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http://mathoverflow.net/feeds/question/99415 | Is there any solution to this kind of equation? Or any clue to explore it? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-21T06:32:58Z http://mathoverflow.net/feeds/question/99415 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99415/is-there-any-solution-to-this-kind-of-equation-or-any-clue-to-explore-it Is there any solution to this kind of equation? Or any clue to explore it? Zou Fangyu 2012-06-13T08:59:09Z 2012-06-13T09:29:24Z <blockquote> <p><strong>Possible Duplicate:</strong><br> <a href="http://mathoverflow.net/questions/17605/how-to-solve-ffx-cosx" rel="nofollow">How to solve f(f(x)) = cos(x) ?</a> </p> </blockquote> <p>$f(f(x))=sin x$</p> http://mathoverflow.net/questions/99415/is-there-any-solution-to-this-kind-of-equation-or-any-clue-to-explore-it/99417#99417 Answer by 4v4l0n42 for Is there any solution to this kind of equation? Or any clue to explore it? 4v4l0n42 2012-06-13T09:21:21Z 2012-06-13T09:21:21Z <p>I don't know if this helps you, but you may write it also as:</p> <p>$f(f(x)) = \frac{1}{2} ie^{-i x}-\frac{1}{2} i e^{ix}$</p> http://mathoverflow.net/questions/99415/is-there-any-solution-to-this-kind-of-equation-or-any-clue-to-explore-it/99419#99419 Answer by Moustafa for Is there any solution to this kind of equation? Or any clue to explore it? Moustafa 2012-06-13T09:29:24Z 2012-06-13T09:29:24Z <p>Answered here <a href="http://mathoverflow.net/questions/17605/how-to-solve-ffx-cosx" rel="nofollow">http://mathoverflow.net/questions/17605/how-to-solve-ffx-cosx</a> Or even more general here <a href="http://mathoverflow.net/questions/17614/solving-ffxgx" rel="nofollow">http://mathoverflow.net/questions/17614/solving-ffxgx</a></p> | 2013-05-21 06:32:57 | {"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": 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": 0.34545430541038513, "perplexity": 6859.3992016528755}, "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-2013-20/segments/1368699755211/warc/CC-MAIN-20130516102235-00042-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathoverflow.net/revisions/24132/list | Post Closed as "no longer relevant" by Kevin Lin, quid, Qiaochu Yuan, Zev Chonoles, Gjergji Zaimi
2 added 42 characters in body
It's a common observation in Lie theory that Cartan matrices and the Killing form are named after the wrong people; they were discovered by Killing and Cartan, respectively. I remember learning about many other examples of this phenomenon, but can't think of too many at the moment. Wikipedia has a short listsome examples here and here, but I'm curious about more obscure examples. So I thought I'd ask MO for a nice list.
Bonus points for an interesting story behind why the concept was incorrectly named. Concepts that were deliberately named in honor of another mathematician don't count. | 2013-05-24 12:40:29 | {"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": 0.8154335618019104, "perplexity": 478.6619786293213}, "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/1368704658856/warc/CC-MAIN-20130516114418-00059-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.transtutors.com/questions/find-the-optimal-contract-length-when-the-marginal-cost-of-writing-a-contract-of-len-89730.htm | +1.617.933.5480
# Q: Find the optimal contract length when the marginal cost of writing a contract of length L
1. Suppose the marginal benefit of writing a contract is $50, independent of its length. Find the optimal contract length when the marginal cost of writing a contract of length L is: a. MC(L) = 10 + 2L. b. MC(L) = 5 + 2L. c. What happens to the optimal contract length when the marginal cost of writing a contract declines?2.Suppose the marginal cost of writing a contract of length L is MC(L) = 10 + 2L. Find the optimal contract length when the marginal benefit of writing a contract is: a. MB(L) = 100. b. MB(L) = 150. c. What happens to the optimal contract length when the marginal benefit of writing a contract increases? Want an Answer? Choose a Subject » Select Duration » Schedule a Session Related Questions in Others • Q: Optimal quantity of labor (Solved) April 14, 2013 Assume the price of output is p = 10 dollars, the marginal product of labor is given by the equation MPL= 20-( 1/2 ) L , and the price of labor is w L =... Solution Preview : 20 - (1/2)L, and the price of labor is wL = 100 dollars. Then, the optimal quantity of labor is a) 5... • Q: Assignment (Solved) February 11, 2012 could you do it please ! • Q: Suppose that Honda is on the verge of signing a 15-year contract with TRW... January 28, 2012 introduced a comparable airbag using a new technology that reduces the cost by 30 percent. How would this information affect Honda’s optimal contract length with... • Q: general equilibrium-pure exchange economy (Solved) April 07, 2013 I have a question regarding the demands that are calculated on page 85 , from the exercise starting in page 84. I don’t understand the calculations that have been done to reach the result... Solution Preview : Maximization problem is max v XAYA subject to the budget constraint Px XA + Py YA = Px + 2Py (XAYA) So the Lagrange is L= (XA *YA )^(1/2) + ? ( Px *XA+ Py * YA- Px-2* PY ) (* indicates... • Q: Economic Assignment (Solved) August 20, 2012 As attached. Solution Preview : Question 1. EverClean Services provides daily cleaning maintenance of toilets in food courts in Singapore. Dozens of firms provide similar service. The service is standardized; each company... ## Ask a New Question Copy and paste your question here... Have Files to Attach? Similar question? edit & resubmit » ## Transtutors Study Membership • Unlimited Access to 600,000+ textbook solutions and Classroom Assignments • 24/7 Study Help from experts • Plans start from$20/mo
“8” Micro Economics experts Online | 2014-11-27 08:11:40 | {"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": 0.2656248211860657, "perplexity": 3986.523074153038}, "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-2014-49/segments/1416931008215.58/warc/CC-MAIN-20141125155648-00053-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://standards.globalspec.com/std/10342665/nen-en-480-1 | # NEN-EN 480-1
## Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
active, Most Current
Organization: NEN Publication Date: 1 November 2014 Status: active Page Count: 15 ICS Code (Cement. Gypsum. Lime. Mortar): 91.100.10 ICS Code (Concrete and concrete products): 91.100.30
##### scope:
NEN-EN 480-1 specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of admixtures in accordance with the series EN 934.
### Document History
NEN-EN 480-1
November 1, 2014
Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
NEN-EN 480-1 specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of admixtures...
March 1, 2014
Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
NEN-EN 480-1 specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of admixtures...
July 1, 2011
Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
This European Standard specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of...
November 1, 2006
Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
This European Standard specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of...
February 1, 2005
Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
This European Standard specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of...
August 1, 1998
Admixtures for concrete, mortar and grout - Test methods - Part 1: Reference concrete and reference mortar for testing
This standard specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of...
January 1, 1993
Admixtures for concrete, mortar and grout - Test methods - Reference concrete and reference mortar for testing
This standard specifies the constituent materials, the composition and the mixing method to produce reference concrete and reference mortar for testing the efficacy and the compatibility of... | 2019-03-18 15:51:02 | {"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": 0.844484269618988, "perplexity": 8325.938731375423}, "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-2019-13/segments/1552912201455.20/warc/CC-MAIN-20190318152343-20190318174343-00428.warc.gz"} |
https://proofwiki.org/wiki/Finite_Ordinal_is_not_Subset_of_one_of_its_Elements | # Finite Ordinal is not Subset of one of its Elements
## Theorem
Let $n$ be a finite ordinal.
Then:
$\nexists x \in n: n \subseteq x$
that is, $n$ is not a subset of one of its elements.
## Proof
Let $S$ be the set of all those finite ordinals $n$ which are not a subset of any of its elements.
That is:
$n \in S \iff n \in \omega \land \forall x \in n: n \nsubseteq x$
We know that $0 = \varnothing$ is not a subset of any of its elements, as $\varnothing$ by definition has no elements.
So $0 \in S$.
Now suppose $n \in S$.
$n \subseteq n$
But as $n \in S$ it follows by definition of $S$ that:
$n \notin n$
By definition of the successor of $n$, it follows that:
$n^+ \nsubseteq n$
Now from Subset Relation is Transitive:
$n^+ \subseteq x \implies n \subseteq x$
But since $n \in S$ it follows that:
$x \notin n$
So:
$n^+ \nsubseteq n$
and:
$\forall x \in n: n^+ \nsubseteq x$
So $n^+$ is not a subset of any of its elements.
That is:
$n^+ \in S$
So by the Principle of Mathematical Induction:
$S = \omega$
Hence the result.
$\blacksquare$ | 2020-07-13 01:07:15 | {"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": 0.9779123067855835, "perplexity": 210.04832520803646}, "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-2020-29/segments/1593657140746.69/warc/CC-MAIN-20200713002400-20200713032400-00317.warc.gz"} |
http://www.juanofwords.com/2015/10/la-reyna-del-facebook/ | If this isn’t a sign of the times, we’re not sure what is!
The song is aptly titled “The Queen of Facebook” and as you might imagine, it’s all about that little obsession so many of us seem to have as of late: social media.
More to the point. Facebook. Feis. Or El Feis. Whatever you choose to call it.
The group performing the song is Los Cocineros Del Norte from Fresno, California.
Here’s our interpretation of the lyrics in English:
Not sure if you’ve noticed
for being a flirt and a liar
for being stuck up and conceded
You are the Queen of Facebook
pictures in only underwear
And that’s how your ex is, and my ex and the next
and that’s how your ex is, and my ex and the next
I think you like
that people click like on everything
that everyone look at you
and start to comment
You publish locations
everywhere you go
showing off a new love
that poor “
guey” who’s with you
And that’s how your ex is, and my ex and the next
and that’s how your ex is, and my ex and the next
that according to you are provocative
but you don’t provoke me
and that you are in love
and what that guey” doesn’t know
is that I left you all washed up
And that’s how your ex is, and my ex and the next
and that’s how your ex is, and my ex and the next
And that’s how your ex is, and my ex and the next
and that’s how your ex is, and my ex and the next
¿Cómo la ven? What do you think about the song? | 2017-07-26 16:44:25 | {"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": 0.8867164254188538, "perplexity": 6315.142925846464}, "config": {"markdown_headings": true, "markdown_code": false, "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-2017-30/segments/1500549426234.82/warc/CC-MAIN-20170726162158-20170726182158-00632.warc.gz"} |
https://www.asvabtestbank.com/arithmetic-reasoning/t/76/p/practice-test/848021/5 | ## ASVAB Arithmetic Reasoning Operations on Exponents Practice Test 848021
Questions 5 Focus Operations on Exponents Topics Adding & Subtracting Exponents, Exponent to a Power, Multiplying & Dividing Exponents, Negative Exponent Question Type Problems
#### Study Guide
###### Adding & Subtracting Exponents
To add or subtract terms with exponents, both the base and the exponent must be the same. If the base and the exponent are the same, add or subtract the coefficients and retain the base and exponent. For example, 3x2 + 2x2 = 5x2 and 3x2 - 2x2 = x2 but x2 + x4 and x4 - x2 cannot be combined.
###### Exponent to a Power
To raise a term with an exponent to another exponent, retain the base and multiply the exponents: (x2)3 = x(2x3) = x6
###### Multiplying & Dividing Exponents
To multiply terms with the same base, multiply the coefficients and add the exponents. To divide terms with the same base, divide the coefficients and subtract the exponents. For example, 3x2 x 2x2 = 6x4 and $${8x^5 \over 4x^2}$$ = 2x(5-2) = 2x3.
###### Negative Exponent
A negative exponent indicates the number of times that the base is divided by itself. To convert a negative exponent to a positive exponent, calculate the positive exponent then take the reciprocal: $$b^{-e} = { 1 \over b^e }$$. For example, $$3^{-2} = {1 \over 3^2} = {1 \over 9}$$ | 2023-03-26 05:59:23 | {"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": 0.7371509671211243, "perplexity": 1140.0686052812193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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/1679296945433.92/warc/CC-MAIN-20230326044821-20230326074821-00564.warc.gz"} |
http://mymathforum.com/linear-algebra/339756-characteristic-polynomial.html | My Math Forum Characteristic Polynomial
Linear Algebra Linear Algebra Math Forum
March 28th, 2017, 04:52 PM #1 Member Joined: Nov 2016 From: Kansas Posts: 68 Thanks: 0 Characteristic Polynomial I have been given the characteristic polynomial p(x)=x(2-x)(1-x) of Matrix A. I have been given two diagonal entries of A that are -3 and 5. I am now supposed to calculate the remaining diagonal entries. How to do this?
March 28th, 2017, 06:32 PM #2 Member Joined: Jan 2016 From: Athens, OH Posts: 69 Thanks: 37 For any n by n square matrix A, the trace of A is the negative of the coefficient of $x^{n-1}$ of the characteristic polynomial. I hope it is now clear how to solve your problem Thanks from topsquark and ZMD
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Similar Threads Thread Thread Starter Forum Replies Last Post motant Linear Algebra 1 May 27th, 2015 01:02 PM skrat Linear Algebra 2 May 17th, 2013 05:04 AM page929 Linear Algebra 2 November 28th, 2011 12:09 PM KamilJ Linear Algebra 2 June 4th, 2011 08:10 PM Aske Linear Algebra 1 November 22nd, 2008 02:22 PM
Contact - Home - Forums - Cryptocurrency Forum - Top | 2018-01-23 21:43:03 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6563405394554138, "perplexity": 2057.968340743647}, "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-2018-05/segments/1516084892699.72/warc/CC-MAIN-20180123211127-20180123231127-00306.warc.gz"} |
https://forum.snap.berkeley.edu/t/inexact-square-roots/12524 | # Inexact square roots
It should be sqrt(10) instead of this otherwise this isnt exact
(i understand you should not express reals but why not express this as
)
offtopic:replit ghost writer is good at writing things
Summary
(this is example of not that intelegent
)
Summary
its called ghost writer
Exact rationals work well because the answer to a problem is always a single number, even if the numerator and denominator have lots of digits. But the result of a ringed √⎺⎺⎺⎺ operator can't be added to, say, 𝜋, it'd have to be
(+ sqrt(10) pi)
which can't be reduced at all. Then you do more arithmetic and the result of the computation still can't be reduced at all.
That's not what people want when they do floating point arithmetic. They want a pretty good approximation to the answer, quickly.
Remember that hardly any real numbers can be represented exactly, regardless of what notation you use, because there are uncountably many real numbers, and only countably many computer programs, since a program is a finite stream from a finite alphabet, and there are $$\aleph_0$$ of those.
and get a block called "quickly smash expression into value" | 2022-12-08 02:01:18 | {"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": 0.7645981907844543, "perplexity": 841.3383582784151}, "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/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00687.warc.gz"} |
http://www.solutioninn.com/the-following-information-describes-a-companys-usage-of-direct-labor | # Question
The following information describes a company’s usage of direct labor in a recent period. Compute the direct labor rate and efficiency variances for the period.
Actual direct labor hours used . . . . . . . . . . . . . . . . . . . . . . 65,000
Actual direct labor rate per hour . . . . . . . . . . . . . . . . . . . . \$ 15
Standard direct labor rate per hour . . . . . . . . . . . . . . . . . . \$ 14
Standard direct labor hours for units produced . . . . . . . . . 67,000
Sales1
Views126 | 2016-10-28 01:09:49 | {"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": 0.9890519976615906, "perplexity": 133.52347896062986}, "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/1476988721415.7/warc/CC-MAIN-20161020183841-00343-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://plainmath.net/pre-algebra/80270-how-do-you-solve-and-graph-mstyle-di | Ellen Chang
2022-07-02
How do you solve and graph $-x-3<-5$ ?
zlepljalz2
Expert
Step 1
To solve, first treat the inequality like an equation.
$-x-3<-5$
Add 3 to each side to isolate the variable. So you get
$-x<-2$
To get rid of the negative, you must divide by -1 on both sides because x is being multiplied by -1. When dividing an inequality by a negative number, you have to flip the sign.
$x>2$
Now use this equation to graph. You are trying to locate all points where the x value is greater than 2.
First, find the horizontal line $x=2$ . Since the inequality is greater than and not greater than or equal to 2, $x=2$ is not a value.
So this line will be dotted. (if the equation was $x\ge 2$ , the line would be solid.) You are looking for all points where x is greater than 2, so shade in the whole portion of the graph which is to the right of the dotted line.
These are all the points whose x-values are greater than 2.
Do you have a similar question? | 2023-02-06 17:05:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 33, "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": 0.5505303144454956, "perplexity": 233.32480575230565}, "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-2023-06/segments/1674764500356.92/warc/CC-MAIN-20230206145603-20230206175603-00369.warc.gz"} |
https://zenodo.org/record/3876154 | Dataset Open Access
# CauseNet: Towards a Causality Graph Extracted from the Web
Heindorf, Stefan; Scholten, Yan; Wachsmuth, Henning; Ngonga Ngomo, Axel-Cyrille; Potthast, Martin
Causal knowledge is seen as one of the key ingredients to advance artificial intelligence. Yet, few knowledge bases comprise causal knowledge to date, possibly due to significant efforts required for validation. Notwithstanding this challenge, we compile CauseNet, a large-scale knowledge base of claimed causal relations between causal concepts. By extraction from different semi- and unstructured web sources, we collect more than 11 million causal relations with an estimated extraction precision of 83% and construct the first large-scale and open-domain causality graph. We analyze the graph to gain insights about causal beliefs expressed on the web and we demonstrate its benefits in basic causal question answering. Future work may use the graph for causal reasoning, computational argumentation, multi-hop question answering, and more.
When using the data, please make sure to refer to it as follows:
@inproceedings{heindorf2020causenet,
author = {Stefan Heindorf and
Yan Scholten and
Henning Wachsmuth and
Axel-Cyrille Ngonga Ngomo and
Martin Potthast},
title = {CauseNet: Towards a Causality Graph Extracted from the Web},
booktitle = {{CIKM}},
pages = {3023--3030},
publisher = {{ACM}},
year = {2020}
}
Files (2.0 GB)
Name Size
causenet-full.jsonl.bz2
md5:78273d177c5096f89d2367a876b64645
1.8 GB
causenet-precision.jsonl.bz2
md5:8bf12257e71713a63403bc8fe8bf71bf
137.9 MB
causenet-sample.json
md5:662cefd755f046751d1a345fe6abbdf7
55.2 kB
• Stefan Heindorf, Yan Scholten, Henning Wachsmuth, Axel-Cyrille Ngonga Ngomo, and Martin Potthast. CauseNet: Towards a Causality Graph Extracted from the Web. In CIKM 2020, pages 2023-3030. ACM.
57
24
views | 2021-08-03 15:23:44 | {"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": 0.3409169018268585, "perplexity": 14853.733321318376}, "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-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00016.warc.gz"} |
https://cstheory.stackexchange.com/questions/11997/is-tensor-rank-is-in-vnp | # Is tensor rank is in VNP?
Is it known if tensor rank of three dimensional tensors lies in VNP (non deterministic valiant class)? If yes, what is known about high dimensional tensor rank?
In fact I am interested in much more simple problem. I would like to know if one can construct class non-zero polynomials $f_n$ which lies in VNP, in $n^3$ variables such that $f_i(T)=0$ if tensor rank of $T$ less than $n^{1.9}$. For simplicity let us assume that we are working over $\mathbb{C}$.
I would like to mention that it is O.K. if $f_i(T)=0$ for $T$ of high rank only what I need is that $f_i(T)=0$ for all small rank tensors.
The collection of tensors of a given rank, or even of tensors with rank at most $k$ is not a (Zariski-)closed set, so it cannot be described as the vanishing locus of any set of polynomials, regardless of their complexity. (However, over finite fields tensor-rank is $NP$-complete and over $\mathbb{Q}$ it is $NP$-hard but not known to be in $NP$. But these are the usual Boolean classes, not the Valiant analogues.)
The closure of the the set of tensors of rank at most $k$ is the set of tensors of border-rank at most $k$. Call a set of polynomials whose vanishing locus is the set of tensors of border-rank at most $k$ a system of (set-theoretic) defining equations for border rank at most $k$. Such defining equations are known for small $k$, but for most $k$ finding such defining equations is a long-standing open problem, related the border-rank and multiplicative complexity of matrix multiplication.
• Thanks for answer. I would like just to note that it will be O.K. if $f(T)=0$ for $T$ of high rank I need only that $f(T)=0$ on all small rank tensors. – Klim Jul 11 '12 at 3:47
• @Klim: Presumably you also want $f$ to be not the zero function... Beyond that, is there some additional nontriviality condition you want $f$ to have, for example, that $f$ depend on all $n^{3}$ of its inputs? (If so you might add that clarification to the question.) – Joshua Grochow Jul 11 '12 at 4:18
• No $f$ may not depend on all its inputs. – Klim Jul 11 '12 at 5:09 | 2019-11-14 06:38:55 | {"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": 0.9353167414665222, "perplexity": 267.95158561060714}, "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-2019-47/segments/1573496668004.65/warc/CC-MAIN-20191114053752-20191114081752-00471.warc.gz"} |
https://www.gamedev.net/forums/topic/624031-2d-isometric-screen-to-tile-coordinates/ | 2D isometric: screen to tile coordinates
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I'm writing an isometric 2D game and I'm having difficulty figuring precisely on which tile the cursor is. Here's a drawing:
[Not allowed to post pictures :( here's a link : http://imageshack.us.../tilespace.png/ ]
where xs and ys are screen coordinates (pixels), xt and yt are tile coordinates, W and H are tile width and tile height in pixels, respectively.
The best I could figure out so far is this:
int xtemp = xs / (W / 2); int ytemp = ys / (H / 2); int xt = (xs - ys) / 2; int yt = ytemp + xt;
This seems almost correct but is giving me a very imprecise result, making it hard to select certain tiles, or sometimes it selects a tile next to the one I'm trying to click on. I don't understand why and I'd like if someone could help me understand the logic behind this.
Thanks!
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I wrote an article on the subject a while ago: http://www.wildbunny.co.uk/blog/2011/03/27/isometric-coordinate-systems-the-modern-way/
Hope it helps!
Cheers, Paul.
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Use a mouse map to make things way easier: Isometric 'n' Hexagonal Maps Part I
(Skip down to the part labeled 'Mouse Matters' and things will become clear)
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I wrote an article on the subject a while ago: http://www.wildbunny...the-modern-way/
Hope it helps!
Cheers, Paul.
Wow, such a simple approach. I ended up using a transformation matrix composed of a translation, a rotation and a scaling, so that getting going back-and-forth between pixels and tile coordinates is as simple as applying the transformation or its inverse; but this seems even simpler.
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× | 2018-07-18 22:34:08 | {"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": 0.1841726005077362, "perplexity": 2584.242347126498}, "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-2018-30/segments/1531676590329.62/warc/CC-MAIN-20180718213135-20180718233135-00397.warc.gz"} |
https://www.physicsforums.com/threads/d-e-boundary-value-problem.674490/ | # D.E.: Boundary Value Problem
1. Feb 25, 2013
### Jeff12341234
I'm not sure if my answer is correct. Did I make a mistake somewhere? I'm not sure the ± needs to be there.
2. Feb 25, 2013
### HallsofIvy
Staff Emeritus
How in the world did you get a quadratic equation out of this? $y(2)= (C_1+ 6C_2)e^6= e^6$ and $y'(1)= (3C_1+ 4C_2)e^3= e^3$. The derivative is $y'= 3C_1e^{3x}+ C_2e^{3x}+ 3C_2xe^{3x}= ([3C_1+ C_2]+ 3C_2x)e^x$. It does not involve "$C_1C_2$"!
You have $C_1+ 6C_2= 1$ and $3C_1+ 4C_2= 1$, two linear equations.
3. Feb 25, 2013
### Jeff12341234
c1 is represented by c, c2 is represented by d
That's y'
I did make an error by leaving out the + sign between c1 and c2 for y'
That makes c1 = -1 and c2 = 1
Last edited: Feb 25, 2013 | 2017-08-22 12:15:24 | {"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": 0.569328784942627, "perplexity": 1101.5720442854742}, "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/1502886110578.17/warc/CC-MAIN-20170822104509-20170822124509-00186.warc.gz"} |
http://mathoverflow.net/questions/69292/is-endoscopy-interesting-in-simply-laced-cases | # Is endoscopy interesting in simply-laced cases?
Let $G$ be a complex algebraic group, and write $Z(g)$ for the centralizer of a semisimple element $g$ in $G$. I will assume $G$ is simply connected, in which case $Z(g)$ is connected. Let $G^\vee$ and $Z(g)^\vee$ be the Langlands dual complex algebraic groups. If I understand, $Z(g)^\vee$ is called an "endoscopic group" for $G^\vee$, though I've taken all of the arithmetic out of it.
Most of the time, $Z(g)$ is a Levi subgroup of $G$, in which case $Z(g)^\vee$ is naturally a Levi subgroup of $G^\vee$. The handful of centralizers that are not Levis were classified by Kac. It's often emphasized that in these more interesting cases the associated endoscopic group is not a subgroup of $G^\vee$. For instance, $Z(g) = SL(2) \times SL(2)$ is a centralizer of an element of order 2 in $G = Sp(4)$, but there is no way to include $Z(g)^\vee = PGL(2) \times PGL(2)$ into $G^\vee = SO(5)$.
I just noticed that the endoscopic groups of $G^\vee$ do include into $G^\vee$ whenever $G$ is simply laced. This works out in type A because all centralizers are Levis, in type D essentially because of the self-duality of the groups $SO(2n)$, and in types $E_6,E_7,E_8$ by checking the centralizers one by one.
1. There are 2 interesting centralizers in $E_6$, 4 in $E_7$, and 8 in $E_8$, so plenty of opportunities for me to have made a mistake. Is my claim correct?
2. If correct, is there a simpler explanation for it than a case-by-case check?
3. Is the existence or nonexistence of an endoscopic sub group relevant in the kinds of endoscopic things people study in the Langlands program?
-
"The handful of centralizers that are not Levis were classified by Kac." -- I would've thought to credit rather [Borel-de Siebenthal]. mathoverflow.net/questions/28878/… – Allen Knutson Jul 1 '11 at 22:15 | 2015-11-27 17:18:59 | {"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": 0.8466783761978149, "perplexity": 282.441539786938}, "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-2015-48/segments/1448398449793.41/warc/CC-MAIN-20151124205409-00298-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.biostars.org/p/135663/ | how to generate setID file?
1
0
Entering edit mode
6.4 years ago
la.sy • 0
i want to generate setID file for SKAT(r package)
so i use "annovar"
but i don't know how to use annovar after i read guide
could anyone provide me some suggestion
annovar • 2.2k views
0
Entering edit mode
what exactly are you not understanding ? The annovar documentation is quite straight forward. Alternatively, try wANNOVAR
0
Entering edit mode
10 weeks ago
I know this is for a long time, but I found till now there is no clear answer
so to use annovar firstly you download annovar from this link https://annovar.openbioinformatics.org/en/latest/ and then in your Linux unzip the file tar xvfz annovar.latest.tar.gz then module load annovar then run this annotate_variation.pl -out ex1 -build hg19 example/ex1.avinput humandb/ as an example to understand what is happening here, all the examples files will be downloaded automatically
marwa | 2021-08-02 03:00:28 | {"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": 0.17138947546482086, "perplexity": 8975.81847419084}, "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-2021-31/segments/1627046154302.46/warc/CC-MAIN-20210802012641-20210802042641-00391.warc.gz"} |
https://email.esm.psu.edu/pipermail/macosx-tex/2009-October/041470.html | # [OS X TeX] Per-folder project root
Chris Goedde cgg.lists at gmail.com
Mon Oct 12 14:16:00 EDT 2009
```On Oct 12, 2009, at 12:21 PM, Herbert Schulz wrote:
> Howdy,
>
> I guess I don't really understand what you're trying to accomplish.
> What do you mean by a ``project root folder''? It almost sound like
> you have a particular file that contains definitions that are used
> by the other files. If that is the case why not just make the file
> containing the definitions generic (no documentclass, etc.) and just
> \input it into the other files. A bit more sophisticated is to
> create your own package, put it somewhere in ~/Library/texmf/tex/
> latex/ (where ~ is you HOME directory) and then just \usepackage in
> each file to include the definitions. That way each document is
> completely separate.
something different.
In regards to Themis' suggestion to use the %!TEX syntax, I'd
forgotten about that. I guess I don't like to clutter up my files with
front-end specific information. I'd rather do things through the front
end itself (which is why I use the "Set Project Root" menu item). I'd
just like to be able to set the project root for every file in a given
folder with a single setting.
Chris
``` | 2020-09-27 19:26:38 | {"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": 0.8260247707366943, "perplexity": 5845.119403030994}, "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/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00538.warc.gz"} |
https://brilliant.org/problems/poly-trolly/ | # Poly Trolly
Geometry Level 2
A polygon of $$n$$ sides has 275 diagonals then the number of sides is:
× | 2018-09-22 21:41:29 | {"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": 0.5526173710823059, "perplexity": 5625.932919328072}, "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/1537267158691.56/warc/CC-MAIN-20180922201637-20180922222037-00239.warc.gz"} |
https://mathematica.stackexchange.com/questions/235767/what-is-keyboard-shortcut-combination-for-resourcefunction | # What is keyboard shortcut combination for ResourceFunction?
I have seen in some notebooks that functions called with ResourceFunction["PairwiseScatterPlot"] appear with a red set of square brackets enclosing a red filled square. It would be great to know the shortcut instead of having to type out ResourceFunction every time. Any help is appreciated.
• I don't think there is one. This is a display form, not a form one types in manually. Dec 2 '20 at 13:14
• Perhaps ResourceFunctionInput over at the function repository will do what you are asking: resources.wolframcloud.com/FunctionRepository/resources/… Dec 2 '20 at 14:27
• (+1) Mostly for the pointing out PairwiseScatterPlot. Dec 2 '20 at 14:28
• @JoshuaSchrier that’s it for sure, you should post it as an answer so that OP can accept it! Dec 9 '20 at 11:52
ResourceFunction["ResourceFunctionInput"]["InstallAlias"]
permanently adds an interactive input for ResourceFunction symbols as input alias esc-rfi-esc that allows for inline creation of ResourceFunction symbols. There are also other options for adding menu bar items and other ways to use this functionality.
• Not sure why but on my machine (Ubuntu 18.08 with MMA 12.0) this fails with the message SystemPacletUninstall::shdw: Symbol PacletUninstall appears in multiple contexts {System, PacletManager}; definitions in context System may shadow or be shadowed by other definitions. Anyone having the same experience? Jan 18 '21 at 17:37 | 2022-01-26 07:40:01 | {"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": 0.357421338558197, "perplexity": 2176.357102045}, "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/1642320304928.27/warc/CC-MAIN-20220126071320-20220126101320-00577.warc.gz"} |
https://physics.stackexchange.com/questions/595193/why-liquids-evaporate-completely-when-heated-at-their-boiling-points | # Why liquids evaporate completely when heated at their boiling points?
I'm confused about why the boiling of liquids happen. The boiling point of a liquid is defined as the temperature in which it's vapor pressure is equal to the pressure of the gas above the liquid( for example the atmospheric pressure ), and vapor pressure is defined as the (temperature dependent) partial pressure of the gas state of the liquid in which the rate of condensation is equal to the rate of evaporation. So for example, let say we have a beaker of water at sea level( 1 atm of atmospheric pressure) and we heat it constantly( for example with a bunsen burner ) to 100ºC, since at that temperature the vapor pressure of water is equal to the atmospheric pressure of water, we have heated it to it's boiling point. What I don't understand is why after some time all beaker's water will became a gas and no liquid water will be left in the beaker, because the bubbles of water gas that form in the beaker will rise( due to lower density ), but once the reach the level of water they should constantly condense and evaporate at the same rate( due to the vapor pressure ) so the level of water should remain constant, because the amount of water that leaves as a gas is the same that condenses to the liquid, but we know that after some time all water will evaporate and diffuse into the atmosphere, so no liquid water will be left in the beaker.
I'm confused about this, why does the liquid completely evaporates when according to the vapor pressure, gas and liquid should be in equilibrium and some water should remain liquid in the beaker? What am I missing?. Thank you for your help, I haven't really found any explanation to this in the internet or in a textbook.
• @Chet Miller: You are right. I was not thinking clearly because I was worried wwhat would happen the to any air. If there is only water and water vapour, and one holds at fixed $T$, then it is the volume that determines the fractions of water and vapour. Nov 20, 2020 at 18:16 | 2022-05-28 21:04:19 | {"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": 0.7564493417739868, "perplexity": 310.4235112981523}, "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/1652663019783.90/warc/CC-MAIN-20220528185151-20220528215151-00733.warc.gz"} |
https://pendulumedu.com/blog/qotd-quantitative-aptitude-hcf-lcm-26-09-2019 | # QOTD - Quantitative Aptitude - HCF & LCM Problem
2019-09-26 | Team PendulumEdu
The HCF of $$\frac{2}{25}$$,$$\frac{6}{5}$$, and $$\frac{8}{15}$$ will be
Options:
Solution:
HCF of any fraction is given as
HCF of two or more numbers is the greatest number which divides each of them exactly.
Thus, numbers which can exactly divide all the numbers 2, 6 and 8 will be either 1 or 2
Greatest number which divides each of them exactly will be 2
Thus, HCF of (2, 6 and 8) will be 2
LCM is the smallest number which is the multiple of all the numbers.
Thus, LCM of the numbers 25, 5, and 15 will be
Therefore,
Hence, (D) is the correct answer.
Such type of question is asked in Quantitative Aptitude/Numerical Ability section of various exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB Office Assistant, IBPS Clerk, RBI Assistant, etc. Try and attempt free mock tests at PendulumEdu.
RRB NTPC Quizzes
Attempt Now
Share Blog | 2020-09-19 10:05:55 | {"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": 0.5335214138031006, "perplexity": 5386.92192041832}, "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/1600400191160.14/warc/CC-MAIN-20200919075646-20200919105646-00013.warc.gz"} |
https://www.rdocumentation.org/packages/igraph/versions/0.5.2-2 | # igraph v0.5.2-2
0
0th
Percentile
## Routines for simple graphs, network analysis.
Routines for simple graphs and network analysis. igraph can handle large graphs very well and provides functions for generating random and regular graphs, graph visualization, centrality indices and much more. | 2020-01-26 20:14:36 | {"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": 0.1952866017818451, "perplexity": 2861.456439383375}, "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-2020-05/segments/1579251690379.95/warc/CC-MAIN-20200126195918-20200126225918-00478.warc.gz"} |
https://www.semanticscholar.org/paper/Chapter-%CE%B1-Engineering-Complex-Systems-Norman-Kuras/40faf511fec354018e82b9e7d168e5ce34692c0e?p2df | • Corpus ID: 16846877
Chapter α Engineering Complex Systems
@inproceedings{Norman2004ChapterE,
title={Chapter $\alpha$ Engineering Complex Systems},
author={Douglas O. Norman and Michael L. Kuras},
year={2004}
}
• Published 2004
Using the current instantiation of the Air and Space Operations Center (AOC), and the desired evolution of it, the AOC is shown to be best thought of as a complex system. Complex Systems are alive and constantly changing. They respond and interact with their environments – each causing impact on (and inspiring change in) the other. We make the case that a traditional systems engineering (TSE) approach does not scale to the AOC; consequently, we don’t believe TSE scales to the “enterprise.”
1 Citations
References
SHOWING 1-10 OF 11 REFERENCES
When systems engineering fails-toward complex systems engineering
• Y. Bar-Yam
SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483)
• 2003
It is suggested that there are two effective strategies for overcoming problems with systems engineering: restricting the conventional systems engineering process to not-too-complex projects and adopting an evolutionary paradigm for complex systems engineering that involves rapid parallel exploration and a context designed to promote change.
DSE-A Decision Support Environment | 2022-05-17 13:13:57 | {"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": 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": 0.280779093503952, "perplexity": 5213.957004951061}, "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/1652662517485.8/warc/CC-MAIN-20220517130706-20220517160706-00375.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-10th-edition/chapter-10-analytic-geometry-chapter-review-cumulative-review-page-701/8 | ## Precalculus (10th Edition)
$\theta=30$ degrees $-\infty\lt r\lt \infty$
A polar equation of the line containing the origin and making an angle $\theta_0=30$ degrees with the positive $x$-axis is: $\theta=\theta_0$ $\theta=30$ degrees $-\infty\lt r\lt \infty$ | 2021-10-16 05:26:18 | {"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": 0.952745795249939, "perplexity": 576.1703777973819}, "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-2021-43/segments/1634323583423.96/warc/CC-MAIN-20211016043926-20211016073926-00261.warc.gz"} |
http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/analysis/MultivariateFunction.html | org.apache.commons.math3.analysis
## Interface MultivariateFunction
• ### Method Summary
Methods
Modifier and Type Method and Description
double value(double[] point)
Compute the value for the function at the given point.
• ### Method Detail
• #### value
double value(double[] point)
Compute the value for the function at the given point.
Parameters:
point - Point at which the function must be evaluated.
Returns:
the function value for the given point.
Throws:
DimensionMismatchException - if the parameter's dimension is wrong for the function being evaluated.
MathIllegalArgumentException - when the activated method itself can ascertain that preconditions, specified in the API expressed at the level of the activated method, have been violated. In the vast majority of cases where Commons Math throws this exception, it is the result of argument checking of actual parameters immediately passed to a method. | 2016-02-08 12:27:52 | {"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": 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": 0.1987483948469162, "perplexity": 1584.880627761748}, "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/1454701153323.32/warc/CC-MAIN-20160205193913-00225-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://clay6.com/qa/3137/the-area-of-the-region-bounded-by-the-curve-y-x-1-and-the-lines-x-2-and-x-3 | Browse Questions
# The area of the region bounded by the curve $y=x+1$ and the lines $x=2$ and $x=3$ is $(A)\frac{7}{2} sq.units\quad(B)\;\frac{9}{2}sq. units\quad(C)\frac{11} {2}sq.units\quad(D)\frac{13}{2} sq.units$
Toolbox:
• The area enclosed by the curve $y=f(x)$,the $x$-axis and the ordinates $x=a$ and $x=b$ is given by $\int_a^b ydx.$
• $\int x^ndx=\large\frac{x^{n+1}}{n+1}$$+c$
Step 1:
Given curve is $y=x+1$ which is a straight line bounded between the lines $x=2$ and $x=3$
The required area is the shaded portion as shown in the fig.
Area of the shaded portion is $A=\int_2^3(x+1)dx.$
Step 2:
On integrating we get,
$\begin{bmatrix}\large\frac{x^2}{2}\normalsize +x\end{bmatrix}_2^3$
On applying limits we get,
$\begin{bmatrix}\large\frac{1}{2}\normalsize(3^2-2^2)+(3-2)\end{bmatrix}=\begin{bmatrix}\large\frac{1}{2}\normalsize(9-4)+(3-2)\end{bmatrix}$
$\qquad\qquad\qquad\qquad\qquad=\begin{bmatrix}\large\frac{5}{2}\normalsize +1\end{bmatrix}=\large\frac{7}{2}$sq.units.
Hence the correct option is A. | 2017-02-22 01:45:59 | {"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": 2, "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": 0.9804207682609558, "perplexity": 259.7177834532147}, "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-2017-09/segments/1487501170875.20/warc/CC-MAIN-20170219104610-00148-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/equivalent-expressions.890975/ | Equivalent Expressions
1. Oct 27, 2016
Veronica_Oles
1. The problem statement, all variables and given/known data
State an equivalent expression in terms of the related acute angle?
(A) cot(-π/4)
2. Relevant equations
3. The attempt at a solution
(A) I made the the unit circle and since its negative I went clockwise and made it into the fourth quadrant. I ended up getting -cotπ/4. However the answer is not the one that the text book has given. Im a little confused.
The text book has given the answer cot3π/4, but I thought we were supposed to go clockwise because it is negative?
2. Oct 27, 2016
PeroK
An acute angle is one that is less than $\pi /2$. I've never seen this used for negative angles, so I'm not sure whether $-\pi /4$ would be considered acute. In any case, $3\pi /4$ is not an acute angle. It's actually a "reflex" angle (I had to look that one up).
I thought your answer was correct. $\pi /4$ is definitely an acute angle.
Last edited: Oct 27, 2016
3. Oct 27, 2016
Staff: Mentor
I agree with @PeroK -- $3\pi/4$ is not an acute angle.
I'll bet what you actually looked up was "reflex".
4. Oct 27, 2016
Veronica_Oles
I just asked my teacher, I got the angle correct. Thx. | 2017-08-22 04:29:51 | {"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": 0.6423775553703308, "perplexity": 863.4911744687134}, "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-2017-34/segments/1502886109893.47/warc/CC-MAIN-20170822031111-20170822051111-00257.warc.gz"} |
https://zbmath.org/?q=an%3A0991.35059 | ## A Kato type theorem on zero viscosity limit of Navier-Stokes flows.(English)Zbl 0991.35059
The author presents a necessary and sufficient condition for the convergence of a solution $$u^{\nu}$$ of the incompressible Navier-Stokes equations in a spatial domain $$\Omega$$ to a solution $$u^0$$ of the Euler equations at vanishing viscosity. He proves that $$u^{\nu} \rightarrow u^0$$ as $$\nu\rightarrow 0$$ in $$C([0,T], L^2(\Omega))$$ iff there exist $$\delta (\nu)$$ such that $$\lim_{\nu\rightarrow 0} \nu/\delta (\nu)=0$$ and $$\lim_{\nu\rightarrow 0} \int_0^T \int_{\Gamma_{\delta}} |\nabla_t u^{\nu}_n|^2 dx dt=0$$, where $$\Gamma_{\delta}$$ is a $$\delta$$-neighborhood of the wall $$\partial \Omega$$, $$\nabla_t$$ denotes tangential derivatives, and $$u^{\nu}_n$$ denotes the normal component of the velocity.
### MSC:
35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35Q05 Euler-Poisson-Darboux equations
Full Text: | 2022-08-16 18:38:15 | {"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": 0.895318329334259, "perplexity": 209.4373802318338}, "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/1659882572515.15/warc/CC-MAIN-20220816181215-20220816211215-00665.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=Ring_of_integers&diff=prev&oldid=20924 | # Difference between revisions of "Ring of integers"
Let $K$ be a finite algebraic field extension of $\mathbb{Q}$. Then the integral closure of ${\mathbb{Z}}$ in $K$, which we denote by $\mathfrak{o}_K$, is called the ring of integers of $K$. Rings of integers are always Dedekind domains with finite class numbers. | 2021-01-15 18:28:08 | {"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": 6, "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": 0.9574864506721497, "perplexity": 79.7178517662498}, "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/1610703495936.3/warc/CC-MAIN-20210115164417-20210115194417-00369.warc.gz"} |
https://www.andrewlienhard.io/tags/back-pain/ | • It’s a long way to my toes. From up here, in the stratosphere of human elevation, I see my distant phalanges pressing against the wilds of the earth — a… | 2022-08-09 17:58:44 | {"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": 0.8257986903190613, "perplexity": 2442.0047438725232}, "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/1659882571056.58/warc/CC-MAIN-20220809155137-20220809185137-00777.warc.gz"} |
https://quant.stackexchange.com/questions/61005/quantlib-python-why-is-the-npv-different-npv0-1-0-110-should-be-100-not-9 | QuantLib Python: why is the NPV different? NPV(0.1,[0,110]) should be 100, not 99.53
I am trying to learn QuantLib for Python. Further to my previous question on the syntax for CashFlows.npv(), now that I understand how the syntax works, I have a question on why the output differs from what I'd expect (which is why I think a separate question is justified).
In my toy example, my cashflows are zero on 15-Jan-2001 and 110 on 15-Jan-2002. If I discount them at 10%, I'd expect the pv to be 100, but I get 99.53211. Why? What am I missing? That would imply that 384 days have gone by, not 365. Those are not leap years. I have tried with act/365 and 30/360: they both give the same result, which is not 100.
import QuantLib as ql
d1 = ql.Date(15,1,2001)
ql.Settings.instance().setEvaluationDate(d1)
cfs = [ql.SimpleCashFlow(0, d1),
ql.SimpleCashFlow(110, d1 + 365)]
calc_date = d1
risk_free_rate = 0.1
curve_act_365 = ql.YieldTermStructureHandle(
ql.FlatForward(calc_date, risk_free_rate, ql.Actual365Fixed()))
pv_act_365 = ql.CashFlows.npv(cfs, curve_act_365, True)
curve_30_360 = ql.YieldTermStructureHandle(
ql.FlatForward(calc_date, risk_free_rate, ql.Thirty360()))
pv_30_360 = ql.CashFlows.npv(cfs, curve_30_360, True)
By default, QuantLib expects a continuously compounded rate in the FlatForward constructor.
So the PV you are getting is basically:
from math import exp
print(110 * exp(-0.1))
If you define your curve with an annually compounded rate like so:
curve_30_360 = ql.YieldTermStructureHandle(
ql.FlatForward(calc_date, risk_free_rate, ql.Thirty360(), ql.Compounded, ql.Annual))
You will get 100. | 2021-05-06 16:48:34 | {"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": 0.5480121970176697, "perplexity": 4784.020518889049}, "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-2021-21/segments/1620243988758.74/warc/CC-MAIN-20210506144716-20210506174716-00426.warc.gz"} |
https://sttp.softwaremill.com/en/v3.7.3/requests/authentication.html | # Authentication
sttp supports basic, bearer-token based authentication and digest authentication. Two first cases are handled by adding an Authorization header with the appropriate credentials.
Basic authentication, using which the username and password are encoded using Base64, can be added as follows:
import sttp.client3._
val username = "mary"
val password = "p@assword"
A bearer token can be added using:
val token = "zMDjRfl76ZC9Ub0wnz4XsNiRVBChTYbJcE3F"
basicRequest.auth.bearer(token)
## Important Note on the Authorization Header and Redirects
The Authorization header is by default removed during redirects. See redirects for more details.
## Digest authentication
This type of authentication works differently. In its assumptions it is based on an additional message exchange between client and server. Due to that a special wrapping backend is need to handle that additional logic.
In order to add digest authentication support just wrap other backend as follows:
val myBackend: SttpBackend[Identity, Any] = HttpClientSyncBackend()
new DigestAuthenticationBackend(myBackend)
Then only thing which we need to do is to pass our credentials to the relevant request:
val secureRequest = basicRequest.auth.digest(username, password)
It is also possible to use digest authentication against proxy:
val secureProxyRequest = basicRequest.proxyAuth.digest(username, password)
Both of above methods can be combined with different values if proxy and target server use digest authentication.
Also keep in mind that there are some limitations with the current implementation:
• there is no caching so each request will result in an additional round-trip (or two in case of proxy and server)
• authorizationInfo is not supported
• scalajs supports only md5 algorithm
## OAuth2
You can use sttp with OAuth2. Looking at the OAuth2 protocol flow, sttp might be helpful in the second and third step of the process:
1. (A)/(B) - Your UI needs to enable the user to authenticate. Your application will then receive a callback from the authentication server, which will include an authentication code.
2. (C)/(D) - You need to send a request to the authentication server, passing in the authentication code from step 1. You’ll receive an access token in response (and optionally a refresh token). For example, if you were using GitHub as your authentication server, you’d need to take the values of clientId and clientSecret from the GitHub settings, then take the authCode received in step 1 above, and send a request like this:
import sttp.client3.circe._
import io.circe._
import io.circe.generic.semiauto._
val authCode = "SplxlOBeZQQYbYS6WxSbIA"
val clientId = "myClient123"
val clientSecret = "s3cret"
case class MyTokenResponse(access_token: String, scope: String, token_type: String, refresh_token: Option[String])
implicit val tokenResponseDecoder: Decoder[MyTokenResponse] = deriveDecoder[MyTokenResponse]
val backend = HttpClientSyncBackend()
val tokenRequest = basicRequest
.auth
.basic(clientId, clientSecret)
val authResponse = tokenRequest.response(asJson[MyTokenResponse]).send(backend)
val accessToken = authResponse.body.map(_.access_token)
1. (E)/(F) - Once you have the access token, you can use it to request the protected resource from the resource server, depending on its specification. | 2022-11-27 01:35:18 | {"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": 0.21693286299705505, "perplexity": 7617.532372524984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2022-49/segments/1669446710155.67/warc/CC-MAIN-20221127005113-20221127035113-00172.warc.gz"} |
https://datascience.stackexchange.com/questions/87754/interpreting-a-confusion-matrix | Interpreting a confusion matrix [closed]
I have a binary classification problem.
The accuracy score is 52%
The precision for 0 is 53% and the precision for 1 is 49%
When using predict_proba() does this mean my model more accurately predicts when the outcome should be classified zero as opposed to one?
I'm not sure if this is telling me that I should be using the the first value (ynew[0][0]) returned from predict_proba() as opposed to the second (ynew[0][1]).
Here is the entire confusion matrix:
• one can compare both values and decide on largest proba – Nikos M. Jan 10 at 18:34 | 2021-01-19 17:39:12 | {"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": 0.7720202207565308, "perplexity": 933.4074234044845}, "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-2021-04/segments/1610703519600.31/warc/CC-MAIN-20210119170058-20210119200058-00413.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/dcds.2009.24.523 | Article Contents
Article Contents
# Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
• In this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system $dx_i (t) = x_i(t)$[($b_i(t)$-$\sum_{j=1}^{n} a_{ij}(t)x_j(t))$$dt$$+ \sigma_i(t) d B_i(t)]$, where $B_i(t)$($i=1 ,\ 2,\cdots,\ n$) are independent standard Brownian motions. Some dynamical properties are discussed and the sufficient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated.
Mathematics Subject Classification: Primary: 62F10, 34F05; Secondary: 92B05.
Citation: | 2022-12-06 17:11:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.45430174469947815, "perplexity": 648.7387616472816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00629.warc.gz"} |
https://brilliant.org/problems/rps-002-eulers-totient/ | # RPS - Rimba's Problem Series #001
How many positive integers $$\leq 2015$$ which is not relatively prime with $$2015$$?
(Find other problem series in my profile!)
× | 2018-01-23 04:12:37 | {"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": 0.5699269771575928, "perplexity": 5992.208784778598}, "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-2018-05/segments/1516084891706.88/warc/CC-MAIN-20180123032443-20180123052443-00251.warc.gz"} |
https://www.gamedev.net/forums/topic/163370-lesson-7/ | • ### Popular Now
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# Lesson 7
This topic is 5393 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
i''ve added a diffuselight source to my project with the help of lesson 7 but it seems that the lightsource rotates along with my cube. Yet i can find out why. May anyone has an idea? Grtz iTec
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You have to be carefull about the order you do your conversions. If I recall correctly first insert geometry, then do all the translations/rotations of geometry, then insert the light via glLightfv(light.name,GL_POSITION,light.position);.
If that doesn''t help, try doing the following:
glPushMatrix(); { // Do rotations + translations // Insert geometry } glPopMatrix(); // Insert Lights
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Don''t know anything about glPushMatrix() and glPopMatrix() yet but I insert the light in the initGL just like in the tutorial (only a bit modified)
glEnable(GL_TEXTURE_2D);
glClearColor(0.0f, 0.0f, 0.0f, 0.5f);
glClearDepth(1.0f);
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LEQUAL);
glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);
glLightfv(GL_LIGHT1, GL_AMBIENT, World.Light.Ambient.Color);
bool chk = false;
cDiffuseLight Current = (cDiffuseLight) *(World.Light.firstDiffuse());
do{
glLightfv(Current.Name, GL_DIFFUSE, Current.Color);
glLightfv(Current.Name, GL_POSITION,Current.Position);
glEnable(Current.Name);
if(Current.Volgende!=NULL){
cDiffuseLight *tc = Current.Volgende;
Current = (cDiffuseLight) *tc;
chk = true;
}else{
chk = false;
}
}while (chk);
glEnable(GL_LIGHTING);
return TRUE;
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Sorry, but it''s a bit difficult to see what part of your code you''re posting exactly.
quote:
glEnable(GL_TEXTURE_2D);
glClearColor(0.0f, 0.0f, 0.0f, 0.5f);
glClearDepth(1.0f);
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LEQUAL);
glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);
All this is initialisation stuff, and should only be done once (=beginning of your programm).
quote:
glLightfv(Current.Name, GL_POSITION,Current.Position);
While this is a part of code you''ll need to put into the main loop. You''ll have to insert the light every time you changed the orientation of the geometry, otherwise the changes will affect the light as well (which you don''t want obviously).
As for glPush/PopMatrix: These function store/restore the transformation matrix. That is: if you do glPushMatrix, then do some transformations (glRotate, glTranslate), then do glPopMatrix the original Matrix is restored. Resulting in geometry outside the Push/Pop block not being affected by any of the translations inside. | 2018-03-22 22:12:55 | {"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": 0.2251991629600525, "perplexity": 5531.191592722442}, "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-2018-13/segments/1521257648003.58/warc/CC-MAIN-20180322205902-20180322225902-00503.warc.gz"} |
http://ncatlab.org/nlab/show/tangent+Lie+algebra | # nLab tangent Lie algebra
Given an algebraic group $G$ in characteristic zero, or a finite dimensional Lie group, one associates to it a Lie algebra, its tangent Lie algebra which is the Lie subalgebra $\mathcal{X}^{linv}(G)$ of the Lie algebra $\mathcal{X}^(G)$ left invariant vector fields on $G$ with respect to the usual Lie bracket of vector fields.
The value of a left-invariant vector field $X$ at the unit element $e$ is a tangent vector $X_e$ at $e$. It appears that the specialization/evaluation at the unit element map $\mathcal{X}^{linv}(G)\to T_e G$ is an isomorphism of vector spaces, which is often considered as an identification. However, one needs to look into vector fields in order to find the bracket, hence defining the tangent Lie algebra as the tangent vector space at $e$ misses the bracket (which come from consideration of infintesimals of second order). One can instead work with right invariant vector fields $\mathcal{X}^{rinv}(G)$ and obtain an isomorphic Lie algebra; the isomorphism is of course, by comparing the specialization at $e$.
Within $\mathcal{X}^(G)$, all right invariant vector fields commute with all left invariant vector fields.
The correspondence $G\mapsto\mathcal{X}^{linv}(G)$ is functorial.
A generalization of a tangent Lie algebra of a Lie group is the tangent Lie algebroid.
The first idea of the tangent Lie algebra was explained in a letter of Sophus Lie to his friend Meyer in 1874 (See the historical appendix to Bourbaki, Lie groups and Lie algebras vol. 3).
Created on November 11, 2012 23:28:05 by Zoran Škoda (193.55.36.32) | 2014-11-28 13:25:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 14, "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": 0.8920319080352783, "perplexity": 179.1109768794699}, "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-2014-49/segments/1416931010402.68/warc/CC-MAIN-20141125155650-00156-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3286477/integration-of-multi-valued-function | # Integration of multi-valued function
Graph
I have a set of discrete (x,y) points and need to find the area between the curve and the y-axis. However, the curve seems to be a multi-valued function (multiple x for the same y). Is such an operation valid, and if so, how?
edit: The image of the curve is in the link above. Kindly take a look.
I tried to do trapezoidal integration for this in MATLAB and got a negative answer. What is the interpretation of this negative area (even when all data are positive)? To check if area becoming negative was wrong, it tried doing the integration as ($$xy - \int ydx$$). I got the same answer in both cases.
This shows the area that I need.
This shows the area that I need when multiple x occurs for a single y. Area for all x is required.
• Comments are not for extended discussion; this conversation has been moved to chat. – Aloizio Macedo Jul 12 at 22:15 | 2019-08-25 15:27:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7759360671043396, "perplexity": 439.3062402531074}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027330750.45/warc/CC-MAIN-20190825151521-20190825173521-00546.warc.gz"} |
https://web2.0calc.com/questions/parabolas_18 | +0
# Parabolas
0
111
2
The parabolas defined by the equations y = -x^2 - x + 3 and y = 2x^2 - 1 intersect at points (a, b) and (c, d), where c is greater than or equal to a. What is c - a? Express your answer as a common fraction.
Dec 30, 2021
#1
0
You are only looking for the 'x' coordinates of the poits of intersection ....so
-x^2-x+3 = 2x^2-1
3x^2+x - 4 = 0 x = 1 and - 4/3 <===== you can finish
Dec 30, 2021
#2
+13724
+1
What is c - a?
Hello Guest!
$$-x^2 - x + 3 = 2x^2 - 1\\ \color{blue}3x^2+x-4=0$$
$${\color{blue}a=}\frac{-1+7}{6}=\color{blue}1\\ b=1\\ {\color{blue}c=}2\cdot \frac{16}{9}-1=\color{blue}\frac{23}{9}\\ d=\frac{-1-7}{6}=-\frac{4}{3}\\$$
$$c-a=\frac{14}{9}$$
!
Dec 30, 2021 | 2022-06-29 21:52:58 | {"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": 0.5954315066337585, "perplexity": 1556.4305857436834}, "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-2022-27/segments/1656103645173.39/warc/CC-MAIN-20220629211420-20220630001420-00398.warc.gz"} |
https://math.stackexchange.com/questions/408403/applications-of-computation-on-very-large-groups | # Applications of computation on very large groups
I have been studying computational group theory and I am reading and trying to implement these algorithms. But what that is actually bothering me is, what is the practical advantage of computing all properties of extremely large groups, moreover it is a hard problem?
It might give birth to new algorithms but does it solve any problem specific to group theory or other branches affected by it?
• I recently proved a theorem for which the smallest example of one of the cases had order $37,646,400$. We had to computationally verify its existence. – Alexander Gruber Jun 1 '13 at 16:00 | 2020-02-22 08:04:56 | {"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": 0.44188305735588074, "perplexity": 249.30961269812533}, "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-2020-10/segments/1581875145654.0/warc/CC-MAIN-20200222054424-20200222084424-00364.warc.gz"} |
http://crypto.stackexchange.com/questions/6515/are-rsa-signatures-deterministic?answertab=votes | # Are RSA signatures deterministic?
If I sign the word HELLO with the mechanism "NONEwithRSA" with the same private key, do I always will have the same signature?
A Java example always return different byte array :
PKCS11Provider provider = new PKCS11Provider(this);
List<PKCS11Slot> slots = PKCS11Slot.enumerateSlots(provider);
PKCS11Session session = null;
if (slots.size() > 0) {
session = PKCS11Session.open(slots.get(0),
}
PKCS11KeyStoreSpi keyStore = new PKCS11KeyStoreSpi(provider, "PKCS11");
PKCS11PrivateKey privateKey = PKCS11PrivateKey.getPrivateKeys(session).get(0);
Signature signature = Signature.getInstance("NONEwithRSA", provider);
signature.initSign(privateKey);
signature.update("HELLO".getBytes(), 0, "HELLO".getBytes().length);
byte[] realSig = signature.sign();
-
Some signature algorithms are deterministic (you always get the same signature for the same private key and input), others are not. In the case of RSA, as specified by PKCS#1, the "old-style" (aka "v1.5") signatures are deterministic, while the "new-style" ("PSS") signatures are not (padding includes some random bytes).
In Java, the "NONEwithRSA" mechanism ought to select the old-style signatures, and the input data should be already hashed (a normal signature begins by hashing the input data); in your code, you use unhashed data as input, which is a bad idea for security. The "NONEwithRSA" mechanism was added to support contexts where data is hashed externally, and also SSL/TLS which insists (in its pre-1.2 versions) on using the concatenation of MD5 and SHA-1 as its "hash function". This does not explain why you get different outputs, but you are still doing it wrong.
To investigate further, convert the signature to a BigInteger and apply the public key on it, to see what the padded data looks like:
BigInteger n = ... (the public key modulus)
BigInteger e = ... (the public key exponent)
BigInteger x = new BigInteger(1, realSig);
System.out.printf("%X\n", x.modPow(e, n));
With PKCS#1 v1.5, this should look like:
1FFFFFFFFF....FFFFF0048454C4C4F
(The 48454C4C4F is the encoding of "HELLO" -- because your code puts the raw data here instead of the hash value suitably encoded in an ASN.1 structure which designates the hash function.)
Since you are using a PKCS#11, you will sign data depending on what the underlying device can do. It is possible that your device does not allow such "NONEwithRSA" mechanism, or allows it only if it already looks like a properly encoded hash value. This may be your issue after all. The debug code above should show what happens.
(Also, don't use String.getBytes() without any argument. This converts the input string with the default encoding of the current machine, which depends on how the machine was configured; for some people it will be UTF-8, others will have UTF-16 or latin-1 or something else. It is much better to specify an explicit encoding, as: s.getBytes("UTF-8"))
- | 2014-11-23 06:21:19 | {"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": 0.21856945753097534, "perplexity": 3587.9945830886295}, "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-2014-49/segments/1416400379190.66/warc/CC-MAIN-20141119123259-00135-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://research.utwente.nl/en/publications/extinction-probability-in-a-birth-death-process-with-killing-2 | # Extinction probability in a birth-death process with killing
Erik A. van Doorn, A.I. Zeifman
Research output: Book/ReportReportProfessional
## Abstract
We study birth-death processes on the non-negative integers where $\{1,2,\ldots\}$ is an irreducible class and $0$ an absorbing state, with the additional feature that a transition to state $0$ may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence as $t\to\infty$ of the probability of absorption at time $t$, and relate it to the common rate of convergence of the transition probabilities which do not involve state $0$. Finally, we derive upper and lower bounds for the probability of absorption at time $t$ by applying a technique which involves the logarithmic norm of an appropriately defined operator.
Original language Undefined Enschede University of Twente, Faculty of Mathematical Sciences 20 Published - 2004
### Publication series
Name Memorandum Faculty of Mathematical Sciences Department of Applied Mathematics, University of Twente 1723 0169-2690
## Keywords
• MSC-60J27
• MSC-60J80
• IR-65907
• METIS-218214
• EWI-3543 | 2023-01-28 17:48:47 | {"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": 0.5934985280036926, "perplexity": 585.875598236671}, "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-2023-06/segments/1674764499646.23/warc/CC-MAIN-20230128153513-20230128183513-00267.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/write-in-terms-of-factorial-6-7-8-9-concept-of-factorial-function_160914 | # Write in terms of factorial:6 × 7 × 8 × 9 - Mathematics and Statistics
Sum
Write in terms of factorial:
6 × 7 × 8 × 9
#### Solution
6 × 7 × 8 × 9 = 9 × 8 × 7 × 6
Multiplying and dividing by 5!, we get
= (9xx8xx7xx6xx5!)/(5!)
= (9xx8xx7xx6xx5xx4xx3xx2xx1)/(5!)
= (9!)/(5!)
Concept: Concept of Factorial Function
Is there an error in this question or solution?
#### APPEARS IN
Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.2 | Q 4. (iii) | Page 75 | 2022-10-04 10:18:05 | {"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": 0.28754186630249023, "perplexity": 2587.679880330931}, "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/1664030337490.6/warc/CC-MAIN-20221004085909-20221004115909-00638.warc.gz"} |
http://mathhelpforum.com/geometry/16246-could-somebody-please-help-me.html | 2. Originally Posted by sanee66
I attached the diagram below. By the way, the triangle is AMN not ABC
Note that the altitude of an equilateral triangle bisects one of it's angles and divides the base it hits in two equal parts. This means that $MH = \frac {1}{2} (7m - 1)$
Also, since $\triangle AMN$ is equilateral, $AN = AM$
We are told that the sum of AM and MH gives 11m - 4
$\Rightarrow AM + MH = 11m - 4$
$\Rightarrow 7m - 1 + \frac {7m - 1}{2} = 11m - 4$
$\Rightarrow 7m + \frac {7m}{2} - 11m = -4 + \frac {3}{2}$
$\Rightarrow - \frac {1}{2} m = - \frac {5}{2}$
$\Rightarrow m = 5$
The side length of the triangle is equal to the side-length of AN
So, the side-length is 7m - 1 = 7(5) - 1 = 34 | 2013-12-08 18:50:12 | {"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": 0.7958809733390808, "perplexity": 445.51529351628716}, "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-2013-48/segments/1386163791972/warc/CC-MAIN-20131204132951-00051-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Category:Conversion_between_Cartesian_and_Polar_Coordinates_in_Plane | # Category:Conversion between Cartesian and Polar Coordinates in Plane
Jump to navigation Jump to search
## Pages in category "Conversion between Cartesian and Polar Coordinates in Plane"
The following 4 pages are in this category, out of 4 total. | 2023-03-21 14:48:51 | {"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": 0.9758334755897522, "perplexity": 2421.570990339112}, "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/1679296943698.79/warc/CC-MAIN-20230321131205-20230321161205-00788.warc.gz"} |
https://www.physicsforums.com/threads/the-magnitude-of-a-vector.956391/ | # The Magnitude of a Vector
CivilSigma
## Homework Statement
For any vector in 2D space, it can be broken down into its horizontal and vertical components.
## Homework Equations
In one of my engineering classes, we are using the following equation to determine the magnitude of a vector:
$$u=v_1 \cdot cos\theta +u_2 \cdot sin\theta$$
Where $\theta$ is the angle with respect to the horizontal, v1 is the horizontal component and v2 is the vertical component of the vector.
I know this equation works but I don't understand why.
I feel like I am missing a fundamental concept, because to determine the magnitude of a vector, I would use Pythagoras theorem, and I cannot derive the above equation from Pythagoras's equation.
## The Attempt at a Solution
Mentor
Can you provide some context for where this equation is applied? Perhaps give a specific example.
In general, this equation will not work for a single vector whose x and y components are ##u_1## and ##u_2##. Perhaps they are summing the horizontal components of two different vectors to obtain a net horizontal resultant?
Staff Emeritus
Homework Helper
That equation doesn't give the magnitude of the vector. It gives you the component of the vector in the direction of ##\hat n = \cos\theta\,\hat i + \sin\theta\,\hat j##.
Homework Helper
Gold Member
In one of my engineering classes, we are using the following equation to determine the magnitude of a vector:
u=v1⋅cosθ + u2⋅sinθ
Where $\theta$ is the angle with respect to the horizontal, v1 is the horizontal component and v2 is the vertical component of the vector.
I know this equation works but I don't understand why.
It comes from geometry... See this diagram... If that's not clear do say and I will explain some more.
#### Attachments
• Magnitude of Vector.png
6.6 KB · Views: 410
CivilSigma
Mentor
I think you meant to write the equation as $$u=u_1\cos{\theta}+u_2\sin{\theta}\tag{1}$$where $$u_1=u\cos{\theta}\tag{2}$$and$$u_2=u\sin{\theta}\tag{3}$$If you substitute Eqns. 2 and 3 into Eqn. 1, you get:
$$u=u\cos^2{\theta}+u\sin^2{\theta}=u$$
CivilSigma and SammyS | 2022-08-10 14:05:50 | {"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": 0.7695695757865906, "perplexity": 413.75822939307636}, "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/1659882571190.0/warc/CC-MAIN-20220810131127-20220810161127-00044.warc.gz"} |
https://myaptitude.in/science/in-case-of-negative-work-the-angle-between-the-force-and-displacement-is | # In case of negative work the angle between the force and displacement is
In case of negative work the angle between the force and displacement is
1. 45°
2. 90°
3. 180°
Work done, W = F.d cos θ
Work done at θ = 0°
W = F.d cos 0° = F.d
For angle θ = 0°, the work done is positive, so it is not true.
For angle θ = 45°, W = F.d/√2
In this case also, work done is positive, so it is not true.
Work done at θ = 90°, W = 0
So, it is not true.
Now, work done at θ = 180°, W = -F.d
For negative work, the angle between the force and displacement should be 180°.
The correct option is D. | 2020-07-14 04:42:39 | {"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": 0.8462815880775452, "perplexity": 1144.285232823893}, "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-2020-29/segments/1593657147917.99/warc/CC-MAIN-20200714020904-20200714050904-00157.warc.gz"} |
https://questioncove.com/updates/508716dde4b0c59b90b447c9 | OpenStudy (anonymous):
A rancher has 200 ft of fencing to enclose two adjacent rectangular corrals and run a strip of fencing down between them to separate the corrals. What dimensions should be used so that the inclosed area will be a maximum?
OpenStudy (anonymous):
@Hero or @lgbasallote
OpenStudy (anonymous):
guess and check?
OpenStudy (anonymous):
this is what ive got... $P=2x+2y~~~~~~~~~~~~~~A=xy$$200=2y+3x~~~~~~\implies~~~~~~y=100-{3\over2}~x~~~~~~and~~~~~~x={200\over3}~-{2\over3}~y$$A=\left(100-{3\over2}~x\right)\times\ x$ $\implies~~~~*plug~into~graphing~calculator~and~find~maximum~y-value*$$Max~Area~is~~ 1666~{2\over3}~ft~~~~~~\implies~~~~~~dimensions~are~~x=33{1\over3}~~and~~y=50{$
OpenStudy (anonymous):
$Max~Area~is~~ 1666~{2\over3}~ft~~~~~~\implies~~~~~~dimensions~are~~x=33{1\over3}~~and~~y=50$
OpenStudy (anonymous):
♥ I ROCK ^_^ ♥
OpenStudy (anonymous):
no you see there are 3 x's
OpenStudy (anonymous):
|dw:1351119771929:dw|
OpenStudy (anonymous):
|dw:1351119807736:dw|theres a STRIP GOING DOWN THE MIDDLE which is included in the fencing....so that added equals 200 | 2017-08-19 01:55:00 | {"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": 0.7183651924133301, "perplexity": 10387.789475960128}, "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/1502886105291.88/warc/CC-MAIN-20170819012514-20170819032514-00537.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/simplify-following-surd-rationalisation-of-surds_76597 | # Simplify the Following Surd. - Algebra
Simplify.
sqrt 7 - 3/5 sqrt 7 + 2 sqrt 7
#### Solution
sqrt 7 - 3/5 sqrt 7 + 2 sqrt 7
= 3 sqrt 7 - 3/5 sqrt 7
= 15/5 sqrt 7 - 3/5 sqrt 7
= 12/5 sqrt 7
Is there an error in this question or solution?
#### APPEARS IN
Balbharati Mathematics 1 Algebra 9th Standard Maharashtra State Board
Chapter 2 Real Numbers
Practice Set 2.3 | Q 6.4 | Page 30 | 2021-04-22 17:31:36 | {"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": 0.8834527134895325, "perplexity": 7227.893687423555}, "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/1618039594341.91/warc/CC-MAIN-20210422160833-20210422190833-00210.warc.gz"} |
https://math.stackexchange.com/questions/1700093/combinations-of-letters-with-restrictions | Combinations of letters with restrictions
Create a string of five letters using the letters: A, B, C, D, E, F, G, H, I, J, K, L, M.
a) How many words contain at least one A?
b) How many words contain exactly two A's?
For a) by my understanding is the total amount of combinations - the total amount of words without them. Which is what I believe to be $13^5 - 12^5$, however it feels as though it is too high/wrong
As for b), my train of thought is along the lines of:
$$\frac{13!}{2!\cdot 11!} \cdot \frac{12!}{3!\cdot 9!} \cdot \tfrac12$$
The first fraction is for the two A's, the second fraction is for the letters in the other three positions and the half is to get rid of the doubles in the set. ie AABCD and AABCD where the A's are swapped.
The (a) part is correct. For the (b) part, think that indeed you must choose the places for putting the two $A$'s: $\binom{5}{2}$. Then, each of the other three places can be ocuped for any of the remaining 12 letters: $12^3$. So, the (b) answer is $\binom{5}{2}12^3$. | 2020-08-08 09:43:18 | {"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": 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": 0.8346050381660461, "perplexity": 217.53254390459674}, "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-2020-34/segments/1596439737319.74/warc/CC-MAIN-20200808080642-20200808110642-00125.warc.gz"} |
https://math.stackexchange.com/questions/846434/sums-of-power-law-random-variables | # Sums of Power Law random variables
Suppose $F$ is a Pareto distribution with scale parameter $x_m$ and shape parameter $\alpha$. Assume $X_1, X_2 , \dots, X_n$ are iid random variables drawn from $F$.
Let $S_n(k) = X_1 ^k + X_2 ^k + \dots + X_n ^k$.
Can we say anything about $\frac{S_n(k)}{S_n(1)}$ as $n \rightarrow \infty$ ?
Will it be easier to solve, if the distribution $F$ is power law but bounded (that is, $(\forall i)[1 \leq X_i \leq n]$)?
• My intuition is that the ratio will be constant or a non-degenarate distributed random variable. I know that the sum of power law random variables behaves same as the maxima(in asymptotic sense), therefore the sum of the $k^{th}$ power would be even more skewed towards the maxima. Hence, the two terms would be of the same order. Jun 25, 2014 at 14:35 | 2022-08-09 08:09:20 | {"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": 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": 0.9330439567565918, "perplexity": 158.53966238668556}, "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/1659882570913.16/warc/CC-MAIN-20220809064307-20220809094307-00124.warc.gz"} |
https://nigerianscholars.com/past-questions/mathematics/question/364382/ | Home » » Evaluate $$3.0\times 10^1 - 2.8\times 10^{-1}$$leaving the answer in standard f...
# Evaluate $$3.0\times 10^1 - 2.8\times 10^{-1}$$leaving the answer in standard f...
### Question
Evaluate $$3.0\times 10^1 - 2.8\times 10^{-1}$$leaving the answer in standard form
### Options
A) $$2\times 10^{-1}$$
B) $$2\times 10^{2}$$
C) $$2.972 \times 10^{1}$$
D) $$2.972 \times 10^{2}$$ | 2022-07-05 22:38:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.883784294128418, "perplexity": 7223.0121584358985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104628307.87/warc/CC-MAIN-20220705205356-20220705235356-00574.warc.gz"} |
http://randomservices.org/random/apps/CauchyExperiment.html | ### Cauchy Experiment
Distribution graph
Light
#### Description
A light source is located $$b$$ units directly across from position $$a$$ on an infinite, straight wall. The random experiment consists of shining the light on the wall at an angle $$\Theta$$ with the perpendicular, that is uniformly distributed on the interval $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$. The position $$X = a + b \tan(\Theta)$$ of the light beam on the wall has the Cauchy distribution with location parameter $$a$$ and scale parameter $$b$$. On each run of the experiment, the angle $$\Theta$$ and the position $$X$$ are recorded in the data table. The probability density function of $$X$$ is shown in blue in the distribution graph and is recorded in the distribution table. When the experiment runs, the empirical density function is shown in red in the distribution graph and is recorded in the distribution table. The parameters $$a$$ and $$b$$ can be varied with the input controls. | 2017-09-19 13:41:00 | {"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": 0.6754046082496643, "perplexity": 146.65520750860554}, "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-2017-39/segments/1505818685698.18/warc/CC-MAIN-20170919131102-20170919151102-00535.warc.gz"} |
https://math.stackexchange.com/questions/595482/is-an-equivalence-an-adjunction | # Is an equivalence an adjunction?
Let $C$ and $D$ be categories and $F:C\to D$, $G:D\to C$ two functors.
$F$ is left-adjoint to $G$, if there are natural transformations $\eta:id_C\to GF$ and $\epsilon:FG\to id_D$ such that \begin{eqnarray} F&\xrightarrow{F\eta}&FGF&\xrightarrow{\epsilon F}F\\ G&\xrightarrow{\eta G}&GFG&\xrightarrow{G\epsilon}G \end{eqnarray} are the identity (!) transformations.
$F$ is an equivalence of categories (with inverse $G$) if there are natural isomorphisms $\eta:id_C\to GF$ and $\epsilon:FG\to id_D$ without any further properties.
Is $F$ left-adjoint to $G$, if $F$ is an equivalence of categories (with inverse $G$)?
If not, suppose that $F$ is an equivalence of categories with inverse $G':D\to C$ and suppose further that $F$ is left-adjoint to $G$. Does it follow that there is a natural isomorphism $G\to G'$ or is there even an identity $G=G'$?
• The answer to the first question is "yes", $F$ is both left-adjoint and right-adjoint to $G$. The answer to the second question is "yes, there exists a natural isomorphism $G\to G'$, but it is not necessarily an identity". Dec 6, 2013 at 14:47
• Suppose we have already shown that the natural iso $\eta : 1_{\mathbf{C}} \to GF$ witnessing the equivalence is the unit of the desired adjunction. Why can't the counit just be the other iso $\epsilon : FG \to 1_{\mathbf{D}}$ of the equivalence in general? It satisfies the UMP the counit since for each $g: FC \to D$, we have $\epsilon_D \circ (\epsilon_D^{-1} \circ g) = g$ and $\epsilon_D^{-1} \circ g = Ff$ for some unique $f : C \to GD$, since we can show that $F$ is fully faithful. What is wrong with this argument? Jan 28, 2016 at 7:35 | 2022-08-09 05:08:49 | {"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": 0.9374719262123108, "perplexity": 103.42477461541984}, "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/1659882570901.18/warc/CC-MAIN-20220809033952-20220809063952-00240.warc.gz"} |
https://socratic.org/questions/what-is-dynamic-equilibrium-1 | # What is dynamic equilibrium?
May 2, 2018
A state of equilibrium in which the forward and backward reactions are occurring at the same rate with no net change.
#### Explanation:
To illustrate dynamic equilibrium, let's take a look at this reaction:
${N}_{2} \left(g\right) + 3 {H}_{2} \left(g\right) r i g h t \le f t h a r p \infty n s 2 N {H}_{3} \left(g\right)$
In this reaction, nitrogen gas and hydrogen gas are in a dynamic equilibrium with ammonia gas.
• When ${N}_{2}$ and ${H}_{2}$ are first placed into a reaction vessel, they will begin to react to form $N {H}_{3}$. The rate of the forward reaction, ${N}_{2} \left(g\right) + 3 {H}_{2} \left(g\right) \to 2 N {H}_{3} \left(g\right)$, is high.
• However, eventually, $N {H}_{3}$ will start to reform ${N}_{2}$ and ${H}_{2}$.
The rate of the backward reaction, $2 N {H}_{3} \left(g\right) \to {N}_{2} \left(g\right) + 3 {H}_{2} \left(g\right)$, begins to rise.
• Eventually, the rates of the two reactions will be the same. Equilibrium has been reached.
We should remember, though, that this is a dynamic equilibrium!
This means that, although it may seem like nothing is happening (because the concentrations of the reactants and products essentially stay constant), ${N}_{2}$ and ${H}_{2}$ are still constantly forming $N {H}_{3}$. $N {H}_{3}$ is also constantly reforming into ${N}_{2}$ and ${H}_{2}$.
It's just that the rates at which they do this are the same.
So, although reactions are occurring, there is no net change. | 2022-05-22 23:25:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "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": 0.7796439528465271, "perplexity": 561.2719740742031}, "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/1652662550298.31/warc/CC-MAIN-20220522220714-20220523010714-00253.warc.gz"} |
https://math.stackexchange.com/questions/2286116/what-is-sin-pi-2-iln2/2286126 | # What is $sin(\pi/2 +iln2)$
I have tried this is a couple of different ways and have different answers.
1. $\sin(\pi/2+i\ln2)=\cos(i\ln2)=\cosh(\ln2)=\frac{e^{\ln2}+e^{-\ln2}}{2}=5/4$
2. $\sin(\pi/2+i\ln2)={\rm Im}(e^{i(\pi/2+i\ln2)})={\rm Im}(ie^{-\ln2})={\rm Im}(1/2i)=1/2$
I have a feeling the first is correct, but I am not sure where the other could have gone wrong.
• Something's fishy about all of these up-votes in just 20 minutes. – user384138 May 18 '17 at 8:09
• @OpenBall It's not my doing if there is something going on! I just posted the question, went to a lecture, and am checking again now! I presume it is because the distinction of when the expansions/methods are valid is not taught well in schools(certainly I have never come across this) so it seems like an strange conundrum until you know one method is simply not valid. – Meep May 18 '17 at 9:28
My guess is that $\sin(x)=\mathrm{Im}(e^{ix})$ only works for $x\in \mathbb{R}$. Take for example the series representation of $$\sin(x)=\sum_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{(2n+1)!}$$ Now if we insert $\sin(ix)$ with real $x$, then we see that $\sin(ix)\in\mathbb{C}$. On the other hand we see that $\sin(ix)=\mathrm{Im}(e^{i(ix)}) = \mathrm{Im}(e^{-x})=0$ which clearly contradicts our earlier finding. Only valid solution for complex $x$ would be $$\sin(x)=\frac{1}{2i}(e^{ix}-e^{-ix})$$
The first is correct. In the second, you are using that $\sin(x)=\text{im}(e^{ix}),$ but that only applies if $x$ is real, which is not the case here. We know that $e^{ix}=\cos(x)+i\sin(x)$, which makes it look like $\sin(x)$ is the imaginary part of $e^{ix}$, but what if $\cos(x)$ and $\sin(x)$ themselves are not real? | 2019-09-20 22:40:32 | {"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": 0.8058142066001892, "perplexity": 176.68138878189873}, "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-2019-39/segments/1568514574084.88/warc/CC-MAIN-20190920221241-20190921003241-00159.warc.gz"} |
https://stats.stackexchange.com/questions/202770/binary-logistic-regression-with-multiple-independent-variables | # Binary logistic regression with multiple independent variables
I have a group of 196 patients. I want to know if infection (the outcome, or dependent variable) depends on other variables. I am running a binary logistic regression with 8 independent variables (age, gender, type of surgery—6 different types, type of fixation, type of antibiotics). The categorical variables are automatically put into dummies by SPSS.
Some of my categorical variables have low frequencies (<5).
Can I run a binary logistic regression? Are the results reliable?
Update:
I have no categories with 0 patients, only some with only 1 or 2 patients. So I ran the regression and SPSS gives me the output above. Can I say that TRTCD2 and QSORRES are statistically significant? And that the p value or 1 or almost 1 are due to the small frequencies in this group?
• I edited your question. I assume that you switched dependent (the variable you want to explain) and independent variables (the variables that do the explaining). Correct me if I am wrong. – Maarten Buis Mar 21 '16 at 10:33
• You can say it is significant based on the P values...but we usually like to check for multicollinearty and reduce the number of predictors before assessing significance. I would suggest providing more information about your hypotheses and predictors. You should also note that some people do not consider Wald tests to be reliable and if you have a particular hypothesis in mind, you might be better off comparing nested models using a likelihood ratio test. – coreydevinanderson Dec 16 '17 at 3:11
At the heart of binary logistic regression is the estimation of the probability of an event. As detailed in RMS Notes 10.2.3 the minimum sample size needed just to estimate the intercept in a logistic model is 96 and that still results in a not great margin of error of +/- 0.1 in the estimated (constant) probability of event. If you had a single binary predictor the minimum sample size is 96 per each of the levels. So your sample size is insufficient for the task at hand. Not that p-values do not help this situation in any way.
Let's start with the easy case: If an independent variable has 0 people in one category, that category can't add anything to the model as ... well, there is nothing to model.
When categories have small numbers (but not 0), the standard errors tend to be large. E,g,
set.seed(123)
age <- rnorm(100, 25, 10)
catvar <- c("A", rep("B", 99))
depvar <- c(rep(0, 50), rep(1, 50))
mod1 <- glm(depvar~age + catvar, family = "binomial")
summary(mod1)
• – erica Mar 21 '16 at 12:04
• That seems logic. I have no categories with 0 patients, only some with only 1 or 2 patients. So I ran the regression and SPSS gives me the output above. Can I say that TRTCD2 and QSORRES are statistically significant. And that the p value or 1 or almost 1 are due to the small frequencies in this group? – erica Mar 21 '16 at 12:04 | 2019-08-22 09:46:52 | {"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": 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": 0.718084454536438, "perplexity": 737.8229540413432}, "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-2019-35/segments/1566027317037.24/warc/CC-MAIN-20190822084513-20190822110513-00100.warc.gz"} |
https://pos.sissa.it/336/077/ | Volume 336 - XIII Quark Confinement and the Hadron Spectrum (Confinement2018) - B: Light quarks
Chiral symmetry breaking corrections to thepseudoscalar pole contribution of the HadronicLight-by-Light piece of $a_\mu$
A.E. Guevara Escalante*, P. Roig Garcés and J.J. Sanz-Cillero
Full text: pdf
Pre-published on: September 12, 2019
Published on: September 26, 2019
Abstract
We have studied the $P\to\gamma^\star\gamma^\star$ form factor in Resonance Chiral Theory, with $P = \pi^0\eta\eta'$, to compute the contribution of the pseudoscalar pole to the hadronic light-by-light piece of the anomalous magnetic moment of the muon. In this work we allow the leading $U(3)$ chiral symmetry breaking terms, obtaining the most general expression for the form factor up to $\mathcal{O}(m_P^2)$. The parameters of the Effective Field Theory are obtained by means of short distance constraints on the form factor and matching with the expected behavior from QCD. Those parameters that cannot be fixed in this way are fitted to experimental determinations of the form factor within the spacelike region. Chiral symmetry relations among the transition form factors for $\pi^0,\eta$ and $\eta'$ allow for a simultaneous fit to experimental data for the three mesons. This shows an inconsistency between the BaBar $\pi^0$ data and the rest of the experimental inputs. Thus, we find a total pseudoscalar pole contribution of $a_\mu^{P,HLbL}=(8.47\pm 0.16)\cdot 10^{-10}$ for our best fit (that neglecting the BaBar $\pi^0$ data). Also, a preliminary rough estimate of the impact of NLO in $1/N_C$ corrections and higher vector multiplets (asym) enlarges the uncertainty up to $a_\mu^{P,HLbL}=(8.47\pm 0.16_{\rm stat}\pm 0.09_{N_C}{}^{+0.5}_{-0.0_{\rm asym}})10^{-10}$.
DOI: https://doi.org/10.22323/1.336.0077
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access | 2023-02-09 13:10:51 | {"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": 0.7227585911750793, "perplexity": 1112.1104069590078}, "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-2023-06/segments/1674764499966.43/warc/CC-MAIN-20230209112510-20230209142510-00639.warc.gz"} |
https://space.stackexchange.com/questions/15518/how-to-construct-b-drag-term-in-tle | # How to construct $B^*$ drag term in TLE?
Is it possible to calculate $B^*$ term in TLE data using only a few or more velocity and position vectors for a satellite?
Dwight E. Andersen claims that its an impossible task in his thesis "Computing Norad Mean Elements From a State Vector" (1994)
An extension of this [calculating other TLE elements than drag and mean motion] would be to compute, from just the state, the mean elements and the drag terms and B* in SGP4, SDP4, SGP8, and SDP8. Future research on satellite drag and methods of estimating the drag would be valuable. Since the drag term is a function of the physical geometry as well as atmospheric conditions, some aspects of the satellites' physical characteristics would be needed. | 2019-08-25 03:05:00 | {"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": 0.6612298488616943, "perplexity": 1365.2737986100071}, "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-2019-35/segments/1566027322170.99/warc/CC-MAIN-20190825021120-20190825043120-00209.warc.gz"} |
https://mailman.ntg.nl/pipermail/ntg-context/2014/078469.html | # [NTG-context] hyperlinks within a PDF
Robert Zydenbos context at zydenbos.net
Mon Jun 16 03:11:09 CEST 2014
Forgive me for what must seem a beginners’ question, but I really could not find the solution in the documentation or the Wiki:
How do I create hyperlinks within a PDF to another spot in the text of that same PDF? I had expected I could do something like: | 2022-01-29 13:58:21 | {"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": 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": 0.9194709658622742, "perplexity": 1477.1856170955118}, "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/1642320306181.43/warc/CC-MAIN-20220129122405-20220129152405-00558.warc.gz"} |
https://math.stackexchange.com/questions/3684353/lipschitz-constant-of-continuous-and-piecewise-linear-functions | # Lipschitz constant of continuous and piecewise linear functions
I want to calculate the Lipschitz constant of a continuous and piecewise linear function $$f:[0,1]^2\rightarrow R$$, like this \begin{equation*} f(x_1,x_2)=\left\{ \begin{aligned} 2x_1+x_2, &\quad\text{if} \quad x_1+x_2\leq 1\\ x_1+1, &\quad\text{if} \quad x_1+x_2>1 \end{aligned} \right. \end{equation*} I guess it is equal to the greatest Lipschitz constant among all pieces. Is there any textbook that contain related theorem?
• Yes, but also check the case in which one point is in each piece. May 20, 2020 at 22:29
• @Ramita I don't know how to prove it. I'm looking for a textbook on this issue. May 20, 2020 at 22:33
• There is no well known theorem but it is not difficult to prove either. For the above it is $\sqrt{5}$ with the Euclidean norm. May 20, 2020 at 22:36
• @copper.hat I find a theorem of the vector-valued form for this issue, threesquirrelsdotblog.com/2018/03/16/…, and I feel the proof not easy. I want to cite such results, but I can not find any textbook that contain this issue. And it is not proper for me to cite a website. May 21, 2020 at 10:37
Note that $$f(x_1,x_2) = \min (2 x_1+x_2,x_1+1)$$.
To see that the $$\min$$ of Lipschitz functions is Lipschitz:
Suppose $$f_1,...,f_m$$ are Lipschitz with rank $$L$$, then $$f_k(x)-f_k(y) \le L \|x-y\|$$ for all $$k,x,y$$. Then $$\min_i f_i(x)-f_k(y) \le L \|x-y\|$$ and choosing $$k$$ such that $$\min_j f_j(y) = f_k(y)$$ we see that $$\min_i f_i(x)-\min_j f_j(y) \le L \|x-y\|$$. Swapping $$x,y$$ shows that $$\min_k f_k$$ is Lipschitz with rank $$L$$. (This result is true more generally, but the finite case contains the basic idea.)
Note that $$x \mapsto 2x_1+x_2$$ has Lipschitz rank $$\sqrt{5}$$ and $$x \mapsto x_1+1$$ has Lipschitz rank $$1$$, so the smallest $$L$$ that will work is $$L= \max(1,\sqrt{5})$$. | 2022-10-06 14:01:38 | {"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": 21, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9352271556854248, "perplexity": 245.17373969164993}, "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/1664030337836.93/warc/CC-MAIN-20221006124156-20221006154156-00236.warc.gz"} |
http://rpg.stackexchange.com/questions/30843/how-do-psion-at-will-powers-work | # How do Psion At-Will Powers work?
Where can I find the list of Psion Powers? I know where the At-Wills, Encounters, etc. are, but where are the powers upon which I can spend power points?
I'm a fairly green DM, and this is my first tango with a Psion, I suppose an added question would be, do Psions have anything akin to a spellbook, and if so, how does it work?
- | 2016-07-01 04:26:24 | {"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": 0.8850420713424683, "perplexity": 3141.3183206900885}, "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-2016-26/segments/1466783400031.51/warc/CC-MAIN-20160624155000-00130-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://www.albert.io/ie/sat-physics-subject-test/playground-ride-acceleration | ?
Free Version
Moderate
Playground Ride Acceleration
SATPHY-EMKXYJ
The picture below shows a child (small brown circle) from above on a playground ride (large blue circle) that spins horizontally. The red arrows show the direction of rotation of the ride.
The ride is NOT rotating at constant speed, but is slowing down.
Which of the following arrows best represents the direction of the acceleration of the child at the location in the picture?
A
$\rightarrow$
B
$\searrow$
C
$\uparrow$
D
$\nearrow$
E
$\downarrow$ | 2016-12-07 22:12:38 | {"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": 0.526807963848114, "perplexity": 1382.0565637437571}, "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-2016-50/segments/1480698542250.48/warc/CC-MAIN-20161202170902-00145-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://byjus.com/free-gre-prep/gre-general-test/ | # GRE General Test- An Introduction
The Graduate Record Examination (GRE) is the only test that any person needs to take for admissions into graduate or business schools abroad. The GRE General test evaluates candidate’s skills in Verbal Reasoning, Quantitative Reasoning and Analytical Writing. Prospective students wanting to do a Masters, MBA or a Doctorate degree, need to take this test, as it forms a major part of the application to the universities. The GRE General test provides a common platform to assess all the students qualification through a single measure.
## GRE Revised General Test
The GRE revised General test is just a revamped version of the old GRE General test. The new GRE test moved to a new scoring system, effectively replacing the old method of scoring between 200-800 with scores between 130-170 marks with one mark increments for right answers. The Verbal and Quantitative Reasoning sections are now scored between 130 – 170 marks while the Analytical Writing is scored between 0 – 6 with half mark increments. The test also allows candidates to go back to questions previously skipped or change the answers to previous questions. The revised GRE test also introduced the adaptive test format.
## The Official Guide to GRE Test
ETS provides the candidates with a few free preparation guides. The POWERPREP Online is a tool which can be used to simulate the GRE Computer-based test and it is available for two attempts. The Practice Test for Paper-delivered GRE General Test can be used as a preparation for the paper-based test. The Math Review is a free document that revises the math concepts which are important for the GRE test. Apart from the free materials, there are more paid preparation materials which can be brought. However, there are a number of free GRE apps which are easily available online among which – BYJU’S GRE Learning App is the leading provider of app based study; the app can be downloaded from Google Play Store and App Store.
The GRE General test costs US$205 irrespective of the type of test the candidate chooses, viz. Computer-based or Paper-based. In terms of Indian Rupee, the GRE test costs approximately INR. 13330. ## GRE General Test Syllabus Section Syllabus Verbal Reasoning Syllabus Basic sentence structure, verb tense, idioms and idiomatic expression, pronoun agreement, subject verb agreement, modifiers, parallelism, great vocabulary Quantitative Reasoning Syllabus Number, percentage, profit and loss, ratio and proportion, simple and compound interest, speed distance and time, permutation and combination, linear equation, quadratic equation, set theory, statistics, powers and roots, probability, work and time, geometry, coordinate geometry, mensuration Analytical Writing Syllabus Basic sentence structure ## GRE General Test vs GRE Subject Test Bases GRE General Test GRE Subject Test Purpose Entry to Graduate, Business or Doctoral degree Entry to technical graduate programs Required by Graduate or Business schools Scientific and technical universities or individual dept. Adaptive Computer adaptive test, paper-based Paper based test Duration 3 hours 45 minutes 2 hours and 50 minutes Fees US$205 US\$150
Test contents Verbal, Quant and AWA Specific specialization in the 7 subjects like: Biochemistry, Cell and Molecular Biology
Biology
Chemistry
Literature in English
Mathematics
Physics
Psychology
BYJU’S will be glad to help you in your GRE preparation journey. You can ask for any assistance related to GRE from us by just giving a missed call at +918884544444, or you can drop an SMS. You can write to us at gre@byjus.com. | 2019-01-16 22:41:44 | {"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": 0.17100602388381958, "perplexity": 2370.7846658353633}, "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/1547583657907.79/warc/CC-MAIN-20190116215800-20190117001800-00124.warc.gz"} |
http://mathhelpforum.com/geometry/88554-volume-pentagonal-prism.html | # Math Help - Volume of a pentagonal prism
1. ## Volume of a pentagonal prism
Find the volume of a regular pentagonal prism with a height of 5 feet and a perimeter of 20 feet
Is there an easier way to find the area of the prism with out finding the area of the base then multiply by the height.
to find the area of the base i did it (4^2*5)/(4tan(pi/5) can this be done easier?
Thank you | 2015-07-01 21:15:59 | {"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": 0.8821679949760437, "perplexity": 339.3300551184586}, "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-2015-27/segments/1435375095270.70/warc/CC-MAIN-20150627031815-00124-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/239470/uniform-approximation-of-a-continuous-flow-by-a-mathcalc1-flow | # Uniform approximation of a continuous flow by a $\mathcal{C}^1$ flow
Setup: Consider a (smooth) compact Riemannian manifold $M$, whose distance is denoted by $d$. Let $\Phi$ be a continuous flow, namely a continuous application from $\mathbb{R} \times M$ to $M$ satisfying:
• $\forall t \in \mathbb{R}, \Phi(t,\cdot) \in \text{Homeo}(M)$
• $\forall t,s \in \mathbb{R}, \Phi(t+s,\cdot) = \Phi(t,\Phi(s,\cdot))$
We consider the following $\mathcal{C}^0$ metric on continuous flows: $$\delta(\Phi,\Psi) = \sup_{t \in [0,1],x \in M} d(\Phi(t,x),\Psi(t,x))$$
Question: Is it possible to approximate a $\mathcal{C}^0$ flow by a $\mathcal{C}^1$ flow (or even $\mathcal{C}^{\infty}$) in the $\mathcal{C}^0$ topology ? In other words, given a $\varepsilon > 0$, is there a $\mathcal{C}^1$ flow $\Psi$ such that $\delta(\Phi,\Psi) < \varepsilon$ ?
I know (from http://arxiv.org/abs/0901.1002) that this result is far from being trivial for homeomorphisms. It is true in dimension $\leq 3$ (any homeomorphism can be uniformly approximated by a diffeomorphism) and in dimension $\geq 5$ if and only if the homeo is isotopic to a diffeo. Apparently, it is still open in dimension $4$. In particular, this shows, that any element $\Phi^t$ of a continuous flow can be individually uniformly approximated by a diffeo, but this doesn't answer the question.
I have tried to look up for a reference in literature, but I couldn't find any. Has anyone any idea and/or reference on the question ? | 2019-03-23 03:29:17 | {"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": 0.9622950553894043, "perplexity": 145.41048008993005}, "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-2019-13/segments/1552912202711.3/warc/CC-MAIN-20190323020538-20190323042538-00455.warc.gz"} |
https://socratic.org/questions/a-customer-in-a-computer-store-can-choose-one-of-four-monitors-one-of-three-keyb | # A customer in a computer store can choose one of four monitors, one of three keyboards, and one of five computers. How do you determine the number of possible system configurations?
Dec 31, 2017
60
#### Explanation:
Given:
Monitors: 1 of 4
Keyboards: 1 of 3
Computers: 1 of 5
Notice the pattern:
I can pair 4 monitors with first keyboard. Then once more 4 monitors but now with the second keyboard. Then again with the third keyboard.
That is $4 + 4 + 4 = 12$ or Monitors $\times$ Keyboard=4*3=12
If we include computers into the pattern we get:
Monitors x Keyboards x Computers$= 4 \times 3 \times 5 = 60$
We have 60 different possibilities of choosing monitors, keyboards and computers. | 2020-07-09 04:39:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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": 0.4214193522930145, "perplexity": 4130.600526406655}, "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-2020-29/segments/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00380.warc.gz"} |
http://www.solutioninn.com/civil-engineers-believe-that-w-the-amount-of-weight-in | Question
Civil engineers believe that W, the amount of weight (in units of 1000 pounds) that a certain span of a bridge can withstand without structural damage resulting, is normally distributed with mean 400 and standard deviation 40. Suppose that the weight (again, in units of 1000 pounds) of a car is a random variable with mean 3 and standard deviation .3. Approximately how many cars would have to be on the bridge span for the probability of structural damage to exceed .1?
Sales0
Views25 | 2016-10-22 09:59:42 | {"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": 0.9094549417495728, "perplexity": 176.67718601384175}, "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-2016-44/segments/1476988718866.34/warc/CC-MAIN-20161020183838-00017-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/show-me-a-derivation-of-the-bke.83059/ | # Show me a derivation of the BKE
For any of you advanced dynamics people, can you please show me a derivation of the BKE. (Basic Kinematic Equation)
The BKE is.....
e d/dt(Vector) = u d/dt(Vector) + omega between e and u X (Vector)
sometimes an additional term is added which is the linear velocity between the frames but for some simplicity lets assume this is zero.
e is the inertial frame
and u is the working frame
omega is the angular velocity
X is the cross product operator
I know just by looking at a simple single rotation problem, the solution is trivial but does anyone know of a formal proof?
FredGarvin | 2021-08-02 00:45:46 | {"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": 0.8439816236495972, "perplexity": 1256.6108203630502}, "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-2021-31/segments/1627046154277.15/warc/CC-MAIN-20210801221329-20210802011329-00005.warc.gz"} |
https://answers.ros.org/question/276307/how-to-share-common-libs-in-ros-workspace/ | # How to share common lib's in ROS workspace
I'm having several packages in my workspace and I'm currently at the point where a want to avoid code duplicity. At the moment I have package called myproject_common in which all msg and srv files are located. After building the workspace they are properly available in all my other packages. Now I want to my common .py files into the common packages and also make them available. After calling catkin_make the msg and srv classes are available under ./devel/lib/python2.7/dist-packages/ which is quiet nice because this makes them also available in my IDE without the need to import something manually. How can I accomplish this with self written common python files? What do I need to change in my CMakeLists.txt to get this working
edit:
I separated the msg / srv from the common modules, because the msg / srv stuff work fine so now my pkg with the shared modules is named myproject_common_lib
this is my directory structure
myproject_common_lib
├── CMakeLists.txt
├── package.xml
├── setup.py
└── src
└── myproject_common_lib
├── coordinate.py
├── coordinate.pyc
└── __init__.py
2 directories, 6 files
The content of my __init__.py looks like this
from coordinate import Coordinate
The content of my setup.py
## ! DO NOT MANUALLY INVOKE THIS setup.py, USE CATKIN INSTEAD
from distutils.core import setup
from catkin_pkg.python_setup import generate_distutils_setup
# fetch values from package.xml
setup_args = generate_distutils_setup(
packages=['myproject_common_lib'],
package_dir={'': 'src'},
)
setup(**setup_args)
The content of my CMakeLists.txt
cmake_minimum_required(VERSION 2.8.3)
project(myproject_common_lib)
find_package(catkin REQUIRED COMPONENTS
rospy
)
catkin_python_setup()
catkin_package()
include_directories(
$(catkin_INCLUDE_DIRS) ) When I want to import the shared module I use the following import (which does not work) from myproject_common_lib.coordinate import Coordinate The content of my devel folder looks like this (short version) devel ├── lib │ └── python2.7 │ └── dist-packages │ └── myproject_common_lib │ ├── __init__.py │ └── __init__.pyc └── share ├── myproject_common_lib │ └── cmake │ ├── myproject_common_libConfig.cmake │ └── myproject_common_libConfig-version.cmake I cannot see any difference to the posted tutorial. Also when watching this video I cannot see any difference :-( edit 2: This is what PyCharm sees edit retag close merge delete ## 1 Answer Sort by » oldest newest most voted You have to write Python modules (= libraries) and declare them, see this tutorial. So your modules will be available from your other packages and you will be able to import them using: import myproject_common.my_module more ## Comments When I follow the tutorial it works for the script but it does not work for my modules. The import cannot be found. The error I get is Cannot find reference 'coordinate' in '__init__.py', which comes from PyCharm ( 2017-11-20 10:26:22 -0500 )edit Did you add an __init__.py file to the directory that contains your libraries/modules? ( 2017-11-20 11:54:22 -0500 )edit @jayess and @rreignier I updated my post with more information. Actually I cannot see any difference between my stuff and the provided tutorial ( 2017-11-21 02:22:37 -0500 )edit I found the error in the CMakeLists.txt the $(catkin_INCLUDE_DIRS) part must be written with {}
( 2017-11-21 09:03:51 -0500 )edit | 2021-08-02 04:04:53 | {"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": 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": 0.18970030546188354, "perplexity": 9398.80822291755}, "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-2021-31/segments/1627046154302.46/warc/CC-MAIN-20210802012641-20210802042641-00402.warc.gz"} |
https://www.physicsforums.com/threads/problem-resolving-url.729173/ | Problem resolving url
I encountered a strange problem resolving the url of a repository.
I am running opensuse 12.1 and firefox.
The repository of opensuse I want to browse is
however I am told that it does not exist.
When I surf to
avr is shown but I also get a link does not exist when I click on it.
However it works from another computer (windows).
Any ideas?
Mentor
Try: Flush the DNS cache on the ubuntu box & windows. Somebody is out of sync. Is the DNS server local?
Code:
sudo /etc/init.d/dns-clean restart
windoze: from cmd.exe window --
Code:
ipconfig /flushdns
Do you get a 404 error? Usually the system will tell you it cannot connect to the site. Meaning it does resolve but the physical server is not responding.
I tried out a couple of things in the meanwhile, including restarting both the router and the computer.
First, the url is correctly resolved when starting the computer under windows.
Under opensuse, when I click on "/avr" on the page | 2022-12-05 10:46:40 | {"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": 0.41815176606178284, "perplexity": 3391.6783257902875}, "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-2022-49/segments/1669446711016.32/warc/CC-MAIN-20221205100449-20221205130449-00687.warc.gz"} |
https://hiphive.materialsmodeling.org/moduleref/cluster_space.html | # Cluster space¶
class hiphive.ClusterSpace(prototype_structure, cutoffs, sum_rules=True, symprec=1e-05, length_scale=0.1)[source]
Primitive object handling cluster and force constants for a structure.
Parameters: prototype_struture (ASE Atoms object) – prototype structure; spglib will be used to find a suitable cell based on this structure. cutoffs (list) – cutoff radii for different orders starting with second order sum_rules (bool) – If True the aucostic sum rules will be enforced by constraining the parameters. symprec (float) – numerical precision that will be used for analyzing the symmetry (this parameter will be forwarded to spglib) length_scale (float) – This will be used as a normalization constant for the eigentensors
Examples
To instantiate a ClusterSpace object one has to specify a prototype structure and cutoff radii for each cluster order that should be included. For example the following snippet will set up a ClusterSpace object for a BCC structure including second order terms up to a distance of 5 A and third order terms up to a distance of 4 A.
>>> from ase.build import bulk
>>> prim = bulk('W')
>>> cs = ClusterSpace(prim, [5.0, 4.0])
atom_list
AtomList – The atoms within the cutoff from the center cell
cluster_list
ClusterList – Contains the clusters possible within the cutoff
copy()[source]
cutoffs
Cutoffs obj – The cutoffs used for construcring the cluster space
get_sum_rule_constraint_matrices(symbolic=True, rotational=False)[source]
Return the constraint matrices needed for imposing the (acoustic=translational) sum rule.
Returns: dictionary of constraint matrices, where the key is the order of the respective constraint matrix dict
length_scale
float – The normalization of the force constants
number_of_dofs
int – The number of free parameters in the model
If the sum rules are not enforced the number of DOF is the same as the total number of eigentensors in all orbits
orbit_data
list – list of dictionaries containing detailed information for each orbit, e.g. cluster radius and atom types.
orbits
list of Orbit objects – The orbits of the structure
permutations
list of vectors – lookup for permutation references
prim
Atoms – the structure of the lattice
print_orbits()[source]
Prints a list of all orbits.
read(f)[source]
Load a ClusterSpace instance from file
Parameters: f (string or file object) – name of input file (string) or stream to load from (file object)
rotation_matrices
list of 3x3 matrices – The rotation for each symmetry
spacegroup
str – The space group of the lattice obtained from spglib
sum_rules
bool – whether the sum rules are enforced
symprec
float – The symprec value used when constructing the cluster space
translation_vectors
list of 3-vectors – the translation for each symmetry
write(fileobj)[source]
Saves to file or to a file-like object
The instance is saved into a custom format based on tar-files. The resulting file will be a valid tar file and can be browsed by by a tar reader. The included objects are themself either pickles, npz or other tars.
Parameters: fileobj (str or file-like obj) – If the input is a string a tar archive will be created in the current directory. If not a string the input must be a valid file like obj.
wyckoff_sites
The wyckoff sites in the primitive cell | 2018-04-21 11:41:30 | {"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": 0.3444492816925049, "perplexity": 2831.7749937331696}, "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-2018-17/segments/1524125945143.71/warc/CC-MAIN-20180421110245-20180421130245-00083.warc.gz"} |
https://electronics.stackexchange.com/questions/353253/what-kind-of-signal-processing-circuitry-do-i-need-to-generate-a-line-level-outp | # What kind of signal processing circuitry do I need to generate a line level output on an Arduino?
I am trying to create an Arduino based music synthesizer. How can I safely generate line level output (+/- 2 volts centered at zero, with a frequency range from 20Hz-20KHz) from my Arduino using a minimal number of components? This is what I imagine the flow will look like, but please correct me if this is wrong.
• Generate a sine wave tone using a DAC (I'm doing this already using MCP4725)
• Level shift the signal -2.5 volts and lower gain
• To perform level shifting I think I need to generate a negative 5 volts to supply to a dual supply op amp, but I'm not sure if this is correct
There is a lot of confusing/mixed information on line level requirements. I hooked up the output jack of my macbook pro to an oscilloscope and generated a square wave. It looks like the macbook pro puts out -2 to 2 volts, so I think this is where my target output voltage should be.
Edit: My target output voltage is 1.25VRMS, since I am using a QSC PLX3602 amplifier with an input sensitivity of 1.25VRMS.
Some questions:
• How many milliamps do I need to be able to source for line level
• Given that I am going to be outputting square waves (which can sometimes damage speakers), is there anything I should keep in mind? I am planning on matching my amplifiers RMS wattage rating with the speakers RMS rating. Do square waves produce higher current than RMS?
• Can anyone recommend a schematic or components I can use to accomplish the signal conditioning needed to do this safely/without damaging audio equipment?
• – Transistor Jan 31 '18 at 18:41
To perform level shifting I think I need to generate a negative 5 volts to supply to a dual supply op amp, but I'm not sure if this is correct.
It's much simpler than that. Just add a DC blocking capacitor in series with the output. We'll calculate the value in a moment.
It looks like the macbook pro puts out -2 to 2 volts, so I think this is where my target output voltage should be.
See Wikipedia's Line leve for more on this but that will be plenty.
How many milliamps do I need to be able to source for line level?
Use Ohm's law. You'll need to find the input impedance of what you are driving but it's usually > 10k so current drain won't be a problem.
Given that I am going to be outputting square waves (which can sometimes damage speakers), is there anything I should keep in mind? I am planning on matching my amplifiers RMS wattage rating with the speakers RMS rating. Do square waves produce higher current than RMS?
You're getting mixed up. An RMS measurement allows comparison between different waveforms. If they have the same RMS value then they will have the same heating effect or power as each other or a DC current of the same value.
The problem with squarewaves is that they are high in harmonic content and, theoretically, these continue up to infinity. You can get an understanding of this from the Fourier transform of a squarish wave.
Figure 1. Fourier transform from time domain to frequency domain. Source: unknown to me.
Can anyone recommend a schematic or components I can use to accomplish the signal conditioning needed to do this safely/without damaging audio equipment?
simulate this circuit – Schematic created using CircuitLab
The capacitor and amplifier input will form a high-pass filter. (Think: it blocks DC which is 0 Hz.) The cut-off value is determined by $f_c = \frac {1}{2 \pi RC}$. You can read more and find a calculator on Learning Electronics.
• My amplifier's input sensitivity is 1.25 Vrms at 8 ohms. Does this mean I need to be able to source 156 mA (1.25/8)*1000? – circuitry Jan 31 '18 at 19:06
• Surely the 8 Ω refers to the amplifier output impedance? – Transistor Jan 31 '18 at 19:24
• Hmm I'm looking at qsc.com/resource-files/productresources/amp/plx2/…, for PLX3602. It says "input sensitivity at 8 ohms", but it also says "input impedance 10 kohms unbalanced, 20 kohms balanced." – circuitry Jan 31 '18 at 19:31
• In that event it seems like I would do (1.25/10k)*1000, and the current would be 0.125 mA. I am going to be driving a 4 ohm speaker though so I'm not sure if that would change things. – circuitry Jan 31 '18 at 19:33
• That figure is telling you that you will get the rated output into 8 Ω speakers with that level on the 10 kΩ input. Your ear has a logarithmic response to volume. Double the volume requires ten times the power. Turn the volume down and plug it in. Given that you're generating the sound from an Arduino I'd say you or your audience aren't going to listen to it for very long so I wouldn't waste too much time on the calculations. – Transistor Jan 31 '18 at 19:36 | 2019-10-22 04:06:22 | {"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": 0.45671820640563965, "perplexity": 1048.7583174943145}, "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/1570987798619.84/warc/CC-MAIN-20191022030805-20191022054305-00111.warc.gz"} |
https://nips.cc/Conferences/2019/ScheduleMultitrack?event=14131 | `
Timezone: »
Poster
Communication-Efficient Distributed Blockwise Momentum SGD with Error-Feedback
Shuai Zheng · Ziyue Huang · James Kwok
Thu Dec 12 05:00 PM -- 07:00 PM (PST) @ East Exhibition Hall B + C #211
Communication overhead is a major bottleneck hampering the scalability of distributed machine learning systems. Recently, there has been a surge of interest in using gradient compression to improve the communication efficiency of distributed neural network training. Using 1-bit quantization, signSGD with majority vote achieves a 32x reduction in communication cost. However, its convergence is based on unrealistic assumptions and can diverge in practice. In this paper, we propose a general distributed compressed SGD with Nesterov's momentum. We consider two-way compression, which compresses the gradients both to and from workers. Convergence analysis on nonconvex problems for general gradient compressors is provided. By partitioning the gradient into blocks, a blockwise compressor is introduced such that each gradient block is compressed and transmitted in 1-bit format with a scaling factor, leading to a nearly 32x reduction on communication. Experimental results show that the proposed method converges as fast as full-precision distributed momentum SGD and achieves the same testing accuracy. In particular, on distributed ResNet training with 7 workers on the ImageNet, the proposed algorithm achieves the same testing accuracy as momentum SGD using full-precision gradients, but with $46\%$ less wall clock time. | 2022-01-22 08:04:43 | {"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": 0.5916031002998352, "perplexity": 1248.3106440096965}, "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-2022-05/segments/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00005.warc.gz"} |
https://www.proofwiki.org/wiki/Definition:Unbounded_Divergent_Complex_Sequence | # Definition:Unbounded Divergent Sequence/Complex Sequence
## Definition
Let $\sequence {z_n}$ be a sequence in $\C$.
Then $\sequence {z_n}$ tends to $\infty$ or diverges to $\infty$ if and only if:
$\forall H > 0: \exists N: \forall n > N: \cmod {z_n} > H$
where $\cmod {z_n}$ denotes the modulus of $z_n$.
We write:
$x_n \to \infty$ as $n \to \infty$. | 2022-08-09 07:06:15 | {"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": 0.9991110563278198, "perplexity": 417.69526363737356}, "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/1659882570913.16/warc/CC-MAIN-20220809064307-20220809094307-00412.warc.gz"} |
https://projecteuclid.org/euclid.aoms/1177706261 | ## The Annals of Mathematical Statistics
### K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests
J. Kiefer
#### Abstract
The main purpose of this paper is to obtain the limiting distribution of certain statistics described in the title. It was suggested by the author in [1] that these statistics might be useful for testing the homogeneity hypothesis $H_1$ that $k$ random samples of real random variables have the same continuous probability law, or the goodness-of-fit hypothesis $H_2$ that all of them have some specified continuous probability law. Most tests of $H_1$ discussed in the existing literature, or at least all such tests known to the author before [1] in the case $k > 2$, have only been shown to have desirable consistency or power properties against limited classes of alternatives (see e.g., [2], [3], [4] for lists of references on these tests), while those suggested here are shown to be consistent against all alternatives and to have good power properties. Some test statistics whose distributions can be computed from known results are also listed.
#### Article information
Source
Ann. Math. Statist., Volume 30, Number 2 (1959), 420-447.
Dates
First available in Project Euclid: 27 April 2007
https://projecteuclid.org/euclid.aoms/1177706261
Digital Object Identifier
doi:10.1214/aoms/1177706261
Mathematical Reviews number (MathSciNet)
MR102882
Zentralblatt MATH identifier
0134.36707
JSTOR | 2019-07-18 13:12:31 | {"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": 0.5001745820045471, "perplexity": 766.0438414086406}, "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/1563195525634.13/warc/CC-MAIN-20190718125048-20190718151048-00093.warc.gz"} |
https://www.albert.io/learn/waves-and-sounds/question/freezing-a-sine-wave-with-strobe-light | Limited access
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A stroboscope illuminates a continuous sine wave of wavelength $\lambda$ m traveling on a long string. When the strobe is flashing at a frequency of $F$ Hz the wave on the string no longer seems to be moving--the fixed sine shape of the wave appears stationary. What expression below correctly predicts the possible value or values of the wave speed, $v$, on the string?
A
$v = \cfrac{\lambda} {F}$ is the only value for the speed.
B
$v = F \lambda$ is the only value for the speed.
C
$v = n \lambda F$ where $n$ = any positive integer.
D
$v = n \lambda F$ where $n$ = any non-zero integer positive or negative.
E
$v = n \lambda F$ where $n$ = any odd integer.
Accuracy 0%
Select an assignment template | 2017-03-24 17:58:52 | {"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": 0.4265153110027313, "perplexity": 1882.1924595335943}, "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/1490218188550.58/warc/CC-MAIN-20170322212948-00130-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://agenda.infn.it/event/12464/contributions/14396/ | # SPIN 2018
9-14 September 2018
University of Ferrara
Europe/Rome timezone
23RD INTERNATIONAL SPIN SYMPOSIUM
## Electric dipole moment searches using storage rings
10 Sep 2018, 12:10
40m
Teatro Nuovo - Piazza Trento e Trieste, 52
#### Teatro Nuovo - Piazza Trento e Trieste, 52
Piazza Trento e Trieste, 52
Plenary Sessions (for INVITED PLENARY TALKS only!) Fundamental Symmetries and Spin Physics Beyond the Standard Model
### Speaker
Dr Frank Rathmann (Forschungszentrum Jülich)
### Description
The Standard Model (SM) of Particle Physics is not capable to account for the apparent matter-antimatter asymmetry of our Universe. Physics beyond the SM is required and is either probed by employing highest energies (e.g., at LHC), or by striving for ultimate precision and sensitivity (e.g., in the search for electric dipole moments). Permanent electric dipole moments (EDMs) of particles violate both time reversal $(T)$ and parity $(P)$ invariance, and are via the $CPT$-theorem also $CP$-violating. Finding an EDM would be a strong indication for physics beyond the SM, and pushing upper limits further provides crucial tests for any corresponding theo\-retical model, e.g., SUSY. Up to now, EDM searches focused on neutral systems (neutrons, atoms, and molecules). Storage rings, however, offer the possibility to measure EDMs of charged particles by observing the influence of the EDM on the spin motion in the ring~\cite{Eversmann:2015jnk, PhysRevAccelBeams.20.072801, PhysRevAccelBeams.21.042002}. Direct searches of proton and deuteron EDMs bear the potential to reach sensitivities beyond $\SI{e-29}{e.cm}$. Since the Cooler Synchrotron COSY at the Forschungszentrum J\"ulich provides polarized protons and deuterons up to momenta of 3.7 GeV/c, it constitutes an ideal testing ground and starting point for such an experimental programme. The talk will present the JEDI plans for the measurement of charged hadron EDMs and discuss recent results.
### Primary author
Dr Frank Rathmann (Forschungszentrum Jülich)
Slides | 2020-10-26 21:42:29 | {"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": 0.33993837237358093, "perplexity": 7678.280426510202}, "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/1603107892062.70/warc/CC-MAIN-20201026204531-20201026234531-00294.warc.gz"} |
https://content.ces.ncsu.edu/agricultural-subsurface-drainage-cost-in-north-carolina | NC State Extension Publications
Improving drainage of poorly drained soils improves trafficability for timely field operations. In addition, drainage improves crop yield by eliminating long periods of excess water. An important advantage of subsurface drains is that drainage occurs without taking land out of production. In North Carolina, subsurface drains are generally installed with closer spacing than typical open ditches. Subsurface drains, along with good surface drainage, effectively protect crops from excessive soil water conditions.
Subsurface drainage cost in North Carolina can vary greatly depending on location and is highly dependant on soil properties. The most important soil property affecting the cost per acre for drainage installation is soil texture, which determines the ability of the soil to move water both vertically and laterally. Figure 1 and Table 1 show the estimated costs of material and installation for subsurface drainage pipes in North Carolina with varying drain spacing. These cost estimates are based on 50 cents per linear foot of 4-inch perforated drains with fabric filter and average installation cost of 60 cents per linear foot. Installation cost may vary depending on the number of acres drained, drain depth, connections, system design, and ease of installation. The material cost of 4-inch drains may also vary depending on the supplier and whether fabric filters are included. A fabric filter prevents fine sands from entering and clogging the drains. You should choose the drain spacing that provides adequate drainage while avoiding unnecessary installation costs.
Figure 1. Estimated per acre subsurface drainage cost (50 cents per linear foot for 4-inch drains with fabric; 60 cents per linear foot for installation).
Table 1. Estimated per acre subsurface drainage cost (50 cents per linear foot for 4-inch drains with fabric; 60 cents per linear foot for installation)
Spacing $/ac 30$1,597 40 $1,198 50$958 60 $799 70$685 80 $599 90$532 Spacing $/ac 100$479 110 $436 120$399 130 $369 140$342 150 $319 160$299 Spacing $/ac 170$282 180 $266 190$252 200 $240 210$228 220 $218 230$208 Spacing $/ac 240$200 250 $192 260$184 270 $177 280$171 290 $165 300$160
# Authors
Assistant Professor and Extension Specialist
Biological & Agricultural Engineering
Professor
Biological & Agricultural Engineering
William Neal Reynolds and Distinguished University Professor Emeritus
Biological & Agricultural Engineering
Find more information at the following NC State Extension websites:
Publication date: Jan. 10, 2020
AG-871
N.C. Cooperative Extension prohibits discrimination and harassment regardless of age, color, disability, family and marital status, gender identity, national origin, political beliefs, race, religion, sex (including pregnancy), sexual orientation and veteran status. | 2020-07-07 20:23:01 | {"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": 0.3612617552280426, "perplexity": 12543.64822639708}, "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-2020-29/segments/1593655894904.17/warc/CC-MAIN-20200707173839-20200707203839-00081.warc.gz"} |
http://amplitudes.org/amplitudes/1507_01950/ | Paper and ancilary files.
Abstract:
Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the $A_n$ cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.
Tags:
Categories:
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http://webdice.rdcep.org/glossary/climate_model | ### Climate model
webDICE includes a model of how emissions of CO2 affect temperatures. The model has two components. The first is how carbon moves around the earth, between the oceans and the atmosphere. This component determines long emissions of CO2 stay in the atmosphere. The second is how the emissions that stay in the atmosphere increase temperatures. This latter component is called radiative forcing.
The model of how emission move around the earth assumes that emissions from economic activity are released into the atmosphere. Some of these emissions are absorbed by the upper layers of the ocean and from there into the lower ocean. The rate of absorption into the upper and lower ocean determines how long emissions stay in the atmosphere. There are no parameters choices for the climate model, but in Advanced Move, you can choose the default model, which is used in Nordhaus’s DICE models, or the ‘BEAM, simplified‘ model, which is a more accurate but slightly slower running model. (Optimization using BEAM may be particularly slow and possibly time out.) more
The default climate model in DICE simulates the carbon cycle using a linear there-reservoir model where the three reservoirs are the deep oceans, the upper ocean and the atmosphere. Each of these reservoirs is well-mixed in the short run. A transition matrix governs the transfer of carbon among the reservoirs. If $M_{i}(t)$, is he mass of carbon (gigatons) in reservoir $i$, then: $\left[\begin{array}{c} M_{AT}(t)\\ M_{UP}(t)\\ M_{LO}(t) \end{array}\right]=\left[\begin{array}{ccc} \phi_{11} & \phi_{12} & 0\\ 1-\phi_{11} & 1-\phi_{12}-\phi_{32} & \phi_{23}\\ 0 & \phi_{32} & 1-\phi_{23} \end{array}\right]\left[\begin{array}{c} M_{AT}(t-1)\\ M_{UP}(t-1)\\ M_{L0}(t-1) \end{array}\right]+\left[\begin{array}{c} E(t-1)\\ 0\\ 0 \end{array}\right],$ where the parameters $\phi_{i,j}$ represent the transfer rate from reservoir $i$ to reservoir $j$ (per time period), and $E(t)$ is emissions at time $t$. The model only includes CO2 in its emissions factor and atmospheric carbon concentration. Other greenhouse gases are assumed to be exogenous and enter the forcing equation separately. | 2018-01-20 15:04:59 | {"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": 2, "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": 0.6154309511184692, "perplexity": 1087.825432173136}, "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-2018-05/segments/1516084889660.55/warc/CC-MAIN-20180120142458-20180120162458-00767.warc.gz"} |
https://mathematica.stackexchange.com/questions/180416/mathematica-can-solve-the-eigenvalues-of-a-large-sparse-non-hermitian-non-symme | # Mathematica can solve the eigenvalues of a large sparse non-Hermitian (non-symmetrical) matrix?
The Arnoldi algorithms of function "Eigensystems" in Mathematica can be used to solve the eigenvalues of a Large Sparse non-Hermitian (non-symmetrical) Complex matrix?
• I'm not entirely sure what your question is. Are you asking if Arnoldi algorithms can be used to solve sparse matrix problems in Mathematica? If so, yes. See the Method section under the Options section on the documentation page for Eigensystem. – b3m2a1 Aug 22 '18 at 2:25
• Then the Arnoldi algorithms can be used for complex non-symmetrical matrix ? – Steven Aug 22 '18 at 5:37
• Yes, it can be used to compute few eigenvalues and eigenvectors. Why don't you just try it? – Henrik Schumacher Aug 22 '18 at 7:20 | 2020-10-29 22:41:00 | {"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": 0.6542541980743408, "perplexity": 837.4117111993513}, "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/1603107905965.68/warc/CC-MAIN-20201029214439-20201030004439-00139.warc.gz"} |
https://demo7.dspace.org/items/a0bf7e29-20ff-4513-a138-c4f644b7bd16 | ## String Equations of the q-KP Hierarchy
Tian, Kelei
He, Jingsong
Su, Yucai
Cheng, Yi
##### Description
Based on the Lax operator $L$ and Orlov-Shulman's $M$ operator, the string equations of the $q$-KP hierarchy are established from special additional symmetry flows, and the negative Virasoro constraint generators \{$L_{-n}, n\geq1$\} of the $2-$reduced $q$-KP hierarchy are also obtained.
Comment: 11pages
##### Keywords
Nonlinear Sciences - Exactly Solvable and Integrable Systems | 2022-12-05 15:26:04 | {"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": 0.8123407959938049, "perplexity": 9632.523544079437}, "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-2022-49/segments/1669446711017.45/warc/CC-MAIN-20221205132617-20221205162617-00833.warc.gz"} |
https://answerofmath.com/solved-when-are-correlated-normal-random-variables-multivariate-normal/ | # Solved – When are correlated Normal random variables multivariate Normal?
I know that there are many example of correlated normal random variables which are not jointly (multivariate) normal. However, are there conditions which state when correlated normal random variables are jointly normal?
Say I observe n univariate random variables $$X_1, dots, X_n$$ that are each $$N(mu, sigma^2)$$ with common correlation $$rho$$. Is it possible that these are jointly normal? If so, what are the conditions and how would I know if they are jointly normal.
Contents
Say I observe n univariate random variables $$X_1, dots, X_n$$ that are each $$N(mu, sigma^2)$$ with common correlation $$rho$$. Is it possible that these are jointly normal? If so, what are the conditions and how would I know if they are jointly normal.
There are no conditions based only on the marginal pdfs that can ensure joint normality. Let $$phi(cdot)$$ denote the standard normal density. Then, if $$X$$ and $$Y$$ have joint pdf $$f_{X,Y}(x,y) = begin{cases} 2phi(x)phi(y), & x geq 0, y geq 0,\ 2phi(x)phi(y), & x < 0, y < 0,\ 0, &text{otherwise},end{cases}$$ then $$X$$ and $$Y$$ are (positively) correlated standard normal random variables (work out the marginal densities to verify this if it is not immediately obvious) that do not have a bivariate joint normal density. So, given only that $$X$$ and $$Y$$ are correlated standard normal random variables, how can we tell whether $$X$$ and $$Y$$ have the joint pdf shown above or the bivariate joint normal density with the same correlation coefficient ?
In the opposite direction, if $$X$$ and $$Y$$ are independent random variables (note the utter lack of mention of normality of $$X$$ and $$Y$$) and $$X+Y$$ is normal, then $$X$$ and $$Y$$ are normal random variables (Feller, Chapter XV.8, Theorem 1). | 2023-03-25 16:21:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 23, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7623329758644104, "perplexity": 135.90010360742127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945368.6/warc/CC-MAIN-20230325161021-20230325191021-00673.warc.gz"} |
https://www.physicsforums.com/threads/compressible-fluid-mechanics.257999/ | # Compressible Fluid Mechanics
1. Sep 21, 2008
### dcs23
Hi Guys,
I know that the compressible Euler Equations are:
$$\partial_t (\rho \mathbf u) + (\mathbf u \cdot \nabla)(\rho \mathbf u) + \nabla p = 0$$
$$\partial_t \rho + \nabla \cdot (\rho \mathbf u) = 0$$
Subject to suitable initial conditions and solving for $$\mathbf u, \; \rho$$ unknown.
Does anybody have an example of a pair of functions which satisfies these relations in a non-1D case?
2. Sep 21, 2008
### dcs23
Non trivial solutions would also be nice | 2017-06-22 14:39:17 | {"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": 0.4239549934864044, "perplexity": 1924.8978570766471}, "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/1498128319575.19/warc/CC-MAIN-20170622135404-20170622155404-00383.warc.gz"} |
http://math.ipm.ir/frontiers/printevent.jsp?eventID=199 | MINI COURSE
TITLE
Model Theory, Motivic Integration, and Zeta Function
SPEAKER
Jamshid Derakhshan
University of Oxford
TIME
Saturday, July 15, 2017, 11:00 - 12:30 Saturday, July 15, 2017, 14:00 - 15:30 Saturday, July 15, 2017, 16:00 - 17:30
VENUE Lecture Hall 1, Niavaran Bldg.
SUMMARY
I will first give an introduction to the model theory of fields with valuations (for example the $p$-adic numbers), and the theory of $p$-adic and motivic integration. I will then consider the case of number fields, and present results on Dirichlet series and zeta functions which are Euler products of local integals, and give applications to some questions on algebraic groups, and rational points on algebraic varieties. | 2018-07-21 15:13:18 | {"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": 0.3884001076221466, "perplexity": 892.960743843126}, "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/1531676592636.68/warc/CC-MAIN-20180721145209-20180721165209-00450.warc.gz"} |
https://search.datacite.org/works/10.5162/IMCS2012/6.4.2 | ### 6.4.2 A Particle Sampler for Trace Detection of Explosives
Sebastian Beer, Gerhard Müller & Jürgen Wöllenstein
We present our developments toward a handheld field-ready trace explosives detection system using an electrostatic particle sampler with an integrated thermal desorber. Particle sampling with subsequent thermal desorption is used to overcome the problem of low vapor pressure of explosives. A degree of selectivity toward high electron affinity, characteristic for most explosives, is demonstrated experimentally. This reduces the detection background and improves the system performance. Detection is shown in applications of the sampler to both... | 2018-11-12 19:57:18 | {"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": 0.8282745480537415, "perplexity": 4777.882891592865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2018-47/segments/1542039741087.23/warc/CC-MAIN-20181112193627-20181112215627-00107.warc.gz"} |
https://mhuig.github.io/NoteBook/posts/32ffa341.html | 0%
# 附录
找到MySQL的安装路径： which mysql
假设找到的是:/home/user1/mysql/bin/mysql
Writing is not easy. Thank you for your support. | 2020-08-04 18:04:53 | {"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": 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": 0.4677717685699463, "perplexity": 5324.470163054237}, "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-2020-34/segments/1596439735881.90/warc/CC-MAIN-20200804161521-20200804191521-00319.warc.gz"} |
https://chemistry.stackexchange.com/questions/90263/small-but-modest-displacements-at-negligible-forces-from-dft | Small but modest displacements at negligible forces from DFT
When looking at a Gaussian log file today, I noticed the following information in the convergence criterion section after an analytical frequency calculation was performed:
Item Value Threshold Converged? Maximum Force 0.000001 0.000450 YES RMS Force 0.000000 0.000300 YES Maximum Displacement 0.000190 0.001800 YES RMS Displacement 0.000030 0.001200 YES
This struck me as odd. How could the forces be so low but the maximum displacement still be non-negligible? Does anyone have any hypothesis about why this phenomenon would occur? This makes me wonder if the convergence condition for the maximum displacement is unreasonably low if essentially no acting forces can result in a maximum displacement that's merely 1 order of magnitude lower than the default threshold. I believe the force units are Hartrees/Bohr and the distance units are angstroms.
• It is pretty common to see this: that is why we have four different convergence criteria in Gaussian – Greg Feb 8 '18 at 0:07
• I get that, but I'm wondering why it occurs. – Argon Feb 8 '18 at 1:43
• I'm not sure what units those numbers are in, but geometry convergence and its criteria are a bit of a dark art. – TAR86 Feb 8 '18 at 6:09
• I assume that's a displacement in atomic units, and that's just not a very large displacement at all. – jheindel Feb 9 '18 at 7:00
• @Argon What why? Why do you expect similar force constant associated to the stretch of a strong bond and eg a rotation? There is no mystery in the fact that they can have very different forces/ displacements. – Greg Feb 10 '18 at 14:00
For clarity I will assume Gaussian performs a generic Newton-Raphson minimization (NR), which should suffice to explain the phenomenon. In NR, the linear problem $$\nabla\nabla^\ast E \Delta + \nabla E = 0$$ is solved, where $\Delta$ is the displacement. In order to arrive at "large" displacements despite "small" (but non-zero) forces ($-\nabla E$), it suffices for the Hessian ($\nabla\nabla^\ast E$) to have eigenvalues close to 0 itself, because a small number is divided by an even smaller number. This happens when the potential energy surface is very flat. | 2021-03-02 14:34:37 | {"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": 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": 0.689388632774353, "perplexity": 737.5093089279557}, "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-2021-10/segments/1614178364008.55/warc/CC-MAIN-20210302125936-20210302155936-00105.warc.gz"} |
http://mathoverflow.net/revisions/71794/list | MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
2 corrected spelling in title
# Where are $+$, $-$ and §\infty\infty$in bordered Heegaard-Floer theory? 1 # Where are$+$,$-$and §\infty$ in bordered Heegaard-Floer theory?
Here goes my first MO-question. I've just read Lipshitz, Ozsváth and Thurston's recently updated "A tour of bordered Floer theory". To set the stage let me give two quotes from this paper.
Heegaard Floer homology has several variants; the technically simplest is $\widehat{HF}$, which is sufficient for most of the 3-dimensional applications discussed above. Bordered Heegaard Floer homology, the focus of this paper, is an extension of $\widehat{HF}$ to 3-manifolds with boundary.
[...]
the Heegaard Floer package contains enough information to detect exotic smooth structures on 4-manifolds. For closed 4-manifolds, this information is contained in $HF^+$ and $HF^-$; the weaker invariant $\widehat{HF}$ is not useful for distinguishing smooth structures on closed 4-manifolds.
Since I am mainly interested in closed 4-manifolds, I have not paid too much attention to the developments in bordered Heegaard-Floer thoery. But right from the beginning I have wondered why only $\widehat{HF}$ appears in the bordered context. So my question is:
Why are there no $^+$, $^-$ or $^\infty$ flavors of bordered Heegaard-Floer theory? Are the reasons of technical nature or is there an explanation that the theory cannot give more than $\widehat{HF}$?
I assume there are issues with the moduli spaces of holomorphic curves that would be relevant to defining bordered versions of the other flavors of Heegaard-Floer theory, but I am neither enough of an expert on holomorphic curves to immediately see the problems nor could I find anything in the literature that pins down the problems.
Any information is very much appreciated. | 2013-06-19 06:56:21 | {"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": 0.6638982892036438, "perplexity": 275.6439439663111}, "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/1368708143620/warc/CC-MAIN-20130516124223-00089-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://stats.libretexts.org/Bookshelves/Probability_Theory/Probability_Mathematical_Statistics_and_Stochastic_Processes_(Siegrist)/16%3A_Markov_Processes | Skip to main content
# 16: Markov Processes
A Markov process is a random process in which the future is independent of the past, given the present. Thus, Markov processes are the natural stochastic analogs of the deterministic processes described by differential and difference equations. They form one of the most important classes of random processes.
This page titled 16: Markov Processes is shared under a CC BY 2.0 license and was authored, remixed, and/or curated by Kyle Siegrist (Random Services) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
• Was this article helpful? | 2022-10-03 02:15:15 | {"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": 0.8691002130508423, "perplexity": 629.6509363249016}, "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-2022-40/segments/1664030337371.9/warc/CC-MAIN-20221003003804-20221003033804-00164.warc.gz"} |
https://www.physicsforums.com/members/children.138824/recent-content | # Recent content by children
1. ### Fourier Transform of a wavefunction
Why shud one take the Fourier transform of a wavefunction and multiply the result with its conjugate to get the probability? Why can't it be fourier transform of the probability directly? thank you | 2019-09-17 20:38:53 | {"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": 0.9212926030158997, "perplexity": 632.1347110296801}, "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-2019-39/segments/1568514573121.4/warc/CC-MAIN-20190917203354-20190917225354-00355.warc.gz"} |
http://www.maa.org/publications/maa-reviews/classical-galois-theory-with-examples?device=desktop | Classical Galois Theory with Examples
Lisl Gaal
Publisher:
American Mathematical Society Chelsea
Publication Date:
1998
Number of Pages:
248
Format:
Hardcover
Price:
30.00
ISBN:
0-8218-1375-7
Category:
Textbook
BLL Rating:
The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.
There is no review yet. Please check back later.
* Prerequisites: 1.1 Group theory; 1.2 Permutations and permutation groups; 1.3 Fields; 1.4 Rings and polynomials; 1.5 Some elementary theory of equations; 1.6 Vector spaces
* Fields: 2.1 Degree of an algebraic extension; 2.2 Isomorphisms of fields; 2.3 Automorphisms of fields; 2.4 Fixed fields
* Fundamental theorem: 3.1 Splitting fields; 3.2 Normal extensions and groups of automorphisms; 3.3 Conjugate fields and elements; 3.4 Fundamental theorem
* Applications: 4.1 Solvability of equations; 4.2 Solvable equations have solvable groups; 4.3 General equation of degree $n$; 4.4 Roots of unity and cyclic equations; 4.5 How to solve a solvable equation; 4.6 Ruler-and-compass constructions; 4.7 Lagrange's theorem; 4.8 Resolvent of a polynomial; 4.9 Calculation of the Galois group; 4.10 Matrix solutions of equations; 4.11 Finite fields; 4.12 More applications
* Bibliography
* Index | 2015-03-01 21:12:50 | {"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": 0.3615626096725464, "perplexity": 13049.005315261338}, "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-2015-11/segments/1424936462555.21/warc/CC-MAIN-20150226074102-00115-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.illustrativemathematics.org/content-standards/5/NF/B/5/tasks/22 | Update all PDFs
# Running a Mile
Alignments to Content Standards: 5.NF.B.5
Curt and Ian both ran a mile. Curt's time was $\frac89$ Ian's time. Who ran faster? Explain and draw a picture.
## IM Commentary
There is a subtlety worth noting: we are given information about the boys' times but asked about their speeds. Since the distance they run is the same, this isn't difficult to reason through, but teachers need to be aware of this.
The two solutions reflect different competencies described in 5.NF.5. The first solution uses the idea that multiplying by a fraction less than 1 results in a smaller value. The second actually uses the meaning of multiplying by $\frac89$ to explain why multiplying by that fraction will result in a smaller value.
## Solutions
Solution: Scaling by a number less than 1
To find Curt's time, you would multiply Ian's time by $\frac89$. Since we are multiplying Ian's time by a number less than 1, Curt's time will be less than Ian's time. The picture shows Ian's time multiplied by 1 above the number line and Ian's time multiplied by $\frac89$ below the number line.
Since they both ran the same distance but Curt ran it in less time, he must have been running faster.
Solution: Using the meaning of fraction multiplication
Curt's time is $\frac89 \times$ Ian's time. That means that if you divide Ian's time into 9 equal time intervals and take 8 of those intervals, you will have Curt's time. So Curt's time to run a mile is less than Ian's and he must be going faster. | 2018-04-25 14:11:13 | {"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": 0.47592446208000183, "perplexity": 1189.7338732672436}, "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-2018-17/segments/1524125947822.98/warc/CC-MAIN-20180425135246-20180425155246-00174.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-linear-algebra-7th-edition/chapter-4-vector-spaces-review-exercises-page-221/36 | ## Elementary Linear Algebra 7th Edition
Published by Cengage Learning
# Chapter 4 - Vector Spaces - Review Exercises - Page 221: 36
#### Answer
$S$ is a basis for $M_{2,2}$.
#### Work Step by Step
Let $S$ be given by $$S=\left\{\left[\begin{array}{cc}{1} & {0} \\ {0} & {1}\end{array}\right],\left[\begin{array}{cc}{-1} & {0} \\ {1} & {1}\end{array}\right],\left[\begin{array}{cc}{2} & {1} \\ {1} & {0}\end{array}\right],\left[\begin{array}{cc}{1} & {1} \\ {0} & {1}\end{array}\right]\right\}.$$ Consider the combination $$a \left[\begin{array}{cc}{1} & {0} \\ {0} & {1}\end{array}\right]+b\left[\begin{array}{cc}{-1} & {0} \\ {1} & {1}\end{array}\right]+c\left[\begin{array}{cc}{2} & {1} \\ {1} & {0}\end{array}\right]+d \left[\begin{array}{cc}{1} & {1} \\ {0} & {1}\end{array}\right]=0, \quad a,b,cd,\in R.$$ Which yields the following system of equations \begin{align*} a-b+2c+d&=0\\ c+d&=0\\ b+c&=0\\ a+b+d&=0. \end{align*} The coefficient matrix of the above system is given by $$\left[ \begin {array}{cccc} 1&-1&2&1\\ 0&0&1&1 \\ 0&1&1&0\\ 1&1&0&1\end {array} \right] .$$ One can see that the determinant of the coefficient matrix is non zero, hence the system has only the trivial solution and hence, $S$ is linearly independent set of vectors. Since, $M_{2,2}2$ has dimension $4$, then by Theorem 4.12 $S$ is a basis for $M_{2,2}$.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2019-12-08 10:49:51 | {"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": 0.962666928768158, "perplexity": 371.59544254289654}, "config": {"markdown_headings": true, "markdown_code": false, "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-2019-51/segments/1575540508599.52/warc/CC-MAIN-20191208095535-20191208123535-00267.warc.gz"} |
https://www.landfx.com/kb/planting-issues/schedules/item/4239-spacing.html | Plant Schedule is Not Recognizing the Spacing Option for Plant Types
sales@landfx.com
+1 805-541-1003
## Issue
You tried to place a Plant Schedule with the Spacing option selected for one or more of your plant types (example: Shrubs).
When you placed the Plant Schedule, it did not include a colum for the Spacing option for this plant type – even though you're positive that the option was selected when you placed the schedule.
## Cause
This is a known issue we've seen occurring when the Spacing option is selected in the Plant Schedule default settings.
## Solution
We are currently working to find a solution to this issue. For now, you can use the following workaround:
1. Open the Plant Schedule tool again.
2. When asked Re-generate the existing schedule? click No.
3. In the Plant Schedule dialog box, uncheck the Spacing option for the plant type(s) for which you're trying to show the spacing.
4. Select the Spacing option for that plant type again.
Click OK to place the schedule.
The Plant Schedule should now include the Spacing option for the plant type(s) where you've selected it. | 2023-03-23 02:44:30 | {"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": 0.8874620199203491, "perplexity": 3066.3445488772513}, "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/1679296944606.5/warc/CC-MAIN-20230323003026-20230323033026-00181.warc.gz"} |
https://rosettacommons.org/node/11027 | # hbond_sr_bb and hbond_lr_bb for different chains
3 posts / 0 new
hbond_sr_bb and hbond_lr_bb for different chains
#1
In the rosetta scoring function, what energy term describes backbone-backbone hydrogen bonding between residues on different protein chains
hbond_sr_bb Backbone-backbone hbonds close in primary sequence. All hydrogen bonding terms support canonical and noncanonical types.
hbond_lr_bb Backbone-backbone hbonds distant in primary sequence.
Do the above terms only specify hydrogen bonding on a single chain? (as they are stratified by distance in primary sequence)
Thanks,
Tyler
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Tue, 2020-10-13 13:41
tylerborrman
The hbond_sr_bb type is intended for alpha helical hydrogen bonds, and is only active if you're on the same chain and within a short (less than 4 or so) distance of the other residue.
The hbond_lr_bb is intended for beta sheets (and other), and does not have a chain dependence. Two beta strands making hydrogen bonds with identical geometries will score the same whether the strands are in the same chain or are split between chains.
(The rationale for the difference is because Rosetta tends to really like forming alpha helicies because they're easy to find with a local structural search, versus beta strand pairings, which need a more global search. It was found that specifically downweighting the alpha helical hydrogen bonds tended to help counteract that bias with older scorefunctions. Recent scorefunctions, though, have a sightly different overall weighting scheme, and it's been found that there is no longer a need to weight the terms differently. They're still listed separately, but in the Talaris and REF energy functions all of the backbone hydrogen bonds have identical weights.)
Wed, 2020-10-14 08:25
rmoretti
Excellent thanks!
Tue, 2021-02-09 16:33
tylerborrman | 2023-01-28 14:16:09 | {"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": 0.19445620477199554, "perplexity": 4879.297987624495}, "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-2023-06/segments/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00811.warc.gz"} |
https://collegephysicsanswers.com/openstax-solutions/even-when-head-held-erect-figure-940-its-center-mass-not-directly-over-0 | Change the chapter
Question
Even when the head is held erect, as in Figure 9.40, its center of mass is not directly over the principal point of support (the atlanto-occipital joint). The muscles at the back of the neck should therefore exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. (a) Calculate the force exerted by these muscles using the information in the figure. (b) What is the force exerted by the pivot on the head?
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1. $25\textrm{ N}$
2. $75 \textrm{ N}$
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# OpenStax College Physics for AP® Courses Solution, Chapter 9, Problem 32 (Problems & Exercises) (1:42)
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This is College Physics Answers with Shaun Dychko. The atlanto-occipital joint is exerting a force upwards on the skull and there's a center of gravity positioned here which is exerting a torque about a pivot at this joint and it's 2.5 centimeters away and then there's neck muscles pulling straight down on this side exerting a counter-clockwise torque 5.0 centimeters from the pivot and when you say the two torque's have to be equal in order for the head to be stationary, and so we can solve for F M by dividing both sides by 5.0 centimeters. So by the way, this is the torque due to the weight of the head its weight multiplied by its lever arm— 2.5 centimeters— and here's the twerk due to the neck muscles the neck muscle force times 5 centimeters. So the neck muscle force then is the weight times 2.5 centimeters divided by 5.0 centimeters and it's okay to leave the units in centimeters instead of converting them into meters because since we are dividing these lengths, the centimeter units will cancel since they are the same. So we have 50 newtons times 2.5 divided by 5.0 which is 25 newtons is the force due to the muscles and that's downwards. The force due to this joint is the only force upwards and it has to balance the two forces downwards: force due to the muscle and the weight of the head. So it's going to be 25 newtons plus 50 newtons which is 75 newtons and that will be upwards. | 2022-01-22 14:19:44 | {"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": 0.505829393863678, "perplexity": 684.5098361106479}, "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-2022-05/segments/1642320303864.86/warc/CC-MAIN-20220122134127-20220122164127-00341.warc.gz"} |
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3504029 | # Gauge Transformations in the Dual Space, and Pricing and Estimation in the Long Run in Affine Jump-Diffusion Models
23 Pages Posted: 13 Jan 2020 Last revised: 26 Mar 2021
See all articles by Svetlana Boyarchenko
## Svetlana Boyarchenko
University of Texas at Austin - Department of Economics
## Sergei Levendorskii
Calico Science Consulting
Date Written: December 14, 2019
### Abstract
We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model with an operator of the form $e^{i\Phi(-\sqrt{-1}\dd_x)}$ (gauge transformation in the dual space). A general procedure for the calculation of the function $\Phi$ is given, with examples. As applications, we consider pricing in jump-diffusion models and their subordinated versions using the eigenfunction expansion technique, and estimation of the extremely rare jumps component. The beliefs of the market about yet unobserved extreme jumps and pricing kernel can be recovered: the market prices allow one to see "the shape of things to come".
Keywords: affine jump-diffusions, eigenfunction expansion, long run, estimation, Ornstein-Uhlenbeck model, Vasicek model, square root model, CIR model
JEL Classification: C58, C63, C65, G12
Suggested Citation
Boyarchenko, Svetlana I. and Levendorskii, Sergei Z., Gauge Transformations in the Dual Space, and Pricing and Estimation in the Long Run in Affine Jump-Diffusion Models (December 14, 2019). Available at SSRN: https://ssrn.com/abstract=3504029 or http://dx.doi.org/10.2139/ssrn.3504029 | 2022-01-22 00:37:12 | {"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": 0.5658562183380127, "perplexity": 2402.1326062363783}, "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/1642320303717.35/warc/CC-MAIN-20220121222643-20220122012643-00387.warc.gz"} |