acid-binding proteins from intestine in order to define the factors that control molecular recognition in this family of proteins. We have established sequential resonance assignments for uniformly {sup 13}C/{sup 15}N-enriched I-FABP complexed with perdeuterated palmitate at pH7.2 and 37{degrees}C. The assignment strategy was similar to that introduced for calmodulin. We employed seven three-dimensional NMR experiments to establish scalar couplings between backbone and sidechain atoms. Backbone atoms were correlated using triple-resonance HNCO, HNCA, TOCSY-HMQC, HCACO, and HCA(CO)N experiments. Sidechain atoms were correlated using CC-TOCSY, HCCH-TOCSY, and TOCSY-HMQC. The correlations of peaks between three-dimensional spectra were established in a computer-assisted manner using NMR COMPASS (Molecular Simulations, Inc.) Using this approach, {sup 1}H, {sup 13}C, and {sup 15}N resonance assignments have been established for 120 of the 131 residues of I-FABP. For 18 residues, amide {sup 1}H and {sup 15}N resonances were unobservable, apparently because of the rapid exchange of amide protons with bulk water at pH 7.2. The missing amide protons correspond to distinct amino acid patterns in the protein sequence, which will be discussed. During the assignment process, several sources of ambiguity in spin correlations were observed. To overcome this ambiguity, the additional inter-residue correlations often observed in the HNCA experiment were used as cross-checks for the sequential backbone assignments. 4. Evaluation of the protein metabolism during hepatic coma evidenced by 15N tracer data International Nuclear Information System (INIS) In patients in coma hepaticum as well as in pigs with experimental hepatic coma the protein metabolism was studied under conditions of parenteral application of an amino acid diet using 15N-glycine as tracer 5. Measurement of marine productivity using 15N and 13C tracers: Some methodological aspects Indian Academy of Sciences (India) Naveen Gandhi; Sanjeev Kumar; S Prakash; R Ramesh; M S Sheshshayee 2011-02-01 Various experiments involving the measurement of new, regenerated and total productivity using 15N and 13C tracers were carried out in the Bay of Bengal (BOB) and in the Arabian Sea. Results from 15N tracer experiments indicate that nitrate uptake can be underestimated by experiments with incubation time > 4 hours. Indirect evidence suggests pico- and nano-phytoplankton, on their dominance over microphytoplankton, can also influence the f-ratios. Difference in energy requirement for assimilation of different nitrogen compounds decides the preferred nitrogen source during the early hours of incubation. Variation in light intensity during incubation also plays a significant role in the assimilation of nitrogen. Results from time course experiments with both 15N and 13C tracers suggest that photoinhibition appears significant in BOB and the Arabian Sea during noon. A significant correlation has been found in the productivity values obtained using 15N and 13C tracers. 6. 15N NMR Spectroscopic Study on Nitrogen Formsin1mmHumic Substances of Soils Institute of Scientific and Technical Information of China (English) 2001-01-01 Nitrogen forms of humic substances from a subalpine meadow soil, alateritic red soil and a weathered coal and the effect of acidhydrolysis on N structures of soil humic substances were studied byusing {15N cross-polarization magic angle spinning nuclearmagnetic resonance (CPMAS NMR) spectroscopy. Of the detectable15N-signal intensity in the spectra of soil humic substances71%79% may be attributed to amide groups, 10%18%to aromatic/aliphatic amines and 6%11% to indole- andpyrrole-like N. Whereas in the spectrum of the fulvic acid fromweathered coal 46%, at least, of the total 15N-signalintensity might be assigned to pyrrole-like N, 14% toaromatic/aliphatic amines, and the remaining intensities could not beassigned with certainty. Data on nonhydrolyzable residue ofprotein-sugar mixture and a 15N-labelled soil fulvic acidconfirm the formation of nonhydrolyzable heterocyclic N during acidhydrolysis. 7. Metabolic studies in colostomized laying hens using 15N-labelled wheat. 3 International Nuclear Information System (INIS) In colostomized laying hens fed with 15N-labelled wheat protein the atomic percentage 15N excess (15N') was determined in the total, lysine, histidine, and arginine N, respectively, of isolated ovarian follicles of the residual ovary and of the oviduct. The labelling of the basic amino acids became smaller with decreasing size of the follicles. The proportions between the 3 amino acids were inconsistent and typical for the individual hens, whereas in the yolk a constant ratio of the amino acids was found. The 15N' in the 3 amino acids of the residual ovary and of the oviduct revealed greater differences between the individual hens. In the lysine, histidine and arginine 21.2% of the labelled N of the follicles was demonstrated 8. Methodical investigation of the endogenous N excretion in feces by 15N-labelled rats International Nuclear Information System (INIS) Wistar rats (approximately 100g live weight, n = 8) received a wheat diet and were labelled over a period of 7 days with 15N-ammonium acetate. From day 1 - 5 of the experiment after the end of the labelling feces and urine were collected and analysed. After the animals were killed (day 5 of the experiment) the atom-% 15N excess (15N') in the contents of the digestive tract as well as in the tissues of stomach wall, intestinal wall, liver, pancreas and blood plasma was determined. The TCA-soluble fraction of the blood plasma showed 0.44 atom-% 15N' on day 5 after the end of 15N labelling. 3 hours before the killing fecal N also showed 0.44 and during the last collection period (24 hours before) an average of 0.51 atom-% 15N'. Urine decreased in the same period from 0.71 to 0.59 atom-% 15N'. The endogenous fecal N is calculated to 88%. As the tissues of the digestive tract are likely to supply the biggest part of the endogenous fecal protein, the values of atom-% 15N' from the TCA-precipitable fraction of the intestinal wall and of the pancreas gland was calculed to an average of 0.526. According to this the calculation endogenous fecal N is 84%. It is probable that the quota of endogenous fecal N in the total amount of fecal N varies in dependence on the fermentable crude fiber in the diet as well as on the age of the test animals and thus the bacterial protein synthesis in the colon. As the N used by the bacteria is likely to come from the TCA-soluble fraction of the blood, the calculation formula suggested, which uses the TCA-soluble fraction of the blood plasma, achieves good approximate values also for higher bacterial protein synthesis in the colon. (author) 9. The First in Vivo Observation of 13C- 15N Coupling in Mammalian Brain Science.gov (United States) Kanamori, Keiko; Ross, Brian D. 2001-12-01 [5-13C,15N]Glutamine, with 1J(13C-15N) of 16 Hz, was observed in vivo in the brain of spontaneously breathing rats by 13C MRS at 4.7 T. The brain [5-13C]glutamine peak consisted of the doublet from [5-13C,15N]glutamine and the center [5-13C,14N]glutamine peak, resulting in an apparent triplet with a separation of 8 Hz. The time course of formation of brain [5-13C,15N]glutamine was monitored in vivo with a time resolution of 20-35 min. This [5-13C,15N]glutamine was formed by glial uptake of released neurotransmitter [5-13C]glutamate and its reaction with 15NH3 catalyzed by the glia-specific glutamine synthetase. The neurotransmitter glutamate C5 was selectively13C-enriched by intravenous [2,5-13C]glucose infusion to 13C-label whole-brain glutamate C5, followed by [12C]glucose infusion to chase 13C from the small and rapidly turning-over glial glutamate pool, leaving 13C mainly in the neurotransmitter [5-13C]glutamate pool, which is sequestered in vesicles until release. Hence, the observed [5-13C,15N]glutamine arises from a coupling between 13C of neuronal origin and 15N of glial origin. Measurement of the rate of brain [5-13C,15N]glutamine formation provides a novel noninvasive method of studying the kinetics of neurotransmitter uptake into glia in vivo, a process that is crucial for protecting the brain from glutamate excitotoxicity. 10. Synthesis of methotrexate-1-15N and methotrexate-4-15NH2 International Nuclear Information System (INIS) This paper describes an application of the pterin synthesis of methotrexate specifically labelled at the N1-ring nitrogen and at the 4-amino group with 99 atom percent 15N. Oximination of ethyl cyanoacetate-15N followed by reduction afforded ethyl 2-aminocyanoacetate-C15N. Condensation with 3-bromopyruvaldoxime and 4-methylamino-benzoic acid afforded 2-amino-3-carbethoxy-5-N-methyl-p-carboxy-anilinomethylpyrazine-1-oxide-2-15NH2. Treatment with ammonium hydroxide at room temperature gave the 3-carboxamide. Reduction of the N-oxide (Pl3), esterification, and dehydration of the amide (POCl3) afforded the 2-amino-3-cyano-pyrazine benzoate ester. Ring closure with guanidine followed by benzoate ester hydrolysis, glutamate coupling and hydrolysis of the glutamate diester yielded methotrexate-1-15N. Animation of the unlabeled 2-amino-3-carbethoxy pyrazine intermediate with 15N-labelled ammonium hydroxide gave the 15N-carboxamide which was carried through the process described above to afford methotrexate-4-15NH2. (author) 11. Quantifying below-ground nitrogen of legumes: Optimizing procedures for 15N shoot-labelling International Nuclear Information System (INIS) Quantifying below-ground nitrogen (N) of legumes is fundamental to understanding their effects on soil mineral N fertility and on the N economies of following or companion crops in legume-based rotations. Methodologies based on 15N-labelling of whole plants with subsequent measurement of 15N in recovered plant parts and in the root-zone soil have proved promising. We report four glasshouse experiments with objectives to develop appropriate protocols for in situ 15N labelling of four pulses, faba bean (Vicia faba), chickpea (Cicer arietinum), mung bean (Vigna radiata) and pigeon pea (Cajanus cajan). Treatments included 15N-urea concentration, feeding technique, leaflet/petiole position, and frequency of feeding. Nitrogen-15-labelling via the leaf-flap was best for faba bean, mung and pigeon pea, whilst petiole feeding was best for chickpea, in all cases using 0.2-mL volumes of 0.5% urea (98 atom% 15N excess). The implications of uneven enrichment of the nodulated roots because of effects of the 15N-depleted nodules when calculating root-derived N in soil are discussed. (author) 12. Highly 15N-Enriched Chondritic Clasts in the Isheyevo Meteorite Energy Technology Data Exchange (ETDEWEB) Bonal, L; Huss, G R; Krot, A N; Nagashima, K; Ishii, H A; Bradley, J P; Hutcheon, I D 2009-01-14 The metal-rich carbonaceous chondrites (CB and CH) have the highest whole-rock {sup 15}N enrichment ({delta}{sup 15}N up to +1500{per_thousand}), similar to {delta}{sup 15}N values reported in micron-sized regions (hotspots) of Interplanetary Dust Particles (IDPs) of possibly cometary origin and fine-grained matrices of unmetamorphosed chondrites. These {sup 15}N-rich hotspots are commonly attributed to low-temperature ion-molecule reactions in the protosolar molecular cloud or in the outer part of the protoplanetary disk. The nature of the whole-rock {sup 15}N enrichment of the metal-rich chondrites is not understood. We report a discovery of a unique type of primitive chondritic clasts in the CH/CB-like meteorite Isheyevo, which provides important constraints on the origin of {sup 15}N anomaly in metal-rich chondrites and nitrogen-isotope fractionation in the Solar System. These clasts contain tiny chondrules and refractory inclusions (5-15 {micro}m in size), and abundant ferromagnesian chondrule fragments (1-50 {micro}m in size) embedded in the partly hydrated, fine-grained matrix material composed of olivines, pyroxenes, poorly-organized aromatic organics, phyllosilicates and other hydrous phases. The mineralogy and oxygen isotope compositions of chondrules and refractory inclusions in the clasts are similar to those in the Isheyevo host, suggesting formation at similar heliocentric distances. In contrast to the previously known extraterrestrial samples, the fine-grained material in the clasts is highly and rather uniformly enriched in {sup 15}N, with bulk {delta}{sup 15}N values ranging between +1000 and +1300{per_thousand}; the {delta}{sup 15}N values in rare hotspots range from +1400 to +4000{per_thousand}. Since fine-grained matrices in the lithic clasts are the only component containing thermally unprocessed (during CAI and chondrule formation or during impact melting) materials that accreted into the metal rich chondrite parent body(ies), the {sup 15}N 13. Radiation safety system (RSS) backbones: Design, engineering, fabrication and installation Energy Technology Data Exchange (ETDEWEB) Wilmarth, J.E.; Sturrock, J.C.; Gallegos, F.R. 1998-12-01 The Radiation Safety System (RSS) Backbones are part of an electrical/electronic/mechanical system insuring safe access and exclusion of personnel to areas at the Los Alamos Neutron Science Center (LANSCE) accelerator. The RSS Backbones control the safety fusible beam plugs which terminate transmission of accelerated ion beams in response to predefined conditions. Any beam or access fault of the backbone inputs will cause insertion of the beam plugs in the low energy beam transport. The Backbones serve the function of tying the beam plugs to the access control systems, beam spill monitoring systems and current-level limiting systems. In some ways the Backbones may be thought of as a spinal column with beam plugs at the head and nerve centers along the spinal column. The two Linac Backbone segments and experimental area segments form a continuous cable plant over 3,500 feet from beam plugs to the tip on the longest tail. The Backbones were installed in compliance with current safety standards, such as installation of the two segments in separate conduits or tray. Monitoring for ground-faults and input wiring verification was an added enhancement to the system. The system has the capability to be tested remotely. 14. Seasonal changes in nitrogen availability, and root and microbial uptake of 15N13C9-phenylalanine and 15N-ammonium in situ at a temperate heath DEFF Research Database (Denmark) Andresen, Louise C.; Michelsen, Anders; Jonasson, Sven Evert; 2011-01-01 In the plant biosynthesis of secondary compounds, phenylalanine is a precursor of condensed tannins. Tannins are deposited into the soil in plant root exudates and dead plant material and have been suggested to precipitate some soil nutrients and hence reduce nutrient availability for plants. Free...... amino acid,inorganic and microbial N concentration during the growing season was investigated in an ecosystem with a natural tannin chemosphere. The influence of tannins on the uptake of nitrogen in plants and microbes was followed by injecting tannic acid (TA), ammonium-15N and phenylalanine-15N/13C9....... Plants preferred ammonium over phenylalanine, while microbes had no preference. Soil microbes had a 77% uptake of intact phenylalanine. Phenylalanine was acquired intact by both grasses and Calluna, with 63% and 38% uptake of intact phenylalanine in grass fine roots and Calluna roots, respectively... 15. Acetylene inhibition of N2O reduction in laboratory soil and groundwater denitrification assays: evaluation by 15N tracer and 15N site preference of N2O Science.gov (United States) Weymann, Daniel; Well, Reinhard; Lewicka-Szczebak, Dominika; Lena, Rohe 2013-04-01 The measurement of denitrification in soils and aquifers is still challenging and often enough associated with considerable experimental effort and high costs. Against this background, the acetylene inhibition technique (AIT) applied in laboratory soil and groundwater denitrification assays is by far the most effective approach. However, this method has been largely criticized, as it is susceptible to underestimate denitrification rates and adds an additional carbon source to the substrates to be investigated. Here we provide evidence that the AIT is not necessarily an inappropriate approach to measure denitrification, that its reliability depends on the drivers governing the process, and that the 15N site preference of N2O (SP) may serve as a tool to assess this reliability. Two laboratory batch experiments were conducted, where sandy aquifer material and a peat soil were incubated as slurries. We established (i) a standard anaerobic treatment by adding KNO3 (10 mg N L-1), (ii) an oxygen treatment by adding KNO3 and O2 (5 mg L-1), and (iii) a glucose treatment by adding KNO3 supplemented with glucose (200 mg C L-1). Both experiments were run under 10 % (v/v) acetylene atmosphere and as 15N tracer treatments using labeled K15NO3 (60 atom % 15N). In the case of the standard anaerobic treatments, we found a very good agreement of denitrification potential obtained by the AIT and 15N tracer methods. SP of N2O of the AIT samples from this treatment ranged between -4.8 and 2.6 ‰ which is indicative for N2O production during bacterial denitrification but not for N2O reduction to N2. In contrast, we observed substantial underestimation of denitrification by AIT for the glucose treatments compared to the 15N method, i.e. denitrification was underestimated by 36 % (sandy aquifer material) and 47 % (peat soil). SP of N2O of the AIT samples from this treatment ranged between 4.5 and 9.6 ‰, which suggests occurrence of bacterial N2O reduction. In the case of the oxygen 16. Revision of the 15N(p, γ)16O reaction rate and oxygen abundance in H-burning zones Science.gov (United States) Caciolli, A.; Mazzocchi, C.; Capogrosso, V.; Bemmerer, D.; Broggini, C.; Corvisiero, P.; Costantini, H.; Elekes, Z.; Formicola, A.; Fülöp, Zs.; Gervino, G.; Guglielmetti, A.; Gustavino, C.; Gyürky, Gy.; Imbriani, G.; Junker, M.; Lemut, A.; Marta, M.; Menegazzo, R.; Palmerini, S.; Prati, P.; Roca, V.; Rolfs, C.; Rossi Alvarez, C.; Somorjai, E.; Straniero, O.; Strieder, F.; Terrasi, F.; Trautvetter, H. P.; Vomiero, A. 2011-09-01 Context. The NO cycle takes place in the deepest layer of a H-burning core or shell, when the temperature exceeds T ≃ 30 × 106 K. The O depletion observed in some globular cluster giant stars, always associated with a Na enhancement, may be due to either a deep mixing during the red giant branch (RGB) phase of the star or to the pollution of the primordial gas by an early population of massive asymptotic giant branch (AGB) stars, whose chemical composition was modified by the hot bottom burning. In both cases, the NO cycle is responsible for the O depletion. Aims: The activation of this cycle depends on the rate of the 15N(p, γ)16O reaction. A precise evaluation of this reaction rate at temperatures as low as experienced in H-burning zones in stellar interiors is mandatory to understand the observed O abundances. Methods: We present a new measurement of the 15N(p, γ)16O reaction performed at LUNA covering for the first time the center of mass energy range 70-370 keV, which corresponds to stellar temperatures between 65 × 106 K and 780 × 106 K. This range includes the 15N(p, γ)16O Gamow-peak energy of explosive H-burning taking place in the external layer of a nova and the one of the hot bottom burning (HBB) nucleosynthesis occurring in massive AGB stars. Results: With the present data, we are also able to confirm the result of the previous R-matrix extrapolation. In particular, in the temperature range of astrophysical interest, the new rate is about a factor of 2 smaller than reported in the widely adopted compilation of reaction rates (NACRE or CF88) and the uncertainty is now reduced down to the 10% level. 17. True cooking aroma or artefact. {sup 15}N gives the answer; Veritable arome de cuisson ou artefact. {sup 15}N fournit la reponse Energy Technology Data Exchange (ETDEWEB) Metro, F.; Boudaud, N.; Dumont, J.P. [INRA, 44 - Nantes (France) 1994-12-31 In order to determine the respective contributions of the various nitrous precursor families in aroma preparations, the usually added amino acids were substituted with {sup 15}N isotope labelled homologous components. Results concerning isotope ratios for the volatile fraction nitrous components collected from poultry meat aromatic preparations, are presented. Terminal product labelling appears to allow for a better determination of the substrate and functional additive contributions. 4 figs., 6 refs. 18. Stickstoffausnutzungseffizienz von 15N-markierter Schafsgülle und 15N-markiertem Mineraldünger in biologisch und konventionell bewirtschafteten Anbausystemen OpenAIRE Bosshard, Christine; Sorensen, Peter; Frossard, Emmanuel; Mayer, Jochen; Mäder, Paul; Nanzer, Simone; Oberson, Astrid 2009-01-01 Nitrogen (N) utilisation by crops has to be improved to minimize losses to the environment. We investigated N use efficiency of animal manure and mineral fertiliser and fate of fertiliser N not taken up by crops in a bio-organic (BIOORG) and a conventional (CONMIN) cropping system of a long-term experiment over three vegetation periods (wheat-soybean-maize). Microplots received a single application of 15N-labelled slurries or mineral fertiliser. At the end of each vegetation pe... 19. Absorption of ammonium sulphate {sup 15}N by coffee plants; Recuperacao do {sup 15}N do sulfato de amonio por plantas de cafe Energy Technology Data Exchange (ETDEWEB) Fenilli, Tatiele Anete Bergamo; Reichardt, Klaus; Bacchi, Osny Oliveira Santos [Centro de Energia Nuclear na Agricultura (CENA), Piracicaba, SP (Brazil). Lab. de Fisica do Solo]. E-mail: tatiele@cena.usp.br; Trivelin, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura (CENA), Piracicaba, SP (Brazil). Lab. de Isotopos Estaveis; Dourado Neto, Durval [Sao Paulo Univ., Piracicaba, SP (Brazil). Escola Superior de Agricultura Luiz de Queiroz. Dept. de Producao Vegetal 2005-07-01 The objective of this study was to quantify the absorption of ammonium sulphate {sup 15}N by coffee plants. Treatments consisted of five sub-plots of 9 plants, of which the three central ones received 280 kg ha{sup -1} of {sup 15}N, applied at four times: 1/4 on 01 Set 03; 1/4 on 03 Nov 03; 1/4 on 15 Dec 03 and 1/4 on 30 Jan 04. The isotopic enrichment was 2,072 {+-} 0,001 atom % {sup 15}N. The dry matter of the shoot was evaluated every 60 days, using one plant per replicate, collected outside the sub-plot. They were as similar as possible to the labeled plants, which were used only for isotopic and Total N analysis, after being dried at 65 deg C until constant weight. At harvest, plants had absorbed 42,88% of the fertilizer N. Leaves accumulated the largest amount of fertilizer N, and were also the compartments that received most N from other parts of the plant. The following partition of the fertilizer N was found at harvest: 23.01% in young leaves, 6.23% in old leaves, 4,46% in stem, 3.46% in fruits, 3.10% in young branches and 2.63% in old branches. (author) 20. Soil N and 15N variation with time in a California annual grassland ecosystem Science.gov (United States) Brenner, D.L.; Amundson, Ronald; Baisden, W. Troy; Kendall, C.; Harden, J. 2001-01-01 The %N and ??15N values of soils and plants were measured along a chronosequence spanning 3 to 3000 Ky in a California annual grassland. Total soil N decreased with increasing soil age (1.1 to 0.4 kg N m-2) while the mean ?? 15N values of the soil N increased by several ??? from the youngest to oldest sites (+3.5 to +6.2 ???). The ?? 15N values of plants varied along the gradient, reflecting changing soil N pools and differences in the form of N uptake. The decline in total N storage with time is hypothesized to be due to a shift from N to P limitation with increasing soil age. The general increase in ?? 15N values with time is interpreted using a N mass balance model, and appears to reflect a shift toward an increasing proportional losses of inorganic mineral forms of N (vs. organic forms) with increasing soil age. We develop a quantitative index of this trend (mineral vs. organic forms of N loss) using mass balance considerations and parameters. The %N and ?? 15N values along the California age gradient were compared to the published data for a comparably aged chronosequence in Hawaii. Most striking in this comparison is the observation that the California soil and plant ?? 15N values are several ??? greater than those on comparably aged Hawaiian sites. Multiple explanations are plausible, but assuming the sites have a similar range in ?? 15N values of atmospheric inputs, the isotopic differences suggest that N may be, at least seasonally, in greater excess in the strongly seasonal, semi-arid, California grassland. Copyright ?? 2001 Elsevier Science Ltd. 1. Barley Benefits from Organic Nitrogen in Plant Residues Applied to Soil using 15N Isotope Dilution International Nuclear Information System (INIS) The experiment was carried out in pots (sandy soil cultivated with Barley plant) under greenhouse conditions, at Inshas, Egypt. The aim was to evaluate the transformation of nitrogen applied either as mineral form (15NH4)2SO4, or as organic-material-N (plant residues) .Basal recommended doses of P and K were applied. Labeled 15N as(15NH4)2SO4 (5 % a.e) or plant residues (ground leuceana forage, compost, and mixture of them) were applied at a rate of 20 kg N/ ha). 15N technique was used to evaluate N-uptake and fertilizer use efficiency. The treatments were arranged in a completely randomized block design under greenhouse conditions. The obtained results showed that the dry weight of barley shoots was positively affected by reinforcement of mineral- N with organic-N. On the other hand, the highest dry weight was estimated with leuceana either applied alone or reinforced with mineral N. Similar trend was noticed with N uptake but only with organic N, while with treatment received 50% organic-N. plus 50% mineral- N. the best value of N uptake was recorded with mixture of leuceana and compost. The amount of Ndff was lowest where fertilizer 15N was applied alone. Comparing Ndff for the three organic treatments which received a combination of fertilizer-15N+organic-material-N, results showed that the highest Ndff was occurred with mixture of leuceana and compost, whereas the lowest was induced with individual leuceana treatment. 15N recovery in shoots of barley ranged between 22.14 % to 82.16 %. The lowest occurred with application of mineral 15N alone and; the highest occurred where mineral 15N was mixed with compost or leucaena-compost mixture 2. Partitioning Residue-derived and Residue-induced Emissions of N2O Using 15N-labelled Crop Residues Science.gov (United States) Farrell, R. E.; Carverhill, J.; Lemke, R.; Knight, J. D. 2014-12-01 Estimates of N2O emissions in Canada indicate that 17% of all agriculture-based emissions are associated with the decomposition of crop residues. However, research specific to the western Canadian prairies (including Saskatchewan) has shown that the N2O emission factor for N sources in this region typically ranges between 0.2 and 0.6%, which is well below the current IPCC default emission factor of 1.0%. Thus, it stands to reason that emissions from crop residues should also be lower than those calculated using the current IPCC emission factor. Current data indicates that residue decomposition, N mineralization and N2O production are affected by a number of factors such as C:N ratio and chemical composition of the residue, soil type, and soil water content; thus, a bench-scale incubation study was conducted to examine the effects of soil type and water content on N2O emissions associated with the decomposition of different crop residues. The study was carried out using soils from the Black, Dark Brown, Brown, and Gray soil zones and was conducted at both 50% and 70% water-filled pore space (WFPS); the soils were amended with 15N-labeled residues of wheat, pea, canola, and flax, or with an equivalent amount of 15N-labeled urea; 15N2O production was monitored using a Picarro G5101-i isotopic N2O analyzer. Crop residue additions to the soils resulted in both direct and indirect emissions of N2O, with residue derived emissions (RDE; measured as 15N2O) generally exceeding residue-induced emissions (RIE) at 50% WFPS—with RDEs ranging from 42% to 88% (mean = 58%) of the total N2O. Conversely, at 70% WFPS, RDEs were generally lower than RIEs—ranging from 21% to 83% (mean = 48%). Whereas both water content and soil type had an impact on N2O production, there was a clear and consistent trend in the emission factors for the residues; i.e., emissions were always greatest for the canola residue and lowest for the wheat residue and urea fertilizer; and intermediate for pea 3. Revision of the 15N(p,{\\gamma})16O reaction rate and oxygen abundance in H-burning zones CERN Document Server Caciolli, A; Capogrosso, V; Bemmerer, D; Broggini, C; Corvisiero, P; Costantini, H; Elekes, Z; Formicola, A; Fulop, Zs; Gervino, G; Guglielmetti, A; Gustavino, C; Gyurky, Gy; Imbriani, G; Junker, M; Lemut, A; Marta, M; Menegazzo, R; Palmerini, S; Prati, P; Roca, V; Rolfs, C; Alvarez, C Rossi; Somorjai, E; Straniero, O; Strieder, F; Terrasi, F; Trautvetter, H P; Vomiero, A 2011-01-01 The NO cycle takes place in the deepest layer of a H-burning core or shell, when the temperature exceeds T {\\simeq} 30 {\\cdot} 106 K. The O depletion observed in some globular cluster giant stars, always associated with a Na enhancement, may be due to either a deep mixing during the RGB (red giant branch) phase of the star or to the pollution of the primordial gas by an early population of massive AGB (asymptotic giant branch) stars, whose chemical composition was modified by the hot bottom burning. In both cases, the NO cycle is responsible for the O depletion. The activation of this cycle depends on the rate of the 15N(p,{\\gamma})16O reaction. A precise evaluation of this reaction rate at temperatures as low as experienced in H-burning zones in stellar interiors is mandatory to understand the observed O abundances. We present a new measurement of the 15N(p,{\\gamma})16O reaction performed at LUNA covering for the first time the center of mass energy range 70-370 keV, which corresponds to stellar temperatures... 4. Rivermouth alteration of agricultural impacts on consumer tissue δ(15N. Directory of Open Access Journals (Sweden) James H Larson 5. The 15N isotope to evaluate fertilizer nitrogen absorption efficiency by the coffee plant. Science.gov (United States) Fenilli, Tatiele A B; Reichart, Klaus; Bacchi, Osny O S; Trivelin, Paulo C O; Dourado-Neto, Durval 2007-12-01 The use of the 15N label for agronomic research involving nitrogen (N) cycling and the fate of fertilizer-N is well established, however, in the case of long term experimentation with perennial crops like citrus, coffee and rubber tree, there are still shortcomings mainly due to large plant size, sampling procedures, detection levels and interferences on the system. This report tries to contribute methodologically to the design and development of 15N labeled fertilizer experiments, using as an example a coffee crop fertilized with 15N labeled ammonium sulfate, which was followed for two years. The N of the plant derived from the fertilizer was studied in the different parts of the coffee plant in order to evaluate its distribution within the plant and the agronomic efficiency of the fertilizer application practice. An enrichment of the fertilizer-N of the order of 2% 15N abundance was sufficient to study N absorption rates and to establish fertilizer-N balances after one and two years of coffee cropping. The main source of errors in the estimated values lies in the inherent variability among field replicates and not in the measurements of N contents and 15N enrichments of plant material by mass-spectrometry. 6. Grafting and carbonated irrigation water in transport of 15N and in the tomato production International Nuclear Information System (INIS) The effects of CO2 application through irrigation water, and of grafting in transport of 15N and in the tomato production, were studied. These treatments were arranged in a 2 x 2 factorial scheme (with and without CO2 in irrigation water and grafted and non-grafted tomato), in a completely randomized design, with four replications. The injection of CO2 into the water began at 34 days after transplant of seedlings (DAT) and continued for all irrigations. The application of the sulfate of ammonium with abundance in atoms of 15N of 3.13% in plants destined to analysis was done at 45 DAT when the plants were in the middle of fructification. After 14 days of fertilizer (15N) application the plants were harvested, washed, dried and sent for analysis of 15N in plant tissue. The results demonstrated that CO2 and the grafting did not alter the transport of 15N in the plant. The production of commercial fruits was larger when CO2 was applied in water. (author) 7. Quantitative Proteomics: Measuring Protein Synthesis Using 15N Amino Acids Labeling in Pancreas Cancer Cells Science.gov (United States) Zhao, Yingchun; Lee, Wai-Nang Paul; Lim, Shu; Go, Vay Liang; Xiao, Jing; Cao, Rui; Zhang, Hengwei; Recker, Robert; Xiao, Gary Guishan 2010-01-01 Pancreatic cancer MIA PaCa cells were cultured in the presence and absence of 15N amino acids mixture for 72 hours. During protein synthesis, the incorporation of 15N amino acids results in a new mass isotopomer distribution in protein, which is approximated by the concatenation of two binomial distributions of 13C and 15N. Fraction of protein synthesis (FSR) can thus be determined from the relative intensities of the ‘labeled’ (new) and the ‘unlabeled” (old) spectra. Six prominent spots were picked from 2-D gels of proteins from lysates of cells cultured in 0% (control), and 50% and 33% 15N enriched media. These protein spots were digested and analyzed with MALDI-TOF/TOF. The isotopomer distribution of peptides after labeling can be fully accounted for by the labeled (new) and unlabeled (old) peptides. The ratio of the new and old peptide fractions was determined using multiple regression analysis of the observed spectrum as a linear combination of the expected new and the old spectra. The fractional protein synthesis rates calculated from such ratios of same peptide from cells grown in 50% and 33% 15N amino acid enrichments were comparable to each other. The FSR of these six identified proteins ranged between 44–76%. PMID:19072287 8. The 15N isotope to evaluate fertilizer nitrogen absorption efficiency by the coffee plant International Nuclear Information System (INIS) The use of the 15N label for agronomic research involving nitrogen (N) cycling and the fate of fertilizer-N is well established, however, in the case of long term experimentation with perennial crops like citrus, coffee and rubber tree, there are still shortcomings mainly due to large plant size, sampling procedures, detection levels and interferences on the system. This report tries to contribute methodologically to the design and development of 15N labeled fertilizer experiments, using as an example a coffee crop fertilized with 15N labeled ammonium sulfate, which was followed for two years. The N of the plant derived from the fertilizer was studied in the different parts of the coffee plant in order to evaluate its distribution within the plant and the agronomic efficiency of the fertilizer application practice. An enrichment of the fertilizer-N of the order of 2% 15N abundance was sufficient to study N absorption rates and to establish fertilizer-N balances after one and two years of coffee cropping. The main source of errors in the estimated values lies in the inherent variability among field replicates and not in the measurements of N contents and 15N enrichments of plant material by mass-spectrometry. (author) 9. The {sup 15}N isotope to evaluate fertilizer nitrogen absorption efficiency by the coffee plant Energy Technology Data Exchange (ETDEWEB) Fenilli, Tatiele A.B. [Universidade Regional de Blumenau, (FURB), SC (Brazil); Reichart, Klaus; Bacchi, Osny O.S.; Trivelin, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura (CENA/USP), Piracicaba, SP (Brazil)]. E-mail: klaus@cena.usp.br; Dourado-Neto, Durval [Universidade de Sao Paulo (USP), Piracicaba, SP (Brazil). Escola Superior de Agricultura Luiz de Queiroz (ESALQ) 2007-12-15 The use of the {sup 15}N label for agronomic research involving nitrogen (N) cycling and the fate of fertilizer-N is well established, however, in the case of long term experimentation with perennial crops like citrus, coffee and rubber tree, there are still shortcomings mainly due to large plant size, sampling procedures, detection levels and interferences on the system. This report tries to contribute methodologically to the design and development of {sup 15}N labeled fertilizer experiments, using as an example a coffee crop fertilized with {sup 15}N labeled ammonium sulfate, which was followed for two years. The N of the plant derived from the fertilizer was studied in the different parts of the coffee plant in order to evaluate its distribution within the plant and the agronomic efficiency of the fertilizer application practice. An enrichment of the fertilizer-N of the order of 2% {sup 15}N abundance was sufficient to study N absorption rates and to establish fertilizer-N balances after one and two years of coffee cropping. The main source of errors in the estimated values lies in the inherent variability among field replicates and not in the measurements of N contents and {sup 15}N enrichments of plant material by mass-spectrometry. (author) 10. Utilization of 15N-labelled urea in laying hens. 5 International Nuclear Information System (INIS) In the series of experiments with labelled urea three colostomized laying hybrids were butchered after a six-day application of 1% urea with 96.06 atom-% 15N excess (15N') in the ration and another 2 days with a supplement of 1% unlabelled urea. Out of the individual samples from crop, gizzard, small intestine, caecum and rectum, the content of the small intestine and the caecum showed the highest labelling with > 1 atom-% 15N'. The TCA soluble fraction of the content of the gizzard was more highly and that of the intestines less labelled than the total nitrogen. The tissue of the gizzard is distinctly less labelled than the 'omasum system' and the small intestine. The atom-% 15N' of the oesophagus with crop and glandular stomach largely showed agreement in the individual hens with that of intestinal tissue and ranged between 0.71 and 0.89 atom-%. 2% of the 15N' supplemented with the urea could be recovered in the content and the tissue of the gastro-intestinal tract. (author) 11. A sampling approach for protein backbone fragment conformations. Science.gov (United States) Yu, J Y; Zhang, W 2013-01-01 In protein structure prediction, backbone fragment bias information can narrow down the conformational space of the whole polypeptide chain significantly. Unlike existing methods that use fragments as building blocks, the paper presents a probabilistic sampling approach for protein backbone torsion angles by modelling angular correlation of (phi, psi) with a directional statistics distribution. Given a protein sequence and secondary structure information, this method samples backbone fragments conformations by using a backtrack sampling algorithm for the hidden Markov model with multiple inputs and a single output. The proposed approach is applied to a fragment library, and some well-known structural motifs are sampled very well on the optimal path. Computational results show that the method can help to obtain native-like backbone fragments conformations. PMID:23777175 12. VIRTUAL BACKBONE CONTENT ROUTING IN WIRELESS AD-HOC NETWORK Directory of Open Access Journals (Sweden) Longxiang Gao 2009-11-01 Full Text Available We developed a new content routing based on the virtual backbone structure, which groups wireless nodes and contents into a virtual architecture. Our approach is scalable, works with local information,and does not rely on address information. The naming system uses flat naming to identify nodes and contents, and organizes these identifiers together. Backbone nodes can be selected automatically or predefined to direct their associated normal nodes in a local area. The normal nodes are guided by the backbone nodes to full fill the searching and routing processes. With a virtual structure, the searching performance can be improved by using the DHT technique.Experiments using ns2 simulator demonstrate that this virtual backbone routing architecture has the following significances: workable without being aware address in a mobile situation; scalable with the size of network; efficient in terms of the reduced hop counts and short end-to-end delay, and also resistant to the dead-end problem. 13. LOAD AWARE ADAPTIVE BACKBONE SYNTHESIS IN WIRELESS MESH NETWORKS Institute of Scientific and Technical Information of China (English) Yuan Yuan; Zheng Baoyu 2009-01-01 Wireless Mesh Networks (WMNs) are envisioned to support the wired backbone with a wireless Backbone Networks (BNet) for providing internet connectivity to large-scale areas.With a wide range of internet-oriented applications with different Quality of Service (QoS) requirement,the large-scale WMNs should have good scalability and large bandwidth.In this paper,a Load Aware Adaptive Backbone Synthesis (LAABS) algorithm is proposed to automatically balance the traffic flow in the WMNs.The BNet will dynamically split into smaller size or merge into bigger one according to statistic load information of Backbone Nodes (BNs).Simulation results show LAABS generates moderate BNet size and converges quickly,thus providing scalable and stable BNet to facilitate traffic flow. 14. 使用Backbone JS搭建SPA Institute of Scientific and Technical Information of China (English) 吕婷 2012-01-01 Backbone JSR从2010年发布以来，受到了业界的广泛关注。“豆瓣说”和“豆瓣阅读（阅读器）”是两款以它为基础框架搭建的SPA，本文将结合这两款产品，向读者介绍BackboneJS的方方面面。 15. High Performance Infiltrated Backbones for Cathode-Supported SOFC's DEFF Research Database (Denmark) Gil, Vanesa; Kammer Hansen, Kent 2014-01-01 -supported SOFC. The cathodes are obtained by infiltrating LSM into a sintered either thick (300 μm) yttria stabilized zirconia (YSZ) backbone or a thin YSZ backbone (10-15 μm) integrated onto a thick (300 μm) porous strontium substituted lanthanum manganite (LSM) and YSZ composite. Fabrication challenges...... with infiltrated LSM nanoparticles is shown in Fig. 1. Figure 1. Cross section of LSM infiltrated cathode supported cell. [Formula]... 16. Side chain and backbone ordering in a polypeptide CERN Document Server Wei, Y; Hansmann, U H E 2006-01-01 We report results from multicanonical simulations of polyglutamic acid chains of length of ten residues. For this simple polypeptide we observe a decoupling of backbone and side-chain ordering in the folding process. While the details of the two transitions vary between the peptide in gas phase and in an implicit solvent, our results indicate that, independent of the specific surroundings, upon continuously lowering the temperature side-chain ordering occurs only after the backbone topology is completely formed. 17. Fossil Fuel Combustion-Related Emissions Dominate Atmospheric Ammonia Sources during Severe Haze Episodes: Evidence from (15)N-Stable Isotope in Size-Resolved Aerosol Ammonium. Science.gov (United States) Pan, Yuepeng; Tian, Shili; Liu, Dongwei; Fang, Yunting; Zhu, Xiaying; Zhang, Qiang; Zheng, Bo; Michalski, Greg; Wang, Yuesi 2016-08-01 The reduction of ammonia (NH3) emissions is urgently needed due to its role in aerosol nucleation and growth causing haze formation during its conversion into ammonium (NH4(+)). However, the relative contributions of individual NH3 sources are unclear, and debate remains over whether agricultural emissions dominate atmospheric NH3 in urban areas. Based on the chemical and isotopic measurements of size-resolved aerosols in urban Beijing, China, we find that the natural abundance of (15)N (expressed using δ(15)N values) of NH4(+) in fine particles varies with the development of haze episodes, ranging from -37.1‰ to -21.7‰ during clean/dusty days (relative humidity: ∼ 40%), to -13.1‰ to +5.8‰ during hazy days (relative humidity: 70-90%). After accounting for the isotope exchange between NH3 gas and aerosol NH4(+), the δ(15)N value of the initial NH3 during hazy days is found to be -14.5‰ to -1.6‰, which indicates fossil fuel-based emissions. These emissions contribute 90% of the total NH3 during hazy days in urban Beijing. This work demonstrates the analysis of δ(15)N values of aerosol NH4(+) to be a promising new tool for partitioning atmospheric NH3 sources, providing policy makers with insights into NH3 emissions and secondary aerosols for regulation in urban environments. PMID:27359161 18. Fossil Fuel Combustion-Related Emissions Dominate Atmospheric Ammonia Sources during Severe Haze Episodes: Evidence from (15)N-Stable Isotope in Size-Resolved Aerosol Ammonium. Science.gov (United States) Pan, Yuepeng; Tian, Shili; Liu, Dongwei; Fang, Yunting; Zhu, Xiaying; Zhang, Qiang; Zheng, Bo; Michalski, Greg; Wang, Yuesi 2016-08-01 The reduction of ammonia (NH3) emissions is urgently needed due to its role in aerosol nucleation and growth causing haze formation during its conversion into ammonium (NH4(+)). However, the relative contributions of individual NH3 sources are unclear, and debate remains over whether agricultural emissions dominate atmospheric NH3 in urban areas. Based on the chemical and isotopic measurements of size-resolved aerosols in urban Beijing, China, we find that the natural abundance of (15)N (expressed using δ(15)N values) of NH4(+) in fine particles varies with the development of haze episodes, ranging from -37.1‰ to -21.7‰ during clean/dusty days (relative humidity: ∼ 40%), to -13.1‰ to +5.8‰ during hazy days (relative humidity: 70-90%). After accounting for the isotope exchange between NH3 gas and aerosol NH4(+), the δ(15)N value of the initial NH3 during hazy days is found to be -14.5‰ to -1.6‰, which indicates fossil fuel-based emissions. These emissions contribute 90% of the total NH3 during hazy days in urban Beijing. This work demonstrates the analysis of δ(15)N values of aerosol NH4(+) to be a promising new tool for partitioning atmospheric NH3 sources, providing policy makers with insights into NH3 emissions and secondary aerosols for regulation in urban environments. 19. Preparation of 15N labelled protein sample by gene engineering technology International Nuclear Information System (INIS) Using the advanced multi-dimension heteronuclear pulses and isotope labelled protein technique, nuclear magnetic resonance spectroscopy has become an important tool in analysis of the solution conformation of protein. On the basis of the high level expression of a protein-trichosanthin in recombinant E.coli using DNA, 15N was used to label the protein, the 15N labelled trichosanthin was obtained by affinity chromatography on Ni-NTA agarose. Terminating pregnant effect in mice showed that this recombinant protein had the same activity as natural trichosanthin. A 1H-15N heteronuclear single-quantum coherence (HSQC) spectrum was obtained from an AM-500 NMR spectrometer, demonstrating that this method is suitable in preparing labelled protein sample for NMR 20. Coral skeletal δ15N reveals isotopic traces of an agricultural revolution International Nuclear Information System (INIS) This study introduces a new method of tracing the history of nutrient loading in coastal oceans via δ15N analysis of organic nitrogen preserved in the skeleton of the massive Porites coral. Four coral cores were collected in Bali, Indonesia, from reefs exposed to high levels of fertilizers in agricultural run-off, from lagoonal corals impacted by sewage, and from a reef located 30 km offshore. Skeletal δ15N in the agriculturally exposed coral declined from 10.7 ± 0.4 per mille in 1970-1971, when synthetic fertilizers (-0.8 per mille ± 0.2 per mille ) were introduced to Bali, to a depleted 'anthropogenic' baseline of 3.5 per mille ± 0.4% in the mid-1990s. δ15N values were negatively correlated with rainfall, suggesting that marine δ15N lowers during flood-born influxes of waste fertilizers. Reef cores exposed to untreated sewage in terrestrial discharge were enriched (7.8 and 7.3 ± 0.4 per mille ), while the offshore core reflected background oceanic signals (6.2 ± 0.4 per mille). δ15N, N concentration, and C:N systematics indicate that the N isotopic composition of skeletal organic matter was generally well preserved over 30 years. We suggest that skeletal organic δ15N can serve as a recorder of past nitrogen sources. In Bali, this tracer suggests that the intensification of Western style agricultural practices since 1970 are contributing to the degradation of coastal coral reefs 1. Optical $\\Lambda$ transitions and quantum computing in the $^{15}$N-V$^{-}$ Center in Diamond OpenAIRE González, Gabriel; Leuenberger, Michael N. 2009-01-01 We present a thorough derivation of the excited state energy levels of the negatively charged $^{15}$N-V$^{-}$ center in diamond for the strong applied electric field case. We show that in the $^{15}$N-V$^{-}$ center a spin non-conserving two-photon $\\Lambda$ transition exists that is mediated by the hyperfine interaction, which provides the possibility to write quantum information. Using second order perturbation theory we obtain a $\\Lambda$ transition rate of the order of 10 MHz at room tem... 2. Compaction stimulates denitrification in an urban park soil using 15N tracing technique DEFF Research Database (Denmark) Li, Shun; Deng, Huan; Rensing, Christopher Günther T; 2014-01-01 Soils in urban areas are subjected to compaction with accelerating urbanization. The effects of anthropogenic compaction on urban soil denitrification are largely unknown. We conducted a study on an urban park soil to investigate how compaction impacts denitrification. By using 15N labeling method......, no statistical difference in total N losses and 15N-(N2O+N2) flux between the uncompacted soil and the compacted soil was detected. Compaction promoted soil denitrification and may impact urban N biogeochemical cycling. © 2013 Springer-Verlag Berlin Heidelberg.... 3. Constraints on oceanic N balance/imbalance from sedimentary 15N records Directory of Open Access Journals (Sweden) M. A. Altabet 2007-01-01 Full Text Available According to current best estimates, the modern ocean's N cycle is in severe deficit. N isotope budgeting provides an independent geochemical constraint in this regard as well as the only means for past reconstruction. Overall, it is the relative proportion of N2 fixation consumed by water column denitrification that sets average oceanic δ15N under steady-state conditions. Several factors (conversion of organic N to N2, Rayleigh closed and open system effects likely reduce the effective fractionation factor (ε for water column denitrification to about half the inherent microbial value for εden. If so, the average oceanic δ15N of ~5‰ is consistent with a canonical contribution from water column denitrification of 50% of the source flux from N2 fixation. If an imbalance in oceanic N sources and sinks changes this proportion then a transient in average oceanic δ15N would occur. Using a simple model, changing water column denitrification by ±30% or N2 fixation by ±15% produces detectable (>1‰ changes in average oceanic δ15N over one residence time period or more with corresponding changes in oceanic N inventory. Changing sedimentary denitrification produces no change in δ15N but does change N inventory. Sediment δ15N records from sites thought to be sensitive to oceanic average δ15N all show no detectible change over the last 3 kyr or so implying a balanced marine N budget over the latest Holocene. A mismatch in time scales is the most likely meaningful interpretation of the apparent conflict with modern flux estimates. Decadal to centennial scale oscillations between net N deficit and net surplus may occur but on the N residence timescale of several thousand years, net balance is achieved in sum. However, sediment δ15N records from the literature covering the period since the last glacial maximum show excursions of up to several ‰ that are consistent with sustained N deficit during the deglaciation followed by readjustment 4. Constraints on oceanic N balance/imbalance from sedimentary 15N records Directory of Open Access Journals (Sweden) M. A. Altabet 2006-07-01 Full Text Available According to current best estimates, the modern ocean's N cycle is in severe deficit. N isotope budgeting provides an independent geochemical constraint in this regard as well as the only means for past reconstruction. Overall, it is the relative proportion of N2 fixation consumed by water column denitrification that sets average oceanic δ15N under steady-state conditions. Several factors (conversion of organic N to N2, Rayleigh closed and open system effects likely reduce the effective fractionation factor (ε for water column denitrification to about half the inherent microbial value for εden. If so, the average oceanic δ15N of ~5 is consistent with a canonical contribution from water column denitrification of 50% of the source flux from N2 fixation. If an imbalance in oceanic N sources and sinks changes this proportion then a transient in average oceanic δ15N would occur. Using a simple model, changing water column denitrification ±30% or N2 fixation by ±15% produces detectable (>1 changes in average oceanic δ15N over one residence time period or more with corresponding changes in oceanic N inventory. Changing sedimentary denitrification produces no change in δ15N but does change N inventory. Sediment δ15N records from sites thought to be sensitive to oceanic average δ15N all show no detectible change over the last 3 kyr or so implying a balanced marine N budget over the latest Holocene. A mismatch in time scales is the most likely meaningful interpretation of the apparent conflict with modern flux estimates. Decadal to centennial scale oscillations between net N deficit and net surplus may occur but on the N residence timescale of several thousand years, net balance is achieved in sum. However, sediment δ15N records from the literature covering the period since the last glacial maximum show excursions of up to several that are consistent with sustained N deficit during the deglaciation followed by readjustment and establishment of 5. Histidine-Directed Arylation/Alkenylation of Backbone N-H Bonds Mediated by Copper(II). Science.gov (United States) Ohata, Jun; Minus, Matthew B; Abernathy, Morgan E; Ball, Zachary T 2016-06-22 Chemical modification of proteins and peptides represents a challenge of reaction design as well as an important biological tool. In contrast to side-chain modification, synthetic methods to alter backbone structure are extremely limited. In this communication, copper-mediated backbone N-alkenylation or N-arylation of peptides and proteins by direct modification of natural sequences is described. Histidine residues direct oxidative coupling of boronic acids at the backbone NH of a neighboring amino acid. The mild reaction conditions in common physiological buffers, at ambient temperature, are compatible with proteins and biological systems. This simple reaction demonstrates the potential for directed reactions in complex systems to allow modification of N-H bonds that directly affect polypeptide structure, stability, and function. PMID:27249339 6. Automated assignment of NMR chemical shifts based on a known structure and 4D spectra. Science.gov (United States) Trautwein, Matthias; Fredriksson, Kai; Möller, Heiko M; Exner, Thomas E 2016-08-01 Apart from their central role during 3D structure determination of proteins the backbone chemical shift assignment is the basis for a number of applications, like chemical shift perturbation mapping and studies on the dynamics of proteins. This assignment is not a trivial task even if a 3D protein structure is known and needs almost as much effort as the assignment for structure prediction if performed manually. We present here a new algorithm based solely on 4D [(1)H,(15)N]-HSQC-NOESY-[(1)H,(15)N]-HSQC spectra which is able to assign a large percentage of chemical shifts (73-82 %) unambiguously, demonstrated with proteins up to a size of 250 residues. For the remaining residues, a small number of possible assignments is filtered out. This is done by comparing distances in the 3D structure to restraints obtained from the peak volumes in the 4D spectrum. Using dead-end elimination, assignments are removed in which at least one of the restraints is violated. Including additional information from chemical shift predictions, a complete unambiguous assignment was obtained for Ubiquitin and 95 % of the residues were correctly assigned in the 251 residue-long N-terminal domain of enzyme I. The program including source code is available at https://github.com/thomasexner/4Dassign . PMID:27484442 7. Subpicosecond protein backbone changes detected during the green-absorbing proteorhodopsin primary photoreaction. Science.gov (United States) Amsden, Jason J; Kralj, Joel M; Chieffo, Logan R; Wang, Xihua; Erramilli, Shyamsunder; Spudich, Elena N; Spudich, John L; Ziegler, Lawrence D; Rothschild, Kenneth J 2007-10-11 Recent studies demonstrate that photoactive proteins can react within several picoseconds to photon absorption by their chromophores. Faster subpicosecond protein responses have been suggested to occur in rhodopsin-like proteins where retinal photoisomerization may impulsively drive structural changes in nearby protein groups. Here, we test this possibility by investigating the earliest protein structural changes occurring in proteorhodopsin (PR) using ultrafast transient infrared (TIR) spectroscopy with approximately 200 fs time resolution combined with nonperturbing isotope labeling. PR is a recently discovered microbial rhodopsin similar to bacteriorhodopsin (BR) found in marine proteobacteria and functions as a proton pump. Vibrational bands in the retinal fingerprint (1175-1215 cm(-1)) and ethylenic stretching (1500-1570 cm(-1)) regions characteristic of all-trans to 13-cis chromophore isomerization and formation of a red-shifted photointermediate appear with a 500-700 fs time constant after photoexcitation. Bands characteristic of partial return to the ground state evolve with a 2.0-3.5 ps time constant. In addition, a negative band appears at 1548 cm(-1) with a time constant of 500-700 fs, which on the basis of total-15N and retinal C15D (retinal with a deuterium on carbon 15) isotope labeling is assigned to an amide II peptide backbone mode that shifts to near 1538 cm(-1) concomitantly with chromophore isomerization. Our results demonstrate that one or more peptide backbone groups in PR respond with a time constant of 500-700 fs, almost coincident with the light-driven retinylidene chromophore isomerization. The protein changes we observe on a subpicosecond time scale may be involved in storage of the absorbed photon energy subsequently utilized for proton transport. PMID:17880126 8. Solution structure and backbone dynamics of the defunct domain of calcium vector protein. Science.gov (United States) Théret, I; Baladi, S; Cox, J A; Gallay, J; Sakamoto, H; Craescu, C T 2001-11-20 CaVP (calcium vector protein) is a Ca(2+) sensor of the EF-hand protein family which is highly abundant in the muscle of Amphioxus. Its three-dimensional structure is not known, but according to the sequence analysis, the protein is composed of two domains, each containing a pair of EF-hand motifs. We determined recently the solution structure of the C-terminal domain (Trp81-Ser161) and characterized the large conformational and dynamic changes induced by Ca(2+) binding. In contrast, the N-terminal domain (Ala1-Asp86) has lost the capacity to bind the metal ion due to critical mutations and insertions in the two calcium loops. In this paper, we report the solution structure of the N-terminal domain and its backbone dynamics based on NMR spectroscopy, nuclear relaxation, and molecular modeling. The well-resolved three-dimensional structure is typical of a pair of EF-hand motifs, joined together by a short antiparallel beta-sheet. The tertiary arrangement of the two EF-hands results in a closed-type conformation, with near-antiparallel alpha-helices, similar to other EF-hand pairs in the absence of calcium ions. To characterize the internal dynamics of the protein, we measured the (15)N nuclear relaxation rates and the heteronuclear NOE effect in (15)N-labeled N-CaVP at a magnetic field of 11.74 T and 298 K. The domain is mainly monomeric in solution and undergoes an isotropic Brownian rotational diffusion with a correlation time of 7.1 ns, in good agreement with the fluorescence anisotropy decay measurements. Data analysis using a model-free procedure showed that the amide backbone groups in the alpha-helices and beta-strands undergo highly restricted movements on a picosecond to nanosecond time scale. The amide groups in Ca(2+) binding loops and in the linker fragment also display rapid fluctuations with slightly increased amplitudes. PMID:11705378 9. Carbon-rich presolar grains from massive stars. Subsolar 12C/13C and 14N/15N ratios and the mystery of 15N CERN Document Server Pignatari, M; Hoppe, P; Jordan, C J; Gibson, B K; Trappitsch, R; Herwig, F; Fryer, C; Hirschi, R; Timmes, F X 2015-01-01 Carbon-rich grains with isotopic anomalies compared to the Sun are found in primitive meteorites. They were made by stars, and carry the original stellar nucleosynthesis signature. Silicon carbide grains of Type X and C, and low-density graphites condensed in the ejecta of core-collapse supernovae. We present a new set of models for the explosive He shell and compare them with the grains showing 12C/13C and 14N/15N ratios lower than solar. In the stellar progenitor H was ingested into the He shell and not fully destroyed before the explosion. Different explosion energies and H concentrations are considered. If the SN shock hits the He-shell region with some H still present, the models can reproduce the C and N isotopic signatures in C-rich grains. Hot-CNO cycle isotopic signatures are obtained, including a large production of 13C and 15N. The short-lived radionuclides 22Na and 26Al are increased by orders of magnitude. The production of radiogenic 22Ne from the decay of 22Na in the He shell might solve the pu... 10. Pathways of nitrogen assimilation in cowpea nodules studied using 15N2 and allopurinol International Nuclear Information System (INIS) In the presence of 0.5 millimolar allopurinol (4-hydroxypyrazolo [3,4-d]pyrimidine), an inhibitor of NAD:xanthine oxidoreductase (EC 1.2.3.2), intact attached nodules of cowpea (vigna unguiculata L. Walp. cv Vita 3) formed [15N]xanthine from 15N2 at rates equivalent to those of ureide synthesis, confirming the direct assimilation of fixed nitrogen into purines. Xanthine accumulated in nodules and was exported in increasing amounts in xylem of allopurinol-treated plants. Other intermediates of purine oxidation, de novo purine synthesis, and ammonia assimilation did not increase and, over the time course of experiments (4 hours), allopurinol had no effect on nitrogenase (EC 1.87.99.2) activity. Negligible 15N -labeling of asparagine from 15N2 was observed, suggesting that the significant pool (up to 14 micromoles per gram of nodule fresh weight) of this amide in cowpea nodules was not formed directly from fixation but may have accumulated as a consequence of phloem delivery 11. Determination of level widths in 15N using nuclear resonance fluorescence Directory of Open Access Journals (Sweden) Szücs T. 2015-01-01 Full Text Available Level widths in 15N have been measured with the nuclear resonance fluorescence (NRF technique. Solid nitrogen compounds, bremsstrahlung, and HPGe detectors have been used as target, beam, and detectors, respectively. The preliminarily level widths are in agreement with the literature values, but more precise. 12. An improved method for delta 15N measurements in ice cores Directory of Open Access Journals (Sweden) M. Leuenberger 2008-02-01 Full Text Available The use of isotopic ratios of nitrogen gas (δ15N trapped in ice cores as a paleothermometer to characterise abrupt climate changes is becoming a widespread technique. The versatility of the technique could be enhanced, for instance in quantifying small temperature changes during the last glacial period in Antarctic ice cores, by using high precision methods. In this paper, we outline a method for measuring δ15N to a precision of 0.006permil (1σ, n=9 from replicate ice core samples. The high precision results from removing oxygen, carbon dioxide and water vapour from the air extracted from ice cores. The advantage of the technique is that it does not involve correction for isobaric interference due to CO+ ions. We also highlight the importance of oxygen removal from the sample, and how it influences δ15N measurements. The results show that a small amount of oxygen in the sample can be detrimental to achieving an optimum precision in δ15N measurements of atmospheric nitrogen trapped ice core samples. 13. δ15N as a proxy for historic anthropogenic nitrogen loading in Charleston Harbor, SC, USA Science.gov (United States) Payne, T. N.; Andrus, C. F. T. 2015-12-01 Bivalve shell geochemistry can serve as a useful indicator of changes in coastal environments. There is increasing interest in developing paleoenvironmental proxies from mollusk shell organic components. Numerous studies have focused on how the δ15N obtained from bivalve tissues can be used to trace present-day wastewater input into estuaries. However, comparatively little attention has been paid to tracing the impact of anthropogenic nitrogen loading into estuaries over time. By measuring historic levels of δ15N in the organic fraction of oyster shells (Crassostrea virginica) from archaeological sites around Charleston Harbor and comparing those levels to the δ15N content of modern shells, it is possible to assess how nitrogen has fluctuated historically in the area. Whole-shell samples from the Late Archaic Period (~3000-4000 BP, Late Woodland Period (~1400-800 BP), 18th and 19th centuries, and modern controls were measured for %N and d15N. Evidence of increased anthropogenic input of N is expected to begin in the early historic period based on similar analysis in Chesapeake Bay. More ancient samples may give insight into baseline conditions prior to recent population growth and industrialization. This information could help understand how large-scale anthropogenic nitrogen loading has affected coastal ecosystems over time and guide future remediation. Furthermore, this project will help refine and improve this novel proxy of past environmental conditions. 14. Using a Macroalgal δ15N Bioassay to Detect Cruise Ship Waste Water Effluent Inputs Science.gov (United States) Nitrogen stable isotopes are a powerful tool for tracking sources of N to marine ecosystems. I used green macroalgae as a bioassay organism to evaluate if the δ15N signature of cruise ship waste water effluent (CSWWE) could be detected in Skagway Harbor, AK. Opportunistic green... 15. Nitrate Removal in Two Relict Oxbow Urban Wetlands: A 15N Mass-balance Approach Science.gov (United States) A 15N-tracer method was used to quantify nitrogen (N) removal processes in two relict oxbow wetlands located adjacent to the Minebank Run restored stream reach in Baltimore County (Maryland, USA) during summer 2009 and early spring 2010. A mass-balance approach was used to determ... 16. Recovery of 15N-urea in soil-plant system of tanzania grass pasture International Nuclear Information System (INIS) The economic attractiveness and negative environmental impact of nitrogen (N) fertilization in pastures depend on the N use efficiency in the soil-plant system. However, the recovery of urea-15N by Panicum maximum cv. Tanzania pastures, one of the most widely used forage species in intensified pastoral systems, is still unknown. This experiment was conducted in a randomized complete block design with four treatments (0, 40, 80 and 120 kg ha-1 of N-urea) and three replications, to determine the recovery of 15N urea by Tanzania grass. Forage production, total N content and N yield were not affected by fertilization (p > 0.05), reflecting the high losses of applied N under the experimental conditions. The recovery of 15N urea (% of applied N) in forage and roots was not affected by fertilization levels (p > 0.05), but decreased exponentially in the soil and soil-plant system (p 15N (kg ha-1) in forage and roots (15 to 30 cm) increased with increasing urea doses (p < 0.05). (author) 17. 15N NMR Spectroscopic Study on Nitrogen Forms in Humic Substances of Soils Institute of Scientific and Technical Information of China (English) WENQIXAIO; ZHUOSUNENG; 等 2001-01-01 Nitrogen forms of humic substances from a subalpine meadow soil,a lateritic red soil and a weathered cola and the effect of acid hydrolysis on N structures of soil humic substances were studied by using 15N cross-polarization magic angle spinning nuclear magnetic resonance(CPMAS NMR) spectroscopy,Of the detectable 15N-signal intensity in the spectra of soil humic substances 71%-79% may be attributed to amide groups ,10%-18% to aromatic/aliphatic amines and 6%-11% to indole-and pyrrole-like N.Whereas in the spectrum of the fulvic acid from weathered coal 46%,at least,of the total 15N-signal intensity might be assigned to pyrrole-like N,14% to aromatic/aliphatic amines,and the reamining intensities could not be assigned with certainty,Data on nonhydrolyzable reside of protein-sugar mixture and a 15N-labelled soil fulvic acid confirm the formation of nonhydrolyzable heterocyclic N during acid hydrolysis. 18. Studies of the endogeneous N metabolism in 15N-labelled pigs. 2 International Nuclear Information System (INIS) 4 pigs were labelled with 15N-ammonium salt over a period of 10 days in the feeding of a fishmeal diet (1), a fishmeal diet + partly hydrolyzed straw meal (2), a field bean diet (3) and a field bean diet + partly hydrolyzed straw meal (4). The 14N-amino acids and the 15N-amino acids excreted in feces showed highly significant correlation coefficient with the increasing content of crude fiber in the diets, which amounted to 3.0, 5.3, 10.0 and 12.1% in the dry matter. The following sequence was established for the growth angle of the essential 14N-amino acids: Leu, Lys, Arg, Thr, Phe, Ile, Val, His and of the 15N-amino acids: Lys, Arg, Val, Leu, Ile, Thr, Phe and His. As Lys, His and Thr cannot incorporate 15N in transamination reactions in the intermediate metabolism, their level of labelling was considerable in case of diet 4. Nevertheless, tan α is highest for 15N-Lys and lowest for 15N-His. This means that His in contrast to Lys, parallel to increased synthesis, is also increasingly decomposed in the large intestine. In contrast to this, proline was not labelled with 15N even with the highest content of crude fiber in the diet. Despite this, 14N-proline excretion, next to glutamic acid, increased most with the growing content of crude fiber in the diet. Due to the hydrophilic character of glutamic acid and the increased water influx in the large intestine and the increased content of crude fiber in the diet, a growing proline transport parallel to the increased influx of crude fiber and water must be assumed. If the growth angle tan α for the excretion of 14N-amino acids is ascertained regressively for a crude fiber content of diet of 10 %, one can prove from the proportion of the amino acids and a comparison from literature for fecal bacteria and ileum digesta that the amino acid composition for this measuring point largely corresponds to that of bacterial protein. (author) 19. Fertilizer 15N balance in a coffee cropping system: a case study in Brazil International Nuclear Information System (INIS) Knowledge about the fate of fertilizer nitrogen in agricultural systems is essential for the improvement of management practices in order to maximize nitrogen (N) recovery by the crop and reduce N losses from the system to a minimum. This study involves fertilizer management practices using the 15N isotope label applied in a single rate to determine the fertilizer-N balance in a particular soil-coffee-atmosphere system and to deepen the understanding of N plant dynamics. Five replicates consisting of plots of about 120 plants each were randomly defined within a 0.2 ha coffee plantation planted in 2001, in Piracicaba, SP, Brazil. Nine plants of each plot were separated in sub-plots for the 15N balance studies and treated with N rates of 280 and 350 kg ha-1 during 2003/2004 and 2004/ 2005, respectively, both of them as ammonium sulfate enriched to a 15N abundance of 2.072 atom %. Plant shoots were considered as separate parts: the orthotropic central branch, productive branches, leaves of productive branches, vegetative branches, leaves of vegetative branches and fruit. Litter, consisting of dead leaves accumulated below the plant canopy, was measured by the difference between leaves at harvest and at the beginning of the following flowering. Roots and soil were sampled down to a depth of 1.0 at intervals of 0.2 m. Samples from the isotopic sub-plots were used to evaluate total N and 15N, and plants outside sub-plots were used to evaluate dry matter. Volatilization losses of NH3 were estimated using special collectors. Leaching of fertilizer-N was estimated from deep drainage water fluxes and 15N concentrations of the soil solution at 1 m soil depth. At the end of the 2-year evaluation, the recovery of 15N applied as ammonium sulfate was 19.1 % in aerial plant parts, 9.4 % in the roots, 23.8 % in the litter, 26.3 % in the fruit and 12.6 % remaining in the 0-1.0 m soil profile. Annual leaching and volatilization losses were very small (2.0 % and 0.9 %, respectively 20. Bradyrhizobium strain and the 15N natural abundance quantification of biological N2 fixation in soybean International Nuclear Information System (INIS) In commercial plantations of soybean in both the Southern and the Cerrado regions, contributions from biological nitrogen fixation (BNF) are generally proportionately high. When using the 15N natural abundance technique to quantify BNF inputs, it is essential to determine, with accuracy, the 15N abundance of the N derived from BNF (the 'B' value). This study aimed to determine the effect of four recommended strains of Bradyrhizobium spp. (two B. japonicum and two B. elkanii) on the 'B' value of soybean grown in pots in an open field using an equation based on the determination of δ15N natural abundance in a non-labelled soil, and estimate of the contribution of BNF derived from the use of 15N-isotope dilution in soils enriched with 15N. To evaluate N2 fixation by soybean, three non-N2-fixing reference crops were grown under the same conditions. Regardless of Bradyrhizobium strain, no differences were observed in dry matter, nodule weight and total N between labelled and non-labelled soil. The N2 fixation of the soybeans grown in the two soil conditions were similar. The mean 'B' values of the soybeans inoculated with the B. japonicum strains were -1.84 per mille and -0.50 per mille, while those inoculated with B. elkanii were -3.67 per mille and -1.0 per mille, for the shoot tissue and the whole plant, respectively. Finally, the 'B' value for the soybean crop varied considerably in function of the inoculated Bradyrhizobium strain, being most important when only the shoot tissue was utilised to estimate the proportion of N in the plant derived from N2 fixation. (author) 1. Araucaria cunninghamii Seedling Response to Different Forms and Rates of 15N-Labelled Fertiliser Institute of Scientific and Technical Information of China (English) T.J.BLUMFIELD; XU Zhi-Hong 2006-01-01 Nitrogenous fertilisers are under consideration for promoting the growth of nursery-reared hoop pine (Araucaria cunninghamii Aiton ex A. Cunn) seedlings in the establishment phase of second rotation (2R) plantations. Using 15Nlabelled fertilisers, we investigated the effect of different forms (ammonium sulphate, ammonium nitrate, potassium nitrate and urea) and rates of application (0, 150 and 300 mg N kg-1 dried soil) of fertilisers on the growth, 15N recovery and carbon isotope composition (δ13C) of hoop pine seedlings in a 12-month glasshouse trial in southeast Queensland,Australia. The 15N-labelled fertilisers were applied to nursery-reared hoop pine seedlings, which were then grown in pots,containing ca. 1.2 kg dried soil, under well watered conditions for 12 months. Four seedlings from each treatment were harvested at 4-month intervals, divided into roots, stem and foliage, with a further subdivision for new and old foliage,and then analysed for 15N, total N, δ13C and total C. There was no significant response in the seedling growth to the form or rate of application of nitrogen (N) fertiliser within the 12-month period, indicating that the seedlings did not experience N deficiency when grown on second rotation hoop pine soils. While the combined 15N recovery from soil and plant remained at around 70% throughout the experiment, the proportion of 15N recovered from the plants increasing steadily over time. Nitrate containing fertilisers at 150 mg N kg-1 soil gradually increased seedling foliage δ13C over the 12-month period, indicating an increase in seedling water use efficiency. 2. Variable δ(15N diet-tissue discrimination factors among sharks: implications for trophic position, diet and food web models. Directory of Open Access Journals (Sweden) Jill A Olin Full Text Available The application of stable isotopes to characterize the complexities of a species foraging behavior and trophic relationships is dependent on assumptions of δ(15N diet-tissue discrimination factors (∆(15N. As ∆(15N values have been experimentally shown to vary amongst consumers, tissues and diet composition, resolving appropriate species-specific ∆(15N values can be complex. Given the logistical and ethical challenges of controlled feeding experiments for determining ∆(15N values for large and/or endangered species, our objective was to conduct an assessment of a range of reported ∆(15N values that can hypothetically serve as surrogates for describing the predator-prey relationships of four shark species that feed on prey from different trophic levels (i.e., different mean δ(15N dietary values. Overall, the most suitable species-specific ∆(15N values decreased with increasing dietary-δ(15N values based on stable isotope Bayesian ellipse overlap estimates of shark and the principal prey functional groups contributing to the diet determined from stomach content analyses. Thus, a single ∆(15N value was not supported for this speciose group of marine predatory fishes. For example, the ∆(15N value of 3.7‰ provided the highest percent overlap between prey and predator isotope ellipses for the bonnethead shark (mean diet δ(15N = 9‰ whereas a ∆(15N value < 2.3‰ provided the highest percent overlap between prey and predator isotope ellipses for the white shark (mean diet δ(15N = 15‰. These data corroborate the previously reported inverse ∆(15N-dietary δ(15N relationship when both isotope ellipses of principal prey functional groups and the broader identified diet of each species were considered supporting the adoption of different ∆(15N values that reflect the predators' δ(15N-dietary value. These findings are critical for refining the application of stable isotope modeling approaches as inferences regarding a species 3. Variable δ(15)N diet-tissue discrimination factors among sharks: implications for trophic position, diet and food web models. Science.gov (United States) Olin, Jill A; Hussey, Nigel E; Grgicak-Mannion, Alice; Fritts, Mark W; Wintner, Sabine P; Fisk, Aaron T 2013-01-01 The application of stable isotopes to characterize the complexities of a species foraging behavior and trophic relationships is dependent on assumptions of δ(15)N diet-tissue discrimination factors (∆(15)N). As ∆(15)N values have been experimentally shown to vary amongst consumers, tissues and diet composition, resolving appropriate species-specific ∆(15)N values can be complex. Given the logistical and ethical challenges of controlled feeding experiments for determining ∆(15)N values for large and/or endangered species, our objective was to conduct an assessment of a range of reported ∆(15)N values that can hypothetically serve as surrogates for describing the predator-prey relationships of four shark species that feed on prey from different trophic levels (i.e., different mean δ(15)N dietary values). Overall, the most suitable species-specific ∆(15)N values decreased with increasing dietary-δ(15)N values based on stable isotope Bayesian ellipse overlap estimates of shark and the principal prey functional groups contributing to the diet determined from stomach content analyses. Thus, a single ∆(15)N value was not supported for this speciose group of marine predatory fishes. For example, the ∆(15)N value of 3.7‰ provided the highest percent overlap between prey and predator isotope ellipses for the bonnethead shark (mean diet δ(15)N = 9‰) whereas a ∆(15)N value shark (mean diet δ(15)N = 15‰). These data corroborate the previously reported inverse ∆(15)N-dietary δ(15)N relationship when both isotope ellipses of principal prey functional groups and the broader identified diet of each species were considered supporting the adoption of different ∆(15)N values that reflect the predators' δ(15)N-dietary value. These findings are critical for refining the application of stable isotope modeling approaches as inferences regarding a species' ecological role in their community will be influenced with consequences for conservation and 4. Influence of open ocean nitrogen supply on the skeletal δ15N of modern shallow-water scleractinian corals Science.gov (United States) Wang, Xingchen T.; Sigman, Daniel M.; Cohen, Anne L.; Sinclair, Daniel J.; Sherrell, Robert M.; Cobb, Kim M.; Erler, Dirk V.; Stolarski, Jarosław; Kitahara, Marcelo V.; Ren, Haojia 2016-05-01 The isotopic composition of skeleton-bound organic nitrogen in shallow-water scleractinian corals (hereafter, CS-δ15N) is an emerging tool for studying the marine nitrogen cycle in the past. The CS-δ15N has been shown to reflect the δ15N of nitrogen (N) sources to corals, with most applications to date focusing on the anthropogenic/terrestrial N inputs to reef environments. However, many coral reefs receive their primary N sources from the open ocean, and the CS-δ15N of these corals may provide information on past changes in the open ocean regional and global N cycle. Using a recently developed persulfate/denitrifier-based method, we measured CS-δ15N in modern shallow-water scleractinian corals from 8 sites proximal to the open ocean. At sites with low open ocean surface nitrate concentrations typical of the subtropics and tropics, measured CS-δ15N variation on seasonal and annual timescales is most often less than 2‰. In contrast, a broad range in CS-δ15N (of ∼10‰) is measured across these sites, with a strong correlation between CS-δ15N and the δ15N of the deep nitrate supply to the surface waters near the reefs. While CS-δ15N can be affected by other N sources as well and can vary in response to local reef conditions as well as coral/symbiont physiological changes, this survey indicates that, when considering corals proximal to the open ocean, the δ15N of the subsurface nitrate supply to surface waters drives most of the CS-δ15N variation across the global ocean. Thus, CS-δ15N is a promising proxy for reconstructing the open ocean N cycle in the past. 5. On Backbone Structure for a Future Multipurpose Network DEFF Research Database (Denmark) Gutierrez Lopez, Jose Manuel; Cuevas, Ruben; Riaz, M. Tahir; 2008-01-01 Telecommunications are evolving towards the unification of services and infrastructures. This unification must be achieved at the highest hierarchical level for a complete synergy of services. Therefore, one of the requirements is a multipurpose backbone network capable of supporting all the curr......Telecommunications are evolving towards the unification of services and infrastructures. This unification must be achieved at the highest hierarchical level for a complete synergy of services. Therefore, one of the requirements is a multipurpose backbone network capable of supporting all...... the current and future services over the same infrastructure, offering high QoS levels. This paper analyzes different possibilities of a future backbone in order to find the best option among the studied ones. This option is a two level structure formed by the combination of N2R and Grid topologies which... 6. Adding diverse noncanonical backbones to rosetta: enabling peptidomimetic design. Directory of Open Access Journals (Sweden) Kevin Drew Full Text Available Peptidomimetics are classes of molecules that mimic structural and functional attributes of polypeptides. Peptidomimetic oligomers can frequently be synthesized using efficient solid phase synthesis procedures similar to peptide synthesis. Conformationally ordered peptidomimetic oligomers are finding broad applications for molecular recognition and for inhibiting protein-protein interactions. One critical limitation is the limited set of design tools for identifying oligomer sequences that can adopt desired conformations. Here, we present expansions to the ROSETTA platform that enable structure prediction and design of five non-peptidic oligomer scaffolds (noncanonical backbones, oligooxopiperazines, oligo-peptoids, [Formula: see text]-peptides, hydrogen bond surrogate helices and oligosaccharides. This work is complementary to prior additions to model noncanonical protein side chains in ROSETTA. The main purpose of our manuscript is to give a detailed description to current and future developers of how each of these noncanonical backbones was implemented. Furthermore, we provide a general outline for implementation of new backbone types not discussed here. To illustrate the utility of this approach, we describe the first tests of the ROSETTA molecular mechanics energy function in the context of oligooxopiperazines, using quantum mechanical calculations as comparison points, scanning through backbone and side chain torsion angles for a model peptidomimetic. Finally, as an example of a novel design application, we describe the automated design of an oligooxopiperazine that inhibits the p53-MDM2 protein-protein interaction. For the general biological and bioengineering community, several noncanonical backbones have been incorporated into web applications that allow users to freely and rapidly test the presented protocols (http://rosie.rosettacommons.org. This work helps address the peptidomimetic community's need for an automated and expandable 7. Fertilizer {sup 15}N balance in a coffee cropping system: a case study in Brazil Energy Technology Data Exchange (ETDEWEB) Fenilli, Tatiele Anete Bergamo [Universidade Regional de Blumenau (URB), SC (Brazil). Dept. de Engenharia Florestal]. E-mail: tfenilli@furb.br; Reichardt, Klaus; Bacchi, Osny Oliveira Santos [Centro de Energia Nuclear na Agricultura (CENA/USP), Piracicaba, SP (Brazil). Lab. de Fisica do Solo]. E-mails: klaus@cena.usp.br; osny@cena.usp.br; Favarin, Jose Laercio [Escola Superior de Agricultura Luiz de Queiroz (ESALQ/USP), Piracicaba, SP (Brazil). Dept. de Producao Vegetal; Silva, Adriana Lucia [Centro de Tecnologia Canavieira (CTC), Piracicaba, SP (Brazil). Fazenda Santo Antonio]. E-mail: adriana.silva@ctc.com.br; Timm, Luis Carlos [Universidade Federal de Pelotas (UFPel), RS (Brazil). Dept. de Engenharia Rural]. E-mail: lcartimm@yahoo.com.br 2008-07-15 Knowledge about the fate of fertilizer nitrogen in agricultural systems is essential for the improvement of management practices in order to maximize nitrogen (N) recovery by the crop and reduce N losses from the system to a minimum. This study involves fertilizer management practices using the {sup 15}N isotope label applied in a single rate to determine the fertilizer-N balance in a particular soil-coffee-atmosphere system and to deepen the understanding of N plant dynamics. Five replicates consisting of plots of about 120 plants each were randomly defined within a 0.2 ha coffee plantation planted in 2001, in Piracicaba, SP, Brazil. Nine plants of each plot were separated in sub-plots for the {sup 15}N balance studies and treated with N rates of 280 and 350 kg ha-1 during 2003/2004 and 2004/ 2005, respectively, both of them as ammonium sulfate enriched to a {sup 15}N abundance of 2.072 atom %. Plant shoots were considered as separate parts: the orthotropic central branch, productive branches, leaves of productive branches, vegetative branches, leaves of vegetative branches and fruit. Litter, consisting of dead leaves accumulated below the plant canopy, was measured by the difference between leaves at harvest and at the beginning of the following flowering. Roots and soil were sampled down to a depth of 1.0 at intervals of 0.2 m. Samples from the isotopic sub-plots were used to evaluate total N and {sup 15}N, and plants outside sub-plots were used to evaluate dry matter. Volatilization losses of NH{sub 3} were estimated using special collectors. Leaching of fertilizer-N was estimated from deep drainage water fluxes and {sup 15}N concentrations of the soil solution at 1 m soil depth. At the end of the 2-year evaluation, the recovery of {sup 15}N applied as ammonium sulfate was 19.1 % in aerial plant parts, 9.4 % in the roots, 23.8 % in the litter, 26.3 % in the fruit and 12.6 % remaining in the 0-1.0 m soil profile. Annual leaching and volatilization losses were 8. STARD6 on steroids: solution structure, multiple timescale backbone dynamics and ligand binding mechanism Science.gov (United States) Létourneau, Danny; Bédard, Mikaël; Cabana, Jérôme; Lefebvre, Andrée; LeHoux, Jean-Guy; Lavigne, Pierre 2016-01-01 START domain proteins are conserved α/β helix-grip fold that play a role in the non-vesicular and intracellular transport of lipids and sterols. The mechanism and conformational changes permitting the entry of the ligand into their buried binding sites is not well understood. Moreover, their functions and the identification of cognate ligands is still an active area of research. Here, we report the solution structure of STARD6 and the characterization of its backbone dynamics on multiple time-scales through 15N spin-relaxation and amide exchange studies. We reveal for the first time the presence of concerted fluctuations in the Ω1 loop and the C-terminal helix on the microsecond-millisecond time-scale that allows for the opening of the binding site and ligand entry. We also report that STARD6 binds specifically testosterone. Our work represents a milestone for the study of ligand binding mechanism by other START domains and the elucidation of the biological function of STARD6. PMID:27340016 9. Structure and backbone dynamics of a microcrystalline metalloprotein by solid-state NMR. Science.gov (United States) Knight, Michael J; Pell, Andrew J; Bertini, Ivano; Felli, Isabella C; Gonnelli, Leonardo; Pierattelli, Roberta; Herrmann, Torsten; Emsley, Lyndon; Pintacuda, Guido 2012-07-10 We introduce a new approach to improve structural and dynamical determination of large metalloproteins using solid-state nuclear magnetic resonance (NMR) with (1)H detection under ultrafast magic angle spinning (MAS). The approach is based on the rapid and sensitive acquisition of an extensive set of (15)N and (13)C nuclear relaxation rates. The system on which we demonstrate these methods is the enzyme Cu, Zn superoxide dismutase (SOD), which coordinates a Cu ion available either in Cu(+) (diamagnetic) or Cu(2+) (paramagnetic) form. Paramagnetic relaxation enhancements are obtained from the difference in rates measured in the two forms and are employed as structural constraints for the determination of the protein structure. When added to (1)H-(1)H distance restraints, they are shown to yield a twofold improvement of the precision of the structure. Site-specific order parameters and timescales of motion are obtained by a gaussian axial fluctuation (GAF) analysis of the relaxation rates of the diamagnetic molecule, and interpreted in relation to backbone structure and metal binding. Timescales for motion are found to be in the range of the overall correlation time in solution, where internal motions characterized here would not be observable. 10. Recovery of 15N-Urea under groundnut-sorghum sequence International Nuclear Information System (INIS) In 2 field experiments conducted at Agricultural Research Station, Tamil Nadu Agricultural University Farm, Bhavanisagar in red loamy soil (Typic Ustropept), the recovery of added 15N-urea was monitored under groundnut-sorghum cropping sequence. Fertilizer 15N was applied as urea at 5, 10 and 15 kg N/ha levels. The highest pod yield (2.18 t/ha) and haulm yield (13.19 t/ha) were recorded at 10 kg N ha-1 level. Out of 10 kg N applied, 51.86 per cent was recovered by the first crop of groundnut and found distributed as 43.13, 1.70 and 8.03 per cent in haulm, shell and kernel, respectively. The residual N recorded by the second crop of sorghum was only 0.63 per cent. (author). 4 refs., 4 tabs 11. Study of organic N transformation in red soils by 15N tracer method Institute of Scientific and Technical Information of China (English) YeQing－Fu; ZhangQin－Zheng; 等 1997-01-01 Uniformly 15N-labelled ryegrass was used to investigate NH4+-production,microbial transformation and humification of organic N in two types of red soils by incubating the soils amended with labelled material.The results showed that there was little significant difference in biomass N transformation in the tested solis between 15N tracer method and conventional method,but the amount of NH4++-N released form the ryegrass in the clayey soil than in the sandy soil at all sampling time .By 120d of incubation,humified N was less than 10% of the amount of the applied N in two types of red soils and the amount of residual N in the clayey red soil was obviously higher than that in the sandy red soil. 12. 1H, 13C and 15N NMR assignments of phenazopyridine derivatives. Science.gov (United States) Burgueño-Tapia, Eleuterio; Mora-Pérez, Yolanda; Morales-Ríos, Martha S; Joseph-Nathan, Pedro 2005-03-01 Phenazopyridine hydrochloride (1), a drug in clinical use for many decades, and some derivatives were studied by one- and two-dimensional (1)H, (13)C and (15)N NMR methodology. The assignments, combined with DFT calculations, reveal that the preferred protonation site of the drug is the pyridine ring nitrogen atom. The chemoselective acetylation of phenazopyridine (2) and its influence on the polarization of the azo nitrogen atoms were evidenced by the (15)N NMR spectra. Molecular calculations of the phenazopyridines 2-4 show that the pyridine and phenyl groups are oriented in an antiperiplanar conformation with intramolecular hydrogen bonding between the N-b atom and the C-2 amino group preserving the E-azo stereochemistry. PMID:15625718 13. Using delta15N values to characterise the nitrogen nutrient pathways from intensive animal units. Science.gov (United States) Skinner, R A; Ineson, P; Jones, H; Sleep, D; Rank, R 2006-01-01 Previous studies on foliar delta15N values, in certain bryophytes, have indicated signature similarities to source pollutants. The object of this study was to investigate the effect further, by examining the mechanisms whereby isotopic fractionation occurs in systems such as atmospheric ammonia (NH3), throughfall, vegetation and soil. Measurements taken in and around point emission sources will then be used to characterise the various fractionation effects associated with these N transformations, as well as to demonstrate some of the issues associated with using delta15N values as pollution indicators. The atmospheric dispersion model UK-ADMS has also been used to model atmospheric delta15NH3 emissions, with signatures exhibiting marked negative shifts immediately downwind of an agricultural NH3 source. Similar dispersion patterns were mapped for NH3 concentration data illustrating the link between these two forms of measurement. 14. Study of the giant dipole resonances of 16O and 15N by means of radiative captures International Nuclear Information System (INIS) The giant dipole resonance in 16O and 15N is studied with reactions 14N(d,γ0)16O, 13C(3He,γ0)16O and 11B(α,γ0)15N. The same energy range is observed with transfert reactions as 12C(7Li,αγ)15N. A comparative study of radiative captures leading to 16O and 15N point out the importance of nsub(p)-nsub(t) configurations. Apparatus and experimental techniques developed are also described 15. Internal protein dynamics on ps to μs timescales as studied by multi-frequency 15N solid-state NMR relaxation International Nuclear Information System (INIS) A comprehensive analysis of the dynamics of the SH3 domain of chicken alpha-spectrin is presented, based upon 15N T1 and on- and off-resonance T1ρ relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from 15N–1H dipole–dipole couplings. It is demonstrated that such a multi-frequency approach enables access to motional correlation times spanning about 6 orders of magnitude. We asses the validity of different motional models based upon orientation autocorrelation functions with a different number of motional components. We find that for many residues a “two components” model is not sufficient for a good description of the data and more complicated fitting models must be considered. We show that slow motions with correlation times on the order of 1–10 μs can be determined reliably in spite of rather low apparent amplitudes (below 1 %), and demonstrate that the distribution of the protein backbone mobility along the time scale axis is pronouncedly non-uniform and non-monotonic: two domains of fast (τ −10 s) and intermediate (10−9 s −7 s) motions are separated by a gap of one order of magnitude in time with almost no motions. For slower motions (τ > 10−6 s) we observe a sharp ∼1 order of magnitude decrease of the apparent motional amplitudes. Such a distribution obviously reflects different nature of backbone motions on different time scales, where the slow end may be attributed to weakly populated “excited states.” Surprisingly, our data reveal no clearly evident correlations between secondary structure of the protein and motional parameters. We also could not notice any unambiguous correlations between motions in different time scales along the protein backbone emphasizing the importance of the inter-residue interactions and the cooperative nature of protein dynamics 16. Internal protein dynamics on ps to μs timescales as studied by multi-frequency {sup 15}N solid-state NMR relaxation Energy Technology Data Exchange (ETDEWEB) Zinkevich, Tatiana [Martin-Luther-Universität Halle-Wittenberg, NMRGroup, Faculty of Natural Sciences II, Institut für Physik (Germany); Chevelkov, Veniamin [Max-Planck-Institut für Biophysikalische Chemie (Germany); Reif, Bernd [Technische Universität München, Department Chemie (Germany); Saalwächter, Kay; Krushelnitsky, Alexey, E-mail: krushelnitsky@physik.uni-halle.de [Martin-Luther-Universität Halle-Wittenberg, NMRGroup, Faculty of Natural Sciences II, Institut für Physik (Germany) 2013-09-19 A comprehensive analysis of the dynamics of the SH3 domain of chicken alpha-spectrin is presented, based upon {sup 15}N T{sub 1} and on- and off-resonance T{sub 1ρ} relaxation times obtained on deuterated samples with a partial back-exchange of labile protons under a variety of the experimental conditions, taking explicitly into account the dipolar order parameters calculated from {sup 15}N–{sup 1}H dipole–dipole couplings. It is demonstrated that such a multi-frequency approach enables access to motional correlation times spanning about 6 orders of magnitude. We asses the validity of different motional models based upon orientation autocorrelation functions with a different number of motional components. We find that for many residues a “two components” model is not sufficient for a good description of the data and more complicated fitting models must be considered. We show that slow motions with correlation times on the order of 1–10 μs can be determined reliably in spite of rather low apparent amplitudes (below 1 %), and demonstrate that the distribution of the protein backbone mobility along the time scale axis is pronouncedly non-uniform and non-monotonic: two domains of fast (τ < 10{sup −10} s) and intermediate (10{sup −9} s < τ < 10{sup −7} s) motions are separated by a gap of one order of magnitude in time with almost no motions. For slower motions (τ > 10{sup −6} s) we observe a sharp ∼1 order of magnitude decrease of the apparent motional amplitudes. Such a distribution obviously reflects different nature of backbone motions on different time scales, where the slow end may be attributed to weakly populated “excited states.” Surprisingly, our data reveal no clearly evident correlations between secondary structure of the protein and motional parameters. We also could not notice any unambiguous correlations between motions in different time scales along the protein backbone emphasizing the importance of the inter 17. δ15N in the turtle grass from the Mexican Caribbean Science.gov (United States) Talavera-Saenz, A.; Sanchez, A.; Ortiz-Hernandez, M. 2013-05-01 Nutrient inputs associated with population growth threaten the integrity of coastal ecosystems. To assess the rapid increase in tourism, we compared the δ15N from Thalassia testudinum collected at sites with different levels of tourism development and population to detect the N inputs of wastewater discharge (WD) along the coast of Quintana Roo. The contributions of nitrogen enriched in 15N are directly related to the increase of WD inputs in areas of high tourism development (Nichupte Lagoon in Cancun, >3 million tourists per year from 2007 to 2011 and 0.7 million of resident population) and decreased towards Bahia Akumal and Tulum (>3 million tourists per year from 2007 to 2011 and 0.15 million of resident population). The δ15N from T. testudinum was significantly lower at Mahahual and Puerto Morelos (about 0.4 million tourists per year in 2007 to 2011 and 0.25 million of resident population) than other the sites. In areas of the lowest development and with tourist activity restricted and small population, such as the Yum Balam Reserve and Sian Ka'an Biosphere Reserve, the δ15N values were in much higher enrichment that Mahahual and Puerto Morelos. Therefore is suggested that Mahahual and Puerto Morelos may be used for baseline isotopic monitoring, over environmental pressure on the reef lagoon ecosystem, where tourist activities and population are growing very slow rate. The anthropogenic N input has the potential to impact, both environmentally and economically, the seagrass meadows and the coral reefs along the coast of Quintana Roo and the Caribbean. 18. Determination of the δ15N of total nitrogen in solids; RSIL lab code 2893 Science.gov (United States) Revesz, Kinga; Qi, Haiping; Coplen, Tyler B. 2006-01-01 The purpose of the Reston Stable Isotope Laboratory (RSIL) lab code 2893 is to determine the δ(15N/14N), abbreviated as δ15N , of total nitrogen in solid samples. A Carlo Erba NC 2500 elemental analyzer (EA) is used to convert total nitrogen in a solid sample into N2 gas. The EA is connected to a continuous flow isotope-ratio mass spectrometer (CF-IRMS), which determines relative difference in the isotope-amount ratios of stable nitrogen isotopes (15N/14N)of the product N2 gas. The combustion is quantitative; no isotopic fractionation is involved. Samples are placed in a tin capsule and loaded into the Costech Zero Blank Autosampler of the EA. Under computer control, samples are dropped into a heated reaction tube that contains an oxidant, where the combustion takes place in a helium atmosphere containing an excess of oxygen gas. Combustion products are transported by a helium carrier through a reduction tube to remove excess oxygen and convert all nitrous oxides into N2 and through a drying tube to remove water. The gas-phase products, mainly CO2 and N2, are separated by a gas chromatograph. The gas is then introduced into the isotope-ratio mass spectrometer (IRMS) through a Finnigan MAT (now Thermo Scientific) ConFlo II interface, which also is used to inject N2 reference gas and helium for sample dilution. The IRMS is a Thermo Scientific Delta V Plus CF-IRMS. It has a universal triple collector, two wide cups with a narrow cup in the middle, capable of measuring mass/charge (m/z) 28, 29, 30, simultaneously. The ion beams from N2 are as follows: m/z 28 = N2 = 14N14N; m/z 29 = N2 = 14N15N primarily; m/z 30 = NO = 14N16O primarily, which is a sign of contamination or incomplete reduction. 19. Aqua ammonia 15 N obtaining and application with vainness for sugar-cane fertilization International Nuclear Information System (INIS) Nitrogen compounds marked with the isotope 15 N are continuously being used in agronomic studies and, when associated to the isotopic dilution technique, they constitute an important tool in clarifying the N cycle. At the Centro de Energia Nuclear na Agricultura (CENA/USP), it was obtained ( 15 NH4)2SO4 enhanced at 3,5% of 15 N atoms, by means of the ionic exchange chromatography technique, which made possible to produce aqua ammonia (15 NH3aq). Four repetitions were taken to the aqua ammonia production process to use the nitrogen compound in the field experiment. In each process 150g of ammonium sulfate enhanced at 3,5% of 15 N atoms was used, obtaining 31,0 ± 1,6 g of aqua ammonia on the average (80% yield), with the same enhancement. The incidence of isotopic dilution has not been observed during the procedure, what made the use of such methodology possible. After obtaining the aqua ammonia 15 N through this procedure, it was added to the vinasse (an equivalent to 50 m3 ha-1 ) in doses that corresponded to 70 kg ha-1 of N-NH3aq. The mixture was applied to the sugar-cane straw on the soil's surface, aimed to the crop's fertilization. The compound's isotopic composition was analyzed by means of a spectrometer of masses ANCA-SL Europe Scientific, while the total-N volatilized, by the micro-Kjeldahl. Method. In accordance to the low NH3 (6,4 ± 1,9 kg ha-1 ) volatilization results, it could be concluded that the application of vinasse and aqua ammonia mixture to the straw on the soil's surface was efficient, due to the vinasse's acid character, which allowed the NH3, in presence of the ion H+, to stay in the NH4+ form in solution. (author) 20. Food webs of two intermittently open estuaries receiving 15N-enriched sewage effluent Science.gov (United States) 2007-01-01 Carbon and nitrogen stable isotope signatures were used to assess the response of food webs to sewage effluent discharged into two small intermittently open estuaries in northern New South Wales, Australia. One of these systems, Tallows Creek, has a history of direct sewage inputs, whilst the other, Belongil Creek, receives wastewater via an extensive wetland treatment system. The food webs of both systems were driven by algal sources of carbon, reflecting high autotrophic productivity in response to the nutrients entering the system from sewage effluent. All aquatic biota collected from Tallows Creek had significantly enriched δ15N signatures relative to their conspecifics from Belongil Creek, indicating that sewage nitrogen had been assimilated and transferred throughout the Tallows Creek food web. These δ15N values were higher than those reported from studies in permanently open estuaries receiving sewage effluent. We suggest that these enriched signatures and the transfer of nitrogen throughout the entire food web reflect differences in hydrology and associated nitrogen cycling processes between permanently open and intermittently open estuaries. Although all organisms in Tallows Creek were generally 15N-enriched, isotopically light (less 15N-enriched) individuals of estuary perchlet ( Ambassis marianus) and sea mullet ( Mugil cephalus) were also collected. These individuals were most likely recent immigrants into Tallows Creek, as this system had only recently been opened to the ocean. This isotopic discrimination between resident (enriched) and immigrant (significantly less enriched) individuals can provide information on fish movement patterns and the role of heavily polluted intermittently open estuaries in supporting commercially and recreationally valuable estuarine species. 1. 13N,15N isotope and kinetic evidence against hyponitrite as an intermediate in dentrification. Science.gov (United States) Hollocher, T C; Garber, E; Cooper, A J; Reiman, R E 1980-06-10 13N- and 15N-labeling experiments were carried out with Paracoccus denitrificans, grown anaerobically on nitrate, to determine whether hyponitrite might be an obligatory intermediate in denitrification and a precursor of nitrous oxide. From experiments designed to trap [13N]- or [15N,15N]hyponitrite by dilution into authentic hyponitrite it was calculated that the intracellular concentration of a presumptive hyponitrite pool must be less than 0.4 mM. In order for a pool of this size to turn over rapidly enough to handle the flux of nitrogen during dentrifucation, the spontaneous rate of hyponitrite dehydration must be enhanced by a factor of several thousand through enzyme catalysis. Cell extracts failed to catalyze this reaction under a variety of conditions. It is concluded that hyponitrite cannot be an intermediate in dentrification. In addition, the assimilation of inorganic nitrogen was studied in P. denitrificans using 13N as tracer. At low concentrations (less than 10(-8) M) of labeled nitrate and nitrite 5 to 10% of the label was assimilated into non-volatile metabolites and 90 to 95% was reduced to N2. Similarly, with 15 mM [13N]nitrate, 5% of the label went into metabolites and 95% to N2. High pressure liquid chromatography analysis of the labeled metabolites indicated that the major pathway for assimilation of inorganic nitrogen in P. denitrificans under these conditions is through ammonia incorporation via the aspartase reaction. PMID:7372623 2. Plot-size for 15N-fertilizer recovery studies by tanzania-grass International Nuclear Information System (INIS) The understanding of the N dynamics in pasture ecosystems can be improved by studies using the 15N tracer technique. However, in these experiments it must be ensured that the lateral movement of the labeled fertilizer does not interfere with the results. In this study the plot-size requirements for 15N-fertilizer recovery experiments with irrigated Panicum maximum cv. Tanzania was determined. Three grazing intensities (light, moderate and intensive grazing) in the winter, spring and summer seasons were considered. A 1 m2 plot-size, with a grass tussock in the center, was adequate, irrespective of the grazing intensity or season of the year. Increasing the distance from the area fertilized with 15N negatively affected the N derived from fertilizer (Npfm) recovered in herbage.The lowest decline in Npfm values were observed for moderate and light grazing intensities. This fact might be explained by the vigorous growth characteristics of these plants. Increasing the grazing intensity decreased the tussock mass and, the smaller the tussock mass, the greater was the dependence on fertilizer nitrogen. (author) 3. Behavior of 15N-labelled amino acids in germinated corn International Nuclear Information System (INIS) By investigating the rise and fall of 15N-labelled amino acids in germinated corns, the behavior of amino radicals in free amino acids, the influence of the hydrolysis products of stored proteins on free amino acids and the change from heterotrophy to autotrophy of seeds were clarified. The amount of amino acid production depending on external nitrogen was very small in the early period of germination. 15N incorporation into proline was not observed in the early period of germination, which suggested that the proline may be nitrogen-storing source. Most of the amino-state nitrogen of asparagine accumulated at the time of germination was internal nitrogen, and this fact suggested that aspartic acid serve as the acceptor of ammonia produced in the early stage of germination. 15N content increased significantly on 9 th day after germination, and decreased on 12 th day. These facts prove that there are always active decomposition and production of protein in plant body. (Kobatake, H.) 4. Performance of Flow-Aware Networking in LTE backbone DEFF Research Database (Denmark) Sniady, Aleksander; Soler, José 2012-01-01 technologies, such as Long Term Evolution (LTE). This paper proposes usage of a modified Flow Aware Networking (FAN) technique for enhancing Quality of Service (QoS) in the all-IP transport networks underlying LTE backbone. The results obtained with OPNET Modeler show that FAN, in spite of being relatively... 5. Determination of backbone chain direction of PDA using FFM Science.gov (United States) Jo, Sadaharu; Okamoto, Kentaro; Takenaga, Mitsuru 2010-01-01 The effect of backbone chains on friction force was investigated on both Langmuir-Blodgett (LB) films of 10,12-heptacosadiynoic acid and the (0 1 0) surfaces of single crystals of 2,4-hexadiene-1,6-diol using friction force microscopy (FFM). It was observed that friction force decreased when the scanning direction was parallel to the [0 0 1] direction in both samples. Moreover, friction force decreased when the scanning direction was parallel to the crystallographic [1 0 2], [1 0 1], [1 0 0] and [1 0 1¯] directions in only the single crystals. For the LB films, the [0 0 1] direction corresponds to the backbone chain direction of 10,12-heptacosadiynoic acid. For the single crystals, both the [0 0 1] and [1 0 1] directions correspond to the backbone chain direction, and the [1 0 2], [1 0 0] and [1 0 1¯] directions correspond to the low-index crystallographic direction. In both the LB films and single crystals, the friction force was minimized when the directions of scanning and the backbone chain were parallel. 6. 1H, 13C and 15N NMR spectral and X-ray structural studies of 2-arylsulfonylamino-5-chlorobenzophenones International Nuclear Information System (INIS) Six 2-(4-R-phenylsulfonylamino)-5-chlorobenzophenones were prepared and their 1H, 13C and 15N NMR spectra recorded and assigned. The dependence between the chemical shift of the amide proton and Hammett σ substituent constants is of the V type. Substituent effect on the chemical shift of the amide nitrogen atom was found insignificant. X-ray analysis shows that the terminal benzene rings in 2-(4-nitro-phenylsulfonylamino)-5-chlorobenzophenones are located close to each other. They are not, however, parallel, dihedral angle between them being equal to 10.86 deg (MP2/6-31G//HF/6-31G ab initio calculations show this to be 20.44 deg). This shows that the mutual orientation of two benzene rings in the molecule of this compound is caused by the π-π stacking. It is additionally reinforced by the intramolecular NH...O=C hydrogen bond. Except the dihedral angle between the benzene rings, X-ray determined structure of 2-(4-nitro-phenylsulfonylamino)-5-chlorobenzophenones is very similar to this optimized by the ab initio calculations. (author) 7. A new organic reference material, L-glutamic acid, USGS41a, for δ13C and δ15N measurements − a replacement for USGS41 Science.gov (United States) Qi, Haiping; Coplen, Tyler B.; Mroczkowski, Stanley J.; Brand, Willi A.; Brandes, Lauren; Geilmann, Heike; Schimmelmann, Arndt 2016-01-01 RationaleThe widely used l-glutamic acid isotopic reference material USGS41, enriched in both 13C and 15N, is nearly exhausted. A new material, USGS41a, has been prepared as a replacement for USGS41.MethodsUSGS41a was prepared by dissolving analytical grade l-glutamic acid enriched in 13C and 15N together with l-glutamic acid of normal isotopic composition. The δ13C and δ15N values of USGS41a were directly or indirectly normalized with the international reference materials NBS 19 calcium carbonate (δ13CVPDB = +1.95 mUr, where milliurey = 0.001 = 1 ‰), LSVEC lithium carbonate (δ13CVPDB = −46.6 mUr), and IAEA-N-1 ammonium sulfate (δ15NAir = +0.43 mUr) and USGS32 potassium nitrate (δ15N = +180 mUr exactly) by on-line combustion, continuous-flow isotope-ratio mass spectrometry, and off-line dual-inlet isotope-ratio mass spectrometry.ResultsUSGS41a is isotopically homogeneous; the reproducibility of δ13C and δ15N is better than 0.07 mUr and 0.09 mUr, respectively, in 200-μg amounts. It has a δ13C value of +36.55 mUr relative to VPDB and a δ15N value of +47.55 mUr relative to N2 in air. USGS41 was found to be hydroscopic, probably due to the presence of pyroglutamic acid. Experimental results indicate that the chemical purity of USGS41a is substantially better than that of USGS41.ConclusionsThe new isotopic reference material USGS41a can be used with USGS40 (having a δ13CVPDB value of −26.39 mUr and a δ15NAir value of −4.52 mUr) for (i) analyzing local laboratory isotopic reference materials, and (ii) quantifying drift with time, mass-dependent isotopic fractionation, and isotope-ratio-scale contraction for isotopic analysis of biological and organic materials. Published in 2016. This article is a U.S. Government work and is in the public domain in the USA. 8. Leaf δ15N as an indicator of arbuscular mycorrhizal nitrogen uptake in a coastal-plain forest (restinga forest) at Southeastern Brazil Science.gov (United States) Mardegan, S. F.; Valadares, R.; Martinelli, L. 2013-12-01 Restinga diversity contrasts with a series of adverse environmental conditions that constrain their development, including nutrient limitation. In this sense, the mutualistic symbiosis between plants and arbuscular mycorrhizal fungi (AMF) may contribute in nutrient acquisition, including nitrogen. However, this association deeply affects plant nitrogen isotopic composition (δ15N), since assimilation processes and biochemical reactions within the fungi may reflect in a delivered product with an isotopic composition about 8 to 10 ‰ lower than that observed at the fungal symbiont per se. Here we assessed if the association with AMF affects δ15N values of plant species from a coastal-plain forest (restinga forest) at Southeastern Brazil. Accordingly, we analyzed the nutritional and isotopic compositions from ecosystem key-compartments (soil, litter and leaves), relating plant δ15N with the colonization rates. The study was carried out in a permanent plot (1 ha) at a coastal-plain forest (restinga forest) at the Serra do Mar State Park, SP, Brazil. Sampled vegetation is characterized by the lack of a well-defined stratification and a rather open canopy. It also comprises trees ranging from 10 to 15-m high. Soils are deep and sandy, being characterized by high acidity, nutrient deficiency and a dense litter cover. We randomly collected five samples (250 mg) from topsoil (0-10 cm) and five to ten leaves from individuals belonging to 16 plant species of high relevance within the site (IVI index). We also collected superficial (0-10 cm depth) fine roots (5 g) and 13 samples (100 g) of fine litter next to the individuals sampled. Soil samples were air-dried, sieved, homogenized and used in the physical-chemical characterization. The remainder was ground to a fine powder to determine nitrogen concentrations and δ15N values. Leaves were dried at 50 °C, finely milled and used for the determination of nitrogen concentrations, C/N ratios and δ15N values. Root samples were 9. The Influence of Seed-borne N in 15N Isotope Dilution Studies with Legumes The Influence of Seed-borne N in 15N Isotope Dilution Studies with Legumes DEFF Research Database (Denmark) Jensen, Erik Steen; Andersen, A. J.; Thomsen, J. D. 1985-01-01 The distriution of seed-borne N in shoot and root of pea and field bean was studied using three methods: 1) determination of the N content in shoot and root of plants grown in sand culture without other N sources. 2) 15N isotope dilution in plants grown in Rhizobium-free medium supplied with 15N-... 10. Unusually negative nitrogen isotopic compositions (δ15N) of mangroves and lichens in an oligotrophic, microbially-influenced ecosystem Science.gov (United States) Fogel, M. L.; Wooller, M. J.; Cheeseman, J.; Smallwood, B. J.; Roberts, Q.; Romero, I.; Meyers, M. J. 2008-12-01 Extremes in δ15N values in mangrove tissues and lichens (range =+4 to -22‰) were measured from a mangrove forest ecosystem located on Twin Cays, offshore islands in Belize, Central America. The N isotopic compositions and concentrations of NH4+/NH3 in porewater, rainwater, and atmospheric ammonia, and the δ15N of lichens, mangrove leaves, roots, stems, and wood were examined to study the biogeochemical processes important for establishing these unusual N isotopic ratios. Dwarfed Rhizophora mangle trees had the most negative δ15N, whereas fringing Rhizophora trees, the most positive δ15N values. Porewater ammonium concentrations had little relationship to N isotopic fractionation in mangrove tissues. In dwarfed mangroves, the δ15N of fine and coarse roots were 6-9‰ more positive than leaf tissue from the same tree, indicating different sources of N for root and leaf tissues. When P was added to dwarfed mangrove trees without added N, δ15N increased within one year from -12‰ to -2‰, approaching the δ15N of porewater ammonium (δ15N=+4‰). Isotopically depleted ammonia in the atmosphere (δ15N=-19‰) and in rainwater (δ15N=-10‰) were found on Twin Cays. We propose that foliar uptake of these atmospheric sources by P-stressed, dwarfed mangrove trees and lichens can explain their very negative δ15N values. In environments where P is limiting for growth, uptake of atmospheric N by Rhizophora mangle may be an important adaptive strategy. 11. Unusually negative nitrogen isotopic compositions (δ15N of mangroves and lichens in an oligotrophic, microbially-influenced ecosystem Directory of Open Access Journals (Sweden) I. Romero 2008-12-01 Full Text Available Extremes in δ15N values in mangrove tissues and lichens (range =+4 to −22‰ were measured from a mangrove forest ecosystem located on Twin Cays, offshore islands in Belize, Central America. The N isotopic compositions and concentrations of NH4+/NH3 in porewater, rainwater, and atmospheric ammonia, and the δ15N of lichens, mangrove leaves, roots, stems, and wood were examined to study the biogeochemical processes important for establishing these unusual N isotopic ratios. Dwarfed Rhizophora mangle trees had the most negative δ15N, whereas fringing Rhizophora trees, the most positive δ15N values. Porewater ammonium concentrations had little relationship to N isotopic fractionation in mangrove tissues. In dwarfed mangroves, the δ15N of fine and coarse roots were 6–9‰ more positive than leaf tissue from the same tree, indicating different sources of N for root and leaf tissues. When P was added to dwarfed mangrove trees without added N, δ15N increased within one year from −12‰ to −2‰, approaching the δ15N of porewater ammonium (δ15N=+4‰. Isotopically depleted ammonia in the atmosphere (δ15N=−19‰ and in rainwater (δ15N=−10‰ were found on Twin Cays. We propose that foliar uptake of these atmospheric sources by P-stressed, dwarfed mangrove trees and lichens can explain their very negative δ15N values. In environments where P is limiting for growth, uptake of atmospheric N by Rhizophora mangle may be an important adaptive strategy. 12. Intestinal renal metabolism of L-citrulline and L-arginine following enteral or parenteral infusion of L-alanyl-L-[2,15N]glutamine or L-[2,15N]glutamine in mice. Science.gov (United States) Boelens, Petra G; van Leeuwen, Paul A M; Dejong, Cornelis H C; Deutz, Nicolaas E P 2005-10-01 Previously, we observed increased plasma arginine (ARG) concentrations after glutamine (GLN)-enriched diets, in combination with clinical benefits. GLN delivers nitrogen for ARG synthesis, and the present study was designed to quantify the interorgan relationship of exogenous L-GLN or GLN dipeptide, by enteral or parenteral route, contributing to intestinal citrulline (CIT) and renal de novo ARG synthesis in mice. To study this, we used a multicatheterized mouse model with Swiss mice (n = 43) in the postabsorptive state. Stable isotopes were infused into the jugular vein or into the duodenum {per group either free L-[2,(15)N]GLN or dipeptide L-ALA-L-[2,(15)N]GLN, all with L-[ureido-(13)C-(2)H(2)]CIT and L-[guanidino-(15)N(2)-(2)H(2)]ARG} to establish renal and intestinal ARG and CIT metabolism. Blood flow was measured using (14)C-para-aminohippuric acid. Net intestinal CIT release, renal uptake of CIT, and net renal ARG efflux was found, as assessed by arteriovenous flux measurements. Quantitatively, more de novo L-[2,(15)N]CIT was produced when free L-[2,(15)N]GLN was given than when L-ALA-L-[2,(15)N]GLN was given, whereas renal de novo L-[2,(15)N]ARG was similar in all groups. In conclusion, the intestinal-renal axis is hereby proven in mice in that L-[2,(15)N]GLN or dipeptide were both converted into de novo renal L-[2,(15)N]ARG; however, not all was derived from intestinal L-[2,(15)N]CIT production. In this model, the feeding route and form of GLN did not influence de novo renal ARG production derived from GLN. 13. Refinement of the protein backbone angle {psi} in NMR structure calculations Energy Technology Data Exchange (ETDEWEB) Sprangers, R.; Bottomley, M.J.; Linge, J.P.; Schultz, J.; Nilges, M.; Sattler, M. [European Molecular Biology Laboratory (Germany) 2000-01-15 Cross-correlated relaxation rates involving the C{sup {alpha}}-H{sup {alpha}} dipolar interaction and the carbonyl (C') chemical shift anisotropy (CSA) have been measured using two complementary 3D experiments. We show that the protein backbone angle {psi} can be directly refined against such cross-correlated relaxation rates ({gamma}{sup H{alpha}}{sup C{alpha}}{sup ,C'}) and the three-bond H/D isotope effect on the C{sup {alpha}} chemical shifts ({sup 3}{delta}C{sup {alpha}}{sub (ND)}). By simultaneously using both experimental parameters as restraints during NMR structure calculations, a unique value for the backbone angle {psi} is defined. We have applied the new refinement method to the {alpha}-Spectrin SH3 domain (a {beta}-sheet protein) and to the Sgs1p HRDC domain (an {alpha}-helical protein) and show that the quality of the NMR structures is substantially improved, judging from the atomic coordinate precision and the Ramachandran map. In addition, the {psi}-refined NMR structures of the SH3 domain deviate less from the 1.8 A crystal structure, suggesting an improved accuracy. The proposed refinement method can be used to significantly improve the quality of NMR structures and will be applicable to larger proteins. 14. The structure of the carbohydrate backbone of the lipopolysaccharide of Pectinatus frisingensis strain VTT E-79104. Science.gov (United States) Vinogradov, Evgeny; Li, Jianjun; Sadovskaya, Irina; Jabbouri, Said; Helander, Ilkka M 2004-06-22 The structure of the carbohydrate backbone of the lipopolysaccharide from Pectinatus frisingensis strain VTT E-79104 was analyzed using chemical degradations, NMR spectroscopy, mass spectrometry, and chemical methods. The LPS contains two major structural variants, differing in the presence or absence of an octasaccharide fragment. The largest structure of the carbohydrate backbone of the LPS, that could be deduced from experimental results, consists of 20 monosaccharides arranged in a nonrepetitive sequence: [carbohydrate structure: see text] where R is H or 4-O-Me-alpha-L-Fuc-(1-2)-4-O-Me-beta-Hep-(1-3)-alpha-GlcNAc-(1-2)-beta-Man-(1-3)-beta-ManNAc-(1-4)-alpha-Gal-(1-4)-beta-Hep-(1-3)-beta-GalNAc-(1- where Hep is a residue of D-glycero-D-galacto-heptose; all monosaccharides have the D-configuration except for 4-O-Me-L-Fuc and L-Ara4N. This structure is architecturally similar to the oligosaccharide system reported previously in P. frisingensis VTT E-82164 LPS, but differs from the latter in composition and also in the size of the outer region. 15. Unusually negative nitrogen isotopic compositions (δ15N of mangroves and lichens in an oligotrophic, microbially-influenced ecosystem Directory of Open Access Journals (Sweden) I. Romero 2008-02-01 Full Text Available Extremes in (δ15N values in mangrove tissues and lichens (range = +4 to −22‰ were measured from a mangrove forest ecosystem located on Twin Cays, offshore islands in Belize, Central America. The N isotopic compositions and concentrations of NH4+/NH3 in porewater, rainwater, atmospheric ammonia, mangrove leaves, roots, stems, and wood, and lichens, were examined to study the biogeochemical processes important for establishing these unusual N isotopic ratios. Porewater ammonium concentrations had little to no relationship to N isotopic fractionation in mangrove tissues. The δ15N of fine and coarse roots was 9‰ more positive than leaf tissue from the same tree. When P was added to dwarfed mangrove trees without added N, δ15N increased within one year to a &delta:15N closer to the &delta:15N of porewater ammonium (δ15N=+4‰. Isotopically negative ammonia in the atmosphere (δ15N=−18‰ and in rainwater (δ15N=−9‰ were found on Twin Cays and may be sources of available N for isotopically depleted mangrove trees and lichens. In highly stressed, severely P limited trees, uptake of atmospheric N by Rhizophora mangle may be an important adaptive strategy. 16. Inorganic backbone ionomers: Design and dielectric response of single-ion conducting polymers Science.gov (United States) Bartels, Joshua Ion-conducting polymers were studied primarily through the use of dielectric spectroscopy. The conclusions drawn from ion conduction models of the dielectric data are corroborated by additional independent experiments, including x-ray scattering, calorimetry, prism coupling, and DFT calculations. The broad concern of this dissertation is to understand and clarify a path forward in ion conducting polymer research. This is achieved by considering low-Tg ionomers and the advantages imparted by siloxane and phosphazene backbones. The most successful dielectric spectroscopy model for the materials studied is the electrode polarization model (EP), whereas other models, such as the Dyre random barrier model, fail to describe the experimental results. Seven nonionic ether oxygen (EO) containing polymers were studied in order to observe the effect that backbone chemistry has on dipole motion. Conventional carboncarbon backbone EO-containing polymers show no distinct advantage over similar EO-pendant polysiloxane or polyphosphazene systems. The mobility and effective backbone Tg imparted by the inorganic backbones are comparable. A short EO pendant results in a lower static dielectric constant due to restricted motion of dipoles close to the chain. The flexibility and chemical versatility of inorganic backbone polymers motivates further study of two ionomer systems. A polypohosphazene iodide conducting system was characterized by dielectric spectroscopy and x-ray scattering. Two end "tail" functionalization of the ammonium ion were used, a tail with two EOs and an alkyl tail of six carbons. This functional group plays an important role in ion dynamics and can wrap around the ion and self-solvate when EOs are present. The iodide-ammonium ionomers are observed to have unusually large high-frequency dielectric constants due to atomic polarization of ions. The strength of the atomic polarization scales with ion content. The aggregation state of ions is able to be determined from 17. Macroalgae δ15N values in well-mixed estuaries: Indicator of anthropogenic nitrogen input or macroalgae metabolism? Science.gov (United States) Raimonet, Mélanie; Guillou, Gaël; Mornet, Françoise; Richard, Pierre 2013-03-01 Although nitrogen stable isotope ratio (δ15N) in macroalgae is widely used as a bioindicator of anthropogenic nitrogen inputs to the coastal zone, recent studies suggest the possible role of macroalgae metabolism in δ15N variability. Simultaneous determinations of δ15N of dissolved inorganic nitrogen (DIN) along the land-sea continuum, inter-species variability of δ15N and its sensitivity to environmental factors are necessary to confirm the efficiency of macroalgae δ15N in monitoring nitrogen origin in mixed-use watersheds. In this study, δ15N of annual and perennial macroalgae (Ulva sp., Enteromorpha sp., Fucus vesiculosus and Fucus serratus) are compared to δ15N-DIN along the Charente Estuary, after characterizing δ15N of the three main DIN sources (i.e. cultivated area, pasture, sewage treatment plant outlet). During late winter and spring, when human activities produce high DIN inputs, DIN sources exhibit distinct δ15N signals in nitrate (NO) and ammonium (NH): cultivated area (+6.5 ± 0.6‰ and +9.0 ± 11.0‰), pasture (+9.2 ± 1.8‰ and +12.4‰) and sewage treatment plant discharge (+16.9 ± 8.7‰ and +25.4 ± 5.9‰). While sources show distinct δN- in this multiple source catchment, the overall mixture of NO sources - generally >95% DIN - leads to low variations of δN-NO at the mouth of the estuary (+7.7 to +8.4‰). Even if estuarine δN-NO values are not significantly different from pristine continental and oceanic site (+7.3‰ and +7.4‰), macroalgae δ15N values are generally higher at the mouth of the estuary. This highlights high anthropogenic DIN inputs in the estuary, and enhanced contribution of 15N-depleted NH in oceanic waters. Although seasonal variations in δN-NO are low, the same temporal trends in macroalgae δ15N values at estuarine and oceanic sites, and inter-species differences in δ15N values, suggest that macroalgae δ15N values might be modified by the metabolic response of macroalgae to environmental parameters (e 18. Sinks for nitrogen inputs in terrestrial ecosystems: a meta-analysis of 15N tracer field studies Science.gov (United States) Templer, P.H.; Mack, M.C.; Chapin, F. S.; Christenson, L.M.; Compton, J.E.; Crook, H.D.; Currie, W.S.; Curtis, C.J.; Dail, D.B.; D'Antonio, C. M.; Emmett, B.A.; Epstein, H.E.; Goodale, C.L.; Gundersen, P.; Hobbie, S.E.; Holland, K.; Hooper, D.U.; Hungate, B.A.; Lamontagne, S.; Nadelhoffer, K.J.; Osenberg, C.W.; Perakis, S.S.; Schleppi, P.; Schimel, J.; Schmidt, I.K.; Sommerkorn, M.; Spoelstra, J.; Tietema, A.; Wessel, W.W.; Zak, D.R. 2012-01-01 Effects of anthropogenic nitrogen (N) deposition and the ability of terrestrial ecosystems to store carbon (C) depend in part on the amount of N retained in the system and its partitioning among plant and soil pools. We conducted a meta-analysis of studies at 48 sites across four continents that used enriched 15N isotope tracers in order to synthesize information about total ecosystem N retention (i.e., total ecosystem 15N recovery in plant and soil pools) across natural systems and N partitioning among ecosystem pools. The greatest recoveries of ecosystem 15N tracer occurred in shrublands (mean, 89.5%) and wetlands (84.8%) followed by forests (74.9%) and grasslands (51.8%). In the short term (15N tracer application), total ecosystem 15N recovery was negatively correlated with fine-root and soil 15N natural abundance, and organic soil C and N concentration but was positively correlated with mean annual temperature and mineral soil C:N. In the longer term (3–18 months after 15N tracer application), total ecosystem 15N retention was negatively correlated with foliar natural-abundance 15N but was positively correlated with mineral soil C and N concentration and C: N, showing that plant and soil natural-abundance 15N and soil C:N are good indicators of total ecosystem N retention. Foliar N concentration was not significantly related to ecosystem 15N tracer recovery, suggesting that plant N status is not a good predictor of total ecosystem N retention. Because the largest ecosystem sinks for 15N tracer were below ground in forests, shrublands, and grasslands, we conclude that growth enhancement and potential for increased C storage in aboveground biomass from atmospheric N deposition is likely to be modest in these ecosystems. Total ecosystem 15N recovery decreased with N fertilization, with an apparent threshold fertilization rate of 46 kg N·ha-1·yr-1 above which most ecosystems showed net losses of applied 15N tracer in response to N fertilizer addition. 19. A 15N-poor isotopic composition for the solar system as shown by Genesis solar wind samples. Science.gov (United States) Marty, B; Chaussidon, M; Wiens, R C; Jurewicz, A J G; Burnett, D S 2011-06-24 The Genesis mission sampled solar wind ions to document the elemental and isotopic compositions of the Sun and, by inference, of the protosolar nebula. Nitrogen was a key target element because the extent and origin of its isotopic variations in solar system materials remain unknown. Isotopic analysis of a Genesis Solar Wind Concentrator target material shows that implanted solar wind nitrogen has a (15)N/(14)N ratio of 2.18 ± 0.02 × 10(-3) (that is, ≈40% poorer in (15)N relative to terrestrial atmosphere). The (15)N/(14)N ratio of the protosolar nebula was 2.27 ± 0.03 × 10(-3), which is the lowest (15)N/(14)N ratio known for solar system objects. This result demonstrates the extreme nitrogen isotopic heterogeneity of the nascent solar system and accounts for the (15)N-depleted components observed in solar system reservoirs. 20. A 15N-poor isotopic composition for the solar system as shown by Genesis solar wind samples. Science.gov (United States) Marty, B; Chaussidon, M; Wiens, R C; Jurewicz, A J G; Burnett, D S 2011-06-24 The Genesis mission sampled solar wind ions to document the elemental and isotopic compositions of the Sun and, by inference, of the protosolar nebula. Nitrogen was a key target element because the extent and origin of its isotopic variations in solar system materials remain unknown. Isotopic analysis of a Genesis Solar Wind Concentrator target material shows that implanted solar wind nitrogen has a (15)N/(14)N ratio of 2.18 ± 0.02 × 10(-3) (that is, ≈40% poorer in (15)N relative to terrestrial atmosphere). The (15)N/(14)N ratio of the protosolar nebula was 2.27 ± 0.03 × 10(-3), which is the lowest (15)N/(14)N ratio known for solar system objects. This result demonstrates the extreme nitrogen isotopic heterogeneity of the nascent solar system and accounts for the (15)N-depleted components observed in solar system reservoirs. PMID:21700869 1. Rapid mass spectrometric analysis of 15N-Leu incorporation fidelity during preparation of specifically labeled NMR samples DEFF Research Database (Denmark) Truhlar, Stephanie M E; Cervantes, Carla F; Torpey, Justin W; 2008-01-01 analyzing the isotopic abundance of the peptides in the mass spectra using the program DEX. This analysis determined that expression with a 10-fold excess of unlabeled amino acids relative to the (15)N-amino acid prevents the scrambling of the (15)N label that is observed when equimolar amounts are used......Advances in NMR spectroscopy have enabled the study of larger proteins that typically have significant overlap in their spectra. Specific (15)N-amino acid incorporation is a powerful tool for reducing spectral overlap and attaining reliable sequential assignments. However, scrambling of the label...... during protein expression is a common problem. We describe a rapid method to evaluate the fidelity of specific (15)N-amino acid incorporation. The selectively labeled protein is proteolyzed, and the resulting peptides are analyzed using MALDI mass spectrometry. The (15)N incorporation is determined by... 2. Visualizing the principal component of {sup 1}H,{sup 15}N-HSQC NMR spectral changes that reflect protein structural or functional properties: application to troponin C Energy Technology Data Exchange (ETDEWEB) Robertson, Ian M.; Boyko, Robert F.; Sykes, Brian D., E-mail: brian.sykes@ualberta.ca [University of Alberta, Department of Biochemistry (Canada) 2011-09-15 Laboratories often repeatedly determine the structure of a given protein under a variety of conditions, mutations, modifications, or in a number of states. This approach can be cumbersome and tedious. Given then a database of structures, identifiers, and corresponding {sup 1}H,{sup 15}N-HSQC NMR spectra for homologous proteins, we investigated whether structural information could be ascertained for a new homolog solely from its {sup 1}H,{sup 15}N-HSQC NMR spectrum. We addressed this question with two different approaches. First, we used a semi-automated approach with the program, ORBplus. ORBplus looks for patterns in the chemical shifts and correlates these commonalities to the explicit property of interest. ORBplus ranks resonances based on consistency of the magnitude and direction of the chemical shifts within the database, and the chemical shift correlation of the unknown protein with the database. ORBplus visualizes the results by a histogram and a vector diagram, and provides residue specific predictions on structural similarities with the database. The second method we used was partial least squares (PLS), which is a multivariate statistical technique used to correlate response and predictor variables. We investigated the ability of these methods to predict the tertiary structure of the contractile regulatory protein troponin C. Troponin C undergoes a closed-to-open conformational change, which is coupled to its function in muscle. We found that both ORBplus and PLS were able to identify patterns in the {sup 1}H,{sup 15}N-HSQC NMR data from different states of troponin C that correlated to its conformation. 3. Localization of 15N uptake in a Tibetan alpine Kobresia pasture Science.gov (United States) Schleuß, Per-Marten; Kuzyakov, Yakov 2014-05-01 The Kobresia Pygmea ecotone covers approximately 450.000 km2 and is of large global and regional importance due several socio-ecological aspects. For instance Kobresia pastures store high amounts of carbon, nitrogen and other nutrients, represent large grazing areas for herbivores, provide a fast regrowth after grazing events and protect against mechanical degradation and soil erosion. However, Kobresia pastures are assumed to be a grazing induced and are accompanied with distinct root mats varying in thickness between 5-30 cm. Yet, less is known about the morphology and the functions of this root mats, especially in the background of a progressing degradation due to changes of climate and management. Thus we aimed to identify the importance of single soil layers for plant nutrition. Accordingly, nitrogen uptake from different soil depths and its remain in above-ground biomass (AGB), belowground biomass (BGB) and soil were determined by using a 15N pulse labeling approach during the vegetation period in summer 2012. 15N urea was injected into six different soil depths (0.5 cm, 2.5 cm, 7.5 cm, 12.5 cm, 17.5 cm, 22.5 cm / for each 4 replicates) and plots were sampled 45 days after the labeling. For soil and BGB samples were taken in strict sample intervals of 0-1 cm, 1-5 cm, 5-10 cm, 10-15 cm, 15-20 cm, 20-25 cm. Results indicate that total recovery (including AGB, BGB and soil) was highest, if tracer was injected into the top 5 cm and subsequently decreased with decreasing injection depth. This is especially the case for the 15N recovery of BGB, which is clearly attributed to the root density and strongly decreased with soil depth. In contrast, the root activity derived from the 15N content of roots increased with soil depth, which is primary associated to a proportionate increase of living roots related to dead roots. However, most 15N was captured in plant biomass (67.5-85.3 % of total recovery), indicating high 15N uptake efficiency possibly due to N limitation 4. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 8 International Nuclear Information System (INIS) Over 4 days 12 colostomized laying hens received, together with the ration, 36 g wheat with 14.37 atom-% 15N excess (15N'). The basic amino acids were nearly equally labelled. Three animals each were butchered after 12 h, 36 h, 60 h, and 108 h, resp., after the last 15N' application. Emission spectrometric determination of 15N' in liver and in amino acids was carried out. In addition, atom-% 15N' was determined in free amino acids and peptides. The labelling in the liver 12 h after the last 15N' application amounted to 1.75 atom-% 15N' and decreased after 108 h to 0.81 atom-% 15N'. The average TCA precipitable 15N' quota in the total 15N' amounted to 81.4% and was nearly identical at all four measuring points. The arginine 15N' amount in the liver was twice as high as that of lysine 15N'. In dependence on the period after the last 15N' application the decrease in the labelling of free arginine is considerable in comparison to free lysine. At the first measuring point (12 h) it was 1.69 atom-% 15N' and at the last one (108 h) 0.57 atom-% 15N'. Based on the results of 15N' labelling of peptides in the liver further, more detailed experiments for studies of peptide metabolism in the liver should be carried out. (author) 5. Nitrogen (15N) accumulation in corn grains as affected by source of nitrogen in red latosol International Nuclear Information System (INIS) Nitrogen is the most absorbed mineral nutrient by corn crop and most affects grains yield. It is the unique nutrient absorbed by plants as cation (NH4+) or anion (NO3-). The objectives of this work were to investigate the N accumulation by corn grains applied to the soil as NH4+ or NO3- in the ammonium nitrate form compared to amidic form of the urea, labeled with 15N; to determine the corn growth stage with highest fertilizer N utilization by the grains, and to quantify soil nitrogen exported by corn grains. The study was carried out in the Experimental Station of the Regional Pole of the Sao Paulo Northwestern Agribusiness Development (APTA), in Votuporanga, State of Sao Paulo, Brazil, in a Red Latosol. The experimental design was completely randomized blocks, with 13 treatments and four replications, disposed in factorial outline 6x2 + 1 (control, without N application). A nitrogen rate equivalent to 120 kg N ha-1 as urea-15N or as ammonium nitrate, labeled in the cation NH4+ (15NH4+NO3-) or in the anion NO3- (NH4+15N+O3- ), was applied in six fractions of 20 kg N ha-1 each, in different microplots, from seeding to the growth stage 7 (pasty grains). The forms of nitrogen, NH4+-N and NO3--N, were accumulated equitably by corn grains. The corn grains accumulated more N from urea than from ammonium nitrate. The N applied to corn crop at eight expanded leaves stage promoted largest accumulation of this nutrient in the grains. (author) 6. Effect of estrogens on urinary /sup 15/N balance in girls Energy Technology Data Exchange (ETDEWEB) Zachmann, M.; Kempken, B.; Prader, A. (Zurich Univ. (Switzerland)) 1984-08-01 While the anabolic and growth-promoting effects of testosterone are known to be important for pubertal growth in boys, the role of estrogens (E) in the female spurt is less certain. Adrenal androgens have been considered to be more important than ovarian E. To study the anabolic effects of E, there has been carried out a pilot study in 9 girls aged 11 to 15 years. Before and 6 days after the start of E treatment, urinary /sup 15/N balance studies were performed, using /sup 15/NH/sub 4/Cl. 7. Search for antiproton-{sup 15}N bound state in PANDA Energy Technology Data Exchange (ETDEWEB) Lin, Dexu [Helmholtz Institut Mainz, 55128 Mainz (Germany); Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, 55099 Mainz (Germany); Larionov, Alexei; Mishustin, Igor [Frankfurt Institute for Advanced Studies (FIAS), D-60438 Frankfurt am Main (Germany); National Research Center ' ' Kurchatov Institute' ' , 123182 Moscow (Russian Federation); Ma, Yue [RIKEN, Saitama 351-0198 (Japan); Maas, Frank [Helmholtz Institut Mainz, 55128 Mainz (Germany); Johannes Gutenberg Universitaet Mainz, Institut fuer Kernphysik, 55099 Mainz (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung, GmbH, 64291 Darmstadt (Germany) 2013-07-01 In order to study the antiproton-nucleus potential (antimatter-mater potential), and prepare a possible experiment for the PANDA spectrometer at FAIR facility, we carried out a calculation with the Giessen-Boltzman-Uehling-Uhlenbeck(GiBUU) model. The calculation was performed for an antiproton beam energy 1.5 GeV and an {sup 16}O target. The interesting events, which provide information about the antiproton-{sup 15}N potential, are required to have one knocked-out proton in forward direction and two or more pions from the antiproton annihilation at rest. Preliminary results of these studies are presented. 8. Mineralization of 15N-labelled sheep manure in soils of different texture and water contents OpenAIRE I. K. Thomsen; Schjønning, P.; B. T. Christensen 2003-01-01 In order to investigate the effect of soil moisture and texture on C and N mineralization of applied organic matter, sheep faeces was sandwiched between two halves of intact soil cores and incubated at 20°C. The soils contained 10.8 (L1), 22.4 (L3) and 33.7% (L5) clay, respectively, and were drained to seven different matric potentials in the range –15 to –1500 hPa. Evolution of CO2-C was determined during four weeks of incubation. Contents of NO3-N, 15N and microbial biomass N were determine... 9. Determination of the δ15N of nitrate in water; RSIL lab code 2899 Science.gov (United States) Coplen, Tyler B.; Qi, Haiping; Revesz, Kinga; Casciotti, Karen; Hannon, Janet E. 2007-01-01 The purpose of the Reston Stable Isotope Laboratory (RSIL) lab code 2899 is to determine the δ15N of nitrate (NO3-) in water. The δ15N of the dissolved NO3- is analyzed by conversion of the NO3- to nitrous oxide (N2O), which serves as the analyte for mass spectrometry. A culture of denitrifying bacteria is used in the enzymatic conversion of the NO3- to N2O, which follows the pathway shown in equation 1: NO3- → NO2- → NO → 1/2 N2O (1) Because the bacteria Pseudomonas aureofaciens lack N2O reductive activity, the reaction stops at N2O, unlike the typical denitrification reaction that goes to N2. After several hours, the conversion is complete, and the N2O is extracted from the vial, separated from volatile organic vapor and water vapor by an automated -65 °C isopropanol-slush trap, a Nafion drier, a CO2 and water removal unit (Costech #021020 carbon dioxide absorbent with Mg(ClO4)2), and trapped in a small-volume trap immersed in liquid nitrogen with a modified Finnigan MAT (now Thermo Scientific) GasBench 2 introduction system. After the N2O is released, it is further purified by gas chromatography before introduction to the isotope-ratio mass spectrometer (IRMS). The IRMS is a Thermo Scientific Delta V Plus continuous flow IRMS (CF-IRMS). It has a universal triple collector, consisting of two wide cups with a narrow cup in the middle; it is capable of simultaneously measuring mass/charge (m/z) of the N2O molecule 44, 45, and 46. The ion beams from these m/z values are as follows: m/z = 44 = N2O = 14N14N16O; m/z = 45 = N2O = 14N15N16O or 14N14N17O; m/z = 46 = N2O = 14N14N18O. The 17O contributions to the m/z 44 and m/z 45 ion beams are accounted for before δ15N values are reported. 10. Determination of the δ15N of nitrate in solids; RSIL lab code 2894 Science.gov (United States) Coplen, Tyler B.; Qi, Haiping; Revesz, Kinga; Casciotti, Karen; Hannon, Janet E. 2007-01-01 The purpose of the Reston Stable Isotope Laboratory (RSIL) lab code 2894 is to determine the δ15N of nitrate (NO3-) in solids. The nitrate fraction of the nitrogen species is dissolved by water (called leaching) and can be analyzed by the bacterial method covered in RSIL lab code 2899. After leaching, the δ15N of the dissolved NO3- is analyzed by conversion of the NO3- to nitrous oxide (N2O), which serves as the analyte for mass spectrometry. A culture of denitrifying bacteria is used in the enzymatic conversion of NO3- to N2O, which follows the pathway shown in equation 1: NO3- → NO2- → NO → 1/2 N2O (1) Because the bacteria Pseudomonas aureofaciens lack N2O reductive activity, the reaction stops at N2O, unlike the typical denitrification reaction that goes to N2. After several hours, the conversion is complete, and the N2O is extracted from the vial, separated from volatile organic vapor and water vapor by an automated -65 °C isopropanol-slush trap, a Nafion drier, a CO2 and water removal unit (Costech #021020 carbon dioxide absorbent with Mg(ClO4)2), and trapped in a small-volume trap immersed in liquid nitrogen with a modified Finnigan MAT (now Thermo Scientific) GasBench 2 introduction system. After the N2O is released, it is further purified by gas chromatography before introduction to the isotope-ratio mass spectrometer (IRMS). The IRMS is a Thermo Scientific Delta V Plus continuous flow IRMS (CF-IRMS). It has a universal triple collector, consisting of two wide cups with a narrow cup in the middle; it is capable of simultaneously measuring mass/charge (m/z) of the N2O molecule 44, 45, and 46. The ion beams from these m/z values are as follows: m/z = 44 = N2O = 14N14N16O; m/z = 45 = N2O = 14N15N16O or 14N14N17O; m/z = 46 = N2O = 14N14N18O. The 17O contributions to the m/z 44 and m/z 45 ion beams are accounted for before δ15N values are reported. 11. Renal ischemia and reperfusion assessment with three-dimensional hyperpolarized (13) C,(15) N2-urea DEFF Research Database (Denmark) Nielsen, Per Mose; Szocska Hansen, Esben Søvsø; Nørlinger, Thomas Stokholm; 2016-01-01 . METHODS: Hyperpolarized three-dimensional balanced steady-state (13) C magnetic resonance imaging (MRI) experiments alongside kidney function parameters and quantitative polymerase chain reaction measurements were performed in rats subjected to unilateral renal ischemia for 60-minute and 24-hour......,(15) N2 urea MRI can be used to successfully detect changes in the intrarenal urea gradient post-IRI, thereby enabling in vivo monitoring of the intrarenal functional status in the rat kidney. Magn Reson Med, 2016. © 2016 International Society for Magnetic Resonance in Medicine.... 12. Uptake of stormwater nitrogen in bioretention systems demonstrated from 15N tracer techniques Science.gov (United States) Houdeshel, D.; Hultine, K. R.; Pomeroy, C. A. 2012-12-01 Bioretention stormwater management systems are engineered ecosystems that capture urban stormwater in order to reduce the harmful effects of stormwater pollution on receiving waters. Bioretention systems have been shown to be effective at reducing the volume of runoff, and thereby reduce the nutrient loading to receiving waters from urban areas. However, little work has been done to evaluate the treatment processes that are responsible for reductions in effluent nitrogen (N). We hypothesize that the pulses of inorganic nitrogen associated with urban runoff events are captured in the plat tissues within these systems and not adsorbed to the soil media, thus creating a long-term, sustainable treatment approach to reducing the total nutrient loading to receiving waters. Nitrogen treatment performance was tested on two bioretention systems in Salt Lake City, UT: 1) an upland native community that does not require irrigation in semi-arid climates, and 2) a wetland community that requires 250 l of daily irrigation to offset the relatively high evaporative demand in the region. Each cell is sized to treat a 2.5 cm storm from a 140 m2 impervious surface: the area of the bioretention system is 10 m2. To test the N removal performance of each system, runoff events were simulated to represent an average precipitation regime using a synthetic stormwater blend starting in January, 2012. Effluent was collected from an underdrain and analyzed for total nitrogen (TN); mass removal was calculated for each month by subtracting the TN mass added to the garden minus the TN mass that flowed out of the garden. To test the hypothesis that plants assimilate stormwater N, 4 g of 100 atom% 15N NH4NO3 tracer was used as the N source in the synthetic stormwater during the first 2,000 l synthetic storm event in May. This isotopic label was calculated to enrich the total N pool of each garden to 100‰ 15N/14Nair. New growth was harvested from each plant in both cells and analyzed for 15N 13. Optical Microscopy Characterization for Borehole U-15n#12 in Support of NCNS Source Physics Experiment Energy Technology Data Exchange (ETDEWEB) Wilson, Jennifer E. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Sussman, Aviva Joy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States) 2015-05-22 Optical microscopy characterization of thin sections from corehole U-15n#12 is part of a larger material characterization effort for the Source Physics Experiment (SPE). The SPE program was conducted in Nevada with a series of explosive tests designed to study the generation and propagation of seismic waves inside Stock quartz monzonite. Optical microscopy analysis includes the following: 1) imaging of full thin sections (scans and mosaic maps); 2) high magnification imaging of petrographic texture (grain size, foliations, fractures, etc.); and 3) measurement of microfracture density. 14. Feasibility analysis of organic Tea authentication using 15N natural abundance method International Nuclear Information System (INIS) Organic agricultural products were always adulterated by pollutant-free agricultural products in market because of lacking of available authentication technique. Organic tea was one of the largest organic agricultural products in China which are facing the same problem and can not be accepted by consumers. In this paper, based on the newest information of δ 15N from soil-plant-fertilizer system, a new method was suggested to identify whether N fertilizer was applied to organic tea in producing processing. Meanwhile, the principle of this new method and its feasibility were discussed. (authors) 15. The $^{15}$N($\\bm\\alpha$,$\\bm\\gamma$)$^{19}$F reaction and nucleosynthesis of $^{19}$F OpenAIRE Wilmes, S.; Wilmes, V.; Staudt, G.; Mohr, P; Hammer, J. W. 2002-01-01 Several resonances in the $^{15}$N($\\alpha$,$\\gamma$)$^{19}$F reaction have been investigated in the energy range between 0.6 MeV and 2.7 MeV. Resonance strengths and branching ratios have been determined. High sensitivity could be obtained by the combination of the {\\sc{dynamitron}} high current accelerator, the windowless gas target system {\\sc{rhinoceros}}, and actively shielded germanium detectors. Two levels of $^{19}$F could be observed for the first time in the ($\\alpha$,$\\gamma$) chan... 16. Polystyrene Backbone Polymers Consisting of Alkyl-Substituted Triazine Side Groups for Phosphorescent OLEDs Directory of Open Access Journals (Sweden) Beatrice Ch. D. Salert 2012-01-01 Full Text Available This paper describes the synthesis of new electron-transporting styrene monomers and their corresponding polystyrenes all with a 2,4,6-triphenyl-1,3,5-triazine basic structure in the side group. The monomers differ in the alkyl substitution and in the meta-/paralinkage of the triazine to the polymer backbone. The thermal and spectroscopic properties of the new electron-transporting polymers are discussed in regard to their chemical structures. Phosphorescent OLEDs were prepared using the obtained electron-transporting polymers as the emissive layer material in blend systems together with a green iridium-based emitter 13 and a small molecule as an additional cohost with wideband gap characteristics (CoH-001. The performance of the OLEDs was characterized and discussed in regard to the chemical structure of the new electron-transporting polymers. 17. Toward Atomistic Resolution Structure of Phosphatidylcholine Headgroup and Glycerol Backbone at Different Ambient Conditions. Science.gov (United States) Botan, Alexandru; Favela-Rosales, Fernando; Fuchs, Patrick F J; Javanainen, Matti; Kanduč, Matej; Kulig, Waldemar; Lamberg, Antti; Loison, Claire; Lyubartsev, Alexander; Miettinen, Markus S; Monticelli, Luca; Määttä, Jukka; Ollila, O H Samuli; Retegan, Marius; Róg, Tomasz; Santuz, Hubert; Tynkkynen, Joona 2015-12-10 Phospholipids are essential building blocks of biological membranes. Despite a vast amount of very accurate experimental data, the atomistic resolution structures sampled by the glycerol backbone and choline headgroup in phoshatidylcholine bilayers are not known. Atomistic resolution molecular dynamics simulations have the potential to resolve the structures, and to give an arrestingly intuitive interpretation of the experimental data, but only if the simulations reproduce the data within experimental accuracy. In the present work, we simulated phosphatidylcholine (PC) lipid bilayers with 13 different atomistic models, and compared simulations with NMR experiments in terms of the highly structurally sensitive C-H bond vector order parameters. Focusing on the glycerol backbone and choline headgroups, we showed that the order parameter comparison can be used to judge the atomistic resolution structural accuracy of the models. Accurate models, in turn, allow molecular dynamics simulations to be used as an interpretation tool that translates these NMR data into a dynamic three-dimensional representation of biomolecules in biologically relevant conditions. In addition to lipid bilayers in fully hydrated conditions, we reviewed previous experimental data for dehydrated bilayers and cholesterol-containing bilayers, and interpreted them with simulations. Although none of the existing models reached experimental accuracy, by critically comparing them we were able to distill relevant chemical information: (1) increase of choline order parameters indicates the P-N vector tilting more parallel to the membrane, and (2) cholesterol induces only minor changes to the PC (glycerol backbone) structure. This work has been done as a fully open collaboration, using nmrlipids.blogspot.fi as a communication platform; all the scientific contributions were made publicly on this blog. During the open research process, the repository holding our simulation trajectories and files ( https 18. CHEMICALS CERN Multimedia Medical Service 2002-01-01 It is reminded that all persons who use chemicals must inform CERN's Chemistry Service (TIS-GS-GC) and the CERN Medical Service (TIS-ME). Information concerning their toxicity or other hazards as well as the necessary individual and collective protection measures will be provided by these two services. Users must be in possession of a material safety data sheet (MSDS) for each chemical used. These can be obtained by one of several means : the manufacturer of the chemical (legally obliged to supply an MSDS for each chemical delivered) ; CERN's Chemistry Service of the General Safety Group of TIS ; for chemicals and gases available in the CERN Stores the MSDS has been made available via EDH either in pdf format or else via a link to the supplier's web site. Training courses in chemical safety are available for registration via HR-TD. CERN Medical Service : TIS-ME :73186 or service.medical@cern.ch Chemistry Service : TIS-GS-GC : 78546 19. Using MUSIC and CC(CO)NH for backbone assignment of two medium-sized proteins not fully accessible to standard 3D NMR. Science.gov (United States) Brenner, Annette K; Frøystein, Nils Åge 2014-01-01 The backbone assignment of medium-sized proteins is rarely as straightforward as that of small proteins, and thus often requires creative solutions. Here, we describe the application of a combination of standard 3D heteronuclear methods with CC(CO)NH and a variety of MUltiplicity Selective In-phase Coherence transfer (MUSIC) experiments. Both CC(CO)NH and MUSIC are, in theory, very powerful methods for the backbone assignment of proteins. Due to low sensitivity, their use has usually been linked to small proteins only. However, we found that combining CC(CO)NH and MUSIC experiments simplified the assignment of two challenging medium-sized proteins of 13 and 19.5 kDa, respectively. These methods are to some extent complementary to each other: CC(CO)NH acquired with a long isotropic mixing time can identify amino acids with large aliphatic side chains. Whereas the most sensitive MUSIC experiments identify amino acid types that cannot be detected by CC(CO)NH, comprising the residues with acid and amide groups, and aromatic rings in their side chains. Together these methods provide a means of identifying the majority of peaks in the 2D 15N HSQC spectrum which simplifies the backbone assignment work even for proteins, e.g., small kinases, whose standard spectra resulted in little spectral resolution and low signal intensities. 20. Primerjava JavaScript ogrodij Angular, Backbone in Ember OpenAIRE Simin, Matija 2016-01-01 Diplomsko delo primerja tri JavaScript ogrodja za razvoj spletnih aplikacij, in sicer AngularJS, Ember.js in Backbone.js. V okviru dela smo primerjali njihovo implementacijo MVC arhitekturnega modela ali različice le-tega. Poleg implementacije MVC arhitekturnega modela smo primerjali njihove funkcionalnosti in lastnosti, kot so sistem predlog, implementacija usmerjevalnika, komunikacija s strežnikom, podatkovne povezave, prilagodljivosti, velikost in aktivnost skupnosti, kvaliteta obstoje... 1. Comparison of JavaScript frameworks, Angular, Backbone, and Ember OpenAIRE Simin, Matija 2016-01-01 The thesis compares three JavaScript frameworks for developing web applications: AngularJS, Ember.js and Backbone.js. In the thesis we compared their implementation of the MVC design pattern and their subversions. Besides their implementation of MVC design pattern we compared their functionalities and features, such as templating system, routing implementation, communications with a server, data binding, adjustability, size and activity of the community, quality of existing documentation, pos... 2. Backbone decomposition for continuous-state branching processes with immigration CERN Document Server Ren, A E Kyprianou Y-X 2011-01-01 In the spirit of Duqesne and Winkel (2007) and Berestycki et al. (2011) we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equal in law to a continuous-time Galton Watson process with immigration with Poissonian dressing. The result also characterises the limiting backbone decomposition which is predictable from the work on consistent growth of Galton-Watson trees with immigration in Cao and Winkel (2010). 3. Variation of protein backbone amide resonance by electrostatic field OpenAIRE Sharley, John N. 2015-01-01 Amide resonance is found to be sensitive to electrostatic field with component parallel or antiparallel the amide C-N bond. This effect is linear and without threshold in the biologically plausible electrostatic field range -0.005 to 0.005 au. Variation of amide resonance varies Resonance-Assisted Hydrogen Bonding such as occurs in the hydrogen bonded chains of backbone amides of protein secondary structures such as beta sheet and alpha helix, varying the stability of the secondary structure.... 4. Oxygen determination in materials by 18O(p,αγ)15N nuclear reaction Science.gov (United States) Kumar, Sanjiv; Sunitha, Y.; Reddy, G. L. N.; Sukumar, A. A.; Ramana, J. V.; Sarkar, A.; Verma, Rakesh 2016-07-01 The paper presents a proton induced γ-ray emission method based on 18O(p,αγ)15N nuclear reaction to determine bulk oxygen in materials. The determination involves the measurement of 5.27 MeV γ-rays emitted following the de-excitation of 15N nuclei. A description of the energetics of the reaction is given to provide an insight into the origin of 5.27 MeV γ-rays. In addition, thick target γ-ray yields and the limits of detection are measured to ascertain the analytical potential of the reaction. The thick-target γ-ray yields are measured with a high purity germanium detector and a bismuth germanate detector at 0° as well as 90° angles in 3.0-4.2 MeV proton energy region. The best limit of detection of about 1.3 at.% is achieved at 4.2 MeV proton energy for measurements at 0° as well 90° angles with the bismuth germanate detector while the uncertainty in quantitative analysis is methodology is demonstrated by determining oxygen in several oxide as well as non-oxide materials. 5. MUSIC in triple-resonance experiments: amino acid type-selective (1)H-(15)N correlations Science.gov (United States) Schubert; Smalla; Schmieder; Oschkinat 1999-11-01 Amino acid type-selective triple-resonance experiments can be of great help for the assignment of protein spectra, since they help to remove ambiguities in either manual or automated assignment procedures. Here, modified triple-resonance experiments that yield amino acid type-selective (1)H-(15)N correlations are presented. They are based on novel coherence transfer schemes, the MUSIC pulse sequence elements, that replace the initial INEPT transfer and are selective for XH(2) or XH(3) (X can be (15)N or (13)C). The desired amino acid type is thereby selected based on the topology of the side chain. Experiments for Gly (G-HSQC); Ala (A-HSQC); Thr, Val, Ile, and Ala (TAVI-HSQC); Thr and Ala (TA-HSQC), as well as Asn and Gln (N-HSQC and QN-HSQC), are described. The new experiments are recorded as two-dimensional experiments and therefore need only small amounts of spectrometer time. The performance of the experiments is demonstrated with the application to two protein domains. Copyright 1999 Academic Press. PMID:10527741 6. Constraining the S factor of 15N(p,g)16O at Astrophysical Energies CERN Document Server LeBlanc, P J; Goerres, J; Junker, M; Azuma, R; Beard, M; Bemmerer, D; Best, A; Broggini, C; Caciolli, A; Corvisiero, P; Costantini, H; Couder, M; deBoer, R; Elekes, Z; Falahat, S; Formicola, A; Fulop, Zs; Gervino, G; Guglielmetti, A; Gustavino, C; Gyurky, Gy; Kaeppeler, F; Kontos, A; Kuntz, R; Leiste, H; Lemut, A; Li, Q; Limata, B; Marta, M; Mazzocchi, C; Menegazzo, R; O'Brien, S; Palumbo, A; Prati, P; Roca, V; Rolfs, C; Alvarez, C Rossi; Somorjai, E; Stech, E; Straniero, O; Strieder, F; Tan, W; Terrasi, F; Trautvetter, H P; Uberseder, E; Wiescher, M 2010-01-01 The 15N(p,g)16O reaction represents a break out reaction linking the first and second cycle of the CNO cycles redistributing the carbon and nitrogen abundances into the oxygen range. The reaction is dominated by two broad resonances at Ep = 338 keV and 1028 keV and a Direct Capture contribution to the ground state of 16O. Interference effects between these contributions in both the low energy region (Ep < 338 keV) and in between the two resonances (338 15N(p,g)16O reaction has been remeasured covering the energy range from Ep=1800 keV down to 130 keV. The results have been analyzed in the framework of a multi-level R-matrix theory and a S(0) value of 39.6 keV b has been found. 7. The Origin of Nitrogen on Jupiter and Saturn from the $^{15}$N/$^{14}$N Ratio CERN Document Server Fletcher, Leigh N; Orton, Glenn S; Irwin, Patrick G J; Mousis, Olivier; Sinclair, James A; Giles, Rohini S 2014-01-01 The Texas Echelon cross Echelle Spectrograph (TEXES), mounted on NASA's Infrared Telescope Facility (IRTF), was used to map mid-infrared ammonia absorption features on both Jupiter and Saturn in February 2013. Ammonia is the principle reservoir of nitrogen on the giant planets, and the ratio of isotopologues ($^{15}$N/$^{14}$N) can reveal insights into the molecular carrier (e.g., as N$_2$ or NH$_3$) of nitrogen to the forming protoplanets, and hence the source reservoirs from which these worlds accreted. We targeted two spectral intervals (900 and 960 cm$^{-1}$) that were relatively clear of terrestrial atmospheric contamination and contained close features of $^{14}$NH$_3$ and $^{15}$NH$_3$, allowing us to derive the ratio from a single spectrum without ambiguity due to radiometric calibration (the primary source of uncertainty in this study). We present the first ground-based determination of Jupiter's $^{15}$N/$^{14}$N ratio (in the range from $1.4\\times10^{-3}$ to $2.5\\times10^{-3}$), which is consistent... 8. Nutritional status of sugar cane (planted cane) in 15N experiments International Nuclear Information System (INIS) Studies with stable isotopes are becoming more common due to the increased safety of operation and quality and reliability of results. However, the use of microplots is required to decrease the costs of such studies. Since microplots are small compared to regular plot areas, the purpose of this study was to investigate whether nutritional data based on microplot samples can adequately represent the whole area, in a comparison of the nutritional status of microplot sugar cane plants at their maximum development stage with those of the regular plots in experiments with N rates. Three experiments were set up, with three N rates (40, 80, and 120 kg ha-1 N) and a control, with four repetitions, in a randomized complete block design, in the state of Sao Paulo. Microplots of 3 m2 containing 15N-fertilizer (5.04% atom 15N) were included in the main plots formed by 48 lines of sugar cane spaced 1.5 m apart. At the time of maximum development stage, diagnostic leaves were collected in the main and microplots to evaluate the nutritional status of plants by analyzing the total concentration of macro nutrients. There were no differences in N, P, Ca, Mg, and S concentrations in the diagnostic leaves from the main and microplots, so that the latter can be considered representative of the experimental area. Higher nitrogen fertilizer rates induced increased concentrations of not only N, but also of P, Ca, Mg, and S in the diagnostic leaves. (author) 9. Growth, development, and fertilizer-15N recovery by the coffee plant International Nuclear Information System (INIS) The relationship between growth and fertilizer nitrogen recovery by perennial crops such as coffee is poorly understood and improved understanding of such relations is important for the establishment of rational crop management practices. In order to characterize the growth of a typical coffee crop in Brazil and quantify the recovery of 15N labeled ammonium sulfate, and improve information for fertilizer management practices this study presents results for two consecutive cropping years, fertilized with 280 and 350 kg ha-1 of N, respectively, applied in four splittings, using five replicates. Shoot dry matter accumulation was evaluated every 60 days, separating plants into branches, leaves and fruits. Labeled sub-plots were used to evaluate N-total and 15N abundance by mass spectrometry. During the first year the aerial part reached a recovery of 71% of the fertilizer N applied up to February, but this value was reduced to 34% at harvest and 19% at the beginning of the next flowering period due to leaf fall and fruit export. For the second year the aerial part absorbed 36% of the fertilizer N up to March, 47% up to harvest and 19% up to the beginning of the next flowering period. The splitting into four applications of the used fertilizer rates was adequate for the requirements of the crop at these growth stages of the coffee crop. (author) 10. Growth, development, and fertilizer-{sup 15}N recovery by the coffee plant Energy Technology Data Exchange (ETDEWEB) Fenilli, Tatiele Anete Bergamo [Fundacao Universidade Regional de Blumenau (FURB), Blumenau, SC (Brazil). Dept. de Engenharia Florestal; Reichardt, Klaus; Bacchi, Osny Oliveira Santos [Centro de Energia Nuclear na Agricultura (CENA), Piracicaba, SP (Brazil). Lab. de Fisica do Solo]. E-mail: klaus@cena.usp.br; Dourado-Neto, Durval; Favarin, Jose Laercio [Escola Superior de Agricultura Luiz de Queiroz (ESALQ/USP), Piracicaba, SP (Brazil). Dept. de Producao Vegetal; Trivelim, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura (CENA), Piracicaba, SP (Brazil). Lab. de Isotopos Estaveis; Costa, Flavio Murilo Pereira da [Ministerio do Desenvolvimento Agrario, Brasilia, DF (Brazil). Secretaria de Assuntos Fundiarios - SEAF 2007-09-15 The relationship between growth and fertilizer nitrogen recovery by perennial crops such as coffee is poorly understood and improved understanding of such relations is important for the establishment of rational crop management practices. In order to characterize the growth of a typical coffee crop in Brazil and quantify the recovery of {sup 15}N labeled ammonium sulfate, and improve information for fertilizer management practices this study presents results for two consecutive cropping years, fertilized with 280 and 350 kg ha{sup -1} of N, respectively, applied in four splittings, using five replicates. Shoot dry matter accumulation was evaluated every 60 days, separating plants into branches, leaves and fruits. Labeled sub-plots were used to evaluate N-total and {sup 15}N abundance by mass spectrometry. During the first year the aerial part reached a recovery of 71% of the fertilizer N applied up to February, but this value was reduced to 34% at harvest and 19% at the beginning of the next flowering period due to leaf fall and fruit export. For the second year the aerial part absorbed 36% of the fertilizer N up to March, 47% up to harvest and 19% up to the beginning of the next flowering period. The splitting into four applications of the used fertilizer rates was adequate for the requirements of the crop at these growth stages of the coffee crop. (author) 11. Extracting the multiscale backbone of complex weighted networks Science.gov (United States) Serrano, M. Ángeles; Boguñá, Marián; Vespignani, Alessandro 2009-01-01 A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large-scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions that vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques come into conflict with the multiscale nature of large-scale systems. Here, we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistically significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to real-world network instances and compare the obtained results with alternative backbone extraction techniques. PMID:19357301 12. {delta}{sup 15}N of seagrass leaves for monitoring anthropogenic nutrient increases in coral reef ecosystems Energy Technology Data Exchange (ETDEWEB) Yamamuro, M.; Kayanne, H.; Yamano, H 2003-04-01 In a coral reef environment, a slight increase in dissolved inorganic nitrogen (DIN;{>=}1.0 {mu}M) can alter the ecosystem via macroalgal blooms. We collected seagrass leaves from the tropical and subtropical Pacific Ocean in five countries and examined the interactions between nutrient concentrations (C, N, P), molar ratios of nutrients, and {delta}{sup 15}N to find a possible indicator of the DIN conditions. Within most sites, the concentrations of nutrients and their molar ratios showed large variations owing to species-specific values. On the other hand, almost identical {delta}{sup 15}N values were found in seagrass leaves of several species at each site. The correlations between {delta}{sup 15}N and nutrient concentrations and between {delta}{sup 15}N and molar ratios of nutrients suggested that nutrient availability did not affect the {delta}{sup 15}N value of seagrass leaves by altering the physiological condition of the plants. Increases in {delta}{sup 15}N of seagrass leaves mostly matched increases in DIN concentrations in the bottom water. We suggest that {delta}{sup 15}N in seagrass leaves can be a good tool to monitor time-integrated decrease/increase of DIN concentrations at a site, both in the water column and the interstitial water. 13. {sup 15}N-labeled nitrogen from green manure and ammonium sulfate utilization by the sugarcane ratoon Energy Technology Data Exchange (ETDEWEB) Ambrosano, Edmilson Jose; Rossi, Fabricio, E-mail: ambrosano@apta.sp.gov.b [Agencia Paulista de Tecnologia dos Agronegocios (APTA), Piracicapa, SP (Brazil). Polo Rigional Centro Sul; Trivelin, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura (CENA/USP), Piracicaba, SP (Brazil). Lab. de Isotopos Estaveis; Cantarella, Heitor [Agencia Paulista de Tecnologia dos Agronegocios (APTA/IAC), Campinas, SP (Brazil). Instituto Agronomico de Campinas. Centro de Solos e Recursos Agroambientais; Ambrosano, Glaucia Maria Bovi [Universidade de Campinas (UNICAMP/FOP), Piracicaba, SP (Brazil). Fac. de Odontologia de Piracicaba. Dept. de Odontologia Social, Bioestatistica; Schammass, Eliana Aparecida [Agencia Paulista de Tecnologia dos Agronegocios (APTA/IZ), Nova Odessa, SP (Brazil). Instituto de Zootecnia; Muraoka, Takashi [Centro de Energia Nuclear na Agricultura (CENA/USP), Piracicaba, SP (Brazil). Lab. de Fertilidade do solo 2011-05-15 Legumes as green manure are alternative sources of nitrogen (N) for crops and can supplement or even replace mineral nitrogen fertilization due to their potential for biological nitrogen fixation (BNF). The utilization of nitrogen by sugarcane (Saccharum spp.) fertilized with sunn hemp (Crotalaria juncea L.) and ammonium sulfate (AS) was evaluated using the {sup 15}N tracer technique. N was added at the rate of 196 and 70 kg ha{sup -1} as {sup 15}N-labeled sunn hemp green manure (SH) and as ammonium sulfate (AS), respectively. Treatments were: (I) Control; (II) AS{sup 15}N; (III) SH{sup 15}N + AS; (IV) SH{sup 15}N; and (V) AS{sup 15}N + SH. Sugarcane was cultivated for five years and was harvested three times. {sup 15}N recovery was evaluated in the two first harvests. In the sum of the three harvests, the highest stalk yields were obtained with a combination of green manure and inorganic N fertilizer; however, in the second cutting the yields were higher where SH was used than in plots with AS. The recovery of N by the first two consecutive harvests accounted for 19 to 21% of the N applied as leguminous green manure and 46 to 49% of the N applied as AS. The amounts of inorganic N, derived from both N sources, present in the 0-0.4 m layer of soil in the first season after N application and were below 1 kg ha{sup -1}. (author) 14. Homogeneity of δ15N in needles of Masson pine (Pinus massoniana L.) was altered by air pollution International Nuclear Information System (INIS) The present study investigated the changes of δ15N values in the tip, middle and base section (divided by the proportion to needle length) of current- and previous-year needles of Masson pine (Pinus massoniana L.) from two declining forest stands suffering from air pollution, in comparison with one healthy stand. At the healthy stand, δ15N in the three sections of both current- and previous-year needles were found evenly distributed, while at the polluted stands, δ15N values in the needles were revealed significantly different from the tip to the base sections. The results implied that the distribution of δ15N among different parts or sections in foliages was not always homogeneous and could be affected by air pollution. We suggested that the difference of δ15N values among pine needle sections should be reconsidered and should not be primarily ignored when the needle δ15N values were used to assess plant responses to air pollution. - Values of δ15N in needles of Masson pine (Pinus massoniana L.) were uneven and affected by air pollution. 15. Diffusion technique for 15N and inorganic N analysis of low-N aqueous solutions and Kjeldahl digests. Science.gov (United States) Chen, Rui Rui; Dittert, Klaus 2008-06-01 Diffusion of ammonia is a common sample preparation method for the stable isotope analysis of inorganic nitrogen in aqueous solution. Classical diffusion methods usually require 6-12 days of diffusion and often focus on (15)N/(14)N analysis only. More recent studies have discussed whether complete N recovery was necessary for the precise analysis of stable N isotope ratios. In this paper we present a newly revised diffusion technique that allows correct and simultaneous determination of total N and (15)N at% from aqueous solutions and Kjeldahl digests, with N concentrations down to sub-0.5-mg N L(-1) levels, and it is tested under different conditions of (15)N isotope labelling. With the modification described, the diffusion time was reduced to 72 h, while the ratios of measured and expected (15)N at% were greater than 99% and the simultaneous recovery of total N was >95%. Analysis of soil microbial biomass N and its (15)N/(14)N ratio is one of the most important applications of this diffusion technique. An experiment with soil extracts spiked with (15)N-labelled yeast showed that predigestion was necessary to prevent serious N loss during Kjeldahl digestion of aqueous samples (i.e. soil extracts). The whole method of soil microbial biomass N preparation for (15)N/(14)N analysis included chloroform fumigation, predigestion, Kjeldahl digestion and diffusion. An experiment with soil spiked with (15)N-labelled yeast was carried out to evaluate the method. Results showed a highly significant correlation of recovered and added N, with the same recovery rate (0.21) of both total N and (15)N. A k(N) value of 0.25 was obtained based on the data. In conclusion, the diffusion method works for soil extracts and microbial biomass N determination and hence could be useful in many types of soil/water studies. 16. Oligomeric complexes of some heteroaromatic ligands and aromatic diamines with rhodium and molybdenum tetracarboxylates: 13C and 15N CPMAS NMR and density functional theory studies. Science.gov (United States) Leniak, Arkadiusz; Kamieński, Bohdan; Jaźwiński, Jarosław 2015-05-01 Seven new oligomeric complexes of 4,4'-bipyridine; 3,3'-bipyridine; benzene-1,4-diamine; benzene-1,3-diamine; benzene-1,2-diamine; and benzidine with rhodium tetraacetate, as well as 4,4'-bipyridine with molybdenum tetraacetate, have been obtained and investigated by elemental analysis and solid-state nuclear magnetic resonance spectroscopy, (13)C and (15)N CPMAS NMR. The known complexes of pyrazine with rhodium tetrabenzoate, benzoquinone with rhodium tetrapivalate, 4,4'-bipyridine with molybdenum tetrakistrifluoroacetate and the 1 : 1 complex of 2,2'-bipyridine with rhodium tetraacetate exhibiting axial-equatorial ligation mode have been obtained as well for comparison purposes. Elemental analysis revealed 1 : 1 complex stoichiometry of all complexes. The (15)N CPMAS NMR spectra of all new complexes consist of one narrow signal, indicating regular uniform structures. Benzidine forms a heterogeneous material, probably containing linear oligomers and products of further reactions. The complexes were characterized by the parameter complexation shift Δδ (Δδ = δcomplex - δligand). This parameter ranged from around -40 to -90 ppm in the case of heteroaromatic ligands, from around -12 to -22 ppm for diamines and from -16 to -31 ppm for the complexes of molybdenum tetracarboxylates with 4,4'-bipyridine. The experimental results have been supported by a density functional theory computation of (15)N NMR chemical shifts and complexation shifts at the non-relativistic Becke, three-parameter, Perdew-Wang 91/[6-311++G(2d,p), Stuttgart] and GGA-PBE/QZ4P levels of theory and at the relativistic scalar and spin-orbit zeroth order regular approximation/GGA-PBE/QZ4P level of theory. Nucleus-independent chemical shifts have been calculated for the selected compounds. PMID:25614975 17. Distribution of /sup 15/N fertilizer in field-lysimeters sown with garlic (Allium sativum) and foxtail millet (Setaria italica) Energy Technology Data Exchange (ETDEWEB) Lazzari, M.A. (Universidad Nacional del Sur, Bahia Blanca (Argentina). Dept. de Ciencas Agrarias) 1982-01-01 We examined the distribution of residual /sup 15/N and its uptake by a foxtail millet crop grown in field lysimeters following a previous garlic crop fertilized with either /sup 15/N-urea or /sup 15/N-ammonium sulphate. Garlic apparently removed more N from the lysimeters treated with urea-N than from those treated with (NH/sub 4/)/sub 2/SO/sub 4/. Fertilizer-N in the lysimeters was similar (ca. 32% of original) following millet harvest. About 16 per cent of both fertilizers in the lysimeters was removed by the millet. 18. Medium-term effects of poultry manure on pine N uptake in a 15N labelled burnt soil. OpenAIRE Castro, A; González Prieto, S. J.; T. Carballas 2008-01-01 The effects of poultry manure (PM), used for the reclamation of a 15N-labelled burnt soil, on N nutrition of pine seedlings were evaluated during a year in a pot experiment. Six treatments were used: 15N-labelled soil (LS), 15N-labelled burnt soil (BLS) and BLS+PM at doses equivalent to 1, 2, 4 and 8 Mg ha-1 of dry PM (PM1, PM2, PM4 and PM8, respectively). Either in the whole tree or the different organs, N concentration: a) decreased (P # 0.05) in the order LS > BLS, BLS+PM1, BLS... 19. Distribution of 15N fertilizer in field-lysimeters sown with garlic (Allium sativum) and foxtail millet (Setaria italica) International Nuclear Information System (INIS) We examined the distribution of residual 15N and its uptake by a foxtail millet crop grown in field lysimeters following a previous garlic crop fertilized with either 15N-urea or 15N-ammonium sulphate. Garlic apparently removed more N from the lysimeters treated with urea-N than from those treated with (NH4)2SO4. Fertilizer-N in the lysimeters was similar (ca. 32% of original) following millet harvest. About 16 per cent of both fertilizers in the lysimeters was removed by the millet. (orig.) 20. Influence of Backbone Fluorination in Regioregular Poly(3-alkyl-4-fluoro)thiophenes KAUST Repository Fei, Zhuping 2015-06-03 © 2015 American Chemical Society. We report two strategies toward the synthesis of 3-alkyl-4-fluorothiophenes containing straight (hexyl and octyl) and branched (2-ethylhexyl) alkyl groups. We demonstrate that treatment of the dibrominated monomer with 1 equiv of alkyl Grignard reagent leads to the formation of a single regioisomer as a result of the pronounced directing effect of the fluorine group. Polymerization of the resulting species affords highly regioregular poly(3-alkyl-4-fluoro)thiophenes. Comparison of their properties to those of the analogous non-fluorinated polymers shows that backbone fluorination leads to an increase in the polymer ionization potential without a significant change in optical band gap. Fluorination also results in an enhanced tendency to aggregate in solution, which is ascribed to a more co-planar backbone on the basis of Raman and DFT calculations. Average charge carrier mobilities in field-effect transistors are found to increase by up to a factor of 5 for the fluorinated polymers. 1. Control of polymer-packing orientation in thin films through synthetic tailoring of backbone coplanarity KAUST Repository Chen, Mark S. 2013-10-22 Controlling solid-state order of π-conjugated polymers through macromolecular design is essential for achieving high electronic device performance; yet, it remains a challenge, especially with respect to polymer-packing orientation. Our work investigates the influence of backbone coplanarity on a polymer\\'s preference to pack face-on or edge-on relative to the substrate. Isoindigo-based polymers were synthesized with increasing planarity by systematically substituting thiophenes for phenyl rings in the acceptor comonomer. This increasing backbone coplanarity, supported by density functional theory (DFT) calculations of representative trimers, leads to the narrowing of polymer band gaps as characterized by ultraviolet-visible-near infrared (UV-vis-NIR) spectroscopy and cyclic voltammetry. Among the polymers studied, regiosymmetric II and TII polymers exhibited the highest hole mobilities in organic field-effect transistors (OFETs), while in organic photovoltaics (OPVs), TBII polymers that display intermediate levels of planarity provided the highest power conversion efficiencies. Upon thin-film analysis by atomic force microscropy (AFM) and grazing-incidence X-ray diffraction (GIXD), we discovered that polymer-packing orientation could be controlled by tuning polymer planarity and solubility. Highly soluble, planar polymers favor face-on orientation in thin films while the less soluble, nonplanar polymers favor an edge-on orientation. This study advances our fundamental understanding of how polymer structure influences nanostructural order and reveals a new synthetic strategy for the design of semiconducting materials with rationally engineered solid-state properties. © 2013 American Chemical Society. 2. Protonation–deprotonation of the glycine backbone as followed by Raman scattering and multiconformational analysis Energy Technology Data Exchange (ETDEWEB) Hernández, Belén; Pflüger, Fernando [Groupe de Biophysique Moléculaire, UFR Santé-Médecine-Biologie Humaine, Université Paris 13, Sorbonne Paris Cité, 74 rue Marcel Cachin, 93017 Bobigny cedex (France); Kruglik, Sergei G. [Laboratoire Jean Perrin, FRE 3231, Université Pierre et Marie Curie (Paris 6), Case courrier 138, 75252 Paris Cedex 05 (France); Ghomi, Mahmoud, E-mail: mahmoud.ghomi@univ-paris13.fr [Groupe de Biophysique Moléculaire, UFR Santé-Médecine-Biologie Humaine, Université Paris 13, Sorbonne Paris Cité, 74 rue Marcel Cachin, 93017 Bobigny cedex (France) 2013-11-08 Highlights: • New pH-dependent Raman spectra in the middle wavenumber region (1800-300 cm{sup −1}). • New quantum mechanical calculations for exploring the Gly conformational landscape. • Construction of muticonformation based theoretical Raman spectra. - Abstract: Because of the absence of the side chain in its chemical structure and its well defined Raman spectra, glycine was selected here to follow its backbone protonation–deprotonation. The scan of the recorded spectra in the 1800–300 cm{sup −1} region led us to assign those obtained at pH 1, 6 and 12 to the cationic, zwitterionic and anionic species, respectively. These data complete well those previously published by Bykov et al. (2008) [16] devoted to the high wavenumber Raman spectra (>2500 cm{sup −1}). To reinforce our discussion, DFT calculations were carried out on the clusters of glycine + 5H{sub 2}O, mimicking reasonably the first hydration shell of the amino acid. Geometry optimization of 141 initial clusters, reflecting plausible combinations of the backbone torsion angles, allowed exploration of the conformational features, as well as construction of the theoretical Raman spectra by considering the most stable clusters containing each glycine species. 3. Dynamics of nitrogen in an oxic paleudalf soil with the incorporation of 15N-tagged organic nitrogen (maize straw) and 15N-tagged mineral nitrogen (ammonium sulphate) International Nuclear Information System (INIS) An experiment, carried out under field conditions in 12 lysimeters, each containing 3.0 ton of Oxic Paleudalf soil with four replicates, is described. This objective is labelling soil organic N. Nitrogen was incorporated into soil as maize straw, non-labelled and labelled with 15N and ammonium sulphate - 15N. The soil was sampled every 15 days in three different depths. N as NH+4, NO-3, total-N and (%)C and (%) moisture was analysed. (M.A.C.) 4. A new default restraint library for the protein backbone in Phenix: a conformation-dependent geometry goes mainstream Science.gov (United States) Moriarty, Nigel W.; Tronrud, Dale E.; Adams, Paul D.; Karplus, P. Andrew 2016-01-01 Chemical restraints are a fundamental part of crystallographic protein structure refinement. In response to mounting evidence that conventional restraints have shortcomings, it has previously been documented that using backbone restraints that depend on the protein backbone conformation helps to address these shortcomings and improves the performance of refinements [Moriarty et al. (2014 ▸), FEBS J. 281, 4061–4071]. It is important that these improvements be made available to all in the protein crystallography community. Toward this end, a change in the default geometry library used by Phenix is described here. Tests are presented showing that this change will not generate increased numbers of outliers during validation, or deposition in the Protein Data Bank, during the transition period in which some validation tools still use the conventional restraint libraries. PMID:26894545 5. Fluorous Peptide Nucleic Acids: PNA Analogues with Fluorine in Backbone (γ-CF2-apg-PNA) Enhance Cellular Uptake. Science.gov (United States) Ellipilli, Satheesh; Ganesh, Krishna N 2015-09-18 Fluorous PNA analogues possessing fluorine as inherent part of aminopropylglycine (apg) backbone (γ-CF2-apg PNA) have been synthesized and evaluated for biophysical and cell penetrating properties. These form duplexes of higher thermal stability with cRNA than cDNA, although destabilized compared to duplexes of standard aeg-PNA. Cellular uptake of the fluorinated γ-CF2-apg PNAs in NIH 3T3 and HeLa cells was 2-3-fold higher compared to that of nonfluorinated apg PNA, with NIH 3T3 cells showing better permeability compared to HeLa cells. The backbone fluorinated PNAs, which are first in this class, when combined with other chemical modifications may have potential for future PNA-based antisense agents. PMID:26322827 6. Nitrogen use efficiency evaluation of aerobic rice under field capacity water potential using {sup 15}N isotopic tracer technique Energy Technology Data Exchange (ETDEWEB) Wahid, Ahmad Nazrul Abd, E-mail: a-nazrul@nuclearmalaysia.gov.my [Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, 43600, Selangor (Malaysia); Malaysian Nuclear Agency, Bangi, 43000 Kajang, Selangor (Malaysia); Rahim, Sahibin Abd, E-mail: haiyan@ukm.edu.my [Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, 43600, Selangor (Malaysia); Rahim, Khairuddin Abdul; Harun, Abdul Rahim [Malaysian Nuclear Agency, Bangi, 43000 Kajang, Selangor (Malaysia) 2015-09-25 This study was carried out to evaluate the efficiency use of the nitrogen fertilizer on aerobic rice varieties MR219-4 and MR219-9 which were grown aerobically under field capacity water potential at the controlled environment area or shield house. Direct {sup 15}N isotope tracer method was used in this study, whereby the {sup 15}N isotope was utilized as a tracer for nitrogen nutrient uptake. {sup 15}N isotope presence in the samples is determined by using emission spectrometer analysis and percentage of total nitrogen is determined by using Kjeldahl method. {sup 15}N atom access value contained in the sample will be used in determining the effectiveness of the use of nitrogen in fertilizers through the specific calculation formulas. In this work, the data several data of nitrogen derived from fertilizer (Ndff), total nitrogen, nitrogen uptake and nitrogen use efficiency was obtained. 7. Nitrogen use efficiency evaluation of aerobic rice under field capacity water potential using 15N isotopic tracer technique Science.gov (United States) Wahid, Ahmad Nazrul Abd; Rahim, Sahibin Abd; Rahim, Khairuddin Abdul; Harun, Abdul Rahim 2015-09-01 This study was carried out to evaluate the efficiency use of the nitrogen fertilizer on aerobic rice varieties MR219-4 and MR219-9 which were grown aerobically under field capacity water potential at the controlled environment area or shield house. Direct 15N isotope tracer method was used in this study, whereby the 15N isotope was utilized as a tracer for nitrogen nutrient uptake. 15N isotope presence in the samples is determined by using emission spectrometer analysis and percentage of total nitrogen is determined by using Kjeldahl method. 15N atom access value contained in the sample will be used in determining the effectiveness of the use of nitrogen in fertilizers through the specific calculation formulas. In this work, the data several data of nitrogen derived from fertilizer (Ndff), total nitrogen, nitrogen uptake and nitrogen use efficiency was obtained. 8. d15N dynamics of ammonium and particulate nitrogen during the growth season of a eutrophic estuary DEFF Research Database (Denmark) De Brabandere, Loreto; Brion, N.; Elskens, M.; 2007-01-01 We monitored the stable nitrogen isotopic composition (d15N) of suspended matter and ammonium in the freshwater stretch of the Scheldt estuary (Belgium) over a full year to investigate for seasonal evolution and possible co-variation between isotopic signatures. The d15N value of ammonium remained...... rather constant during winter (average = +11.4 pro mille) but increased significantly with the spring and summer bloom, reaching values as high as +70 pro mille. This enrichment of the ammonium pool in 15N coincided with significant ammonium depletion during summer period, suggesting a close causal...... relationship. Based on a semiclosed system approach we deduced an apparent fractionation factor associated with NH4+ utilization (i.e. combining effects of uptake and nitrification) of 18.4 pro mille (SE = 2.0 pro mille), which is similar to values reported in literature. Observed variations of ammonium d15N... 9. Nitrogen use efficiency evaluation of aerobic rice under field capacity water potential using 15N isotopic tracer technique International Nuclear Information System (INIS) This study was carried out to evaluate the efficiency use of the nitrogen fertilizer on aerobic rice varieties MR219-4 and MR219-9 which were grown aerobically under field capacity water potential at the controlled environment area or shield house. Direct 15N isotope tracer method was used in this study, whereby the 15N isotope was utilized as a tracer for nitrogen nutrient uptake. 15N isotope presence in the samples is determined by using emission spectrometer analysis and percentage of total nitrogen is determined by using Kjeldahl method. 15N atom access value contained in the sample will be used in determining the effectiveness of the use of nitrogen in fertilizers through the specific calculation formulas. In this work, the data several data of nitrogen derived from fertilizer (Ndff), total nitrogen, nitrogen uptake and nitrogen use efficiency was obtained 10. A 15N investigation of mineral fertilizer nitrogen assimilation in apples International Nuclear Information System (INIS) An experiment was made using six seedlings of the apple cv. Golden Delicious in their second year of growing. The roots of each seedling were divided and planted in two vegetation pots of 1 l capacity. Fertilizer application of 1 g NH4NO3 with 49.1 atom % 15N was effected to three of the plants in one of the pots, while to the remaining three plants in both pots the fertilizer application consisted of 0.5 g 15NH4NO3 for each pot. Isotope analysis of fertilizer N taken up was made and the coefficient of its assimilation was determined. Twenty-one days later the plants had assimilated 18.18-21.95% of the mineral N applied. This amount constituted 17.32-22.13% of the total N assimilated. The percent of assimilation was higher in case the fertilizer was applied to both pots 11. Creating 13C- and 15N-enriched tree leaf litter for decomposition experiments Science.gov (United States) Szlavecz, K. A.; Pitz, S.; Chang, C.; Bernard, M. 2013-12-01 Labeling plant material with heavy isotopes of carbon and nitrogen can produce a traceable nutrient signal that can be followed into the different trophic levels and decomposer food web. We treated 60 tree saplings with 13C-enriched CO2 gas and 15N-enriched ammonium nitrate over a three-month period to create dually-labeled plant material for future decomposition experiments. The trees included both early (Red maple, Sweetgum, Tulip poplar) and late (American beech, White oak) successional deciduous tree species, and a conifer, White pine. We constructed a 2.4 m × 2.4 m × 2.4 m environmental chamber that was climate-controlled using an air conditioning system. An Arduino microcontroller interfaced with a Vaisala GMP343 CO2 probe maintained a CO2 concentration between 500-520 ppm by controlling a solenoid valve on the CO2 tank regulator. The trees were placed into the chamber in August 2012 and remained until senescence unless they were lost to death or disease. Ammonium nitrate was added twice, in September and October. Leaf samples were collected prior to the start of the experiment and after senescence, whereas root samples were collected only in December. Samples were dried, ground and analyzed using an isotope ratio mass spectrometer. American beech and White oak had 40% mortality, and 34% of tulip poplar trees were removed because of powdery mildew overgrowth or death. Most tulip poplar trees exhibited a second leaf out following senescence in late September. Nearly 1 kg of litter was produced with tulip poplar representing over half of the total mass. Levels of enrichment varied greatly by species. Beech (-14.2‰) and White oak (-4.8‰) had low levels of enrichment in comparison to early successional species such as Sweetgum (41.7‰) and Tulip poplar (30.7‰ [first leaf fall] and 238.0‰ [second leaf fall]). Leaf enrichment with 15N followed a similar pattern, though it was achieved at a higher level with δ15N values varying from 271.6‰ to 1354.2 12. Bioavailability of nitrogen from sewage sludge using 15N-labelled ammonium sulphate International Nuclear Information System (INIS) The high nutrient nitrogen and organic matter contents of sewage sludge (SS) make it a potential organic fertilizer for sandy soil. In this study, 15N-labelled ammonium sulphate was used to investigate the availability of nitrogen from irradiated and non-irradiated sewage sludge to tomato plants. The application of sewage sludge to sandy soil increased dry matter production (DMP), nitrogen yield (NY) and nitrogen recovery (NR) over two successive years. A positive relationship was found between sludge application rate and DMP and NY. The increase was significantly higher (P=0.05) in irradiated than non-irradiated sewage sludge. Total nitrogen derived from non-irradiated sewage sludge are : 48.0, 63.7, 73.5, 105.2 Kg/ha, whereas, the total nitrogen derived from irradiated sewage sludge are: 55.1, 72.5, 88.9, 141.4 Kg/ha corresponding to application rates of 10 t/ha, 20 t/ha, 30 t/ha, respectively. This was attributed to higher dry matter production in the later than the former. A highly significant correlation (0.945*) was found between dry matter production and sludge nitrogen yield (i.e. nitrogen derived from sewage sludge). Fertilizer nitrogen yield (total nitrogen derived from fertilizer) was high in treatment receiving mineral fertilizer, however, the 15N recovery by tomato was only 13.8%. Soil did not contribute well towards total nitrogen yield in tomato and most nitrogen was derived from sewage sludge. Percent nitrogen derived from sewage sludge was in the range 88-92%, depending on the application rate 13. Nitrogen acquisition, transport and metabolism in intact ectomycorrhizal associations studied by 15N stable isotope techniques International Nuclear Information System (INIS) The focus of this thesis is on the external mycelium and its role in nitrogen uptake, assimilation and translocation. Tree seedlings in association with ectomycorrhizal fungi were grown in observation chambers. The fungal mycelium were fed with 15-N ammonium or 15-N nitrate or a combination of both. The effects of Collembola on the ectomycorrhizal symbiosis were also studied. The results demonstrates an important role of the external mycelium of Paxillus involutus not only in the uptake but also in the assimilation of ammonium into a variety of different amino acids, primarily glutamine but also glutamic acid, aspartic acid, and alanine, immediately after uptake. The results indicate that ammonium is assimilated by GS and GOGAT or GDH in the mycelium at the uptake site. When nitrate was added to the mycelium as the sole nitrogen source nitrate was reduced in the mycelium and the product assimilated into amino acids. When ammonium nitrate was supplied to the fungal mycelium nitrate was taken up the fungus and transferred to the plant, however, apparently no assimilation of nitrate occurred in the external mycelium. Ammonium or an assimilation product, such as glutamine, probably represses nitrate reductase (NR) but not nitrate uptake and transfer in P. involutus. P. involutus nitrogen uptake and transfer to the associated mycorrhizal pine was up to 76% higher when low numbers of the Collembola Onychiurus armatus were present compared to when they were completely absent. This was probably an indirect effect as P. involutus hyphal growth rate and extramatrical biomass increased at a low Collembola density. At high Collembola densities P. involutus hyphal growth rate was retarded. (74 refs.) 14. Variability in δ{sup 15}N of intertidal brown algae along a salinity gradient: Differential impact of nitrogen sources Energy Technology Data Exchange (ETDEWEB) Viana, Inés G., E-mail: inesgviana@gmail.com; Bode, Antonio 2015-04-15 While it is generally agreed that δ{sup 15}N of brown macroalgae can discriminate between anthropogenic and natural sources of nitrogen, this study provides new insights on net fractionation processes occurring in some of these species. The contribution of continental and marine sources of nitrogen to benthic macroalgae in the estuary-ria system of A Coruña (NW Spain) was investigated by analyzing the temporal (at a monthly and annual basis) and spatial (up to 10 km) variability of δ{sup 15}N in the macroalgae Ascophyllum nodosum and three species of the genus Fucus (F. serratus, F. spiralis and F. vesiculosus). Total nitrate and ammonium concentrations and δ{sup 15}N-DIN, along with salinity and temperature in seawater were also studied to address the sources of such variability. Macroalgal δ{sup 15}N and nutrient concentrations decreased from estuarine to marine waters, suggesting larger dominance of anthropogenic nitrogen sources in the estuary. However, δ{sup 15}N values of macroalgae were generally higher than those of ambient nitrogen at all temporal and spatial scales considered. This suggests that the isotopic composition of these macroalgae is strongly affected by fractionation during uptake, assimilation or release of nitrogen. The absence of correlation between macroalgal and water samples suggests that the δ{sup 15}N of the species considered cannot be used for monitoring short-term changes. But their long lifespan and slow turnover rates make them suitable to determine the impact of the different nitrogen sources integrated over long-time periods. - Highlights: • Variability of Fucacean δ{sup 15}N indicates N sources along a salinity gradient. • δ{sup 15}N of Fucaceae and seawater are not correlated at short time scales. • Isotopic fractionation in macroalgal tissue varies at seasonal and at local scale. • Fucacean species are suitable for monitoring chronic N loadings. 15. An optimized method for {sup 15}N R{sub 1} relaxation rate measurements in non-deuterated proteins Energy Technology Data Exchange (ETDEWEB) Gairí, Margarida, E-mail: mgairi@rmn.ub.edu [University of Barcelona (CCiTUB), NMR Facility, Scientific and Technological Centers (Spain); Dyachenko, Andrey [Institute for Research in Biomedicine (IRB) (Spain); González, M. Teresa; Feliz, Miguel [University of Barcelona (CCiTUB), NMR Facility, Scientific and Technological Centers (Spain); Pons, Miquel [University of Barcelona, Biomolecular NMR Laboratory and Organic Chemistry Department (Spain); Giralt, Ernest, E-mail: ernest.giralt@irbbarcelona.org [Institute for Research in Biomedicine (IRB) (Spain) 2015-06-15 {sup 15}N longitudinal relaxation rates are extensively used for the characterization of protein dynamics; however, their accurate measurement is hindered by systematic errors. {sup 15}N CSA/{sup 1}H–{sup 15}N dipolar cross-correlated relaxation (CC) and amide proton exchange saturation transfer from water protons are the two main sources of systematic errors in the determination of {sup 15}N R{sub 1} rates through {sup 1}H–{sup 15}N HSQC-based experiments. CC is usually suppressed through a train of 180° proton pulses applied during the variable {sup 15}N relaxation period (T), which can perturb water magnetization. Thus CC cancellation is required in such a way as to minimize water saturation effects. Here we examined the level of water saturation during the T period caused by various types of inversion proton pulses to suppress CC: (I) amide-selective IBURP-2; (II) cosine-modulated IBURP-2; (III) Watergate-like blocks; and (IV) non-selective hard. We additionally demonstrate the effect of uncontrolled saturation of aliphatic protons on {sup 15}N R{sub 1} rates. In this paper we present an optimized pulse sequence that takes into account the crucial effect of controlling also the saturation of the aliphatic protons during {sup 15}N R{sub 1} measurements in non-deuterated proteins. We show that using cosine-modulated IBURP-2 pulses spaced 40 ms to cancel CC in this optimized pulse program is the method of choice to minimize systematic errors coming from water and aliphatic protons saturation effects. 16. Species specific and environment induced variation of δ13C and δ15N in alpine plants Directory of Open Access Journals (Sweden) Yang eYang 2015-06-01 Full Text Available Stable carbon and nitrogen isotope signals in plant tissues integrate plant-environment interactions over long periods. In this study, we hypothesized that humid alpine life conditions are narrowing the scope for significant deviations from common carbon, water and nitrogen relations as captured by stable isotope signals. We explored the variation in δ13C and δ15N in 32 plant species from tissue type to ecosystem scale across a suite of locations at c. 2500 m elevation in the Swiss Alps. Foliar δ13C and δ15N varied among species by about 3-4 ‰ and 7-8 ‰ respectively. However, there was no overall difference in means of δ13C and δ15N for species sampled in different plant communities or when bulk plant dry matter harvests of different plant communities were compared. δ13C was found to be highly species specific, so that the ranking among species was mostly maintained across 11 habitats. However, δ15N varied significantly from place to place in all species (a range of 2.7 ‰ except in Fabaceae (Trifolium alpinum and Juncaceae (Luzula lutea. There was also a substantial variation among individuals of the same species collected next to each other. No difference was found in foliar δ15N of non-legumes, which were either collected next to or away from the most common legume, T. alpinum. δ15N data place Cyperaceae and Juncaceae, just like Fabaceae, in a low discrimination category, well separated from other families. Soil δ15N was higher than in plants and increased with soil depth. The results indicate a high functional diversity in alpine plants that is similar to that reported for low elevation plants. We conclude that the surprisingly high variation in δ13C and δ15N signals in the studied high elevation plants is largely species specific (genetic and insensitive to obvious environmental cues. 17. Correlation between the synthetic origin of methamphetamine samples and their {sup 15}N and {sup 13}C stable isotope ratios Energy Technology Data Exchange (ETDEWEB) Billault, Isabelle [Laboratoire d' Analyse Isotopique et Electrochimique de Metabolismes, CNRS UMR6006, University of Nantes, BP 92208, 44322 Nantes (France)]. E-mail: Isabelle.Billault@univ-nantes.fr; Courant, Frederique [Laboratoire d' Analyse Isotopique et Electrochimique de Metabolismes, CNRS UMR6006, University of Nantes, BP 92208, 44322 Nantes (France); Pasquereau, Leo [Laboratoire d' Analyse Isotopique et Electrochimique de Metabolismes, CNRS UMR6006, University of Nantes, BP 92208, 44322 Nantes (France); Derrien, Solene [Laboratoire d' Analyse Isotopique et Electrochimique de Metabolismes, CNRS UMR6006, University of Nantes, BP 92208, 44322 Nantes (France); Robins, Richard J. [Laboratoire d' Analyse Isotopique et Electrochimique de Metabolismes, CNRS UMR6006, University of Nantes, BP 92208, 44322 Nantes (France); Naulet, Norbert [Laboratoire d' Analyse Isotopique et Electrochimique de Metabolismes, CNRS UMR6006, University of Nantes, BP 92208, 44322 Nantes (France) 2007-06-12 The active ingredient of ecstasy, N-methyl-3,4-methyldioxyphenylisopropylamine (MDMA) can be manufactured by a number of easy routes from simple precursors. We have synthesised 45 samples of MDMA following the five most common routes using N-precursors from 12 different origins and three different precursors for the aromatic moiety. The {sup 13}C and {sup 15}N contents of both the precursors and the MDMA samples derived therefrom were measured by isotope ratio mass spectrometry coupled to an elemental analyser (EA-IRMS). We show that within-pathway correlation between the {sup 15}N content of the precursor and that of the derived MDMA can be strong but that no general pattern of correlation can be defined. Rather, it is evident that the {delta} {sup 15}N values of MDMA are strongly influenced by a combination of the {delta} {sup 15}N values of the source of nitrogen used, the route by which the MDMA is synthesised, and the experimental conditions employed. Multivariate analysis (PCA) based on the {delta} {sup 15}N values of the synthetic MDMA and of the {delta} {sup 15}N and {delta} {sup 13}C values of the N-precursors leads to good discrimination between the majority of the reaction conditions tested. 18. Single Particle Strengths and Mirror States in $^{15}$N$-^{15}$O below 12.0 MeV CERN Document Server Mertin, C E; Crisp, A M; Keeley, N; Kemper, K W; Momtyuk, O; Roeder, B T; Volya, A 2014-01-01 New $^{14}$N(d,p) angular distribution data were taken at a deuteron bombarding energy of 16 MeV to locate all narrow single particle neutron states up to 15 MeV in excitation. A new shell model calculation is able to reproduce all levels in $^{15}$N up to 11.5 MeV and is used to characterize a narrow single particle level at 11.236 MeV and to provide a map of the single particle strengths. The known levels in $^{15}$N are then used to determine their mirrors in the lesser known nucleus $^{15}$O. The 2s$_{1/2}$ and 1d$_{5/2}$ single particle centroid energies are determined for the $^{15}$N$-^{15}$O mirror pair as: $^{15}$N $(\\text{2s}_{1/2}) = 8.08$ MeV, $^{15}$O $(\\text{2s}_{1/2}) = 7.43$ MeV, $^{15}$N $(\\text{1d}_{5/2}) = 7.97$ MeV, and $^{15}$O $(\\text{1d}_{5/2}) = 7.47$ MeV. These results confirm the degeneracy of these orbits and that the $^{15}$N$-^{15}$O nuclei are where the transition between the $\\text{2s}_{1/2}$ lying below the $\\text{1d}_{5/2}$ to lying above it, takes place. The $\\text{1d}_{3/2}$... 19. Cryptic or day-to-day parts of the riverbed N cycle - new challenges for 15N Science.gov (United States) Trimmer, Mark; Ouyang, Liao; Lansdown, Katrina 2016-04-01 The discovery of anaerobic ammonium oxidation (anammox) not only changed our understanding of the nitrogen cycle in aquatic ecosystems but it also undermined some of the key 15N techniques used to study it. Reformulations of principle equations and the development of new 15N2 and 15N2O techniques enabled the simultaneous quantification of N2 production by anammox and denitrification in mainly soft, cohesive sediments where redox gradients are clearly defined and solute exchanged governed by diffusion. At the heart of the application of 15N, for the quantification of natural 14N cycling, is the key assumption that the respective pools of 15N and 14N are evenly mixed and that both are cycled without bias towards each other. Recent evidence, however, from a variety of aquatic ecosystems, suggests that this may not be the case. For example, organic N may be oxidised directly to N2 gas without ever mixing with the inorganic pool or inorganic intermediates (e.g. nitrite) are 'shunted' internally and also fail to mix evenly with the applied tracer pool. Our most recent work in permeable, oxic gravel riverbeds presents some particular challenges to the application of 15N. In these systems, a tight coupling between aerobic nitrification and anaerobic N2 production - in the presence of 100 20. Cyanobacteria-derived nitrogen uptake by benthic invertebrates in Lake Taihu: a mesocosm study using 15N labeling Directory of Open Access Journals (Sweden) Yu J. 2014-01-01 Full Text Available Eutrophication of lakes can lead to dominance by cyanobacteria, which are hardly used by zooplankton due to their low nutrition value. However, sedimented cyanobacterial detritus may be a useful source for benthic invertebrates. We studied the Microcystis-derived nitrogen incorporation in benthic invertebrates in Lake Taihu using stable isotopic nitrogen (15N as a tracer. The δ15N of all organisms increased significantly with time after addition of the labeled Microcystis detritus. δ15N values of POM and periphyton peaked earlier than for benthic invertebrates, and the maximum levels were also higher than bivalves, snails and worms (Limnodrilus spp.. Among benthic invertebrates, Radix swinhoei peaked later than other invertebrates, but the maximum level and the excess 15N of the last sampling day were higher. At the end of the experiment, approximately 70% of the added 15N was retained in the benthic food web, while only a small fraction (less than 1% of the added detritus 15N occurred in the pelagic food web. Our results suggest that nitrogen from cyanobacteria can be incorporated more in benthic than pelagic food webs and cyanobacterial blooms may contribute to the development of benthic animals. 1. 15N and 13C abundances in marine environments with emphasis on biogeochemical structure of food networks International Nuclear Information System (INIS) Distributions of δ15N and δ13C for biogenic substances in the Antarctic Ocean and in the Otsuchi River estuary in Japan were investigated to construct isotope biogeochemical framework for assessing marine ecosystems. The isotopic compositions of phytoplankton were particularly low in the Antarctic Ocean. High nitrate and CO2 concentrations in the surface sea waters, and the low light intensity seem to enhance the kinetic isotope fractionations that preferred the depletion of 15N and 13C in the algal body. A clear-cut linear relationship between animal δ15N and its trophic level was obtained in the Antarctic system. In the estuary, the variation of isotope ratios were principally governed by the mixing of land-derived organic matter, marine phytoplankton, and seagrasses. A food-chain effect of 15N enrichment was also confirmed. An isotopically ordered structure was presented for a marine estuarine ecosystem. The isotopic abundances in a food network vary mainly because of the variation in 15N and 13C contents of primary producers grown under different environmental conditions and because of the enrichment of 15N along food chains. (author) 2. Nuclear Quadrupole Hyperfine Structure in HC14N/H14NC and DC15N/D15NC Isomerization: A Diagnostic Tool for Characterizing Vibrational Localization CERN Document Server Wong, Bryan M 2010-01-01 Large-amplitude molecular motions which occur during isomerization can cause significant changes in electronic structure. These variations in electronic properties can be used to identify vibrationally-excited eigenstates which are localized along the potential energy surface. This work demonstrates that nuclear quadrupole hyperfine interactions can be used as a diagnostic marker of progress along the isomerization path in both the HC14N/H14NC and DC15N/D15NC chemical systems. Ab initio calculations at the CCSD(T)/cc-pCVQZ level indicate that the hyperfine interaction is extremely sensitive to the chemical bonding of the quadrupolar 14N nucleus and can therefore be used to determine in which potential well the vibrational wavefunction is localized. A natural bonding orbital analysis along the isomerization path further demonstrates that hyperfine interactions arise from the asphericity of the electron density at the quadrupolar nucleus. Using the CCSD(T) potential surface, the quadrupole coupling constants of... 3. Unique optimal solution instance and computational complexity of backbone in the graph bi-partitioning problem Institute of Scientific and Technical Information of China (English) 2007-01-01 As an important tool for heuristic design of NP-hard problems, backbone analysis has become a hot spot in theoretical computer science in recent years. Due to the difficulty in the research on computational complexity of the backbone, many researchers analyzed the backbone by statistic ways. Aiming to increase the backbone size which is usually very small by the existing methods, the unique optimal solution instance construction (UOSIC) is proposed for the graph bi-partitioning problem (GBP). Also, we prove by using the UOSIC that it is NP-hard to obtain the backbone, i.e. no algorithm exists to obtain the backbone of a GBP in polynomial time under the assumption that P ( NP. Our work expands the research area of computational complexity of the backbone. And the UOSIC provides a new way for heuristic design of NP-hard problems. 4. Radiation damage to DNA: electron scattering from the backbone subunits CERN Document Server Tonzani, S; Greene, Chris H.; Tonzani, Stefano 2006-01-01 In the context of damage to DNA by low-energy electrons, we carry out calculations of electron scattering from tetrahydrofuran and phosphoric acid, models of the subunits in the DNA backbone, as a first step in simulating the electron capture process that occurs in the cell. In the case of tetrahydrofuran, we also compare with previous theoretical and experimental data. A comparison of the shape of the resonant structures to virtual orbitals is also performed to gain insight into the systematic connections with electron scattering from similar molecules and dissociative electron attachment experiments. 5. Application of Multicast-based Video Conference on CERNET Backbone Institute of Scientific and Technical Information of China (English) 2002-01-01 Multicast-based video conference is a representative application in advanced network. In multi-point video conference using multicast can get better efficiency facilitated by inner-group broadcast mechanism. In the application, the multicast-based network resources assignment, management and security should be considered together. This paper presents a framework model of multicast-based video conferencing application with three layers. And a practical multicast-based video conferencing is implemented in CERNET(China Education and Research Network) backbone. The practice is valuable for the development of multicast-based video conferencing application in China. 6. Resistance of Feynman diagrams and the percolation backbone dimension. Science.gov (United States) Janssen, H K; Stenull, O; Oerding, K 1999-06-01 We present an alternative view of Feynman diagrams for the field theory of random resistor networks, in which the diagrams are interpreted as being resistor networks themselves. This simplifies the field theory considerably as we demonstrate by calculating the fractal dimension D(B) of the percolation backbone to three loop order. Using renormalization group methods we obtain D(B)=2+epsilon/21-172epsilon(2)/9261+2epsilon(3)[-74 639+22 680zeta(3)]/4 084 101, where epsilon=6-d with d being the spatial dimension and zeta(3)=1.202 057... . 7. Increased Diels-Alderase activity through backbone remodeling guided by Foldit players. Science.gov (United States) Eiben, Christopher B; Siegel, Justin B; Bale, Jacob B; Cooper, Seth; Khatib, Firas; Shen, Betty W; Players, Foldit; Stoddard, Barry L; Popovic, Zoran; Baker, David 2012-02-01 Computational enzyme design holds promise for the production of renewable fuels, drugs and chemicals. De novo enzyme design has generated catalysts for several reactions, but with lower catalytic efficiencies than naturally occurring enzymes. Here we report the use of game-driven crowdsourcing to enhance the activity of a computationally designed enzyme through the functional remodeling of its structure. Players of the online game Foldit were challenged to remodel the backbone of a computationally designed bimolecular Diels-Alderase to enable additional interactions with substrates. Several iterations of design and characterization generated a 24-residue helix-turn-helix motif, including a 13-residue insertion, that increased enzyme activity >18-fold. X-ray crystallography showed that the large insertion adopts a helix-turn-helix structure positioned as in the Foldit model. These results demonstrate that human creativity can extend beyond the macroscopic challenges encountered in everyday life to molecular-scale design problems. PMID:22267011 8. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 4 International Nuclear Information System (INIS) 12 colostomized laying hybrids with an 81% laying performance received 36 g wheat containing a 15N excess (15N') of 14.37 atom-% in a customary ration over 4 days. The wheat lysine contained 13.58 atom-% 15N', histidine 14.38 and arginine 13.63 atom-% 15N'. In the 4-day period of 15N' application 540 mg 15N', 18.1 mg lysine 15N', 21.5 mg histidine 15N' and 47.9 mg arginine 15N' were consumed per hen. Subsequently the animals received the same ration with unlabelled wheat. 12 h, 36 h, 60 h and 108 h after the last 15N' application 3 animals each were butchered. The atom-% 15N' of the lysine was below that of the two other basic and of the non-basic amino acids. The labelling of the amino acids of the egg white decreased rapidly 2 days after 15N' application. The atom-% of the 15N' of the yolk of egg, however, increased after the discontinuation and remained the same for 4 days after the last 15N' application. The 14N and 15N' amounts measured in the complete experiment period are distributed over the 3 basic and the 12 non-basic (excluding thioamino acids) amino acids in the white of egg for 14N as 25.0%:57.6% and for 15N' as 18.2%:57.5%. In the yolk of egg 28.5% 14N for the basic and 56.8% for the non-basic amino acids could be calculated; the corresponding values for 15N' were 17.8% and 55.5%. (author) 9. Controlled Conjugated Backbone Twisting for an Increased Open-Circuit Voltage while Having a High Short-Circuit Current in Poly(hexylthiophene) Derivatives KAUST Repository Ko, Sangwon 2012-03-21 Conjugated polymers with nearly planar backbones have been the most commonly investigated materials for organic-based electronic devices. More twisted polymer backbones have been shown to achieve larger open-circuit voltages in solar cells, though with decreased short-circuit current densities. We systematically impose twists within a family of poly(hexylthiophene)s and examine their influence on the performance of polymer:fullerene bulk heterojunction (BHJ) solar cells. A simple chemical modification concerning the number and placement of alkyl side chains along the conjugated backbone is used to control the degree of backbone twisting. Density functional theory calculations were carried out on a series of oligothiophene structures to provide insights on how the sterically induced twisting influences the geometric, electronic, and optical properties. Grazing incidence X-ray scattering measurements were performed to investigate how the thin-film packing structure was affected. The open-circuit voltage and charge-transfer state energy of the polymer:fullerene BHJ solar cells increased substantially with the degree of twist induced within the conjugated backbone-due to an increase in the polymer ionization potential-while the short-circuit current decreased as a result of a larger optical gap and lower hole mobility. A controlled, moderate degree of twist along the poly(3,4-dihexyl-2,2′:5′,2′′- terthiophene) (PDHTT) conjugated backbone led to a 19% enhancement in the open-circuit voltage (0.735 V) vs poly(3-hexylthiophene)-based devices, while similar short-circuit current densities, fill factors, and hole-carrier mobilities were maintained. These factors resulted in a power conversion efficiency of 4.2% for a PDHTT:[6,6]-phenyl-C 71-butyric acid methyl ester (PC 71BM) blend solar cell without thermal annealing. This simple approach reveals a molecular design avenue to increase open-circuit voltage while retaining the short-circuit current. © 2012 American 10. Recuperação de 15N-ureia no sistema solo-planta de pastagem de capim-tanzânia Recovery of 15N-urea in soil-plant system of tanzania grass pasture Directory of Open Access Journals (Sweden) Geraldo Bueno Martha Júnior 2009-02-01 11. General order parameter based correlation analysis of protein backbone motions between experimental NMR relaxation measurements and molecular dynamics simulations Energy Technology Data Exchange (ETDEWEB) Liu, Qing; Shi, Chaowei [Hefei National Laboratory for Physical Sciences at The Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Yu, Lu [Hefei National Laboratory for Physical Sciences at The Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui, 230026 (China); High Magnetic Field Laboratory, Chinese Academy of Science, Hefei, Anhui, 230031 (China); Zhang, Longhua [Hefei National Laboratory for Physical Sciences at The Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Xiong, Ying, E-mail: yxiong73@ustc.edu.cn [Hefei National Laboratory for Physical Sciences at The Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui, 230026 (China); Tian, Changlin, E-mail: cltian@ustc.edu.cn [Hefei National Laboratory for Physical Sciences at The Microscale and School of Life Sciences, University of Science and Technology of China, Hefei, Anhui, 230026 (China); High Magnetic Field Laboratory, Chinese Academy of Science, Hefei, Anhui, 230031 (China) 2015-02-13 Internal backbone dynamic motions are essential for different protein functions and occur on a wide range of time scales, from femtoseconds to seconds. Molecular dynamic (MD) simulations and nuclear magnetic resonance (NMR) spin relaxation measurements are valuable tools to gain access to fast (nanosecond) internal motions. However, there exist few reports on correlation analysis between MD and NMR relaxation data. Here, backbone relaxation measurements of {sup 15}N-labeled SH3 (Src homology 3) domain proteins in aqueous buffer were used to generate general order parameters (S{sup 2}) using a model-free approach. Simultaneously, 80 ns MD simulations of SH3 domain proteins in a defined hydrated box at neutral pH were conducted and the general order parameters (S{sup 2}) were derived from the MD trajectory. Correlation analysis using the Gromos force field indicated that S{sup 2} values from NMR relaxation measurements and MD simulations were significantly different. MD simulations were performed on models with different charge states for three histidine residues, and with different water models, which were SPC (simple point charge) water model and SPC/E (extended simple point charge) water model. S{sup 2} parameters from MD simulations with charges for all three histidines and with the SPC/E water model correlated well with S{sup 2} calculated from the experimental NMR relaxation measurements, in a site-specific manner. - Highlights: • Correlation analysis between NMR relaxation measurements and MD simulations. • General order parameter (S{sup 2}) as common reference between the two methods. • Different protein dynamics with different Histidine charge states in neutral pH. • Different protein dynamics with different water models. 12. Biological Nitrogen Fixation and Microbial Biomass N in the Rhizosphere of Chickpea as Estimated by 15N Isotope Dilution Technique International Nuclear Information System (INIS) Pot experiment was carried out with chickpea that cultivated in virgin sandy soil and inoculated with Rhizobium (Rh), mycorrhizea (VAM) and mixture of both. The objective of this work is the estimation of biological nitrogen fixation (BNF) and microbial biomass N (MBN) contribution as affected by inoculation and N and P fertilizers levels under chickpea plants. Nitrogen gained from air (Ndf A) was determined using 15N isotope dilution technique, while the MBN was detected through the fumigation-extraction method. Nitrogen and phosphorus fertilizers were applied at three levels, 0; 10 ppm N and 3.3 ppm P and 20 ppm Nand 6.6 ppm P in the form of (15NH4)2SO4 and super-phosphate, respectively. The effect of inoculation and chemical fertilizers on dry matter (DM), N and P uptake (shoot and grain), BNF and MBN were traced. The obtained data revealed that the highest DM and N uptake by chickpea shoot were recorded with the dual inoculation (Rh + VAM) at the moderate level of N and P fertilizers, while the highest DM, N and P uptake by grain were recorded with Rh solely at the same rate of fertilizers. It was clear that inoculation with Rh either alone or in combination with VAM substituted considerable amounts of N via BNF process. In this respect, dual inoculation is still superior over single inoculation. Percentages of N2-fixed was ranged from 45% to 73% in shoot while it was 27% to 69% in grain according to inoculation and fertilization treatments. Fixed N utilized by shoot was positively affected by increasing the N fertilizer rate while that derived by grain was not affected. The fluctuation in the soil microbial biomass N did not gave us a chance to recognize, exactly, the impact of inoculation and/or fertilization levels. (Authors) 13. O potencial da rotulação metabólica de 15N para a pesquisa de esquizofrenia The potential of 15N metabolic labeling for schizophrenia research Directory of Open Access Journals (Sweden) Michaela D. Filiou 2013-01-01 Full Text Available Pesquisas em psiquiatria ainda necessitam de estudos não dirigidos por hipóteses para revelar fundamentos neurobiológicos e biomarcadores moleculares para distúrbios psiquiátricos. Metodologias proteômicas disponibilizam uma série de ferramentas para esses fins. Apresentamos o princípio de rotulação metabólica utilizando 15N para proteômica quantitativa e suas aplicações em modelos animais de fenótipos psiquiátricos com um foco particular em esquizofrenia. Exploramos o potencial de rotulação metabólica por 15N em diferentes tipos de experimentos, bem como suas considerações metodológicas.Psychiatric research is in need of non-hypothesis driven approaches to unravel the neurobiological underpinnings and identify molecular biomarkers for psychiatric disorders. Proteomics methodologies constitute a state-of-the-art toolbox for biomarker discovery in psychiatric research. Here we present the principle of in vivo 15N metabolic labeling for quantitative proteomics experiments and applications of this method in animal models of psychiatric phenotypes, with a particular focus on schizophrenia. Additionally we explore the potential of 15N metabolic labeling in different experimental set-ups as well as methodological considerations of 15N metabolic labeling-based quantification studies. 14. Nitrogen and water utilization by trickle fertigated garlic using the neutron gauge and 15N technologies International Nuclear Information System (INIS) The objective of this study was to increase water and fertilizer use efficiency for conventional fertilization and fertigation. The following treatments were included and studied in an RCB design with four replications of each treatment: Zero N, 30, 60 and 90 ppm N in the irrigation water. Additional soil application equivalent to one fertigation treatment was also included. The fertilizers were injected into the irrigation water by means of an injection pump. Garlic was planted in plot with dimensions of 3mx4.5m. Irrigation was applied to replenish 80% of the Class A pan evaporation on a weekly bases. Access tubes for neutron probe reading were mounted in each plot in three replications. The readings were taken before and after each irrigation or rainfall at 15, 30, 45, 60 and 90 cm soil depth. The labelled N fertilizers (15N) were applied to microplots which contained five plants within each plot. At harvest, plant samples were taken from the microplots for the 15N measurements. Plant samples were collected and prepared according to the instructions for sampling for 15N analysis. The yield and its components were obtained from the macroplot. The yield continued to increase with increasing N fertigation rates. The fresh weight per head and per segment showed a similar trend as the yield did. However, the number of segments per head was not affected significantly by the investigated treatments in this study. This may indicate that the zero N treatments produced heads with small segments compared to that produced with N application. The dry weight of shoot, segment and segment membrane responded positively to the rates of N fertigation, reaching the maximum value at the rates of 80 and 120 kg N, irrespective of N fertigation or soil application. The soil application gave a production as high as the best fertigated N rate but lower than the zero N treatment. The percentage of N content in fruits and leaves was the highest with the fertigation treatments where the 15. Constructing Battery-Aware Virtual Backbones in Wireless Sensor Networks Directory of Open Access Journals (Sweden) Chi Ma 2007-05-01 Full Text Available A critical issue in battery-powered sensor networks is to construct energy efficient virtual backbones for network routing. Recent study in battery technology reveals that batteries tend to discharge more power than needed and reimburse the over-discharged power if they are recovered. In this paper we first provide a mathematical battery model suitable for implementation in sensor networks. We then introduce the concept of battery-aware connected dominating set (BACDS and show that in general the minimum BACDS (MBACDS can achieve longer lifetime than the previous backbone structures. Then we show that finding a MBACDS is NP-hard and give a distributed approximation algorithm to construct the BACDS. The resulting BACDS constructed by our algorithm is at most (8+ÃŽÂ”opt size, where ÃŽÂ” is the maximum node degree and opt is the size of an optimal BACDS. Simulation results show that the BACDS can save a significant amount of energy and achieve up to 30% longer network lifetime than previous schemes. 16. A phylogenetic backbone for Bivalvia: an RNA-seq approach. Science.gov (United States) González, Vanessa L; Andrade, Sónia C S; Bieler, Rüdiger; Collins, Timothy M; Dunn, Casey W; Mikkelsen, Paula M; Taylor, John D; Giribet, Gonzalo 2015-02-22 Bivalves are an ancient and ubiquitous group of aquatic invertebrates with an estimated 10 000-20 000 living species. They are economically significant as a human food source, and ecologically important given their biomass and effects on communities. Their phylogenetic relationships have been studied for decades, and their unparalleled fossil record extends from the Cambrian to the Recent. Nevertheless, a robustly supported phylogeny of the deepest nodes, needed to fully exploit the bivalves as a model for testing macroevolutionary theories, is lacking. Here, we present the first phylogenomic approach for this important group of molluscs, including novel transcriptomic data for 31 bivalves obtained through an RNA-seq approach, and analyse these data with published genomes and transcriptomes of other bivalves plus outgroups. Our results provide a well-resolved, robust phylogenetic backbone for Bivalvia with all major lineages delineated, addressing long-standing questions about the monophyly of Protobranchia and Heterodonta, and resolving the position of particular groups such as Palaeoheterodonta, Archiheterodonta and Anomalodesmata. This now fully resolved backbone demonstrates that genomic approaches using hundreds of genes are feasible for resolving phylogenetic questions in bivalves and other animals. 17. Studies on the protein and amino acid metabolism of laying hens using 15N-labelled casein. 8 International Nuclear Information System (INIS) Four colostomized Leghorn hens were fed, during 6 days, 15N-labelled casein as sole protein source. Two animals were slaughtered 48 hours, the other two 144 hours after the last 15N-application. The share of TCE-soluble N in total N averaged 16% for the body parts analysed, i.e. meat, bone, liver, kidneys, oviducts, residual viscera and other. The variation of the lysine, histidine and arginine levels in the body parts ranged from 3.6 to 7.9 g, 1.1 to 3.7 g and 6.4 to 7.4 g in 16.7 g hydrolysate N, respectively. Except for feathers, the analysed body parts contained an excess amount of heavy nitrogen. The degree of labelling was found to depend on the time of slaughtering after the tracer application. In the liver and in the oviduct being metabolically active organs, the 15N-excess in the total N fraction decreased by 45% between the 2nd and the 6th days after 15N-feeding, whilst in the meat it went down by 20%. The decline of the 15N-concentration in the TCE-soluble N compounds was faster than in the total N-fraction. Out of the body samples analysed, the lysine of the liver having 0.26 atom% 15N-excess was found to be more strongly labelled in hens 1 and 2. The amino acid arginine reached about the same level of labelling, the 15N-frequency of histidine being the lowest. (author) 18. Deformation of redox-active polymer gel based on polysiloxane backbone and bis(benzodithiolyl)bithienyl scaffold. Science.gov (United States) Ohtake, Toshihiro; Tanaka, Hideki; Matsumoto, Tetsuro; Ohta, Akira; Kimura, Mutsumi 2014-12-01 Redox-active polymer gels consisting of polysiloxane backbone and bis(benzodithiolyl)bithienyl units have been designed and synthesized. The bis(benzodithiolyl)bithienyl units, which undergo interconversion between cyclic form and opened dicationic form, have been incorporated into polysiloxane backbone via hydrosilylation of vinyl-terminated bis(benzodithiolyl)bithienyl derivative and poly(methylhydrosiloxane) (PMHS) or poly(dimethylsiloxane-co-hydrogenmethylsiloxane) (PDMS-co-PMHS), resulting in polymer gels cross-linked with bis(benzodithiolyl)bithienyl units. After the incorporation of M1 into polysiloxane backbone, these polymer gels (P1 and P2) also exhibit redox responses associated with the electrochemical interconversion of the bis(benzodithiolyl)bithienyl moieties. The polymer gels show swelling behavior upon chemical oxidization, and bending behavior has been observed for the polymer gel immobilized poly(vinylidene difluoride) (PVdF) film. These results provide a useful perspective for fabricating redox-triggered polymer gel actuators based on the conformational change of the functional molecular unit. PMID:25400032 19. Spin and parity determinations of excited 15N based on polarized and unpolarized 12C(7Li, α)15N reaction data at E lab = 34 MeV International Nuclear Information System (INIS) From an experiment conducted at the Florida State University Accelerator Laboratory with a 34 MeV polarized 7Li beam bombarding a 12C target, we have obtained angular distributions and analyzing powers for states of 15N up to 20 MeV in excitation energy. This study not only offers the possibility to assign spin and parity to several states in 15N, but also serves to obtain nuclear potential parameters used in Distorted Wave Born (DWBA) and Coupled Channel Born (CCBA) Approximations to generate theoretical angular distributions and vector analyzing powers that give the best description of the experimental data. Under the assumption that the reaction mechanism is a three nucleon transfer, the determination of shell model nucleonic configurations and spectroscopic factors is possible for the 15N states studied 20. STELLAR ORIGINS OF EXTREMELY {sup 13}C- AND {sup 15}N-ENRICHED PRESOLAR SIC GRAINS: NOVAE OR SUPERNOVAE? Energy Technology Data Exchange (ETDEWEB) Liu, Nan; Nittler, Larry R.; Alexander, Conel M. O’D.; Wang, Jianhua [Department of Terrestrial Magnetism, Carnegie Institution for Science, Washington, DC 20015 (United States); Pignatari, Marco [E.A. Milne Centre for Astrophysics, Department of Physics and Mathematics, University of Hull, HU6 7RX (United Kingdom); José, Jordi [Department de Fisica, EUETIB, Universitat Politécnica de Catalunya, E-08036 Barcelona (Spain); Nguyen, Ann, E-mail: nliu@carnegiescience.edu [Robert M. Walker Laboratory for Space Science, Astromaterials Research and Exploration Science Directorate, NASA Johnson Space Center, Houston, TX 77058 (United States) 2016-04-01 Extreme excesses of {sup 13}C ({sup 12}C/{sup 13}C < 10) and {sup 15}N ({sup 14}N/{sup 15}N < 20) in rare presolar SiC grains have been considered diagnostic of an origin in classical novae, though an origin in core collapse supernovae (CCSNe) has also been proposed. We report C, N, and Si isotope data for 14 submicron- to micron-sized {sup 13}C- and {sup 15}N-enriched presolar SiC grains ({sup 12}C/{sup 13}C < 16 and {sup 14}N/{sup 15}N < ∼100) from Murchison, and their correlated Mg–Al, S, and Ca–Ti isotope data when available. These grains are enriched in {sup 13}C and {sup 15}N, but with quite diverse Si isotopic signatures. Four grains with {sup 29,30}Si excesses similar to those of type C SiC grains likely came from CCSNe, which experienced explosive H burning occurred during explosions. The independent coexistence of proton- and neutron-capture isotopic signatures in these grains strongly supports heterogeneous H ingestion into the He shell in pre-supernovae. Two of the seven putative nova grains with {sup 30}Si excesses and {sup 29}Si depletions show lower-than-solar {sup 34}S/{sup 32}S ratios that cannot be explained by classical nova nucleosynthetic models. We discuss these signatures within the CCSN scenario. For the remaining five putative nova grains, both nova and supernova origins are viable because explosive H burning in the two stellar sites could result in quite similar proton-capture isotopic signatures. Three of the grains are sub-type AB grains that are also {sup 13}C enriched, but have a range of higher {sup 14}N/{sup 15}N. We found that {sup 15}N-enriched AB grains (∼50 < {sup 14}N/{sup 15}N < ∼100) have distinctive isotopic signatures compared to putative nova grains, such as higher {sup 14}N/{sup 15}N, lower {sup 26}Al/{sup 27}Al, and lack of {sup 30}Si excess, indicating weaker proton-capture nucleosynthetic environments. 1. delta 15N and non-carbonate delta 13C values for two petroleum source rock reference materials and a marine sediment reference material Science.gov (United States) Dennen, Kristin O.; Johnson, Craig A.; Otter, Marshall L.; Silva, Steven R.; Wandless, Gregory A. 2006-01-01 Samples of United States Geological Survey (USGS) Certified Reference Materials USGS Devonian Ohio Shale (SDO-1), and USGS Eocene Green River Shale (SGR-1), and National Research Council Canada (NRCC) Certified Marine Sediment Reference Material (PACS-2), were sent for analysis to four separate analytical laboratories as blind controls for organic rich sedimentary rock samples being analyzed from the Red Dog mine area in Alaska. The samples were analyzed for stable isotopes of carbon (delta13Cncc) and nitrogen (delta15N), percent non-carbonate carbon (Wt % Cncc) and percent nitrogen (Wt % N). SDO-1, collected from the Huron Member of the Ohio Shale, near Morehead, Kentucky, and SGR-1, collected from the Mahogany zone of the Green River Formation are petroleum source rocks used as reference materials for chemical analyses of sedimentary rocks. PACS-2 is modern marine sediment collected from the Esquimalt, British Columbia harbor. The results presented in this study are, with the exceptions noted below, the first published for these reference materials. There are published information values for the elemental concentrations of 'organic' carbon (Wt % Corg measured range is 8.98 - 10.4) and nitrogen (Wt % Ntot 0.347 with SD 0.043) only for SDO-1. The suggested values presented here should be considered 'information values' as defined by the NRCC Institute for National Measurement Reference Materials and should be useful for the analysis of 13C, 15N, C and N in organic material in sedimentary rocks. 2. 13C and 15N natural isotope abundance reflects breast cancer cell metabolism Science.gov (United States) Tea, Illa; Martineau, Estelle; Antheaume, Ingrid; Lalande, Julie; Mauve, Caroline; Gilard, Francoise; Barillé-Nion, Sophie; Blackburn, Anneke C.; Tcherkez, Guillaume 2016-01-01 Breast cancer is the most common cancer in women worldwide. Despite the information provided by anatomopathological assessment and molecular markers (such as receptor expression ER, PR, HER2), breast cancer therapies and prognostics depend on the metabolic properties of tumor cells. However, metabolomics have not provided a robust and congruent biomarker yet, likely because individual metabolite contents are insufficient to encapsulate all of the alterations in metabolic fluxes. Here, we took advantage of natural 13C and 15N isotope abundance to show there are isotopic differences between healthy and cancer biopsy tissues or between healthy and malignant cultured cell lines. Isotope mass balance further suggests that these differences are mostly related to lipid metabolism, anaplerosis and urea cycle, three pathways known to be impacted in malignant cells. Our results demonstrate that the isotope signature is a good descriptor of metabolism since it integrates modifications in C partitioning and N excretion altogether. Our present study is thus a starting point to possible clinical applications such as patient screening and biopsy characterization in every cancer that is associated with metabolic changes. PMID:27678172 3. Tracking the incorporation of 15N from labeled beech litter into mineral-organic associations Science.gov (United States) Kleber, M.; Hatton, P.; Derrien, D.; Lajtha, K.; Zeller, B. 2008-12-01 Nitrogen containing organic compounds are thought to have a role in the complex web of processes that control the turnover time of soil organic matter. The sequential density fractionation technique is increasingly used for the purpose of investigating the association of organic materials with the mineral matrix. Organic materials in the denser fractions (>2.0 kg L-1) typically show 13C NMR signals indicative of carbohydrate and aliphatic structures, an absence of lignin and tannin structures and a narrow C:N ratio, suggesting a microbial origin of organic matter in these fractions. Here we take advantage of a labeling experiment conducted at two different sites in Germany and in France to investigate the incorporation of organic nitrogen into physical fractions of increasing density, representing a proximity gradient to mineral surfaces. 15N labeled beech litter was applied to two acidic forest topsoils 8 and 12 years ago. Although there are differences in the distribution patterns between the two soils, and the majority of the organic nitrogen was recovered in fractions representing organic matter of plant origin and not bound to the mineral matrix, our data clearly show that after a decade, significant amounts of the nitrogen had been incorporated in mineral-organic fractions of supposedly slow turnover. It remains to be shown to which extent the N in the densest fractions was incorporated by soil microbiota and associated with mineral surfaces in organic form or adsorbed to mineral surfaces in inorganic form (NH4+). 4. Use of 15N in nitrification inhibitor studies with special reference to indigenous materials International Nuclear Information System (INIS) Non-edible oil seed cakes and their constituents have been advantageously used for increasing the efficiency of fertilizer nitrogen (N) for crop production. The beneficial effects of these materials have been attributed to retardation of nitrification, which lessen the loss of N associated with nitrification by leaching and denitrification in situations where these losses are high. However, it is possible that some of the effects of these materials could be due to immobilization-remineralization of N particularly when the carbonaceous materials are added with fertilizers at high rates. A methodology involving the use of 15N-labelled fertilizers is advanced to sort out whether the beneficial effects of non-edible oil seed cakes and other materials are due to retardation of nitrification and or immobilization-remineralization of fertilizer N. Using the proposed technique it would be possible to make realistic evaluation of the wealth of indigenous products as nitrification inhibitors. Following the proposed approach it would also be possible to widen the scope and depth of research in this area for ultimately better exploitation of indigenous materials as nitrification inhibitors. (author). 18 refs 5. Partitioning of 15N labelled mineral nitrogen in Acacia and coconut International Nuclear Information System (INIS) Many of the coconut plantations in Cote d'Ivoire have deteriorated owing to loss of legume ground cover and soil fertility. It has not been possible to restore the ground cover but tree legumes have been proposed as an alternative to rejuvenate the soil and at the same time provide a source of fuel wood. Experiments were undertaken to provide background information that will be needed in evaluating the ability of Acacia trees to increase soil N and contribute N to coconut. Partitioning of N in four-year-old coconut and Acacia trees was measured six months after application of 15N labelled ammonium sulphate to the soil. The results showed that the labelled N was distributed throughout both tree types. The highest concentration of label was located in tissues that were actively growing during the six months after N application but a considerable amount of N was also contained in tissues that were physiologically mature. Approximately half of the dry matter of legume trees was contained in the woody tissue but most of the N was contained in the green portion of the trees. It appears that the legume trees could potentially be used as a source of fuel wood and still be useful in increasing the N and organic matter content of the soil. (author). 9 refs, 5 figs 6. Simultaneous quantification of depolymerization and mineralization rates by a novel 15N tracing model Science.gov (United States) Andresen, Louise C.; Björsne, Anna-Karin; Bodé, Samuel; Klemedtsson, Leif; Boeckx, Pascal; Rütting, Tobias 2016-09-01 The depolymerization of soil organic matter, such as proteins and (oligo-)peptides, into monomers (e.g. amino acids) is currently considered to be the rate-limiting step for nitrogen (N) availability in terrestrial ecosystems. The mineralization of free amino acids (FAAs), liberated by the depolymerization of peptides, is an important fraction of the total mineralization of organic N. Hence, the accurate assessment of peptide depolymerization and FAA mineralization rates is important in order to gain a better process-based understanding of the soil N cycle. In this paper, we present an extended numerical 15N tracing model Ntrace, which incorporates the FAA pool and related N processes in order to provide a more robust and simultaneous quantification of depolymerization and gross mineralization rates of FAAs and soil organic N. We discuss analytical and numerical approaches for two forest soils, suggest improvements of the experimental work for future studies, and conclude that (i) when about half of all depolymerized peptide N is directly mineralized, FAA mineralization can be as important a rate-limiting step for total gross N mineralization as peptide depolymerization rate; (ii) gross FAA mineralization and FAA immobilization rates can be used to develop FAA use efficiency (NUEFAA), which can reveal microbial N or carbon (C) limitation. 7. Fate of nitrogen ({sup 15}N) from velvet bean in the soil-plant system Energy Technology Data Exchange (ETDEWEB) Scivittaro, Walkyria Bueno [Empresa Brasileira de Pesquisa Agropecuaria, Pelotas, RS (Brazil). Clima Temperado; Muraoka, Takashi; Boaretto, Antonio Enedi; Trivelin, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura, Piracicaba, SP (Brazil). Lab. de Fertilidade do Solo]. E-mail: wbscivit@cpact.embrapa.br 2004-04-01 Because of their potential for N{sub 2} biological fixation, legumes are an alternative source of nitrogen to crops, and can even replace or supplement mineral fertilization. A greenhouse experiment was carried out to evaluate temporal patterns of velvet bean (Mucuna aterrima) green manure release of nitrogen to rice plants, and to study the fate of nitrogen from velvet bean in rice cultivation. The isotopic dilution methodology was used. Treatments consisted of a control and 10 incubation periods of soil fertilized with {sup 15}N-labeled velvet bean (0, 20, 40, 60, 90, 120, 150, 180, 210, and 240 days). The plant material was previously chopped, sifted (10 mm mesh sieve) and oven-dried (65 deg C). Incubation of the plant material (2.2 g kg{sup -1} soil) was initiated by the longest period, in order to synchronize the planting of the test crop, rice (Oryza sativa), at time zero for all treatments. Green manure incorporation promoted increases in rice dry matter yield and nitrogen uptake. These variables showed maximum values at incubation periods of 38 and 169 days, respectively. Green manure nitrogen utilization by rice plants was highest at an incubation period corresponding to 151 days. More than 60% of the green manure nitrogen remained in the soil after rice cultivation. The highest green manure nitrogen recovery from the soil-plant system occurred at an incubation period equivalent to 77 days. (author) 8. 4-Oxalocrotonate tautomerase, a 41-kDa homohexamer: backbone and side-chain resonance assignments, solution secondary structure, and location of active site residues by heteronuclear NMR spectroscopy. OpenAIRE Stivers, J T; Abeygunawardana, C; Whitman, C. P.; Mildvan, A. S. 1996-01-01 4-Oxalocrotonate tautomerase (4-OT), a homohexamer consisting of 62 residues per subunit, catalyzes the isomerization of unsaturated alpha-keto acids using Pro-1 as a general base (Stivers et al., 1996a, 1996b). We report the backbone and side-chain 1H, 15N, and 13C NMR assignments and the solution secondary structure for 4-OT using 2D and 3D homonuclear and heteronuclear NMR methods. The subunit secondary structure consists of an alpha-helix (residues 13-30), two beta-strands (beta 1, residu... 9. Elucidating the trophodynamics of four coral reef fishes of the Solomon Islands using δ15N and δ13C Science.gov (United States) Greenwood, N. D. W.; Sweeting, C. J.; Polunin, N. V. C. 2010-09-01 Size-related diet shifts are important characteristics of fish trophodynamics. Here, body size-related changes in muscle δ15N and δ13C of four coral reef fishes, Acanthurus nigrofuscus (herbivore), Chaetodon lunulatus (corallivore) , Chromis xanthura (planktivore) and Plectropomus leopardus (piscivore) were investigated at two locations in the Solomon Islands. All four species occupied distinct isotopic niches and the concurrent δ13C' values of C. xanthura and P. leopardus suggested a common planktonic production source. Size-related shifts in δ15N, and thus trophic level, were observed in C. xanthura, C. lunulatus and P. leopardus, and these trends varied between location, indicating spatial differences in trophic ecology. A literature review of tropical fishes revealed that positive δ15N-size trends are common while negative δ15N-size trends are rare. Size-δ15N trends fall into approximately equal groups representing size-based feeding within a food chain, and that associated with a basal resource shift and occurs in conjunction with changes in production source, indicated by δ13C. The review also revealed large scale differences in isotope-size trends and this, combined with small scale location differences noted earlier, highlights a high degree of plasticity in the reef fishes studied. This suggests that trophic size analysis of reef fishes would provide a productive avenue to identify species potentially vulnerable to reef impacts as a result of constrained trophic behaviour. 10. The use of 15N-labelled dinitrogen in the study of nitrogen fixation by blue-green algae International Nuclear Information System (INIS) Prior to the development of the acetylene reduction technique 15N was used as the main qualitative and quantitative measure of nitrogen fixation by free-living cyanobacteria in a variety of aquatic and terrestrial habitats. Despite its expense and the technical difficulty, 15N is a major tool in the study of cyanobacteria, for example, incorporation of 15N2 is the definitive test for nitrogen fixation; it is used in the determination of the correct ratio of acetylene reduction to nitrogen fixation, in in situ nitrogen fixation assays, in tracing the formation and fate of extra-cellular nitrogen and in measuring the turnover and grazing rates of cyanobacterial intra-cellular nitrogen. These latter studies show that 15N-labelled extra-cellular nitrogen can serve as nitrogen sources for a variety of bacteria, fungi, algae and higher plants, and that cyanobacteria are graced and digested by a variety of animals. The turnover rates of cyanobacterial 15N-labelled cells are dependent on the type of cell, species, environmental conditions and the availability of degrading organisms. The breakdown products are rapidly mineralised and used as nitrogen sources by higher plants. (author) 11. Evaluation of a 15 N plot design for estimating plant recovery of fertilizer nitrogen applied to sugar cane International Nuclear Information System (INIS) Two experiments were conducted on commercial sugar cene fields cropped with the variety SP70-1143, with the objective of evaluating a single row microplot design to determine plant recovery of 15 N fertilizer nitrogen. One of them used 15 N-aqua ammonia and 15 N-urea applied to two linear meter microplots of a ratoon crop (four replicates.) The second used one linear meter microplots (three replicates) which received 15 N-aqua ammonia only. The fertilizers were applied on 15cm deep furrows, located 25 cm from both sides of the cane row. One linear meter of ratoon cane, inside and outside of the microplot, and on the same and adjacent rows were harvested twelve months after fertilization. The results indicate the feasibility of using single row regments of ratoon cane with 15 N-fertilizer. The main advantages of this microplot design, when compared to the classical 3 contiguous row segments, is that only one third of the labeled fertilizer is needed. (author). 25 refs, 3 figs, 5 tabs 12. Photosynthetic 14CO2 fixation and [15N]-ammonia assimilation during UV-B radiation of Lithodesmium variabile International Nuclear Information System (INIS) Uptake of [15N]-ammonia was more sensitive to UV-B exposure than the total 14CO2 fixation rate of Lithodesmium variabile Takano. Short-term UV-B radiation (15 min) had practically no effect on the kinetics of [15N]-ammonia, whereas there was an effect on [14C]-bicarbonate uptake rate. A significant reduction was found after 30 and 60 min UV-B stress. The time course of photosynthetic uptake of 15NH4Cl at several wavelengths was markedly depressed at shorter wavelengths (irradiation with WG 280). A short-term (11 min) exposure to ultraviolet radiation had no influence on the [14C]-labeled photosynthetic products. However, the [15N]-label of several amino acids and the ratio of [15N]-glutamine to [15N]-glutamic acid varied after irradiation with different ultraviolet wavebands. The results are discussed with reference to UV damage to the key enzymes of nitrogen metabolism. (author) 13. Use of 15N enriched plant material for labelling of soil nitrogen in legume dinitrogen fixation experiments International Nuclear Information System (INIS) The soil nitrogen in a field plot was labelled with nitrogen-15 (15N) by incorporating labelled plant material derived from previous experiments. The plot was used the following 3 years for determination of the amount of N2 fixed by different leguminous plants. The atom % 15N excess in grains of cereals grown as reference crops was 0.20, 0.05 and 0.03 in the 3 years, respectively. In the first year the level of enrichment was adequate for estimating symbiotic nitrogen fixation. In the second and third year lack of precision in determination of the 15N/14N ratios of legume N, may have caused an error in estimates of nitrogen fixation. About 23% of the labelled N was taken up by plants during the 3 years of cropping; after 4 years about 44% of the labelled N was found still to be present in the top soil. The labelling of the soil nitrogen with organic bound 15N, compared to adding mineral 15N at sowing, is advantageous because the labelled N is released by mineralization so that the enrichment of the plant available soil N pool become more uniform during the growth season; and high levels of mineral N, which may depress the fixation process, is avoided. (author) 7 tabs., 1 ill., 30 refs 14. Stellar Origins of Extremely $^{\\text{13}}C$- and $^{15}N$-enriched Presolar SiC Grains: Novae or Supernovae? CERN Document Server Liu, Nan; Alexander, Conel M O'D; Wang, Jianhuan; Pignatari, Marco; Jose, Jordi; Nguyen, Ann 2016-01-01 Extreme excesses of $^{13}C$ ($^{12}C$/$^{13}C$<10) and $^{15}N$ ($^{14}N$/$^{15}N$<20) in rare presolar SiC grains have been considered diagnostic of an origin in classical novae, though an origin in core collapse supernovae (CCSNe) has also been proposed. We report C, N, and Si isotope data for 14 submicron- to micron-sized $^{13}C$- and $^{15}N$-enriched presolar SiC grains ($^{12}C$/$^{13}C$<16 and $^{14}N$/$^{15}N$<~100) from Murchison, and their correlated Mg-Al, S, and Ca-Ti isotope data when available. These grains are enriched in $^{13}C$ and $^{15}N$, but with quite diverse Si isotopic signatures. Four grains with $^{29,30}Si$ excesses similar to those of type C SiC grains likely came from CCSNe, which experienced explosive H burning occurred during explosions. The independent coexistence of proton- and neutron-capture isotopic signatures in these grains strongly supports heterogeneous H ingestion into the He shell in pre-supernovae. Two of the seven putative nova grains with $^{30}Si$ e... 15. Evaluation of N sub 2 fixation by applying sup 15 N labeled plant material and ammonium sulfate Energy Technology Data Exchange (ETDEWEB) Chiu, C.Y.; Yoshida, T. 1990-06-01 Effect of different {sup 15}N labeled sources on the estimation of N{sub 2} fixation was investigated. The combination of {sup 15}N labeled ammonium sulfate, {sup 15}N labeled plant material, and {sup 15}N labeled ammonium sulfate with unlabeled plant material, was examined in pot experiments. Two cultivars of soybean (Glycine max) and one of mungbean (Vigna radiata) were used. No significant difference was observed among the treatments for the estimation of N{sub 2} fixation. This was due to the homogeneity and stability of the {sup 15}N abundance in soil which resulted in a similar N uptake from the soil by the N{sub 2} fixing and reference crops. The plant yield, total N uptake and amount of N{sub 2} fixed were higher in the Yellow Soil than in the Andosol. The amount of N{sub 2} fixed was strongly influenced by the plant growth and consequently it affected the plant yield. The slow decomposition of plant material in the Andosol resulted in a low yield in both the N{sub 2} fixing and reference crops. Thus, the artificial decrease of the available N content in soil, by application of plant material, did not stimulate N{sub 2} fixation but suppressed plant growth and N{sub 2} fixation. 16. δ 15N Studies of Nitrogen Use by the Red Mangrove, Rhizophora mangle L. in South Florida Science.gov (United States) Fry, B.; Bern, A. L.; Ross, M. S.; Meeder, J. F. 2000-02-01 To help define nitrogen (N) sources and patterns of N processing in mangrove ecosystems, mangrove leaf nitrogen contents and δ 15N values were assayed in three marshes along the south Florida coast. In each marsh, leaf samples were collected from dwarf mangroves at interior locations and taller mangroves at the ocean fringe. Leaf % N and δ 15N values did not differ consistently between dwarf and tall mangroves, even though there were large variations in δ 15N (18‰ range, -5 to +13‰) and % N (1·2% range, 0·9-2·1%). Highest % N and δ 15N values occurred along the western margin of Biscayne Bay where canals draining agricultural lands deliver high-nitrate waters to fringing mangrove marshes. High mangrove δ 15N values may be good biomonitors of anthropogenic N loading to south Florida estuaries. Lower values likely reflect less anthropogenic N entering the mangrove marshes, as well as differences in plant physiology that occur along the fringe-dwarf gradient. 17. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 5 International Nuclear Information System (INIS) 12 colostomized laying hens which received 15N-labelled wheat over 4 days were butchered 12 h, 36 h, and 108 h (3 animals each) after the last 15N application. The intake of 15N exess (15N') from the wheat amounted to 540 mg 15N' during the application period. The 15N' in the blood plasma decreased after the last 15N' application from 0.76 atom-% to 0.55 atom-% after 108 h, the labelling of the corpuscular components at the same measuring points increased from 0.28 to 0.50 atom-% 15N'. 96.6% of the plasma 15N' and 93,8% of that in the corpuscles is precipitable in trichloroacetic acid. The atom-% 15N' of histidine in the total blood remained unchanged in dependence on the butchering time. The 15N amount in lysine and arginine and that in the non-basic amino acids decreased inconsiderably in the period between 12 h and 108 h after the last 15N' wheat feeding. (author) 18. Tamanho da parcela para estudos de recuperação de fertilizante-15N por capim-tanzânia Plot-size for 15N-fertilizer recovery studies by tanzania-grass OpenAIRE Geraldo Bueno Martha Júnior; Paulo Cesar Ocheuze Trivelin; Moacyr Corsi 2009-01-01 O entendimento da dinâmica do N em ecossistemas de pastagens pode ser melhorado por estudos em que se utilize a técnica do traçador 15N. Nesses experimentos, deve-se assegurar que o movimento lateral do traçador não interfira nos resultados. Neste trabalho foram determinadas as exigências quanto ao tamanho da parcela para experimentos com 15N em pastagem irrigada de Panicum maximum cv. Tanzânia. Foram consideradas três intensidades de pastejo (leniente, moderada e intensa) em três épocas do a... 19. {sup 15}N/{sup 14}N isotopic ratio and statistical analysis: an efficient way of linking seized Ecstasy tablets Energy Technology Data Exchange (ETDEWEB) Palhol, Fabien; Lamoureux, Catherine; Chabrillat, Martine; Naulet, Norbert 2004-05-10 In this study, the {sup 15}N/{sup 14}N isotopic ratios of 106 samples of 3,4-methylenedioxymethamphetamine (MDMA) extracted from Ecstasy tablets are presented. These ratios, measured using gas chromatography-combustion-isotope ratio mass spectrometry (GC-C-IRMS), show a large discrimination between samples with a range of {delta}{sup 15}N values between -17 and +19%o, depending on the precursors and the method used in clandestine laboratories. Thus, {delta}{sup 15}N values can be used in a statistical analysis carried out in order to link Ecstasy tablets prepared with the same precursors and synthetic pathway. The similarity index obtained after principal component analysis and hierarchical cluster analysis appears to be an efficient way to group tablets seized in different places. 20. Seasonal δ13C and δ15N isoscapes of fish populations along a continental shelf trophic gradient Science.gov (United States) Radabaugh, Kara R.; Hollander, David J.; Peebles, Ernst B. 2013-10-01 The West Florida Shelf, located in the eastern Gulf of Mexico, transitions from a eutrophic ecosystem dominated by the Mississippi River plume to mesotrophic and oligotrophic ecosystems off the coast of peninsular Florida. Three extensive trawl surveys in this region were used to acquire samples of fish muscle, benthic algae from sea urchin stomach contents, and filtered particulate organic matter (POM) to create δ13C and δ15N isoscapes. Muscle δ15N from three widely distributed fish species, Synodus foetens (inshore lizardfish), Calamus proridens (littlehead porgy), and Syacium papillosum (dusky flounder), exhibited strong longitudinal correlations (Pearson‧s r=-0.67 to -0.90, pwaters. The δ13C depth gradient and the δ15N longitudinal gradient were consistent between seasons and years, providing a foundation for future stable isotope studies of animal migration in the Gulf of Mexico. 1. Recovery and Leaching of 15N-Labeled Coated Urea in a Lysimeter System in the North China Plain Institute of Scientific and Technical Information of China (English) LI Gui-Hua; ZHAO Lin-Ping; ZHANG Shu-Xiang; Y. HOSEN; K. YAGI3 2011-01-01 The effectiveness of polyolefin-coated urea (Meister-5 and Meister-10; CU) in a wheat (Triticum aestivum L.)-maize (Zea mays L.) rotation system was studied in lysimeter plots located in the North China Plain for three consecutive maize- wheat-maize cropping seasons.An isotopic method was used to compare the fate of CU to that of non-coated urea (NCU),and N application rates of 0,100,150 and 225 kg N ha-1 were evaluated.The results showed that the nitrogen use efficiency (15NUE) of CU was 13.3％ 21.4％ greater than that of NCU for the first crop.Alternatively,when the difference method was applied (apparent NUE),no significant variations were observed among treatments in all three seasons.Although inorganic N leached from the 1.3 m layer was less than 1％ of the total applied N,unidentified losses of 15N (losses of 15N =15N applied as fertilizer - 15N absorbed by crops - 15N remaining in the 0-0.2 m layer 15N leached from the 1.3 m layer)in CU-treated plots were 24.2％-26.5％ lower than those of NCU-treated plots.The nitrate concentration in the 0-1.3 m layer of CU plots at the end of the experiment was 53％ lower than that of NCU-treated plots.Thus,CU increased crop N uptake from fertilizer and reduced unidentified losses of applied N,which can reduce the risk of groundwater pollution. 2. A 15N-Labeling Study of the Capture of Deep Soil Nitrate from Different Plant Systems Institute of Scientific and Technical Information of China (English) YANG Zhi-xin; WANG Jue; DI Hong-jie; ZHANG Li-juan; JU Xiao-tang 2014-01-01 The objective of this study was to determine the efifciency of different plant systems in capturing deep soil nitrate (NO3-) to reduce NO3-leaching in a ifeld plot experiment using 15N labelling. The study was conducted on a calcareous alluvial soil on the North China Plains and the plant systems evaluated included alfalfa (Medicago sativa), American black poplar (Populus nigra) and cocksfoot (Dactylis). 15N-labelled N fertilizer was injected to 90 cm depth to determine the recovery of 15N by the plants. With conventional water and nutrient management, the total recovery of 15N-labeled NO3--N was 23.4% by alfalfa after two consecutive growth years. The recovery was signiifcantly higher than those by American black poplar (12.3%) and cocksfoot (11.4%). The highest proportion of soil residual 15N from the labeled fertilizer N (%Ndff) was detected around 90 cm soil depth at the time of the 1st year harvest and at 110-130 cm soil depth at time of the 2nd year harvest. Soil%Ndff in 0-80 cm depth was signiifcantly higher in the alfalfa treatment than those in all the other treatments. The soil%Ndff below 100 cm depth was much lower in the alfalfa than those in all the other treatments. These results indicated that 15N leaching losses in the alfalfa treatment were signiifcantly lower than by those in the black poplar and cocksfoot treatments, due to the higher root density located in nitrate labeling zone of soil proifle. In conclusion, alfalfa may be used as a plant to capture deep soil NO3-left from previous crops to reduce NO3-leaching in high intensity crop cultivation systems of North China Plain. 3. 15N nitrogen-balance studies in patients with testicular feminization, their relatives, and in normal subjects International Nuclear Information System (INIS) Fourteen subjects (4 with testicular feminization, 2 mothers, 1 aunt and 1 father of these patients, 2 normal women, 2 normal men and 2 normal prepubertal boys) were given 0.1 to 0.2 g/kg of 50 percent 15N-labeled NH4Cl before and after 6 daily injections of testosterone (T) 15 mg/m2). In 24-hour urine specimens collected on the test days, 15N was calculated from total N (Kjeldahl) and the percentage of 15N (mass spectrometry or 15N-analyzer Isocommerz). In all normal subjects, urinary 15N-balance was influenced positively by T (+31.3 +- 8.4 percent), in prepubertal boys more (+43 to +66 percent) than in women (+20 to +30 percent) and men (+6 to +23). In testicular feminization, 15N-balance not only failed to become more positive, but was even reduced (-24.7 +- 17.6 percent). The father of a patient had only a slight response (+7 percent) as one of the normal males, probably because of higher endogenous T-levels in adult males. One mother and the aunt had no response (-7.4 to + 1.5 percent). In the mother, the balance became slightly positive (+10 percent) on oral contraceptives. The other mother, who was on estrogen treatment prior to and during the test, had a positive but insufficient change of balance (+17 percent). It is concluded that this test allows detection of patients with testicular feminization and possibly also healthy female carriers. In these cases, estrogen treatment appears to positively influence the response to T 4. Organic vs. conventional grassland management: do (15N and (13C isotopic signatures of hay and soil samples differ? Directory of Open Access Journals (Sweden) Valentin H Klaus Full Text Available Distinguishing organic and conventional products is a major issue of food security and authenticity. Previous studies successfully used stable isotopes to separate organic and conventional products, but up to now, this approach was not tested for organic grassland hay and soil. Moreover, isotopic abundances could be a powerful tool to elucidate differences in ecosystem functioning and driving mechanisms of element cycling in organic and conventional management systems. Here, we studied the δ(15N and δ(13C isotopic composition of soil and hay samples of 21 organic and 34 conventional grasslands in two German regions. We also used Δδ(15N (δ(15N plant - δ(15N soil to characterize nitrogen dynamics. In order to detect temporal trends, isotopic abundances in organic grasslands were related to the time since certification. Furthermore, discriminant analysis was used to test whether the respective management type can be deduced from observed isotopic abundances. Isotopic analyses revealed no significant differences in δ(13C in hay and δ(15N in both soil and hay between management types, but showed that δ(13C abundances were significantly lower in soil of organic compared to conventional grasslands. Δδ(15N values implied that management types did not substantially differ in nitrogen cycling. Only δ(13C in soil and hay showed significant negative relationships with the time since certification. Thus, our result suggest that organic grasslands suffered less from drought stress compared to conventional grasslands most likely due to a benefit of higher plant species richness, as previously shown by manipulative biodiversity experiments. Finally, it was possible to correctly classify about two third of the samples according to their management using isotopic abundances in soil and hay. However, as more than half of the organic samples were incorrectly classified, we infer that more research is needed to improve this approach before it can be 5. Organic vs. Conventional Grassland Management: Do 15N and 13C Isotopic Signatures of Hay and Soil Samples Differ? Science.gov (United States) Klaus, Valentin H.; Hölzel, Norbert; Prati, Daniel; Schmitt, Barbara; Schöning, Ingo; Schrumpf, Marion; Fischer, Markus; Kleinebecker, Till 2013-01-01 Distinguishing organic and conventional products is a major issue of food security and authenticity. Previous studies successfully used stable isotopes to separate organic and conventional products, but up to now, this approach was not tested for organic grassland hay and soil. Moreover, isotopic abundances could be a powerful tool to elucidate differences in ecosystem functioning and driving mechanisms of element cycling in organic and conventional management systems. Here, we studied the δ15N and δ13C isotopic composition of soil and hay samples of 21 organic and 34 conventional grasslands in two German regions. We also used Δδ15N15N plant - δ15N soil) to characterize nitrogen dynamics. In order to detect temporal trends, isotopic abundances in organic grasslands were related to the time since certification. Furthermore, discriminant analysis was used to test whether the respective management type can be deduced from observed isotopic abundances. Isotopic analyses revealed no significant differences in δ13C in hay and δ15N in both soil and hay between management types, but showed that δ13C abundances were significantly lower in soil of organic compared to conventional grasslands. Δδ15N values implied that management types did not substantially differ in nitrogen cycling. Only δ13C in soil and hay showed significant negative relationships with the time since certification. Thus, our result suggest that organic grasslands suffered less from drought stress compared to conventional grasslands most likely due to a benefit of higher plant species richness, as previously shown by manipulative biodiversity experiments. Finally, it was possible to correctly classify about two third of the samples according to their management using isotopic abundances in soil and hay. However, as more than half of the organic samples were incorrectly classified, we infer that more research is needed to improve this approach before it can be efficiently used in practice 6. Variation of protein backbone amide resonance by electrostatic field CERN Document Server Sharley, John N 2015-01-01 Amide resonance is found to be sensitive to electrostatic field with component parallel or antiparallel the amide C-N bond. This effect is linear and without threshold in the biologically plausible electrostatic field range -0.005 to 0.005 au. Variation of amide resonance varies Resonance Assisted Hydrogen Bonding such as occurs in the hydrogen bonded chains of backbone amides of protein secondary structures such as beta sheet and non-polyproline helix such as alpha helix, varying the stability of the secondary structure. The electrostatic properties including permittivity of amino acid residue sidegroups influence the electrostatic field component parallel or antiparallel the C-N bond of each amide. The significance of this factor relative to other factors in protein folding depends on the magnitude of electrostatic field component parallel or antiparallel the C-N bond of each amide, and preliminary protein-scale calculations of the magnitude of these components suggest this factor warrants investigation in ... 7. Bioactivities of fish protein hydrolysates from defatted salmon backbones Directory of Open Access Journals (Sweden) Rasa Slizyte 2016-09-01 Full Text Available Bioactivities of bulk fish protein hydrolysates (FPH from defatted salmon backbones obtained with eight different commercial enzymes and their combinations were tested. All FPH showed antioxidative activity in vitro. DPPH scavenging activity increased, while iron chelating ability decreased with increasing time of hydrolysis. All FPH showed ACE inhibiting effect which depended on type of enzyme and increased with time of hydrolysis. The highest effect was found for FPH produced with Trypsin. Bromelain + Papain hydrolysates reduced the uptake of radiolabelled glucose into CaCo-2 cells, a model of human enterocytes, indicating a potential antidiabetic effect of FPH. FPH obtained by Trypsin, Bromelain + Papain and Protamex showed the highest ACE inhibitory, cellular glucose transporter (GLUT/SGLT inhibitory and in vitro antioxidative activities, respectively. Correlation was observed between the measured bioactivities, degree of hydrolysis and molecular weight profiles, supporting prolonged hydrolysis to obtain high bioactivities. 8. Reconstruction of the Sunspot Group Number: the Backbone Method CERN Document Server Svalgaard, Leif 2015-01-01 We have reconstructed the sunspot group count, not by comparisons with other reconstructions and correcting those where they were deemed to be deficient, but by a re-assessment of original sources. The resulting series is a pure solar index and does not rely on input from other proxies, e.g. radionuclides, auroral sightings, or geomagnetic records. 'Backboning' the data sets, our chosen method, provides substance and rigidity by using long-time observers as a stiffness character. Solar activity, as defined by the Group Number, appears to reach and sustain for extended intervals of time the same level in each of the last three centuries since 1700 and the past several decades do not seem to have been exceptionally active, contrary to what is often claimed. 9. An Unusual Conformational Isomer of Verrucosidin Backbone from a Hydrothermal Vent Fungus, Penicillium sp. Y-50-10 Directory of Open Access Journals (Sweden) Chengqian Pan 2016-08-01 Full Text Available A new verrucosidin derivative, methyl isoverrucosidinol (1, was isolated from the marine fungus Penicillium sp. Y-50-10, dwelling in sulfur rich sediment in the Kueishantao hydrothermal vents off Taiwan. The structure was established by spectroscopic means including HRMS and 2D-NMR spectroscopic analysis. The absolute configuration was defined mainly by comparison of quantum chemical TDDFT calculated and experimental ECD spectra. Among hitherto known compounds with a verrucosidine backbone isolated from natural resource, compound 1 represents the first example of a new conformational isomer of its skeleton, exhibiting antibiotic activity against Bacillus subtilis with MIC value 32 μg/mL. 10. An Unusual Conformational Isomer of Verrucosidin Backbone from a Hydrothermal Vent Fungus, Penicillium sp. Y-50-10. Science.gov (United States) Pan, Chengqian; Shi, Yutong; Auckloo, Bibi Nazia; Chen, Xuegang; Chen, Chen-Tung Arthur; Tao, Xinyi; Wu, Bin 2016-01-01 A new verrucosidin derivative, methyl isoverrucosidinol (1), was isolated from the marine fungus Penicillium sp. Y-50-10, dwelling in sulfur rich sediment in the Kueishantao hydrothermal vents off Taiwan. The structure was established by spectroscopic means including HRMS and 2D-NMR spectroscopic analysis. The absolute configuration was defined mainly by comparison of quantum chemical TDDFT calculated and experimental ECD spectra. Among hitherto known compounds with a verrucosidine backbone isolated from natural resource, compound 1 represents the first example of a new conformational isomer of its skeleton, exhibiting antibiotic activity against Bacillus subtilis with MIC value 32 μg/mL. PMID:27548192 11. Compound specific amino acid δ15N in marine sediments: A new approach for studies of the marine nitrogen cycle Science.gov (United States) Batista, Fabian C.; Ravelo, A. Christina; Crusius, John; Casso, Michael A.; McCarthy, Matthew D. 2014-10-01 The nitrogen (N) isotopic composition (δ15N) of bulk sedimentary N (δ15Nbulk) is a common tool for studying past biogeochemical cycling in the paleoceanographic record. Empirical evidence suggests that natural fluctuations in the δ15N of surface nutrient N are reflected in the δ15N of exported planktonic biomass and in sedimentary δ15Nbulk. However, δ15Nbulk is an analysis of total combustible sedimentary N, and therefore also includes mixtures of N sources and/or selective removal or preservation of N-containing compounds. Compound-specific nitrogen isotope analyses of individual amino acids (δ15NAA) are novel measurements with the potential to decouple δ15N changes in nutrient N from trophic effects, two main processes that can influence δ15Nbulk records. As a proof of concept study to examine how δ15NAA can be applied in marine sedimentary systems, we compare the δ15NAA signatures of surface and sinking POM sources with shallow surface sediments from the Santa Barbara Basin, a sub-oxic depositional environmental that exhibits excellent preservation of sedimentary organic matter. Our results demonstrate that δ15NAA signatures of both planktonic biomass and sinking POM are well preserved in such surface sediments. However, we also observed an unexpected inverse correlation between δ15N value of phenylalanine (δ15NPhe; the best AA proxy for N isotopic value at the base of the food web) and calculated trophic position. We used a simple N isotope mass balance model to confirm that over long time scales, δ15NPhe values should in fact be directly dependent on shifts in ecosystem trophic position. While this result may appear incongruent with current applications of δ15NAA in food webs, it is consistent with expectations that paleoarchives will integrate N dynamics over much longer timescales. We therefore propose that for paleoceanographic applications, key δ15NAA parameters are ecosystem trophic position, which determines relative partitioning of 15N 12. The analysis of 15N/14N ratios in natural samples, with emphasis on nitrate and ammonium in precipitation International Nuclear Information System (INIS) The nitrogen cycle is one of the most important of the earth's elemental cycles. The report describes the procedures used for the analysis of 15N/14N ratios in ammonium and nitrate (and organic nitrogen), and summaries without discussion the data obtained for precipitation (by rain and dust) collected at the Council for Scientific and Industrial Research site. The 15N/14N ratios of nitrogen compounds were determined on N2 gas. This was measured by means of a mass spectrometer. The isotopic analysis of organic nitrogen were conducted in two ways: Kjeldahl digestion to form ammonium, and Dumas combustion directly to N2 13. Impact of charring on cereal grain characteristics: linking prehistoric manuring practice to 15N signatures in archaeobotanical material DEFF Research Database (Denmark) Kanstrup, Marie; Thomsen, Ingrid Kaag; Mikkelsen, Peter Hambro; 2012-01-01 Systematic use of animal manure has been demonstrated to be detectable in the plant δ15N value but evidence of manure affecting isotopic composition is mainly based on studies of fresh plant material. These findings can potentially be applied to archaeobotanical assemblages and thus provide....... However, despite attempts to deliberately tamper and distort the grain δ15N signature, the changes observed in this study were too small to be of any consequences for the archaeobotanical applicability of the method. Thus the isotope method offers unique evidence about prehistoric manuring practice.... 14. Utilization of residual nitrogen (15N) from cover crop and urea by corn International Nuclear Information System (INIS) The majority of N from mineral fertilizers and cover crops is usually not used by the very next corn crop, but can be absorbed by follow-up crops. The objective of this study was to evaluate the use of residual nitrogen from urea, sunnhemp (Crotalaria juncea) and millet (Pennisetum americanum) labeled with 15N, applied to no-tillage corn in the previous growing season, in a Red Latosol of the Cerrado. The study was conducted in an experimental farm of the Sao Paulo State University (UNESP), Ilha Solteira, in Selviria county (MS), Brazil, in different areas. The experiment had a randomized complete block design, with 15 treatments and four replications. Treatments were applied to corn crop in the 2001/02 and 2003/04 growing seasons. They were distributed in a 3 x 5 factorial layout, representing the combination of three cover crops: sunnhemp, millet and spontaneous vegetation (fallow) and five N rates (as urea): 0, 30, 80, 130, and 180 kg ha-1 of N. After corn harvest, the two areas were followed in the dry season and were followed by corn crop in the 2002/03 (experiment 1) and 2003/04 (experiment 2) growing seasons, using the same fertilizer rate on all plots to distinguish the residual effect of N sources. The average use of residual N from the millet and sunnhemp residues (above-ground part) by corn crop was less than 3.5 and 3 %, respectively, of the initial amount. The corn uptake of residual N from urea increased in a quadratic manner in experiment 1 and linearly in experiment Two as a response to the applied N rates, and the recover was below 3 %. The cover crop type did not affect the use of residual N of urea by corn, and vice-versa. (author) 15. Studies of the endogeneous N metabolism in 15N-labelled pigs. 3 International Nuclear Information System (INIS) 4 pigs were labelled over a period of 10 days with 15N in a fishmeal diet (1), a fishmeal diet + partly hydrolyzed straw meal (2), a horse bean diet (3) and a horse bean diet + partly hydrolyzed straw meal (4). After 24 hours fasting the animals were provided with simple fistulae in the upper part of the small intestine. After a further fasting period of 24 h all four pigs received a 14C-leucine injection and the fistula secretion was collected in the subsequent 24 h. After feeding diets without straw meal (1 and 3) there were distinct differences in the secretion in compared to feeding with straw meal supplements (2 and 4) despite the long fasting period (48-72 h). 14C activity could already detected in the TCA-precipitable fraction of the secretion after 3-6 min of the injection in 1 and 3 but only 20 to 25 min after the 14C leucine injection in 2 and 4. The specific 14C-leucine activity of the TCA-soluble fraction of the secretion was, after straw meal supplementation to the fishmeal diet, 15 times higher 25 min after the 14C-leucine injection, 25 times higher after 70 min, 36 times after 2 h and 1.8 times after 4 h than without straw meal supplementation. For all four diets a specific correlation could be ascertained between the increase of 14C activity/mg N in the TCA-soluble fraction and the increasing crude fiber content in the diet between 25 and 180 min after the injection. Furthermore, a distinctly decreased N secretion/h could be ascertained with the increasing crude fiber content in the diet. The influence of the crude fiber on the parameters mentioned is seen in the changed osmotic conditions in the secretion, which may be caused by the changed regulation by hormones of the gastrointestinal tract. (author) 16. Nitrate retention and removal in Mediterranean streams with contrasting land uses: a 15N tracer study Directory of Open Access Journals (Sweden) J. L. Riera 2008-08-01 Full Text Available We used 15N-labelled nitrate (NO−3 additions to investigate nitrogen (N cycling at the whole-reach scale in three Mediterranean streams subjected to contrasting land uses (i.e. forested, urban and agricultural. Our aim was to examine: i the magnitude and relative importance of NO−3 retention (i.e. assimilatory uptake, and removal, (i.e. denitrification, ii the relative contribution of the different primary uptake compartments to NO−3 retention, and iii the regeneration, transformation and export pathways of the retained N. The concentration of NO−3 increased and that of dissolved oxygen (DO decreased from the forested to the agricultural stream, with intermediate values in the urban stream. Standing stocks of primary uptake compartments were similar among streams and dominated by detritus compartments (i.e. fine and coarse benthic organic matter. In agreement, metabolism was net heterotrophic in all streams, although the degree of heterotrophy increased from the forested to the agricultural stream. The NO−3 uptake length decreased along this gradient, whereas the NO−3 mass-transfer velocity and the areal NO−3 uptake rate were highest in the urban stream. Denitrification was not detectable in the forested stream, but accounted for 9% and 68% of total NO−3 uptake in the urban and the agricultural stream, respectively. The relative contribution of detritus compartments to NO−3 assimilatory uptake was highest in the forested and lowest in the agricultural stream. In all streams, the retained N was rapidly transferred to higher trophic levels and regenerated back to the water column. Due to a strong coupling between regeneration and nitrification, most retained N was exported from the experimental reaches in the form of NO−3. This study evidences fast N cycling in Mediterranean streams. Moreover, results indicate that permanent NO−3 removal via denitrification may be enhanced over temporary NO−3 retention via assimilatory 17. Effects of Tryptophan Content and Backbone Spacing on the Uptake Efficiency of Cell-Penetrating Peptides KAUST Repository Rydberg, Hanna A. 2012-07-10 Cell-penetrating peptides (CPPs) are able to traverse cellular membranes and deliver macromolecular cargo. Uptake occurs through both endocytotic and nonendocytotic pathways, but the molecular requirements for efficient internalization are not fully understood. Here we investigate how the presence of tryptophans and their position within an oligoarginine influence uptake mechanism and efficiency. Flow cytometry and confocal fluorescence imaging are used to estimate uptake efficiency, intracellular distribution and toxicity in Chinese hamster ovarian cells. Further, membrane leakage and lipid membrane affinity are investigated. The peptides contain eight arginine residues and one to four tryptophans, the tryptophans positioned either at the N-terminus, in the middle, or evenly distributed along the amino acid sequence. Our data show that the intracellular distribution varies among peptides with different tryptophan content and backbone spacing. Uptake efficiency is higher for the peptides with four tryptophans in the middle, or evenly distributed along the peptide sequence, than for the peptide with four tryptophans at the N-terminus. All peptides display low cytotoxicity except for the one with four tryptophans at the N-terminus, which was moderately toxic. This finding is consistent with their inability to induce efficient leakage of dye from lipid vesicles. All peptides have comparable affinities for lipid vesicles, showing that lipid binding is not a decisive parameter for uptake. Our results indicate that tryptophan content and backbone spacing can affect both the CPP uptake efficiency and the CPP uptake mechanism. The low cytotoxicity of these peptides and the possibilities of tuning their uptake mechanism are interesting from a therapeutic point of view. © 2012 American Chemical Society. 18. Effects of structural differences on the NMR chemical shifts in isostructural dipeptides. Science.gov (United States) Altheimer, Benjamin D; Mehta, Manish A 2014-04-10 Porous crystalline dipeptides have gained recent attention for their potential as gas-storage materials. Within this large class is a group of dipeptides containing alanine, valine, and isoleucine with very similar crystal structures. We report the (13)C (carbonyl and Cα) and (15)N (amine and amide) solid-state NMR isotropic chemical shifts in a series of seven such isostructural porous dipeptides as well as shift tensor data for the carbonyl and amide sites. Using their known crystal structures and aided by ab initio quantum chemical calculations for the resonance assignments, we elucidate trends relating local structure, hydrogen-bonding patterns, and chemical shift. We find good correlation between the backbone dihedral angles and the Cα1 and Cα2 shifts. For the C1 shift tensor, the δ11 value shifts downfield as the hydrogen-bond distance increases, δ22 shifts upfield, and δ33 shows little variation. The C2 shift tensor shows no appreciable correlation with structural parameters. For the N2 tensor, δ11 shows little dependence on the hydrogen-bond length, whereas δ22 and δ33 both show a decrease in shielding as the hydrogen bond shortens. Our analysis teases apart some, but not all, structural contributors to the observed differences the solid-state NMR chemical shifts. 19. Recovery of {sup 15}N-urea in soil-plant system of tanzania grass pasture; Recuperacao de {sup 15}N-ureia no sistema solo-planta de pastagem de capim-Tanzania Energy Technology Data Exchange (ETDEWEB) Martha Junior, Geraldo Bueno; Vilela, Lourival [EMBRAPA Cerrados, Planaltina, DF (Brazil)], e-mail: gbmartha@cpac.embrapa.br; Corsi, Moacyr [Universidade de Sao Paulo (ESALQ/USP), Piracicaba, SP (Brazil). Escola Superior de Agricultura Luiz de Queiroz. Dept. de Zootecnica], e-mail: moa@esalq.usp.br; Trivelin, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura (CENA/USP), Piracicaba, SP (Brazil). Lab. de Isotopos Estaveis], e-mail: pcotrive@cena.usp.br 2009-01-15 The economic attractiveness and negative environmental impact of nitrogen (N) fertilization in pastures depend on the N use efficiency in the soil-plant system. However, the recovery of urea-{sup 15}N by Panicum maximum cv. Tanzania pastures, one of the most widely used forage species in intensified pastoral systems, is still unknown. This experiment was conducted in a randomized complete block design with four treatments (0, 40, 80 and 120 kg ha-1 of N-urea) and three replications, to determine the recovery of {sup 15}N urea by Tanzania grass. Forage production, total N content and N yield were not affected by fertilization (p > 0.05), reflecting the high losses of applied N under the experimental conditions. The recovery of {sup 15}N urea (% of applied N) in forage and roots was not affected by fertilization levels (p > 0.05), but decreased exponentially in the soil and soil-plant system (p < 0.05) with increasing urea doses. The amount of {sup 15}N (kg ha{sup -1}) in forage and roots (15 to 30 cm) increased with increasing urea doses (p < 0.05). (author) 20. Thin Films Formed from Conjugated Polymers with Ionic, Water-Soluble Backbones. Science.gov (United States) Voortman, Thomas P; Chiechi, Ryan C 2015-12-30 This paper compares the morphologies of films of conjugated polymers in which the backbone (main chain) and pendant groups are varied between ionic/hydrophilic and aliphatic/hydrophobic. We observe that conjugated polymers in which the pendant groups and backbone are matched, either ionic-ionic or hydrophobic-hydrophobic, form smooth, structured, homogeneous films from water (ionic) or tetrahydrofuran (hydrophobic). Mismatched conjugated polymers, by contrast, form inhomogeneous films with rough topologies. The polymers with ionic backbone chains are conjugated polyions (conjugated polymers with closed-shell charges in the backbone), which are semiconducting materials with tunable bad-gaps, not unlike uncharged conjugated polymers. 1. Sedimentary records of δ13C, δ15N and organic matter accumulation in lakes receiving nutrient-rich mine waters International Nuclear Information System (INIS) Organic C and total N concentrations, C/N ratios, δ15N and δ13C values in 210Pb-dated sediment cores were used to reconstruct historical changes in organic matter (OM) accumulation in three Swedish lakes receiving nutrient-rich mine waters. Ammonium-nitrate-based explosives and sodium cyanide (NaCN) used in gold extraction were the major N sources, while lesser amounts of P originated from apatite and flotation chemicals. The software IsoSource was used to model the relative contribution of soil, terrestrial and littoral vegetation, and phytoplankton detritus in the lake sediments. In one lake the IsoSource modelling failed, suggesting the presence of additional, unknown OM sources. In two of the lakes sedimentary detritus of littoral vegetation and phytoplankton had increased by 15–20% and 20–35%, respectively, since ∼ 1950, when N- and P-rich mine waters began to reach the lakes. Today, phytoplankton is the dominating OM component in these lake sediments, which appears to be a eutrophication effect related to mining operations. Changes in the N isotopic composition of biota, lake water, and sediments related to the use of ammonium-nitrate-based explosives and NaCN were evident in the two studied systems. However, N isotope signals in the receiving waters (δ15N ∼ + 9‰ to + 19‰) were clearly shifted from the primary signal in explosives (δ15N–NO3 = + 3.4 ± 0.3‰; δ15N–NH4 = − 8.0 ± 0.3‰) and NaCN (δ15N = + 1.1 ± 0.5‰), and direct tracing of the primary N isotope signals in mining chemicals was not possible in the receiving waters. Systems where mine waters with a well known discharge history are a major point source of N with well-defined isotopic composition should, however, be suitable for further studies of processes controlling N isotope signatures and their transformation in aquatic systems receiving mine waters. - Highlights: • Historical mining-related changes in organic matter accumulation were revealed. • Macrophyte and 2. Sedimentary records of δ{sup 13}C, δ{sup 15}N and organic matter accumulation in lakes receiving nutrient-rich mine waters Energy Technology Data Exchange (ETDEWEB) Widerlund, Anders, E-mail: Anders.Widerlund@ltu.se; Chlot, Sara; Öhlander, Björn 2014-07-01 Organic C and total N concentrations, C/N ratios, δ{sup 15}N and δ{sup 13}C values in {sup 210}Pb-dated sediment cores were used to reconstruct historical changes in organic matter (OM) accumulation in three Swedish lakes receiving nutrient-rich mine waters. Ammonium-nitrate-based explosives and sodium cyanide (NaCN) used in gold extraction were the major N sources, while lesser amounts of P originated from apatite and flotation chemicals. The software IsoSource was used to model the relative contribution of soil, terrestrial and littoral vegetation, and phytoplankton detritus in the lake sediments. In one lake the IsoSource modelling failed, suggesting the presence of additional, unknown OM sources. In two of the lakes sedimentary detritus of littoral vegetation and phytoplankton had increased by 15–20% and 20–35%, respectively, since ∼ 1950, when N- and P-rich mine waters began to reach the lakes. Today, phytoplankton is the dominating OM component in these lake sediments, which appears to be a eutrophication effect related to mining operations. Changes in the N isotopic composition of biota, lake water, and sediments related to the use of ammonium-nitrate-based explosives and NaCN were evident in the two studied systems. However, N isotope signals in the receiving waters (δ{sup 15}N ∼ + 9‰ to + 19‰) were clearly shifted from the primary signal in explosives (δ{sup 15}N–NO{sub 3} = + 3.4 ± 0.3‰; δ{sup 15}N–NH{sub 4} = − 8.0 ± 0.3‰) and NaCN (δ{sup 15}N = + 1.1 ± 0.5‰), and direct tracing of the primary N isotope signals in mining chemicals was not possible in the receiving waters. Systems where mine waters with a well known discharge history are a major point source of N with well-defined isotopic composition should, however, be suitable for further studies of processes controlling N isotope signatures and their transformation in aquatic systems receiving mine waters. - Highlights: • Historical mining-related changes in organic 3. Human baby hair amino acid natural abundance 15N-isotope values are not related to the 15N-isotope values of amino acids in mother's breast milk protein. Science.gov (United States) Romek, Katarzyna M; Julien, Maxime; Frasquet-Darrieux, Marine; Tea, Illa; Antheaume, Ingrid; Hankard, Régis; Robins, Richard J 2013-12-01 Since exclusively breast-suckled infants obtain their nutrient only from their mother's milk, it might be anticipated that a correlation will exist between the (15)N/(14)N isotope ratios of amino acids of protein of young infants and those supplied by their mother. The work presented here aimed to determine whether amino nitrogen transfer from human milk to infant hair protein synthesized within the first month of life conserves the maternal isotopic signature or whether post-ingestion fractionation dominates the nitrogen isotope spectrum. The study was conducted at 1 month post-birth on 100 mother-infant pairs. Isotope ratios (15)N/(14)N and (13)C/(12)C were measured using isotope ratio measurement by Mass Spectrometry (irm-MS) for whole maternal milk, and infant hair and (15)N/(14)N ratios were also measured by GC-irm-MS for the N-pivaloyl-O-isopropyl esters of amino acids obtained from the hydrolysis of milk and hair proteins. The δ(15)N and δ(13)C (‰) were found to be significantly higher in infant hair than in breast milk (δ(15)N, P amino acids in infant hair was also significantly higher than that in maternal milk (P < 0.001). By calculation, the observed shift in isotope ratio was shown not to be accounted for by the amino acid composition of hair and milk proteins, indicating that it is not simply due to differences in the composition in the proteins present. Rather, it would appear that each pool-mother and infant-turns over independently, and that fractionation in infant N-metabolism even in the first month of life dominates over the nutrient N-content. 4. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 10 International Nuclear Information System (INIS) Over a period of 4 days 12 colostomized laying hens daily received 36 g coarse wheat meal containing 14.37 atom-% 15N excess (15N') together with a conventional ration. After the homogenisation of each oviduct N and 15N' were determined. After the precipitation with TCA the 15N' of the amino acids was analysed in both the precipitate and the supernatant. In addition, the free amino acids and the peptides were determined in the TCA soluble fraction. The atom-% 15N' in the total N and in the non-basic amino acid N showed a parallel decrease; it diminshed from 1.75 atom-% 15N' to 0.64. Of the three basic amino acids, lysine shows the lowest labelling at all four measuring points. The quotas of non-basic amino acid 14N and 15N' in the total 14N and 15N' of the oviduct are the same and amount to 53%. In contrast to this, the quota of the 14N of the basic amino acids in the total 14N of the oviduct only amounts to 21.6% and that of 15N' only to 15.4%. The average atom-% 15N' of the free amino acids 12 h after the last 15N application is 1.54 and is considerably above that of the peptides with 1.15 atom-% 15N'. 36 h after the last 15N application the ascertained value of 1.25 is identical in both fractions. The labelling of the free amino acids decreases more quickly than that of the peptides the more time has passed after the last 15N application. (author) 5. Synthesis and biosynthesis of {sup 13}C-, {sup 15}N-labeled deoxynucleosides useful for biomolecular structural determinations Energy Technology Data Exchange (ETDEWEB) Ashburn, D.A.; Garcia, K.; Hanners, J.L.; Silks, L.A. III; Unkefer, C.J. [Los Alamos National Laboratory, NM (United States) 1994-12-01 Currently, there is a great emphasis on elucidating the structure, function, and dynamics of DNA. Much of the research involved in this study uses nuclear magnetic resonance (NMR) spectroscopy. Effective use of NMR spectroscopy for DNA molecules with mw > 10,000 requires stable isotope enrichment. We present strategies for site-specific isotopic labeling of the purine bases adenosine and guanosine and the biosynthesis of (U-{sup 13}C, {sup 15}N) DNA from methylotropic bacteria. With commercially available 6-chloropurine, an effective two-step route leads to 2{prime}-deoxy-(amino-{sup 15}N)adenosine (dA). The resulting d(amino-{sup 15}N)A is used in a series of reactions to synthesize 2{prime}-deoxy-(2-{sup 13}C,1,amino-{sup 15}N{sub 2})guanosine or any combination thereof. An improved biosynthesis of labeled DNA has been accomplished using Methylobacterium extorquens AS1. Each liter of growth medium contains 4 g of methanol to yield 1 g of lyophilized cells. As much as 200 mg of RNA per liter of culture has been obtained. We are currently developing large-scale isolation protocols. General synthetic pathways to oligomeric DNA will be presented. 6. Comparison of five soil organic matter decomposition models using data from a 14C and 15N labeling field experiment NARCIS (Netherlands) Pansu, M.; Bottner, P.; Sarmiento, L.; Metselaar, K. 2004-01-01 Five alternatives of the previously published MOMOS model (MOMOS-2 to -6) are tested to predict the dynamics of carbon (C) and nitrogen (N) in soil during the decomposition of plant necromass. 14C and 15N labeled wheat straw was incubated over 2 years in fallow soils of the high Andean Paramo of Ven 7. Variation in hair δ13C and δ15N values in long-tailed macaques (Macaca fascicularis) from Singapore Science.gov (United States) Schillaci, Michael A.; Castellini, J. Margaret; Stricker, Craig A.; Jones-Engel, Lisa; Lee, Benjamin P.Y.-H. 2014-01-01 Much of the primatology literature on stable isotope ratios of carbon (δ13C) and nitrogen (δ15N) has focused on African and New World species, with comparatively little research published on Asian primates. Here we present hair δ13C and δ15N isotope values for a sample of 33 long-tailed macaques from Singapore. We evaluate the suggestion by a previous researcher that forest degradation and biodiversity loss in Singapore have led to a decline in macaque trophic level. The results of our analysis indicated significant spatial variability in δ13C but not δ15N. The range of variation in δ13C was consistent with a diet based on C3 resources, with one group exhibiting low values consistent with a closed canopy environment. Relative to other macaque species from Europe and Asia, the macaques from Singapore exhibited a low mean δ13C value but mid-range mean δ15N value. Previous research suggesting a decline in macaque trophic level is not supported by the results of our study. 8. Range expansion of the jumbo squid in the NE Pacific: δ15N decrypts multiple origins, migration and habitat use. Directory of Open Access Journals (Sweden) Rocio I Ruiz-Cooley Full Text Available Coincident with climate shifts and anthropogenic perturbations, the highly voracious jumbo squid Dosidicus gigas reached unprecedented northern latitudes along the NE Pacific margin post 1997-98. The physical or biological drivers of this expansion, as well as its ecological consequences remain unknown. Here, novel analysis from both bulk tissues and individual amino acids (Phenylalanine; Phe and Glutamic acid; Glu in both gladii and muscle of D. gigas captured in the Northern California Current System (NCCS documents for the first time multiple geographic origins and migration. Phe δ(15N values, a proxy for habitat baseline δ(15N values, confirm at least three different geographic origins that were initially detected by highly variable bulk δ(15N values in gladii for squid at small sizes (60 cm converged, indicating feeding in a common ecosystem. The strong latitudinal gradient in Phe δ(15N values from composite muscle samples further confirmed residency at a point in time for large squid in the NCCS. These results contrast with previous ideas, and indicate that small squid are highly migratory, move into the NCCS from two or more distinct geographic origins, and use this ecosystem mainly for feeding. These results represent the first direct information on the origins, immigration and habitat use of this key "invasive" predator in the NCCS, with wide implications for understanding both the mechanisms of periodic D. gigas population range expansions, and effects on ecosystem trophic structure. 9. Range expansion of the jumbo squid in the NE Pacific: δ15N decrypts multiple origins, migration and habitat use. Science.gov (United States) Ruiz-Cooley, Rocio I; Ballance, Lisa T; McCarthy, Matthew D 2013-01-01 Coincident with climate shifts and anthropogenic perturbations, the highly voracious jumbo squid Dosidicus gigas reached unprecedented northern latitudes along the NE Pacific margin post 1997-98. The physical or biological drivers of this expansion, as well as its ecological consequences remain unknown. Here, novel analysis from both bulk tissues and individual amino acids (Phenylalanine; Phe and Glutamic acid; Glu) in both gladii and muscle of D. gigas captured in the Northern California Current System (NCCS) documents for the first time multiple geographic origins and migration. Phe δ(15)N values, a proxy for habitat baseline δ(15)N values, confirm at least three different geographic origins that were initially detected by highly variable bulk δ(15)N values in gladii for squid at small sizes (60 cm) converged, indicating feeding in a common ecosystem. The strong latitudinal gradient in Phe δ(15)N values from composite muscle samples further confirmed residency at a point in time for large squid in the NCCS. These results contrast with previous ideas, and indicate that small squid are highly migratory, move into the NCCS from two or more distinct geographic origins, and use this ecosystem mainly for feeding. These results represent the first direct information on the origins, immigration and habitat use of this key "invasive" predator in the NCCS, with wide implications for understanding both the mechanisms of periodic D. gigas population range expansions, and effects on ecosystem trophic structure. PMID:23527242 10. Using macroalgal δ15N bioassay to detect cruise ship waste water effluent inputs in Skagway, AK Science.gov (United States) Nitrogen stable isotopes are a powerful tool for tracking sources of N to marine ecosystems. I used green macroalgae as a bioassay organism to evaluate if the δ15N signature of cruise ship waste water effluent (CSWWE) could be detected in Skagway Harbor, AK. Opportunistic green... 11. Determination of the natural abundance δ15N of taurine by gas chromatography-isotope ratio measurement mass spectrometry. Science.gov (United States) Tea, Illa; Antheaume, Ingrid; Besnard, Jorick; Robins, Richard J 2010-12-15 The measurement of the nitrogen isotope ratio of taurine (2-aminoethanesulphonic acid) in biological samples has a large number of potential applications. Taurine is a small water-soluble molecule which is notoriously difficult to analyze due to its polarity and functionality. A method is described which allows the determination of the natural abundance δ(15)N values of taurine and structural analogues, such as 3-amino-1-propanesulphonic acid (APSA), by isotope ratio mass spectrometry interfaced to gas chromatography (GC-irm-MS). The one-step protocol exploits the simultaneous derivatization of both functionalities of these aminosulphonic acids by reaction with triethylorthoacetate (TEOA). Conditions have been established which ensure quantitative reaction thus avoiding any nitrogen isotope fractionation during derivatization and workup. The differences in the δ(15)N values of derivatized and non-derivatized taurine and APSA all fall within the working range of 0.4‰ (-0.02 to 0.39‰). When applied to four sources of taurine with various δ(15)N values, the method achieved excellent reproducibility and accuracy. The optimized method enables the determination of the natural abundance δ(15)N values of taurine over the concentration range 1.5-7.84 µmol.mL(-1) in samples of biological origin. 12. Nutrient dynamics of seagrass ecosystems: 15N evidence for the importance of particulate organic matter and root systems NARCIS (Netherlands) Evrard, V.P.E.; Kiswara, W.; Bouma, T.J.; Middelburg, J.J. 2005-01-01 The availability of nitrogen in sediment phytodetritus to seagrass was investigated in 5 tropical species (Thalassia hemprichii, Halodule uninervis, H. pinifolia, Halophila ovalis/ovata and Syringodium isoetifolium) from Indonesia. 15N-labeled phytodetritus was injected into the sediment and the app 13. Hyperpolarized (13) C,(15) N2 -Urea MRI for assessment of the urea gradient in the porcine kidney DEFF Research Database (Denmark) Hansen, Esben S S; Stewart, Neil J; Wild, Jim M; 2016-01-01 function in healthy porcine kidneys resembling the human physiology. METHODS: Five healthy female Danish domestic pigs (weight 30 kg) were scanned at 3 Tesla (T) using a (13) C 3D balanced steady-state MR pulse sequence following injection of hyperpolarized (13) C,(15) N2 -urea via a femoral vein catheter... 14. The Titan 14N/ 15N and 12C/ 13C isotopic ratios in HCN from Cassini/CIRS Science.gov (United States) Vinatier, Sandrine; Bézard, Bruno; Nixon, Conor A. 2007-11-01 We report the detection of H 13CN and HC 15N in mid-infrared spectra recorded by the Composite Infrared Spectrometer (CIRS) aboard Cassini, along with the determination of the 12C/ 13C and 14N/ 15N isotopic ratios. We analyzed two sets of limb spectra recorded near 13-15° S (Tb flyby) and 83° N (T4 flyby) at 0.5 cm -1 resolution. The spectral range 1210-1310 cm -1 was used to retrieve the temperature profile in the range 145-490 km at 13° S and 165-300 km at 83° N. These two temperature profiles were then incorporated in the atmospheric model to retrieve the abundance profile of H 12C 14N, H 13CN and HC 15N from their bands at 713, 706 and 711 cm -1, respectively. The HCN abundance profile was retrieved in the range 90-460 km at 15° S and 165-305 km at 83° N. There is no evidence for vertical variations of the isotopic ratios. Constraining the isotopic abundance profiles to be proportional to the HCN one, we find C12/C13=89-18+22 at 15° S, and 68-12+16 at 83° N, two values that are statistically consistent. A combination of these results yields a 12C/ 13C value equal to 75±12. This global result, as well as the 15° S one, envelop the value in Titan's methane ( 82.3±1) [Niemann, H.B., and 17 colleagues, 2005. Nature 438, 779-784] measured at 10° S and is slightly lower than the terrestrial inorganic standard value (89). The 14N/ 15N isotopic ratio is found equal to 56-13+16 at 15° S and 56-9+10 at 83° N. Combining the two values yields 14N/ 15N = 56 ± 8, which corresponds to an enrichment in 15N of about 4.9 compared with the terrestrial ratio. These results agree with the values obtained from previous ground-based millimeter observations [Hidayat, T., Marten, A., Bézard, B., Gautier, D., Owen, T., Matthews, H.E., Paubert, G., 1997. Icarus 126, 170-182; Marten, A., Hidayat, T., Biraud, Y., Moreno, R., 2002. Icarus 158, 532-544]. The 15N/ 14N ratio found in HCN is ˜3 times higher than in N 2 [Niemann, H.B., and 17 colleagues, 2005. Nature 438, 779 15. Measuring denitrification after grassland renewal and grassland conversion to cropland by using the 15N gas-flux method Science.gov (United States) Buchen, Caroline; Eschenbach, Wolfram; Flessa, Heinz; Giesemann, Anette; Lewicka-Szczebak, Dominika; Well, Reinhard 2015-04-01 Denitrification, the reduction of oxidized forms of inorganic N to N2O and N2 is an important pathway of gaseous nitrogen losses. Measuring denitrification, especially the reduction of N2O to N2, expressed in the product ratio (N2O/(N2O + N2)), is rather difficult and hence rarely performed under field conditions. But using the 15N gas-flux method allows determining N transformation processes in their natural environment. In order to develop effective climate mitigation strategies understanding the N2O source is essential. We used the 15N gas-flux method to determine N2O and N2 emissions following grassland renewal and conversion techniques. Therefore we selected three different treatments: control (C), mechanical grassland renovation (GR) (autumn 2013) and grassland conversion to maize (GM) (spring 2014) from field plot trials on two different sites (Histic Gleysoil and Plaggic Anthrosol) near Oldenburg, Lower Saxony, Germany. We applied 15N labeled KNO3- (60 atom. % 15N) at a rate equivalent to common farming practices (150 kg Nha-1) using needle injection of fertilizer solution in three different depths (10 cm, 15 cm, 20 cm) for homogeneous soil labeling up to 30 cm in microplots. During the first 10 days after application (May 2014) gas flux measurements from closed chambers were performed every second day and then weekly following a period of 8 weeks. Gas samples were analyzed for δ15N of N2 and N2O by IRMS according to Lewicka-Szczebak et al. (2013). Concentration and 15N enrichment of NO3- in soil water was determined on weekly samples using the SPIN-MAS technique (Stange et al. 2007). Fluxes of N2 and N2O evolved from the 15N labeled soil nitrogen pool were calculated using the equations of Spott et al. (2006). Peak events of N2 and N2O emissions occurred during the first 10 days of measurement, showing differences in soil types, as well as treatment variations. N2 fluxes up to 178 gha-1day-1 and N2O fluxes up to 280 gha-1day-1 were measured on the 16. Retrospective characterization of ontogenetic shifts in killer whale diets via δ13C and δ15N analysis of teeth Science.gov (United States) Newsome, Seth D.; Etnier, Michael A.; Monson, Daniel H.; Fogel, Marilyn L. 2009-01-01 Metabolically inert, accretionary structures such as the dentin growth layers in teeth provide a life history record of individual diet with near-annual resolution. We constructed ontogenetic ??13C and ??15N profiles by analyzing tooth dentin growth layers from 13 individual killer whales Orcinus orca collected in the eastern northeast Pacific Ocean between 1961 and 2003. The individuals sampled were 6 to 52 yr old, representing 2 ecotypes-resident and transient - collected across ???25?? of latitude. The average isotopic values of transient individuals (n = 10) are consistent with a reliance on mammalian prey, while the average isotopic values of residents (n = 3) are consistent with piscivory. Regardless of ecotype, most individuals show a decrease in ??15N values of ???2.5% through the first 3 yr of life, roughly equivalent to a decrease of one trophic level. We interpret this as evidence of gradual weaning, after which, ontogenetic shifts in isotopic values are highly variable. A few individuals (n = 2) maintained relatively stable ??15N and ??13C values throughout the remainder of their lives, whereas ??15N values of most (n = 11) increased by ???1.5%, suggestive of an ontogenetic increase in trophic level. Significant differences in mean ??13C and ??15N values among transients collected off California suggest that individuality in prey preferences may be prevalent within this ecotype. Our approach provides retrospective individual life history and dietary information that cannot be obtained through traditional field observations of free-ranging and elusive species such as killer whales, including unique historic ecological information that pre-dates modern studies. By providing insights into individual diet composition, stable isotope analysis of teeth and/or bones may be the only means of evaluating a number of hypothesized historical dietary shifts in killer whales of the northeast Pacific Ocean. ?? Inter-Research 2009. 17. A 15N stable isotope semen label to detect mating in the malaria mosquito Anopheles arabiensis Patton Directory of Open Access Journals (Sweden) Gludovacz Doris 2008-07-01 Full Text Available Abstract In previous studies it was determined that the stable isotope 13-carbon can be used as a semen label to detect mating events in the malaria mosquito Anopheles arabiensis. In this paper we describe the use of an additional stable isotope, 15-nitrogen (15N, for that same purpose. Both stable isotopes can be analysed simultaneously in a mass spectrometer, offering the possibility to detect both labels in one sample in order to study complex and difficult-to-detect mating events, such as multiple mating. 15N-glycine was added to larval rearing water and the target enrichment was 5 atom% 15N. Males from these trays were mated with unlabelled virgin females, and spiked spermathecae were analysed for isotopic composition after mating using mass spectrometry. Results showed that spermathecae positive for semen could be distinguished from uninseminated or control samples using the raw δ15N‰ values. The label persisted in spermathecae for up to 5 days after insemination, and males aged 10 days transferred similar amounts of label as males aged 4 days. There were no negative effects of the label on larval survival and male longevity. Enrichment of teneral mosquitoes after emergence was 4.85 ± 0.10 atom% 15N. A threshold value defined as 3 standard deviations above the mean of virgin (i.e. uninseminated spermathecae samples was successful in classifying a large proportion of samples correctly (i.e. on average 95%. We conclude that alongside 13C, 15N can be used to detect mating in Anopheles and the suitability of both labels is briefly discussed. 18. Retrospective characterization of ontogenetic shifts in killer whale diets via δ13C and δ15N analysis of teeth Science.gov (United States) Newsome, Seth D.; Etnier, Michael A.; Monson, Daniel H.; Fogel, Marilyn L. 2009-01-01 Metabolically inert, accretionary structures such as the dentin growth layers in teeth provide a life history record of individual diet with near-annual resolution. We constructed ontogenetic δ13C and δ15N profiles by analyzing tooth dentin growth layers from 13 individual killer whales Orcinus orca collected in the eastern northeast Pacific Ocean between 1961 and 2003. The individuals sampled were 6 to 52 yr old, representing 2 ecotypes—resident and transient—collected across ~25° of latitude. The average isotopic values of transient individuals (n = 10) are consistent with a reliance on mammalian prey, while the average isotopic values of residents (n = 3) are consistent with piscivory. Regardless of ecotype, most individuals show a decrease in δ15N values of ~2.5‰ through the first 3 yr of life, roughly equivalent to a decrease of one trophic level. We interpret this as evidence of gradual weaning, after which, ontogenetic shifts in isotopic values are highly variable. A few individuals (n = 2) maintained relatively stable δ15N and δ13C values throughout the remainder of their lives, whereas δ15N values of most (n = 11) increased by ~1.5‰, suggestive of an ontogenetic increase in trophic level. Significant differences in mean δ13C and δ15N values among transients collected off California suggest that individuality in prey preferences may be prevalent within this ecotype. Our approach provides retrospective individual life history and dietary information that cannot be obtained through traditional field observations of free-ranging and elusive species such as killer whales, including unique historic ecological information that pre-dates modern studies. By providing insights into individual diet composition, stable isotope analysis of teeth and/or bones may be the only means of evaluating a number of hypothesized historical dietary shifts in killer whales of the northeast Pacific Ocean 19. Stable isotope tracking of endangered sea turtles: validation with satellite telemetry and δ15N analysis of amino acids. Directory of Open Access Journals (Sweden) Jeffrey A Seminoff Full Text Available Effective conservation strategies for highly migratory species must incorporate information about long-distance movements and locations of high-use foraging areas. However, the inherent challenges of directly monitoring these factors call for creative research approaches and innovative application of existing tools. Highly migratory marine species, such as marine turtles, regularly travel hundreds or thousands of kilometers between breeding and feeding areas, but identification of migratory routes and habitat use patterns remains elusive. Here we use satellite telemetry in combination with compound-specific isotope analysis of amino acids to confirm that insights from bulk tissue stable isotope analysis can reveal divergent migratory strategies and within-population segregation of foraging groups of critically endangered leatherback sea turtles (Dermochelys coriacea across the Pacific Ocean. Among the 78 turtles studied, we found a distinct dichotomy in δ(15N values of bulk skin, with distinct "low δ(15N" and "high δ(15N" groups. δ(15N analysis of amino acids confirmed that this disparity resulted from isotopic differences at the base of the food chain and not from differences in trophic position between the two groups. Satellite tracking of 13 individuals indicated that their bulk skin δ(15N value was linked to the particular foraging region of each turtle. These findings confirm that prevailing marine isoscapes of foraging areas can be reflected in the isotopic compositions of marine turtle body tissues sampled at nesting beaches. We use a Bayesian mixture model to show that between 82 and 100% of the 78 skin-sampled turtles could be assigned with confidence to either the eastern Pacific or western Pacific, with 33 to 66% of all turtles foraging in the eastern Pacific. Our forensic approach validates the use of stable isotopes to depict leatherback turtle movements over broad spatial ranges and is timely for establishing wise conservation 20. Estimation of the endogenous N proportions in ileal digesta and faeces in 15N-labelled pigs International Nuclear Information System (INIS) 4 castrated male pigs 40 kg fitted with simple 'T' cannulas in the terminal ileum were given 15N-labelled ammonium salts, added to a low protein diet, for 6 days. Excretion of 15N in urine and feces was monitored daily throughout the labelling and subsequent experimental periods. During the experimental period the pigs were given a diet based on wheat and fish meal, supplemented with varying levels of partially hydrolyzed straw meal to give crude fiber contents ranging from 40 to 132 g/kg. After adaptation to the particular levels of straw meal, feces and ileal digesta were collected during successive 24 h periods. N digestibility values were determined by the chromium oxide ratio method. The retention of 15N-labelled non-specific N was 0.46 of the dose given. The validity of using urine values as a measure of 15N abundance in endogenous N was demonstrated by the similarity of 15N abundance in urine immediately before slaughter at the end of the experiment and in the digestive secretory organs thereafter. The average amount of endogenous N passing the terminal ileum was 3.4 g/day or 0.30-0.50 of total ileal N flow. This was not affected by dietary fiber level. The proportion of fecal N which was of endogenous origin was similar to that in ileal digesta, suggesting similar utilization of endogenous and residual dietary N by hindgut bacteria. Half the endogenous N entering the large intestine was reabsorbed there. Increasing dietary crude fiber from 40 to 132 g/kg increased fecal endogenous N excretion from 1.3 to 2.0 g/animal and day. (author) 1. Fertilizer 15N Accumulation, Recovery and Distribution in Cotton Plant as Affected by N Rate and Split Institute of Scientific and Technical Information of China (English) YANG Guo-zheng; CHU Kun-yan; TANG Hao-yue; NIE Yi-chun; ZHANG Xian-long 2013-01-01 N fertilization of 300 kg N ha-1 is normally applied to cotton crops in three splits:pre-plant application (PPA, 30%), first bloom application (FBA, 40%) and peak bloom application (PBA, 30%) in the Yangtze River Valley China. However, low fertilizer N plant recovery (NPR) (30-35%) causes problems such as cotton yield stagnation even in higher N rate, low profit margin of cotton production and fertilizer release to the environment. Therefore, it is questioned:Are these three splits the same significance to cotton N uptake and distribution? An outdoor pot trial was conducted with five N rates and 15N labeled urea to determine the recovery and distribution of 15N from different splits in cotton (Gossypium hirsutum L. cv. Huazamian H318) plant. The results showed that, cotton plant absorbed fertilizer 15N during the whole growing period, the majority during flowering for 18-20 d regardless of N rates (150-600 kg ha-1). Fertilizer 15N proportion to the total N accumulated in cotton plant increased with N rates, and it was the highest in reproductive organs (88%averaged across N rates) among all the plant parts. FBA had the highest NPR (70%), the lowest fertilizer N lose (FNL, 19%), and the highest contribution to the fertilizer 15N proportion to the total N (46%) in cotton plant, whereas PPA had the reverse effect. It suggests that FBA should be the most important split for N absorption and yield formation comparatively and allocating more fertilizer N for late application from PPA should improve the benefit from fertilizer. 2. Tamanho da parcela para estudos de recuperação de fertilizante-15N por capim-tanzânia Plot-size for 15N-fertilizer recovery studies by tanzania-grass Directory of Open Access Journals (Sweden) Geraldo Bueno Martha Júnior 2009-04-01 3. Dynamics of amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 1 International Nuclear Information System (INIS) In a 6-day preliminary period with a pelleted ration 12 colostomized laying hybrids received 15N-labelled wheat protein over 4 days. The labelling of the wheat was 14.37 atom-% 15N excess (15N'). During the 4-day application of 15N-labelled wheat protein each hen consumed 12.08 g N, 3.52 g lysine, 2.12 g histidine, 4.41 g arginine, of which were 540 mg 15N', 18.1 mg lysine 15N', 21.5 mg histidine 15N' and 47.9 mg arginine 15N'. Heavy nitrogen was determined in urine and its uric acid N in the daily urine samples of the individual animals. The average daily urine N excretion was 54% of the total nitrogen consumed with the ration. The labelling of the urine N reached a plateau on the fourth day of the experiment with 3.2 atom-% 15N'. On an average of the total experiment the quota of heavy nitrogen of the uric acid in the total 15N' of the urine was 83.4% and that of uric acid nitrogen in the total urine nitrogen 80.8%. (author) 4. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 9 International Nuclear Information System (INIS) Over 4 days 12 colostomized laying hens received 36 g coarse wheat meal with a 15N excess (15N') of 14.37 atom-% together with a conventional diet. The labelling of lysine amounted to 13.58 atom-% 15N', that of histidine to 14.38 and of arginine to 13.63 atom-% 15N'. Three animals each were butchered 12 h, 36 h, 60 h and 108 h after the last 15N application. In the two charges of follicles (above and below 25 g) N and 15N' were determined in the individual basic amino acids as well as their sum in the non-basic ones. The atom-% 15N' was determined in the TCA soluble fraction of the free amino acid and peptide fractions. The average atom-% 15N' of the big follicles is 12 and 36 h after the last 15N application lower, and higher at the last two measuring points than that of the medium and small follicles. The atom-% of the total nitrogen and of the non-basic amino acids was significantly higher in both the bigger and the smaller follicles than in the basic amino acids. 70% of the heavy nitrogen in the total 15N' of the big follicles could be detected in amino acids; its quota in the small follicles was 67%. (author) 5. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 2 International Nuclear Information System (INIS) Over 4 days 12 colostomized laying hens received toghether with a commercial ration labelled wheat with a 15N excess (15N') of 14.37 atom-%. The labelling of the basic amino acids amounted to 13.58 atom-% for lysine, to 14.38 atom-% for histidine and to 13.63 atom-% 15N' for arginine. 3 animals each were butchered 12 h, 36 h, 60 h and 108 h, resp. after the last application of 15N. The heavy nitrogen in the total N and in the N fraction of non-protein origin as well as in the basic amino acids in feces was daily determined for the individual hens in the total experimental period. On average the crude protein of feces contained 5.45% lysine, 2.32% histidine and 3.68% arginine: the protein of feces correspondingly contained 5.43% lysine, 2.32% histidine and 4.07% arginine. The quota of TCA-soluble N in the total N of feces amounts to one third on the 3rd and 4th days of the experiment and that of 15N' to 28%. The average atom-% 15N' of the protein fraction is 3.48 atom-% 15N' and that of the non-protein N fraction of feces 2.93 atom-% 15N'. The apparent digestibility of the 14N of the ration on average amounts to 82.8% and that of the wheat 15N' to 87.5%. The average quota of the basic amino acids in the protein compounds of feces amounts to 70.9% for lysine 15N', 73.7% for histidine 15N' and 70.3% for arginine 15N'. The digestibility of the 15N-labelled amino acids amounts to 80.4% for lysine, 90.8% for histidine and 90.2% for arginine. (author) 6. A Hub Location Problem with Fully Interconnected Backbone and Access Networks DEFF Research Database (Denmark) Thomadsen, Tommy; Larsen, Jesper 2007-01-01 This paper considers the design of two-layered fully interconnected networks. A two-layered network consists of clusters of nodes, each defining an access network and a backbone network. We consider the integrated problem of determining the access networks and the backbone network simultaneously... 7. Thin Films Formed from Conjugated Polymers with Ionic, Water-Soluble Backbones NARCIS (Netherlands) Voortman, Thomas P; Chiechi, Ryan C 2015-01-01 This paper compares the morphologies of films of conjugated polymers in which the backbone (main chain) and pendant groups are varied between ionic/hydrophilic and aliphatic/hydrophobic. We observe that conjugated polymers in which the pendant groups and backbone are matched, either ionic-ionic or h 8. Assessing sources of nitrate contamination in the Shiraz urban aquifer (Iran) using the δ(15)N and δ(18)O dual-isotope approach. Science.gov (United States) Amiri, Haleh; Zare, Mohammad; Widory, David 2015-01-01 Nitrate ([Formula: see text]) is one of the major threats to the quality of the drinking water taken from the Shiraz aquifer. This aquifer undergoes high anthropogenic pressures from multiple local urban (including uncontrolled sewage systems), agricultural and industrial activities, resulting in [Formula: see text] concentrations as high as 149 mg L(-1), well above the 50 mg L(-1) guideline defined by the World Health Organisation. We coupled here classical chemical and dual isotope (δ(15)N and δ(18)O of [Formula: see text]) approaches trying to characterize sources and potential processes controlling the budget of this pollutant. Chemical data indicate that nitrate in this aquifer is explained by distinct end-members: while mineral fertilizers isotopically show to have no impact, our isotope approach identifies natural soil nitrification and organic [Formula: see text] (manure and/or septic waste) as the two main contributors. Isotope data suggest that natural denitrification may occur within the aquifer, but this conclusion is not supported by the study of other chemical parameters. PMID:25941866 9. Performance of a neural-network-based determination of amino acid class and secondary structure from 1H-15N NMR data International Nuclear Information System (INIS) A neural network which can determine both amino acid class and secondary structure using NMR data from 15N-labeled proteins is described. We have included nitrogen chemical shifts,3JHNHα coupling constants, α-proton chemical shifts, and side-chain proton chemical shifts as input to a three-layer feed-forward network. The network was trained with 456 spin systems from several proteins containing various types of secondary structure, and tested on human ubiquitin, which has no sequence homology with any of the proteins in the training set. A very limited set of data,representative of those from a TOCSY-HSQC and HNHA experiment, was used.Nevertheless, in 60% of the spin systems the correct amino acid class was among the top two choices given by the network, while in 96% of the spin systems the secondary structure was correctly identified. The performance of this network clearly shows the potential of the neural network algorithm in the automation of NMR spectral analysis 10. Data acquisition backbone core DABC release v1.0 International Nuclear Information System (INIS) The new experiments at FAIR require new concepts of data acquisition systems for the distribution of self-triggered, time stamped data streams over high performance networks for event building. The Data Acquisition Backbone Core (DABC) is a general purpose software framework developed for the implementation of such data acquisition systems. A DABC application consists of functional components like data input, combiner, scheduler, event builder, filter, analysis and storage which can be configured at runtime. Application specific code including the support of all kinds of data channels (front-end systems) is implemented by C++ program plug-ins. DABC is also well suited as environment for various detector and readout components test beds. A set of DABC plug-ins has been developed for the FAIR experiment CBM (Compressed Baryonic Matter) at GSI. This DABC application is used as DAQ system for test beamtimes. Front-end boards equipped with n-XYTER ASICs and ADCs are connected to read-out controller boards (ROC). From there the data is sent over Ethernet (UDP), or over optics and PCIe interface cards into Linux PCs. DABC does the controlling, event building, archiving and data serving. The first release of DABC was published in 2009 and is available under GPL license. 11. Backbone of complex networks of corporations: The flow of control Science.gov (United States) Glattfelder, J. B.; Battiston, S. 2009-09-01 We present a methodology to extract the backbone of complex networks based on the weight and direction of links, as well as on nontopological properties of nodes. We show how the methodology can be applied in general to networks in which mass or energy is flowing along the links. In particular, the procedure enables us to address important questions in economics, namely, how control and wealth are structured and concentrated across national markets. We report on the first cross-country investigation of ownership networks, focusing on the stock markets of 48 countries around the world. On the one hand, our analysis confirms results expected on the basis of the literature on corporate control, namely, that in Anglo-Saxon countries control tends to be dispersed among numerous shareholders. On the other hand, it also reveals that in the same countries, control is found to be highly concentrated at the global level, namely, lying in the hands of very few important shareholders. Interestingly, the exact opposite is observed for European countries. These results have previously not been reported as they are not observable without the kind of network analysis developed here. 12. Solid state radiation chemistry of the DNA backbone International Nuclear Information System (INIS) The long term goal of this program is to determine the fundamental rules needed to predict the type and yield of damage produced in DNA due to direct effects of ionizing radiation. The focus is on damage to the sugar-phosphate backbone, damage that would lead to strand breaks. Model systems have been chosen that permit various aspects of this problem to be investigated. The emphasis will be on single crystals of monosaccharides, nucleosides, and nucleotides but will also include some powder work on polynucleotides. In these model systems, free radical products and reactions are observed by electron spin resonance (ESR) and electron nuclear double resonance (ENDOR) techniques. The information thus gained is used in constructing rules that predict what primary free radicals are formed in single crystals of model compounds and the reactions stemming from the primary radicals. The formulation of a set of rules that work in model systems will represent a major advance toward formulating a set of rules that predict the direct damage in DNA itself. In a broader context this program is part of the effort to understand and predict the effects of exposure to ionizing radiation received at low dose rates over long periods of time. Assessment of low dose effects requires a basic understanding of the action of radiation at the molecular level. By contributing to that basic understanding, this program will help solve the problems of risk assessment under low dose conditions. 5 refs., 3 figs 13. Use of 15N and the neutron probe in evaluating soil organic matter turnover and water management in wheat International Nuclear Information System (INIS) An experiment was conducted at the experimental station of the Regional Office of Agricultural Development in South Morocco (Errachidia). The soil is a sandy loam, and average rainfall is 50 mm/yr. Temperatures are relatively low in winter (-3 deg. C) and high in summer (45 deg. C). The soil pH was 8.4, with 0.069% N, 0.97% O.M., 5 ppm exchangeable K, 8.8 ppm available P, and 0.25 exchange capacity. Wheat (cv. Massa) was grown on land previously amended with N, P, and K (42, 84, and 42 kg/ha, respectively). Three irrigation treatments were imposed: 20% HCC (soil humidity at 20% of field capacity), 40% HCC, and 60% HCC. Water treatments were maintained by measurement of soil moisture with a neutron probe. Within each watering system, two N treatments were used: 835 g/m2 of wheat residues enriched with 1.711% atom excess 15N (105 mg 15N/m2) at seeding, and 4.10 g N/m2, as ammonium sulphate, a month after seeding; 4.10 g N/m2 ammonium sulphate, enriched with 9.96% atom excess 15N after seeding and another 4.10 g N/m2 enriched in 15N (9.96%) a month later (836 mg 15N/m2). The hydroprobe was calibrated under dry- and humid-soil conditions. Soil samples were taken at various depths (50 cm from the access tubes) to determine soil humidity by drying samples at 105 deg. C for 24 h. Apparent density was determined to calculate soil volumic humidity at the same depths by the cylinders method. Then volumic humidity was correlated with the hydroprobe count ratio (direct count/standard count). Yields and 15N enrichment of seeds, residues, and roots were determined. Soil N and 15N were determined at four depths to determine the fate of residue 15N and fertilizer 15N added to the soil. The results are summarized. A simple mathematical model allowed us to calculate all parameters needed to understand the soil-water relationship with N budget. The use of the neutron probe allowed maintenance of watering levels at particular depths. Water deficit affects wheat yield, and residue 14. Application of δ13C and δ15N isotopic signatures of organic matter fractions sequentially separated from adjacent arable and forest soils to identify carbon stabilization mechanisms Directory of Open Access Journals (Sweden) M. Sommer 2011-10-01 Full Text Available Identifying the chemical mechanisms behind soil carbon bound in organo-mineral complexes is necessary to determine the degree to which soil organic carbon is stabilized belowground. Analysis of δ13C and δ15N isotopic signatures of stabilized OM fractions along with soil mineral characteristics may yield important information about OM-mineral associations and their processing history. We anlayzed the δ13C and δ15N isotopic signatures from two organic matter (OM fractions along with soil mineral proxies to identify the likely binding mechanisms involved. We analyzed OM fractions hypothesized to contain carbon stabilized through organo-mineral complexes: (1 OM separated chemically with sodium pyrophosphate (OM(PY and (2 OM occluded in micro-structures found in the chemical extraction residue (OM(ER. Because the OM fractions were separated from five different soils with paired forest and arable land use histories, we could address the impact of land use change on carbon binding and processing mechanisms. We used partial least squares regression to analyze patterns in the isotopic signature of OM with established mineral and chemical proxies indicative for certain binding mechanisms. We found different mechanisms predominate in each land use type. For arable soils, the formation of OM(PY-Ca-mineral associations was identified as an important OM binding mechanism. Therefore, we hypothesize an increased stabilization of microbial processed OM(PY through Ca2+ interactions. In general, we found the forest soils to contain on average 10% more stabilized carbon relative to total carbon stocks, than the agricultural counter part. In forest soils, we found a positive relationship between isotopic signatures of OM(PY and the ratio of soil organic carbon content to soil surface area (SOC/SSA. This indicates that the OM(PY fractions of forest soils represent layers of slower exchange not directly attached to mineral surfaces. From the isotopic composition 15. Ion microscopy analysis of the intracellular distribution of {sup 14}C-or {sup 15}N-labelled cytotoxic drugs; Analyse par microscopie ionique de la distribution intracellulaire de drogues cytotoxiques marquees par {sup 14}C ou {sup 15}N Energy Technology Data Exchange (ETDEWEB) Bisagni, E.; Carrez, D.; Croisy, A.; Favaudon, V.; Guerquin-Kern, J.L.; Nguyen, C.H.; Rivalle, C. [Institut Curie, 91 - Orsay (France); Dennebouy, R.; Slodzian, G. [Paris-11 Univ., 91 - Orsay (France); Galle, P. [Faculte de Medecine, 94 - Creteil (France) 1994-12-31 This study has concerned the localization, by the means of ion microscopy of human tumoral cells (in culture), of two synthesized cytostatic compounds: BD40 or Pazelliptine and Intoplicine. These two active compounds (cancer research) have been labelled either with {sup 15}N on the terminal amino dialkyl group of the lateral chain, either, for Intoplicine, with {sup 14}C on the carbon 3 of the aromatic cycle. These two drugs are considered as poisons for topo-isomerases, and they were used to localize these cellular multiplication key-enzymes. Unfortunately, pazelliptine and intoplicine specificity appeared much too low. However, encouraging results were obtained, particularly on {sup 15}N-labelling utilization. 4 figs., 9 refs. 16. Simple approach for the preparation of 15-15N2-enriched water for nitrogen fixation assessments: Evaluation, application and recommendations Directory of Open Access Journals (Sweden) Isabell eKlawonn 2015-08-01 Full Text Available Recent findings revealed that the commonly used 15N2 tracer assay for the determination of dinitrogen (N2 fixation can underestimate the activity of aquatic N2-fixing organisms. Therefore, a modification to the method using pre-prepared 15-15N2-enriched water was proposed. Here, we present a rigorous assessment and outline a simple procedure for the preparation of 15-15N2-enriched water. We recommend to fill sterile-filtered water into serum bottles and to add 15-15N2 gas to the water in amounts exceeding the standard N2 solubility, followed by vigorous agitation (vortex mixing ≥5 min. Optionally, water can be degassed at low-pressure (≥950 mbar for ten minutes prior to the 15-15N2 gas addition to indirectly facilitate the 15-15N2 dissolution. This preparation of 15-15N2-enriched water can be done within one hour using standard laboratory equipment. The final 15N-atom% excess was 5% after replacing 2–5% of the incubation volume with 15-15N2-enriched water. Notably, the addition of 15-15N2-enriched water can alter levels of trace elements in the incubation water due to the contact of 15-15N2-enriched water with glass, plastic and rubber ware during its preparation. In our tests, levels of trace elements (Fe, P, Mn, Mo, Cu, Zn increased by up to 0.1 nmol L-1 in the final incubation volume, which may bias rate measurements in regions where N2 fixation is limited by trace elements. For these regions, we tested an alternative way to enrich water with 15-15N2. The 15-15N2 was injected as a bubble directly to the incubation water, followed by gentle shaking. Immediately thereafter, the bubble was replaced with water to stop the 15-15N2 equilibration. This method achieved a 15N-atom excess of 6.6±1.7% when adding 2 mL 15-15N2 per liter of incubation water. The herein presented methodological tests offer guidelines for the 15N2 tracer assay and thus, are crucial to circumvent methodological draw-backs for future N2 fixation assessments. 17. Plot-size for {sup 15}N-fertilizer recovery studies by tanzania-grass; Tamanho da parcela para estudos de recuperacao de fertilizante-{sup 15}N por capim-tanzania Energy Technology Data Exchange (ETDEWEB) Martha Junior, Geraldo Bueno [EMBRAPA Cerrados, Planaltina, DF (Brazil)], e-mail: gbmartha@cpac.embrapa.br; Trivelin, Paulo Cesar Ocheuze [Centro de Energia Nuclear na Agricultura (CENA/USP), Piracicaba, SP (Brazil). Lab. de Isotopos Estaveis], e-mail: pcotrive@cena.usp.br; Corsi, Moacyr [Escola Superior de Agricultura Luiz de Queiroz (ESALQ/USP), Piracicaba, SP (Brazil). Dept. de Zootecnia], e-mail: moa@esalq.usp.br 2009-07-01 The understanding of the N dynamics in pasture ecosystems can be improved by studies using the {sup 15}N tracer technique. However, in these experiments it must be ensured that the lateral movement of the labeled fertilizer does not interfere with the results. In this study the plot-size requirements for {sup 15}N-fertilizer recovery experiments with irrigated Panicum maximum cv. Tanzania was determined. Three grazing intensities (light, moderate and intensive grazing) in the winter, spring and summer seasons were considered. A 1 m{sup 2} plot-size, with a grass tussock in the center, was adequate, irrespective of the grazing intensity or season of the year. Increasing the distance from the area fertilized with {sup 15}N negatively affected the N derived from fertilizer (Npfm) recovered in herbage.The lowest decline in Npfm values were observed for moderate and light grazing intensities. This fact might be explained by the vigorous growth characteristics of these plants. Increasing the grazing intensity decreased the tussock mass and, the smaller the tussock mass, the greater was the dependence on fertilizer nitrogen. (author) 18. Stabilization dynamics of root versus needle-derived 13C and 15N during 10 years in a temperate forest soil. Science.gov (United States) Bird, J. A.; Hatton, P. J.; Castanha, C.; Torn, M. S. 2012-12-01 Belowground plant carbon (C) allocation as fine roots can result in greater retention of C in soils compared with aboveground litter in temperate forest ecosystems. However, much of our understanding of the fate of fine root C and nitrogen (N) in soils comes from short-term studies, often lasting only a few months to a few years. In 2011, we concluded a 10-year field study that compared the fate of dual-labeled (13C/15N) Ponderosa pine fine roots (forest soil of the Sierra Nevada, CA, USA. The 13C- and 15N-labeled fine roots or needles were added to mesocosms at two soil depths (top of O or A horizon) to compare C and N stabilization in mineral versus organic soil horizons. We will present data on retention of litter C and N in soil after 0.5, 1.5, 5 and 10 years in situ. For soil samples recovered after 5 years, litter-derived C and N recovered in the mineral soil was partitioned into several operationally-defined physical and chemical soil organic matter (SOM) fractions, which were also characterized by natural abundance 14C. In addition, we compared two fractionation methods (i.e., with and without occluded light fraction isolation) on the partitioning of litter-derived C and N in mineral soil. After 5 years in situ the retention of fine root C in soil (59.9±3.8%) was significantly greater than that of added needle C (38.4±2.0%); however the depth of litter placement in the soil did not affect total litter C or N recovery. Our results provide a direct, decade-scale measure of stabilization of above- and belowground plant inputs to soil, including a portrait of the dominant stabilization mechanisms. 19. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 11 International Nuclear Information System (INIS) Over a period of 4 days 12 colostomized laying hens daily received 36 g 15N-labelled wheat with 15N excess (15N') of 14.37 atom-% together with a conventional feed mixture for laying hens. The labelling of the lysine N in the wheat was 13.58 atom-%, that of histidine N 14.38 and that of arginine 15N' 13.63 atom-% 15N'. Three hens each were butchered 12, 36, 60 and 108 h after the last 15N' feeding. The first three hens did not receive any feed before being butchered. The following three hens each received the unlabelled feed ration for another 1, 2 or 4 days, resp., after the main period until they were butchered. The total of skeleton muscles, heart and stomach muscle (without inner skin) of each hen were combined into one sample, cut thinly, drenched with fluid nitrogen and pulverized. N, 15N' and the basic and non-basic amino acids as well as their 15N' were determined in the individual samples. In contrast to the organs, the proteins in the muscle tissue have a long half-life so that a slight decrease of atom-% 15N' in the muscles could only be detected after 108 h. The 14N and 15N' quota of the non-basic amino acids in the total nitrogen of the muscles is 50 %. The 14N quota of the basic amino acids is 30% and the 15N' quota only 22.5% in the total muscle N. The heavy nitrogen of the free lysine in the TCA soluble N fraction is hardly detectable 36 h and 60 h after the last 15N' supply and not at all after 108 h. In contrast to this, the other two free basic amino acids remain significantly higher labelled in dependence on the last butchering time. (author) 20. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 3 International Nuclear Information System (INIS) 12 colostomized laying hybrids received a ration meeting their requirement of 15N-labelled wheat with a 15N excess (15N') of 14.37 atom-% over 4 days. The 15N' of the total ration amounted to 4.47 atom-%. Each hen consumed 135 mg 15N' per day. On another 4 days the same rations with non-labelled wheat were fed. The 12 hens laid 56 eggs during the 8 days of the experiment. They were divided into egg shell, white and yolk of egg. In addition, the protein of the white and yolk of egg was precipitated with trichloric acetic acid (TCA) and the nitrogen in these fractions was determined. On an average the N quota in the egg shell was 5.3%, in the white of egg 49.1% and in the yolk 45.6%. The atom-% 15N' in the shells of the eggs laid on the first day of the experiment was on an average 0.21, whereas only 0.03 and 0.02 atom-% 15N' resp. could be detected in the white and yolks of the eggs. On the first day after the last 15N application the atom-% 15N' in the egg shell and the white of egg was highest and amounted to 2.33 and 2.43 atom-% resp. The highest value of 1.83 atom-% 15N' in the yolk was ascertained 3 days after the last 15N intake. The mean quota of TCA-precipitable N in the white of egg is 97.6% and in the yolk 94.4% of the respective total N. The atom-% 15N' in the non-protein N compounds was higher than in the protein fractions. (author) 1. Dynamics of the amino acid and protein metabolism of laying hens after the application of 15N-labelled wheat protein. 6 International Nuclear Information System (INIS) 12 colostomized laying hens received, together with a conventional feed ration, 15N-labelled wheat with a 15N excess (15N') of 14.37 atom-% over 4 days. 3 animals each were butchered after 12 h, 36 h, 60 h and 108 h after the last 15N' application and, apart from various organs, the contents and the tissue of the gastrointestinal tract of each hen was divided into 3 fractions. TCA precipitation was carried out with the contents and the tissue of the 3 fractions. Nitrogen and its atom-% 15N' were determined in the supernatant and the precipitate. The 15N' amount in the contents of the crop and the stomachs, the small and large intestines is still considerable 12 h after the last 15N wheat feeding and still clearly detectable 108 h after it. The TCA precipitable amounts of 14N and 15N' of the contents of crop and stomach and that of the small intestine agree well; they are 75% and 50% resp. of the total N. The amount of atom-% 15N' of the contents of the small and large intestines remains the same up to 36 h after the last 15N' application and is higher at the following measuring points in the contents of the large intestine. A close correlation could be ascertained between the atom-% 15N' in the contents and tissue of the small and large intestines. The TCA soluble N quotas of both 14N and 15N' in the pancreas are above 50%. (author) 2. Effect of four plant species on soil 15N-access and herbage yield in temporary agricultural grasslands DEFF Research Database (Denmark) Pirhofer-Walzl, Karin; Eriksen, J.; Høgh-Jensen, H.; 2013-01-01 Abstract Background and aims We carried out field experiments to investigate if an agricultural grassland mixture comprising shallow- (perennial ryegrass: Lolium perenne L.; white clover: Trifolium repens L.) and deep- (chicory: Cichorium intybus L.; Lucerne: Medicago sativa L.) rooting grassland...... species has greater herbage yields than a shallow-rooting two-species mixture and pure stands, if deep-rooting grassland species are superior in accessing soil 15N from 1.2 m soil depth compared with shallow-rooting plant species and vice versa, if a mixture of deep- and shallow-rooting plant species has......-access of pure stands, two-species and four-species grassland communities. Results Herbage yield and soil 15N-access of the mixture including deep- and shallow-rooting grassland species were generally greater than the pure stands and the two-species mixture, except for herbage yield in pure stand lucerne... 3. Transfer of organic matter in the deep Arabian Sea zooplankton community: insights from δ15N analysis Science.gov (United States) Koppelmann, Rolf; Weikert, Horst Zooplankton samples were obtained in the central Arabian Sea using a 1 m2-MOCNESS with 333 μm mesh aperture to investigate the nitrogen stable isotopic composition of different mesozooplankton size classes (zone (1000-2500 m) showed an increase in δ15N with increasing depth for all size classes. In April 1997, the size-dependent distribution showed higher values in the larger size classes, indicating higher trophic levels as compared to smaller size classes. Such a size-dependent increase was not evident in February 1998. Below 2500 m, the δ15N values were more or less stable with increasing depth, or even decreased as exemplified by the smallest size class (zone (1000-2500 m) and one to two trophic levels in the lower bathypelagic zone (>2500 m) . The amount of diet needed by the different mesozooplankton size classes to build up the measured biomass is estimated for the deep bathypelagic zone. 4. Separation Between d$_{5/2}$ and s$_{1/2}$ Neutron Single Particle Strength in $^{15}$N CERN Document Server Mertin, C E; Crisp, A M; Keeley, N; Kemper, K W; Momotyuk, O; Roeder, B T; Volya, A 2014-01-01 The separation between single particle levels in nuclei plays the dominant role in determining the location of the neutron drip line. The separation also provides a test of current crossed shell model interactions if the experimental data is such that multiple shells are involved. The present work uses the $^{14}$N(d, p)$^{15}$N reaction to extract the 2s$_{1/2}$, and 1d$_{5/2}$ total neutron single particle strengths and then compares these results with a shell model calculation using a p-sd crossed shell interaction to identify the J$^\\pi$ of all levels in $^{15}$N up to 12.8 MeV in excitation. 5. Mercury and stable isotopes (δ15N and δ13C as tracers during the ontogeny of Trichiurus lepturus Directory of Open Access Journals (Sweden) Ana Paula Madeira Di Beneditto 2013-03-01 Full Text Available This study applies total mercury (THg concentration and stable isotope signature (δ15N and δ13C to evaluate the trophic status and feeding ground of Trichiurus lepturus during its ontogeny in northern Rio de Janeiro, south-eastern Brazil. The trophic position of T. lepturus is detected well by THg and δ15N as the sub-adult planktivorous specimens are distinct from the adult carnivorous specimens. The δ13C signatures suggest a feeding ground associated with marine coastal waters that are shared by fish in different ontogenetic phases. The diet tracers indicated that the fish feeding habits do not vary along seasons of the year, probably reflecting the prey availability in the study area. This fish has economic importance and the concentration of THg was compared to World Health Organization limit, showing that the adult specimens of T. lepturus are very close to the tolerable limit for safe regular ingestion. 6. O potencial da rotulação metabólica de 15N para a pesquisa de esquizofrenia Directory of Open Access Journals (Sweden) Michaela D. Filiou 2013-01-01 Full Text Available Pesquisas em psiquiatria ainda necessitam de estudos não dirigidos por hipóteses para revelar fundamentos neurobiológicos e biomarcadores moleculares para distúrbios psiquiátricos. Metodologias proteômicas disponibilizam uma série de ferramentas para esses fins. Apresentamos o princípio de rotulação metabólica utilizando 15N para proteômica quantitativa e suas aplicações em modelos animais de fenótipos psiquiátricos com um foco particular em esquizofrenia. Exploramos o potencial de rotulação metabólica por 15N em diferentes tipos de experimentos, bem como suas considerações metodológicas. 7. Bicarbonate as tracer for plant assimilated C and homogeneity of 14C and 15N distribution in ryegrass and white clover tissue by alternative labeling approaches DEFF Research Database (Denmark) Rasmussen, Jim; Kusliene, Gedrime; Jacobsen, Ole Stig; 2013-01-01 parts with high and low 14C activity were separated and analyzed for 15N enrichment. Results Bicarbonate applied by leaf-labeling efficiently introduced 14C into both white clover and ryegrass, although the 14C activity in particular for white clover was found predominantly in the labeled leaf. Using 14...... that 15N also had a heterogeneous distribution (up to two orders of magnitude). Conclusion Bicarbonate can efficiently be used to introduce 14C or 13C into plant via the leaf-labeling method. Both 14C and 15N showed heterogeneous distribution in the plant, although the distribution of 15N was more even... 8. Determining the source of nitrate pollution in the Niger discontinuous aquifers using the natural {15N }/{14N } ratios Science.gov (United States) Girard, Pierre; Hillaire-Marcel, Claude 1997-12-01 In the semi-arid Niamey area (Niger), more than 10% of the deep wells exploiting the fracture network of the Precambrian aquifer are contaminated by nitrates, with concentrations as high as 10 meq l -1. In order to identify the source(s) of this pollution, nitrate and 15N contents in the polluted wells were monitored over a 20-month period. Potential sources of nitrate contamination were also analyzed for their 15N content. The isotopic compositions of nitrate in polluted waters were > + 12‰ and in rare cases exceeded +17‰. Latrines (˜ + 15‰) may be the major nitrate source for wells showing δ15N values above +15‰. Below this value, waters may be polluted by a combination of nitrates from both latrine and soil sources (˜ + 10‰). In some cases, the soil may account for up to 85% of the groundwater nitrate load. This mode of groundwater pollution is thought to be a consequence of deforestation. Despite their reputation as polluting agents, fertilizers ( +0.5 < δ 15N < + 3.6‰ ) which are used in rice paddies close to the contaminated areas, do not appear to be a significant source of nitrate contamination. Denitrification is probably not a significant process in the study area. Results suggest that nitrate contamination of the aquifer is a consequence of unregulated urbanization (home-made latrines) and deforestation. While latrines are limited to the urban zones, intensive cutting of the forest to meet the city dwellers' wood demand occurs in an ever increasing area around the capital, threatening the local water supply. 9. Use of a 15N tracer to determine linkages between a mangrove and an upland freshwater swamp Science.gov (United States) MacKenzie, R. A.; Cormier, N. 2005-05-01 Mangrove forests and adjacent upland freshwater swamps are important components of subsistence-based economies of Pacific islands. Mangroves provide valuable firewood (Rhizophora apiculata) and mangrove crabs (Scylla serrata); intact freshwater swamps are often used for agroforestry (e.g., taro cultivation). While these two systems are connected hydrologically via groundwater and surface flows, little information is available on how they may be biogeochemically or ecologically linked. For example, mangrove leaf litter was once thought to be an important food source for resident and transient nekton and invertebrates, but this value may have been overestimated. Instead, nutrients or allochthonous material (e.g., phytoplankton, detritus) delivered via groundwater or surface water from upland freshwater swamps may play a larger role in mangrove food webs. Understanding the linkages between these two ecologically and culturally important ecosystems will help us to understand the potential impacts of hydrological alterations that occur when roads or bridges are constructed through them. We conducted a 15N tracer study in the Yela watershed on the island of Kosrae, Federated States of Micronesia. K15NO3 was continually added at trace levels for 4 weeks to the Yela River in an upland freshwater swamp adjacent to a mangrove forest. Nitrate and ammonium pools, major primary producers, macroinvertebrates, and fish were sampled from stations 5 m upstream (freshwater swamp) and 138, 188, 213, and 313 m downstream (mangrove) from the tracer addition. Samples were collected once a week prior to, during, and after the 15N addition for a total of 6 weeks. Preliminary results revealed no significant enrichment (< 1 ‰) in the 15N isotope composition of either resident shrimp (Macrobrachium sp.) or mudskipper fish (Periophthalmus sp.). However, the 15N signature of ammonium pools was enriched 10-60 ‰ by the end of the third week. These results suggest that the tracer was present 10. Evaluating mercury biomagnification in fish from a tropical marine environment using stable isotopes (delta13C and delta15N). Science.gov (United States) Al-Reasi, Hassan A; Ababneh, Fuad A; Lean, David R 2007-08-01 Concentrations of total mercury (T-Hg) and methylmercury (MeHg) were measured in zooplankton and 13 fish species from a coastal food web of the Gulf of Oman, an arm of the Arabian Sea between Oman and Iran. Stable isotope ratios (delta13C and delta15N) also were determined to track mercury biomagnification. The average concentration of T-Hg in zooplankton was 21 +/- 8.0 ng g(-1) with MeHg accounting 10% of T-Hg. Total mercury levels in fish species ranged from 3.0 ng g(-1) (Sardinella longiceps) to 760 ng g(-1) (Rhizoprionodon acutus) with relatively lower fraction of MeHg (72%) than that found in other studies. The average trophic difference (Deltadelta13C) between zooplankton and planktivorous fish (Selar crumenopthalmus, Rastrelliger kanagurta, and S. longiceps) was higher (3.4 per thousandth) than expected, suggesting that zooplankton may not be the main diet or direct carbon source for these fish species. However, further sampling would be required to compensate for temporal changes in zooplankton and the influence of their lipid content. Trophic position inferred by delta15N and and slopes of the regression equations (log10[T-Hg] = 0.13[delta15N] - 3.57 and log10[MeHg] = 0.14[delta15N] - 3.90) as estimates of biomagnification indicate that biomagnification of T-Hg and MeHg was lower in this tropical ocean compared to what has been observed in arctic and temperate ecosystems and tropical African lakes. The calculated daily intake of methylmercury in the diet of local people through fish consumption was well below the established World Health Organization (WHO) tolerable daily intake threshold for most of the fish species except Euthynnus affinis, Epinephelus epistictus, R. acutus, and Thunnus tonggol, illustrating safe consumption of the commonly consumed fish species. PMID:17702328 11. Evaluating mercury biomagnification in fish from a tropical marine environment using stable isotopes (delta13C and delta15N). Science.gov (United States) Al-Reasi, Hassan A; Ababneh, Fuad A; Lean, David R 2007-08-01 Concentrations of total mercury (T-Hg) and methylmercury (MeHg) were measured in zooplankton and 13 fish species from a coastal food web of the Gulf of Oman, an arm of the Arabian Sea between Oman and Iran. Stable isotope ratios (delta13C and delta15N) also were determined to track mercury biomagnification. The average concentration of T-Hg in zooplankton was 21 +/- 8.0 ng g(-1) with MeHg accounting 10% of T-Hg. Total mercury levels in fish species ranged from 3.0 ng g(-1) (Sardinella longiceps) to 760 ng g(-1) (Rhizoprionodon acutus) with relatively lower fraction of MeHg (72%) than that found in other studies. The average trophic difference (Deltadelta13C) between zooplankton and planktivorous fish (Selar crumenopthalmus, Rastrelliger kanagurta, and S. longiceps) was higher (3.4 per thousandth) than expected, suggesting that zooplankton may not be the main diet or direct carbon source for these fish species. However, further sampling would be required to compensate for temporal changes in zooplankton and the influence of their lipid content. Trophic position inferred by delta15N and and slopes of the regression equations (log10[T-Hg] = 0.13[delta15N] - 3.57 and log10[MeHg] = 0.14[delta15N] - 3.90) as estimates of biomagnification indicate that biomagnification of T-Hg and MeHg was lower in this tropical ocean compared to what has been observed in arctic and temperate ecosystems and tropical African lakes. The calculated daily intake of methylmercury in the diet of local people through fish consumption was well below the established World Health Organization (WHO) tolerable daily intake threshold for most of the fish species except Euthynnus affinis, Epinephelus epistictus, R. acutus, and Thunnus tonggol, illustrating safe consumption of the commonly consumed fish species. 12. Resistance issues with new nucleoside/nucleotide backbone options. Science.gov (United States) Wainberg, Mark A; Turner, Dan 2004-09-01 The nucleoside and nucleotide reverse transcriptase inhibitors (NRTIs/NtRTIs) remain an enduring feature of combination therapy. As NRTI/NtRTI options continue to expand, questions arise about how best to combine these agents to create effective dual NRTI/NtRTI backbones in antiretroviral regimens while avoiding treatment-emergent drug resistance. Clinicians must consider how NRTIs/NtRTIs such as tenofovir DF (TDF), abacavir (ABC), and emtricitabine (FTC), as well as new once-daily and coformulated NRTIs/NtRTIs, interact with older agents when combined in novel regimens and how sequencing the new NRTIs can preserve future treatment options. Resistance data from clinical trials have revealed important information on the patterns, prevalence, and effects of resistance seen among patients experiencing virologic failure. In recent years, the prevalence of some mutations such as M184V and Q151M has remained relatively constant, while the L74V mutation, the 69 insertions, and thymidine analogue mutations have decreased in prevalence. Other mutations such as K65R and Y115F, while still relatively uncommon, are increasing in prevalence. This increase may be due to the use of new treatment combinations that select for these mutations at a higher rate. Clinical trials suggest that new regimens containing TDF or ABC select for K65R and that this mutation is observed more frequently with TDF; in contrast, L74V is observed more frequently in ABC-containing regimens but is not commonly selected by TDF-containing regimens. Several lines of evidence are converging to suggest that the presence of zidovudine may decrease the risk of L74V and K65R in ABC- or TDF-containing regimens. This review summarizes the clinical implications of resistance profiles associated with new NRTI/NtRTI regimens in current use and in advanced clinical studies. PMID:15319668 13. Fate of 15N-urea applied to wheat-soybean succession crop Destino de 15N-uréia aplicada em sucessão trigo-soja Directory of Open Access Journals (Sweden) Antonio Enedi Boaretto 2004-01-01 14. Application of δ13C and δ15N isotopic signatures of organic matter fractions sequentially separated from adjacent arable and forest soils to identify carbon stabilization mechanisms Directory of Open Access Journals (Sweden) M. Sommer 2011-03-01 Full Text Available Identifying the chemical mechanisms behind soil carbon bound in organo-mineral complexes is necessary to determine the degree to which soil organic carbon is stabilized belowground. We used the δ13C and δ15N isotopic signatures from two organic matter (OM fractions from soil to identify the likely binding mechanisms involved. We used OM fractions hypothesized to contain carbon stabilized through organo-mineral complexes: (1 OM separated chemically with sodium pyrophosphate (OM(PY and (2 OM stabilized in microstructures found in the chemical extraction residue (OM(ER. Furthermore, because the OM fractions were separated from five different soils with paired forest and arable land use histories, we could address the impact of land use change on carbon binding and processing mechanisms within these soils. We used partial least squares regression to analyze patterns in the isotopic signature of OM with established proxies of different binding mechanisms. Parsing soil OM into different fractions is a systematic method of dissection, however, we are primarily interested in how OM is bound in soil as a whole, requiring a means of re-assembly. Thus, we implemented the recent zonal framework described by Kleber et al. (2007 to relate our findings to undisturbed soil. The δ15N signature of OM fractions served as a reliable indicator for microbial processed carbon in both arable and forest land use types. The δ13C signature of OM fractions in arable sites did not correlate well with proxies of soil mineral properties while a consistent pattern of enrichment was seen in the δ13C of OM fractions in the forest sites. We found a significant difference in δ13C of pooled OM fractions between the forest and arable land use type although it was relatively small (<1‰. We found different binding mechanisms predominate in each land use type. The isotopic signatures of OM fractions from arable soils were highly related to the clay and silt size particles 15. Application of δ13C and δ15N isotopic signatures of organic matter fractions sequentially separated from adjacent arable and forest soils to identify carbon stabilization mechanisms Science.gov (United States) Kayler, Z. E.; Kaiser, M.; Gessler, A.; Ellerbrock, R. H.; Sommer, M. 2011-03-01 Identifying the chemical mechanisms behind soil carbon bound in organo-mineral complexes is necessary to determine the degree to which soil organic carbon is stabilized belowground. We used the δ13C and δ15N isotopic signatures from two organic matter (OM) fractions from soil to identify the likely binding mechanisms involved. We used OM fractions hypothesized to contain carbon stabilized through organo-mineral complexes: (1) OM separated chemically with sodium pyrophosphate (OM(PY)) and (2) OM stabilized in microstructures found in the chemical extraction residue (OM(ER)). Furthermore, because the OM fractions were separated from five different soils with paired forest and arable land use histories, we could address the impact of land use change on carbon binding and processing mechanisms within these soils. We used partial least squares regression to analyze patterns in the isotopic signature of OM with established proxies of different binding mechanisms. Parsing soil OM into different fractions is a systematic method of dissection, however, we are primarily interested in how OM is bound in soil as a whole, requiring a means of re-assembly. Thus, we implemented the recent zonal framework described by Kleber et al. (2007) to relate our findings to undisturbed soil. The δ15N signature of OM fractions served as a reliable indicator for microbial processed carbon in both arable and forest land use types. The δ13C signature of OM fractions in arable sites did not correlate well with proxies of soil mineral properties while a consistent pattern of enrichment was seen in the δ13C of OM fractions in the forest sites. We found a significant difference in δ13C of pooled OM fractions between the forest and arable land use type although it was relatively small (<1‰). We found different binding mechanisms predominate in each land use type. The isotopic signatures of OM fractions from arable soils were highly related to the clay and silt size particles amount while 16. Patterns of δ13 C and δ15 N in wolverine Gulo gulo tissues from the Brooks Range, Alaska Institute of Scientific and Technical Information of China (English) Fredrik DALERUM; Anders ANGERBJ(O)RN; Kyran KUNKEL; Brad S.SHULTS 2009-01-01 Knowledge of carnivore diets is essential to understand hew carnivore populations respond demographically to variations in prey abundance. Analysis of stable isotopes is a useful complement to traditional methods of analyzing carnivore diets. We used data on δ13 C and δ15 N in wolverine tissues to investigate patterns of seasonal and annual diet variation in a wolverine Gulo gulo population in the western Brooks Range, Alaska, USA. The stable isotope ratios in wolverine tissues generally reflected that of terrestrial carnivores, corroborating previous diet studies on wolverines. We also found variation in δ13 C and δ15 N both between muscle samples collected over several years and between tissues with different assimilation rates, even after correcting for isotopic fractionation. This suggests both annual and seasonal diet variation. Our results indicate that data on δ13 C and δ15 N holds promise for qualitative assessments of wolverine diet changes over time. Such temporal variation may be important indicators of ecological responses to environmental perturbations, and we suggest that more refined studies of stable isotopes may be an important tool when studying temporal change in diets of wolverines and similar carnivores. 17. Differentiation of Histidine Tautomeric States using 15N Selectively Filtered 13C Solid-State NMR Spectroscopy Science.gov (United States) Miao, Yimin; Cross, Timothy A.; Fu, Riqiang 2014-01-01 The histidine imidazole ring in proteins usually contains a mixture of three possible tautomeric states (two neutral - τ and π states and a charged state) at physiological pHs. Differentiating the tautomeric states is critical for understanding how the histidine residue participates in many structurally and functionally important proteins. In this work, one dimensional 15N selectively filtered 13C solid-state NMR spectroscopy is proposed to differentiate histidine tautomeric states and to identify all 13C resonances of the individual imidazole rings in a mixture of tautomeric states. When 15N selective 180° pulses are applied to the protonated or non-protonated nitrogen region, the 13C sites that are bonded to the non-protonated or protonated nitrogen sites can be identified, respectively. A sample of 13C,15N labeled histidine powder lyophilized from a solution at pH 6.3 has been used to illustrate the usefulness of this scheme by uniquely assigning resonances of the neutral τ and charged states from the mixture. PMID:25026459 18. Differentiation of Pigment in Eggs Using Carbon ((13)C/(12)C) and Nitrogen ((15)N/(14)N) Stable Isotopes. Science.gov (United States) Sun, Feng M; Shi, Guang Y; Wang, Hui W 2016-07-01 Consumers prefer natural and healthy food, but artificial pigments are often abused in egg products. The study aimed at differentiating the origin of pigments in eggs by applying the technique of carbon ((13)C/(12)C) and nitrogen ((15)N/(14)N) stable isotope analysis. Five hundred sixty laying hens were randomly distributed into 14 treatments, which were divided into four groups: maize, carophyll red pigment, carophyll yellow pigment, and a mixture of carophyll red and yellow pigments. Eggs were collected and pretreated to determe the values of the Roche Yolk Color Fan (RCF), δ(13)C, and δ(15)N. With increasing maize content, the RCF and δ(13)C values of yolks increased. Moreover, the RCF values in the three pigment groups were significantly influenced by the artificial colors, but δ(13)C values were not significantly different, regardless of the existence of pigment. The δ(15)N values in all treatments did not vary as regularly as the carbon stable isotope. A strong positive correlation was found between RCF and δ(13)C in the maize group, but no such correlation was be observed in the pigment groups. It is concluded that carbon stable isotope ratio analysis (δ(13)C) of the yolk can be used to differentiate the origin of the pigment added to eggs. 19. /sup 13/N, /sup 15/N isotope and kinetic evidence against hyponitrite as an intermediate in denitrification Energy Technology Data Exchange (ETDEWEB) Hollocher, T.C. (Brandeis Univ., Waltham, MA); Garber, E.; Cooper, A.J.L.; Reiman, R.E. 1980-06-10 /sup 13/N- and /sup 15/N-labeling experiments were carried out with Paracoccus denitrificans, grown anaerobically on nitrate, to determine whether hyponitrite might be an obligatory intermediate in denitrification and a precursor of nitrous oxide. From experiments designed to trap (/sup 13/N)- or (/sup 15/N, /sup 15/N)hyponitrite by dilution into authentic hyponitrite it was calculated that the intracellular concentration of a presumptive hyponitrite pool must be less than 0.4 mm. In order for a pool of this size to turn over rapidly enough to handle the flux of nitrogen during denitrification, the spontaneous rate of hyponitrite dehydration must be enhanced by a factor of several thousand through enzyme catalysis. Cell extracts failed to catalyze this reaction under a variety of conditions. It is concluded that hyponitrite cannot be an intermediate in denitrification. In addition, the assimilation of inorganic nitrogen was studied in P. dentrificans using /sup 13/N as tracer. At low concentrations (<10/sup -8/ M) of labeled nitrate and nitrite 5 to 10% of the label was assimilated into non-volatile metabolites and 90 to 95% was reduced to N/sub 2/. Similarly, with 15 mm (/sup 13/N)nitrate, 5% of the label went into metabolites and 95% to N/sub 2/. High pressure liquid chromatography analysis of the labeled metabolites indicated that the major pathway for assimilation of inorganic nitrogen in P. denitrificans under these conditions is through ammonia incorporation via the aspartase reaction. 20. The excretion of isotope in urea and ammonia for estimating protein turnover in man with [15N]glycine International Nuclear Information System (INIS) Four normal adults were given [15N]-glycine in a single dose either orally or intravenously. Rates of whole-body protein turnover were estimated from the excretion of 15N in ammonia and in urea during the following 9 h. The rate derived from urea took account of the [15N]urea retained in body water. In postabsorptive subjects the rates of protein synthesis given by ammonia were equal to those from urea, when the isotope was given orally, but lower when an intravenous dose was given. In subjects receiving equal portions of food every 2 h rates of synthesis calculated from ammonia were much lower than those from urea whether an oral or intravenous isotope was given. Comparison of rates obtained during the postabsorptive and absorptive periods indicated regulation by food intake primarily of synthesis when measurements were made on urea, but regulation primarily of breakdown when measurements were made on ammonia. These inconsistencies suggest that changes in protein metabolism might be assessed better by correlating results given by different end-products, and it is suggested that the mean value given by urea and ammonia will be useful for this purpose. (author) 1. Affordable uniform isotope labeling with {sup 2}H, {sup 13}C and {sup 15}N in insect cells Energy Technology Data Exchange (ETDEWEB) Sitarska, Agnieszka; Skora, Lukasz; Klopp, Julia; Roest, Susan; Fernández, César; Shrestha, Binesh; Gossert, Alvar D., E-mail: alvar.gossert@novartis.com [Novartis Institutes for BioMedical Research (Switzerland) 2015-06-15 For a wide range of proteins of high interest, the major obstacle for NMR studies is the lack of an affordable eukaryotic expression system for isotope labeling. Here, a simple and affordable protocol is presented to produce uniform labeled proteins in the most prevalent eukaryotic expression system for structural biology, namely Spodoptera frugiperda insect cells. Incorporation levels of 80 % can be achieved for {sup 15}N and {sup 13}C with yields comparable to expression in full media. For {sup 2}H,{sup 15}N and {sup 2}H,{sup 13}C,{sup 15}N labeling, incorporation is only slightly lower with 75 and 73 %, respectively, and yields are typically twofold reduced. The media were optimized for isotope incorporation, reproducibility, simplicity and cost. High isotope incorporation levels for all labeling patterns are achieved by using labeled algal amino acid extracts and exploiting well-known biochemical pathways. The final formulation consists of just five commercially available components, at costs 12-fold lower than labeling media from vendors. The approach was applied to several cytosolic and secreted target proteins. 2. Tracing the diet of the monitor lizard Varanus mabitang by stable isotope analyses (δ15N, δ13C) Science.gov (United States) Struck, Ulrich; Altenbach, Alexander; Gaulke, Maren; Glaw, Frank 2002-09-01 In this study, we used analyses of stable isotopes of nitrogen (δ15N) and carbon (δ13C) to determine the trophic ecology of the monitor lizard Varanus mabitang. Stable isotopes from claws, gut contents, and soft tissues were measured from the type specimen. Samples from Varanus olivaceus, Varanus prasinus, Varanus salvator, the herbivorous agamid lizard Hydrosaurus pustulatus, and some plant matter were included for comparison. Our data show a rapid decrease in δ13C (about10‰) from food plants towards gut contents and soft tissues of herbivorous species. For the varanids, we found a significant linear correlation of decreasing δ13C and increasing δ15N from herbivorous towards carnivorous species. In terms of trophic isotope ecology, the type specimen of V. mabitang is a strict herbivore. Thus it differs significantly in its isotopic composition from the morphologically next closest related species V. olivaceus. The most highly carnivorous species is V. salvator, while δ15N values for V. prasinus and V. olivaceus are intermediate. Claws provide very valuable samples for such measurements, because they can be sampled from living animals without harm. Additionally, their range of variability is relatively small in comparison with measurements from soft tissues. 3. Individual protein balance strongly influences δ15N and δ13C values in Nile tilapia, Oreochromis niloticus Science.gov (United States) Gaye-Siessegger, Julia; Focken, Ulfert; Abel, Hansjörg; Becker, Klaus Although stable isotope ratios in animals have often been used as indicators of the trophic level and for the back-calculation of diets, few experiments have been done under standardized laboratory conditions to investigate factors influencing δ15N and δ13C values. An experiment using Nile tilapia [Oreochromis niloticus (L.)] was therefore carried out to test the effect of different dietary protein contents (35.4, 42.3, and 50.9%) on δ15N and δ13C values of the whole tilapia. The fish were fed the isoenergetic and isolipidic semi-synthetic diets at a relatively low level. δ15N and δ13C values of the lipid-free body did not differ between the fish fed the diets with different protein contents, but the trophic shift for N and C isotopes decreased with increasing protein accretion in the individual fish, for N from 6.5‰ to 4‰ and for C in the lipid-free body from 4‰ to 2.5‰. This is the first study showing the strong influence of the individual protein balance to the degree to which the isotopic signature of dietary protein was modified in tissue protein of fish. The extrapolation of the trophic level or the reconstruction of the diet of an animal from stable isotope ratios without knowledge of the individual physiological condition and the feeding rate may lead to erroneous results. 4. Individual protein balance strongly influences delta15N and delta13C values in Nile tilapia, Oreochromis niloticus. Science.gov (United States) Gaye-Siessegger, Julia; Focken, Ulfert; Abel, Hansjörg; Becker, Klaus 2004-02-01 Although stable isotope ratios in animals have often been used as indicators of the trophic level and for the back-calculation of diets, few experiments have been done under standardized laboratory conditions to investigate factors influencing delta(15)N and delta(13)C values. An experiment using Nile tilapia [ Oreochromis niloticus (L.)] was therefore carried out to test the effect of different dietary protein contents (35.4, 42.3, and 50.9%) on delta(15)N and delta(13)C values of the whole tilapia. The fish were fed the isoenergetic and isolipidic semi-synthetic diets at a relatively low level. delta(15)N and delta(13)C values of the lipid-free body did not differ between the fish fed the diets with different protein contents, but the trophic shift for N and C isotopes decreased with increasing protein accretion in the individual fish, for N from 6.5 per thousand to 4 per thousand and for C in the lipid-free body from 4 per thousand to 2.5 per thousand. This is the first study showing the strong influence of the individual protein balance to the degree to which the isotopic signature of dietary protein was modified in tissue	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.701935887336731, "perplexity": 9955.964460682642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189472.3/warc/CC-MAIN-20170322212949-00114-ip-10-233-31-227.ec2.internal.warc.gz"}
https://econpapers.repec.org/article/sprjglopt/v_3a68_3ay_3a2017_3ai_3a1_3ad_3a10.1007_5fs10898-016-0461-1.htm	# Improving simulated annealing through derandomization Mathieu Gerber () and Luke Bornn Mathieu Gerber: Harvard University Luke Bornn: Harvard University Journal of Global Optimization, 2017, vol. 68, issue 1, 189-217 Abstract: Abstract We propose and study a version of simulated annealing (SA) on continuous state spaces based on $$(t,s)_R$$ ( t , s ) R -sequences. The parameter $$R\in \bar{\mathbb {N}}$$ R ∈ N ¯ regulates the degree of randomness of the input sequence, with the case $$R=0$$ R = 0 corresponding to IID uniform random numbers and the limiting case $$R=\infty$$ R = ∞ to (t, s)-sequences. Our main result, obtained for rectangular domains, shows that the resulting optimization method, which we refer to as QMC-SA, converges almost surely to the global optimum of the objective function $$\varphi$$ φ for any $$R\in \mathbb {N}$$ R ∈ N . When $$\varphi$$ φ is univariate, we are in addition able to show that the completely deterministic version of QMC-SA is convergent. A key property of these results is that they do not require objective-dependent conditions on the cooling schedule. As a corollary of our theoretical analysis, we provide a new almost sure convergence result for SA which shares this property under minimal assumptions on $$\varphi$$ φ . We further explain how our results in fact apply to a broader class of optimization methods including for example threshold accepting, for which to our knowledge no convergence results currently exist. We finally illustrate the superiority of QMC-SA over SA algorithms in a numerical study. Keywords: Global optimization; Quasi-Monte Carlo; Randomized quasi-Monte Carlo; Simulated annealing; Threshold accepting (search for similar items in EconPapers) Date: 2017 References: View references in EconPapers View complete reference list from CitEc Citations: View citations in EconPapers (1) Track citations by RSS feed Access to the full text of the articles in this series is restricted. Related works: This item may be available elsewhere in EconPapers: Search for items with the same title. Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Ordering information: This journal article can be ordered from http://www.springer. ... search/journal/10898	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6077166795730591, "perplexity": 1436.1238694485457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986649232.14/warc/CC-MAIN-20191014052140-20191014075140-00218.warc.gz"}
https://motls.blogspot.com/2013/11/currency-interventions-are-immature.html	## Thursday, November 07, 2013 ... ///// ### Currency interventions are immature assaults on free markets Expletives appropriate after the insane war was declared against the Czech crown A few hours ago, the Czech National Bank has done something insane that hasn't taken place for 11 years: interventions against the Czech currency. Within minutes, the exchange rate weakened by stunning 4 and 6 percent relatively to the euro and the U.S. dollar, respectively. Their stated purpose is to encourage inflation (they look like an arsonist who boasts that he set a big building on fire) and they expect this thing to add 1 percentage point to the inflation for the next 12 months. CZK 2,000 was worth $104.8 in the morning and$99 now, a decrease by nearly 6 percent (contributed by the drop of the euro due to the ECB's lowering of the rate). Sources differ about the amount of crowns that were sold to increase the euro reserves. Reuters said it was just EUR 0.5 billion, others say it was EUR 3 billion. The figure doesn't really matter. They have stated that they will print the crowns and sell them to reach the rate around CZK 27 per euro – it was just 25.7 a few hours ago – so the rate will be close to CZK 27 per euro whether they actually need to print the new crowns or not simply because they obviously have the potential to weaken their own (well, our) currency. I have to emphasize that this is an extremely different procedure from quantitative easing in the U.S. that we recently discussed. In the quantitative easing, the long-term bonds are being repaid i.e. bought back i.e. liquidated and the same amount of money is printed. In the case of interventions, money is being printed and sold to the market and no bonds or other forms of debt are being absorbed at the same moment. So of course that the intervention against the crown immediately contributes to inflation and has many other consequences. According to the discussion forums hosted by Czech news servers, I think that most citizens disagree with such an operation. I disagree for many reasons, economic and ethical ones, too. It seems virtually unthinkable to me that there are no people who have made profit (or at least who avoided the loss) because of some insider knowledge. In my opinion, the system in which individual people may decide about such big operations that don't need any sensible justification is defective, it is really corrupt. I also completely disagree with the idea that the inflation rate near 1.5 percent is too low. The stated inflation target is said to be around 3%. The inflation rate around 4 percent was just OK with the central bank just a year or two years ago. But suddenly 1.5 percent is too low? These data are completely inconsistent with the stated target. If they wanted to be honest, they should raise the official inflation target to 3 percent because this is what they're targeting in the medium or long term (real interest rates are minus 1-2 percent in the last decade or so). But with their "apolitical" status and the flexibility of the rules that determine their policies, there is nothing that would make them honest. The Czech consumers will have more expensive Christmas and at least the domestic consumption will be hurt as a result. Because of the Marshall-Lerner condition, one may doubt that the intervention will improve the trade figures. Moreover, there is no good justification for improving the trade figures. The latest Czech trade surplus was CZK 35 billion per month. That would be CZK 0.42 trillion per year, not too much below 10% of the GDP! We don't need even larger surpluses. What we may need is to increase the domestic consumption and the intervention will do the opposite, especially because the savers will feel poorer and they're the essential contributors of the Czech domestic consumption. By any sensible market measure, the Czech crown is still significantly undervalued; the trade surpluses are one sign of that (the total current account is closer to zero or sometimes showing deficits but smaller deficits than the surpluses of the trade figures). Markets determine the currency exchange rate wisely – more or less with the idea of making the co-existence of all the economies sustainable which pretty much means that markets move the exchange rates to keep the trade surpluses and deficits low (near zero). That's the right motion that should take place. The Czech Central Bank's openly declared goal is exactly the opposite – a way to see that the markets are much more intelligent than the manipulators in the central bank, to see that manipulations with the exchange rates are always wrong. The potential for huge swings such as this one is an argument against the independent currencies of small enough countries like ours. With the situation in Greece etc. looking much better than a year or two years ago, my personal desire to join the eurozone has surely increased dramatically after the today's experience. The ability of a few individuals to manipulate with a currency in this way is just wrong. The right of a country to demand huge external injections just because they share a currency is also wrong but the today's procedure has decreased the Czechs' wealth more than all the hassle in Greece has. Update: I wrote these comments long before I saw the reaction by ex-president Klaus so I was only reassured that his opinions matched mine: The intervention is a flawed and risky step that brings highly questionable benefits but indisputable costs such as more expensive imports and an upward push on the price level in the country. He also criticized the justification of the intervention by the desire to fulfill the inflation target, something that the bank has imposed on itself. We don't need interventions, we need a sensible fiscal policy and the return to normal parliamentary politics, Klaus said. In an article featuring these Klaus' comments, there is a poll and only 9% of respondents think that the event is a net positive for the economy, 83% think it is a net negative.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23415014147758484, "perplexity": 1514.7780232371601}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864626.37/warc/CC-MAIN-20180522053839-20180522073839-00122.warc.gz"}
http://nag.com/numeric/fl/nagdoc_fl24/html/C06/c06pwf.html	C06 Chapter Contents C06 Chapter Introduction NAG Library Manual # NAG Library Routine DocumentC06PWF Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details. ## 1 Purpose C06PWF computes the two-dimensional inverse discrete Fourier transform of a bivariate Hermitian sequence of complex data values. ## 2 Specification SUBROUTINE C06PWF ( M, N, Y, X, IFAIL) INTEGER M, N, IFAIL REAL (KIND=nag_wp) X(MN) COMPLEX (KIND=nag_wp) Y((M/2+1)N) ## 3 Description C06PWF computes the two-dimensional inverse discrete Fourier transform of a bivariate Hermitian sequence of complex data values ${z}_{{j}_{1}{j}_{2}}$, for ${j}_{1}=0,1,\dots ,m-1$ and ${j}_{2}=0,1,\dots ,n-1$. The discrete Fourier transform is here defined by $x^ k1 k2 = 1mn ∑ j1=0 m-1 ∑ j2=0 n-1 z j1 j2 × exp 2πi j1 k1 m + j2 k2 n ,$ where ${k}_{1}=0,1,\dots ,m-1$ and ${k}_{2}=0,1,\dots ,n-1$. (Note the scale factor of $\frac{1}{\sqrt{mn}}$ in this definition.) Because the input data satisfies conjugate symmetry (i.e., ${z}_{{k}_{1}{k}_{2}}$ is the complex conjugate of ${z}_{\left(m-{k}_{1}\right){k}_{2}}$, the transformed values ${\stackrel{^}{x}}_{{k}_{1}{k}_{2}}$ are real. A call of C06PVF followed by a call of C06PWF will restore the original data. This routine calls C06PQF and C06PRF to perform multiple one-dimensional discrete Fourier transforms by the fast Fourier transform (FFT) algorithm in Brigham (1974) and Temperton (1983). ## 4 References Brigham E O (1974) The Fast Fourier Transform Prentice–Hall Temperton C (1983) Fast mixed-radix real Fourier transforms J. Comput. Phys. 52 340–350 ## 5 Parameters 1: M – INTEGERInput On entry: $m$, the first dimension of the transform. Constraint: ${\mathbf{M}}\ge 1$. 2: N – INTEGERInput On entry: $n$, the second dimension of the transform. Constraint: ${\mathbf{N}}\ge 1$. 3: Y($\left({\mathbf{M}}/2+1\right)×{\mathbf{N}}$) – COMPLEX (KIND=nag_wp) arrayInput On entry: the Hermitian sequence of complex input dataset $z$, where ${z}_{{j}_{1}{j}_{2}}$ is stored in ${\mathbf{Y}}\left({j}_{2}×\left(m/2+1\right)+{j}_{1}+1\right)$ , for ${j}_{1}=0,1,\dots ,m/2$ and ${j}_{2}=0,1,\dots ,n-1$. That is, if Y is regarded as a two-dimensional array of dimension $\left(0:{\mathbf{M}}/2,0:{\mathbf{N}}-1\right)$, then ${\mathbf{Y}}\left({j}_{1},{j}_{2}\right)$ must contain ${z}_{{j}_{1}{j}_{2}}$. 4: X(${\mathbf{M}}×{\mathbf{N}}$) – REAL (KIND=nag_wp) arrayOutput On exit: the real output dataset $\stackrel{^}{x}$, where ${\stackrel{^}{x}}_{{k}_{1}{k}_{2}}$ is stored in ${\mathbf{X}}\left({k}_{2}×m+{k}_{1}+1\right)$, for ${k}_{1}=0,1,\dots ,m-1$ and ${k}_{2}=0,1,\dots ,n-1$. That is, if X is regarded as a two-dimensional array of dimension $\left(0:{\mathbf{M}}-1,0:{\mathbf{N}}-1\right)$, then ${\mathbf{X}}\left({k}_{1},{k}_{2}\right)$ contains ${\stackrel{^}{x}}_{{k}_{1}{k}_{2}}$. 5: IFAIL – INTEGERInput/Output On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details. For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit. On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6). ## 6 Error Indicators and Warnings If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF). Errors or warnings detected by the routine: ${\mathbf{IFAIL}}=1$ On entry, ${\mathbf{M}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{M}}\ge 1$. ${\mathbf{IFAIL}}=2$ On entry, ${\mathbf{N}}=⟨\mathit{\text{value}}⟩$. Constraint: ${\mathbf{N}}\ge 1$. ${\mathbf{IFAIL}}=3$ An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance. ${\mathbf{IFAIL}}=-999$ Dynamic memory allocation failed. ## 7 Accuracy Some indication of accuracy can be obtained by performing a forward transform using C06PVF and a backward transform using C06PWF, and comparing the results with the original sequence (in exact arithmetic they would be identical). The time taken by C06PWF is approximately proportional to $mn\mathrm{log}\left(mn\right)$, but also depends on the factors of $m$ and $n$. C06PWF is fastest if the only prime factors of $m$ and $n$ are $2$, $3$ and $5$, and is particularly slow if $m$ or $n$ is a large prime, or has large prime factors. Workspace is internally allocated by C06PWF. The total size of these arrays is approximately proportional to $mn$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 60, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9960063695907593, "perplexity": 1763.7367268358526}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661023.80/warc/CC-MAIN-20160924173741-00031-ip-10-143-35-109.ec2.internal.warc.gz"}
http://archive.numdam.org/item/AFST_2001_6_10_1_23_0/	Large and moderate deviations for moving average processes Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 10 (2001) no. 1, pp. 23-31. @article{AFST_2001_6_10_1_23_0, author = {Djellout, H. and Guillin, A.}, title = {Large and moderate deviations for moving average processes}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {23--31}, publisher = {Universit\'e Paul Sabatier. Facult\'e des sciences}, volume = {Ser. 6, 10}, number = {1}, year = {2001}, zbl = {1002.60028}, mrnumber = {1928987}, language = {en}, url = {http://archive.numdam.org/item/AFST_2001_6_10_1_23_0/} } TY - JOUR AU - Djellout, H. AU - Guillin, A. TI - Large and moderate deviations for moving average processes JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2001 DA - 2001/// SP - 23 EP - 31 VL - Ser. 6, 10 IS - 1 PB - Université Paul Sabatier. Faculté des sciences PP - Toulouse UR - http://archive.numdam.org/item/AFST_2001_6_10_1_23_0/ UR - https://zbmath.org/?q=an%3A1002.60028 UR - https://www.ams.org/mathscinet-getitem?mr=1928987 LA - en ID - AFST_2001_6_10_1_23_0 ER - Djellout, H.; Guillin, A. Large and moderate deviations for moving average processes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 10 (2001) no. 1, pp. 23-31. http://archive.numdam.org/item/AFST_2001_6_10_1_23_0/ [BD90] Burton (R.M.) and Dehling (H.). - Large deviations for some weakly dependent random processes. Statistics and Probability Letters, 9:397-401, 1990. \| MR 1060081 \| Zbl 0699.60016 [DS89] Deuschel (J.D.) and Stroock (D.W.). - Large deviations. Academic Press, Boston, 1989. \| MR 997938 \| Zbl 0705.60029 [DV85] Donsker (M.D.) and Varadhan (S.R.S.). - Large deviations for stationary gaussian processes. Communications in Mathematical Physics, 97:187-210, 1985. \| MR 782966 \| Zbl 0646.60030 [DZ93] Dembo (A.) and Zeitouni (O.). - Large deviations techniques and their applications. Jones and Bartlett, Boston, MA, 1993. \| MR 1202429 \| Zbl 0793.60030 [HH80] Hall (P.) and Heyde (C.C.). - Martingale limit theory and its application. Academic Press, New York, 1980. \| MR 624435 \| Zbl 0462.60045 [Hoe63] Hoeffding (W.). - Probability inequalities for sums of bounded random variables. American Statistical Association Journal, pages 13-30, 1963. \| MR 144363 \| Zbl 0127.10602 [IL71] Ibragimov (I.A.) and Linnik (Y.V.). - Independent and stationnary sequences of random variables. Wolters-Noordhoff Publishing, 1971. \| Zbl 0219.60027 [JWR92] Jiang (T.), Wang (X.) and Rao (M.B.). - Moderate deviations for some weakly dependent random processes. Statistics and Probability Letters, 15:71-76, 1992. \| MR 1190249 \| Zbl 0761.60023 [JWR95] Jiang (T.), Wang (X.) and Rao (M.B.). - Large deviations for moving average processes. Stochastic Processes and Their Applications, 59:309-320, 1995. \| MR 1357658 \| Zbl 0836.60025 [Led96] Ledoux (M.). - On Talagrand's deviation inequalities for product measures. ESAIM: Probability and Statistics, 1:63-87, 1996. \| Numdam \| MR 1399224 \| Zbl 0869.60013 [Led99] Ledoux (M.). - Concentration of measure and logarithmic Sobolev inequalities. Séminaire de Probab. XXXIII, LNM Springer, 1709:120-216, 1999. \| Numdam \| MR 1767995 \| Zbl 0957.60016	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5176666975021362, "perplexity": 8810.700084922613}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304309.59/warc/CC-MAIN-20220123202547-20220123232547-00217.warc.gz"}
https://www.physicsforums.com/threads/easier-way-to-get-exact-sum-avr.225405/	# Easier way to get exact sum/avr? 1. Mar 30, 2008 ### buddingscientist Easier way to get exact sum/avr? [SOLVED, thanks awvvu] Greetings, First I will explain what I am trying to do. I am trying to find the 'average' distance from the bottom and right edges of this box: Basically (using 11 approximations) What I am after for is equal to 1 + sqrt (1 + 0.1^2) + sqrt (1 + 0.2^2) + sqrt (1 + 0.3^2) + sqrt (1 + 0.4^2) + sqrt (1 + 0.5^2) + sqrt (1 + 0.6^2) + sqrt (1 + 0.8^2) + sqrt (1 + 0.8^2) + sqrt (1 + 0.9^2) + sqrt(2) And then that divided by 11 I've used a nice messy excel spreadsheet to get this to 1000 approximations (1000 little 'slices') to get an average of 1.148001 and also using 5000 slices I get 1.147835 Basically as a summation what I _think_ I am looking for is (1000 slices): $$\frac{1}{n} \sum_{n=1}^{1000} \sqrt{1^2 + (0.001n)^2}$$ (that right?) And extended to an infinte amount of slices: $$\lim_{k\rightarrow\infty} \frac{1}{k} \sum_{n=1}^{k} \sqrt{1^2 + (\frac{n}{k})^2}$$ (is this right/possible?) What I am looking for is, using integration, or if it is do-able to evaluate that sum, to know if it is possible to get an 'exact' answer for the 'average' distance? I imagine it would be very similar to the 1.1478 answer above, but I'm looking for more accuracy (basically to whatever precision the infinite sum gives) or if it just happens to equal a nice fraction for me (8/7 which is 1.14285...) or you know.. something nice and round Thanks for reading, please let me know if you need any more info, or if I have gone wrong somewhere, or any hints to get me on the right track, etc. Last edited by a moderator: Apr 23, 2017 at 11:55 AM 2. Mar 30, 2008 ### awvvu You can set it up as an integral. Let's place the bottom-left corner of the square at the origin. The distance from the top-left corner to any x is $\sqrt{1+x^2}$. And we want to integrate from x = 0 to x = 1. I stuck it into integrator and the antiderivative is $\frac{1}{2}(x \sqrt{1 + x^2} + arcsinh(x))$. Plugging in our limits gives $\frac{1}{2}(\sqrt{2} + arcsinh(1)) \approx 1.14779$. It's a pretty unexpected exact expression. I think with some prodding, your sum can be turned into a Riemann sum and you'll get the same results as setting it up as an integral directly. edit: The integral and final expression should be divided by its length (1) to find the average. Last edited: Mar 30, 2008 3. Mar 31, 2008 ### buddingscientist Thanks very much ! I knew there would be a simpler way through integrating than my messy summations. Could I ask what you mean by "It's a pretty unexpected exact expression" ? (Just out of interest) Thanks again Similar Discussions: Easier way to get exact sum/avr?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9376568794250488, "perplexity": 827.1343153890219}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122886.86/warc/CC-MAIN-20170423031202-00099-ip-10-145-167-34.ec2.internal.warc.gz"}
https://tech.bluesmoon.info/2011/07/couchdb-drivers-for-nodejs.html	# The other side of the moon /bb\|[^b]{2}/ Never stop Grokking ## Thursday, July 14, 2011 ### CouchDB drivers for NodeJS I've been looking at writing some code in NodeJS, and wanted to use CouchDB as the data store (note, I don't have relational data). I've come across the following libraries, all coincidentally on github. • couch-client • noddycouch • node-couch • node-couchdb • node-couchdb-min At this point I've only looked at the documentation, so I don't have a detailed idea of which I'd use. If you have your own favourites, please mention them in the comments. #### couch-client The documentation seems reasonably rich, and it has all the methods that I'd like to use. My only concern at this point is that it batches up writes. This may not be ideal for my particular use case, but it isn't a show stopper. There are no installation/setup docs, so I assume I've got to clone the github repo to get it. I've been impressed with cradle's docs so far, and it's also available through npm, which is a plus. It also distinguishes between creating a document with and without an id, which may be required in my use case. Lastly, cradle mentions an SSL use case, which I think is important. The other libraries may also have SSL support, but they don't explicitly call it out. #### noddycouch No docs available, but example.js has code examples on how to use it. #### node-couch Again, no docs available, except to say that it was inspired by the jQuery module for NodeJS. #### node-couchdb Very good documentation and seems to be a very thorough API, but the owner says he isn't maintaining the package any more. That's a big downside. #### node-couchdb-min This appears to be a minimal version of node-couchdb. Filip Noetzel I use mikeal's request module, with a 10-line wrapper that keeps a little state (host, port) and does a little json-parsing. You don't need much more. Philip Thanks, but I didn't see any documentation for it. Do I need any? Siddiq My driver is easier to use. You get started in 59 seconds.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1665119081735611, "perplexity": 2075.5203328674047}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662541747.38/warc/CC-MAIN-20220521205757-20220521235757-00075.warc.gz"}
https://xianblog.wordpress.com/tag/knapsack-problem/	## Le Monde puzzle [#1053] Posted in Books, Kids, R with tags , , , , , , , on June 21, 2018 by xi'an An easy arithmetic Le Monde mathematical puzzle again: 1. If coins come in units of 1, x, and y, what is the optimal value of (x,y) that minimises the number of coins representing an arbitrary price between 1 and 149? 2. If the number of units is now four, what is the optimal choice? The first question is fairly easy to code coinz <- function(x,y){ z=(1:149) if (y<x){xx=x;x=y;y=xx} ny=z%/%y nx=(z%%y)%/%x no=z-nyy-nxx return(max(no+nx+ny)) } and returns M=12 as the maximal number of coins, corresponding to x=4 and y=22. And a price tag of 129. For the second question, one unit is necessarily 1 (!) and there is just an extra loop to the above, which returns M=8, with other units taking several possible values: [1] 40 11 3 [1] 41 11 3 [1] 55 15 4 [1] 56 15 4 A quick search revealed that this problem (or a variant) is solved in many places, from stackexchange (for an average—why average?, as it does not make sense when looking at real prices—number of coins, rather than maximal), to a paper by Shalit calling for the 18¢ coin, to Freakonomics, to Wikipedia, although this is about finding the minimum number of coins summing up to a given value, using fixed currency denominations (a knapsack problem). This Wikipedia page made me realise that my solution is not necessarily optimal, as I use the remainders from the larger denominations in my code, while there may be more efficient divisions. For instance, running the following dynamic programming code coz=function(x,y){ minco=1:149 if (x<y){ xx=x;x=y;y=xx} for (i in 2:149){ if (i%%x==0) minco[i]=i%/%x if (i%%y==0) minco[i]=min(minco[i],i%/%y) for (j in 1:max(1,trunc((i+1)/2))) minco[i]=min(minco[i],minco[j]+minco[i-j]) } return(max(minco))} returns the lower value of M=11 (with x=7,y=23) in the first case and M=7 in the second one. ## Le Monde puzzle [#1022 & #1023] Posted in Books, Kids with tags , , , , , on September 29, 2017 by xi'an Another Le Monde mathematical puzzle where I could not find a solution by R programming (albeit one by cissors and papers was readily available!): An NT is a T whose head () is made of 3 50×50 squares and whose body (\|) is made of N 50×50 squares. What is the smallest possible side of a square containing four non-intersecting NT’s when N=1,2,4? And what is the smallest value of N such that this square also contains a fifth NT? The questions could have been solved by brute force simulation (or a knapsack algorithm?!) but I could not fathom an efficient way to code throwing T’s at random over an MxM grid.So instead I took scissors and paper and tried to fit four 1T, 2T, and 4T into the smallest squares, ending up with 4×4, 5×5, and 7×7 squares. Interestingly, four 5T also fit in a 7×7 square. And a 9×9 square accommodates the extra 7T. Compared with the “impossible” puzzle of last week, this is pretty anticlimactic..! (Actually, once the solutions were published, I realised the square containing the T’s did not have to be with integer side. Which means the smallest square for 3Ts was incorporating the glued T’s sideway. Fortunately, this did not impact the answer for the 7T’s!) Going back to this “impossible” puzzle, the posted solution is somewhat… puzzling in that the resolution posits that the majority rule is the optimal allocation, when I am not sure it is [optimal]. Just because, when rerunning the same R code, I found instances when the minimal acceptable number of councillors was lower than the one returned by the majority rule. And since this post get pushed down in the queue, here is as a bonus the equally anticlimactic puzzle #1023, Find (a) a multiplication of two three-prime-digit numbers such that all digits everywhere in the long multiplication are prime and all three intermediary products have four prime digits, while the final result has six prime digits, and (b) a multiplication of two three-digit numbers such that the digits of the first one are odd (o), the digits of the second are even (e), the three intermediary products are all of the form eoe, and the final product is of the form eoeo. [The website has two pictures to help if this description is too unclear!] This is indeed straightforward to code with one solution to (a) and two to (b) since the number of cases to examine is quite limited. ## A knapsack riddle [#2]? Posted in Kids, R, Statistics with tags , , , on February 17, 2017 by xi'an Still about this allocation riddle of the past week, and still with my confusion about the phrasing of the puzzle, when looking at a probabilistic interpretation of the game, rather than for a given adversary’s y, the problem turns out to search for the maximum of $\mathbb{E}[L(x,Y)]=\sum_{i=1}^{10} i\{P(Y_ix_i)\}$ where the Y’s are Binomial B(100,p). Given those p’s, this function of x is available in closed form and can thus maximised by a simulated annealing procedure, coded as utility=function(x,p){ ute=2pbinom(x[1]-1,100,prob=p[1])+ dbinom(x[1],100,p[1]) for (i in 2:10) ute=ute+2ipbinom(x[i]-1,100,prob=p[i])+ idbinom(x[i],100,p[i]) return(ute)} #basic term in utility baz=function(i,x,p){ return(idbinom(x[i],100,p[i])+ idbinom(x[i]-1,100,p[i]))} #relies on a given or estimated p x=rmultinom(n=1,siz=100,prob=p) maxloz=loss=0 newloss=losref=utility(x,p) #random search T=1e3 Te=1e2 baza=rep(0,10) t=1 while ((t<T)\|\|(newloss>loss)){ loss=newloss i=sample(1:10,1,prob=(10:1)(x>0)) #moving all other counters by one xp=x+1;xp[i]=x[i] #corresponding utility change for (j in 1:10) baza[j]=baz(j,xp,p) proz=exp(log(t)(baza-baza[i])/Te) #soft annealing move j=sample(1:10,1,prob=proz) if (i!=j){ x[i]=x[i]-1;x[j]=x[j]+1} newloss=loss+baza[j]-baza[i] if (newloss>maxloz){ maxloz=newloss;argz=x} t=t+1 if ((t>T-10)&(newloss<losref)){ t=1;loss=0 x=rmultinom(n=1,siz=100,prob=p) newloss=losref=utility(x,p)}} which seems to work, albeit not always returning the same utility. For instance, > p=cy/sum(cy) > utility(argz,p) [1] 78.02 > utility(cy,p) [1] 57.89 or > p=sy/sum(sy) > utility(argz,p) [1] 82.04 > utility(sy,p) [1] 57.78 Of course, this does not answer the question as intended and reworking the code to that purpose is not worth the time! ## Le Monde puzzle [#958] Posted in Books, Kids, R with tags , , , on April 11, 2016 by xi'an A knapsack Le Monde mathematical puzzle: Given n packages weighting each at most 5.8kg for a total weight of 300kg, is it always possible to allocate these packages to 12 separate boxes weighting at most 30kg each? weighting at most 29kg each? This can be checked by brute force using the following R code #generate packages paca=runif(1,0,5.8) while (sum(paca)<300){ paca=c(paca,runif(1,0,5.8))} paca=paca[-length(paca)] paca=c(paca,300-sum(paca)) and #check if they can be partitioned into #12 groups of weight less than 30 box=vector(mode="list",length=12) #random allocation alloc=sample(1:12,length(paca),rep=TRUE) content=rep(0,12) for (i in 1:12){ box[[i]]=paca[alloc==i] content[i]=sum(box[[i]])} content=content(content>0) #wrong allocation while (max(content)>30){ i=sample(1:12,1,prob=content) j=sample(1:length(box[[i]]),1,prob=box[[i]]) #reallocation k=sample(1:12,1,prob=max(content)-content) while (k==i){ k=sample(1:12,1,prob=max(content)-content)} content[i]=content[i]-box[[i]][j] content[i]=content[i](content[i]>0) content[k]=content[k]+box[[i]][j] box[[k]]=c(box[[k]],box[[i]][j]) box[[i]]=box[[i]][-j]} repeatedly and could not find an endless while loop. (Empty boxes sometimes lead to negative contents, hence my fix setting negative contents to zero.) But neither did I find an issue when the upper bound on the weight is 29kg… So it is either possible or rarely impossible! The R code immediately gets stuck when setting the bound at 25kg. After reading the solution of April 13 in Le Monde, it appears that there is a counter example for the 29kg limit, namely 60 packages weighting 4.91kg plus one package weighting 5.4kg, since the first 60 packages fit inside 12 boxes and the last one is left out.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7258445620536804, "perplexity": 1684.8434891550291}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988961.17/warc/CC-MAIN-20210509062621-20210509092621-00127.warc.gz"}
https://zxi.mytechroad.com/blog/category/algorithms/array/	# Posts published in “Array” A chef has collected data on the satisfaction level of his n dishes. Chef can cook any dish in 1 unit of time. Like-time coefficient of a dish is defined as the time taken to cook that dish including previous dishes multiplied by its satisfaction level i.e. time[i]satisfaction[i] Return the maximum sum of Like-time coefficient that the chef can obtain after dishes preparation. Dishes can be prepared in any order and the chef can discard some dishes to get this maximum value. Example 1: Input: satisfaction = [-1,-8,0,5,-9] Output: 14 Explanation: After Removing the second and last dish, the maximum total Like-time coefficient will be equal to (-11 + 02 + 53 = 14). Each dish is prepared in one unit of time. Example 2: Input: satisfaction = [4,3,2] Output: 20 Explanation: Dishes can be prepared in any order, (21 + 32 + 43 = 20) Example 3: Input: satisfaction = [-1,-4,-5] Output: 0 Explanation: People don't like the dishes. No dish is prepared. Example 4: Input: satisfaction = [-2,5,-1,0,3,-3] Output: 35 Constraints: • n == satisfaction.length • 1 <= n <= 500 • -10^3 <= satisfaction[i] <= 10^3 ## Solution 1: Sort+ Brute Force Time complexity: O(nlogn + n^2) Space complexity: O(1) ## Solution 2: Sort + prefix sum Sort in reverse order, accumulate prefix sum until prefix sum <= 0. Time complexity: O(nlogn + n) Space complexity: O(1) [9, 8, 5, 2, 1, -1] sum = 9 4 + 8 * 3 + 2 * 3 + 1 * 2 + -1 * 1 <=> sum += 9 sum += (9 + 8 = 17) sum += (17 + 2 = 19) sum += (19 + 1 = 20) sum += (20 – 1 = 19) ## C++ There are n soldiers standing in a line. Each soldier is assigned a unique rating value. You have to form a team of 3 soldiers amongst them under the following rules: • Choose 3 soldiers with index (ijk) with rating (rating[i]rating[j]rating[k]). • A team is valid if: (rating[i] < rating[j] < rating[k]) or (rating[i] > rating[j] > rating[k]) where (0 <= i < j < k < n). Return the number of teams you can form given the conditions. (soldiers can be part of multiple teams). Example 1: Input: rating = [2,5,3,4,1] Output: 3 Explanation: We can form three teams given the conditions. (2,3,4), (5,4,1), (5,3,1). Example 2: Input: rating = [2,1,3] Output: 0 Explanation: We can't form any team given the conditions. Example 3: Input: rating = [1,2,3,4] Output: 4 Constraints: • n == rating.length • 1 <= n <= 200 • 1 <= rating[i] <= 10^5 ## Solution 1: Brute Force Time complexity: O(n^3) Space complexity: O(1) ## Solution 2: Math For each soldier j, count how many soldiers on his left has smaller ratings as left[j], count how many soldiers his right side has larger ratings as right[j] ans = sum(left[j] * right[j] + (j – left[j]) * (n – j – 1 * right[j]) Time complexity: O(n^2) Space complexity: O(1) ## C++ Given a m * n matrix of distinct numbers, return all lucky numbers in the matrix in any order. A lucky number is an element of the matrix such that it is the minimum element in its row and maximum in its column. Example 1: Input: matrix = [[3,7,8],[9,11,13],[15,16,17]] Output: [15] Explanation: 15 is the only lucky number since it is the minimum in its row and the maximum in its column Example 2: Input: matrix = [[1,10,4,2],[9,3,8,7],[15,16,17,12]] Output: [12] Explanation: 12 is the only lucky number since it is the minimum in its row and the maximum in its column. Example 3: Input: matrix = [[7,8],[1,2]] Output: [7] Constraints: • m == mat.length • n == mat[i].length • 1 <= n, m <= 50 • 1 <= matrix[i][j] <= 10^5. • All elements in the matrix are distinct. ## Solution: Pre-processing Two pass. First pass, record the min val of each row, and max val of each column. Second pass, identify lucky numbers. Time complexity: O(m * n) Space complexity: O(m + n) ## C++ Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties: • Integers in each row are sorted in ascending from left to right. • Integers in each column are sorted in ascending from top to bottom. Example: Consider the following matrix: [ [1, 4, 7, 11, 15], [2, 5, 8, 12, 19], [3, 6, 9, 16, 22], [10, 13, 14, 17, 24], [18, 21, 23, 26, 30] ] Given target = 5, return true. ## Solution 1: Two Pointers Start from first row + last column, if the current value is larger than target, –column; if smaller then ++row. e.g. 1. r = 0, c = 4, v = 15, 15 > 5 => –c 2. r = 0, c = 3, v = 11, 11 > 5 => –c 3. r = 0, c = 2, v = 7, 7 > 5 => –c 4. r = 0, c = 1, v = 4, 4 < 5 => ++r 5. r = 1, c = 1, v = 5, 5 = 5, found it! Time complexity: O(m + n) Space complexity: O(1) ## C++ Given an integer array of size n, find all elements that appear more than ⌊ n/3 ⌋ times. Note: The algorithm should run in linear time and in O(1) space. Example 1: Input: [3,2,3] Output: [3] Example 2: Input: [1,1,1,3,3,2,2,2] Output: [1,2] ## Solution: Boyer–Moore Voting Algorithm Time complexity: O(n) Space complexity: O(1) ## Related Problem Mission News Theme by Compete Themes.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26385295391082764, "perplexity": 3683.950615314429}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371660550.75/warc/CC-MAIN-20200406200320-20200406230820-00518.warc.gz"}
http://rainnic.altervista.org/index.php/en/content/another-latex-template-2013-europass-cv?language_content_entity=en	# Another LaTeX template for the 2013 Europass CV Submitted by Nicola Rainiero on 2015-07-26 It's time to upgrade my old LaTeX version of the Europass CV with a new one that follows the 2013 release, fortunately it has been an easy task because there are many attempts on Internet. I choose the latest class available on CTAN and I have updated it inserting new font icons, the selector for languages and moving on the left the picture in the personal information area. The resulting document is easy to edit and improve directly on your browser if you have a subscription in an online editor like Overleaf, or you can download it. The Europass CV is one of the "five documents to make your skills and qualifications clearly and easily understood in Europe" as cited in the official home page. It is often required in some job applications but generally the recruiters don't like it because it is too standardized. I was used to edit the classic unofficial version for LaTeX, the europecv - Unofficial class for European curricula vitae written by Nicola Vitacolonna. I think this is the oldest class and although it is up-to-date as of 2014-06-27, it has an old fashioned page layout. After looking the new one released in the 2013, I have decided to migrate towards the most recent. In the image below, you can see the differences between them: Anyway the Europass CV official home page is full of resource that allows you to: • create your CV online using tutorials • download the template, examples and instructions (very useful the instructions for filling in the own CV data, a step by step guide to edit this kind of document in general). Obviously there are the CV templates for the several European languages and in two downloadable formats: ODF and DOC. However where is the LaTeX format? Never mind Internet helps us with two valid unofficial versions: 1. written by Roberto Leinardi and available in his GitHub account, it is a valid version and has three languages, but differs the items showed in the header and footer of the pages that following the first. 2. this version is up-to-date as of 2015-03-10, it is written by Giacomo Mazzamuto and it follows very well the latest ufficial version. The two classes are released under The LATEX Project Public License version 1.3 and are based on the original one written by Nicola Vitacolonna. As reported in the article Some links with LaTeX models for a good CV, I started with the oldest version and recently I have decided to upgrade it starting from the second unofficial class above. ## My changes The version of Giacomo Mazzamuto is very good and he also wrote the full documentation of his class, always available from the its CTAN repository. Nevertheless I have made some little changes, most of them localized in the personal info section as follows: • new commands for the mobile number and for the profiles to: linkedin, github, twitter and skype • the icons, in the original they are images, while in my version they are fonts (thanks to the marvosym package) and tikz pictures (thanks to the answers read on TeX - LaTeX Stack Exchange) • the profile picture, moved into the left side First page Third page ## Requirements • Out of the box in Overleaf1, but a registration is needed in order to upload the files and to edit my template. • If you want to use it in your computer, you need a LaTeX installation, an editor and the following packages: eurosym, comment, marvosym and tikz. ## Instructions to change the language At present there are only two languages: English and Italian. If you want to swap them, you have to put the correct language in the highlighted text below and include and exclude the correct comments: \documentclass[english,a4paper]{europasscv} \usepackage{comment} \usepackage{eurosym} %---------------------------------------------------------------------------------------- % SELECTOR FOR COMMENT PACKAGE %---------------------------------------------------------------------------------------- % excludecomment means OFF % includecomment means ON \includecomment{en} % English language \excludecomment{it} % Italian language \excludecomment{extraInfo} % To enable extra Additional Information and Annexes sections You can find and download my template and class in Overleaf and GitHub at these following links: • 1. Overleaf is the new collaborative writing and publishing system developed by the team behind the popular writeLaTeX editor. Overleaf is designed to make the whole process of writing, editing and producing scientific papers much quicker for both authors and publishers. Overleaf: Real-time Collaborative Writing and Publishing Tools with Integrated PDF Preview.Here is my sign up link to Overleaf. ## Related Content: ### Nicola Rainiero A civil geotechnical engineer with the ambition to facilitate own work with free software for a knowledge and collective sharing. Also, I deal with green energy and in particular shallow geothermal energy. I have always been involved in web design and 3D modelling. Samuel (not verified) Tue, 08/07/2018 - 23:51 ### Hello Sir, your template is… Hello Sir, your template is very nice and I would like to use it. I want to know how to replace the dummy profile picture with my own. Thank you very much. ### Hello Samuel, it's very… Hello Samuel, it's very simple if you use Overleaf: add your real profile.png file by clicking on PROJECT in the menu on the top and overwriting the original one. ### Thank you very much. It was… Thank you very much. It was helpful	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2017398625612259, "perplexity": 2592.1627742071173}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526401.41/warc/CC-MAIN-20190720004131-20190720030131-00036.warc.gz"}
https://puzzling.stackexchange.com/questions/101201/can-you-fold-a-square-into-a-square-of-one-fifth-the-area/101203	Can you fold a square into a square of one-fifth the area? I love origami, and it recently gave me an idea for a very hard but beautiful puzzle. I'm really curious whether anyone here can solve it. So here's the puzzle. You are given a large perfectly square piece of paper with no marks on it. With this square, you have to make a square of exactly one-fifth the area of the original square. You are given no tools such as a ruler or scissors, and all you can do is fold the paper. How do you solve this? • I would suggest "one fifth the size" as "five times smaller" doesn't really make sense. ell.stackexchange.com/a/96873/76722 – nasch Aug 17 '20 at 2:48 • @nasch For me 5 times smaller makes sense. The issue in the top answer (not the question) in the linked post is the confusion from having three items being compared ($10,$8, and the new one). For this one it is clear (also from the fact that you are sure that OP means new area equals 0.2 of the old area) since we are comparing only two objects. The convention that I often see is that when we use multiples, we simple multiply/divide by the number, when we use percentage, we do addition/subtraction. So twice larger does not mean 3x the original, but 200% larger is 3x the original. – justhalf Aug 17 '20 at 4:33 • @justhalf It doesn't make sense to say "five TIMES smaller" because you need to DIVIDE by five. "Times" means multiplication, not division. If you are going to multiply by something it would be one fifth, so it's one fifth times the size, which is correct but extremely awkward at best. It can never really be "x times smaller" because there is no unit of smallness that can have a greater magnitude. It's a unit of largeness with a smaller magnitude. – nasch Aug 17 '20 at 14:03 • @marshalcraft : I'm not a native speaker, and if my original wording was confusing or ambiguous, that wasn't my intent. The puzzle is intended to be a purely imagination puzzle, not a puzzle whose point is a tricky wording. – Mitsuko Aug 17 '20 at 18:51 • @nasch you are being pedantic just for the sake of it. "fives times smaller" is neither ambiguous nor grammatically incorrect. It is clear what is meant. Moreover, if you want to get mathematical about it you are also wrong as you have defined neither the statement "five times smaller" or "five times larger". You don't need to "divide anything by five", besides division is defined as multiplication of the inverse, which could mean "smaller". It is perfectly valid to define "$a$ is $n$ times smaller than $b$ if $na=b$". – epiliam Aug 19 '20 at 3:13 The way to do this is: - Fold the paper in half along both axes. You've now marked the midpoint of all four sides. - Fold along the knight's-move diagonals, drawn here: This creates the red square. All five colored regions have the same area, so the red square is 1/5 the size of the square you started with. • In case anyone else is wondering, it took me a minute to figure this out. You can make those diagonal folds because you have the horizontal and vertical centerlines marked with creases. Fold between (for example) the upper right corner and the bottom center. – nasch Aug 17 '20 at 2:52 • @nasch thank you - that's totally an optical illusion that the opposite intersections are not at the same height! – rrauenza Aug 17 '20 at 4:26 • Proof: consider the triangle consisting of both yellow tiles + the small teal triangle. Assuming a 1x1 square, the total area is (1/2)(1/2)(1) = 1/4. The small triangles are each 1/4th the area of the larger colored triangles (since they're similar triangles with half the base); thus the large yellow triangle takes up 4/5th of that area, or (4/5)(1/4) = 1/5 total area. So all triangles together = 4/5 area, leaving 1/5 for the red square. – BlueRaja - Danny Pflughoeft Aug 17 '20 at 23:43 • @BlueRaja-DannyPflughoeft The proof I had in mind was easier (for me at least): You can reassemble the two shapes of each color into a square the same size as the red. (This is a square because (1) all four angles are right angles; (2) two adjacent sides are the same, because each of the four lines touching the corners are the same by symmetry.) – Deusovi Aug 18 '20 at 1:16 • @Chris We can see that e.g the large teal triangle is similar, but double the size of, the small teal triangle, because we know the small triangle's base is half as long. Given that, we can see that the red square runs along exactly half of the large teal triangle's side, because it ends where the small triangle begins. – TenMinJoe Aug 18 '20 at 12:09 Fold the paper horizontally exactly in the middle; fold each of the two $$1\times\frac 1 2$$ rectangles diagonally such that the two diagonals are parallel. Rotate the paper by a quarter turn and do exactly the same. The four diagonals you have just created enclose a square of area $$\frac 1 5$$. We need to show that the distance between two parallel diagonals is $$\frac 1 {\sqrt 5}$$. This distance equals the height over the diagonal of one of the large triangles we have created. These triangles have area $$\frac 1 4$$ while the base length i.e. the length of a diagonal is $$\frac {\sqrt 5} 2$$. The statement follows immediately. • Beat me to it as I was making the picture! +1. – Deusovi Aug 16 '20 at 17:55 • Could you expand on the assertion in the second sentence of your second paragraph? I was able to confirm it by subtracting the legs of the smallest triangle out of the large diagonals. Is there a more direct way of showing those 2 segments are similar? – Simon Aug 17 '20 at 19:11 • @Simon Not sure I understand your doubts. The area of the triangle is 1/4 because there are four of them tiling the full square. Taking the diagonal as the base the hight of each of these triangles must therefore be 2 x 1/4 / length of diagonal. I suspect you are overthinking it. But feel free to prove me wrong ;-) – Paul Panzer Aug 17 '20 at 19:49 • That's not the part that seemed like a leap. Sorry if I was unclear--I was trying to avoid spoilers in the comments. It wasn't immediately clear to me why the distance between the parallel diagonals is equal to the height over the diagonal. It took me several steps of reasoning about lengths of segments of the diagonals to reach that conclusion, so I thought your answer could be improved by expanding on that assertion. Or should the similarity of those segments be obvious for a reason I'm missing? – Simon Aug 18 '20 at 19:02 • Oh, I see the "easy" way to get there now. Considering the colored triangles in Deusovi's picture, the line intersecting each bisects the diagonal (by definition). That forms a half-scale similar triangle. Therefore the 2 segments in question are congruent. – Simon Aug 18 '20 at 21:42 here is a solution I think using it similarly we can have any desired square fraction. (imp the long grey line is 1st grey line the relatively shorter one is 2nd grey line.) 1. what we do is get the blue lines first by folding in halves multiple time in this case we get 1/8th division. 2. Take five continuous such division from right edge. 3. fold paper to meet the top right corner of the full square and the point which is the bottom end of the 5th blue line (in the image one blue line overlaps the black which is the 4th blue line ). 4. we get the grey line by joining the "end of 5th blue line" and "one corner ". 5. no we have one triangle with sides x and (5/8)x; 6. Do a similar operation for the second grey line of triangle(with sides x and (3/8)x) , this time use the endpoint of the 3rd blue line. 7. fold the top edge of paper to get the x/8 length green line which intersects the first grey line and the right edge of the paper.(could be done easily) 8. the region of green line between the 2 grey line is length x/20. >! 9. fold the right edge to get the red line which passes from the point of intersection of the green line and 2nd grey line. 10. now we have this x/20 length measurement on one side which we can copy 4 times by folding the paper to get x/5 length and then make a square. Now when we have x/5 lenght we will take x/5 length on one edge lets say right edge and 2x/5 length on top edge(thus these 2 length are perpendicular to each other) this x/sqrt(5) can be used to create a square of area 1/5 of the larger; imgur is still slow PS: I made a big mistake earlier and got 1/5 th length the edit now give 1/sqrt(5) length PS: We can generalize it to get any fraction of area if the fraction can be written as sum of 2 sqaures mean here 5 = 22+11 , also if you are really really hardworking you can actually get any desired fractions , but you have to do these last steps multiple time . • The question asks for a square with 1/5th the area of the original square, not 1/5th the side length. By the way, there is a quicker way to get 1/5th the side length with just two folds: Fold in half side-to-side to create a crease down the middle, making two rectangles. Then fold one rectangle in half along its diagonal, and the corner point marks one fifth of the way across from the opposite side of the square. – Jaap Scherphuis Aug 17 '20 at 5:14 • I see I have made a blunder – Aakash Mathur Aug 17 '20 at 5:33 • I have done a edit to correct is – Aakash Mathur Aug 17 '20 at 6:01 • although a tough process but now we can have any fraction desired , @JaapScherphuis thankyou for pointing out – Aakash Mathur Aug 17 '20 at 6:02 Not an answer. Here is only an animation to visualize the Deusovi nice answer. I hope you enjoy it. Extending on Deusovi's answer, you can fold a square to any fraction square of the fraction $$n^2/(a^2+b^2)$$, where $$n <= a-b$$. To achieve $$1/5$$, choose $$n=1$$, $$a=2$$, $$b=1$$. Split the edges in $$a$$ equal parts. Then fold lines "knight-moves" $$(a,b)$$. This will generate $$(a-b)^2$$ sqaures of size $$1/(a^2+b^2)$$. Now gather $$n^2$$ of these to generate the desired fraction. • An interesting idea, but the generalised "Split the edges in a equal parts." step isn't trivial when you have no pre-existing marks on the paper and no other tools (unless a is a power of 2) – Steve Aug 21 '20 at 9:35 • That's true Steve. I intentionally left that sub-problem out of my answer, to focus on the most interesting part – XPlatformer Aug 21 '20 at 10:21 • It wasn't clear what within the "most interesting part" wasn't already adequately covered by the other answers. Perhaps worth highlighting what the new contribution you are making is? – Steve Aug 21 '20 at 13:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7920718193054199, "perplexity": 695.4758507163092}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038061820.19/warc/CC-MAIN-20210411085610-20210411115610-00104.warc.gz"}
https://coding-gym.org/challenges/maxsubarray/	# The maximum subarray See the original problem on HackerRank. ## Solutions • find the maximum sum of any nonempty subarray • find the maximum sum of any nonempty subsequence The latter is clearly esier since the elements in a subsequence are not necessarily contiguous. The former is a very classical problem that we’ll deal with in a moment. To solve the first task, we can sum all the positive elements. This works as long as we have at least one positive (or zero) element. What if we have all negative values? The max sum is just the biggest value (the one closest to zero). Here is the idea in Python: 1 2 3 4 5 6 7 def max_sum_subsequence(a, n): m = a[0] t = 0 for i from 0 to n-1: m = max(m, a[i]) if a[i] >= 0: t += a[i] return (m >= 0 ? t : m) Here is a similar approach in C++: 1 2 3 4 5 6 7 8 int maxSubSequence(const vector& v) { auto m = max_element(begin(v), end(v)); auto s = accumulate(begin(v), end(v), 0, [](int curr, int toSum) { return (toSum>0) ? (curr+toSum) : curr; }); return m >= 0 ? s : m; } Clearly, we might iterate only once but we like showing the patterns which shape the solution. Just for completeness, the algorithm above is greedy and takes linear time. Now, we can face with the other - more difficult - task: the maximum sum of any nonempty subarray. A quadratic solution exists: we run two loops. The outer loop picks the beginning element, the inner loop finds the maximum possible sum with first element picked by outer loop and compares this maximum with the overall maximum. Finally return the overall maximum. Clearly, we are interested in a better approach. A simple idea is to look for all positive contiguous segments of the array (max_ending_here is used for this). And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this). Each time we get a positive sum compare it with max_so_far and update max_so_far if it is greater than max_so_far. Here is some C++ code: 1 2 3 4 5 6 7 8 9 10 11 int maxSubArray(const vector& v) { int max_ending_here, max_so_far; max_ending_here = max_so_far = v[0]; for (auto i=1u; i This solution is called as Kadane’s Algorithm and the time complexity is linear. Kadane’s algorithm is usually used to explain the basics of Dynamic Programing that is is one of the problem solving paradigms where we try to find a solution by breaking the larger problem into subproblems. As Marco Arena noted, Kadane’s algorithm can be rewritten as the combination of two patterns: • prefix sum (with a special binary function) • maximum So here is a possible C++ alternative (clearly, it does two iterations and changes the original array): 1 2 3 4 5 6 7 int maxSubArray(vector& v) { partial_sum(begin(v), end(v), begin(v), [](int sum, int current){ return max(current, sum + current); }); return max_element(begin(v), end(v)); } In C++20 this solution can be implemented elegantly and efficiently (single pass) with ranges: 1 2 3 4 int maxSubArray(vector& v) { return ranges::max(view::partial_sum(v, [](auto m, auto i) { return std::max(m+i, i); })); } Not shown here, there is another interesting solution which adopts the Divide and Conquer approach. Find it here. So, here is a complete solution: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 int maxSubArray(vector& v) { partial_sum(begin(v), end(v), begin(v), [](int sum, int current){ return max(current, sum + current); }); return max_element(begin(v), end(v)); } int maxSubSequence(const vector& v) { auto m = max_element(begin(v), end(v)); auto s = accumulate(begin(v), end(v), 0, [](int curr, int toSum) { return (toSum>0) ? (curr+toSum) : curr; }); return m >= 0 ? s : m; } int main() { size_t T; cin >> T; while (T--) { size_t size; cin >> size; vector v; v.reserve(size); copy_n(istream_iterator(cin), size, back_inserter(v)); auto msb = maxSubSequence(v); auto msa = maxSubArray(v); cout << msa << " " << msb << "\n"; } } A complete solution is also found on HackerRank: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 for _ in range(input()): n = input() arr = map(int,raw_input().split()) max_sum = -999999999 c_sum = 0 sum1 = 0 for i in range(n): sum1+=arr[i] if arr[i]>0: c_sum += arr[i] if sum1>max_sum: max_sum = sum1 if sum1<0: sum1 = 0 if c_sum == 0: c_sum = max(arr) print max_sum,c_sum We've worked on this challenge in these gyms: modena	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43309980630874634, "perplexity": 2188.7476088989947}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704795033.65/warc/CC-MAIN-20210126011645-20210126041645-00000.warc.gz"}
https://economics.stackexchange.com/questions/20370/impact-on-interest-rates-of-massive-government-spending	# Impact on interest rates of massive government spending At the last State of the Union address, the President of the United States has reaffirmed his intentions to undertake a massive 1.5 trillion dollar infrastructure spending project over the coming years. If you believe simple macroeconomic models, like the IS-LM model, this kind of government spending should lead to higher real GDP and higher interest rates. I am assuming that, in the real world, this would correspond to a steepening of the yield curve, i.e. medium and long term yields go up. However, looking at yield curve data, I cannot discern any significant uptick in long term yields DoD. Does this mean that either: 1. the yield curve should not actually respond the way I assumed? 2. this announcement carried no real information that would have changed market participants' expectations about the future? 3. the IS-LM model is too simplistic to even adequately predict the directional impact of government spending on interest rates? I realize that I may be abusing the IS-LM model here, as it probably takes a more long term, qualitative view. However, I would think, due to market efficiency, its predictions should be priced into the yield curve immediately. • Did you look at the 7 year rate? – Hot Licks Feb 1 '18 at 3:35 • 7y look up insignificantly, i.e. definitely within one standard deviation DoD. – braaterAfrikaaner Feb 1 '18 at 3:38 • It was 2.22 on the first of November, began steadily climbing shortly after that. This was about the time it became clear that the tax cut would be pushed through. – Hot Licks Feb 1 '18 at 3:47 • DoD = Day on Day? (1 day change)? – Brian Romanchuk Feb 1 '18 at 12:18 • @Brian, yes Day on Day – braaterAfrikaaner Feb 5 '18 at 3:02 You could say IS-LM is too simplistic. The fundamental discrete time consumption-based asset pricing equation says that if $r_t$ is the risk-free interest rate at time $t$, we have $$\beta (1+r_t) \frac{u'(C_{t+1})}{u'(C_t)} = 1$$ (I'm dropping the expectation since I will be working with a perfect foresight model later on) where $u$ is the utility function of any consumer, $0 < \beta < 1$ is a discount factor which measures "impatience" of the same consumer, and $c_t, c_{t+1}$ is the consumption of the same consumer in time $t$ and $t+1$ respectively. The most elegant form of the relation is with the assumption of power utility $u(c) = c^{1 - \gamma}/(1 - \gamma)$ with $\gamma > 0$, in which case we get (after log-linearization) $$r_t = R + \gamma \Delta c_t$$ where $\Delta c_t$ is log consumption growth and $R = -\log(\beta)$ is the real interest rate consistent with flat consumption. The intuition is simple: people want to smooth consumption over time. If they expect their consumption in the future to be much higher than their consumption today, they will try to borrow against the better future and push real interest rates up, and vice versa. Consider a baseline economy with no investment, perfect foresight, and a representative consumer first. (This is unrealistic, but IS-LM is even more unrealistic, so...) In this case, the resource constraint of the economy reads $Y_t = C_t + G_t$ in every period, where $G_t$ is government spending. If you assume consumers have utility that is additively separable over time (the asset pricing relation assumes this as well), then the no investment assumption turns their decision problem into a set of one-period decision problems. (This is a technical condition to ensure what I am doing is well-defined.) Define $D_t$ as the level of output consistent at time $t$ with $G_t = 0$, and let $m_t$ be the "fiscal multiplier", defined by $$m_t = \frac{dY_t}{dG_t}$$ Most models won't give constant $m$, but if necessary we may linearize the model around somewhere other than $G_t = 0$ and make this assumption locally. These assumptions imply $Y_t = D_t + m_t G_t$ at any time $t$, so we may express consumption as $C_t = D_t + (m_t -1) G_t$. Plugging into the relation gives $$r_t \approx R + \gamma \Delta d_t + \gamma (m_t -1) \Delta \left( \frac{g_t}{1 - m_t g_t} \right)$$ where $g_t = G_t/Y_t$ is the ratio of government spending to GDP and $\Delta d_t = \Delta \log(D_t)$. (Ignore the pole of the denominator - we're working around $g_t = 0$.) The fraction $\frac{g_t}{1 - m_t g_t}$ is increasing in $g_t$ with $m \geq 0$, so we see that the real interest rate at time $t$ depends on two things: the "natural" growth rate of the economy given by $\Delta d_t$, and the consumption growth induced by changes in government spending rel to GDP $g_t$. However, the sign of the effect of an anticipated increase in government spending depends on the value of the fiscal multiplier $m$. If $m < 1$, then government spending crowds out consumption, and rising government spending is associated with low real interest rates, i.e expectations of high spending in the future would push rates down today, and vice versa if $m > 1$. Most everyone would agree that the fiscal multiplier in the US economy today is less than $1$, so news of higher spending in the future should be associated with lower real interest rates now, if with anything at all. It also matters, of course, if government spending affects $\Delta d_t$ - if we're speaking of an infrastructure investment program, for instance, then we should expect that the change in government spending also leads to a change in the path of $D_t$. The two effects for such a program act in opposite directions, so the net effect of a government investment program tomorrow on real interest rates today could go either way, even in this simple economy. I won't work out the model with investment (allowing consumers to invest) here, but the effect of investment is to allow consumers to trade consumption now for consumption in the future in aggregate; so it dampens the impact of a change in government spending on real interest rates (since now consumers have a tool for smoothing consumption in the face of government expenditure shocks). It's also true that the announcement in the State of the Union address probably carried less information than an announcement in this model, since market participants were already aware of such an infrastructure investment plan for months (maybe a year?), but with a fiscal multiplier less than $1$ it's not easy to say anything about the direction of the real interest rate response.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7646239399909973, "perplexity": 878.3588755987142}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514578201.99/warc/CC-MAIN-20190923193125-20190923215125-00131.warc.gz"}
https://huggingface.co/NbAiLab/nb-bert-base	NbAiLab /nb-bert-base Copied like 13 • Release 1.1 (March 11, 2021) • Release 1.0 (January 13, 2021) NB-BERT-base Description NB-BERT-base is a general BERT-base model built on the large digital collection at the National Library of Norway. This model is based on the same structure as BERT Cased multilingual model, and is trained on a wide variety of Norwegian text (both bokmål and nynorsk) from the last 200 years. Intended use & limitations The 1.1 version of the model is general, and should be fine-tuned for any particular use. Some fine-tuning sets may be found on GitHub, see Training data The model is trained on a wide variety of text. The training set is described on Mask token: [MASK]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2270563244819641, "perplexity": 3422.0890192894767}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662562410.53/warc/CC-MAIN-20220524014636-20220524044636-00373.warc.gz"}
http://physics.stackexchange.com/questions/26108/where-to-find-lunar-eclipse-data?answertab=oldest	# Where to find Lunar Eclipse data I am wondering whether there's a good resource to find data about upcoming Lunar Eclipses. For example, showing the percentage of the eclipse over time. Such as: 17:23 GMT - 0%, 17:40 GMT - 10%, etc. - An excellent site for eclipse data, both lunar and solar, is NASA's Eclipse Web Site. It shows maps, tracks and illumination data for all upcoming eclipses. Find the date of the eclipse you're interested in and click on the link to find all the information you need. For example, the total lunar eclipse on June 15, 2011 has this data: Penumbral Eclipse Begins: 17:24:34 UT Partial Eclipse Begins: 18:22:56 UT Total Eclipse Begins: 19:22:30 UT Greatest Eclipse: 20:12:37 UT Total Eclipse Ends: 21:02:42 UT Partial Eclipse Ends: 22:02:15 UT Penumbral Eclipse Ends: 23:00:45 UT - I use the same Celestia here too. It's a completely offline free simulation software for real-time 3D space environment. In light of your question, Celestia has its own inbuilt Eclipse finder. You give a set of dates (possibly, a range), select the planet, select its moons and allow it to compute. Within barely 2 seconds, you get the approx. results. If you wanna look at it (in order to make sure whether I'm telling the truth), you could select Set Date and Goto Planet and the journey begins.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4905293583869934, "perplexity": 2038.825436724578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609538824.34/warc/CC-MAIN-20140416005218-00440-ip-10-147-4-33.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/240654/lebesgue-integrable-function?answertab=oldest	# Lebesgue Integrable Function My professor posed a question to us last week about the limit of a function as $k \to \infty$. He asked us to prove that $\int \lim_{k \to \infty} f(x)e^{-\frac{x^2}{k}} dx = \int f(x)dx$. This seems fairly basic, since it can be directly shown that the exponential part of the integrand, $e^{-\frac{x^2}{k}} \to 1$ as $k \to \infty$. Is there something I am missing? Are there extra steps needed to show that the integral of the limit is equal to the limit of the integral? Is this even necessary? I feel like this question is too simple relative to the rest of the material in class, but I'm not sure what I am missing. - well, $f=g$ implies $\int f=\int g$... – leo Nov 20 '12 at 21:29 Are you sure he didn't ask $\lim_{k\rightarrow \infty}\int f(x)e^{-x^2/k}\,dx$? In that case, you need to justify switching the integral and the limit. – asmeurer Dec 3 '12 at 5:12 Over an interval or compact set, $f(x) e^{-x^2/k} \to f(x)$ uniformly. Then you can get $\int \lim = \lim \int$ from Riemann integration. Indeed, $f(x) e^{-x^2/k} \to f(x)$ pointwise and $\|f(x) e^{-x^2/k}\| \leq f(x)$. Therefore $$\lim_{k \to \infty} \int f(x) e^{-x^2/k} \, dx \to \int f(x) \, dx$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9569453597068787, "perplexity": 179.30620390131654}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999655160/warc/CC-MAIN-20140305060735-00051-ip-10-183-142-35.ec2.internal.warc.gz"}
http://mathhelpforum.com/advanced-algebra/138359-elements-symmetric-groups-centralizers.html	# Math Help - elements of symmetric groups and centralizers 1. ## elements of symmetric groups and centralizers Let P = (1, 2, 3, .... n) in $S_n$. a. Show there are (n-1)! distinct n-cycles in $S_n$. b. How many conjugates does P have in $S_n$? c. Let C(P)=N(P) be the centralizer of P in $S_n$. Using (b), find \|C(P)\|. d. Find the subgroup C(P). my thoughts: a -- this seems really obvious, but I never actually learned how to show it! I have no ideas. b. by part (a), wouldn't this be simply (n-1)!, since that's the property of symmetric groups? c & d, I really don't know what to do. Do I use the class equation somehow, or another theorem? Thanks so much for any help! 2. Originally Posted by kimberu Let P = (1, 2, 3, .... n) in $S_n$. a. Show there are (n-1)! distinct n-cycles in $S_n$. b. How many conjugates does P have in $S_n$? c. Let C(P)=N(P) be the centralizer of P in $S_n$. Using (b), find \|C(P)\|. d. Find the subgroup C(P). my thoughts: a -- this seems really obvious, but I never actually learned how to show it! I have no ideas. b. by part (a), wouldn't this be simply (n-1)!, since that's the property of symmetric groups? c & d, I really don't know what to do. Do I use the class equation somehow, or another theorem? Thanks so much for any help! For (a), observe that (1 2 3 ... n )= (2 3 .. n 1) = (3, 4, .. n 1 2 ). To find the number of distinct n-cycles, you need to fix the first element in the n-cycle, let's say 1, and consider the permutation of the remaining elements. So there are (n-1)! distinct n-cycles in S_n. For (b), a conjugacy class in S_n has the same cycle type. So there are (n-1)! memebers in the conjugacy class of n-cycle in S_n. (c). The centralizer of (1 2 3 .. n) in S_n is simply a group generated by (1 2 3 .. n), which is <(1 2 3 .. n)>. If this is not immediate for you, cosider the permutation with two line notation. The members in the group <(1 2 3...n)> have a pattern in the two line notation. Try some members in the above group with two line notation and observe how they commute with (1 2 3 .. n). However, if you need to find the centralizer of (1 2 3 .. m) in S_n with m<n, the above needs a little bit of modification. For instance, the centralizer of (1 2 3 4 5 ) in S_8 is the group <(1 2 3 4 5), (6 8), (7 8)>. 3. Originally Posted by aliceinwonderland (c). The centralizer of (1 2 3 .. n) in S_n is simply a group generated by (1 2 3 .. n), which is <(1 2 3 .. n)>. If this is not immediate for you, cosider the permutation with two line notation. The members in the group <(1 2 3...n)> have a pattern in the two line notation. Try some members in the above group with two line notation and observe how they commute with (1 2 3 .. n). Thanks a lot - I understand parts a&b, but I'm a little shaky on the centralizer. I don't think I know which unique pattern you mean in the two-line notation. (Also, is the order of <(1 2 3 .. n)> also (n-1)!, that is, is this group the same as the conjugacy class? I'm not sure how to find that either.) 4. Originally Posted by kimberu Thanks a lot - I understand parts a&b, but I'm a little shaky on the centralizer. I don't think I know which unique pattern you mean in the two-line notation. (Also, is the order of <(1 2 3 .. n)> also (n-1)!, that is, is this group the same as the conjugacy class? I'm not sure how to find that either.) The order of <(1 2 3 ... n)> is n. It is the cyclic group generated by (1 2 3 .. n) in S_n. So it is an abelian group. For instance, if n=4 and let $\tau = (1 2 3 4 )$, then the cyclic group generated by $\tau$ is $\{1, \tau, \tau^2, \tau^3\}$. I encourage you to verify this with the two line notation. All elements in this group commute with $\tau$, which implies $\rho\tau\rho^{-1}=\tau$ where $\rho \in \{1, \tau, \tau^2, \tau^3\}$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9372479915618896, "perplexity": 716.3638499290673}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246658061.59/warc/CC-MAIN-20150417045738-00059-ip-10-235-10-82.ec2.internal.warc.gz"}
https://nips.cc/Conferences/2015/ScheduleMultitrack?event=5722	Timezone: » Poster Reflection, Refraction, and Hamiltonian Monte Carlo Hadi Mohasel Afshar · Justin Domke Tue Dec 08 04:00 PM -- 08:59 PM (PST) @ 210 C #43 #None Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics with non-smooth functions, leading to poor performance. This paper is motivated by the behavior of Hamiltonian dynamics in physical systems like optics. We introduce a modification of the Leapfrog discretization of Hamiltonian dynamics on piecewise continuous energies, where intersections of the trajectory with discontinuities are detected, and the momentum is reflected or refracted to compensate for the change in energy. We prove that this method preserves the correct stationary distribution when boundaries are affine. Experiments show that by reducing the number of rejected samples, this method improves on traditional HMC.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9169958829879761, "perplexity": 984.9323026916866}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107889651.52/warc/CC-MAIN-20201025183844-20201025213844-00117.warc.gz"}
http://physics.stackexchange.com/questions/93904/speed-of-light-energy	# Speed of light energy Considering the amount of energy necessary to accelerate a particle to the speed of light (ie; half the energy in the entire universe) how could we have so many things already going the speed of light? Maybe there should be only two or three things (objects or particles etc.) in the universe already going that fast. Just a few photons for example, in the whole universe. - half the energy in the entire universe No, it's MUCH bigger, infinite in fact. – jinawee Jan 16 at 16:55	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8982224464416504, "perplexity": 514.7362861555354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802773058.130/warc/CC-MAIN-20141217075253-00104-ip-10-231-17-201.ec2.internal.warc.gz"}
https://arxiv.org/list/astro-ph.CO/1607	# Cosmology and Nongalactic Astrophysics ## Authors and titles for astro-ph.CO in Jul 2016 [ total of 341 entries: 1-25 \| 26-50 \| 51-75 \| 76-100 \| ... \| 326-341 ] [ showing 25 entries per page: fewer \| more \| all ] [1] Title: The dimensionless age of the Universe: a riddle for our time Authors: Arturo Avelino (1), Robert P. Kirshner (1 and 2) ((1) Harvard University, (2) Gordon and Betty Moore Foundation) Comments: 14 pages, 12 figures. Accepted for publication in the Astrophysical Journal (ApJ) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc) [2] Title: Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [3] Title: H0LiCOW I. $H_0$ Lenses in COSMOGRAIL's Wellspring: Program Overview Comments: 16 pages, 3 figures, submitted to MNRAS and revised based on referee's comments Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA) [4] Title: Cosmological Hydrodynamical Simulations of Galaxy Clusters: X-ray Scaling Relations and their Evolution Comments: 23 pages, 11 figures, 5 tables Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [5] Title: A Combined View of Sterile-Neutrino Constraints from CMB and Neutrino Oscillation Measurements Comments: 6 pages, 3 figures, Version accepted by Physics Letters B, minor changes to text, results unchanged Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Experiment (hep-ex); High Energy Physics - Phenomenology (hep-ph) [6] Title: Perturbative approach to covariance matrix of the matter power spectrum Comments: 22 pages, 17 figures, 1 table Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [7] Title: Testing anthropic reasoning for the cosmological constant with a realistic galaxy formation model Comments: 6 pages, 4 figures, accepted for publication in MNRAS Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th) [8] Title: Constraining $f(R)$ Gravity Theory Using Weak Lensing Peak Statistics from the Canada-France-Hawaii-Telescope Lensing Survey Comments: 6 pages, 3 figures. Updated to journal version Journal-ref: Phys. Rev. Lett. 117, 051101 (2016) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [9] Title: Cosmological constraints from $μE$ cross-correlations Authors: Atsuhisa Ota Journal-ref: Phys. Rev. D 94, 103520 (2016) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) [10] Title: Constraining the dark energy equation of state using Bayes theorem and the Kullback-Leibler divergence Comments: 9 pages, 3 tables, 5 figures; published in MNRAS Journal-ref: MNRAS (2016) 466 (1): 369-377 Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Instrumentation and Methods for Astrophysics (astro-ph.IM) [11] Title: H0LiCOW II. Spectroscopic survey and galaxy-group identification of the strong gravitational lens system HE0435-1223 Comments: Version revised to address referee's comments, submitted to MNRAS, 21 pages (incl. Appendix). Data associated to the paper available from the H0LICOW website www.h0licow.org Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA) [12] Title: Correcting cosmological parameter biases for all redshift surveys induced by estimating and reweighting redshift distributions Comments: 14 pages, 1 table, 7 figures, updated to match version accepted in the MNRAS Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [13] Title: Endlessly flat scalar potentials and $α$-attractors Journal-ref: Phys.Lett. B761 (2016) 111-114 Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph) [14] Title: Precise measurements of inflationary features with 21 cm observations Comments: 7 pages, 3 figures, replaced with revised version Journal-ref: Phys. Rev. D 94, 123518 (2016) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [15] Title: CosmicFish Validation Notes V1.0 Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Instrumentation and Methods for Astrophysics (astro-ph.IM) [16] Title: Integrated approach to cosmology: Combining CMB, large-scale structure and weak lensing Comments: 29 pages, 19 figures, 3 tables, to appear in PRD, updated following referee's comments including small changes in results Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [17] Title: Constraining a halo model for cosmological neutral hydrogen Authors: Hamsa Padmanabhan (ETHZ), Alexandre Refregier (ETHZ) Comments: 10 pages, 9 figures, 2 tables; version accepted for publication in MNRAS Journal-ref: MNRAS, Volume 464, Issue 4, p.4008-4017 (2017) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [18] Title: Numerical simulations challenged on the prediction of massive subhalo abundance in galaxy clusters: the case of Abell 2142 Comments: 8 pages, 2 figures. Modified to match the version published in ApJL Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA) [19] Title: Linear and non-linear bias: predictions vs. measurements Comments: Added systematic tests and extended discussion. Accepted for publication in MNRAS Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [20] Title: Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres Comments: 17 pages, 18 figures, updated corresponding to published version Journal-ref: Mon Not R Astron Soc (2017) 466 (2): 2067-2084 Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [21] Title: Synchrotron Emission from Dark Matter Annihilation: Predictions for Constraints from Non-detections of Galaxy Clusters with New Radio Surveys Comments: accepted to ApJ; removal of LOFAR Tier 2 limits; other minor text changes; conclusions largely unchanged Journal-ref: ApJ (2017) 839, 33 Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Astrophysical Phenomena (astro-ph.HE); High Energy Physics - Phenomenology (hep-ph) [22] Title: Measuring neutrino mass imprinted on the anisotropic galaxy clustering Comments: 11 pages, 4 figures, 2 tables Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Phenomenology (hep-ph) [23] Title: The Quantum Field Theory of K-mouflage Journal-ref: Phys. Rev. D 94, 043529 (2016) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) [24] Title: WISE x SuperCOSMOS photometric redshift catalog: 20 million galaxies over 3pi steradians Comments: Data available from this http URL Journal-ref: The Astrophysical Journal Supplement Series, Volume 225, Number 1 (2016) Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA); Instrumentation and Methods for Astrophysics (astro-ph.IM) [25] Title: The SuperCOSMOS all-sky galaxy catalogue Comments: Submitted to MNRAS. Data available at this http URL Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); Astrophysics of Galaxies (astro-ph.GA) [ total of 341 entries: 1-25 \| 26-50 \| 51-75 \| 76-100 \| ... \| 326-341 ] [ showing 25 entries per page: fewer \| more \| all ] Disable MathJax (What is MathJax?)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30661535263061523, "perplexity": 20948.67316815255}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948572676.65/warc/CC-MAIN-20171215133912-20171215155912-00707.warc.gz"}
https://www.physicsforums.com/threads/help-friction-on-ice-involving-weight.188350/	# HELP Friction on Ice involving weight 1. Oct 1, 2007 ### imadagron89 You are driving a 2580.0 kg car at a constant speed of 14.0 m/s along an icy, but straight, level road. As you approach an intersection, the traffic light turns red. You slam on the brakes. Your wheels lock, the tires begin skidding, and the car slides to a halt in a distance of 26.4 m. What is the coefficient of kinetic friction between your tires and the icy road. 3. The attempt at a solution I found the acceleration to be -.5303 by taking -14/26.4 (v=v0+at) but now I'm confused as how to find the kinetic friction by stopping 2. Oct 1, 2007 ### Staff: Mentor Find the acceleration or deceleration, then a/g = $\mu$, since Ffriction = ma = $\mu$ W = $\mu$mg. 3. Oct 1, 2007 ### imadagron89 im sorry man still not getting it, is there some sort of website that has all the equations on it? Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Similar Discussions: HELP Friction on Ice involving weight	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8334468603134155, "perplexity": 2675.488519100613}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818686117.24/warc/CC-MAIN-20170920014637-20170920034637-00136.warc.gz"}
https://arxiv.org/abs/1509.03890	cond-mat.dis-nn (what is this?) # Title: Many-body Localization Transition in Rokhsar-Kivelson-type wave functions Abstract: We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the R\'enyi entropies are non-Gaussian. We find that R\'enyi entropies with different R\'enyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior. Comments: Published version. Improved version with 1 new references; 17 pages, 68 references and 16 figures 9some have been reordered) Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Journal reference: Physical Review B 92, 214204 (2015) DOI: 10.1103/PhysRevB.92.214204 Cite as: arXiv:1509.03890 [cond-mat.dis-nn] (or arXiv:1509.03890v5 [cond-mat.dis-nn] for this version)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8652524948120117, "perplexity": 1736.1446792271406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267155814.1/warc/CC-MAIN-20180919004724-20180919024724-00141.warc.gz"}
https://www.nature.com/articles/s41467-017-01792-x?error=cookies_not_supported&code=87dfdee0-d8c2-47e0-9e8e-ed51daa9ef9e	Article \| Open \| Published: # New science of climate change impacts on agriculture implies higher social cost of carbon ## Abstract Despite substantial advances in climate change impact research in recent years, the scientific basis for damage functions in economic models used to calculate the social cost of carbon (SCC) is either undocumented, difficult to trace, or based on a small number of dated studies. Here we present new damage functions based on the current scientific literature and introduce these into an integrated assessment model (IAM) in order to estimate a new SCC. We focus on the agricultural sector, use two methods for determining the yield impacts of warming, and the GTAP CGE model to calculate the economic consequences of yield shocks. These new damage functions reveal far more adverse agricultural impacts than currently represented in IAMs. Impacts in the agriculture increase from net benefits of $2.7 ton−1 CO2 to net costs of$8.5 ton−1, leading the total SCC to more than double. ## Introduction Climate science has advanced significantly in the past 20 years so that our understanding of the physical consequences of greenhouse gas emissions is now well established1. The biophysical effects of changes in temperature and rainfall on, for example, ecosystems, agricultural yields, and sea-level rise are also increasingly well understood. However, this new science is not reflected in some of the highly influential economic models currently used to determine the social cost of carbon (SCC)—a measure of the total damages from an additional ton of CO2 emissions used to quantify the benefits of emissions reduction. In most cases, the scientific basis for damage functions (reduced-form expressions for how climate change affects economic welfare) in these models is undocumented, tautological (based on damages from previous versions of the models), or dates from between 10 and 20 years ago and therefore may have been superseded by more recent results2. ## Discussion Here we show that the current science of climate change impacts on agriculture, combined with up-to-date economic modeling, implies larger damages to the sector than currently represented in models used to calculate the SCC. In contrast to existing regional damage functions, which show benefits in every region up to at least 3 °C of warming, we find potential for welfare declines even at much lower levels of warming. Though the range of possible effects of climate change on yields is substantial, our finding that the SCC should be increased is robust to this variation, as well as to uncertainties relating to the discount rate, economic modeling, and extrapolation of the damage function. Of the three IAMs used to estimate the SCC, only FUND explicitly represents the agricultural sector, so that has been the focus of comparison in this paper. However, agricultural impacts are a part of damages in the two other models. In PAGE (2009 version) agricultural impacts are represented within the market impacts damage function and in DICE (2013 version) they are in the non-sea level rise damage function29, 30. Given the same socio-economic assumptions and climate model used to calculate SCC values reported in the previous section, these damage functions give SCC values of $6.6 ton−1 and$18.9 ton−1, respectively (3% discount rate)28. In the case of PAGE, market impacts are substantially smaller than agricultural damages estimated using the meta-analysis (\$8.5 ton−1), implying either that there are large off-setting benefits in other market sectors or that the empirical basis for the market impacts damage function may need to be reviewed. In the case of DICE, our results imply that agricultural impacts make up between 19% (AgMIP) and 45% (meta-analysis) of non-sea level rise damages. Governments are currently relying on IAMs to evaluate climate and energy policy and these models have already come under legal scrutiny as a result31, 32, 5. It is therefore important, from both a regulatory and an academic perspective, that the representation of damages reflect current scientific consensus on impacts in a timely and transparent manner. Here we have shown that improving the empirical basis of just one sector, agriculture, results in a large increase in the SCC. In addition, we have demonstrated the potential of an end-to-end analysis directly linking the biophysical impacts of climate change to economic welfare and ultimately the SCC. Damage functions resulting from this approach are more clearly tied to underlying science and can be easily updated in light of future findings. This approach, which can also be extended to other sectors, therefore represents an essential step in maintaining and improving the integrity of IAM results going forward. ## Methods ### Meta-analysis of yield response to climate change The yield–temperature response functions used in this paper are derived from a database of studies estimating the climate change impact on yield compiled for the IPCC 5th Assessment Report17, also described in a meta-analysis by Challinor et al.16. Methods for sampling the literature and criteria for inclusion are described in Challinor et al.16. as a “broad and inclusive literature search” combined with quality-control procedures documented in the Supplemental Information of that paper. In this study, we focus on four major crops—maize, rice, wheat, and soybeans. The bulk of the scientific literature on yield response to temperature relates to these crops, which collectively account for about 20% of the value of global agricultural production, 65% of harvested crop area, and nearly 50% of calories directly consumed33. For the four crops, the database contains 1010 observations (344, 238, 336, and 92 for maize, rice, wheat, and soybeans, respectively) from 56 different studies (many studies report multiple yield changes for different crops, different locations, different levels of temperature change, or different assumptions about adaptation). The studies include 8 empirical studies and 48 process-based studies, published between 1997 and 2012. Supplementary Figs 14 and 15 show the geographic coverage of production areas within the database and the distribution of publication dates. Of the 1010 data points, 451 are reported as including some form of on-farm, within-crop, agronomic adaptation. The vast majority of these adaptations involve adjusting either planting date (10%) or cultivar (12%) or both (44%). Recognizing the existence of a more recent and possibly more systematic literature review for wheat yields, we perform a robustness check where we incorporate additional results identified in Wilcox and Makowski34. This substantially increases the number of observations for wheat but does not affect our estimated response curve (Supplementary Fig. 16). We merge this database with information on baseline growing-season temperature for each data point. To do this, each data point was assigned to a country. For the 14% of studies looking at more than one country, the country assigned was the one with the highest production of the relevant crop. Average baseline growing-season temperatures were calculated using planting and harvest dates from Sacks et al35. and gridded monthly temperatures for 1979–2013 from the Climate Research Unit36. These were averaged to the country level using year 2000 crop production weights from Monfreda et al37. The response functions are jointly estimated from the point-estimates in the database using a multi-variate: $$\begin{array}{ccccc}\\ \Delta Y_{ijk} = {\mathrm{\beta }}_{1{{j}}}\Delta T_{ijk}{\mathrm{}}Crop_j + {\mathrm{\beta }}_{2{{j}}}\Delta T_{ijk}^2{\mathrm{}}Crop_j + {\mathrm{\beta }}_{3{\mathrm{j}}}\Delta T_{ijk}{\mathrm{}}Crop_j{\mathrm{}}\bar T_{jk} \\ + {\mathrm{\beta }}_{4{{j}}}\Delta T_{ijk}^2{\mathrm{}}Crop_j{\mathrm{}}\bar T_{jk} + \beta _5f_1\left( {\Delta {\rm CO}_{2ijk}} \right){\mathrm{}}C_{3j} \\ + \beta _6f_2\left( {\Delta {\rm CO}_{2ijk}} \right){\mathrm{}}C_{4j} + \beta _7\Delta P_{ijk} + \beta _8\Delta T_{ijk}{\mathrm{*}}Adapt_{ijk} + \beta _9Adapt_{ijk} + \varepsilon _{ijk}\end{array}$$ (1) where $$\Delta Y_{ijk}$$ is the change in yield from point-estimate i for crop j in country k (in %). $$\Delta T_{ijk},\Delta CO_{2ijk}$$ and $$\Delta P_{ijk}$$ are the changes in temperature (in degree C), CO2 concentration (in parts per million (ppm)), and rainfall (in percent) for point-estimate ijk, $$\bar T_{jk}$$ is the baseline growing-season temperature for crop j in country k, $$C_{3j}$$ and $$C_{4j}$$ are dummy variables indicating whether crop j is C3 or C4, and $$Adapt_{ijk}$$ is a dummy variable indicating whether the point-estimate includes any on-farm adaptation. Eq. 1 is estimated using an ordinary least squares regression. Uncertainty in the parameters is estimated through 1500 block bootstraps, with blocks defined at the study level, allowing for possible correlation between point-estimates from the same study. Error bars reported throughout the paper are based on the 2.5th and 97.5th quantiles of the bootstrapped distribution. This treatment of the errors does assume independence between studies, which may be questionable if the same model is used in multiple studies. In total, 28 models, made up of 17 process-based model families (i.e., treating CERES-maize, CERES-rice, and CERES-wheat as a single model) and 11 statistical models, are used in the 56 studies. Supplementary Fig. 17 shows response curves with standard errors based on a model block bootstrap as a robustness check. These are qualitatively similar to the error bars shows in Fig. 1, particularly for warming <3 °C that is the focus of the economic analysis, suggesting the study block bootstrap is capturing the bulk of residual covariance. All error bars reported in the paper show confidence intervals rather than prediction intervals. This is appropriate since the relevant uncertainty is in the expected response of yield to temperature change, which is given by confidence intervals. There are a number of important things to note about this specification shown in Eq. 1. First, the impacts of temperature are modeled as crop-specific quadratics ($${\mathrm{\beta }}_{1{{j}}}$$ and $${\mathrm{\beta }}_{2{{j}}}$$ terms), allowing the effects of warming to vary by crop. In addition, the effects of warming are allowed to vary with baseline growing-season temperature ($${\mathrm{\beta }}_{3{{j}}}$$ and $${\mathrm{\beta }}_{4{{j}}}$$ terms), capturing the intuition that the impacts of a 1 °C warming should be different in a cold location than in a hot location. Second, there is no intercept term, thereby forcing response functions without adaptation through the origin. This is consistent with the expected functional form of a climate damage function, which should have no impacts if there are no changes in climate variables. However, we include an intercept for studies that do include adaptation ($$\beta _9$$). This is prompted by the observation that, in many studies, ‘adaptation’ is represented by changing management practices that would improve yields even in the current climate, such as adoption of improved varieties or increasing fertilizer or irrigation inputs22. Failing to include an adaptation intercept in this context will lead to an overestimation of the potential of these kinds of changes to reduce the negative impacts of a warming climate. This adaptation intercept is subtracted in our estimates of the effect of climate on yield to produce an adjusted damage function that goes through the origin. (In other words, we calculate the effect of a change in temperature of X on yields to be the yield change predicted from Eq. 1 for a temperature change of X minus the yield change predicted for a temperature change of zero (i.e., $$\beta _6\,\,Adapt_{ij}$$)). The true effect of adaptation is the interaction with temperature change, given by the $$\beta _8$$ term in Eq. 1, which is included in all subsequent analyses. This term captures the effect of management changes that are not beneficial today but that will become beneficial under a changed climate, the standard definition of adaptation. Finally, the functions $$f_1()$$ and $$f_2()$$ are concave, allowing for a declining marginal effect of CO2, consistent with a number of field studies20, 38. Specifically, the function takes the form $$f\left( {\Delta {\rm CO}_{2ij}} \right) = \frac{{\Delta {\rm CO}_{2ij}}}{{\Delta {\rm CO}_{2ij} + A}}$$ where A is a free parameter set at 100 ppm for $$C_3$$ crops and at 50 ppm for $$C_4$$ crops based on a comparison of the R 2 across models using multiple possible values. The changes in CO2 are adjusted so that all are relative to a modern baseline of 360 ppm (the most common baseline value for studies included in the analysis). In addition to Eq. 1, our preferred specification, we investigate the effects of several alternate specifications. Specifically we first investigate whether newer studies (publication date of 2005 or later) give a different temperature response compared to the full sample; second investigate the effect of individual agronomic adaptations, specifically changing cultivar and planting date; third allow the effect of temperature to differ depending on whether the study was a process-based or empirical study; fourth add a $$\Delta T_{ijk}^3$$ term in the specification; and finally perform F-tests on individual terms within the model. These findings are documented in the SI (Supplementary Figs 1820, Supplementary Tables 6 and 7). They do not substantially alter our estimates of the yield response to climate change. ### Gridded yield changes After estimating Eq. 1, we developed global gridded yield change scenarios for the four major crops (maize, wheat, rice, and soybeans). Although IAM damage functions are typically based on global temperature changes, it is important to account for the fact that local warming may differ significantly from global warming in estimating impacts. Local yield impacts will depend on local temperature changes, which scale in a predictable way with global temperature change. We estimate this scaling using the CMIP5 multi-model ensemble mean for the high emissions scenario RCP 8.539. For each grid cell, we take the change in temperature between a future (2035–2065) and baseline (1861–1900) period and divide by the mean global warming over this time period, giving the pattern scaling relationship between global and local temperature change for each grid cell (Supplementary Fig. 21). For a given increase in global mean temperature, warming is larger over land than over the ocean and at high latitudes compared to the tropics. These gridded temperature changes are combined with the yield–temperature response function estimated using Eq. 1 and baseline growing-season temperature to give yield changes at different levels of global warming. We calculate yield changes for warming of 1, 2, and 3 degree Celsius including the estimated effect of on-farm adaptation. Any predicted yield losses >100% are set to losses of 99%. The CO2 fertilization effect is included for all crops. CO2 concentrations for a given level of global temperature change are determined based on a fitted quadratic relationship between global temperature change and CO2 concentrations from the RCP 8.5 CMIP5 multi-model ensemble mean (adjusted R 2 > 0.999, 98 degrees of freedom). ### AgMIP GGCMI ensemble The AgMIP GGCMI is the one other source of global, multi-crop, multi-model yield responses and so we compare the results of our meta-analysis against these results. This ensemble of gridded crop model outputs includes up to seven process-based crop models, run using five General Circulation Models (GCMs)18. Yield changes are calculated relative to the 1981–2000 average. In order to determine yield changes for specific levels of temperature change (1–3 °C), we find the year in which warming passes each specific level for each GCM for the RCP 8.5 emissions scenario (taking the average of multiple ensemble members, if available) and take the 11-year yield average around that year40. We determine irrigated areas using crop-specific irrigation areas from Monfreda et al37. and use irrigated results for cells where irrigated crop area exceeds non-irrigated crop area. We use runs including CO2 fertilization for all analyses. The results reported in the main text use a preferred AgMIP ensemble that only includes models that explicitly represent nitrogen stress (EPIC, GEPIC, PEGASUS, and pDSSAT). We believe these results are preferred given crop response to changing temperature and, in particular, CO2 conditions is known to depend on nutrient availability41, 42 and crops in many areas of the world are currently under-fertilized43. Moreover, the distinction between models based on representation of nitrogen stress has been identified as significant in understanding ensemble results by the AgMIP team18. Results in the main text should therefore be interpreted as impacts assuming continuation of current nutrient management practices. In the SI, we report results using the full AgMIP ensemble, which differ substantially from those of the restricted ensemble (Supplementary Fig. 11 and Supplementary Table 5). For both ensembles, the mean is calculated as a simple mean of yield change for each level of warming using all crop model×GCM combinations. ### Welfare consequences of yield changes To estimate the economic implications of warming-induced yield shocks, we use the Global Trade Analysis Project (GTAP) general equilibrium model and its accompanying database23, 24. GTAP is a widely used, comparative static general equilibrium model that exhaustively tracks bilateral trade flows between all countries in the world and explicitly models the consumption and production for all commodities of each national economy. Producers are assumed to maximize profits, while consumers maximize utility. Factor market clearing requires that supply equal demand for agricultural and non-agricultural skilled and unskilled labor and capital, natural resources, and agricultural land, and adjustments in each of these markets in response to the climate change shocks determines the resulting wage and rental rate impacts. The model has been validated with respect to its performance in predicting the price impacts of exogenous supply side shocks, such as those that might result from global climate change44. Additional information on the structure of GTAP is given in Supplementary Fig. 22. GTAP captures a number of dimensions important for determining the welfare implications of climate change impacts on agriculture. These include the shifting of land area between crops, potential intensification of production, shifting of consumption between commodities and sources of goods, and the adjustment of global trade patterns (Supplementary Table 2). For the purposes of this study, GTAP is run with 140 regions and 14 commodities—with the latter designed to place an emphasis on the agricultural sector. Productivity changes are introduced to GTAP as a Hicks-neutral shift in the production function such that farmers employing the same combination of inputs would experience X% lower output in the presence of a X% climate-driven yield shock. Wheat and rice are modeled as individual sectors within each region. Maize is part of the coarse grains sector and soybeans is part of the oilseeds sector. Impacts in these sectors are scaled downwards based on the relative importance of maize and soybeans for sectoral production in each region. Yields of crops not covered in the meta-analysis (coarse grains nec., oilseeds nec., sugarcane, cotton, and fruits and vegetables) are not altered. Absent normalization, this will lead to an underestimate of potential climate impacts, since these other sectors are also likely to be affected by climate change. Therefore, in the results that follow, welfare changes are normalized by the value of production of the crops covered in the meta-analysis. Global and regional welfare changes are measured in terms of equivalent variation and are decomposed into the three components shown in Fig. 2 following Hertel and Randhir25. In order to explore uncertainty in the economic modeling, we perform a systematic sensitivity analysis of GTAP output to perturbations in four sets of key parameters governing the supply and demand behavior in this model. On the supply side, these pertain to the parameters determining the intensive (substitution of other inputs for land) and extensive (land supply elasticities) margins of crop supply response to commodity price. On the demand side, these are the parameters that govern the price elasticity of demand for food and the price elasticity of demand for imports—which in turn govern the price responsiveness of export demands. Parameters vary by commodity/sector. We develop symmetric, triangular distributions for each parameter value, based on estimates in the literature (Supplementary Table 8) and sample from these distributions using the Gaussian Quadrature approach implemented by Arndt45. This approach has been shown to perform nearly as well as a complete Monte Carlo analysis in the context of CGE modeling, but it is much more efficient, requiring far fewer model solutions46. Due to the computational burden of conducting a complete, systematic sensitivity analysis in the 140 region model, we collapse those regions down to the 16 FUND regions for purposes of this robustness check. The resulting mean and standard deviations for regional welfare are reported in Supplementary Fig. 13. Because on the dominance of direct effects (i.e., the impact of climate change in yields) in many of the regions’ total welfare, variation of the economic parameters has a modest impact on the underlying uncertainty. ### Calculating the social cost of carbon Results of the economic modeling are used to create damage functions that relate changes in economic welfare (measured as percentage of the value of agricultural sector output) with temperature change. GTAP results are aggregated from the country level to the 16 FUND regions. Damage functions are based on a linear interpolation between the point-estimates of welfare changes at 1, 2, and 3 °C of warming and then a linear extrapolation beyond 3 °C (results reported in main text) or on a quadratic fitted through the point estimates (Supplementary Table 5). These agricultural damage functions are then incorporated into a sectorally and regionally disaggregated SCC damage module based on the FUND model, keeping the rest of the impact sectors unchanged28, 47. Damage functions in the module use the central parameter estimates of FUND. The full FUND model includes probability distributions over many parameters and is designed to be run in a Monte Carlo mode47. This uncertainty is not dealt with in this paper, meaning uncertainty reported in the SCC reflects only the uncertainty in the yield response derived from the meta-analysis. The damage module is driven by a standardized socio-economic and emissions pathway and climate model28. We use a business-as-usual emissions scenario (Scenario 2 in ref. 3), paired with the DICE climate module48. This produces a warming of 4 °C of warming above preindustrial by 2100. The SCC is calculated by adding a 1 Gt pulse of CO2 emissions to this reference emissions path in 2020 and comparing the time path of damages along the perturbed pathway to the reference case. Then these incremental damages (or benefits) are discounted back to 2020 at a 3% discount rate and normalized by the CO2 pulse volume to give the SCC. Results using alternative discount rates are given in Supplementary Table 5. As the SCC is additive, it can be decomposed by sector and region, allowing a detailed comparison of the regional impacts in agriculture between FUND and the revised regional damage functions. ### Code availability Code for GTAP is open source and available for download at http://www.gtap.agecon.purdue.edu/resources/res_display.asp?RecordID=2458. The FUND model is open source and available at http://www.fund-model.org/source-code. All other code is available from the authors upon request. ### Data availability Data for the meta-analysis is available at ag-impacts.org. Gridded yield changes based on the meta-analysis are available at 10.6084/m9.figshare.5417548. Welfare changes for GTAP regions based on yield shocks from both the meta-analysis and AgMIP are available at 10.6084/m9.figshare.5417557 and 10.6084/m9.figshare.5417560. Other data are available from the authors upon request. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. ## References 1. 1. IPCC. Climate Change 2013: The Physical Science Basis. Contribution of Working Group 1 to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge University Press, Cambridge, 2013). 2. 2. NAS. Valuing Climate Damages: Updating Estimation of the Social Cost of Carbon Dioxide (National Academies Press, Washington, DC, 2017). 3. 3. IAWG Technical Support Document: Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis under Executive Order 12866 Environmental Protection Agency, Washington DC (2013). 4. 4. Nordhaus, W. D. Revisiting the social cost of carbon. Proc. Natl. Acad. Sci. 114, 1518–1523 (2017). 5. 5. Schlatter, L. Findings of Fact, Conclusions, and Recommendations: Carbon Dioxide Values (2016). State of Minnesota, Office of Administrative HearingsSt Paul, MN 6. 6. State of California, Assembly Bill 197 (2016). 7. 7. Larson, A. Subsidies Proposed for New York’s Upstate Power Plants. Available at: http://www.powermag.com/subsidies-proposed-for-new-yorks-upstate-nuclear-power-plants/. (Accessed: 1st September 2016) (2016) 8. 8. Burke, M. et al. Opportunities for advances in climate change economics. Science 352, 292–293 (2016). 9. 9. Pindyck, R. S. Climate change policy: what do the models tell us? J. Econ. Lit. 51, 860–872 (2013). 10. 10. Revesz, R. et al. Improve economic models of climate change. Nature 508, 173–175 (2014). 11. 11. Stern, N. Economics: current climate models are grossly misleading. Nature 530, 407–409 (2016). 12. 12. Carleton, T. A. & Hsiang, S. M. Social and economic impacts of climate. Science 353, 1112 (2016). 13. 13. IPCC. in Climate Change 2014: Impacts, Adaptation and Vulnerability. Working Group 2 Contribution to the IPCC 5th Assessment Report (eds Field, C. B. et al.) (Cambridge University Press, Cambridge, 2014). 14. 14. Hsiang, S. et al. Estimating economic damage from climate change in the United States. Science 356, 1362–1369 (2017). 15. 15. Houser, T., Hsiang, S., Kopp, R. & Larsen, K. Economic Risks of Climate Change: an American Prospectus (Columbia University Press, New York, 2015). 16. 16. Challinor, A. J. et al. A meta-analysis of crop yield under climate change and adaptation. Nat. Clim. Chang. 4, 287–291 (2014). 17. 17. Porter, J. R. et al. in Climate Change 2014: Impacts, Adaptation and Vulnerability. Working Group 2 Contribution to the IPCC 5th Assessment Report, Ch. 7 (Cambridge University Press, Cambridge, 2014). 18. 18. Rosenzweig, C. et al. Assessing agricultural risks of climate change in the 21st century in a global gridded crop model intercomparison. Proc. Natl. Acad. Sci. USA 111, 3268–3273 (2014). 19. 19. Asseng, S. et al. Rising temperatures reduce global wheat production. Nat. Clim. Chang. 5, 143–147 (2014). 20. 20. Long, S. P., Ainsworth, E. a., Leakey, A. D. B., Nösberger, J. & Ort, D. R. Food for thought: lower-than-expected crop yield stimulation with rising CO2 concentrations. Science 312, 1918–1921 (2006). 21. 21. Leakey, A. D. B. et al. Photosynthesis, productivity, and yield of maize are not affected by open-air elevation of CO2 concentration in the absence of drought. Plant. Physiol. 140, 779–790 (2006). 22. 22. Lobell, D. Climate change adaptation in crop production: Beware of illusions. 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The PAGE09 Integrated Assessment Model: A Technical Description. Cambridge Judge Business School Working Paper (2011). 30. 30. Nordhaus, W. D. & Sztorc, P. DICE 2013R: Introduction and User’s Manual (2013). 31. 31. MPUC. In the Matter of the Further Investigation into Environmental and Socioeconomic Costs Under Minnesota Statutes Section 216B.24222, Subdivision 3 (2016). 32. 32. U.S. Court of Appeals, Zero Zone, Inc. et al., v. United States Department of Energy, et al. (2016). 33. 33. FAO. FAOSTAT, V.3. Available at: faostat3.fao.org. (2016). 34. 34. Wilcox, J. & Makowski, D. A meta-analysis of the predicted effects of climate change on wheat yields using simulation studies. Food Crops Res. 156, 180–190 (2014). 35. 35. Sacks, W. J., Deryng, D., Foley, J. A. & Ramankutty, N. Crop planting dates: an analysis of global patterns. Glob. Ecol. Biogeogr. 19, 607–620 (2010). 36. 36. CRU. Temperature Data. Available at: http://crudata.uea.ac.uk/cru/data/temperature/ (2016). 37. 37. Monfreda, C., Ramankutty, N. & Foley, J. A. Farming the planet: 2. Geographic distribution of crop areas, yields, physiological types, and net primary production in the year 2000. Glob. Biogeochem. Cycles 22, n/a–n/a (2008). 38. 38. Tubiello, F. N. et al. Crop response to elevated CO2 and world food supply. A comment on ‘ Food for Thought…’ by Long et al., Science 312: 1918–1921, 2006. 26, 215–223 (2007). 39. 39. Taylor, K. E., Stouffer, R. J. & Meehl, G. A. Bulletin of the American Meteorological Society. Bull Am. Meteorol. Soc. doi:10.1175/BAMS-D-11-00094.1 (2012). 40. 40. KNMI. Climate Explorer. Available at: climexp.knmi.nl (2015). 41. 41. Leakey, A. D. B. et al. Elevated CO2 effects on plant carbon, nitrogen, and water relations: six important lessons from FACE. J. Exp. Bot. 60, 2859–2876 (2009). 42. 42. Reich, P. B., Hobbie, S. E. & Lee, T. D. Plant growth enhancement by elevated CO2 eliminated by joint water and nitrogen limitation. Nat. Geosci. 7, 920–924 (2014). 43. 43. Mueller, N. D. et al. Closing yield gaps through nutrient and water management. Nature 490, 254–257 (2012). 44. 44. Valenzuela, E., Hertel, T. W., Keeney, R. & Reimer, J. J. Assessing global computable general equilibrium model validity using agricultural price volatility. Am. J. Agric. Econ. 89, 383–397 (2007). 45. 45. Arndt, C. An Introduction to Systematic Sensitivity Analysis via Gaussian Quadrature. Purdue University, West Lafayette IN (1996). 46. 46. DeVuyst, E. A. & Preckel, P. V. Sensitivity analysis revisted: a quadrature-based approach. J. Policy Model 19, 175–185 (1997). 47. 47. Anthoff, D. & Tol, R. S. J. FUNDv3.8 Scientific Documentation. Available at www.fund-model.org/versions (2014). 48. 48. Nordhaus, W. D. Economic aspects of global warming in a post-Copenhagen environment. Proc. Natl. Acad. Sci. USA 107, 11721–11726 (2010). ## Acknowledgements We thank Max Auffhammer, Sol Hsiang, Jerry Nelson, and David Lobell for comments on earlier drafts of this paper. T.H. acknowledges the support of the National Science Foundation (award 0951576) under the auspices of the RDCEP project at the University of Chicago and USDA-NIFA, Hatch Project 1003642. F.C.M. acknowledges support of this project by USDA NIFA (award 12225279). ## Author information ### Affiliations 1. #### Department of Environmental Science and Policy, University of California Davis, 2140 Wickson Hall, One Shields Avenue, Davis, CA, 95616, USA • Frances C. Moore 2. #### Global Trade Analysis Project, Purdue University, 403 West State Street, West Lafayette, IN, 47907, USA • Uris Baldos • & Thomas Hertel 3. #### Department of Agricultural Economics, Purdue University, 403 West State Street, West Lafayette, IN, 47907, USA • Uris Baldos • & Thomas Hertel 4. #### Purdue Climate Change Research Center, 203 S. Martin Jischke Drive Gerald D. and Edna E. Mann Hall, Suite 105, West Lafayette, IN, 47907, USA • Thomas Hertel 5. #### Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305, USA • Delavane Diaz ### Contributions F.C.M. conceived the paper, conducted the yield meta-analysis, and wrote the paper. U.B. ran the GTAP model and analyzed welfare results. T.H. ran the GTAP model and wrote the paper. D.D. ran the FUND damage module and wrote the paper. ### Competing interests The authors declare no competing financial interests. ### Corresponding author Correspondence to Frances C. Moore.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5601913332939148, "perplexity": 3441.260439426035}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658662.31/warc/CC-MAIN-20190117000104-20190117022104-00387.warc.gz"}
https://link.springer.com/chapter/10.1007/978-94-007-7362-2_49	# Nonlinear Forced Convective Hydromagnetic Flow of Unsteady Biomagnetic Fluid Over a Wedge with Convective Surface Condition • M. M. Rahman • M. A. Sattar Conference paper Part of the Springer Proceedings in Complexity book series (SPCOM) ## Abstract Nonlinear forced convective hydromagnetic flow of an unsteady biomagnetic fluid over a wedge with convective surface has been analyzed numerically. The highly nonlinear coupled governing equations for the momentum, energy, angular momentum for the blood corpuscles and the magnetic induction are reduced to ordinary differential similarity equations by the introduction of a new similarity transformation. These equations are solved using very robust computer algebra software Maple 13. The effects of the various material parameters on the flow, temperature and microrotation fields are investigated. The results show that unsteadiness significantly controls the flow and heat transfer characteristics of the biomagnetic fluid. Strong unsteadiness may trigger back flow even for an accelerated flow. Due to the strong magnetic effect blood corpuscles may oscillate along the surface of the wedge. Induced magnetic field reduces fluid velocity and gives rise to its temperature significantly, which suggests that in the modeling of biomagnetic fluid the effect of induced magnetic field should be taken into account. ## Keywords Nusselt Number Boundary Layer Thickness Biot Number Skin Friction Coefficient Momentum Thickness These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. ## Nomenclature Bi Biot number Cf Skin friction coefficient cp Specific heat at constant pressure Ec Eckert number f Dimensionless stream function h Induced magnetic field parameter hf Heat transfer coefficient H* Induced magnetic field intensity H Dimensionless H* H0 Applied magnetic field intensity Hw Induced magnetic field j Micro-inertia per unit mass K M Magnetic field parameter m Velocity exponent N Dimensionless microrotation Nu Local Nusselt number n Microrotation parameter P Pressure Pm Magnetic Prandtl parameter Pr Prandtl number qw Surface heat flux Re Local Reynolds number S Coefficient of vortex viscosity t Time T Temperature within boundary layer Tf Temperature at the bottom Tw Temperature at the surface T Temperature of the ambient fluid u Velocity along x-axis U Free stream velocity U0 Characteristic velocity U* Nondim. free stream velocity v Velocity along y-axis X Characteristic length x Coordinate along the surface y Coordinate normal to surface ## Greek Symbols ρ Density of the fluid β Wedge angle parameter δ Length scale μ Dynamic viscosity μe Magnetic permeability υ Kinematic viscosity υs Δ Vortex viscosity parameter ξ Micro-inertia parameter ω Microrotation σ Fluid electric conductivity ψ Stream function κ Thermal conductivity η Similarity parameter τw Shear stress λ Nondim boundary layer thickness λ1 Dimensionless displacement thickness λ2 Dimensionless momentum thickness θ Dimensionless temperature Δη Step size ## Subscripts w Surface condition Boundary layer edge ## Notes ### Acknowledgment M.M. Rahman would like to thank the Sultan Qaboos University for financial support through the research grant IG/SCI/DOMAS/10/02. M.A. Sattar expresses his sincere gratitude to Sultan Qaboos University for proving local hospitality during his visit. ## References 1. Ahmadi G (1976) Self-similar solution of incompressible micropolar boundary layer flow over a semi- infinite plate. Int J Eng Sci 14(7):639–646 2. Anad M, Rajagopal KR (2004) A shear-thinning viscoelastic fluid model for describing the flow of blood. Int J Cardiol Med Sci 4(2):59–68Google Scholar 3. Anjali Devi SP, Kandasamy R (2001) Thermal stratification effects on laminar boundary-layer flow over a wedge with suction or injection. Mech Res Commun 28(3):349–354 4. Ariman T, Turk NA, Sylvester ND (1974) On steady pulsatile flow of blood. ASME J Appl Mech 41(1):1–7 5. Atefi and Moosaie MA (2005) Analysis of blood flow through arteries using the theory of micropolar fluids. In: Proceedings of the 12th Iranian biomedical engineering conference, TabrizGoogle Scholar 6. Aziz A (2009) A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition. Commun Nonlinear Sci Numer Simul 14(4):1064–1068 7. Bataller RC (2008) Radiation effects for the Blassius and Sakiadis flows with a convective surface boundary condition. Appl Math Comput 206(2):832–840 8. Charm S, Paltiel B, Kurland GS (1968) Heat transfer coefficient in blood flow. Biorheology 5:133–145Google Scholar 9. Charny CK (1992) Mathematical models of bioheat transfer. Bioengineering heat transfer, special issue. Adv Heat Transf 22:19–155 10. Chato JC (1980) Heat transfer to blood vessels. J Biomech Eng 102(2):110–118 11. Chaudhary RC, Sharma BK (2006) Combined heat and mass transfer by laminar mixed convection flow from a vertical surface with induced magnetic field. J Appl Phys 99:034901–034910 12. 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Dinglers Polytechnol J 326(321):1911Google Scholar 19. Hogan HA, Henriksen M (1989) An evaluation of a micropolar model for blood flow through an idealized stenosis. J Biomech 22(3):211–218 20. Ishak A (2010) Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition. Appl Math Comput 217(2):837–842 21. Kafoussias NG, Nanousis ND (1997) Magnetohydrodynamic laminar boundary-layer flow over a wedge with suction or injection. Can J Phys 75(11):733–745 22. Kandasamy R, Periasamy K, Prabhu KKS (2005) Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection. Int J Heat Mass Tran 48(7):1388–1394 23. Kays WM, Crawford ME (1987) Convective heat and mass transfer, 2nd edn. McGraw-Hill, New YorkGoogle Scholar 24. Kuo BL (2005) Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method. Int J Heat Mass Tran 48(23–24):5036–5046 25. Lin HT, Lin LK (1987) Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number. Int J Heat Mass Tran 30(6):1111–1118 26. Na TY (1979) Computational methods in engineering boundary value problems. Academic, New York 27. Pennes HH (1948) Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol 1(2):93–122 28. Plavins J, Lauva M (1993) Study of colloidal magnetite binding erythrocytes: prospects for cell separation. J Magn Magn Mater 122(1–3):349–353 29. Rahman MM (2011a) Heat transfer in biomagnetic fluid over a wedge with convective surface boundary condition in the presence of induced magnetic field. Int J Energy Technol 3(17):1–8Google Scholar 30. Rahman MM (2011b) Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition. Meccanica 46:1127–1143 31. Rahman MM, Eltayeb IA (2011) Convective slip flow of rarefied fluids over a wedge with thermal jump and variable transport properties. Int J Therm Sci 50(4):468–479 32. Rahman MM, Sattar MA (2006) Magnetohydrodynamic convective flow of a micropolar fluid past a continuously moving vertical porous plate in the presence of heat generation/absorption. ASME J Heat Tran 128(2):142–152 33. Rajagopal KR, Gupta AS, Na TY (1983) A note on the Falkner-Skan flows of a non-Newtonian fluid. Int J Nonlinear Mech 18(4):313–320 34. Rashad AM, Bakier AY (2009) MHD effects on non-Darcy forced convection boundary layer flow past a permeable wedge in a porous medium with uniform heat flux. Nonlinear Anal Model Contr 14(2):249–261 35. Rubinsky B (1999) Heat transfer in biomedical engineering and biotechnology. In: Proceedings of the 5th ASME/JSME joint thermal engineering conference, San Diego, CA, March 15--19, AJTE-6528Google Scholar 36. Ruuge EK, Rusetski AN (1993) Magnetic fluid as drug carriers: targeted transport of drugs by a magnetic field. J Magn Magn Mater 122(1–3):335–339 37. Sattar MA (2011) A local similarity transformation for the unsteady two-dimensional hydrodynamic boundary layer equations of a flow past a wedge. Int J Appl Math Mech 7(1):15–28 38. Schlichting H (1968) Boundary layer theory. McGraw Hill, New YorkGoogle Scholar 39. Skalak R, Chien S (1982) Rheology of blood cells as soft tissues. Biorheology 19:453–461Google Scholar 40. Srivastava VP (2003) Flow of a couple stress fluid representing blood through stenotic vessels with a peripheral layer. Indian J Pure Appl Math 34:1727–1740 41. Stewartson K (1954) Further solutions of Falkner-Skan equation. Math Proc Cambridge Philo Soci 50(3):454–465 42. Tzirtzilakis EE, Tanoudis GB (2003) Numerical study of biomagnetic fluid flow over a stretching sheet with heat transfer. Int J Numer Method Fluid Flow 13(7):830–848 43. Valvano JW, Nho S, Anderson GT (1994) Analysis of the Weibaum-Jiji model of blood flow in the canine kidney cortex for self-heated thermistors. J Biomech Eng 116(2):201–207 44. Watanabe T (1990) Thermal boundary layers over a wedge with uniform suction or injection in forced flow. Acta Mech 83(3–4):119–126 45. Yao S, Fang T, Zhong Y (2011) Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun Nonlinear Sci Numer Simul 16(2):752–760 46. Yih KA (1998) Uniform suction/blowing effect on the forced convection about a wedge: uniform heat flux. 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http://biztalkdeployment.codeplex.com/discussions/444095	# Include file in outdir, but not in Msi Topics: Server Deployment Wiki Link: [discussion:444095] adrach87 May 17, 2013 at 9:17 PM I have a need to copy a batch file from the Deployment folder to the outdir while building the MSI installer. Normally I'd just set Copy to Output folder to true in VS, but since the deployment framework isn't a project template, I don't have that option. I tried creating a postbuild action that just copies the file, but that doesn't seem to be executed. Here's how I set that up: `````` xcopy ..\..\MsiDeploy.bat . `````` But even after creating the MSI all I get are the ProjectName-Version.msi and Install-ProjectName-Version.bat files. What am I missing? tfabraham Coordinator May 19, 2013 at 5:18 AM Use this: `````` `````` Thanks, Tom adrach87 May 20, 2013 at 4:14 PM Thanks, but that doesn't seem to be working for me. This goes in the btdfproj file, in the Project element, right? The CreateItem node is underlined with the message "Target element has invalid child element CreateItem. List of possible elements expected: Task, PropertyGroup, ItemGroup, OnError". When I build an MSI, it works as normal, but the MsiDeploy.bat doesn't show up in the \bin\release folder. tfabraham Coordinator May 21, 2013 at 6:35 AM Yes. Then I would assume that the path to MsiDeploy.bat is incorrect. The path is relative to the Deployment project folder. Try a full explicit path if you can't get a relative path to work, just to see if you can get the file copied. Thanks, Tom adrach87 May 22, 2013 at 4:12 AM I updated to use an absolute path but that didn't work either. I even tried using msbuild and pointed it to the CustomPostInstaller target to determine if it maybe it just wasn't running that target, but again nothing. I also don't see any errors or warnings about not finding the MsiDeploy.bat file, so I don't think it's the path. One other possibility to get the file I need would be to customize the Install-ProjectName-Version.bat file. Is that possible? Thanks for your help. tfabraham Coordinator May 22, 2013 at 6:33 AM On BizTalk 2010 and newer you can use: `````` `````` See if the Message tasks write something out and whether the values are valid. It is not easily possible to modify the .bat file contents on initial creation. Thanks, Tom adrach87 May 23, 2013 at 3:21 AM This worked, once I got the correct path for the file I wanted to copy. Thanks.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8564311265945435, "perplexity": 1549.9736070163663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323870.46/warc/CC-MAIN-20170629051817-20170629071817-00353.warc.gz"}
http://www.sciforums.com/threads/fire-fighters-refuse-to-fight-fire-homeowners-forgot-to-pay-fee.104391/page-10	# Fire Fighters Refuse to Fight Fire, Homeowners Forgot to Pay Fee Discussion in 'Politics' started by spidergoat, Oct 6, 2010. 1. ### countezeroRegistered Senior Member Messages: 5,590 Again, you're been intentionally dense or just don't understand why this isn't worth posting. 2. ### Google AdSenseGuest Advertisement to hide all adverts. 3. ### spidergoatVenued Serial MemberlistValued Senior Member Messages: 53,811 Property taxes. 4. ### Google AdSenseGuest Advertisement to hide all adverts. 5. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 Absolutely, but unfortunately the amount of money allocated from their tax revenue by the Obion County government to fight fires was $0.00. The average for the surrounding counties was$158,000. The City put together a detailed plan that would have provided coverage to everyone in the County for a measly $3 per month per household (less than half of the annual Subscription cost). The County turned it down. Arthur 6. ### Google AdSenseGuest Advertisement to hide all adverts. 7. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 As detailed in their plan for universal coverage, the Fire Dept also bills someone$500 if they have to come out for a fire (yes, that's less than the actual cost), but less than half the people pay the bill and the Fire Dept does not have the legal authority to collect the bill. 245 Rural calls were handled in 2006. So that's $117,000 worth of bills, but less than$60,000 collected. To put these costs in perspective, Union city has 42 fireman, which at a low average fully loaded cost of $50,000 per year is well over 2 million dollars just in salary, forget training, cost of the fire stations etc. Union city alone has over$1.2 million in equipment that they use to fight these fires. The county is getting a GREAT deal and not paying for it. Arthur 8. ### PandaemoniValued Senior Member Messages: 3,631 CAVEAT to my response below: When I say “in your mind” or “in your model” "you assume that" or words to that effect, I am really saying “if I understand you correctly, I believe that your position is…” I am not intending to be a presumptuous mind reader, but rather I am too lazy to preference those sorts of thoughts with “if I understand you correctly” every time. I am also aware that I could be mischaracterizing your position, which is why I feel the need to state what I understand your position to be. Oh dear. This is one of those cases where I prepared a long a detailed response, line by line, and then managed through an unfortunate set of keystrokes, to close the tab I was working in, thus losing my very long and time consuming post. Drats. As is always the case, I haven't the heart to rework my prior answer in full, so allow me to summarize. With no animosity towards you for disagreeing with me, here is why I am not persuaded by your argument. It seems to me that you are drawing a moral conclusion based on assumptions that I find open to debate. First, you seem to be assuming that lives are at risk. In fact, no lives were at risk. The fire chief refused to risk the lives and safety of his men and to incur costs to save the homeowner's property. The reports said that if lives were on the line, the fire chief would have made a different call. It seems to me that you verge on calling the fire chief and his men immoral, when I actually think they satisfy much of the test you would impose on them. Second, you start with the premise that public servants must serve all members of the public. I understand that it the traditional model, but I do not agree that anyone who wants a different model is setting up an undesirable world in which public servants behave in an immoral way. In fact, a model where public servants serve those who "opt in" and have the right to "opt out" is a very libertarian model. You are free to live in a community that uses the traditional model, and I likely would join you there, but I would fight hard for the right of anyone who wanted the other model. You seem poised to deny them the choice entirely, as I read your post. Your assumption boils down to saying that public servants have a duty to the entire public, whether they pay or are deadbeats. That flows naturally from the traditional model, but the traditional model itself is not a categorical imperative...it just happens to be tradition (and a very modern tradition that arose in the last century or so in the U.S.). It is also not required by the economics of the situation. In fact, the private sector uses the model of serving only paying clients to great economic effect. Still, because you start with the assumption of this universal duty that public servants have, you reject the comparison to private actors...except in one case--your lifeguard metaphor. In the case of a lifeguard, of course, they traditionally also have a duty to all swimmers. I assume you would agree--again since no lives were on the line, just property--that a lifeguard is well within his rights to refuse to risk his life to save a surf board that is being swept out to sea. More fundamentally though the lifeguard analogy is a good one if you make your assumption about the universal duty of public servants. Let's relax that assumption a bit. Consider a related case, where you have a "lifeguard" who is hired to protect everyone on the beach and you have a bodyguard (or chaperone, or government hired secret service agent), who has been hired to protect specific people. If the poor swimmer is the person being protected by the bodyguard, and that person starts to drown. Both the lifeguard and (likely) the bodyguard have some duty to act. Imagine that as the lifeguard and bodyguard look on that another swimmer who is not the bodyguard's charge starts to drown. In that case the lifeguard has the same duty as before, but the bodyguard is off the hook (and is not behaving badly by staying with those under his protection). The lifeguard and the bodyguard has substantially similar jobs in the relevant respects (even if both are government employees) except for the assumption of who it is that they are "supposed" to protect. In your mind, you assume that firefighters are supposed to be equal opportunity. To be honest, I generally agree and that assumption swims around in my head too. Again, though, if anyone chooses to live in a community where that is not the case, that is their choice. if anyone there then chooses to opt out, that is another choice. Your preferred path eliminates the right to choose duifferently than you or I would by requiring all fire companies follow the traditional model. I see no reason to impose my preferences in that manner. If anyone lives in this particular community that happens to use the "libertarian" model, and they prefer the traditional model, they can simply move into the city. In the city in question, they use the traditional model, where you have no choice and must pay for fire protection services through your increased taxes. It seems that, far from being a bad world, my world accommodates whatever preference individuals may have in this regard. The only caveat is that I see it as destructive of the liberty I would like to allow to let people who knowingly choose to "opt out" to change their mind as soon as there is a fire. It's not that I hate them, it's that I love liberty and personal responsibility more. [You can count your lucky stars that the "long version" of this, complete with a better economic analysis, was deleted.] Please Register or Log in to view the hidden image! Last edited: Oct 7, 2010 9. ### TrooperSecular SanityValued Senior Member Messages: 1,784 Bravo, Pandaemoni! :bravo: 10. ### spidergoatVenued Serial MemberlistValued Senior Member Messages: 53,811 And finally, that is because the County is a bunch of Republican idiots, which was the whole point of this thread. 11. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 Ah, they might be idiots, but not providing fire service to your community is NOT a plank of the Republican party. Oh, and the Mayor, who apparently was the one to OK not fighting the fire, is a Democrat. Arthur 12. ### spidergoatVenued Serial MemberlistValued Senior Member Messages: 53,811 No, of course not, they don't believe government should be doing anything but fighting wars, and even that should be privatized in many areas. 13. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 So are you defending the Democrat Mayor for his 'burn baby burn' approach? 14. ### spidergoatVenued Serial MemberlistValued Senior Member Messages: 53,811 I'm not sure what the Mayor's position on this is, or what his or her role would be in allocating funds from property taxes. 15. ### joepistoleDeacon BluesValued Senior Member Messages: 22,908 I think maybe you should check your facts my dear Arthur because it is not consistent with what is being reported. http://thinkprogress.org/2010/10/04/county-firefighters-subscription It is being reported the mayor of South Bend is a Republican. And the other funny thing about your claim is that it is not consistent with the local GOP party web site. They have the mayor (David Crocker) that you are claiming to be a Democrat listed as one of their own, a Republican...fancy that. Please Register or Log in to view the hidden image! http://www.obiongop.com/?page_id=85 If you have some references to support your positions and claims it would be nice to post them. Last edited: Oct 7, 2010 16. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 My bad, I thought it was the Mayor of Union City, but it was the Republican Mayor of South Fulton (not South Bend) Arthur 17. ### TrooperSecular SanityValued Senior Member Messages: 1,784 Is this just a rumor or is he a repeat offender? Did the fire department already bend the rules for them once? :shrug: Insurance Journal News 18. ### NeverflyBannedBanned Messages: 3,576 No, sorry- I have actual experience. I guess that doesn't quite measure up to your guesses... But I'm willing to bet it comes close. 19. ### NeverflyBannedBanned Messages: 3,576 Considering the media attention... Farm Bureau is doing an excellent job of really getting down on all fours and kissing some serious booty. 20. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 So if you were there you'd tell the Chief to take this job and shove it and start putting out the fire? Easy to act like a big man on the internet isn't it? http://www.youtube.com/watch?v=dYT89iItQgw But of course the ACTUAL fireman there did not do so. Arthur Last edited: Oct 8, 2010 21. ### NeverflyBannedBanned Messages: 3,576 I'd have started hooking up the hose- yes. Wouldn't be the first time. And for the record, my "Chief" and I had MANY Disagreements. The other guys often remarked that we were like brothers we argued so much. I had similar occurrences while I was in the Army and I came pretty damn close to getting myself in a Lot Of Trouble. But I was lucky and the higher ups agreed with my reasoning and I ended up getting a slap on the wrist. This coming from the guy talking about swinging dicks. I dunno Adoucette, perhaps you should let your personal bigotry step aside long enough to ask yourself whether a small man is to afraid to speak up or stand out. I don't think I'm acting like the Big Man, at all. I'm acting like the average man. The problem is one of perspective-- You're just acting small. So average looks big, to you. And that was them. Not me. Apparently, they also went to the family tail tucked between their legs... 22. ### adoucetteCaca OccursValued Senior Member Messages: 7,829 Funny, Anyone I know who would do it, wouldn't brag that they would do it. In real life, none did it. On the internet though everybody acts brave. Wonder why that is? Arthur 23. ### BellsStaff Member Messages: 23,026 How did they know though? How did the person on the phone know for sure? The people who rang them may have said no, but how can they be sure that someone had not strayed onto their property and was not trapped? There have been many times where firemen will be called and will be told that there is no on trapped, and then later in the debris, they find that someone had been? I will put it this way.. A few years ago our family home was taken out by a mudslide, as was that of our neighbour's, in the middle of the night. When the fire brigade were called, they asked if anyone was trapped inside and were told no. They came regardless and checked, just in case.. Now, prior to this fire getting to their house, it was actually a field fire. Field fires are known to be unpredictable and quite dangerous. They would have known that from the phone call. Yet the operator chose to ignore the dangers connected to field fires and told them no. Here is what the Government in Indianna describe field fires: Now, we know this one was dangerous enough to take out the neighbour's field as well. So how can the operator know on the phone what the conditions were there on the ground and could assure that no one was in danger? I'll give you an actual example. My parents live next door to a wide track of bushland. From their fenceline, is a very wide track of overly dense bushland. And in the summer in Australia, bushfires are an extreme danger. Several times over the years, fires have started in that tract of bushland, fairly far away from my parents house. When they see smoke rise on the horizon, they call the fire brigade, because they know that fires can spread very quickly. Now, even though that fire may be over 1km away from their property, the fire brigade or the volunteer fire brigade come regardless and check to make sure there is no danger to anyone or property. At no time have my parents ever been told no. Yet, in this instance, a 911 operator took it upon themselves to determine that no one was in danger, when they could not be certain for sure and had determined for themselves that a field fire was apparently not dangerous. That decision proved costly, not just to the Cranick, but also to the neighbour who lost part of their fields as a result. Had the fire brigade done their job and actually responded immediately from that first call, the neighbour would not have lost their field and the Cranick's would not have lost their home and pet. But since the operator determined that the field fire was not dangerous to warrant that actual firemen come out and check the fire, over a $75 fee, that fire did go on to destroy property and family pets. Why would you be upset? You view it as being "just property". Would you expect a fire fighter to actually put out a fire? Or would you expect that a phone operator would decide if you are in danger or not before they send out a fire fighter? You mean the local news that the Fire Chief tried to have arrested when they asked him why the firemen were not actually fighting the fire at all and had refused to? That local media? Let me tell you something. When insurers pay out people, it costs everyone collectively, something. And I mean everyone in the country. Now, as a result of this little exercise in lesson teaching, Cranick is the recipient in emergency payments, which actually comes from the Government, to cover immediate costs. So in the end, everyone has paid over that$75 lesson.. So tell me, how is this supposedly good? What lesson has been taught? Ah yes, the lesson of condemnation from fire fighters around the world by way of the international body? That lesson? How about those fire fighters now receiving hate mail and threats for their refusing to put out that fire (as noted in the link above)? Good lesson or bad lesson? People do forget. It does happen. No one has denied that he had paid in the past. But what I'd like to know is why they refused to accept the payment before the fire actually got to his house? In fact, he offered to compensate them for more than the $75 and they refused. But instead, in that little lesson he and the County apparently needed to be taught, he will have received in excess of that$75 out of the public's pocket for emergency funding. Excellent philosophy there. Instead of the fire department being compensated by him for more than the $75, everyone gets to compensate him for more. Astounding reasoning there.. Yes. We know that Cranick and his neighbour offered to pay the fire department the$75 and more, as much as they wanted at the time. And they refused. Since they appear to be running the fire department as a business in that part of the world, it does not make good business sense to refuse even more at the scene. Quite the contrary, it makes no sense at all. The fire department would have benefited financially, emotionally and benefitted in receiving praise in the eyes of the general public as well. The house would have been saved, the pets saved and the general public would not have had their tax dollars be spent on emergency funding to the Cranick's or medical costs of the fire chief and Cranick's son, nor would the insurance have had to make everyone pay in paying out the Cranick's for their loss. Instead, they elected to refuse not just payment at the scene, they refused to be paid more or be compensated more, their actions also cost the public more in relation to the insurance pay out and cost the tax payers more since the Cranick's are now recipients of emergency payment/welfare from the Government. The firemen in that City have been abused and threatened by one and all for their lack of action and the fire chief injured when he was knocked out by the Cranick's son afterwards, who also cost the tax payers money as he was then arrested and charged, using up precious police resources to do so, and then taken to hospital to receive free care to his injured hand (an injury that he received when he punched the fire chief), the fire chief for his part, also cost the tax payers more since his treatment would have come out of public funding/insurance - paid for by the tax payers. All of which, I can assure you, will have cost well in excess of the $75 they could have recouped at the scene and could recouped afterwards, hell, they could have recouped much more at the scene. And that is why, for that$75, those firemen ensured the tax payers as a whole, would now have to cover thousands of dollars in emergency payments, medical costs, and other costs associated (such as paying for media consultation, legal consultation, etc). 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https://codegolf.stackexchange.com/questions/5105/tips-for-golfing-in-perl/32884	# Tips for golfing in Perl? What general tips do you have for golfing in Perl? I'm looking for ideas that can be applied to code golf problems in general that are at least somewhat specific to Perl (e.g. "remove comments" is not an answer). Please post one tip per answer. ## TMTOWTDI That's the most important Perl golfing tip you need to know. Whenever you're looking at some too-long sequence of characters you absolutely have to have in order to accomplish your task, ask yourself if there isn't some other way to get the same effect using a different feature. There usually is. Here are just a handful: • ~~ enforces a scalar context and is 4 chars shorter than scalar. • y///c is one char shorter than length when getting the length of $_. • Need to iterate over the chars in $_? Replace split//,$x with $x=~/./gs. (Or use $x=~/./g if you also want to skip newlines.) • Every Perl builtin returns something. print returns 1, for example, to indicate successful I/O. If you need to initialize $_ to a true value, for example, $_=print$foo allows you to kill two birds with one stone. • Almost every statement in Perl can be written as an expression, allowing it to be to used in a wider variety of contexts. Multiple statements can be become multiple expressions chained together with commas. Tests can be done with short-circuiting operators ?: && \|\|, and also with and and or, which do the same thing but with precedence lower than all other operators (including assignment). Loops can be done via map or grep. Even keywords like next, last and return can be used in an expression context, even though they don't return! Keeping these kinds of transformations in mind give you opportunities to replace code blocks with expressions that can be stuffed into a wider variety of contexts. • $_=print"" is shorter than $_=print$foo. – ASCIIThenANSI Dec 18 '15 at 18:23 • The idea is that you already need to print $foo. Otherwise, $_=1 is much shorter than $_=print"" and has the same effect. – breadbox Feb 19 '16 at 23:59 • For the third do you mean iterating over the chars in $x? Otherwise you could just do /./gs and /./g. – redbmk Apr 14 '16 at 10:44 Abuse Perl's special variables! • As noted in a previous answer $/ and $" are initialized by default to "\n" and " ", respectively. • $, and $\ are both set to undef by default, and are 3 chars shorter. • Setting $\ to a value will cause it to be appended to every print. For example: perl -ple '$\="=".hex.$/' is a handy hex-to-decimal converter. • If you're not reading files from the command-line, you can use the -i command-line switch as an extra channel for inputting a string. Its value will be stored in $^I. • $= forces whatever is assigned to it to be an integer. Try running perl -ple '$_=$==$_' and giving it various inupts. Likewise, $- forces its value to be a non-negative integer (i.e. a leading dash is treated as a non-numeric character). • You can use $. as a boolean flag that is automatically reset to a true (nonzero) value on every iteration of a while(<>) loop. # -n and unmatched curly brackets It is well known that the command line switch -n can be used to execute the script once for every line. perl --help says: -n assume "while (<>) { ... }" loop around program What it doesn't say explicitly is that Perl doesn't just assume a loop around the program; it literally wraps while (<>) { ... } around it. This way, the following commands are equivalent to each other: perl -e 'while(<>){code}morecode' perl -ne 'code;END{morecode}' perl -ne 'code}{morecode' # -p and unmatched curly brackets Similarly to the above, the -p switch wraps while (<>) { ... ; print } around the program. By using unmatched curly brackets, perl -p 'code}{morecode' will only print once after executing code for all lines of input, followed by morecode. Since $_ is undefined when morecode;print is executed, the output record separator $\ can be abused to print the actual output. For example perl -pe '$\+=$_}{' reads one number per line from STDIN and prints their sum. • I'm assuming you could accomplish this with #!perl -n on the first line, right? – ASCIIThenANSI May 2 '15 at 16:56 • @ASCIIThenANSI: Yes, that is correct. (Sorry for the late answer.) – Dennis Jun 14 '15 at 15:22 • Giving credit where credit is due, I think I saw the combination of these three tricks (unmatched curly brackets, -p and $\) for the first time in one of @primo's Perl answers. To read his answers is a good Perl tip on its own. – Dennis Jun 14 '15 at 15:24 • Throwing a }for(...){ in between the braces is often quite handy as well, e.g. codegolf.stackexchange.com/a/25632 – primo Oct 2 '15 at 9:53 • One thing I found useful in conjunction with -n is the \|\|= default value assignment operator. Gets around not being able to assign a value before the loop. – deltaray Dec 17 '16 at 5:55 Use $_ to eliminate scalar references. It is the special variable that is used as a default by most functions, and just leaving out parameters is a shortcut to reference this variable. By changing $n to $_, you can change $n=<>;chop$n;print$n to $_=<>;chop;print Here, the print function prints the contents of $_ by default, and chop also works on $_. • Is $_=<>; required, doesn't <>; read the line into $_ automatically? – sundar Aug 20 '13 at 18:55 • No, I don't think so. I compared the programs $_=<>;print and <>;print. The first one repeats back to me what I type, while the other one doesn't. – PhiNotPi Aug 21 '13 at 21:22 • Oh, thanks, turns out that happens only in cases like print while(<>). Not sure if it's a special case or there's some coherent logic behind it, neither <>'s part in perlop nor while part of perlsyn seem to mention this behaviour. – sundar Aug 21 '13 at 22:36 • @sundar while(<>) is a special case, documented in perlsyn, I/O Operators: 'If and only if the input symbol is the only thing inside the conditional of a "while" statement (even if disguised as a "for(;;)" loop), the value is automatically assigned to the global variable $_, destroying whatever was there previously." – kernigh Nov 9 '14 at 0:22 Use Perl's special variables where-ever you can, eg: • Use $" instead of " " • Use $/ instead of "\n" They have the added benefit of being a guaranteed one-character long identifier, with help from the lexer. This makes it possible to glue it to the keyword following it, as in: print$.for@_ The list of all the special variables is available here: Special Variables Don't use qw. This is waste of two characters that could be used in better way. For example, don't write the following. @i=qw(unique value); @i=(unique,value); Or if you cannot use barewords, use glob syntax. @i=<unique value>; glob syntax can also be used for interesting effects. @i=<item{1,2,3}>; Use statement modifiers instead of compound statements. Compound statements tend to require parentheses for the argument and braces for the block, whereas statement modifiers need neither. Compare: • $a++,$b++while$n-- vs while($n--){$a++;$b++} • chop$,if$c vs if($c){chop$,} Note that the last example ties with $c&&chop$,, but starts really shining for most multi-statement operations. Basically anything that loses operator precedence to &&. Don't use strict. (don't quote me on this, PCG.SE context kinda matters) And, more importantly, don't code as if under strict. The usual suspects: • don't my-declare variables if you can avoid it. The only variables that really need my are those you want lexically scoped. That's barely any of them when golfing, where you don't need scope protection and tend to fully control recursion. • don't quote one-word strings: (example). Do ensure you don't have a function with the same name, though. • print hello won't work. It actually means print hello $_ (print $_ to filehandle hello). – Konrad Borowski Oct 22 '12 at 12:25 • @GlitchMr thanks! (and now I'm bummed, because my point is still valid, just not with print, and now I can't find a nice and short example) – J B Oct 22 '12 at 18:10 • @JB here's a good example: codegolf.stackexchange.com/a/8746/3348 – ardnew Oct 22 '12 at 19:45 I'm sure some of these have formal names and I'm just not aware of them. • If you have a while loop (or a for loop you can make into a while loop) you can define the "while" after the command: print $n++ while ($n < 10) • If you need to read everything from STDIN into a string: $var = join('',<>) • As CeilingSpy pointed out, using$/ instead of \n is faster in some situations: print ('X'10) . "\n"; is longer than print ('X'10) . $/; • Perl's say function is shorter than print, but you'll have to run the code with -E instead of -e • Use ranges like a..z or even aa..zz. If needed as a string, use join. • Incrementing strings: $z = 'z'; print ++$z; will display aa That's all I can think of right now. I may add some more later. • What is print ('X'10) .$/; supposed to do? For me it prints 0 and no newline. For one thing, the parentheses become a function-style call argument to print, which binds tighter than .. And did you mean x instead of or something? – aschepler Jul 30 '17 at 0:45 • No parentheses needed in postfix while, join'',<>; also works without them. – choroba Oct 21 '17 at 23:36 # Use non-word characters as variable names Using $% instead of $a can allow you to place the variable name right next to an if, for or while construct as in: @r=(1,2,3,4,5);$%=4; print$_*$%for@r Many can be used, but check the docs and @BreadBox's answer for which ones have magic effects! # Use map when you can't use statement modifiers If you can't use statement modfiers as per @JB's answer, map might save a byte: for(@c){} vs. map{}@c; and is useful if you want to do nested iterations as you can put postfix for loops inside the map. # Use all the magic Regular Expression variables Perl has magic variables for 'text before match' and 'text after match' so it is possible to split to groups of two with potentially fewer characters: ($x,$y)=split/,/,$_; ($x,$y)=/(.+),(.+)/; /,/; # $x=$, $y=$' # Note: you will need to save the variables if you'll be using more regex matches! This might also work well as a replacement for substr: $s=substr$_,1; /./;# $s=$' $s=substr$_,4; /.{4}/;# $s=$' If you need the contents of the match, $& can be used, eg: # assume input like '10 PRINT "Hello, World!"' ($n,$c,$x)=split/ /,$_; / .+ /; #$n=$,$c=$&,$x=$' # Replace subs with long names with a shorter name If you call say print four or more times in your code (this obviously varies with the length of the routine you're calling), replace it with a shorter sub name: sub p{print@_}p;p;p;p vs. print;print;print;print # Replace conditional incrementors/decrementors If you have code like: $i--if$i>0 you can use: $i-=$i>0 instead to save some bytes. # Convert to integer If you aren't assigning to a variable and so can't use breadbox's tip, you can use the expression 0\|: rand 25 # random float eg. 19.3560355885212 int rand 25 # random int 0\|rand 25 # random int rand 25\|0 # random int ~~rand 25 # random int It's worth noting however than you don't need to use an integer to access an array index: @letters = A..Z;$letters[rand 26]; # random letter redo adds loop behavior to a block without for or while. {redo} is an infinite loop. Don't parenthesize function calls. Perl lets you call a known (core or predeclared) function using the NAME LIST syntax. This lets you drop the & sigil (if you were still using it) as well as the parentheses. For example: $v=join'',<> Full documentation Try to use the value of an assignment expression, like so: # 14 characters$n=pop;$o=$n&1 # 13 characters, saves 1 $o=($n=pop)&1 This works because $n is 2 characters in Perl. You may change $n to () at no cost, and save 1 semicolon by moving the assignment into the parentheses. You can run multiple different statements within nested ternary logic. Suppose you have a big if-elsif statement. This could be any logic and any number of statements. if( $_ < 1 ) {$a=1; $b=2;$c=3; say $a.$b.$c; } elsif($_ < 2 ) { $a=3;$b=2; $c=1; say$a.$b.$c; } elsif( $_ < 3) {$a=2; $b=2;$c=2; say $a.$b.$c; } You can use (cmd1, cmd2, cmd3) inside the ternary operator to run all of the commands. $_ < 1 ? ($a=1,$b=2,$c=3,say$a.$b.$c): $_ < 2 ? ($a=3,$b=2,$c=1,say$a.$b.$c):$_ < 3 ? ($a=2,$b=2,$c=2,say$a.$b.$c): 0; #put the else here if we have one Here's a dummy example: perl -nE'$_<1?($a=1,$b=2,$c=3,say$a.$b.$c):$_<2?($a=3,$b=2,$c=1,say$a.$b.$c):$_<3?($a=2,$b=2,$c=2,say$a.$b.$c):0;' <(echo 2) # Use select(undef,undef,undef,$timeout) instead of Time::HiRes (Taken from https://stackoverflow.com/a/896928/4739548) Many challenges require you to sleep with greater precision than integers. select()'s timeout argument can do just that. select($u,$u,$u,0.1) is much more efficient than: import Time::HiRes qw(sleep);sleep(0.1) The former is only 20 bytes, whereas the latter takes up 39. However, the former requires you aren't using $u and have never defined it. If you're going to use it a lot importing Time::HiRes pays off, but if you only need it once, using select($u,$u,$u,0.1) saves 19 bytes, which is definitely an improvement in most cases. # Shorten your print statements Unless the challenge specifies otherwise, you don't need trailing newlines. Our 'challenge' says 'output a random number from 0 to 9 to STDOUT'. We can take this code (28 bytes): $s=int(rand(10));print"$s\n" And shorten it to this (25 bytes): $s=int(rand(10));print \$s by simply printing the variable. This last one only applies to this challenge specifically (19 bytes): print int(rand(10)) but that only works when you don't have to do anything to the variable in between assignment and printing. • The last one's already listed here. – Sp3000 May 2 '15 at 18:58 • @Sp3000 Thank you, I've updated my answer. – ASCIIThenANSI May 2 '15 at 20:22 # Use globs like string literals Occasionally (often when dealing with or challenges) you benefit greatly from the ability to nest string literals. Normally, you'd do this with q(…). However, depending on what characters you need inside the string, you may be able to save a byte and use <…>, the glob operator. (Note that what's inside the angle brackets can't look like a filehandle, and can't look like it's meant to be expanded into a list of filenames, which means that quite a lot of characters won't work correctly.)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2504371106624603, "perplexity": 2499.9317615829596}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999740.32/warc/CC-MAIN-20190624211359-20190624233359-00387.warc.gz"}
https://access.openupresources.org/curricula/our6-8math-v1/7/students/1/5.html	Lesson 5: The Size of the Scale Factor Let’s look at the effects of different scale factors. 5.1: Number Talk: Missing Factor Solve each equation mentally. $16x=176$ $16x=8$ $16x=1$ $\frac15x=1$ $\frac25x=1$ 5.2: Scaled Copies Card Sort Your teacher will give you a set of cards. On each card, Figure A is the original and Figure B is a scaled copy. 1. Sort the cards based on their scale factors. Be prepared to explain your reasoning. 2. Examine cards 10 and 13 more closely. What do you notice about the shapes and sizes of the figures? What do you notice about the scale factors? 3. Examine cards 8 and 12 more closely. What do you notice about the figures? What do you notice about the scale factors? 5.3: Scaling A Puzzle Your teacher will give you 2 pieces of a 6-piece puzzle. 1. If you drew scaled copies of your puzzle pieces using a scale factor of $\frac12$, would they be larger or smaller than the original pieces? How do you know? 2. Create a scaled copy of each puzzle piece on a blank square, with a scale factor of $\frac12$. 3. When everyone in your group is finished, put all 6 of the original puzzle pieces together like this: Next, put all 6 of your scaled copies together. Compare your scaled puzzle with the original puzzle. Which parts seem to be scaled correctly and which seem off? What might have caused those parts to be off? 4. Revise any of the scaled copies that may have been drawn incorrectly. 5. If you were to lose one of the pieces of the original puzzle, but still had the scaled copy, how could you recreate the lost piece? 5.4: Missing Figure, Factor, or Copy 1. What is the scale factor from the original triangle to its copy? Explain or show your reasoning. 2. The scale factor from the original trapezoid to its copy is 2. Draw the scaled copy. 3. The scale factor from the original figure to its copy is $\frac32$. Draw the original figure. 4. What is the scale factor from the original figure to the copy? Explain how you know. 5. The scale factor from the original figure to its scaled copy is 3. Draw the scaled copy. Summary The size of the scale factor affects the size of the copy. When a figure is scaled by a scale factor greater than 1, the copy is larger than the original. When the scale factor is less than 1, the copy is smaller. When the scale factor is exactly 1, the copy is the same size as the original. Triangle $DEF$ is a larger scaled copy of triangle $ABC$, because the scale factor from $ABC$ to $DEF$ is $\frac32$. Triangle $ABC$ is a smaller scaled copy of triangle $DEF$, because the scale factor from $DEF$ to $ABC$ is $\frac23$. This means that triangles $ABC$ and $DEF$ are scaled copies of each other. It also shows that scaling can be reversed using reciprocal scale factors, such as $\frac23$ and $\frac32$. In other words, if we scale Figure A using a scale factor of 4 to create Figure B, we can scale Figure B using the reciprocal scale factor, $\frac14$, to create Figure A.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7781659960746765, "perplexity": 595.8854653678125}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703524858.74/warc/CC-MAIN-20210121132407-20210121162407-00601.warc.gz"}
https://www.hpmuseum.org/forum/showthread.php?tid=11400&pid=104195&mode=threaded	(11C) Arithmetic with Fractions 09-19-2018, 07:45 AM (This post was last modified: 09-19-2018 07:47 AM by Massimo Gnerucci.) Post: #18 Massimo Gnerucci Senior Member Posts: 2,376 Joined: Dec 2013 RE: (11C) Arithmetic with Fractions (09-18-2018 10:38 PM)Dieter Wrote: The English word "numerator" and the Spanish "numerador" are both derived from the Latin verb "numerare" = "to count". So a "numerator" is someone or something that "counts". A "counter", if you like. And that's exactly what the German word means: "Zähler" simply is a direct translation of the Latin "numerator". Which makes the use of a word like "nominator" look even more strange. #-) Dieter And, of course, we are close to the latin root: numeratore and denominatore. Greetings, Massimo -+×÷ ↔ left is right and right is wrong « Next Oldest \| Next Newest » Messages In This Thread (11C) Arithmetic with Fractions - Gamo - 09-15-2018, 07:02 AM RE: (11C) Arithmetic with Fractions - Dieter - 09-16-2018, 04:58 PM RE: (11C) Arithmetic with Fractions - Thomas Klemm - 09-16-2018, 09:17 PM RE: (11C) Arithmetic with Fractions - Dieter - 09-16-2018, 10:06 PM RE: (11C) Arithmetic with Fractions - Steve Simpkin - 09-17-2018, 01:46 AM RE: (11C) Arithmetic with Fractions - Thomas Klemm - 09-16-2018, 11:41 PM RE: (11C) Arithmetic with Fractions - Dieter - 09-18-2018, 06:51 PM RE: (11C) Arithmetic with Fractions - Valentin Albillo - 09-18-2018, 09:25 PM RE: (11C) Arithmetic with Fractions - Dieter - 09-18-2018, 10:38 PM RE: (11C) Arithmetic with Fractions - Massimo Gnerucci - 09-19-2018 07:45 AM RE: (11C) Arithmetic with Fractions - Albert Chan - 09-17-2018, 01:12 AM RE: (11C) Arithmetic with Fractions - Albert Chan - 09-17-2018, 04:04 PM RE: (11C) Arithmetic with Fractions - Gamo - 09-17-2018, 03:47 AM RE: (11C) Arithmetic with Fractions - Carsen - 09-17-2018, 08:14 AM RE: (11C) Arithmetic with Fractions - Gamo - 09-17-2018, 09:40 AM RE: (11C) Arithmetic with Fractions - Albert Chan - 09-17-2018, 06:44 PM RE: (11C) Arithmetic with Fractions - Thomas Klemm - 09-18-2018, 07:19 PM RE: (11C) Arithmetic with Fractions - Thomas Klemm - 09-18-2018, 07:29 PM RE: (11C) Arithmetic with Fractions - Gamo - 09-22-2018, 06:33 AM RE: (11C) Arithmetic with Fractions - Dieter - 09-24-2018, 12:59 PM RE: (11C) Arithmetic with Fractions - Dieter - 09-24-2018, 05:29 PM User(s) browsing this thread: 1 Guest(s)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9280164837837219, "perplexity": 24979.401503426394}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320302355.97/warc/CC-MAIN-20220120160411-20220120190411-00495.warc.gz"}
http://mathhelpforum.com/trigonometry/202553-requiring-help-graphing-csc-print.html	Requiring help on graphing CSC • August 25th 2012, 03:33 PM waleedrabbani Requiring help on graphing CSC The function is Y= CSC(0.5x + 3.14) Would the phase shift be pie units to the left? or pie/2 units to the left.? would the asymptotes be affected by the phase shift? if so, would i adjust the asymptotes to the new period first then adjust it to the phase shift or vice versa? Thanks sorry if its a stupid question • August 25th 2012, 05:32 PM Prove It Re: Requiring help on graphing CSC It's easiest to think of \displaystyle \begin{align} \csc{X} = \frac{1}{\sin{X}} \end{align}. The asymptotes are wherever \displaystyle \begin{align} \sin{X} = 0 \end{align} and the phase shift is surely the same as the phase shift for \displaystyle \begin{align} \sin{X} \end{align}... • August 25th 2012, 05:41 PM Plato Re: Requiring help on graphing CSC Quote: Originally Posted by waleedrabbani The function is Y= CSC(0.5x + 3.14) Would the phase shift be pie units to the left? or pie/2 units to the left.? This is what is stupid. Pie is an after-meal dish, as in apple pie. $\pi$ (spelled pi) is a number. AND $\pi\neq 3.14$. • August 25th 2012, 05:54 PM waleedrabbani Re: Requiring help on graphing CSC Quote: Originally Posted by Prove It It's easiest to think of \displaystyle \begin{align} \csc{X} = \frac{1}{\sin{X}} \end{align}. The asymptotes are wherever \displaystyle \begin{align} \sin{X} = 0 \end{align} and the phase shift is surely the same as the phase shift for \displaystyle \begin{align} \sin{X} \end{align}... Thanks that helps! And plato im sorry if i offended you :P	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.929309070110321, "perplexity": 6759.74027279908}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860111374.13/warc/CC-MAIN-20160428161511-00101-ip-10-239-7-51.ec2.internal.warc.gz"}
https://bioinformatics.stackexchange.com/questions/531/samtools-depth-print-out-all-positions	# samtools depth print out all positions I am trying to use samtools depth (v1.4) with the -a option and a bed file listing the human chromosomes chr1-chr22, chrX, chrY, and chrM to print out the coverage at every position: cat GRCh38.karyo.bed \| awk '{print $3}' \| datamash sum 1 3088286401 I would like to know how to run samtools depth so that it produces 3,088,286,401 entries when run against a GRCh38 bam file: samtools depth -b$bedfile -a inputfile I tried it for a few bam files that were aligned the same way, and I get differing number of entries: 3087003274 3087005666 3087007158 3087009435 3087009439 3087009621 3087009818 3087010065 3087010408 3087010477 3087010481 3087012115 3087013147 3087013186 3087013500 3087149616 Is there a special flag in samtools depth so that it reports all entries from the bed file? If samtools depth is not the best tool for this, what would be the equivalent with sambamba depth base? sambamba depth base --min-coverage=0 --regionsbedfile $inputfile Any other options? • Out of interest, does -aa at least give the same number of bases each time? -a -a (or -aa) output absolutely all positions, including unused ref. sequences There is also an old but relevant discussion about -a and BED behaviour on github/samtools/#374 – Sam Nicholls Jun 7 '17 at 9:59 • I tried with -a and with -aa, and given a bed file, it seems to produce the same number of entries. – 719016 Jun 7 '17 at 12:35 • Two samtools commits from May 2016; Added 30ish new tests for depth/mpileup -a and -aa and Depth/Mpileup -a fixes. Fixes #374 are somewhat enlightening. My gut feeling is that although possible, using -a/-aa with a BED file is not entirely supported with samtools depth (i.e. has potentially undefined behaviour) and perhaps you would want to investigate another tool as you've suggested? – Sam Nicholls Jun 7 '17 at 13:43 • I dont work with human genomes, so excuse my naive question...why do you need to provide a bed file if you want every position? – Nathan S. Watson-Haigh Jun 7 '17 at 14:07 • If every reference defined in the BAM file is touched by at least one read, then -a and -aa will produce the same output. The second option, -aa is useful if you want to produce zero-depth information for sequences that are completely uncovered. – gringer Jun 7 '17 at 22:24 ## 2 Answers You might try using bedtools genomecov instead. If you provide the -d option, it reports the coverage at every position in the BAM file. bedtools genomecov -d -ibam$inputfile > "${inputfile}.genomecov" You can also provide a BED file if you just want to calculate in the target region. Just replace the -a option with -aa: samtools depth -b$bedfile -aa \$inputfile I see that you're using the GRCh38 human reference genome build, which includes alternate scaffolds that represent a wider variety of genomic variation in the human genome. This was quite a substantial change from previous reference genome builds, and many bioinformatics tools still haven't been updated to accept the GRCh38 reference. The discrepancy in entry size is probably because there are alternate contigs that are uncovered by the reads that have been mapped. This is expected, but can cause a bit of confusion. • Yes, the reason why I use GRCh38 bed file is to have the depth values for only the karyotypic chromosomes, rather than the scaffolds and decoys. The -aa option gave the same output as the -a option. – 719016 Jun 8 '17 at 8:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28959259390830994, "perplexity": 3482.9092812236995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038468066.58/warc/CC-MAIN-20210418043500-20210418073500-00028.warc.gz"}
https://physics.aps.org/articles/v9/s90	Synopsis World of Weyl Craft Physics 9, s90 Researchers provide new evidence for the existence of type-II Weyl semimetals, which would be both conducting and insulating in different spatial directions. Over the last year, much excitement has surrounded Weyl semimetals. These materials have an asymmetric crystal structure that results in never-before-seen collective excitations called Weyl fermions. Hints have also emerged that transition metal dichalcogenides, such as molybdenum ditelluride ( ${\text{MoTe}}_{2}$), represent a distinct category of Weyl semimetals (type-II), characterized by bizarre symmetry properties. Anna Tamai from the University of Geneva, Switzerland, and colleagues performed a careful assessment of ${\text{MoTe}}_{2}$ and argue that it is indeed a strong candidate for a type-II Weyl semimetal. Weyl semimetals have a complex electronic band structure, in which two bands meet at points. In a type-I Weyl semimetal (see 8 September 2015 Viewpoint), these so-called Weyl points are connected by arc-shaped features, known as Fermi arcs, which can be observed in data obtained with angle-resolved photoemission spectroscopy (ARPES). A type-II Weyl semimetal would also exhibit Fermi arcs, but the endpoints would not correspond to the Weyl points—making them harder to identify. This difference arises because the type-II band structure is predicted to have a large tilt, resulting in Weyl fermions that violate Lorentz symmetry. This violation would produce exotic properties such as the material acting as a conductor for electrons moving in certain directions, while being an insulator in others, depending on the orientation of an applied magnetic field. Several groups claimed to have observed a type-II Weyl semimetal. However, Tamai et al. argue that candidate materials may exhibit arcs that are actually “false positives.” Bearing this in mind, the authors identified several arc-like features in their ARPES data for ${\text{MoTe}}_{2}$ and then compared them to detailed electronic-structure calculations. They showed that some of these arcs can be explained without Weyl points, but others are only reproduced in scenarios with at least eight Weyl points, consistent with ${\text{MoTe}}_{2}$ being a type-II Weyl semimetal. This research is published in Physical Review X. –Michael Schirber Michael Schirber is a Corresponding Editor for Physics based in Lyon, France. Related Articles Condensed Matter Physics A Macroscopic Probe of Quantum States A simple measurement of the magnetic susceptibility of a material can reveal the population of specific quantum states in the material. Read More » Atomic and Molecular Physics Cold Atoms Go Topological A lattice of highly excited atoms can exhibit a topological phase, a new theoretical study shows. Read More » Condensed Matter Physics Stretching Solves a Mystery of Magic-Angle Graphene Numerical simulations show that discrepancies between experiments on graphene bilayers can be attributed to tiny amounts of strain applied to the samples. Read More »	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.902971625328064, "perplexity": 1934.589075106676}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151672.96/warc/CC-MAIN-20210725111913-20210725141913-00436.warc.gz"}
http://physics.stackexchange.com/users/6247/vijay-murthy	# Vijay Murthy less info reputation 1413 bio website location age member for 2 years, 5 months seen 18 hours ago profile views 236 I work in statistical mechanics, (soft) condensed matter physics, biological physics. 12 Is it possible to witness a circular rainbow? 8 How much is 1 electron-volt (eV)? 8 Deriving Planck's radiation law from microscopic considerations? 6 How many particles is needed to observe a phase transition? 5 What is the return probability for Brownian motion in three dimensions? # 1,643 Reputation +10 Percolation in a 2D Ising model +10 Deriving Planck's radiation law from microscopic considerations? +10 some hints/introductions/textbooks for LBM(Lattice Boltzmann methods) fluid simulation? +10 How much is 1 electron-volt (eV)? # 0 Questions This user has not asked any questions # 80 Tags 28 quantum-mechanics × 9 10 statistical-mechanics × 4 12 fluid-dynamics × 5 10 units × 2 12 optics 9 energy × 2 12 refraction 8 photons 12 visible-light 8 thermal-radiation # 15 Accounts Physics 1,643 rep 1413 Mathematics 196 rep 23 Computational Science 166 rep 3 Meta Stack Exchange 101 rep 1 TeX - LaTeX 101 rep 1	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.846904993057251, "perplexity": 6743.719398579533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00041-ip-10-147-4-33.ec2.internal.warc.gz"}
https://bmgt.wordpress.com/page/2/	# Bộ môn Giải tích ## 31/12/2009 ### Chúc mừng năm mới 2010 Filed under: Không toán học, Trao đổi — doanchi @ 22:35 ## 29/10/2009 ### Mathematics Subject Classification: MSC2010 Filed under: Không toán học, Tra cứu, Trao đổi — Ngô Quốc Anh @ 16:53 Mathematical Reviews (MR) and Zentralblatt MATH (Z-MATH) collaborate in maintaining the Mathematics Subject Classification (MSC), which is used by these reviewing services and many others to categorize items in the mathematical sciences literature. The MSC has undergone a general revision, with some additions, changes, and corrections, to create MSC2010, the successor to MSC2000, the scheme for the past 10 years. MR and Z-MATH carefully considered input received from the community in recent years, especially since the announcement of the projected revision in December 2006, and used it in the preparation of their joint MSC revision. As anticipated, there are no changes at the two-digit level but refinements have been made at the three- and five-digit levels. With July 2009 MR and Z-MATH started to use MSC2010 as their classification scheme. MR and Z-MATH welcome and encourage community adoption of MSC2010. Comments can be submitted through the Web form found at http://msc2010.org/feedback or by email to feedback@msc2010.org. All information about MSC2010 is jointly shared by MR and Z-MATH. The Editors and their staffs wish to express their gratitude to the numerous members of the community for their assistance in this lengthy revision process. Bernd Wegner, Editor-in-Chief, Z-MATH ## 20/09/2009 ### eCalendar 4.0: Quyển lịch Bloc bỏ túi dành cho người Việt Filed under: Không toán học, Tra cứu, Trao đổi, Vui chơi — Ngô Quốc Anh @ 14:52 Mùa Xuân sắp đến, đây cũng là lúc mọi người trang hoàng nhà cửa và mua cho mình một quyển lịch Bloc mới. Tuy nhiên, có một quyển lịch Bloc bạn có thể đem về dùng mà không cần phải trả bất cứ chi phí nào, đó là eCalendar 4.0, một quyển lịch treo trên desktop với giao diện tiếng Việt thân thiện. Những tính năng hấp dẫn của eCalendar 4.0: • Tra cứu âm dương lịch từ năm 1901 đến 3001 (1100 năm). • Tờ lịch ngày (Bloc) thiết kế theo hình dáng của bloc treo tường thông dụng, có đủ tháng, ngày, giờ âm lịch theo can chi. Cửa sổ xem trăng cho biết chính xác mức độ tròn của mặt trăng hiện hành. • Cho phép chọn một ngày bất kỳ trong khoảng thời gian 1100 năm bằng vài thao tác chuột hoặc phím bấm. • Hiển thị các ngày lễ, tết, kỷ niệm, sinh nhật… Cho phép người sử dụng tự định nghĩa và sửa đổi những ngày đặc biệt. • Cài đặt hệ thống lịch hẹn với tính năng tự động báo giờ. • Sổ tay ghi chép. • Tùy biến ảnh nền của cuốn lịch. • Tùy biến các câu thơ, thành ngữ, tục ngữ… theo định dạng HTML để hiển thị trên Bloc… Có 2 bản Bản full (~70 MB): Đầy đủ các tính năng Bản mini (~10 MB): Không có hình nền, cách ngôn… → Sau đó, tải về tính năng cộng thêm nào mình thích: I. Các bước cài thêm hình nền cho bloc: 3. Nhấp nút BROWSE, chỉ đến thư mục …\imgBloc (mặc định là C:\Program Files\Enter PVH\eCalendar 4.0\imgBloc) 4. Nhấp chuột phải lên biểu tượng “Calendar” trên Taskbar, chọn “Thiết lập cấu hình…”II. Các bước tùy biến dòng chữ (Cách ngôn, ngạn ngữ…) trên bloc:1. Download Text on bloc: RS / UL / FF 2. Xả nén vào thư mục …\HTML (mặc định là C:\Program Files\Enter PVH\eCalendar 4.0\HTML) 3. Dùng các phần mềm chuyên dụng (như FrontPage…) để chỉnh sửa các file .htm theo ý thích. ————————————————— (*) Do sơ suất trong đóng gói, khi gọi trợ giúp CT sẽ báo lỗi không tìm thấy file: eCalendar.chm → Cách khắc phục: Sau khi cài đặt xong, vào thư mục trợ giúp (mặc định là: “C:\Program Files\Enter PVH\eCalendar 4.0\Help\“) đổi tên file Calendar.chm thành ECalendar.chm. Theo Echip và PVH’s Weblog ## 10/09/2009 ### When is next Thursday? Filed under: Không toán học, Trao đổi, Vui chơi — Ngô Quốc Anh @ 22:21 Yesterday one of my colleagues circulated an email about a future event, specifying the time as “just before the lab meeting next Thursday”. It set off a whole bundle of confusion (does she mean “The next Thursday we will experience”, or “Thursday of next week”?) and got me thinking about this kind of reference to time. There are quite a few ways to express a future day of the week: my own variant of English makes a strong distinction between “This Thursday” and “Next Thursday”. The former refers to the next Thursday that will be experienced, while “Next Thursday” is the Thursday that follows “This Thursday”. This is in addition to the simple “Thursday” which is essentially synonymous with “This Thursday”. “This” and “Next” when used with days don’t seem to work the same as “This” and “Next” in other contexts (I would use “This bus” only if it can be seen, otherwise “The next bus” to refer to the bus-equivalent of “This Thursday”), and there are additional constraints. For example, if today is Wednesday (which it is not), it doesn’t sound correct to say “This Thursday” when “Tomorrow” is a possibility (unless I have lost track of which day it is [sadly this is a fairly common occurrence]). So in this circumstance “This Thursday” has been replaced by “Tomorrow” while “Next Thursday” remains “Thursday of next week”. And it also gets awkward once Thursday of a particular week has passed; if today is Friday, “this Thursday” used in a future tense then means “Thursday of next week” (“this Thursday” may also be used in the past tense in order to mean “The previous Thursday”; fortunately English verbs allow this ambiguity to be avoided), but “next Thursday” is much more ambiguous (it could mean “Thursday of next week”, although I still typically use it to mean “the second Thursday in the future”. But the use of “next” for a day 13 days in the future may be a bit much). My distinction between “This” and “Next” does not depend on the boundary between weeks; I would still use “This Monday” to refer to the upcoming Monday even if today is Thursday (which it is not), and “Next Monday” to refer to the following one. However, other English speakers do not typically use “This Thursday” as I do (I also occasionally use “This coming Thursday” or “This past Thursday”, but this kind of disambiguation is not really necessary). Hence the confusion arising from my cow-orker’s email (She meant “Next Thursday” in the sense in which I use it, but other colleagues misinterpreted it as meaning “This Thursday”). This may be because British English uses “next” differently, thanks to the “week” expression. UK “Thursday week” apparently has the same meaning as my “Next Thursday”, and UK “Next Thursday” has the same meaning as my “This Thursday” (one of OED’s definitions of “week” is “Seven days after the day specified”). Here’s an instance of someone who ran into the next/week problem (The blogger’s user info suggests that this is also a US/UK translation difference); and here is a discussion related to learning English as a second language. It’s unclear to me whether such expressions also apply for a day that has just passed (if today is Wednesday [which it is not], is “Tuesday week” six or 13 days in the future?). Or expressions like “Next Tuesday week” which just make my head spin. ## 17/05/2009 ### Maple 13 Filed under: Không toán học, Tra cứu, Trao đổi — Ngô Quốc Anh @ 02:20 ## 13/05/2009 ### L’Oise, a sunny day Filed under: Không định dạng — doanchi @ 23:05 I try to test the utile of posting from email. That’s good, I hope. ## 22/03/2009 ### Birds and Frogs, part 4 Filed under: Không toán học, Tra cứu, Trao đổi — Ngô Quốc Anh @ 00:51 Weak Chaos If von Neumann had known about chaos when he spoke in Amsterdam, one of the unsolved problems that he might have talked about was weak chaos. The problem of weak chaos is still unsolved fifty years later. The problem is to understand why chaotic motions often remain bounded and do not cause any violent instability. A good example of weak chaos is the orbital motions of the planets and satellites in the solar system. It was discovered only recently that these motions are chaotic. This was a surprising discovery, upsetting the traditional picture of the solar system as the prime example of orderly stable motion. The mathematician Laplace two hundred years ago thought he had proved that the solar system is stable. It now turns out that Laplace was wrong. Accurate numerical integrations of the orbits show clearly that neighboring orbits diverge exponentially. It seems that chaos is almost universal in the world of classical dynamics. Chaotic behavior was never suspected in the solar system before accurate long-term integrations were done, because the chaos is weak. Weak chaos means that neighboring trajectories diverge exponentially but never diverge far. The divergence begins with exponential growth but afterwards remains bounded. Because the chaos of the planetary motions is weak, the solar system can survive for four billion years. Although the motions are chaotic, the planets never wander far from their customary places, and the system as a whole does not fly apart. In spite of the prevalence of chaos, the Laplacian view of the solar system as a perfect piece of clockwork is not far from the truth. We see the same phenomena of weak chaos in the domain of meteorology. Although the weather in New Jersey is painfully chaotic, the chaos has firm limits. Summers and winters are unpredictably mild or severe, but we can reliably predict that the temperature will never rise to 45 degrees Celsius or fall to minus 30, extremes that are often exceeded in India or in Minnesota. There is no conservation law of physics that forbids temperatures from rising as high in New Jersey as in India, or from falling as low in New Jersey as in Minnesota. The weakness of chaos has been essential to the long-term survival of life on this planet. Weak chaos gives us a challenging variety of weather while protecting us from fluctuations so severe as to endanger our existence. Chaos remains mercifully weak for reasons that we do not understand. That is another unsolved problem for young frogs in the audience to take home. I challenge you to understand the reasons why the chaos observed in a great diversity of dynamical systems is generally weak. The subject of chaos is characterized by an abundance of quantitative data, an unending supply of beautiful pictures, and a shortage of rigorous theorems. Rigorous theorems are the best way to give a subject intellectual depth and precision. Until you can prove rigorous theorems, you do not fully understand the meaning of your concepts. In the field of chaos I know only one rigorous theorem, proved by Tien-Yien Li and Jim Yorke in 1975 and published in a short paper with the title, “Period Three Implies Chaos”, [4]. The Li-Yorke paper is one of the immortal gems in the literature of mathematics. Their theorem concerns nonlinear maps of an interval onto itself. The successive positions of a point when the mapping is repeated can be considered as the orbit of a classical particle. An orbit has period N if the point returns to its original position after N mappings. An orbit is defined to be chaotic, in this context, if it diverges from all periodic orbits. The theorem says that if a single orbit with period three exists, then chaotic orbits also exist. The proof is simple and short. To my mind, this theorem and its proof throw more light than a thousand beautiful pictures on the basic nature of chaos. The theorem explains why chaos is prevalent in the world. It does not explain why chaos is so often weak. That remains a task for the future. I believe that weak chaos will not be understood in a fundamental way until we can prove rigorous theorems about it. String Theorists I would like to say a few words about string theory. Few words, because I know very little about string theory. I never took the trouble to learn the subject or to work on it myself. But when I am at home at the Institute for Advanced Study in Princeton, I am surrounded by string theorists, and I sometimes listen to their conversations. Occasionally I understand a little of what they are saying. Three things are clear. First, what they are doing is first-rate mathematics. The leading pure mathematicians, people like Michael Atiyah and Isadore Singer, love it. It has opened up a whole new branch of mathematics, with new ideas and new problems. Most remarkably, it gave the mathematicians new methods to solve old problems that were previously unsolvable. Second, the string theorists think of themselves as physicists rather than mathematicians. They believe that their theory describes something real in the physical world. And third, there is not yet any proof that the theory is relevant to physics. The theory is not yet testable by experiment. The theory remains in a world of its own, detached from the rest of physics. String theorists make strenuous efforts to deduce consequences of the theory that might be testable in the real world, so far without success. My colleagues Ed Witten and Juan Maldacena and others who created string theory are birds, flying high and seeing grand visions of distant ranges of mountains. The thousands of humbler practitioners of string theory in universities around the world are frogs, exploring fine details of the mathematical structures that birds first saw on the horizon. My anxieties about string theory are sociological rather than scientific. It is a glorious thing to be one of the first thousand string theorists, discovering new connections and pioneering new methods. It is not so glorious to be one of the second thousand or one of the tenth thousand. There are now about ten thousand string theorists scattered around the world. This is a dangerous situation for the tenth thousand and perhaps also for the second thousand. It may happen unpredictably that the fashion changes and string theory becomes unfashionable. Then it could happen that nine thousand string theorists lose their jobs. They have been trained in a narrow specialty, and they may be unemployable in other fields of science. Why are so many young people attracted to string theory? The attraction is partly intellectual. String theory is daring and mathematically elegant. But the attraction is also sociological. String theory is attractive because it offers jobs. And why are so many jobs offered in string theory? Because string theory is cheap. If you are the chairperson of a physics department in a remote place without much money, you cannot afford to build a modern laboratory to do experimental physics, but you can afford to hire a couple of string theorists. So you offer a couple of jobs in string theory, and you have a modern physics department. The temptations are strong for the chairperson to offer such jobs and for the young people to accept them. This is a hazardous situation for the young people and also for the future of science. I am not saying that we should discourage young people from working in string theory if they find it exciting. I am saying that we should offer them alternatives, so that they are not pushed into string theory by economic necessity. Finally, I give you my own guess for the future of string theory. My guess is probably wrong. I have no illusion that I can predict the future. I tell you my guess, just to give you something to think about. I consider it unlikely that string theory will turn out to be either totally successful or totally useless. By totally successful I mean that it is a complete theory of physics, explaining all the details of particles and their interactions. By totally useless I mean that it remains a beautiful piece of pure mathematics. My guess is that string theory will end somewhere between complete success and failure. I guess that it will be like the theory of Lie groups, which Sophus Lie created in the nineteenth century as a mathematical framework for classical physics. So long as physics remained classical, Lie groups remained a failure. They were a solution looking for a problem. But then, fifty years later, the quantum revolution transformed physics, and Lie algebras found their proper place. They became the key to understanding the central role of symmetries in the quantum world. I expect that fifty or a hundred years from now another revolution in physics will happen, introducing new concepts of which we now have no inkling, and the new concepts will give string theory a new meaning. After that, string theory will suddenly find its proper place in the universe, making testable statements about the real world. I warn you that this guess about the future is probably wrong. It has the virtue of being falsifiable, which according to Karl Popper is the hallmark of a scientific statement. It may be demolished tomorrow by some discovery coming out of the Large Hadron Collider in Geneva. Manin Again To end this talk, I come back to Yuri Manin and his book Mathematics as Metaphor. The book is mainly about mathematics. It may come as a surprise to Western readers that he writes with equal eloquence about other subjects such as the collective unconscious, the origin of human language, the psychology of autism, and the role of the trickster in the mythology of many cultures. To his compatriots in Russia, such many-sided interests and expertise would come as no surprise. Russian intellectuals maintain the proud tradition of the old Russian intelligentsia, with scientists and poets and artists and musicians belonging to a single community. They are still today, as we see them in the plays of Chekhov, a group of idealists bound together by their alienation from a superstitious society and a capricious government. In Russia, mathematicians and composers and filmproducers talk to one another, walk together in the snow on winter nights, sit together over a bottle of wine, and share each others’ thoughts. Manin is a bird whose vision extends far beyond the territory of mathematics into the wider landscape of human culture. One of his hobbies is the theory of archetypes invented by the Swiss psychologist Carl Jung. An archetype, according to Jung, is a mental image rooted in a collective unconscious that we all share. The intense emotions that archetypes carry with them are relics of lost memories of collective joy and suffering. Manin is saying that we do not need to accept Jung’s theory as true in order to find it illuminating. More than thirty years ago, the singer Monique Morelli made a recording of songs with words by Pierre MacOrlan. One of the songs is La Ville Morte, the dead city, with a haunting melody tuned to Morelli’s deep contralto, with an accordion singing counterpoint to the voice, and with verbal images of extraordinary intensity. Printed on the page, the words are nothing special: “En pénétrant dans la ville morte, Je tenait Margot par le main… Nous marchions de la nécropole, Les pieds brisés et sans parole, Devant ces trous indéfinis, Devant ces portes sans parole Et ces poubelles pleines de cris”. “As we entered the dead city, I held Margot by the hand…We walked from the graveyard on our bruised feet, without a word, passing by these doors without locks, these vaguely glimpsed holes, these doors without a word, these garbage cans full of screams.” I can never listen to that song without a disproportionate intensity of feeling. I often ask myself why the simple words of the song seem to resonate with some deep level of unconscious memory, as if the souls of the departed are speaking through Morelli’s music. And now unexpectedly in Manin’s book I find an answer to my question. In his chapter, “The Empty City Archetype”, Manin describes how the archetype of the dead city appears again and again in the creations of architecture, literature, art and film, from ancient to modern times, ever since human beings began to congregate in cities, ever since other human beings began to congregate in armies to ravage and destroy them. The character who speaks to us in MacOrlan’s song is an old soldier who has long ago been part of an army of occupation. After he has walked with his wife through the dust and ashes of the dead city, he hears once more: “Chansons de charme d’un clairon Qui fleurissait une heure lointaine Dans un rêve de garnison”. “The magic calls of a bugle that came to life for an hour in an old soldier’s dream”. The words of MacOrlan and the voice of Morelli seem to be bringing to life a dream from our collective unconscious, a dream of an old soldier wandering through a dead city. The concept of the collective unconscious may be as mythical as the concept of the dead city. Manin’s chapter describes the subtle light that these two possibly mythical concepts throw upon each other. He describes the collective unconscious as an irrational force that powerfully pulls us toward death and destruction. The archetype of the dead city is a distillation of the agonies of hundreds of real cities that have been destroyed since cities and marauding armies were invented. Our only way of escape from the insanity of the collective unconscious is a collective consciousness of sanity, based upon hope and reason. The great task that faces our contemporary civilization is to create such a collective consciousness. References 1. M. J. Bertin et al., Pisot and Salem Numbers, Birkhäuser Verlag, Basel, 1992. 2. M. L. Cartwright and J. E. Littlewood, On nonlinear differential equations of the second order, I, Jour. London Math. Soc. 20 (1945), 180–189. 3. Freeman Dyson, Prof. Hermann Weyl, For.Mem.R.S., Nature 177 (1956), 457–458. 4. Tien-Yien Li and James A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975), 985–992. 5. Yuri I. Manin, Mathematics as Metaphor: Selected Essays, American Mathematical Society, Providence, Rhode Island, 2007. [The Russian version is: Manin, Yu. I., Matematika kak Metafora, Moskva, Izdatyelstvo MTsNMO, 2008.] 6. Andrew M. Odlyzko, Primes, quantum chaos and computers, in Number Theory, Proceedings of a Symposium, National Research Council, Washington DC, 1990, pp. 35–46. 7. Hermann Weyl, Gravitation und elektrizität, Sitz. König. Preuss. Akad. Wiss. 26 (1918), 465–480. 8. ——— , Elektron und gravitation, Zeits. Phys. 56 (1929), 350–352. 9. ——— , Selecta, Birkhäuser Verlag, Basel, 1956, p. 192. 10. Chen Ning Yang, Integral formalism for gauge fields, Phys. Rev. Letters 33 (1974), 445–447. 11. Chen Ning Yang and Robert L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954), 191–195. 12. ——— , Hermann Weyl’s contribution to physics, in Hermann Weyl, 1885–1985, (K. Chandrasekharan, ed.), Springer-Verlag, Berlin, 1986, p. 19. Adapted from NOTICES OF AMS 2/2009 ### Birds and Frogs, part 3 Filed under: Không toán học, Toán học, Tra cứu, Trao đổi — Ngô Quốc Anh @ 00:39 John von Neumann Another important figure in twentieth century mathematics was John von Neumann. Von Neumann was a frog, applying his prodigious technical skill to solve problems in many branches of mathematics and physics. He began with the foundations of mathematics. He found the first satisfactory set of axioms for set-theory, avoiding the logical paradoxes that Cantor had encountered in his attempts to deal with infinite sets and infinite numbers. Von Neumann’s axioms were used by his bird friend Kurt Gödel a few years later to prove the existence of undecidable propositions in mathematics. Gödel’s theorems gave birds a new vision of mathematics. After Gödel, mathematics was no longer a single structure tied together with a unique concept of truth, but an archipelago of structures with diverse sets of axioms and diverse notions of truth. Gödel showed that mathematics is inexhaustible. No matter which set of axioms is chosen as the foundation, birds can always find questions that those axioms cannot answer. Von Neumann went on from the foundations of mathematics to the foundations of quantum mechanics. To give quantum mechanics a firm mathematical foundation, he created a magnificent theory of rings of operators. Every observable quantity is represented by a linear operator, and the peculiarities of quantum behavior are faithfully represented by the algebra of operators. Just as Newton invented calculus to describe classical dynamics, von Neumann invented rings of operators to describe quantum dynamics. Von Neumann made fundamental contributions to several other fields, especially to game theory and to the design of digital computers. For the last ten years of his life, he was deeply involved with computers. He was so strongly interested in computers that he decided not only to study their design but to build one with real hardware and software and use it for doing science. I have vivid memories of the early days of von Neumann’s computer project at the Institute for Advanced Study in Princeton. At that time he had two main scientific interests, hydrogen bombs and meteorology. He used his computer during the night for doing hydrogen bomb calculations and during the day for meteorology. Most of the people hanging around the computer building in daytime were meteorologists. Their leader was Jule Charney. Charney was a real meteorologist, properly humble in dealing with the inscrutable mysteries of the weather, and skeptical of the ability of the computer to solve the mysteries. John von Neumann was less humble and less skeptical. I heard von Neumann give a lecture about the aims of his project. He spoke, as he always did, with great confidence. He said, “The computer will enable us to divide the atmosphere at any moment into stable regions and unstable regions. Stable regions we can predict. Unstable regions we can control.” Von Neumann believed that any unstable region could be pushed by a judiciously applied small perturbation so that it would move in any desired direction. The small perturbation would be applied by a fleet of airplanes carrying smoke generators, to absorb sunlight and raise or lower temperatures at places where the perturbation would be most effective. In particular, we could stop an incipient hurricane by identifying the position of an instability early enough, and then cooling that patch of air before it started to rise and form a vortex. Von Neumann, speaking in 1950, said it would take only ten years to build computers powerful enough to diagnose accurately the stable and unstable regions of the atmosphere. Then, once we had accurate diagnosis, it would take only a short time for us to have control. He expected that practical control of the weather would be a routine operation within the decade of the 1960s. Von Neumann, of course, was wrong. He was wrong because he did not know about chaos. We now know that when the motion of the atmosphere is locally unstable, it is very often chaotic. The word “chaotic” means that motions that start close together diverge exponentially from each other as time goes on. When the motion is chaotic, it is unpredictable, and a small perturbation does not move it into a stable motion that can be predicted. A small perturbation will usually move it into another chaotic motion that is equally unpredictable. So von Neumann’s strategy for controlling the weather fails. He was, after all, a great mathematician but a mediocre meteorologist. Von Neumann got into trouble at the end of his life because he was really a frog but everyone expected him to fly like a bird. In 1954 there was an International Congress of Mathematicians in Amsterdam. These congresses happen only once in four years and it is a great honor to be invited to speak at the opening session. The organizers of the Amsterdam congress invited von Neumann to give the keynote speech, expecting him to repeat the act that Hilbert had performed in Paris in 1900. Just as Hilbert had provided a list of unsolved problems to guide the development of mathematics for the first half of the twentieth century, von Neumann was invited to do the same for the second half of the century. The title of von Neumann’s talk was announced in the program of the congress. It was “Unsolved Problems in Mathematics: Address by Invitation of the Organizing Committee”. After the congress was over, the complete proceedings were published, with the texts of all the lectures except this one. In the proceedings there is a blank page with von Neumann’s name and the title of his talk. Underneath, it says, “No manuscript of this lecture was available.” Adapted from NOTICES OF AMS 2/2009 ## 28/02/2009 ### Hội nghị tổng kết hoạt động KHCN ĐHQGHN năm 2008 Filed under: Giải tích toán học, Tra cứu, Trao đổi — bmgt @ 07:00 Hội nghị đã diễn ra ngày 27/2/2009 với sự tham dự của GS.TSKH Vũ Minh Giang – Phó giám đốc cùng lãnh đạo văn phòng, các ban chức năng, thủ trưởng các đơn vị trực thuộc, lãnh đạo các khoa, các trung tâm, các giáo sư, đại diện các nhà khoa học trong ĐHQGHN. GS.TS Nguyễn Cao Huần – Trưởng ban Khoa học – Công nghệ ĐHQGHN đã trình bày báo cáo tổng kết hoạt động khoa học – công nghệ năm 2008 và các nhiệm vụ, giải pháp trọng tâm của hoạt động khoa học – công nghệ năm 2009. Năm 2008, hoạt động khoa học – công nghệ của ĐHQGHN đã tập trung triển khai theo 3 mục tiêu, nhiệm vụ trọng tâm là: Tiếp tục phấn đấu để ĐHQGHN có nhiều công trình, sản phẩm KHCN tầm cỡ quốc gia, quốc tế; thông qua hoạt động NCKH nhanh chóng đào tạo, xây dựng, bổ sung đội ngũ cán bộ khoa học đầu ngành, đầu đàn; xây dựng và phát triển các công nghệ cao ở ĐHQGHN. Các giải pháp quan trọng đã được triển khai rộng rãi là đầu tư xây dựng các nhóm nghiên cứu mạnh, gắn với việc tập trung tham gia giải quyết các nhiệm vụ khoa học công nghệ lớn, quan trọng, nằm trong chiến lược phát triển khoa học – công nghệ của quốc gia, trên cơ sở thế mạnh và định hướng ưu tiên phát triển của ĐHQGHN. Đề án xây dựng 16 chuyên ngành đào tạo đại học, 23 chuyên ngành đào tạo thạc sĩ, 23 chuyên ngành đào tạo tiến sĩ (16 – 23) đạt trình độ chuẩn khu vực và quốc tế đã được triển khai thí điểm tại một số đơn vị đào tạo. Bên cạnh việc tiếp tục hoàn thành thực hiện các dự án đầu tư chiều sâu của Trường ĐHKHTN và Trường ĐH Công nghệ, ĐHQGHN đã ưu tiên đầu tư chiều sâu cho Viện Vi sinh vật – Công nghệ sinh học, Trung tâm Thông tin thư viện và Khoa Sư phạm. Vấn đề phát triển, khai thác mạnh mẽ các quan hệ quốc tế để ưu tiên cho phát triển công nghệ cao và đào tạo cán bộ, chú trọng hợp tác với thành phố Hà Nội, ĐHQG TP.HCM và tỉnh Hòa Bình cũng đã được lãnh đạo ĐHQGHN quan tâm đúng mức. Năm vừa qua, ĐHQGHN đã triển khai thực hiện được 30 đề tài cấp nhà nước thuộc các chương trình KC, KX… trong đó có 17 đề tài cấp nhà nước thuộc các lĩnh vực khoa học xã hội và nhân văn. Bên cạnh đó, ĐHQGHN cũng đã hoàn thiện Đề án và Điều lệ hoạt động của Quỹ phát triển khoa học công nghệ, hoàn thành Kế hoạch chiến lược phát triển công nghệ thông tin của ĐHQGHN đến năm 2010, tầm nhìn đến năm 2020. Năm 2009, trên cơ sở “Chiến lược phát triển khoa học công nghệ đến năm 2010” của Chính phủ, Nghị quyết của BCH Đảng bộ ĐHQGHN khóa III, hoạt động khoa học – công nghệ của ĐHQGHN sẽ đi theo phương hướng: Phát huy mọi nguồn lực, tạo bước đột phá về chất lượng đào tạo và nghiên cứu khoa học, tiếp tục phát triển ĐHQGHN theo định hướng đại học nghiên cứu tiên tiến đa ngành, đa lĩnh vực, cung cấp nguồn nhân lực chất lượng cao cho xã hội, khẳng định thế mạnh hàng đầu cả nước về khoa học cơ bản, tập trung có trọng tâm, trọng điểm cho nghiên cứu khoa học đỉnh cao để tạo ra sản phẩm khoa học có tầm cỡ quốc tế, có phát minh sáng chế quan trọng phục vụ phát triển kinh tế xã hội, an ninh quốc phòng, góp phần giải quyết các nhiệm vụ khoa học – công nghệ quan trọng của quốc gia. Một số chỉ tiêu phấn đấu trong giai đoạn 2009-2010 là: 100% các dự án đấu thầu và nhiệm vụ khoa học cấp nhà nước được triển khai đúng tiến độ; 100% đề tài, đề án cấp bộ/ ngành nghiệm thu đúng thời hạn; Thu hút vốn từ bên ngoài gấp 2 lần kinh phí được đầu tư từ ngân sách; Có trên 100 bài báo được in trong các tạp chí quốc tế; Có hơn 10 giải thưởng khoa học công nghệ từ cấp ĐHQGHN trở lên… Phát biểu chỉ đạo tại hội nghị, GS.TSKH Vũ Minh Giang đã đánh giá cao những đổi mới, những kết quả toàn diện, sâu sắc và đột phá của hoạt động khoa học – công nghệ trong năm qua, biểu dương sự nỗ lực của các đơn vị và các nhà khoa học. Phó giám đốc cũng nhấn mạnh cần đặc biệt chú trọng tới chất lượng, hiệu quả của các hoạt động khoa học – công nghệ của ĐHQGHN, chú trọng tới tính liên thông, liên kết, liên ngành – thế mạnh của đại học đa ngành, đa lĩnh vực. Nhân dịp này, GS.TSKH Vũ Minh Giang đã thay mặt Giám đốc ĐHQGHN trao Giải thưởng công trình khoa học tiêu biểuGiải thưởng nhà khoa học trẻ năm 2008 cho các tác giả của các công trình/ cụm công trình. Danh sách các công trình/ cụm công trình khoa học tiêu biểu năm 2008 của ĐHQGHN 1/ “Nghiên cứu sự tồn tại nghiệm yếu của các bài toán biên không đều đối với phương trình và hệ phương trình Elliptic không tuyến tính”; các tác giả: PGS.TS Hoàng Quốc Toàn, ThS. Ngô Quốc Anh; Trường ĐHKHTN 2/ “Hệ nano dây spin Ca2CuO3”; tập thể tác giả: PGS.TS Hoàng Nam Nhật, GS.TSKH Nguyễn Châu, TS. Huỳnh Đăng Chính, CN. Nguyễn Thùy Trang; Trường ĐHKHTN 3/ “Giải pháp tổng quát để phân tích và thiết kế các anten mạch dải siêu cao tần tích hợp trên bề mặt bán cầu nhiều lớp và ứng dụng”; tác giả: TS. Trương Vũ Bằng Giang; Trường ĐH Công nghệ 4/ “Nghiên cứu quy trình chiết tách Ent-Kauran Ditecpenoit có tác dụng chống ung thư và chống viêm từ cây khổ sâm bắc bộ”; tập thể tác giả đề tài độc lập cấp nhà nước, mã số ĐTĐL-2005/05 do GS.TSKH Phan Tống Sơn chủ nhiệm; Trường ĐHKHTN 5/ “Việt Nam 1919 – 1930: Thời kỳ tìm tòi và định hướng”; tác giả: GS.TS Nguyễn Văn Khánh; Trường ĐHKHXH&NV 6/ “Văn học trung đại Việt Nam dưới góc nhìn văn hóa”; tác giả: PGS.TS Trần Nho Thìn; Trường ĐHKHXH&NV 7/ “Văn học Việt Nam thế kỷ X – XIX (những vấn đề lý luận và lịch sử)”; tập thể tác giả do PGS.TS Trần Ngọc Vương chủ biên; Trường ĐHKHXH&NV Danh sách các công trình/ cụm công trình được tặng Giải thưởng nhà khoa học trẻ năm 2008 của ĐHQGHN 1/ “Nghiên cứu và xây dựng các phương thức hiện đại cho tương tác người máy”; tác giả: TS. Bùi Thế Duy; Trường ĐH Công nghệ 2/ “Chế tạo và nghiên cứu một số vật liệu nano và bước đầu thử nghiệm khả năng ứng dụng hạt nano từ tính trong sinh học”; tác giả: TS. Nguyễn Hoàng Hải; Trường ĐHKHTN 3/ “Cảm biến gia tốc ba bậc tự do kiểu áp trở”; tác giả: ThS. Trần Đức Tân; Trường ĐH Công nghệ Văn Trương Minh [Trang Tin tức Sự kiện] Nguồn:VNU ## 21/02/2009 ### Birds and Frogs, part 2 Filed under: Không toán học, Trao đổi — Ngô Quốc Anh @ 22:12 Abram Besicovitch and Hermann Weyl Let me now introduce you to some notable frogs and birds that I knew personally. I came to Cambridge University as a student in 1941 and had the tremendous luck to be given the Russian mathematician Abram Samoilovich Besicovitch as my supervisor. Since this was in the middle of World War Two, there were very few students in Cambridge, and almost no graduate students. Although I was only seventeen years old and Besicovitch was already a famous professor, he gave me a great deal of his time and attention, and we became life-long friends. He set the style in which I began to work and think about mathematics. He gave wonderful lectures on measure-theory and integration, smiling amiably when we laughed at his glorious abuse of the English language. I remember only one occasion when he was annoyed by our laughter. He remained silent for a while and then said, “Gentlemen. Fifty million English speak English you speak. Hundred and fifty million Russians speak English I speak.” Besicovitch was a frog, and he became famous when he was young by solving a problem in elementary plane geometry known as the Kakeya problem. The Kakeya problem was the following. A line segment of length one is allowed to move freely in a plane while rotating through an angle of 360 degrees. What is the smallest area of the plane that it can cover during its rotation? The problem was posed by the Japanese mathematician Kakeya in 1917 and remained a famous unsolved problem for ten years. George Birkhoff, the leading American mathematician at that time, publicly proclaimed that the Kakeya problem and the fourcolor problem were the outstanding unsolved problems of the day. It was widely believed that the minimum area was π /8, which is the area of a three-cusped hypocycloid. The three-cusped hypocycloid is a beautiful three-pointed curve. It is the curve traced out by a point on the circumference of a circle with radius one-quarter, when the circle rolls around the inside of a fixed circle with radius three-quarters. The line segment of length one can turn while always remaining tangent to the hypocycloid with its two ends also on the hypocycloid. This picture of the line turning while touching the inside of the hypocycloid at three points was so elegant that most people believed it must give the minimum area. Then Besicovitch surprised everyone by proving that the area covered by the line as it turns can be less than $\varepsilon$ for any positive $\varepsilon$. Besicovitch had actually solved the problem in 1920 before it became famous, not even knowing that Kakeya had proposed it. In 1920 he published the solution in Russian in the Journal of the Perm Physics and Mathematics Society, a journal that was not widely read. The university of Perm, a city 1,100 kilometers east of Moscow, was briefly a refuge for many distinguished mathematicians after the Russian revolution. They published two volumes of their journal before it died amid the chaos of revolution and civil war. Outside Russia the journal was not only unknown but unobtainable. Besicovitch left Russia in 1925 and arrived at Copenhagen, where he learned about the famous Kakeya problem that he had solved five years earlier. He published the solution again, this time in English in the Mathematische Zeitschrift. The Kakeya problem as Kakeya proposed it was a typical frog problem, a concrete problem without much connection with the rest of mathematics. Besicovitch gave it an elegant and deep solution, which revealed a connection with general theorems about the structure of sets of points in a plane. The Besicovitch style is seen at its finest in his three classic papers with the title, “On the fundamental geometric properties of linearly measurable plane sets of points”, published in Mathematische Annalen in the years 1928, 1938, and 1939. In these papers he proved that every linearly measurable set in the plane is divisible into a regular and an irregular component, that the regular component has a tangent almost everywhere, and the irregular component has a projection of measure zero onto almost all directions. Roughly speaking, the regular component looks like a collection of continuous curves, while the irregular component looks nothing like a continuous curve. The existence and the properties of the irregular component are connected with the Besicovitch solution of the Kakeya problem. One of the problems that he gave me to work on was the division of measurable sets into regular and irregular components in spaces of higher dimensions. I got nowhere with the problem, but became permanently imprinted with the Besicovitch style. The Besicovitch style is architectural. He builds out of simple elements a delicate and complicated architectural structure, usually with a hierarchical plan, and then, when the building is finished, the completed structure leads by simple arguments to an unexpected conclusion. Every Besicovitch proof is a work of art, as carefully constructed as a Bach fugue. A few years after my apprenticeship with Besicovitch, I came to Princeton and got to know Hermann Weyl. Weyl was a prototypical bird, just as Besicovitch was a prototypical frog. I was lucky to overlap with Weyl for one year at the Princeton Institute for Advanced Study before he retired from the Institute and moved back to his old home in Zürich. He liked me because during that year I published papers in the Annals of Mathematics about number theory and in the Physical Review about the quantum theory of radiation. He was one of the few people alive who was at home in both subjects. He welcomed me to the Institute, in the hope that I would be a bird like himself. He was disappointed. I remained obstinately a frog. Although I poked around in a variety of mud-holes, I always looked at them one at a time and did not look for connections between them. For me, number theory and quantum theory were separate worlds with separate beauties. I did not look at them as Weyl did, hoping to find clues to a grand design. Weyl’s great contribution to the quantum theory of radiation was his invention of gauge fields. The idea of gauge fields had a curious history. Weyl invented them in 1918 as classical fields in his unified theory of general relativity and electromagnetism, [7]. He called them “gauge fields” because they were concerned with the non-integrability of measurements of length. His unified theory was promptly and publicly rejected by Einstein. After this thunderbolt from on high, Weyl did not abandon his theory but moved on to other things. The theory had no experimental consequences that could be tested. Then in 1929, after quantum mechanics had been invented by others, Weyl realized that his gauge fields fitted far better into the quantum world than they did into the classical world, [8]. All that he needed to do, to change a classical gauge into a quantum gauge, was to change real numbers into complex numbers. In quantum mechanics, every quantum of electric charge carries with it a complex wave function with a phase, and the gauge field is concerned with the non-integrability of measurements of phase. The gauge field could then be precisely identified with the electromagnetic potential, and the law of conservation of charge became a consequence of the local phase invariance of the theory. Weyl died four years after he returned from Princeton to Zürich, and I wrote his obituary for the journal Nature, [3]. “Among all the mathematicians who began their working lives in the twentieth century,” I wrote, “Hermann Weyl was the one who made major contributions in the greatest number of different fields. He alone could stand comparison with the last great universal mathematicians of the nineteenth century, Hilbert and Poincaré. So long as he was alive, he embodied a living contact between the main lines of advance in pure mathematics and in theoretical physics. Now he is dead, the contact is broken, and our hopes of comprehending the physical universe by a direct use of creative mathematical imagination are for the time being ended.” I mourned his passing, but I had no desire to pursue his dream. I was happy to see pure mathematics and physics marching ahead in opposite directions. The obituary ended with a sketch of Weyl as a human being: “Characteristic of Weyl was an aesthetic sense which dominated his thinking on all subjects. He once said to me, half joking, ‘My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful’. This remark sums up his personality perfectly. It shows his profound faith in an ultimate harmony of Nature, in which the laws should inevitably express themselves in a mathematically beautiful form. It shows also his recognition of human frailty, and his humor, which always stopped him short of being pompous. His friends in Princeton will remember him as he was when I last saw him, at the Spring Dance of the Institute for Advanced Study last April: a big jovial man, enjoying himself splendidly, his cheerful frame and his light step giving no hint of his sixty-nine years.” The fifty years after Weyl’s death were a golden age of experimental physics and observational astronomy, a golden age for Baconian travelers picking up facts, for frogs exploring small patches of the swamp in which we live. During these fifty years, the frogs accumulated a detailed knowledge of a large variety of cosmic structures and a large variety of particles and interactions. As the exploration of new territories continued, the universe became more complicated. Instead of a grand design displaying the simplicity and beauty of Weyl’s mathematics, the explorers found weird objects such as quarks and gamma-ray bursts, weird concepts such as supersymmetry and multiple universes. Meanwhile, mathematics was also becoming more complicated, as exploration continued into the phenomena of chaos and many other new areas opened by electronic computers. The mathematicians discovered the central mystery of computability, the conjecture represented by the statement P is not equal to NP. The conjecture asserts that there exist mathematical problems which can be quickly solved in individual cases but cannot be solved by a quick algorithm applicable to all cases. The most famous example of such a problem is the traveling salesman problem, which is to find the shortest route for a salesman visiting a set of cities, knowing the distance between each pair. All the experts believe that the conjecture is true, and that the traveling salesman problem is an example of a problem that is P but not NP. But nobody has even a glimmer of an idea how to prove it. This is a mystery that could not even have been formulated within the nineteenth-century mathematical universe of Hermann Weyl. Frank Yang and Yuri Manin The last fifty years have been a hard time for birds. Even in hard times, there is work for birds to do, and birds have appeared with the courage to tackle it. Soon after Weyl left Princeton, Frank Yang arrived from Chicago and moved into Weyl’s old house. Yang took Weyl’s place as the leading bird among my generation of physicists. While Weyl was still alive, Yang and his student Robert Mills discovered the Yang-Mills theory of non-Abelian gauge fields, a marvelously elegant extension of Weyl’s idea of a gauge field, [11]. Weyl’s gauge field was a classical quantity, satisfying the commutative law of multiplication. The Yang-Mills theory had a triplet of gauge fields which did not commute. They satisfied the commutation rules of the three components of a quantum mechanical spin, which are generators of the simplest non-Abelian Lie algebra A2 . The theory was later generalized so that the gauge fields could be generators of any finite-dimensional Lie algebra. With this generalization, the Yang-Mills gauge field theory provided the framework for a model of all the known particles and interactions, a model that is now known as the Standard Model of particle physics. Yang put the finishing touch to it by showing that Einstein’s theory of gravitation fits into the same framework, with the Christoffel three-index symbol taking the role of gauge field, [10]. In an appendix to his 1918 paper, added in 1955 for the volume of selected papers published to celebrate his seventieth birthday, Weyl expressed his final thoughts about gauge field theories (my translation), [12]: “The strongest argument for my theory seemed to be this, that gauge invariance was related to conservation of electric charge in the same way as coordinate invariance was related to conservation of energy and momentum.” Thirty years later Yang was in Zürich for the celebration of Weyl’s hundredth birthday. In his speech, [12], Yang quoted this remark as evidence of Weyl’s devotion to the idea of gauge invariance as a unifying principle for physics. Yang then went on, “Symmetry, Lie groups, and gauge invariance are now recognized, through theoretical and experimental developments, to play essential roles in determining the basic forces of the physical universe. I have called this the principle that symmetry dictates interaction.” This idea, that symmetry dictates interaction, is Yang’s generalization of Weyl’s remark. Weyl observed that gauge invariance is intimately connected with physical conservation laws. Weyl could not go further than this, because he knew only the gauge invariance of commuting Abelian fields. Yang made the connection much stronger by introducing non-Abelian gauge fields. With non-Abelian gauge fields generating nontrivial Lie algebras, the possible forms of interaction between fields become unique, so that symmetry dictates interaction. This idea is Yang’s greatest contribution to physics. It is the contribution of a bird, flying high over the rain forest of little problems in which most of us spend our lives. Another bird for whom I have a deep respect is the Russian mathematician Yuri Manin, who recently published a delightful book of essays with the title Mathematics as Metaphor [5]. The book was published in Moscow in Russian, and by the American Mathematical Society in English. I wrote a preface for the English version, and I give you here a short quote from my preface. “Mathematics as Metaphor is a good slogan for birds. It means that the deepest concepts in mathematics are those which link one world of ideas with another. In the seventeenth century Descartes linked the disparate worlds of algebra and geometry with his concept of coordinates, and Newton linked the worlds of geometry and dynamics with his concept of fluxions, nowadays called calculus. In the nineteenth century Boole linked the worlds of logic and algebra with his concept of symbolic logic, and Riemann linked the worlds of geometry and analysis with his concept of Riemann surfaces. Coordinates, fluxions, symbolic logic, and Riemann surfaces are all metaphors, extending the meanings of words from familiar to unfamiliar contexts. Manin sees the future of mathematics as an exploration of metaphors that are already visible but not yet understood. The deepest such metaphor is the similarity in structure between number theory and physics. In both fields he sees tantalizing glimpses of parallel concepts, symmetries linking the continuous with the discrete. He looks forward to a unification which he calls the quantization of mathematics. “Manin disagrees with the Baconian story, that Hilbert set the agenda for the mathematics of the twentieth century when he presented his famous list of twenty-three unsolved problems to the International Congress of Mathematicians in Paris in 1900. According to Manin, Hilbert’s problems were a distraction from the central themes of mathematics. Manin sees the important advances in mathematics coming from programs, not from problems. Problems are usually solved by applying old ideas in new ways. Programs of research are the nurseries where new ideas are born. He sees the Bourbaki program, rewriting the whole of mathematics in a more abstract language, as the source of many of the new ideas of the twentieth century. He sees the Langlands program, unifying number theory with geometry, as a promising source of new ideas for the twenty-first. People who solve famous unsolved problems may win big prizes, but people who start new programs are the real pioneers.” The Russian version of Mathematics as Metaphor contains ten chapters that were omitted from the English version. The American Mathematical Society decided that these chapters would not be of interest to English language readers. The omissions are doubly unfortunate. First, readers of the English version see only a truncated view of Manin, who is perhaps unique among mathematicians in his broad range of interests extending far beyond mathematics. Second, we see a truncated view of Russian culture, which is less compartmentalized than English language culture, and brings mathematicians into closer contact with historians and artists and poets. Adapted from NOTICES OF AMS 2/2009 ## 12/02/2009 ### Birds and Frogs, part 1 Filed under: Giải tích toán học, Trao đổi, Vui chơi — Ngô Quốc Anh @ 00:35 Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. I happen to be a frog, but many of my best friends are birds. The main theme of my talk tonight is this. Mathematics needs both birds and frogs. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. Mathematics is both great art and important science, because it combines generality of concepts with depth of structures. It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper. The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it. This talk is called the Einstein lecture, and I am grateful to the American Mathematical Society for inviting me to do honor to Albert Einstein. Einstein was not a mathematician, but a physicist who had mixed feelings about mathematics. On the one hand, he had enormous respect for the power of mathematics to describe the workings of nature, and he had an instinct for mathematical beauty which led him onto the right track to find nature’s laws. On the other hand, he had no interest in pure mathematics, and he had no technical skill as a mathematician. In his later years he hired younger colleagues with the title of assistants to do mathematical calculations for him. His way of thinking was physical rather than mathematical. He was supreme among physicists as a bird who saw further than others. I will not talk about Einstein skill as a mathematician. In his later years he hired younger colleagues with the title of assistants to do mathematical calculations for him. His way of thinking was physical rather than mathematical. He was supreme among physicists as a bird who saw further than others. I will not talk about Einstein since I have nothing new to say. Francis Bacon and René Descartes At the beginning of the seventeenth century, two great philosophers, Francis Bacon in England and René Descartes in France, proclaimed the birth of modern science. Descartes was a bird, and Bacon was a frog. Each of them described his vision of the future. Their visions were very different. Bacon said, “All depends on keeping the eye steadily fixed on the facts of nature.” Descartes said, “I think, therefore I am.” According to Bacon, scientists should travel over the earth collecting facts, until the accumulated facts reveal how Nature works. The scientists will then induce from the facts the laws that Nature obeys. According to Descartes, scientists should stay at home and deduce the laws of Nature by pure thought. In order to deduce the laws correctly, the scientists will need only the rules of logic and knowledge of the existence of God. For four hundred years since Bacon and Descartes led the way, science has raced ahead by following both paths simultaneously. Neither Baconian empiricism nor Cartesian dogmatism has the power to elucidate Nature’s secrets by itself, but both together have been amazingly successful. For four hundred years English scientists have tended to be Baconian and French scientists Cartesian. Faraday and Darwin and Rutherford were Baconians; Pascal and Laplace and Poincaré were Cartesians. Science was greatly enriched by the cross-fertilization of the two contrasting cultures. Both cultures were always at work in both countries. Newton was at heart a Cartesian, using pure thought as Descartes intended, and using it to demolish the Cartesian dogma of vortices. Marie Curie was at heart a Baconian, boiling tons of crude uranium ore to demolish the dogma of the indestructibility of atoms. In the history of twentieth century mathematics, there were two decisive events, one belonging to the Baconian tradition and the other to the Cartesian tradition. The first was the International Congress of Mathematicians in Paris in 1900, at which Hilbert gave the keynote address, charting the course of mathematics for the coming century by propounding his famous list of twenty-three outstanding unsolved problems. Hilbert himself was a bird, flying high over the whole territory of mathematics, but he addressed his problems to the frogs who would solve them one at a time. The second decisive event was the formation of the Bourbaki group of mathematical birds in France in the 1930s, dedicated to publishing a series of textbooks that would establish a unifying framework for all of mathematics. The Hilbert problems were enormously successful in guiding mathematical research into fruitful directions. Some of them were solved and some remain unsolved, but almost all of them stimulated the growth of new ideas and new fields of mathematics. The Bourbaki project was equally influential. It changed the style of mathematics for the next fifty years, imposing a logical coherence that did not exist before, and moving the emphasis from concrete examples to abstract generalities. In the Bourbaki scheme of things, mathematics is the abstract structure included in the Bourbaki textbooks. What is not in the textbooks is not mathematics. Concrete examples, since they do not appear in the textbooks, are not mathematics. The Bourbaki program was the extreme expression of the Cartesian style. It narrowed the scope of mathematics by excluding the beautiful flowers that Baconian travelers might collect by the wayside. Jokes of Nature For me, as a Baconian, the main thing missing in the Bourbaki program is the element of surprise. The Bourbaki program tried to make mathematics logical. When I look at the history of mathematics, I see a succession of illogical jumps, improbable coincidences, jokes of nature. One of the most profound jokes of nature is the square root of minus one that the physicist Erwin Schrödinger put into his wave equation when he invented wave mechanics in 1926. Schrödinger was a bird who started from the idea of unifying mechanics with optics. A hundred years earlier, Hamilton had unified classical mechanics with ray optics, using the same mathematics to describe optical rays and classical particle trajectories. Schrödinger’s idea was to extend this unification to wave optics and wave mechanics. Wave optics already existed, but wave mechanics did not. Schrödinger had to invent wave mechanics to complete the unification. Starting from wave optics as a model, he wrote down a differential equation for a mechanical particle, but the equation made no sense. The equation looked like the equation of conduction of heat in a continuous medium. Heat conduction has no visible relevance to particle mechanics. Schrödinger’s idea seemed to be going nowhere. But then came the surprise. Schrödinger put the square root of minus one into the equation, and suddenly it made sense. Suddenly it became a wave equation instead of a heat conduction equation. And Schrödinger found to his delight that the equation has solutions corresponding to the quantized orbits in the Bohr model of the atom. It turns out that the Schrödinger equation describes correctly everything we know about the behavior of atoms. It is the basis of all of chemistry and most of physics. And that square root of minus one means that nature works with complex numbers and not with real numbers. This discovery came as a complete surprise, to Schrödinger as well as to everybody else. According to Schrödinger, his fourteen-year-old girl friend Itha Junger said to him at the time, “Hey, you never even thought when you began that so much sensible stuff would come out of it.” All through the nineteenth century, mathematicians from Abel to Riemann and Weierstrass had been creating a magnificent theory of functions of complex variables. They had discovered that the theory of functions became far deeper and more powerful when it was extended from real to complex numbers. But they always thought of complex numbers as an artificial construction, invented by human mathematicians as a useful and elegant abstraction from real life. It never entered their heads that this artificial number system that they had invented was in fact the ground on which atoms move. They never imagined that nature had got there first. Another joke of nature is the precise linearity of quantum mechanics, the fact that the possible states of any physical object form a linear space. Before quantum mechanics was invented, classical physics was always nonlinear, and linear models were only approximately valid. After quantum mechanics, nature itself suddenly became linear. This had profound consequences for mathematics. During the nineteenth century Sophus Lie developed his elaborate theory of continuous groups, intended to clarify the behavior of classical dynamical systems. Lie groups were then of little interest either to mathematicians or to physicists. The nonlinear theory of Lie groups was too complicated for the mathematicians and too obscure for the physicists. Lie died a disappointed man. And then, fifty years later, it turned out that nature was precisely linear, and the theory of linear representations of Lie algebras was the natural language of particle physics. Lie groups and Lie algebras were reborn as one of the central themes of twentieth century mathematics. A third joke of nature is the existence of quasicrystals. In the nineteenth century the study of crystals led to a complete enumeration of possible discrete symmetry groups in Euclidean space. Theorems were proved, establishing the fact that in three-dimensional space discrete symmetry groups could contain only rotations of order three, four, or six. Then in 1984 quasi-crystals were discovered, real solid objects growing out of liquid metal alloys, showing the symmetry of the icosahedral group, which includes five-fold rotations. Meanwhile, the mathematician Roger Penrose discovered the Penrose tilings of the plane. These are arrangements of parallelograms that cover a plane with pentagonal long-range order. The alloy quasi-crystals are three-dimensional analogs of the two-dimensional Penrose tilings. After these discoveries, mathematicians had to enlarge the theory of crystallographic groups to include quasicrystals. That is a major program of research which is still in progress. A fourth joke of nature is a similarity in behavior between quasi-crystals and the zeros of the Riemann Zeta function. The zeros of the zetafunction are exciting to mathematicians because they are found to lie on a straight line and nobody understands why. The statement that with trivial exceptions they all lie on a straight line is the famous Riemann Hypothesis. To prove the Riemann Hypothesis has been the dream of young mathematicians for more than a hundred years. I am now making the outrageous suggestion that we might use quasi-crystals to prove the Riemann Hypothesis. Those of you who are mathematicians may consider the suggestion frivolous. Those who are not mathematicians may consider it uninteresting. Nevertheless I am putting it forward for your serious consideration. When the physicist Leo Szilard was young, he became dissatisfied with the ten commandments of Moses and wrote a new set of ten commandments to replace them. Szilard’s second commandment says: “Let your acts be directed towards a worthy goal, but do not ask if they can reach it: they are to be models and examples, not means to an end.” Szilard practiced what he preached. He was the first physicist to imagine nuclear weapons and the first to campaign actively against their use. His second commandment certainly applies here. The proof of the Riemann Hypothesis is a worthy goal, and it is not for us to ask whether we can reach it. I will give you some hints describing how it might be achieved. Here I will be giving voice to the mathematician that I was fifty years ago before I became a physicist. I will talk first about the Riemann Hypothesis and then about quasi-crystals. There were until recently two supreme unsolved problems in the world of pure mathematics, the proof of Fermat’s Last Theorem and the proof of the Riemann Hypothesis. Twelve years ago, my Princeton colleague Andrew Wiles polished off Fermat’s Last Theorem, and only the Riemann Hypothesis remains. Wiles’ proof of the Fermat Theorem was not just a technical stunt. It required the discovery and exploration of a new field of mathematical ideas, far wider and more consequential than the Fermat Theorem itself. It is likely that any proof of the Riemann Hypothesis will likewise lead to a deeper understanding of many diverse areas of mathematics and perhaps of physics too. Riemann’s zeta-function, and other zeta-functions similar to it, appear ubiquitously in number theory, in the theory of dynamical systems, in geometry, in function theory, and in physics. The zeta-function stands at a junction where paths lead in many directions. A proof of the hypothesis will illuminate all the connections. Like every serious student of pure mathematics, when I was young I had dreams of proving the Riemann Hypothesis. I had some vague ideas that I thought might lead to a proof. In recent years, after the discovery of quasi-crystals, my ideas became a little less vague. I offer them here for the consideration of any young mathematician who has ambitions to win a Fields Medal. Quasi-crystals can exist in spaces of one, two, or three dimensions. From the point of view of physics, the three-dimensional quasi-crystals are the most interesting, since they inhabit our threedimensional world and can be studied experimentally. From the point of view of a mathematician, one-dimensional quasi-crystals are much more interesting than two-dimensional or threedimensional quasi-crystals because they exist in far greater variety. The mathematical definition of a quasi-crystal is as follows. A quasi-crystal is a distribution of discrete point masses whose Fourier transform is a distribution of discrete point frequencies. Or to say it more briefly, a quasi-crystal is a pure point distribution that has a pure point spectrum. This definition includes as a special case the ordinary crystals, which are periodic distributions with periodic spectra. Excluding the ordinary crystals, quasi-crystals in three dimensions come in very limited variety, all of them associated with the icosahedral group. The two-dimensional quasicrystals are more numerous, roughly one distinct type associated with each regular polygon in a plane. The twodimensional quasi-crystal with pentagonal symmetry is the famous Penrose tiling of the plane. Finally, the onedimensional quasi-crystals have a far richer structure since they are not tied to any rotational symmetries. So far as I know, no complete enumeration of one-dimensional quasi-crystals exists. It is known that a unique quasi-crystal exists corresponding to every Pisot-Vijayaraghavan number or PV number. A PV number is a real algebraic integer, a root of a polynomial equation with integer coefficients, such that all the other roots have absolute value less than one, [1]. The set of all PV numbers is infinite and has a remarkable topological structure. The set of all one-dimensional quasi-crystals has a structure at least as rich as the set of all PV numbers and probably much richer. We do not know for sure, but it is likely that a huge universe of one-dimensional quasi-crystals not associated with PV numbers is waiting to be discovered. Here comes the connection of the onedimensional quasi-crystals with the Riemann hypothesis. If the Riemann hypothesis is true, then the zeros of the zeta-function form a onedimensional quasi-crystal according to the definition. They constitute a distribution of point masses on a straight line, and their Fourier transform is likewise a distribution of point masses, one at each of the logarithms of ordinary prime numbers and prime-power numbers. My friend Andrew Odlyzko has published a beautiful computer calculation of the Fourier transform of the zeta-function zeros, [6]. The calculation shows precisely the expected structure of the Fourier transform, with a sharp discontinuity at every logarithm of a prime or prime-power number and nowhere else. My suggestion is the following. Let us pretend that we do not know that the Riemann Hypothesis is true. Let us tackle the problem from the other end. Let us try to obtain a complete enumeration and classification of one-dimensional quasicrystals. That is to say, we enumerate and classify all point distributions that have a discrete point spectrum. Collecting and classifying new species of objects is a quintessentially Baconian activity. It is an appropriate activity for mathematical frogs. We shall then find the well-known quasi-crystals associated with PV numbers, and also a whole universe of other quasicrystals, known and unknown. Among the multitude of other quasi-crystals we search for one corresponding to the Riemann zeta-function and one corresponding to each of the other zeta-functions that resemble the Riemann zeta-function. Suppose that we find one of the quasi-crystals in our enumeration with properties that identify it with the zeros of the Riemann zeta-function. Then we have proved the Riemann Hypothesis and we can wait for the telephone call announcing the award of the Fields Medal. These are of course idle dreams. The problem of classifying onedimensional quasi-crystals is horrendously difficult, probably at least as difficult as the problems that Andrew Wiles took seven years to explore. But if we take a Baconian point of view, the history of mathematics is a history of horrendously difficult problems being solved by young people too ignorant to know that they were impossible. The classification of quasi-crystals is a worthy goal, and might even turn out to be achievable. Problems of that degree of difficulty will not be solved by old men like me. I leave this problem as an exercise for the young frogs in the audience. Adapted from NOTICES OF AMS 2/2009 ## 16/01/2009 ### Chúc mừng đ/c N.Đ. Mạnh bảo vệ thành công luận văn Thạc sỹ! Filed under: Giải tích toán học, Trao đổi — Ngô Quốc Anh @ 20:24 Chúc mừng đ/c N.Đ. Mạnh bảo vệ thành công luận văn Thạc sỹ! Hi vọng với điềm 10 vừa có được, đây sẽ là hành trang tốt cho đ/c Mạnh mang sang DTU vào tháng 2 tới. Nhiệt liệt chúc mừng! ## 04/01/2009 ### Quy định mới về việc phong PGS và GS Filed under: Giải tích toán học, Tra cứu, Trao đổi — Ngô Quốc Anh @ 14:56 Sáng ngay ngủ dậy, vào dantri.com đọc được cái tin này thấy hay hay. Tổng kết lại cho mọi người cùng tham khảo. Giáo sư, Phó Giáo sư phải sử dụng thành thạo một ngoại ngữ phục vụ cho công tác chuyên môn và phải giao tiếp được bằng tiếng Anh. Đó là một nội dung quan trọng trong Quyết định số 174/2008/QĐ-TTg mà Thủ tướng Chính phủ vừa ký ngày 31/12/2008, nêu quy định tiêu chuẩn, thủ tục bổ nhiệm, miễn nhiệm chức danh Giáo sư, Phó Giáo sư. Theo quyết định, người được công nhận chức danh GS, PGS phải có 1. bằng tiến sĩ từ đủ 36 tháng trở lên kể từ ngày có quyết định cấp bằng; 2. có đủ số công trình khoa học quy đổi theo quy định của Bộ trưởng Bộ GD-ĐT, trong đó có ít nhất 50% số công trình khoa học quy đổi từ các bài báo khoa học và 25% số công trình khoa học quy đổi được thực hiện trong 3 năm cuối tính đến thời điểm hết hạn nộp hồ sơ; 3. có báo cáo kết quả nghiên cứu khoa học, công nghệ dưới dạng một công trình khoa học tổng quan. Với chức danh GS, các ứng viên 1. phải được bổ nhiệm chức danh PGS từ đủ 3 năm trở lên; 2. hướng dẫn chính ít nhất 2 nghiên cứu sinh đã bảo vệ thành công luận án tiến sĩ (trước 1/1/2011, chỉ yêu cầu hướng dẫn chính 1 nghiên cứu sinh đã bảo vệ thành công luận án tiến sĩ và đang hướng dẫn 1 nghiên cứu sinh khác); 3. biên soạn sách sử dụng trong đào tạo từ trình độ đại học trở lên (sách phải được xuất bản, nộp lưu chuyển trước thời điểm hết hạn nộp hồ sơ) và 4. chủ trì ít nhất 1 đề tài nghiên cứu khoa học cấp bộ hoặc đề tài cấp cao hơn đã nghiệm thu với kết quả từ đạt yêu cầu trở lên. Với chức danh PGS, các ứng viên 1. phải có ít nhất 6 năm thâm niên làm nhiệm vụ giáo dục, giảng dạy từ trình độ đại học trở lên, trong đó 3 năm thâm niên cuối tính đến thời điểm hết hạn nộp hồ sơ đang làm nhiệm vụ giáo dục, giảng dạy trình độ đại học hoặc cao hơn; 2. hướng dẫn chính ít nhất 2 học viên cao học đã bảo vệ thành công luận văn thạc sĩ hoặc hướng dẫn 1 nghiên cứu sinh đã bảo vệ thành công luận án tiến sĩ (trước 1/1/2011, chỉ yêu cầu hướng dẫn chính ít nhất 1 học viên cao học bảo vệ thành công luận văn thạc sĩ hoặc 1 nghiên cứu sinh bảo vệ thành công luận án tiến sĩ); 3. ứng viên PGS phải chủ trì ít nhất 2 đề tài nghiên cứu khoa học cấp cơ sở hoặc 1 đề tài nghiên cứu khoa học cấp bộ hoặc đề tài cấp cao hơn đã nghiệm thu với kết quả từ đạt yêu cầu trở lên. Tham khảo thêm ở: http://dantri.com.vn/c25/s25-301288/gs-pgs-phai-su-dung-thanh-thao-mot-ngoai-ngu.htm http://www.vietnamnet.vn/giaoduc/2009/01/822013/ ## 03/01/2009 ### THES – QS World University Rankings 2008 Filed under: Không toán học, Tra cứu, Trao đổi, Vui chơi — Ngô Quốc Anh @ 00:29 Khởi động năm 2009 bài entry về bảng xếp hạng các trường đại học hàng đầu thế giới do THES thống kê. The Times Higher Education – QS World University Rankings identified these to be the world’s top 100 universities in 2008. These institutions represent 20 countries with Israel represented for the first time. Whilst North America dominates with 42 universities, Europe and Asia Pacific are well represented with 36 and 22 respectively. 2008 2007 School Name Country Source: QS Quacquarelli Symonds (www.topuniversities.com) 1 1 HARVARD University United States 2 2= YALE University United States 3 2= University of CAMBRIDGE United Kingdom 4 2= University of OXFORD United Kingdom 5 7= CALIFORNIA Institute of Technology (Calt… United States 6 5 IMPERIAL College London United Kingdom 7 9 UCL (University College London) United Kingdom 8 7= University of CHICAGO United States 9 10 MASSACHUSETTS Institute of Technology (M… United States 10 11 COLUMBIA University United States 11 14 University of PENNSYLVANIA United States 12 6 PRINCETON University United States 13= 13 DUKE University United States 13= 15 JOHNS HOPKINS University United States 15 20= CORNELL University United States 16 16 AUSTRALIAN National University Australia 17 19 STANFORD University United States 18 38= University of MICHIGAN United States 19 17 University of TOKYO Japan 21 20= CARNEGIE MELLON University United States 22 24 KING’S College London United Kingdom 23 23 University of EDINBURGH United Kingdom 24 42 ETH Zurich (Swiss Federal Institute of T… Switzerland 25 25 KYOTO University Japan 26 18 University of HONG KONG Hong Kong 27 32 BROWN University United States 28 26 École Normale Supérieure, PARIS France 29 30 University of MANCHESTER United Kingdom 30= 33= National University of SINGAPORE(NUS) Singapore 30= 41 University of CALIFORNIA, Los Angeles (U… United States 32 37 University of BRISTOL United Kingdom 33 29 NORTHWESTERN University United States 34= 28 ÉCOLE POLYTECHNIQUE France 34= 33= University of BRITISH COLUMBIA Canada 36 22 University of California, BERKELEY United States 37 31 The University of SYDNEY Australia 38 27 The University of MELBOURNE Australia 39 53= HONG KONG University of Science & Techno… Hong Kong 40 49 NEW YORK University (NYU) United States 41 45 University of TORONTO Canada 42 38= The CHINESE University of Hong Kong Hong Kong 43 33= University of QUEENSLAND Australia 44 46 OSAKA University Japan 45 44 University of NEW SOUTH WALES Australia 46 47 BOSTON University United States 47 43 MONASH University Australia 48 93= University of COPENHAGEN Denmark 49 53= TRINITY College Dublin Ireland 50= 117= Ecole Polytechnique Fédérale de LAUSANNE… Switzerland 50= 36 PEKING University China 50= 51= SEOUL National University Korea, South ## 31/12/2008 ### HaPpY nEw YeAr 2oog… Filed under: Không toán học, Trao đổi, Vui chơi — Ngô Quốc Anh @ 21:34 Đong cho đầy Hạnh phúc. Gói cho trọn Lộc tài. Giữ cho mãi An Khang. Thắt cho chặt Phú quý. Cùng chúc nhau Như ý, Chúc năm mới Bình An. Cả nhà đều Sung túc! ╔══╦══╦══╦══╗ ╚═╗║╔╗║╔╗║╔╗║ ╔═╝║║║║║║║╚╝║ ║╔═╣║║║║║╠═╗║ ║╚═╣╚╝║╚╝╠═╝║ ╚══╩══╩══╩══╝ ¤ø„¸¨°º¤ø„¸ ¸„ø¤º°¨¸„ø¤º ## 26/12/2008 ### Đổi mới phương pháp giảng dạy Filed under: Không định dạng — doanchi @ 17:18 Có cảm giác hiện nay công tác quản lý giáo dục Đại học ở mức độ vĩ mô nhất đang rơi vào một trạng thái khủng hoảng, một sự khủng hoảng về đường hướng. Ấy thế nên mới có những mục tiêu “ngọn”, như Trường ĐH Quốc tế, 20000 TS,…, những con số mang nặng sự duy ý chí, những quyết tâm không có tính biện chứng chút nào. Sự phát triển giáo dục, với tư cách mà nền tảng của sự phát triển đất nước, cần phải có một chiến lược dài hơi, một sự quản lý đồng bộ, và một đội ngũ lãnh đạo chuyên nghiệp hơn bây giờ. Khi người ta nói nhiều thì người ta ít thời gian để làm điều người ta nói. Cần có sự thay đổi tư duy, thay đổi nhận thức. ## 12/12/2008 ### Gương mặt trẻ tiêu biểu cấp Đại học Quốc gia Hà Nội năm 2008 Filed under: Toán học, Tra cứu, Trao đổi, Vui chơi — Ngô Quốc Anh @ 04:30 Nhân dịp kỷ niệm 15 năm ngày thành lập ĐHQGHN, ngày 10/12/2008 tại hội trường Lê Văn Thiêm, 19 Lê Thánh Tông đã diễn ra Lễ tuyên Gương mặt trẻ tiêu biểu ĐHQGHN 2008. Đây là hoạt động thường niên được tổ chức hàng năm của ĐHQGHN. GS.TS. Mai Trọng Nhuận – Giám đốc ĐHQGHN và các đồng chí lãnh đạo ĐHQGHN và các đơn vị trực thuộc đã về dự buổi lễ. Vượt qua hơn 1.300 cá nhân ưu tú đạt danh hiệu “Gương mặt trẻ tiêu biểu” cấp cơ sở, 150 gương mặt trẻ tiêu biểu đại diện cho gần 50.000 học sinh, sinh viên, học viên cao học, nghiên cứu sinh và hàng trăm cán bộ trẻ của ĐHQGHN đã vinh dự nhận danh hiệu này. Trong số đó có 23 học sinh khối phổ thông chuyên, 91 sinh viên và 36 cán bộ trẻ. Đặc biệt có 5 cá nhân được nhận danh hiệu Gương mặt trẻ tiêu biểu cấp ĐHQGHN lần thứ ba trở lên, 20 cá nhân đuợc nhận danh hiệu này lần thứ hai. Bên cạnh đó, Giám đốc ĐHQGHN cũng tặng bằng khen cho 7 gương mặt trẻ tiêu biểu đợt này. Phát biểu tại buổi lễ, Giám đốc Mai Trọng Nhuận đã ghi nhận và biểu dương những thành quả mà thế hệ trẻ ĐHQGHN đã đạt được trong năm học vừa qua trong học tập, nghiên cứu khoa học, giảng dạy và rèn luyện đạo đức. Giám đốc chúc mừng những cá nhân đã vinh dự được nhận danh hiệu “Gương mặt trẻ tiêu biểu cấp ĐHQGHN năm 2008” đồng thời bày tỏ niềm tin tưởng những gương mặt trẻ tiêu biểu được vinh danh ngày hôm nay sẽ tiếp tục đóng góp trí tuệ, sức lực để cùng với toàn ĐHQGHN thực hiện thắng lợi Nghị quyết 14 của Chính phủ về đổi mới toàn diện giáo dục đại học Việt Nam; sự chỉ đạo của Thủ tướng Chính phủ Nguyễn Tấn Dũng về phát triển hai ĐHQG sớm đạt trình độ quốc tế; sự tin tưởng của Ủy viên Bộ Chính trị, Bí thư Trung ương Đảng, Trưởng ban Tổ chức Trung ương Hồ Đức Việt về sự phát triển cao hơn (Trình độ cao – Chất lượng cao – Nghiên cứu khoa học đỉnh cao – Đáp ứng cao yêu cầu của sự nghiệp đổi mới đất nước) và nhanh hơn (nhanh chóng đạt trình độ khu vực, quốc tế) để đưa ĐHQGHN nhanh chóng trở thành trung tâm đào tạo đại học, sau đại học và nghiên cứu, ứng dụng, chuyển giao khoa học – công nghệ đa ngành, đa lĩnh vực, chất lượng cao, ngang tầm các đại học tiên tiến trong khu vực, từng bước tiến tới đạt trình độ quốc tế. Trong số 150 gương mặt trẻ tiêu biểu có 78 gương mặt là của trường ĐHKHTN, chiếm 52%. Năm nay chi đoàn cán bộ Khoa Toán – Cơ – Tin học có các đồng chí sau được vinh dự nhận danh hiệu trong lễ tuyên dương này: 1. TS. Lê Huy Chuẩn – tổ Giải tích. 2. TS. Đặng Anh Tuấn – tổ Giải tích. 3. ThS. Ninh Văn Thu – tổ Giải tích. 4. CN. Đào Phương Bắc – tổ Đại số – Hình học – Tôpô. 5. ThS. Vũ Tuấn Anh – tổ Văn phòng. Nhiệt liệt chúc mừng các đồng chí L.H. Chuẩn, Đ.A. Tuấn và N.V. Thu. Source: http://hus.edu.vn/News/NewsContent.asp?g1=NG01000300010001&g2=524&NewsPerPageG5=5&Status=1 ## 28/11/2008 ### Mathematica 7 Filed under: Không toán học, Tra cứu, Trao đổi — Ngô Quốc Anh @ 18:09 Following closely on the dramatic reinvention of Mathematica in 2007, Mathematica 7 continues the momentum of innovation to deliver an array of new capabilities, greatly extending the state of the art in many areas, and bringing a dozen major new application fields into the integrated framework of Mathematica. http://rapidshare.com/files/172367522/Mathematica_7.0.0_Linux.part1.rar http://rapidshare.com/files/172366075/Mathematica_7.0.0_Linux.part2.rar http://rapidshare.com/files/172367582/Mathematica_7.0.0_Linux.part3.rar http://rapidshare.com/files/172367665/Mathematica_7.0.0_Linux.part4.rar http://rapidshare.com/files/172173196/Mathematica_7.0.0_Mac_OS_X.part1.rar http://rapidshare.com/files/172174968/Mathematica_7.0.0_Mac_OS_X.part2.rar http://rapidshare.com/files/172175051/Mathematica_7.0.0_Mac_OS_X.part3.rar http://rapidshare.com/files/172175090/Mathematica_7.0.0_Mac_OS_X.part4.rar http://rapidshare.com/files/172215760/Mathematica_7.0.0_Solaris.part1.rar http://rapidshare.com/files/172216284/Mathematica_7.0.0_Solaris.part2.rar http://rapidshare.com/files/172216925/Mathematica_7.0.0_Solaris.part3.rar http://rapidshare.com/files/172216998/Mathematica_7.0.0_Solaris.part4.rar http://rapidshare.com/files/172339954/Mathematica_7.0.0_Windows.part1.rar http://rapidshare.com/files/172340183/Mathematica_7.0.0_Windows.part2.rar http://rapidshare.com/files/172340233/Mathematica_7.0.0_Windows.part3.rar http://rapidshare.com/files/171594319/KeyGen_EDGE.rar http://sitelic.colorado.edu/mathematica/download/win/ ## 17/11/2008 ### Trân trọng chúc mừng các thầy BMGT được phong tặng danh hiệu NGND, NGƯT Filed under: Không toán học, Trao đổi — Ngô Quốc Anh @ 19:27 ## Nhà giáo trường ĐHKHTN được phong tặng danh hiệu NGND, NGƯT Ngày 17/11/2008, Chủ tịch nước đã ký Quyết định số 1641/QĐ – CTN về việc phong tặng Danh hiệu Nhà giáo Nhân dân, Nhà giáo Ưu tú năm 2008. Trong đợt phong tặng lần này, Trường ĐHKHTN có 10 nhà giáo được phong tặng danh hiệu Nhà giáo nhân dân, 31 nhà giáo được phong tặng danh hiệu Nhà giáo ưu tú. Trước đó, Hội đồng xét tặng danh hiệu Nhà giáo nhân dân, Nhà giáo ưu tú cấp Nhà nước được thành lập theo Quyết định số 1019/QĐ-TTg ngày 31/7/2008 của Thủ tướng Chính phủ. Ngày 27 tháng 9 năm 2008 Hội đồng xét tặng danh hiệu NGND-NGƯT cấp Nhà nước đã họp phiên toàn thể để thảo luận, xem xét và tiến hành bỏ phiếu tán thành các nhà giáo đề nghị Thủ tướng Chính phủ xét trình Chủ tịch nước phong tặng danh hiệu Nhà giáo nhân dân, Nhà giáo ưu tú lần thứ mười năm 2008. Kết quả: • Số hồ sơ Nhà giáo nhân dân: 106 hồ sơ (trong đó diện đặc cách 51 hồ sơ). • Số hồ sơ Nhà giáo ưu tú: 834 hồ sơ (trong đó diện đặc cách 77 hồ sơ và 01 hồ sơ đề nghị truy tặng đó là GS.TS Dương Thiệu Tống sinh năm 1925, nguyên giảng viên Trường Đại học Ngoại ngữ-Tin học thành phố Hồ Chí Minh từ trần ngày 03 tháng 9 năm 2008) Ngày 30 tháng 10 năm 2008, Phó Thủ tướng- Bộ trưởng Bộ Giáo dục và Đào tạo Nguyễn Thiện Nhân, Chủ tịch Hội đồng xét tặng danh hiệu Nhà giáo nhân dân, Nhà giáo ưu tú cấp Nhà nước đã ký Tờ trình số 533/TTr-BGDĐT đề nghị Thủ tướng Chính phủ xét trình Chủ tịch nước phong tặng danh hiệu Nhà giáo nhân dân, Nhà giáo ưu tú lần thứ mười năm 2008. a) Danh sách các nhà giáo trường ĐHKHTN trong số 106 nhà giáo đề nghị Thủ tướng Chính phủ xét trình Chủ tịch nước phong tặng danh hiệu Nhà giáo nhân dân: 1. GS.TS Phạm Kỳ Anh, Giám đốc Trung tâm tính toán hiệu năng cao, Trường Đại học Khoa học Tự nhiên 2. GS.TS Đặng Ứng Vận, Giảng viên cao cấp khoa Hoá học, Trường Đại học Khoa học Tự nhiên 3. GS.TS Ngô Thị Thuận, nguyên Giảng viên cao cấp Khoa Hoá học, Trường Đại học Khoa học Tự nhiên 4. GS Đàm Trung Đồn, nguyên Giảng viên cao cấp Khoa Vật lý, Trường Đại học Khoa học Tự nhiên 5. GS.TS Nguyễn Trọng Uyển, nguyên Giảng viên cao cấp, Khoa Hoá học, Trường Đại học Khoa học Tự nhiên 6. GS.TS Trần Văn Nhân, nguyên Giảng viên cao cấp Khoa Hoá học, Trường Đại học Khoa học Tự nhiên 7. GS.TS Đinh Văn Hoàng, nguyên Chủ nhiệm bộ môn, Khoa Vật lý, Trường Đại học Khoa học Tự nhiên NGND. DIỆN ĐẶC CÁCH 1. PGS.TS Phan Đức Chính, nguyên Giảng viên cao cấp Khoa Toán-Cơ-Tin học, Trường Đại học Khoa học Tự nhiên 2. GS.TS Phạm Ngọc Thao, nguyên Giảng viên cao cấp Khoa Toán-Cơ-Tin học, Trường Đại học Khoa học Tự nhiên 3. GS.TS Nguyễn Thừa Hợp, nguyên Giảng viên cao cấp Khoa Toán-Cơ-Tin học, Trường Đại học Khoa học Tự nhiên b) Danh sách các nhà giáo trường ĐHKHTN trong số 834 nhà giáo đề nghị Thủ tướng Chính phủ xét trình Chủ tịch nước phong tặng danh hiệu Nhà giáo ưu tú (trong đó có 01 truy tặng): 1. GS.TS Nguyễn Cao Huần, Chủ nhiệm khoa Địa lý, trường ĐH Khoa học Tự nhiên 2. PGS.TS Lưu Văn Bôi, Chủ nhiệm khoa Hoá học trường ĐH Khoa học Tự nhiên 3. GS.TS Nguyễn Nghĩa Thìn, Giảng viên cao cấp khoa Sinh học, trường ĐH Khoa học Tự nhiên 4. PGS.TS Tạ Đình Cảnh, Chủ nhiệm bộ môn Vật lý Chất rắn, khoa Vật lý, trường ĐH Khoa học Tự nhiên 5. GS.TS Đỗ Ngọc Liên, Giảng viên cao cấp khoa Sinh học, trường ĐH Khoa học tự nhiên 6. GS.TS Đặng Hùng Thắng, Giảng viên cao cấp khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 7. PGS.TS Hoàng Quốc Toàn, Giảng viên chính khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 8. PGS.TS Nguyễn Xuân Trung, Giảng viên chính khoa Hoá học trường ĐH Khoa học Tự nhiên 9. PGS.TS Nguyễn Đình Bảng, Trưởng phòng Thí nghiệm khoa Hóa học trường ĐH Khoa học Tự nhiên 10. PGS.TS Đào Hữu Hồ, Giảng viên chính khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 11. PGS.TS Hoa Hữu Thu, Giảng viên chính khoa Hoá học, trường ĐH Khoa học Tự nhiên 12. PGS.TS Chu Văn Ngợi, Chủ nhiệm khoa Địa chất, trường ĐH Khoa học Tự nhiên 13. PGS.TS Phạm Văn Huấn, Phó Chủ nhiệm khoa Khí tượng-Thuỷ văn-Hải dương học, trường ĐH Khoa học Tự nhiên 14. Ông Nguyễn Ngọc Thắng, Giảng viên chính khối chuyên THPT khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 15. GS.TS Nguyễn Thế Hoàn, Nguyên Giảng viên cao cấp khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 16. PGS.TS Nguyễn Thuỷ Thanh, Nguyên giảng viên cao cấp khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 17. GS.TS Ngô Duy Cường, Nguyên Giảng viên cao cấp, khoa Hoá học, trường ĐH Khoa học Tự nhiên 18. PGS.TS Trần Huy Hổ, Nguyên Phó Hiệu trưởng trường ĐH Khoa học Tự nhiên 19. PGS.TS Trần Trọng Huệ, Nguyên Giảng viên chính khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 20. GS.TS Lâm Ngọc Thiềm, Nguyên Giảng viên cao cấp khoa Hoá học, trường ĐH Khoa học Tự nhiên 21. GS.TS Phan Văn Tường, Nguyên Giảng viên cao cấp khoa Hoá học, trường ĐH Khoa học Tự nhiên 22. PGS.TS Nguyễn Hữu Ngự, Nguyên Giảng viên chính, khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 23. GS.TS Đào Đình Bắc, Nguyên Giảng viên cao cấp khoa Địa lý, trường ĐH Khoa học Tự nhiên 24. PGS.TS Nguyễn Như Hiền, Nguyên Giảng viên chính khoa Sinh học, trường ĐH Khoa học Tự nhiên 25. GS.TS Nguyễn Quý Hỷ, Nguyên Giảng viên cao cấp khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 26. PGS.TS Hoàng Đức Nguyên, Nguyên Giảng viên chính, khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 27. PGS.TS Lê Đình Thịnh, Nguyên Giảng viên chính khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 28. PGS.TS Trịnh Xuân Sén, Nguyên Giảng viên cao cấp khoa Hoá học, trường ĐH Khoa học Tự nhiên NGUT. DIỆN ĐẶC CÁCH 1. GS.TS Hoàng Hữu Như, Nguyên Giảng viên cao cấp khoa Toán-Cơ-Tin học, trường ĐH Khoa học Tự nhiên 2. GS.TS Đào Đình Thức, Nguyên Giảng viên cao cấp khoa Hoá học, trường ĐH Khoa học Tự nhiên 3. Ông Nguyễn Công Thuý, Nguyên Giảng viên khoa Toán-Cơ-Tin học trường ĐH Tổng hợp Hà Nội Nguồn: Thông báo số 558/TB-BGDĐT, ngày 06 tháng 11 năm 2008 của Bộ Giáo dục và Đào tạo (moet.edu.vn)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 2, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45906689763069153, "perplexity": 13110.986154145692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886106358.80/warc/CC-MAIN-20170820073631-20170820093631-00308.warc.gz"}
http://avidemux.org/admWiki/doku.php?id=build:problems_with_compiling&rev=1352620301&do=diff	# Avidemux ### Site Tools build:problems_with_compiling # Differences This shows you the differences between two versions of the page. build:problems_with_compiling [2010/04/17 08:23]j.m build:problems_with_compiling [2012/11/11 08:51] (current) Both sides previous revision Previous revision 2010/04/17 08:24 j.m 2010/04/17 08:23 j.m 2010/04/16 06:40 j.m created Go Next revision Previous revision 2010/04/17 08:24 j.m 2010/04/17 08:23 j.m 2010/04/16 06:40 j.m created Go Line 13: Line 13: One of two things happened. One of two things happened. - - You need to provide the <nowiki>--with-newfaad switch for ./configure <code>./configure --with-jsapi-include=xxxx <nowiki>--with-newfaad This is needed for the linux distribution of Gentoo and Ubuntu. + - You need to provide the <nowiki>--with-newfaad switch for ./configure <code>./configure --with-jsapi-include=xxxx --with-newfaad This is needed for the linux distribution of Gentoo and Ubuntu. - You do not need to give the <nowiki>--with-newfaad switch for ./configure. The solution is try the ./configure command without it <nowiki>--with-newfaad. - You do not need to give the <nowiki>--with-newfaad switch for ./configure. The solution is try the ./configure command without it <nowiki>--with-newfaad. Line 42: Line 42: If you have trouble with jsapi, one of two things has happened. If you have trouble with jsapi, one of two things has happened. - - If it had trouble finding jsapi.h, the solution is simple. <code>./configure <nowiki>--with-jsapi-include=xxxx [[<nowiki>--with-newfaad\|for gentoo or ubuntu]] Using the 'locate jsapi.h' command will usually find the directory you need with the jsapi.h file. Replace the xxxx is the directory where jsapi.h is. + - If it had trouble finding jsapi.h, the solution is simple. <code>./configure --with-jsapi-include=xxxx [[-->with-newfaad\|for gentoo or ubuntu]] Using the 'locate jsapi.h' command will usually find the directory you need with the jsapi.h file. Replace the xxxx is the directory where jsapi.h is. - If there was a problem locating the library, the trouble could be several things. - If there was a problem locating the library, the trouble could be several things. * One probability is the libjs.so, libsmjs.so, and other necessary libraries are not in the standard path. You can either add them to your path value or you can put symlinks /usr/lib to the libraries themselves. * One probability is the libjs.so, libsmjs.so, and other necessary libraries are not in the standard path. You can either add them to your path value or you can put symlinks /usr/lib to the libraries themselves.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9182610511779785, "perplexity": 4790.541267942059}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875143373.18/warc/CC-MAIN-20200217205657-20200217235657-00030.warc.gz"}
http://www.lmfdb.org/Variety/Abelian/Fq/1/27/ak	# Properties Label 1.27.ak Base Field $\F_{3^3}$ Dimension $1$ $p$-rank $1$ Principally polarizable Contains a Jacobian ## Invariants Base field: $\F_{3^3}$ Dimension: $1$ Weil polynomial: $1 - 10 x + 27 x^{2}$ Frobenius angles: $\pm0.0877398280459$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-2})$$ Galois group: $C_2$ This isogeny class is simple. ## Newton polygon This isogeny class is ordinary. $p$-rank: $1$ Slopes: $[0, 1]$ ## Point counts This isogeny class contains a Jacobian, and hence is principally polarizable. $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 18 684 19494 530784 14347458 387423756 10460425014 282430166400 7625601845298 205891158689964 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 18 684 19494 530784 14347458 387423756 10460425014 282430166400 7625601845298 205891158689964 ## Decomposition This is a simple isogeny class. ## Base change This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{3^3}$. Subfield Primitive Model $\F_{3}$ 1.3.c	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9050201773643494, "perplexity": 1621.2068542814995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256184.17/warc/CC-MAIN-20190521002106-20190521024106-00184.warc.gz"}
https://www.physicsforums.com/threads/maximum-distance.192822/	# Maximum distance 1. Oct 21, 2007 ### princessfrost A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.050 m. A 0.200-kg lump of putty is dropped from rest onto the frame from a height of 30.0 cm. Find the maximum distance the frame moves downward from its initial position in meters. First I found the spring constant, k, which is given by F = -kx. F = -kx k = -F/x = -(0.150kg 9.8 m/s2)/(0.050m) = 29.4 N/m Next, I found the force that the lump of putty makes on the frame. The force is given by F = ma. The mass of the putty, 0.200kg, and the acceleration which is due to gravity, -9.8m/s2. F = ma = 0.200kg -9.8m/s2 = 1.96 N Now the spring constant, k (29.4N/m), and the force of the putty, 1.96N, so I finally solve for the distance the frame moves. F = -kx x = -k/F = -(29.4N/m)/(1.96N) = -15m It is negative, because it moves in the -x direction. So, the frame moves 15m downwards is what I get but my program says it is wrong. Can someone please help me? 2. Oct 21, 2007 ### hage567 This part looks OK: For the next part, the 1.96 N is not the force that the putty exerts on the frame, since the putty was released 0.3 m above the frame. You can consider conservation of energy to get the distance the spring will go to bring the putty to a stop. 3. Oct 21, 2007 ### princessfrost 1/2mv^2= 1/2 kx^2 F= - k x where F= mg = (0.150-) (9.80m/s2) F = 1.47 N 1.47 N= -k ( - 0.050 ) k = 1.47N/0.050m k = 29.4N/m then: v22 = v12 - 2gh, where v1 = 0 and h =- 30 cm = - 0.30m v22 = - 2(9.80m/s2)(- 0.30m) v22 = 5.88 v2 = 2.425 m/s Now, plugging these values in I get mv2 = k x2 x2 = mv2/k = (0.200)(5.88 m2/s2)/(29.4N/m) x2 = 0.04 x = 0.2 m So the maximum distance is: X = 0.05 m + 0.20 m X = 0.25 m Is this right? 4. Oct 21, 2007 ### hage567 Looks OK to me. Similar Discussions: Maximum distance	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8633573055267334, "perplexity": 3281.393633657713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426372.41/warc/CC-MAIN-20170726182141-20170726202141-00405.warc.gz"}
https://puzzling.stackexchange.com/questions/41646/whats-a-good-way-to-introduce-someone-to-puzzle-making/41660	# What's a good way to introduce someone to puzzle-making? First off THIS ISN'T A PUZZLE. It's a question about puzzle making, as the title suggests, though I thought I would make it clear, as I can see someone out there making a puzzle with such a title. The title is misleading slightly, I want this for my own personal gain, though I feel others would benefit from the answers too, in all honesty though I didn't know what else to put. So here I am, Sat at my desk, hoping to get some information, because I love puzzles a lot. What I wanted from this community of well spoken, amazing puzzle makers and solvers, was some advice on how to go about making puzzles. What's my best approach, what I shouldn't try to do, etc. I was going to go ahead and attempt to make a riddle, however the current meta topic of sandboxing has thrown off my confidence a little, as I think it's a little strenuous and that my first ever puzzle would just be thrown under and forgotten. Any tips on how I should go about it, What techniques, knowledge, or other things do I need to know about beforehand? For example, I see a lot of questions that include the need to decipher things using ASCII or something like that (I honestly don't know if that's right because I only know of Ascii as a programming language that I heard a few times from a friend.) I don't have any programming knowledge. So I think having me work up a puzzle from that would be a little strenuous on my part, which I don't want. Though would it still be a good idea to get a little knowledge? • Sandbox is all about improving riddles and getting up front feedback on how to improve. If anything sandbox should increase your confidence ad you can get advice from some great riddlers before it goes public. – gtwebb Aug 29 '16 at 19:43 • So... Why is this here instead of Meta? – user24580 Aug 29 '16 at 19:57 • @ObviouslyJake You don't need to worry at all, the question is totally appropriate for here. :) Questions about puzzling are appropriate and encouraged. Meta is for questions about puzzling.SE (the website itself) - which this question isn't. – A E Aug 29 '16 at 21:45 • @ObviouslyJake (I like how your name works as beginning of this sentence) there are many answers below which are way too long imo as there is no "way" to do that. I can tell you one thing: have fun and do whatever keeps you going. Feel free to send your riddles to someone, perhaps by email, if you want feedback or support. – Avigrail Aug 30 '16 at 5:55 • @MariaDeleva (and everyone else): One important thing to consider when discussing difficulty of puzzles is the Many-Eyes Effect. – GentlePurpleRain Aug 30 '16 at 14:45 There are a few things I do when creating a puzzle, and a few of my own rules I have created through experience, which I shall list below... ### 1. Planning is important Puzzlemaking takes time and effort. Without your puzzle will have a massive drop in standard. Remember this equation: $Puzzle$ $Value$ $=$ $Effort$ $X$ $Time$ $X$ $Ability$ Ability is a small factor, if you try hard you will succeed. Puzzles require planning, make sure you know what you want to do. Don't be afraid to change your ideas though. ### 2. Make it tricky! A puzzle is supposed to be hard, otherwise it wouldn't be a puzzle - simply a question. Puzzles are designed to make you think. However it can't be too tricky either. You must make sure others will be able to follow your train of thought to completion. It also must be on-topic to not be closed. @DanRussell makes a good point in the comments below. Though a puzzle should be hard and (ideally) not solved within a few minutes, this is an excellent community of puzzlers so even if your puzzle is solved within 5 minutes, that doesn't mean it's a bad puzzle. It simply means your puzzle has been solved by people with higher puzzling IQ :) ### 3. Make it interesting! The purpose of this site is based on having fun. You don't want to create a boring puzzle which others won't enjoy, you want them riveted to their screens, scratching their heads and having sleepless nights over your puzzles (No maliciousness intended). Creating an interestng puzzle is better than creating an incredibly tricky puzzle. Use weird things and odd displaying methods to confuse (but not blind) users. Don't post inappropriate questions either ### 4. Make note of your ideas I have a list of ideas for puzzles on my desk, ready for me to transfer to reality. You want to be able to have options and if you think of a really good idea for a puzzle, write it down! or use a note-taking app to make sure you don't forget it. Every idea you think of could be a good one. Only use ideas that contribute to your puzzle, drop the ones that don't. Some ideas can be combined, others that don't quite fit can be used in later puzzles. ### 5. Bounce your ideas off someone Sometimes its hard to know whether you had a good idea. Ask someone else! Check if they're able to solve it and if they enjoy it. Get more than 1 opinion for sureness. If they don't think something works or have a better idea for a part of your puzzle then listen to them, however much you think there is no way their idea could improve your puzzle, they might just be right. A 2nd, and hopefully 3rd one, is the best thing you can have. ### 6. Look but don't copy Look at some of the best puzzles on this site to see what ideas go down well and what contributes to a great puzzle. However, I must emphasize, DON'T PLAGIARIZE! Low level copying is fine, we all do it. 'Copy' can be defined as 'imitating the style of something'. What we don't want is 'taking someone's idea and using it as your own' - which would be plagiarism. ### 7. Learn from mistakes If you post a puzzle which doesn't go down well, ask in the comments how you could make it better, or why the community doesn't think it's very good. Take this into account in your next puzzles. Gain as much experience as you can. You don't just have to learn form your own mistakes, learn from other's errors too! ### 8. Visit the help center The help center is here, yes, to help and give advice. This will stop you making newbie mistakes and give you invaluable knowledge of this site. ### 9. Participate in the chat rooms Ask all the questions you want, we're here to help! Read other users questions and answers and learn. # Remember we all started at the bottom, it's how high you want to climb that matters Hope this helps and hope to see some fantastic puzzles from you in the future. Happy Puzzling! :) Open to other suggestions as well to add! • Seeing as I can't edit your post unless I find something else to add, I suggest doing so next time you have a chance to add, or edit it in some way. Change 'right', to 'write' in the 3rd point made. I'm currently following up the links provided, I hope to be posting puzzles of quality as soon as I'm able to :D – ObviouslyJake Aug 29 '16 at 19:03 • @ObviouslyJake and No. 9. Use spellcheck. I forgot about that one :) – Beastly Gerbil Aug 29 '16 at 19:18 • you're -> your; its hard -> it's hard – Chaotic Aug 29 '16 at 19:34 • Actually #9 is the worst of all. That shouldn't be your motivation. – Avigrail Aug 30 '16 at 6:06 • I think you've got some good suggestions here, but I worry whenever I see "make it hard". I think some people are too worried that their puzzles will be solved quickly instead of whether they're fun and/or challenging to solve, and thus end up making things extremely obscure/unsolvable. Then come the many hints, etc. This is a community of good puzzlers, so time-until-solving shouldn't be an important metric. – Dan Russell Aug 30 '16 at 18:01 I'm not sure how representative it is of the "right" way, or even a common way, but here's the rough workflow my puzzles go through (sorry in advance for the wordiness). ## 1. Play to your strengths You say you don't have any programming knowledge, great! Now you know where not to start. Have a dig through the tags and see what jumps out at you. Browse some existing content and see what you gravitate towards. If you like the sound of something, but don't have any experience, go through the top puzzles in that tag and either read through the accepted answers, or better yet, have a crack yourself - you'd be surprised how quickly you can pick up seemingly impenetrable topics. (Also as an aside, the riddle sandbox is probably actually a great opportunity for you, as you'll get feedback on your ideas so you can iterate/polish rapidly with more experienced puzzler's help). ## 2. Brainstorm Keep a notebook (or text file, or note keeping app, etc) and just dump anything in that pops into your head. It doesn't have to be complete ideas, it can just be fragments, or themes, or story ideas, etc. A lot of what you capture will be discarded or go nowhere, but you'll also find that random fragments tend to naturally clump together. • Observed that dice can be called "bones" in slang and that the singular is "die"? • Just learned what an ambigram is, or what amphibrach meter is, or a heteronym? • Standing in the shower wondering if you could make a fractal sudoku? • Noticed the little shapes in the background of the PSE site and wondered how you could build a puzzle around them? • Realised that all matter is merely energy condensed into a slow vibration? ...Awesome, write it all down. Note: At any point from here on, you need to be willing to throw things away and go back a step or more (see refine for more). Don't force an idea - all ideas are made better by what's left on the cutting room floor, and sometimes a discarded idea can get resurrected months down the track when you have a new insight. ## 3. Iterate Ok, I've got the best idea ever, I'm going to click that "Ask Question" button over there and start writing it up. Not so fast, you've barely started... Once you've got some random fragments of ideas, pick one or two and start to flesh them out. Obviously this step is very vague, and the exact process will depend heavily on the type of puzzle you're creating, but generally try to ask yourself questions like: • What does the goal/solution look like? • How can I get there? (often working backwards from a goal makes puzzle creation easier) • Is my solution unique and well defined (and will you know it when you find it)? • How am I going to present this (theme, story, visuals, etc)? • How will solvers try to solve this? • How can I distract solvers from the true path? • How can I guide solvers towards the true path? • What ties these ideas together? • What other related ideas can I bring in to add interest? • What extraneous ideas can I cut to hone and bring cohesion? • If I didn't know the answer, could I solve this? During this phase, anything goes and your puzzle will likely be changing a lot as it evolves. Don't be afraid to try random ideas out or try to mash multiple layers/ideas together. Don't be afraid to discard ideas, even if you've put work into it - remember the idea still exists, and may resurface later, plus you learned a bunch while trying things out. Also, don't be afraid to "borrow" ideas from other puzzles, especially while you're learning, it's a great way to get started, and if you continue to iterate and refine, the borrowed idea will likely dissolve away and just become "inspiration" anyway (just be sure, when you get to later steps that you haven't outright plagiarised anything). Note 2: All steps presented here, but this one in particular, don't represent work performed in a single "session", it is often five minutes musing here, thirty minutes trying out an idea there, a midnight waking with a new idea, a scrawled brain dump in a notepad, etc, that continues to evolve over a period of time. You'll also often find yourself with multiple "active" ideas running in parallel as you go. ## 4. Refine Awesome, I've got a working puzzle, can I post it now? Nope sorry, once you have something resembling a complete puzzle, it's time to refine things. This stage is all about trimming out extraneous ideas and tidying things up. This is the step that people often skip, much to the puzzle's detriment. It can also be the hardest... that awesome idea about doing it all in French, or that stanza you shoehorned in because you liked the rhyme it produced? Does it still work, is it bringing anything to the table? You need to be willing to let go of ideas if they don't actually add something to your puzzle (don't forget, they can always come back another time in another puzzle). If it's a riddle, spend some time smoothing out the meter/rhyme. If it's a visual puzzle, tidy up your images and make sure things are consistent and look good. If it's a pattern, make sure you're providing enough data points. Flesh out the story/presentation. Go through the questions listed in the Iterate section and make sure you can answer them, but during this stage, the most important one is to MAKE SURE YOUR PUZZLE HAS A PATH TO SUCCESS! By this, I don't mean that a good puzzle must be solvable (although that's obviously important :P), what I mean is that a good puzzle doesn't present an insurmountable wall, it presents a challenging path. Ideally, you want to pepper hints into your presentation (in wording, in visual style, etc) that help to nudge solvers in the right direction. If it's a multi-stage puzzle, the solution to one stage should provide new information that acts as a hint to the next. Just be careful not to provide too much direction (and feel free to throw in some misdirection), because you still want it to be a challenge. Think about what leaps of logic are required at any given point - if you have to make to big a leap, or worse, multiple leaps at once with no way of verifying the intermediate steps, it's likely going to be too hard (and not fun). All that being said, balance is difficult, and you will get it wrong, especially initially, just learn from those experiences and you'll improve. ## 5. Polish Jeez Alconja, I'm getting bored of my own idea, can I just post the damn thing?! Sorry, no, still one more step. At this stage your puzzle is good, it's solvable, it's refined, but I guarantee you've made a mistake. Go over it one last time with a fine-toothed comb (or get someone else to take a look) and make sure there's no spelling/grammar issues, make sure your images are clear, that stack exchange doesn't mess with your layout/formatting, etc. ...Ok, now you're good to go. Final note: It may seem as if the above is written with the assumption that you'll be trying to make a massively elaborate, multi-layered, puzzle, but I think it still applies to the simplest of riddles. Don't be daunted or put off by my wall of text, it may look complex and/or time-consuming, but it doesn't have to be. I guess if I can give you one piece of advice, it's simply to try and not rush a new idea out. Let it stew for a bit, write it, hone it, let it sit some more, re-read it, etc, and you'll end up with a much better puzzle than you started with. • I can see how a lot of people would think "Why would i do that?" about the letting the idea sit and not rushing it part. However, I know better! not from puzzling, however from roleplaying! See, it's all based on quick paced replies there over in the action packed world, so you have to come up with your ideas fast, on the spot. When I come back to my ideas and look over them later for reference, or enjoyment, I see things that I could have done waaay different that would have been a much better fit than before. So I shall take your words of advice well! Thankyou for the insight – ObviouslyJake Aug 30 '16 at 6:21 • Alconja finally reveals his secrets! :D – Beastly Gerbil Aug 30 '16 at 10:49 ## TL;DR Get inspired by other puzzles or find a topic interesting to you, start from the answer, fuzz it up a bit so it's not easy to solve, let sit for a while, come back and clear up ambiguous clues I'll just share my experience with puzzle making. Not sure if they would be considered "best practice", but they work for me. The closest I got to making puzzles before puzzling.SE was drawing mazes in grade school. I enjoyed reading the puzzles here for a while and decided one day to make one and see how it went. Being a computer geek, I thought making something similar to the classic text-adventures from the days of old would be unique and easy to make (no image manipulation or anything like that). I had recently seen a question using Gray Code, which was interesting to me so decided to use that as the base for the answer. I wanted to make it harder than seeing a list of numbers, and the best way I could think to fuzz up the numbers is translating them to different languages. Next up was figuring out how to decide the language for each. I figured Europe has lots of different, popular languages, so just ended up going along using capital city coordinates. This ended up being solved much quicker than I planned. I made a second one that was much more difficult and experimented a bit with cryptography. It may have been a bit too hard from the start, but that's what hints are for, right? Another puzzle I made was just from combining 2 random topics. I liked the puzzles involving moving a knight, and the fortnightly topic was mazes, so I figured I'd try combining them. Since I recently had Conway's Game of Life on the brain, I noticed the cell-structure of it could be used as the board for the knight. Making this into a puzzle proved to be more than I was willing to do, since most attempts proved to simple. Instead, I settled upon this question with slightly different goals. This is getting kinda long, so final example. The Fortnightly Topic turned out to be good inspiration. When it was sports/olympic themed, I saw swimming all the time on random TVs. I never was interested in sports, but learned that there was an event that combined 4 types of swimming. I could use that as an answer and transform it into something interesting to me by fuzzing up the clues. Used Google's search suggestions box that drops down as you type and found words that could lead people to the answer. Was still a bit too easy, so grabbed some images to represent those (after all a picture is worth 1000 words). Changed out one image for something I thought was exceptionally difficult (since the people here are crazy good and I figured even just 3 of 4 could lead to the answer) and I was happy with it. This answer links to a number of posts on this site that discuss how to make great puzzles. It's hard to give generic advice, since the things to consider will be different depending on what type of puzzle you're making. But I think if you read through all the posts mentioned in the above-linked answer, (some of them even link to further resources), you'll be well on your way to constructing a quality puzzle. It can also help to try to solve a bunch of puzzles. Take note of what was done well, and what wasn't. What aspect of a puzzle made it fun to solve? Where did you get really frustrated? Could something have been changed that would have made the solving experience better for you? Cryptic crosswords! Okay, maybe I'm a little biased, but cryptics were my first puzzle type. Some advantages to them include: • easier grids than regular crosswords, so you don't have to worry too much about your words interlocking • a clear, mostly unambiguous set of rules • a wide variety of clue types that don't get repetitive • flexibility - you can use the clues as a base for some other type of puzzle (like my Chess Fortnight (shameless plug)) • Not everyone likes word puzzles. I guess it depends on the OP. – ghosts_in_the_code Sep 26 '16 at 15:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2944859266281128, "perplexity": 1033.5368585683234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400188049.8/warc/CC-MAIN-20200918155203-20200918185203-00045.warc.gz"}
https://www.physicsforums.com/threads/a-chem-problem-help-please.8951/	# A chem problem help please 1. Nov 14, 2003 ### crayzlilgurl I don't know how to answer this question. I have to find the number of moles of water in the hydrate BaCL2*H2O. SOwwie i don't now how to make the 2 smaller. The mass of the hydrate is 5g, the Mass of lost 2. Nov 14, 2003 ### Chemicalsuperfreak It's pretty easy. You know that there was 0.7 grams of water originally. You, should, also know that water is 1/18 moles per gram. I can't make it any easier for you than that without telling you the answer, and that wouldn't do you any good. 3. Nov 15, 2003 ### crayzlilgurl thanks....i noe wut to do it just all the numbers i was given confused the heck outta me... 4. Jan 30, 2007 ### chris2009 i dont kow eitehr	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8858516812324524, "perplexity": 1728.340321770595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221213691.59/warc/CC-MAIN-20180818154147-20180818174147-00584.warc.gz"}
https://www.mis.mpg.de/calendar/lectures/2015/abstract-17767.html	# Abstract for the talk at 10.08.2015 (11:00 h) Arbeitsgemeinschaft ANGEWANDTE ANALYSIS Jinniao Qui (HU Berlin) Hörmander Type Theorem and Maximum Principle for Stochastic PDEs We shall first discuss the Hörmander theorem for general Itô processes and related (Kolmogrov) forward/backward stochastic PDEs, which may be beyond the scope of Markovian framework. Furthermore, we would also present the maximum principle for forward stochastic PDEs under a Hörmander type condition, which states the Lp (p 2) estimates for the time-space uniform norm of weak solutions. 01.03.2017, 13:57	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8721134662628174, "perplexity": 3294.971320164756}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943471.24/warc/CC-MAIN-20230320083513-20230320113513-00084.warc.gz"}
https://hal.inria.fr/hal-00764182	# Simplifying inclusion-exclusion formulas 1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry Abstract : Let F = {F_1, F_2,..., F_n} be a family of n sets on a ground set X, such as a family of balls in R^d. For every finite measure \mu on X, such that the sets of F are measurable, the classical inclusion-exclusion formula asserts that \mu(F_1 \cup F_2 \cup \bullet \bullet \bullet \cup F_n) = \sum_{I:{\O} \neq I\subseteq[n]} (-1)^{\|I\|+1} \mu(\cap_{i\inI} F_i); that is, the measure of the union is expressed using measures of various intersections. The number of terms in this formula is exponential in n, and a significant amount of research, originating in applied areas, has been devoted to constructing simpler formulas for particular families F. We provide the apparently first upper bound valid for an arbitrary F: we show that every system F of n sets with m nonempty fields in the Venn diagram admits an inclusion- exclusion formula with m^O((log n)^2) terms and with \pm1 coefficients, and that such a formula can be computed in m^O((log n)^2) expected time. We also construct systems of n sets on n points for which every valid inclusion-exclusion formula has the sum of absolute values of the coefficients at least \Omega(n^{3/2}). Type de document : Communication dans un congrès European Conference on Combinatorics, Graph Theory and Applications, Sep 2013, Pisa, Italy. 2013 Domaine : https://hal.inria.fr/hal-00764182 Contributeur : Xavier Goaoc <> Soumis le : mercredi 12 décembre 2012 - 15:12:50 Dernière modification le : jeudi 22 septembre 2016 - 14:31:10 ### Identifiants • HAL Id : hal-00764182, version 1 • ARXIV : 1207.2591 ### Citation Xavier Goaoc, Jiří Matoušek, Pavel Paták, Zuzana Safernová, Martin Tancer. Simplifying inclusion-exclusion formulas. European Conference on Combinatorics, Graph Theory and Applications, Sep 2013, Pisa, Italy. 2013. 〈hal-00764182〉 ### Métriques Consultations de la notice	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9401430487632751, "perplexity": 3910.574336382296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823168.74/warc/CC-MAIN-20171018233539-20171019013539-00807.warc.gz"}
https://www.flexiprep.com/NCERT-Exercise-Solutions/Chemistry/Class-11/Ch-10-The-s-Block-Elements-Part-5.html	# Chemistry Class 11 NCERT Solutions: Chapter 10 the s Block Elements Part 5 Q: 15. Compare the solubility and thermal stability of the following compounds of the alkali metals with those of the alkaline earth metals. (A) Nitrates (B) Carbonates (C) Sulphates. (i) Nitrates Thermal stability Nitrates of alkali metals, except decompose on strong heating to form nitrites. on decomposition, given oxide. Similar to lithium nitrate, alkaline earth metal nitrates also decompose to give oxides As we move down group 1 and group 2, the thermal stability of nitrate increases. Solubility Nitrates of both group 1 and group 2 metals are soluble in water. (ii) Carbonates Thermal stability The carbonates of alkali metals are stable towards heat. However, carbonate of lithium, when heated, decomposes to form lithium oxide. The carbonates of alkaline earth metals also decompose on heating to form oxide and carbon dioxide. Solubility Carbonates of alkali metals are soluble in water with the exception of. Also, the solubility increases as we move down the group. Carbonates of alkaline earth metals are insoluble in water. (iii) Sulphates Thermal stability Sulphates of both group 1 and group 2 metals are stable towards heat. Solubility Sulphates of alkali metals are soluble in water. However, sulphates of alkaline earth metals show varied trends. Fairly soluble Soluble Sparingly soluble Insoluble Insoluble In other words, while moving down the alkaline earth metals, the solubility of their sulphates decreases. Explore Solutions for Chemistry	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8154748678207397, "perplexity": 6556.864969473372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806832.87/warc/CC-MAIN-20171123123458-20171123143458-00746.warc.gz"}
http://mathhelpforum.com/discrete-math/99409-cartesian-product-print.html	# Cartesian product • Aug 27th 2009, 02:50 AM The Lama Cartesian product My teatcher wasn't able to explain this for me in a clear way. See if you guys can help. Let A and B be two random sets. Prove that A $\times" alt="\times" /> B (B $\cap" alt="\cap" /> C) = (A $\times" alt="\times" /> B) $\cap" alt="\cap" /> (A $\cap" alt="\cap" /> C) by putting in the element (x,y) • Aug 27th 2009, 04:31 AM Defunkt Sort of difficult to see what you want to prove like this... Did you mean: $A \times (B \times C) = (A \times B) \times (A \times C)$ ? • Aug 27th 2009, 05:09 AM The Lama Sorry about that. Didn't know how to handle the LaTex-codes right. But I think know what's going on now. But yes, that was what I meant. The book wants me to prove the equivalence by putting in the elemet (x,y) into that. • Aug 27th 2009, 06:32 AM Plato LaTex Help: $$A \times \left( {B \times C} \right) \ne \left( {A \times B} \right) \times \left( {A \times C} \right)$$ gives $A \times \left( {B \times C} \right) \ne \left( {A \times B} \right) \times \left( {A \times C} \right)$. Why? $A \times \left( {B \times C} \right)$ is a set of triples. Whereas, $\left( {A \times B} \right) \times \left( {A \times C} \right)$ is a set of pairs made up of pairs. • Aug 27th 2009, 07:17 AM The Lama Ok, this is how the question looks like and what the key says. $A \times (B \cap C) = (A \times B) \cap (A \times C)$ Let (x,y) be a random element in $A \times (B \cap C)$ Then we have that X $\epsilon$ A and y $\epsilon$ B $\cap$C which give y $\epsilon$ B and y $\epsilon$C. (x,y) $\epsilon$ A x B and (x,y) $\epsilon$ A x C so (x,y) $\epsilon$ (A x B) $\cap$ (A x C) and now we can prove that (A x B) $\cap$ (A x C) $\subseteq$ A x (B $\cap$ C). But I don't get a grip over this. For example why do you have to put the x in A and the y in (B $\cap$C) and not the other way around? I would like to see this in a graphic 3D model so I could see what I was doing. • Aug 27th 2009, 07:28 AM Defunkt Quote: Originally Posted by The Lama Ok, this is how the question looks like and what the key says. $A \times (B \cap C) = (A \times B) \cap (A \times C)$ Let (x,y) be a random element in $A \times (B \cap C)$ Then we have that X $\epsilon$ A and y $\epsilon$ B $\cap$C which give y $\epsilon$ B and y $\epsilon$C. (x,y) $\epsilon$ A x B and (x,y) $\epsilon$ A x C so (x,y) $\epsilon$ (A x B) $\cap$ (A x C) and now we can prove that (A x B) $\cap$ (A x C) $\subseteq$ A x (B $\cap$ C). But I don't get a grip over this. For example why do you have to put the x in A and the y in (B $\cap$C) and not the other way around? I would like to see this in a graphic 3D model so I could see what I was doing. You need to show $x \in A$ and $y \in {B \cap C}$ because that's simply the order of the cartesian product -- for example: $X \times Y = \left\{ (x,y) : x \in X ; y \in Y\right\}$ While $Y \times X = \left\{ (y,x) : y \in Y; x \in X\right\}$ And those are ordered pairs, so: $(x,y) \neq (y,x) \Rightarrow X \times Y \neq Y \times X$ Also, your wording is a bit off... You should say "Let $(x,y) \in {A \times B}$", or "Let $(x,y)$ be some element in $A \times B$"; random is not quite the right word here! • Aug 27th 2009, 07:29 AM Plato Quote: Originally Posted by The Lama (x,y) $\epsilon$ A x B and (x,y) $\epsilon$ A x C so (x,y) $\epsilon$ (A x B) $\cap$ (A x C) and now we can prove that (A x B) $\cap$ (A x C) $\subseteq$ A x (B $\cap$ C). But I don't get a grip over this. For example why do you have to put the x in A and the y in (B $\cap$C) and not the other way around? More LaTex help. $$(x,y)\in A\times (B\cap C)$$ gives $(x,y)\in A\times (B\cap C)$. The is simply the way a cross product is defined. $(x,y)\in W\times Z$ means $x\in W\text{ and }y\in Z$ • Aug 27th 2009, 08:51 AM The Lama Quote: Originally Posted by Defunkt Also, your wording is a bit off... You should say "Let $(x,y) \in {A \times B}$", or "Let $(x,y)$ be some element in $A \times B$"; random is not quite the right word here! Alright. Thanks. I just tried to translate it as best I could from a swedish compendium. yea. x and $\times$. Got a bit lazy there I guess.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 62, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 2674.1768288324815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320077.32/warc/CC-MAIN-20170623170148-20170623190148-00631.warc.gz"}
http://nu7026.com/tag/lopinavir/	## Physical fitness can be explained as a couple of components that Physical fitness can be explained as a couple of components that determine exercise influence and ability performance in sports. Measurements of muscles power typically concentrate on the powerful drive generated with the elbow flexors or the leg extensors, at different angles of elbow flexion or knee extension typically. Strength could be measured using the muscles remaining at a set duration (isometric) or while contracting (powerful). The handgrip check, an easy and reliable measure, is by far the most popular measure for assessing isometric strength in epidemiological studies (Bohannon et al. 2011). For dynamic explosive strength, the vertical jump has been the most widely used test. is definitely a performance-related fitness component that relates to the maintenance of a stable body position (Caspersen et al. 1985) which is definitely taken care of by both sensory and engine systems (Tresch 2007). It can be measured using the Balance Error Scoring System (BESS) that is commonly used Lopinavir by experts and clinicians and has a moderate to good reliability (Bell et al. 2011). and as key words. In addition, the research lists of these articles were inspected. Content articles (all-year) published in English and reporting twin correlations and/or heritability estimations of the vertical jump test, handgrip strength, balance and flexibility (sit-and-reach test) in a sample of children, adolescents and/or young adults up to the age of 30 were included, provided that these phenotypes were roughly similar (we.e. protocol) to the phenotypes measured in the current study. These papers are demonstrated in Table?1. For all studies, the unadjusted and univariate correlations and/or quotes had been extracted, aside from the scholarly research by Silventoinen et al. (2008) and Tiainen et al. (2004), who reported age-adjusted quotes only. Without all scholarly research reported twin correlations, an estimation was included by them from the heritability, the meta-analyses were predicated on the heritability estimates therefore. By weighing these heritability quotes from all scholarly tests by Lopinavir the amount of individuals, the weighted typical heritability could be computed using Microsoft Excel Lopinavir (2010) (Li et al. 2003; Neyeloff et al. 2012). When the typical mistakes (SEs) or self-confidence intervals (CIs) from the heritability quotes weren’t Gja1 reported, we were holding computed using the SEs or CIs from research who did survey these figures (Li et al. 2003). All research reported one (equated) heritability estimation for men and women, aside from Maes et al. (1996). These heritability quotes for men and women had been treated if we were holding self-employed samples. Results from the current study were also included in the meta-analyses. For regularity, univariate models were fitted to our four phenotypes and the producing heritability estimations were used in the meta-analyses. The statistic was used to assess heterogeneity and was determined as (? df)/gene. This gene seems to influence the overall performance of fast skeletal muscle mass materials and XX homozygotes may have modestly lower skeletal muscle mass strength in comparison with R-allele service providers (Yang et al. 2003). No large-scale genome-wide association (GWA) studies have been carried out on these phenotypes, which has proven to be a successful approach to understanding the heritability of many health-related risk factors and disease (Flint 2013; Visscher et al. 2012). This is unfortunate, because the components of physical fitness used in this study are relatively easy to measure (compared to for example maximal oxygen usage) in large samples and Lopinavir display substantial heritability, suggesting that a GWA meta-analysis effort could be successful. Moreover, the moderate but significant genetic association between handgrip and vertical jump suggests that meta-analysis over genetic association studies that use similar traits is definitely valid, and that the traits do not need to be exactly related to capture the latent genetic factors. Some limitations must be regarded as while interpreting our results. A significant assumption underlying twin research is that twins are consultant set alongside the general people completely. Silventoinen et al. reported that Lopinavir singletons demonstrated extra deviation in power and fat assessed in comparison to twins, which could result in inflated heritability quotes (Silventoinen et al. 2008). Furthermore, the siblings inside our research had an extremely wide a long time (12C25) which might be a issue as younger siblings may be pubertal, set alongside the remaining subjects. Inter-individual variation in maturation can be an established aspect that affects power and strength. However, whenever we.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8881620168685913, "perplexity": 3484.128277417088}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585321.65/warc/CC-MAIN-20211020121220-20211020151220-00187.warc.gz"}
https://mathematica.stackexchange.com/questions/172582/showing-real-scale-of-the-x-axis-of-a-plot-beside-the-axis-label	# Showing real scale of the x-axis of a plot beside the axis label I am using the code shown below to plot simple functions in which I am going to show the horizontal axes just with integer numbers. For correct presentation, I want to bring * π/2 beside the axes, as also shown below. But I have put * π/2 in the AxesLabel close to the t parameter. I am uncertain about the correctness of making the presentation this way. In fact, I do not know how I must show the exact scale of the horizontal axes when I want to present just integers on the ticks of plot. Any advice? Plot[{Sin[x], Cos[x]}, {x, 0, 5 π/2}, AxesLabel -> {Style["*π/2 t", Bold, 11], Style["C", Bold, 11]}, LabelStyle-> {Bold, 11}, Ticks-> {{{1Pi/2, Style["1"]},{3Pi/2, Style["3"]}, {5Pi/2, Style["5"]}}}]; • Wouldn't it be much better to include the $\pi/2$ factor in your axis tick labels? It would improve readability, at least in my opinion (i.e. Ticks -> {{{Pi/2, Style["π/2"]}, {3 Pi/2, Style["3π/2"]}, {5 Pi/2, Style["5π/2"]}}}) to give this. May 4, 2018 at 18:03 • thanx. maybe!!! May 4, 2018 at 18:14 ## 1 Answer This turned out to be harder than I originally thought it would. The problem is that the x-axis is showing ticks for t, not the plotting variable x, so it is important that the relation between t and x be clearly shown. Further, the OP requested that the information about the relationship be displayed as an x-axis label. That condition caused trouble. I found I couldn't use the option PlotLabels to label the two curves because Mathematica insisted on overwriting the x-axis label with the cosine curve label. I had to resort to using callouts with some explicit positioning. Plot[ {Callout[Sin[x], Sin[x]], Callout[Cos[x], Cos[x], {5 π/2 + 1.2, .6}]}, {x, 0, 5 π/2}, LabelStyle -> {Bold, 12}, AxesLabel -> {Row[{t, ", ", HoldForm[x = π/2], "\[ThinSpace]", t}], "C"}, Ticks -> {{# π/2, #} & /@ Range[1, 5, 2], Automatic}, ImagePadding -> All, ImageSize -> 500] The above conforms to my understanding of what the OP is asking for, but for myself I wouldn't make the plot that way. I would make it like this: Plot[ {Callout[Sin[π t/2 ], Sin[π t/2 ]], Callout[Cos[π t/2], Cos[π t/2], {5 + .9, .4}]}, {t, 0, 5}, LabelStyle -> {Bold, 11}, AxesLabel -> {"t", "C"}, ImagePadding -> All, ImageSize -> 500] I believe the second plot gets the point across better with simpler code. That's two pluses. ### Update I was really unhappy that I had not been able to post a solution using PlotLabels and Placed, so I returned to this problem, spent some time reading the documentation more carefully and trying this and that. After going down some wrong paths, I finally found a way. Plot[{Sin[x], Cos[x]}, {x, 0, 5 π/2}, LabelStyle -> {Bold, 12}, AxesLabel -> {Row[{t, ", ", HoldForm[x = π/2], "\[ThinSpace]", t}], "C"}, Ticks -> {{# π/2, #} & /@ Range[1, 5, 2], Automatic}, PlotLabels -> Placed["Expressions", {{Scaled[.2], Above}, {Scaled[.82], Above}}], ImageSize -> 500] The trick is to give the 2nd argument to Placed, the position specifier, as a list of two elements, one for each curve. Each element should be a pair of the form {offset, position}, where offset is a scaled distance along the x-axis and position indicates where the label should be positioned relative to curve at the offset (the usual Above, Before, etc.). This is never explicitly stated in the documentation, but there is an example of a list plot that hints at this solution.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42984408140182495, "perplexity": 2570.2394501845215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944452.97/warc/CC-MAIN-20230322211955-20230323001955-00797.warc.gz"}
https://research.vumc.nl/en/publications/neighborhood-walkability-physical-activity-and-changes-in-glycemi-2	# Neighborhood walkability, physical activity and changes in glycemic markers in people with type 2 diabetes: The Hoorn Diabetes Care System cohort N R Braver, F Rutters, A J Wagtendonk, J G Kok, P P Harms, J Brug, J W J Beulens, J Lakerveld Research output: Contribution to journalArticleAcademicpeer-review ## Abstract Studies investigating neighborhood walkability and physical activity in people with type 2 diabetes (T2D) mainly used self-report measures, and only few studies assessed the association with glycemic control. This study assessed the associations between objectively measured (i.e. GIS based) and subjectively measured (i.e. questionnaire-based) neighborhood walkability and changes in glycemic markers in people with T2D, and whether this association was mediated by device-measured physical activity (PA), in the Diabetes Care System Cohort (n = 1230). Neither objective or subjectively measured walkability was associated with glycemic control. In mediation analyses we observed no overall mediation by PA. Original language English 102560 Health and Place 69 21 Mar 2021 https://doi.org/10.1016/j.healthplace.2021.102560 Published - May 2021	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9262535572052002, "perplexity": 28663.00678225829}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338213.55/warc/CC-MAIN-20221007143842-20221007173842-00517.warc.gz"}
https://moodle.org/mod/forum/discuss.php?d=221856	## Backup and restore ### Pls help understanding Restore debugging message Pls help understanding Restore debugging message I am trying to restore a 1.9.18 course into a brand new 2.4 Moodle . I have turned on debugging and am attaching the message I get (which relates to "invalid file path" Could anyone advise as to what I need to tell our network manager so he can fix it? Thanks Average of ratings: - Re: Pls help understanding Restore debugging message Hi Mary, I am no great IIS expert, but I have always thought the file path was supposed to not be so long. But that might not be it, rather, does the "advent" folder exist in the backup? While a file might exist in the file list, was it actually included in the backed up data? Can you look inside the zip file? That is usually the first thing I do when a backup does not restore, and it might yield a clue about the actual folder construct used. Cheers. Average of ratings: - Re: Pls help understanding Restore debugging message Yes I must admit I thought it looked odd too. I made that course and I recall there being a lot of flvs in there but you're right; I will open it up and see if it has anything dodgy inside it! Average of ratings: - Re: Pls help understanding Restore debugging message Might be a 'bug' in PHP itself on that platform. Seems to me I saw something in a forum here that said same. Error code: file_invalid_path $a contents: C:\inetpub\moodledata/temp/backup/4e1d322cb5ad4016a3bed113ad8cd734/course_files/adventflv\day01.flv See the last '\' in the path to the file ... right before the file 'day01.flv'? All the others after moodledata lean the other way ... '/' which is the way Linux or Mac uses directory delimiters. IF it's not a 'bug' in php on that platform for which there is a fix (or if there is no fix yet), the only thing I could suggest is to edit the xml files contained in the un-zipped backup and manually change the directory designators (the last one). That's a pain, I know, but .... 'spirit of sharing', Ken Average of ratings: - Re: Pls help understanding Restore debugging message OK I just tried to restore another course and this is the first line of what I got: Debug info: Error code: file_invalid_path$a contents: C:\inetpub\moodledata/temp/backup/9e320bfec3ef29d3ebed790f1a872123/course_files\codebreakers.gif and I see again that the last \ before one of the files inside the course is the "wrong" way round. So you might be onto something, Ken. The only problem is - I don't know what Average of ratings: - Re: Pls help understanding Restore debugging message I would not worry about the slash direction. I've seen before in Moodle. I think the problem has to do with the file system , repository you have set up. Your 1.9.x is looking for /moodledata/(course number) . Your 2.4 needs legacy file system set up as a repository before restoring 1.9 course. I think Average of ratings: - Re: Pls help understanding Restore debugging message Hmm.. it would seem not. I just tried this and I am still getting the error message. I'm sure I've restored 1.9 courses into 2 on other sites without needing legacy course files enabled but, despite being enabled I still get the same error on this site. Well ... perseverance wins in the end Average of ratings: - Re: Pls help understanding Restore debugging message It was worth a shot. Average of ratings: - Re: Pls help understanding Restore debugging message There's a tracker issue open. You should add to the discussion. https://tracker.moodle.org/browse/MDL-37879 Average of ratings:Useful (1) Re: Pls help understanding Restore debugging message Don - very useful thanks! Average of ratings: - Re: Pls help understanding Restore debugging message Sorry to butt in here, but being fairly stodgy and preferring to do things the harder way, what happens if you restore the course to an earlier version? Is it possible there has been a small coding change that could be causing an issue with the fairly substantial leap from v1.9 that was not present in, say, a v2.2 or v2.3? Average of ratings: - Re: Pls help understanding Restore debugging message Colin -et al - thanks to Helen I now see there is a current problem with restoring 1.9 courses with files pointing to course files - /MDL-37774 In the meantime , while waiting for the fix. I saw in the tracker Don linked to here MDL-37879 someone has added a workaround - it says (quote) in the file of ...../moodle/backup/converter/moodle1/lib.php at the line of 1216 // BACKUP RESTORE PROBLEM OCCURED BY THIS SECTION!!! if ($sourcefullpath !== clean_param($sourcefullpath, PARAM_PATH)) { throw new moodle1_convert_exception('file_invalid_path', $sourcefull$ } /// END OF ERROR SECTION!!! If you comment these 3 lines, backup restoration from 1.9 to 2.4 is completed successfully. On my local host Moodle (not our school Moodle!) I thought I would try this but I don't know what "comment" means! I know where the file is but what am I meant to do? I simply replaced those lines with the lines above, but that just gave me a new error message I had never seen before, so I must be doing something wrong. Average of ratings: - Re: Pls help understanding Restore debugging message Hi Mary, you need to comment out the sentence as per PHP rules. You can use /* / or // at the very start of each line, e.g.: // PARAM_PATH must not be used on full OS path!/ if ($sourcepath !== clean_param($sourcepath, PARAM_PATH)) { throw new moodle1_convert_exception('file_invalid_path', $sourcepath); }/ HTH, Matteo Average of ratings:Useful (1) Re: Pls help understanding Restore debugging message Ah thanks- I will try this later Average of ratings: - Re: Pls help understanding Restore debugging message Hi Mary, I have been tied down with huge gobs of administrivia, so sorry i have not been here, how did you get on with this? Average of ratings: - Re: Pls help understanding Restore debugging message When restoring a 1.9.x backup, the files will automagically come in as legacy (at least, that has been the case with versions 2.3.x and below). When Mdl2 sees a zip backup, it states it will attempt to convert the .zip backup to an .mbz (a Mdl2 compat backup) before restoring. It does this in moodledata/temp/backup/ On Windows a '/' is a legal character in a file name, normally. A '\' is not a legal character in a file name as that is Windows delimiter for folders/directories. However, with UTF8 character set the following applies: #### Naming Conventions The following fundamental rules enable applications to create and process valid names for files and directories, regardless of the file system: • Use a period to separate the base file name from the extension in the name of a directory or file. • Use a backslash (\) to separate the components of a path. The backslash divides the file name from the path to it, and one directory name from another directory name in a path. You cannot use a backslash in the name for the actual file or directory because it is a reserved character that separates the names into components. • Use a backslash as required as part of volume names, for example, the "C:\" in "C:\path\file" or the "\\server\share" in "\\server\share\path\file" for Universal Naming Convention (UNC) names. For more information about UNC names, see the Maximum Path Length Limitation section. • Do not assume case sensitivity. For example, consider the names OSCAR, Oscar, and oscar to be the same, even though some file systems (such as a POSIX-compliant file system) may consider them as different. Note that NTFS supports POSIX semantics for case sensitivity but this is not the default behavior. For more information, see CreateFile. • Volume designators (drive letters) are similarly case-insensitive. For example, "D:\" and "d:\" refer to the same volume. • Use any character in the current code page for a name, including Unicode characters and characters in the extended character set (128–255), except for the following: • The following reserved characters: • < (less than) • > (greater than) • : (colon) • " (double quote) • / (forward slash) • \ (backslash) • \| (vertical bar or pipe) • ? (question mark) (asterisk) http://msdn.microsoft.com/en-us/library/windows/desktop/aa365247%28v=vs.85%29.aspx What actually controls the restore process are the xml files created when converting the course into 2 format. If you can, take a gander at: moodledata/temp/backup/ and see if there is a directory with the hash '9e320bfec3ef29d3ebed790f1a872123'. There is probably a files.xml file that checks the 'course_files' folder also found in the '9e32....' folder. Here's what one entry in a files.xml looks like: <file id="13"> <contenthash>dee7a75c740150ee236ec6e0df7661b8d00ad862</contenthash> <contextid>180</contextid> <component>course</component> <filearea>section</filearea> <itemid>10</itemid> <filepath>/</filepath> <filename>audio-headset.png</filename> <userid>3</userid> <filesize>7624</filesize> <mimetype>image/png</mimetype> <status>0</status> <timecreated>1303376359</timecreated> <timemodified>1303376359</timemodified> <source>$@NULL@$</source> <author>Name of author here</author> <license>cc-sa</license> <sortorder>0</sortorder> </file> These two lines: <filepath>/</filepath> <filename>audio-headset.png</filename> determine the 'path' and the filename. If the backup is coming from a Linux/MacOSX server and one is restoring to a Windows platform, the restore php scripts/routine must convert those directory designators or know what to do with them or not do with them. You might have discovered a 'feature'! :\| 'spirit of sharing', Ken Average of ratings:Useful (3) Re: Pls help understanding Restore debugging message Wow thanks Ken - I will read that in great detail when I am awake (early morning here) But one thing I do know is that is IS a 1.9 course from a Linux server and is being restored to a Windows platform.. Average of ratings: - How safe is this workaround? The one earlier in this thread and which I will paste below (thanks Matteo). Our network manager is not keen to use unofficial patches but we are still unable to restore 1.9 courses to 2.4 and are struggling a bit. Could anyone reassure him this won't break our Moodle? (worked fine on my local host but my local host isn't going to house 1000 users) Hi Mary, you need to comment out the sentence as per PHP rules. You can use /* / or // at the very start of each line, e.g.: // PARAM_PATH must not be used on full OS path!/ if ($sourcepath !== clean_param($sourcepath, PARAM_PATH)) { throw new moodle1_convert_exception('file_invalid_path',$sourcepath); }*/ HTH, Matteo Average of ratings: - Re: How safe is this workaround? Hi Mary, AFAIK it breaks nothing if you restore backups into a Windows server from a known source i.e. a known Moodle instance: it would be nice not to have a mixture of \ and / when restoring a backup coming from a Linux hosted Moodle, time to re-ping the Tracker? IMHO while waiting for the official fix - which will probably found the root for those \/ - the safest option is to clone the production site and test the import there, the wiser is to create a new backup from your local Moodle instance where the course backup has been successfully imported: maybe using a Windows->Windows backup will not trigger that issue. HTH, Matteo Edited @ 2013-02-26 14.48 CEST to cleanup the last statement (not mother tongue ) Average of ratings: - Re: How safe is this workaround? Thanks Matteo! Unfortunately we can';t clone the production site because we don't have access to the database (without paying a lot of money -long story) so we are restoring the courses .onto a clean 2.4 - hence the problem. But I will pass on the message. Average of ratings: - Re: How safe is this workaround? Can you update the original site and then export and import to the new site? I always found that the easiest way to get courses over the 1.9 to 2.? hurdles. If not, I would be tempted to import to a 1.9 version, update and move forward that way. Average of ratings: - Re: How safe is this workaround? After applying the work-around, we have imported 14 courses with no problem, and plan to import dozens more this way. There really is no other solution at this point besides to wait. All that function does is "clean" the path to fix the alternating slashes and some other cleanup, but the "unclean" path works fine for the import process to access course files. If there really is a problem with the file, an error will probably the thrown somewhere else in the restore process when it tries to actually put that file into the new class. Average of ratings: - Our network manager applied the workaround over the weekend but I am getting this error when I try to restore a course - does anyone have an idea? Is it a case of not copying/pasting correctly or something else? Parse error:syntax error, unexpected T_IF, expecting T_FUNCTION in C:\inetpub\wwwroot\moodle24\backup\converter\moodle1\lib.php on line 1219 Average of ratings: - Sounds like typo in the attempt to comment out the function. You can do a multi-line comment as shown above, or individual line comments with two forward slashes: //if ($sourcefullpath !== clean_param($sourcefullpath, PARAM_PATH)) { // throw new moodle1_convert_exception('file_invalid_path', \$sourcefullpath); //} Average of ratings: -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40228432416915894, "perplexity": 3500.772464318077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469258918071.75/warc/CC-MAIN-20160723072838-00257-ip-10-185-27-174.ec2.internal.warc.gz"}