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https://astronomy.stackexchange.com/questions/29994/why-is-the-moon-that-special-is-it-really-a-well-built-coincidence/29998 | Why is the moon that special? Is it really a well built coincidence? [duplicate]
I find it funny that the moon is the only object in the solar system to almost perfectly fit the sun, resulting in the spectacular solar eclipses. No other object except maybe a few irregular moons like Pandora from Saturn would do that, and for them, they aren't round, and thus can't fully block out all light. The moon also has a perfect rotation that is almost exactly the same as Earth's rotational period, resulting in a tidal lock, which causes tides.
Is this a coincidence? Any speculation on why this happens? Is this the only observed place where such criteria play into such perfect coincidence?
• If it were really special, there would be a total eclipse every new Moon and every Full Moon. :-) Mar 15, 2019 at 2:43
• @JohnHoltz well its orbit is tilted, but still these two coincidences... what resulted in them? Mar 15, 2019 at 2:47
• -1 and vote to close for primarily opinion-based for explicitly requesting speculation!
– uhoh
Mar 15, 2019 at 5:15
• The moon also has a perfect rotation that is almost exactly the same as Earth's rotational period What?! The Moon's rotational period is nearly 30 times longer than Earth's. Mar 15, 2019 at 6:17
• First about Moon's roundness: Moon is pretty big, so its gravitation forces pull down all of the material so it shapes round. And about "coincidence": there are a lot of moons in the Universe. Some of them are rounded and have the same angular diameter as their star. But this isn't so rare. Mar 15, 2019 at 17:28 | 2022-05-22 16:53:28 | {"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": 0.5561625361442566, "perplexity": 1141.9483631983014}, "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-2022-21/segments/1652662545875.39/warc/CC-MAIN-20220522160113-20220522190113-00474.warc.gz"} |
http://texhacks.blogspot.com/2009/09/numbering-every-paragraph.html | ## Friday, September 25, 2009
### Numbering every paragraph
One occasionally finds cause to number every graf in a document. Well, I never have, but I've seen it done. There's a neat little trick that is mentioned in passing in an exercise in the TeXbook that easily enables this. This relies on a TeX primitive \everypar which is essentially a token register which is to say that it holds a list of tokens that can be used again and again. What exactly a token is is a topic for another post. When TeX starts a new paragraph (or more precisely, when it enters horizontal mode), it does two things. First, it inserts an empty box of width \parindent (this is the indentation that occurs at the start of every graf) and then it will process the tokens defined by \everypar before going on to process the rest of the tokens that make up the graf. The upshot of this is that we can cause TeX to do something at the start of every graf, but after it inserts the indentation glue. The way to use this is to doing something like the following.
```\newcounter{grafcounter}
\setcounter{grafcounter}{0}
```\everypar={\addtocounter{grafcounter}{1}%
```\everypar=\expandafter{\the\everypar | 2019-04-26 09:54:04 | {"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": 0.9660294055938721, "perplexity": 745.5697712902428}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578765115.93/warc/CC-MAIN-20190426093516-20190426115516-00501.warc.gz"} |
https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2-1.18/share/doc/Macaulay2/Macaulay2Doc/html/___Singular_sp__Book_sp1.8.9.html | # Singular Book 1.8.9 -- radical membership
Recall that an element $f$ is in an ideal $I$ if $1 \in (I, tf-1) \subset R[t]$.
i1 : A = QQ[x,y,z]; i2 : I = ideal"x5,xy3,y7,z3+xyz"; o2 : Ideal of A i3 : f = x+y+z;
i4 : B = A[t]; i5 : J = substitute(I,B) + ideal(f*t-1) 5 3 7 3 o5 = ideal (x , x*y , y , x*y*z + z , (x + y + z)t - 1) o5 : Ideal of B i6 : 1 % J o6 = 0 o6 : B
The polynomial f is in the radical. Let's compute the radical to make sure.
i7 : radical I o7 = ideal (z, y, x) o7 : Ideal of A | 2021-09-26 19:29:33 | {"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": 0.8770395517349243, "perplexity": 997.8501673925704}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057913.34/warc/CC-MAIN-20210926175051-20210926205051-00101.warc.gz"} |
http://mathhelpforum.com/algebra/211814-definition-linear.html | 1. ## definition of 'linear'
Of the above list of equations a) c) and f) are said to be linear, but I thought linear equations were not allowed to have fractional exponents? Both a) and f) have the square root of a variable (x_3 and x_2 respectively) no?
2. ## Re: definition of 'linear'
Hey kingsolomonsgrave.
I agree with you in that if the terms are to a non-unit power (i.e. not x^1) then they are not linear.
If its just the coeffecient that is irrational though then this is OK. | 2016-12-10 04:10:17 | {"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": 0.8652338981628418, "perplexity": 1219.5672988757876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542938.92/warc/CC-MAIN-20161202170902-00418-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://www.math.unipd.it/news/lagrangian-and-conservative-solutions-of-the-2d-euler-equations/ | ## “Lagrangian and conservative solutions of the 2D Euler equations”
Mercoledì 17 Giugno 2020, ore 15:00 - Zoom - Gennaro Ciampa (University of Basel, CH)
Abstract
Smooth solutions of the 2D incompressible Euler equations enjoy two very natural properties: the first one is that they are Lagrangian, namely the vorticity is advected by the flow of the velocity; the second property is that smooth solutions conserve the kinetic energy. When we consider solutions in weaker classes, precisely when the initial vorticity is in $L^p$ with $1\leq p \le \infty$, the existence of Lagrangian solutions and the conservation of the energy may depend in general on the approximation scheme. Furthermore, a reasonable question is whether solutions constructed by a given method are unique. In this talk we prove the existence of solutions which enjoy the above properties constructed via different methods. Moreover, we will show that already in the linear case a smooth approximation of the velocity field can produce different solutions in the limit.
Based on joint works with G. Crippa (University of Basel) and S. Spirito (University of L’Aquila).
Seminari di equazioni differenziali e applicazioni
10/07/2020 11:11 | 2020-10-25 19:37:18 | {"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": 0.862750768661499, "perplexity": 645.7476821384644}, "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-2020-45/segments/1603107889651.52/warc/CC-MAIN-20201025183844-20201025213844-00514.warc.gz"} |
https://www.transtutors.com/questions/state-some-of-the-advantages-of-employing-thermal-derating-techniques-in-an-electron-765079.htm | # State some of the advantages of employing thermal derating techniques in an electronic design.
State some of the advantages of employing thermal derating techniques in an electronic design. | 2021-01-19 05:38:41 | {"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": 0.9741657376289368, "perplexity": 1940.9728150645058}, "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/1610703517966.39/warc/CC-MAIN-20210119042046-20210119072046-00370.warc.gz"} |
https://docs.analytica.com/index.php/IndexValue | # IndexValue
## IndexValue(I)
Returns the index value for the given variable or index «I». Some variables have both an index value and a result value. Examples include -- a self-indexed array; a variable or index defined as a list of identifiers or list of expressions; and a Choice list with a self-domain. IndexValue(I) returns the index value of «I», where (I) alone would return its result value.
Array Functions
## Details
The IndexValue function, if it weren't built-in, could easily be defined as:
Function IndexValue(I: IndexType) := I
## Examples
Index L := [I, J, K, "value"]
Index rows := 1..Size(A)
Variable Flat_A := MdArrayToTable(A, rows, IndexValue(L)) | 2023-02-06 03:08:05 | {"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": 0.3412156403064728, "perplexity": 8632.501727045923}, "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/1674764500303.56/warc/CC-MAIN-20230206015710-20230206045710-00013.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2019.02.008 | • •
环境规制的经济效应：“减排”还是“增效”
• 出版日期:2019-02-25 发布日期:2019-03-07
Economic Effects of Environmental Regulations: “Emission Reduction” or “Efficiency Enhancement”
Yu Binbin et al.
• Online:2019-02-25 Published:2019-03-07
Abstract: This paper constructs a theoretical and analytical framework for the economic effects of environmental regulations, and tests the "emission reduction" and "efficiency enhancement" effects of environmental regulations by applying the Chinese urban panel data and the dynamic spatial panel model. It is found that the environmental regulations in China has the economic and spatial spillover effects of "emission reductions only without economic efficiency", and the conclusion is still unchanged with a series of robustness tests. A further heterogeneity study reveals that the environmental effects of "emission reductions only without economic efficiency" are validated in those three parts of China, i.e., East, Central and West. After the international financial crisis, the "emission reductions" effects brought about by the environmental regulations have significantly intensified, but only with an increased "compliance cost", and no "innovation effects". The effects of "emission reductions only without economic efficiency" can only be improved efficiently through speeding up the restructuring of industries. The relationship between economic development and energy efficiency presents a trend of U shape, and China is on the left side of the "U", and so far the Kuznets environmental curve has not been confirmed by Chinese city data yet. | 2022-07-02 09:07:50 | {"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": 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": 0.31025415658950806, "perplexity": 5055.460097934011}, "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-2022-27/segments/1656103989282.58/warc/CC-MAIN-20220702071223-20220702101223-00696.warc.gz"} |
http://math.stackexchange.com/questions/580775/how-to-prove-trigonometry-equation | # How to prove Trigonometry equation?
how to solve following equation
$$\tan^{-1}\left(\frac{1}{4}\right) + \tan^{-1}\left(\frac{1}{9}\right) = \cos^{-1}\left(\frac{3}{5}\right)$$ How to prove the above equation?
-
Have you attempted anything? – Zhoe Nov 25 '13 at 17:04
I was trying with tana+tanb formula but not able to convert it – subodh joshi Nov 25 '13 at 17:05
One problem is of course that the equation is wrong. – Daniel Fischer Nov 25 '13 at 17:10
There may be a mistake in the equation – Dutta Nov 25 '13 at 17:10
*Disprove${}{}{}$ – Alizter Nov 25 '13 at 17:35
-
U mean above equation wrong? – user110715 Nov 25 '13 at 17:28
@user110715 Yes. – Felix Marin Nov 25 '13 at 17:28
From this or Ex$\#5$ of Page $\#276$ of this $$\tan^{-1}x+\tan^{-1}y=\tan^{-1}\frac{x+y}{1-xy}$$ if $xy<1$
Now, as the principal value of $\tan$ lies $\in\left[-\frac\pi2,\frac\pi2\right],$
If $\displaystyle \tan^{-1}z=\theta,\tan\theta=z,$ $\displaystyle\cos\theta=+\frac1{\sqrt{1+z^2}}$
-
how u made cosQ like that? – user110715 Nov 25 '13 at 17:14
@user110715, $\sec^2\theta=1+\tan^2\theta,$ right? – lab bhattacharjee Nov 25 '13 at 17:16
After you apply the formula, let $cos \theta= \frac{3}{5}$. Now convert this to $tan \theta$, which is trivial, and compare both sides.
- | 2015-02-01 21:37:39 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9879705309867859, "perplexity": 2934.906641785675}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422121934081.85/warc/CC-MAIN-20150124175214-00193-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/57315/positive-definite-function-zoo | Positive definite function zoo
A positive definite function $\varphi: G \rightarrow \mathbb{C}$ on a group $G$ is a function that arises as a coefficient of a unitary representation of $G$.
For a definition and discussion of positive definite function see here.
I've often wished I had a collection of diverse examples of positive definite functions on groups, for the purpose of testing various conjectures. I hope the diverse experience of the participants of this forum can help me collect a list of such examples.
To clarify what I'd like to see:
What is an example of a positive definite function on a group $G$ that is not easily seen to be a coefficient of a unitary representation of $G$? What are some positive definite functions that arise in contexts sufficiently removed from studying the coefficients of unitary representations?
Also, the weirder the group $G$ the better.
Edit: There is now a version of this question on MO.
-
As per request, I've made the question CW. – Zev Chonoles Aug 13 '11 at 23:42
Thank you, Zev! – Jon Bannon Aug 13 '11 at 23:45
I guess my favourite example is $\frac{1}{1+x^2}$ on $\mathbb{R}$. But it's not quite clear what exactly you're looking for: explicit positive elements of the Fourier algebra or would a function of the form $f \ast \tilde{f}$ for $f \in L^2(G)$ already be satisfactory for you? I find the exposition on positive definite functions in appendix C of Bekka-de la Harpe-Valette quite nice, but sect 13.4 and the following chapters of Dixmier's book on $C^\ast$-algebras is still the best source in my opinion (few explicit examples, though). – t.b. Aug 14 '11 at 10:06
let me clarify, Theo. – Jon Bannon Aug 14 '11 at 11:43
Thanks for the tag edits, someone! – Jon Bannon Aug 14 '11 at 11:54 | 2014-11-26 16:25:15 | {"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": 0.8031708598136902, "perplexity": 685.3329451443009}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931007150.95/warc/CC-MAIN-20141125155647-00216-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://openstudy.com/updates/55725561e4b0bffbfefe3f66 | ## Afrodiddle one year ago A store had 235 MP3 players in the month of January. Every month, 30% of the MP3 players were sold and 50 new MP3 players were stocked in the store. Which recursive function best represents the number of MP3 players in the store f(n) after n months? A. f(n) = 0.7 × f(n - 1) + 50, f(0) = 235, n > 0 B.f(n) = 237 - 0.7 × f(n - 1) + 50, f(0) = 235, n > 0 C.f(n) = 0.3 × f(n - 1) + 50, f(0) = 235, n > 0 D.f(n) = 237 + 0.7 × f(n - 1) + 50, f(0) = 235, n > 0
1. Afrodiddle
I believe it is A) but I am not entirely sure, can someone walk me through the steps?
2. anonymous
i agree, it is A. the first term $0.7\times f(n-1)$ represents 70% of the total MP3 players of the previous month, that is the remaining quantity since 30% were sold. the other term +50, represents the newly added MP3 players to the stock and if January is indexed by n=0, f(0) should be 235, as is in answer A so, answer A matches all the requirements! | 2016-10-25 17:25:27 | {"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": 0.43446075916290283, "perplexity": 1388.4498963458188}, "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/1476988720238.63/warc/CC-MAIN-20161020183840-00030-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://conferences.famnit.upr.si/event/4/contributions/39/ | # Graphs, groups, and more: celebrating Brian Alspach’s 80th and Dragan Marušič’s 65th birthdays
28 May 2018 to 1 June 2018
Koper
UTC timezone
## Hamilton decompositions of one-ended Cayley graphs
Not scheduled
15m
UP FHS (Koper)
### UP FHS
#### Koper
Titov trg 5,Koper
### Speaker
Florian Lehner (University of Warwick)
### Description
In 1984, Alspach asked whether every Cayley graph of a finite Abelian group admits a Hamilton decomposition. The conjectured answer is yes, but except in some special cases the question remains wide open. In this talk we study an analogous question for infinite, finitely generated groups, using spanning double rays as an infinite analogue of Hamilton cycles. We show that if $G$ is a one-ended Abelian group and $S$ is a generating set only containing non-torsion elements, then the corresponding Cayley graph admits a decomposition into spanning double rays. In particular, any Cayley graph of $\mathbb Z^d$ has such a decomposition. Related results for two-ended groups will also be discussed.
### Primary authors
Florian Lehner (University of Warwick) Joshua Erde (Universität Hamburg) Max Pitz (Universität Hamburg)
### Presentation Materials
There are no materials yet. | 2021-03-07 18:02:56 | {"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": 0.48312291502952576, "perplexity": 3764.2037260987913}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178378043.81/warc/CC-MAIN-20210307170119-20210307200119-00139.warc.gz"} |
https://class12chemistry.com/tag/packing-efficiency-chemistry-notes/ | ## Packing Efficiency Chemistry Notes
→ As we know that the constituent particles in crystal lattice are arranged in close packing. Some spaces remain vacant in this state, which are called voids. The percentage of the total space filled by the particles is called packing efficiency or the fraction of total space filled is called packing fraction.
% Packing efficiency
Packing Eficiency in hcp or ccp or fcc Structures :
Length of edge of a unit cell = a
Volume of one sphere = $$\frac{4}{3}$$ (πr3)
∵ fcc stucture is formed from four spheres.
∴ Volume of four spheres = 4 × $$\frac{4}{3}$$ (πr3) = $$\frac{16}{3}$$ (πr3)
∆ ABC AC2 = AB2 + BC2
= a2 + a2
∴ AC = a√2 … (1)
If we see AC then the arrangement of spheres in it is as follows
Hence, the total volume occupied by spheres or particles in fec or ccp or hep structure is 74%. While the empty space i.e. volume of total voids is 26%.
Packing Efficiency in Body Centred Cubic Sturcture (bcc) :
Edge length of unit cell = a
Since bec structure forms from two spheres.
So, Volume of two spheres = 2 × $$\left(\frac{4}{3} \pi r^{3}\right)$$ = $$\frac{16}{3}$$ πr2
In ∆ABC, AC2 = AB2 + BC2
AC2 = a2 + a2
AC2 = 2a2
In ∆ACD, AD2 = AC2 + CD2
If we see AD, then the arrangement of spheres in it is as follows
On putting the value of AD in equation (i),
Hence, the total volume occupied by spheres or particles in bee structure is 68% While, the empty space i.e. volume of total voids is 32%.
Packing Efficiency in Simple Cubic Unit Cell (scc)
Volume of one sphere = $$\frac{4}{3}$$ πr3 | 2021-12-02 10:24:40 | {"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": 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": 0.8749809265136719, "perplexity": 3953.9483246311474}, "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-2021-49/segments/1637964361253.38/warc/CC-MAIN-20211202084644-20211202114644-00289.warc.gz"} |
https://www.esaral.com/q/if-the-median-of-the-following-frequency-distribution-is-28-5-find-the-missing-frequencies-72702 | # If the median of the following frequency distribution is 28.5 find the missing frequencies:
Question:
If the median of the following frequency distribution is 28.5 find the missing frequencies:
Solution:
Given: Median = 28.5
We prepare the cumulative frequency table, as given below.
Now, we have
$N=60$
$45+f_{1}+f_{2}=60$
$f_{2}=15-f_{1}$.....(1)
$\mathrm{Also}, \frac{N}{2}=30$
Since the median $=28.5$ so the median class is $20-30$.
Here, $l=20, f=20, F=5+f_{1}$ and $h=10$
We know that
Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$
$28.5=20+\left\{\frac{30-\left(5+f_{1}\right)}{20}\right\} \times 10$
$8.5=\frac{\left(25-f_{1}\right) \times 10}{20}$
$8.5 \times 20=250-10 f_{1}$
$10 f_{1}=250-170$
$=80$
$f_{1}=8$
Putting the value of $f_{1}$ in (1), we get
$f=15-8$
$=7$
Hence, the missing frequencies are 7 and 8. | 2023-02-08 03:25:10 | {"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": 0.6698103547096252, "perplexity": 1121.817587995054}, "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/1674764500671.13/warc/CC-MAIN-20230208024856-20230208054856-00026.warc.gz"} |
https://indico.desy.de/event/27991/contributions/101476/ | # ICRC 2021
Jul 12 – 23, 2021
Online
Europe/Berlin timezone
## A novel trigger based on neural networks for radio neutrino detectors
Jul 14, 2021, 12:00 PM
1h 30m
05
#### 05
Poster NU | Neutrinos & Muons
Astrid Anker
### Description
The ARIANNA experiment is a proposed Askaryan detector designed to record radio signals induced by neutrino interactions in the Antarctic ice. Because of the low neutrino flux at high energies, the physics output is limited by statistics. Hence, an increase in sensitivity will significantly improve the interpretation of data and will allow us to probe new parameter spaces. The trigger thresholds are limited by the rate of triggering on unavoidable thermal noise fluctuations. Here, we present a real-time thermal noise rejection algorithm that will allow us to lower the thresholds substantially and increase the sensitivity by up to a factor of two compared to the current ARIANNA capabilities. A deep learning discriminator, based on a Convolutional Neural Network (CNN), was implemented to identify and remove a high percentage of thermal events in real time while retaining most of the neutrino signal. We describe a CNN that runs efficiently on the current ARIANNA microcomputer and retains 94% of the neutrino signal at a thermal rejection factor of $10^5$. Finally, we report on the experimental verification from lab measurements.
### Keywords
Askaryan; UHE neutrinos; in-ice radio detection; trigger optimization; radio; deep learning
Collaboration other (fill field below) ARIANNA Experimental Methods & Instrumentation | 2022-08-11 15:27:50 | {"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": 0.5934070348739624, "perplexity": 2463.3967850086497}, "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-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00603.warc.gz"} |
https://gamedev.stackexchange.com/questions/179064/alternative-path-not-working | # Alternative path not working
I am using Android studio (libGDX), and I can't figure out why alternative paths doesn't work. I've tried it as it said in the book, but it doesn't do anything, it shows a black window and than the program exterminates. If the .png file would be in the .../android/assets/ folder, it wouldn't work either.
This is what the book wants me to do it:
public Spaceship(float x, float y, Stage s){
super(x,y,s);
setBoundaryPolygon(8);
setAcceleration(200);
setMaxSpeed(100);
setDeceleration(10);
}
This is the shortest form that works for me:
public Spaceship(float x, float y, Stage stage) {
super(x, y, stage);
setBoundaryPolygon(8);
setAcceleration(400);
setMaxSpeed(200);
setDeceleration(20);
}
This is what my path looks like:
For a Desktop Application
If you are working on a desktop app it has to do with the Run/Debug Configuration:
The important part is to set the "Working directory" to YourGameName\android\assets | 2020-06-03 01:04:23 | {"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": 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": 0.19484545290470123, "perplexity": 2099.595721887443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347426956.82/warc/CC-MAIN-20200602224517-20200603014517-00093.warc.gz"} |
https://study.com/academy/answer/1-compute-x-2-y-2-da-over-an-annulus-1-x-2-y-2-4-2-compute-0-1-0-1-x-2-x-2-y-2-dy-dx-3-find-the-volume-of-the-solid-bounded-below-by-the-xy-plane.html | # 1. Compute (x^2 + y^2) dA over an annulus 1 x^2 + y^2 4. 2. Compute 0^1 ( 0^ ...
## Question:
1. Compute{eq}\displaystyle \ \int \int \cos (x^2 + y^2) \ dA {/eq} over an annulus {eq}\displaystyle \ 1 \leq x^2 + y^2 \leq 4. {/eq}
2. Compute{eq}\displaystyle \ \int_0^1 \left ( \int_0^{ \sqrt {1 - x^2} } \sin \left ( \sqrt {x^2 + y^2} \right ) \ dy \right ) \ dx {/eq}
3. Find the volume of the solid bounded below by the xy-plane and above by{eq}\displaystyle \ z = 2x; {/eq} on the sides by the cylinder{eq}\displaystyle \ (x - 1)^2 + y^2 = 1. {/eq}
## Double Integrals in Polar Coordinates:
If we have a double integral {eq}\displaystyle\iint_R f(x, y) \: dA, {/eq} where the region {eq}R {/eq} is a circle, annulus, or portion of a circle, and the integrand {eq}f(x, y) {/eq} is a function of {eq}x^2 + y^2, {/eq} then quite often it is easier to first convert the problem to polar coordinates, then evaluate. An annulus centered at the origin can be described as {eq}0 \leq \theta \leq 2\pi, \: a \leq r \leq b, {/eq} and a circle or portion of a circle is similarly described. Next use the fact that {eq}r^2 = x^2 + y^2 {/eq} to convert the integrand, and replace {eq}dA {/eq} with {eq}r \: dr \: d\theta. {/eq} The new integral is ready to go!
1. Compute{eq}\displaystyle \ \iint \cos (x^2 + y^2) \ dA {/eq} over an
The annulus {eq}\displaystyle \ 1 \leq x^2 + y^2 \leq 4 {/eq} can be...
Become a Study.com member to unlock this answer! Create your account | 2019-11-18 16:19:24 | {"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": 0.9994626641273499, "perplexity": 1765.7838412641302}, "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/1573496669809.82/warc/CC-MAIN-20191118154801-20191118182801-00001.warc.gz"} |
https://www.physicsforums.com/threads/a-work-problem.165868/ | A Work problem
1. Apr 15, 2007
rootX
This questions asks what is the work done by the tension in the cable. And, the book answered that it is equal to the work done by the gravity.
But shouldn't it be more than the work done by the gravity? (because there is also a horizontal displacement)
see the attached image
Attached Files:
• lastscan.jpg
File size:
35.2 KB
Views:
39
2. Apr 15, 2007
Andrew Mason
I can't see your attachment yet, what is the direction of the force? So what is $\vec{F} \cdot \vec{d}$ ?
AM | 2017-09-23 02:43:17 | {"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": 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": 0.5503978729248047, "perplexity": 1051.840669426867}, "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-2017-39/segments/1505818689413.52/warc/CC-MAIN-20170923014525-20170923034525-00102.warc.gz"} |
https://ask.libreoffice.org/en/question/90264/formula-to-value-greyed-out/ | # Formula to Value greyed out
This post is a wiki. Anyone with karma >75 is welcome to improve it.
Version: 5.2.5.1
Created a formula in a cell. Did: Data, Calculate, Formula to Value. Worked fine to display value.
However, now I wish to modify the formula slightly. However, when I try to reverse this to display formula, I find it greyed out.
What to do?
edit retag close merge delete
Sort by » oldest newest most voted
Any cell can contain exactly one of the following: a number, a text, or a formula.
As soon as you replaced a formula by its result (either number or text) the formula is no longer present. The only way to get it back is the > 'Edit' > 'Undo' tool (also Ctrl+Z) of the user interface, but only as long as the undo-stack was big enough, and the document was not saved.
more
Thanks. There must be a way to retain the (an) original formula, perhaps in a "protected" cell, and have the results show in another cell?
( 2017-03-15 15:23:59 +0100 )edit
You can always refer to the formula cell in another cell to display its value, e.g. with your formula in A1 just enter into any other cell =A1
( 2017-03-15 15:31:09 +0100 )edit
By default the result of the formula should be shown anyway in the cell containing the formula. If you got shown there permanently (not only during editing) the formula, you must have the setting
'Tools' > 'Options' > 'LibreOffice Calc' > 'View' > 'Display' > 'Formulae'
switched on (wrongly). This is an option only (rarely) useful during the design/debugging of complicated sheets.
( 2017-03-15 15:41:00 +0100 )edit
Thanks to all.
( 2017-03-15 17:01:30 +0100 )edit
@joea:L Would you mind to tell in what way you got rid of your problem?
( 2017-03-15 19:17:35 +0100 )edit | 2019-12-16 07:18:31 | {"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": 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": 0.295967161655426, "perplexity": 3780.4432265516516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541318556.99/warc/CC-MAIN-20191216065654-20191216093654-00284.warc.gz"} |
https://engineeringprep.com/problems/284 | ## Hyperbola
What is the eccentricity of the conic section represented by the below equation?
Hint
The equation for a hyperbola has the below format:
$$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$$$Hint 2 Eccentricity: $$e=\sqrt{1+(b^2/a^2)}$$$
A conic section is a curve obtained from the intersection of a cone’s surface and a flat plane. The eccentricity, $$e$$ , of a conic section indicates how close its shape is a circle. As eccentricity grows larger, the less the shape resembles a circle. The problem’s equation is a hyperbola because it has the below format:
$$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$$$Note the similarities to an ellipse equation, except the two components are being subtracted instead of added. The eccentricity, $$e$$ , of a conic section indicates how close its shape is a circle. To solve for eccentricity: $$e=\sqrt{1+(b^2/a^2)}$$$
Thus,
$$e=\sqrt{1+(64/49)}=\sqrt{1+1.306}=\sqrt{2.306}=1.52$$\$
1.52 | 2022-08-19 11:12:18 | {"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": 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": 0.8228899836540222, "perplexity": 1243.0908865305864}, "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/1659882573667.83/warc/CC-MAIN-20220819100644-20220819130644-00319.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-12th-edition/chapter-2-section-2-2-the-slope-of-a-line-2-2-exercises-page-159/74 | ## Intermediate Algebra (12th Edition)
$\bf{\text{Solution Outline:}}$ To graph the line with the given characteristics: \begin{array}{l}\require{cancel} \text{Through } (5,3) \\ m=0 .\end{array} draw a horizontal line passing through the given point. $\bf{\text{Solution Details:}}$ Since lines with a slope of $0$ are horizontal lines, then the graph is a horizontal line passing through the point $(5,3) .$ | 2018-07-19 15:50:18 | {"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": 0.9992019534111023, "perplexity": 596.2996733470605}, "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/1531676591140.45/warc/CC-MAIN-20180719144851-20180719164851-00522.warc.gz"} |
https://findcitytune.com/az-doe-or-die-ii-album-stream/ | # AZ – Doe Or Die II [Album Stream]
It has been 26 years since AZ released his debut album Doe Or Die and 12 years since his last album. Almost three decades in the making, the legendary New York rapper is back with the sequel to his first effort. Taking it back to the essence, AZ enlists the likes of Rick Ross, Conway the Machine, Lil Wayne, Dave East and T-Pain for Doe Or Die II. It’s only 13 tracks in length, so don’t expect a longwinded project.
Stream it all below and get your dose of AZ music for the new generation. | 2021-10-26 00:23:07 | {"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": 0.9279203414916992, "perplexity": 6884.703469680434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587770.37/warc/CC-MAIN-20211025220214-20211026010214-00452.warc.gz"} |
https://autowarefoundation.gitlab.io/autoware.auto/AutowareAuto/perception-stack.html | Autoware.Auto
Autoware.Auto 3D perception stack
# Running the Autoware.Auto 3D perception stack
This section leverages the velodyne_node, which accepts UDP data as an input. Download the sample pcap file containing two LiDAR point clouds generated by the Velodyne VLP-16 Hi-Res:
Place the pcap file within the adehome directory, for example ade-home/data/.
ADE Terminal 1 - start rviz2:
$ade enter ade$ export LD_LIBRARY_PATH=${LD_LIBRARY_PATH}:/usr/local/nvidia/lib64/ # see the note below ade$ rviz2 -d /home/"${USER}"/AutowareAuto/install/autoware_auto_examples/share/autoware_auto_examples/rviz2/autoware.rviz Note Systems with an NVIDIA graphics card must set the LD_LIBRARY_PATH in order to load the correct driver; see issue #49 for more information. ADE Terminal 2 - start udpreplay:$ ade enter
ade$udpreplay ~/data/route_small_loop_rw-127.0.0.1.pcap ADE Terminal 3 - start the velodyne_node:$ ade enter
ade$cd AutowareAuto ade$ source install/setup.bash
ade$ros2 run velodyne_node velodyne_cloud_node_exe __params:=/home/"${USER}"/AutowareAuto/src/drivers/velodyne_node/param/vlp16_test.param.yaml
Note
The steps above leverage a pcap file, however the velodyne_node can be connected directly to the sensor. Update the IP address and port arguments in the yaml file to connect to live hardware.
When the velodyne_node is running, the resulting LiDAR point cloud can be visualized within rviz2 as a sensor_msgs/PointCloud2 topic type. The data will look similar to the image shown below.
We will now start with the ray ground filter node, for which we will need the Velodyne driver that we ran previously and a pcap capture file being streamed with udpreplay
For this step we will need a fourth ADE terminal, in addition to the previous three:
$ade enter ade$ cd AutowareAuto
ade$source install/setup.bash ade$ ros2 run ray_ground_classifier_nodes ray_ground_classifier_cloud_node_exe __params:=/home/"${USER}"/AutowareAuto/src/perception/filters/ray_ground_classifier_nodes/param/vlp16_lexus.param.yaml This will create two new topics (/nonground_points and /points_ground) that output sensor_msgs/PointCloud2s that we can use to segment the Velodyne point clouds. With rviz2 open, we can add visualizations for the two new topics, alternatively an rviz2 configuration is provided in AutowareAuto/src/tools/autoware_auto_examples/rviz2/autoware_ray_ground.rviz that can be loaded to automatically set up the visualizations. Autoware.Auto ray ground filter snapshot Another component in the Autoware.Auto 3D perception stack is the downsampling filter, which is implemented in the voxel_grid_nodes package. We will run the the voxel grid downsampling node in a new ADE terminal, using the same method as for the other nodes.$ ade enter
ade$cd AutowareAuto ade$ source install/setup.bash
ade$ros2 run voxel_grid_nodes voxel_grid_cloud_node_exe __params:=/home/"${USER}"/AutowareAuto/src/perception/filters/voxel_grid_nodes/param/vlp16_lexus_centroid.param.yaml
After this we will have a new topic, named (/points_downsampled) that we can visualize with the provided rviz2 configuration file in src/tools/autoware_auto_examples/rviz2/autoware_voxel.rviz
Autoware.Auto voxel grid downsampling snapshot | 2020-01-17 20:13:01 | {"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": 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": 0.1724013239145279, "perplexity": 12026.967320329684}, "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/1579250590107.3/warc/CC-MAIN-20200117180950-20200117204950-00488.warc.gz"} |
http://shop.oreilly.com/product/9780937175842.do | Learning GNU Emacs
By Debra Cameron, Bill Rosenblatt
Publisher: O'Reilly Media
Final Release Date: October 1991
Pages: 442
GNU Emacs is the most popular and widespread of the Emacs family of editors. It is also the most powerful and flexible. (Unlike all other text editors, GNU Emacs is a complete working environment---you can stay within Emacs all day without leaving.) This book tells you how to get started with the GNU Emacs editor. It will also "grow" with you: as you become more proficient, this book will help you learn how to use Emacs more effectively. It will take you from basic Emacs usage (simple text editing) to moderately complicated customization and programming.Topics covered include: Using Emacs to read and write electronic mail. Using Emacs as a "shell environment". How to take advantage of "built-in" formatting features. Customizing Emacs. Whys and hows of writing macros to circumvent repetitious tasks. Emacs as a programming environment. The basics of Emacs LISP. The Emacs interface to the X Window System. How to get Emacs. The book is aimed at new Emacs users, whether or not they are programmers. Also useful for readers switching from other Emacs implementations to GNU Emacs. Covers Version 18.57 of the GNU Emacs editor.
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Customer Reviews | 2017-01-19 10:21:20 | {"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": 0.8899415135383606, "perplexity": 6717.550497967958}, "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-2017-04/segments/1484560280504.74/warc/CC-MAIN-20170116095120-00238-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://docs.injective.network/develop/modules/Injective/exchange/ | # Exchange
## Abstract
The exchange module is the heart of the Injective Chain which enables fully decentralized spot and derivative exchange.
It is the sine qua non module of the chain and integrates tightly with the auction, insurance, oracle, and peggy modules.
The exchange protocol enables traders to create and trade on arbitrary spot and derivative markets. The entire process of orderbook management, trade execution, order matching and settlement occurs on chain through the logic codified by the exchange module.
The exchange module enables the exchange of tokens on two types of markets:
1. Derivative Market: Either a Perpetual Swap Market or a Futures Market.
2. Spot Market | 2022-12-02 13:40:21 | {"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": 0.3266350328922272, "perplexity": 6405.763688096362}, "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/1669446710902.80/warc/CC-MAIN-20221202114800-20221202144800-00047.warc.gz"} |
https://cs.stackexchange.com/questions/94117/using-a-2nd-neural-network-to-predict-1st-neural-network-prediction-error | # Using a 2nd neural network to predict 1st neural network prediction error
So for example, we are trying to predict the amount of rainfall in the afternoon base on continuous features such as humidity and temperature in the morning.
1st neural network: Regression neural network on features to give one output label which is a continuous value for predicted rainfall in the afternoon.
2nd neural network: Features will be the same as the 1st neural network. But now, the label will be the absolute difference between the 1st neural network predicted rainfall and the actual rainfall.
From this, we can train the 2nd neural network to recognise what particular set of features will result in the 1st neural network giving a 'bad' prediction and be more wary of that 'bad' prediction. In a way, this is like using another neural network to give the confidence level of the first neural network, solely based on the same features (the humidity and temperature in the morning).
I could not find much literature on this subject and am wondering if this idea makes sense in the first place? Perhaps stacking neural networks over each other is a bad idea because it compounds the error from one network to another?
I tried this with some data except my 2nd neural network is a classifier which classifies if the error is above a certain threshold (bad prediction) or below a certain threshold (good prediction).
However, from a few different model runs, it seems that my 2nd neural network usually gives a matthew's correlation coefficient of about 0. This means my 2nd neural network is as good as guessing whether the 1st neural network prediction is good or bad.
So I am not sure if the problem is the idea itself or that my model hyperparameters are bad.
More details: I used 10 fold cross-validation for the 1st model to get a predicted rainfall for all the data. Then I used another separate 10 fold cross-validation and a siamese neural network for the 2nd model to predict whether the 1st neural network prediction is good or bad.
• If a neural network can identify the error of another neural network with the same structure and features, couldn't the original neural network have learned the error and corrected for it? Jul 10, 2018 at 16:12
• That is true... I was thinking the 2nd network can be used to learn what type of features would make the 1st network perform badly... Jul 11, 2018 at 4:19
It's not an unreasonable approach, but I suspect you'd need to define a custom loss function to make it work well.
I can also suggest two different, more sophisticated approaches: the bootstrap, or a variational neural network.
In the bootstrap, you train many classifiers (say, 100 of them); each is trained on a different random sample of the training set, and then you look at the distribution of outputs from these classifiers when you feed in the input $x$ to each of them.
In a variational network, instead of outputting a single number $y$ for the prediction in response to the input $x$, the network outputs two parameters $(\mu,\sigma)$, with the idea that the network is predicting a Gaussian distribution $\mathcal{N}(\mu,\sigma^2)$ as an approximation for $p(y|x)$. Then you can use this to get a sort of confidence interval for the prediction, e.g., $[\mu-2\sigma,\mu+\sigma]$. I'm not an expert on this, but I think a variational network is actually very close to what you suggested; we can think of it as two networks, one that outputs $\mu$ (your first network) and one that outputs $\sigma$ (your second network). However, variational networks are trained with a special loss function. In particular, if we have an instance $(x_i,y_i)$ in the training set, the loss for the network is the log likelihood $-\log p(y_i)$ where here $p(y_i)$ represents the probability of getting the output $y_i$ from a Gaussian distribution with parameters $\mathcal{N}(\mu,\sigma^2)$, where $\mu,\sigma$ are the two outputs from the network. Since the Gaussian distribution has probability density function
$$p(y_i) = c e^{-(y_i-\mu)/2\sigma}$$
where $c$ is a constant. Therefore, the loss function is
$$-\log p(y_i) = (y_i-\mu)/2\sigma + c'$$
where $c'$ is a constant that can be ignored. Thus, I think you can think of the variational approach as being equivalent to your approach, but with a custom loss function chosen to be appropriate for what you're trying to achieve. | 2023-03-27 06:17:29 | {"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": 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": 0.8491384983062744, "perplexity": 295.80931128429603}, "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/1679296948609.41/warc/CC-MAIN-20230327060940-20230327090940-00117.warc.gz"} |
https://sciencebehindthesport.wvu.edu/science-behind-cycling/brakes | # Brakes
## The Science of Stopping: It's All About Friction - Bicycle Brakes Convert Kinetic Energy (Motion) Into Thermal Energy (Heat).
### Braking Distance
The approximate braking distance can be found by determining the work required to dissipate the bike’s kinetic energy:
Through the Work-Energy Principle it can then be said that:
$\left(\mu ×\mathrm{mass}×\mathrm{gravity}\right)×\mathrm{distance}=\frac{1}{2}×\mathrm{mass}×{\mathrm{velocity}}^{2}$
Finally, by rearranging the equation and cancelling like terms we can form an equation for braking distance:
$\mathrm{distance}=\frac{{\mathrm{velocity}}^{2}}{\left(2×\mu ×\mathrm{gravity}\right)}$
μ = coefficient of friction
### Rim Brake
• How's it Work? Rubber pads are pressed against the rim of the wheel.
• Advantages: inexpensive, lightweight, easy to maintain, mechanically simple
• Disadvantages: easily contaminated, less braking power
### Disc Brake
• How's it Work? Metallic or ceramic pads are pressed against a metal rotor that's attached to the wheel.
• Advantages: powerful, protected from contaminates, better heat dissipation
• Disadvantages: expensive, heavy, difficult to maintain | 2020-06-04 04:23:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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": 0.4596339166164398, "perplexity": 7612.0580869491405}, "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-2020-24/segments/1590347439019.86/warc/CC-MAIN-20200604032435-20200604062435-00472.warc.gz"} |
https://www.semanticscholar.org/paper/The-%24K%24-theory-of-twisted-multipullback-quantum-odd-Hajac-Nest/624b6c5f238158ea805beb47523d45de9c1f8c49 | # The $K$-theory of twisted multipullback quantum odd spheres and complex projective spaces
@article{Hajac2015TheO,
title={The \$K\$-theory of twisted multipullback quantum odd spheres and complex projective spaces},
author={Piotr M. Hajac and Ryszard Nest and David Pask and Aidan Sims and Bartosz Zieli'nski},
journal={Journal of Noncommutative Geometry},
year={2015}
}
• Published 30 December 2015
• Mathematics
• Journal of Noncommutative Geometry
We find multipullback quantum odd-dimensional spheres equipped with natural $U(1)$-actions that yield the multipullback quantum complex projective spaces constructed from Toeplitz cubes as noncommutative quotients. We prove that the noncommutative line bundles associated to multipullback quantum odd spheres are pairwise stably non-isomorphic, and that the $K$-groups of multipullback quantum complex projective spaces and odd spheres coincide with their classical counterparts. We show that these…
18 Citations
• Mathematics
Banach Center Publications
• 2020
By a diagonal embedding of $U(1)$ in $SU_q(m)$, we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ to the $SU_q(m)$-action on the prolongated bundle. Then
• Mathematics
• 2017
The $K_0$-group of the C*-algebra of multipullback quantum complex projective plane is known to be $\mathbb{Z}^3$, with one generator given by the C*-algebra itself, one given by the section module
• Mathematics
• 2015
Our main theorem is that the pullback of an associated noncommutative vector bundle induced by an equivariant map of quantum principal bundles is a noncommutative vector bundle associated via the
• Mathematics
• 2020
The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the nskeleton into the (n + 1)-skeleton does not
• Mathematics
Journal of Noncommutative Geometry
• 2018
Our main theorem is that the pullback of an associated noncommutative vector bundle induced by an equivariant map of quantum principal bundles is a noncommutative vector bundle associated via the
• Mathematics
• 2020
We construct distinguished free generators of the $K_0$-group of the C*-algebra $C(\mathbb{CP}^n_\mathcal{T})$ of the multipullback quantum complex projective space. To this end, first we prove a
Taking a groupoid C*-algebra approach to the study of the quantum complex projective spaces $\mathbb{P}^{n}\left( \mathcal{T}\right)$ constructed from the multipullback quantum spheres introduced by
• Mathematics
• 2022
. In this paper, we refine the classification of compact quantum spaces by K-theory type initiated in [8]. We do it by introducing a multiplicative K-theory functor for unital C*-algebras taking values
• Mathematics
Journal of Noncommutative Geometry
• 2021
Let $H$ be the C*-algebra of a non-trivial compact quantum group acting freely on a unital C*-algebra $A$. It was recently conjectured that there does not exist an equivariant $*$-homomorphism from
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Documenta Mathematica
• 2014
We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish | 2023-01-27 11:28:57 | {"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": 0.8788243532180786, "perplexity": 1937.917977883457}, "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-2023-06/segments/1674764494976.72/warc/CC-MAIN-20230127101040-20230127131040-00412.warc.gz"} |
http://www.math.psu.edu/calendars/meeting.php?id=3773 | # Meeting Details
Title: Floer homology of cotangent bundles Symplectic Topology Seminar David Hurtubise (PSU) talk 1:25PM in McAllister 315 Abstract: Let M be a closed smooth manifold. The cotangent bundle T*M has a natural symplectic structure, and given a time-dependent Hamiltonian on T*M satisfying certain conditions one can define the symplectic Floer homology of T*M. Unlike the compact case, the Floer homology of T*M is not the singular homology of the underlying manifold. Instead, the Floer homology of T*M turns out to be isomorphic to the singular homology of the free loop space of M. In this talk I will outline three different approaches to establishing this isomorphism. The approaches three approaches are due to 1) Viterbo, 2) Abbondandolo and Schwarz, and 3) Salamon and Weber.
### Room Reservation Information
Room Number: MB315 10 / 09 / 2008 01:25pm - 02:15pm | 2014-09-02 09:51:26 | {"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": 0.9120270013809204, "perplexity": 1073.6097957639854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535921872.11/warc/CC-MAIN-20140909042205-00475-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://theoryofcomputing.org/articles/v010a006/ | Volume 10 (2014) Article 6 pp. 133-166
The Need for Structure in Quantum Speedups
Revised: July 10, 2014
Published: August 12, 2014
[PDF (446K)] [PS (1663K)] [PS.GZ (435K)]
[Source ZIP]
Keywords: decision trees, adversary method, collision problem, Fourier analysis, influences, quantum computing, query complexity
ACM Classification: F.1.2, F.1.3
AMS Classification: 81P68, 68Q12, 68Q17
Abstract: [Plain Text Version]
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms operate.
First, we show that for any problem that is invariant under permuting inputs and outputs and that has sufficiently many outputs (like the collision and element distinctness problems), the quantum query complexity is at least the $7^{\text{th}}$ root of the classical randomized query complexity. (An earlier version of this paper gave the $9^{\text{th}}$ root.) This resolves a conjecture of Watrous from 2002.
Second, inspired by work of O'Donnell et al. (2005) and Dinur et al. (2006), we conjecture that every bounded low-degree polynomial has a “highly influential” variable. (A multivariate polynomial $p$ is said to be bounded if $0\le p(x)\le 1$ for all $x$ in the Boolean cube.) Assuming this conjecture, we show that every $T$-query quantum algorithm can be simulated on most inputs by a $T^{O(1)}$-query classical algorithm, and that one essentially cannot hope to prove $\mathsf{P}\neq\mathsf{BQP}$ relative to a random oracle.
A preliminary version of this paper appeared in the Proc. 2nd “Innovations in Computer Science” Conference (ICS 2011). See Sec. 1.3 for a comparison with the present paper. | 2017-04-28 19:48:51 | {"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": 0.7606765627861023, "perplexity": 1322.574753516179}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123048.37/warc/CC-MAIN-20170423031203-00307-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/should-i-use-time-dilation-or-length-contraction.957452/ | # Should I use time dilation or length contraction?
1. Homework Statement [/B]
This is a problem that was in my Physics HW.
Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially ## 2.52 × 10^{12} ## m apart as measured by Liz, an Earth
observer, as shown in Figure P1.59. Both rockets are 50.0 m in length as measured by
Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as
measured by an observer in the other rocket? (c) According to Liz, how long before the
rockets collide? (d) According to rocket 1, how long before they collide? (e) According
to rocket 2, how long before they collide? (f) If both rocket crews are capable of total
evacuation within 90 minutes (their own time), will there be any casualties?
My doubt is on letters (d) and (e). I don't know if I am supposed to apply the time Lorentz transformation using the value obtained in (c) or if I should calculate this time based on the speed each rocket sees the other approaching and the distance using length contraction. I found two answers on the internet.
## Homework Equations
## L = L_{0}\sqrt {1 - \frac {v^2} {c^2}} ##
## \Delta t' = \frac 1 {\sqrt {1 - \frac {v^2} {c^2}}} \Delta t ##
## V' = \frac {u - V_x} {1 - \frac {uV_x} {c^2}} ##
## The Attempt at a Solution
By using the mentioned equations, I obtained that (a) ## L_1 = 83.3 m ## and ## L_2 = 62.5 m ## . (b) ## L_1 = 27.0 m ## in the frame of rocket 2 and ## L_2 = 21.0 m ## in the frame of rocket 1. (c) ## \frac {\Delta S} {v_1 + v_2} = 6000 sec = 100 min ## .
When it comes to letter (d) that something goes wrong. my first approach to it was to use the length contraction observed by 1 and divide it by the speed 1 sees 2 approaching. ## L = L_{0}\sqrt {1 - \frac {v^2} {c^2}} = 2.52 \times 10^{12} \times 0.6 = 1.512 \times 10^{12} ## and ## V' = \frac {u - V_x} {1 - \frac {uV_x} {c^2}} = \frac { 0.8c - ( - 0.6c)} {1 - \frac { (- 0.48c^2)} { c^2 }} = 0.945c ## . Dividing these results we have ## \frac {L} {V'} = 5,333 sec = 88.9 min ## . Although, using ## \Delta t' = \frac 1 {\sqrt {1 - \frac {v^2} {c^2}}} \Delta t ## , where t' is Liz's time of 100 min, we obtain ## 100 min = 1.6666 \times \Delta t ## and ## \Delta t = 60 min ##. This same problem happens when I try to solve (e), and I've taken a look at several solutions on the internet, being half of them solved in the first way, and half in the second. Shouldn't these results agree? If not, why?
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jbriggs444
Homework Helper
As with most relativity problems, the difficulty is with the relativity of simultaneity. According to Liz on Earth, the start event for both Liz and L1 is simultaneous. The end event is a collision and is naturally simultaneous for all parties involved. According to L1, the start event for L1 is not simultaneous with the start event for Liz.
Joao Victor Dantas
This makes sense. So 88.9 min would be the time it takes for the observer in rocket 1 to get to the point of collision from the start of HIS measurement and 60 min would be the time is takes for this observer from the start of Liz's measurement, correct?
robphy
Homework Helper
Gold Member
Can you draw a position-vs-time graph of the problem?
jbriggs444
Homework Helper
This makes sense. So 88.9 min would be the time it takes for the observer in rocket 1 to get to the point of collision from the start of HIS measurement and 60 min would be the time is takes for this observer from the start of Liz's measurement, correct?
I am not sure that I understand your phrasing here. Consider that L1 has a stopwatch. He starts it at some point. And we are asked for its reading at the event of the collision.
At what event does L1 start his stopwatch? I would suggest having him start it at the event that Liz considers to be simultaneous with the scenario start.
Maybe it would help to resolve the issue if you calculated the "contracted" distance that
each ship travels and then the time to traverse this distance.
Use the 100 min. that you calculated as measured by Liz. | 2022-05-23 02:06:17 | {"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": 0.932077169418335, "perplexity": 1403.4258066400305}, "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/1652662552994.41/warc/CC-MAIN-20220523011006-20220523041006-00433.warc.gz"} |
https://elmcip.net/creative-work/nome | # Nome
Creative Work
Year:
1993
Language:
Record Status:
Tags:
Description (in English):
A multimedia project produced in book, video, and CD form.
"The poems of Nome pointed to the necessity of thinking not only about the transformations that the exchange of material artifacts implies in the way we interact with the words, but also in the way they modify the meanings of the words in this mediatic ecology system in which contents are made available to reading in different situations (at the museum, at home or in the street), affecting the poetic perception in a network of meanings that connects and individualizes them."
(Quote from Giselle Beiguelman, "The Reader, the Player and the Executable Poetics: Towards a Literature Beyond the Book") | 2021-09-22 18:30:22 | {"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": 0.8349726796150208, "perplexity": 3281.469124525198}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057371.69/warc/CC-MAIN-20210922163121-20210922193121-00053.warc.gz"} |
https://answers.ros.org/question/341670/subscribing-to-tfs-transformation-change/ | # subscribing to tf's transformation change
Is there a way I could somehow subscribe to a transformation update? I.e. I want to write a callback function each time there is an update of transformation from source_frame to target_frame.
The only way I could think of is polling, or subscribing to /tf and filtering myself - both sounds bad to me.
edit retag close merge delete
1
To avoid an xy-problem could you perhaps add a little info on why you want to do this? There may be easier (and supported) ways to do what you actually want to do.
( 2020-01-14 05:30:13 -0600 )edit
Sort by » oldest newest most voted
With as generic of a statement of your problem you are right that there's limited solutions. However as @gvdhoorn suggests it's likely that if you more clearly define your problem there might be a better solution.
For example a common tool to use for receiving data with low latency is to use a tf2_ros::MessageFilter if you're processing data and need to wait for current information it will do all of that for you.
The only way I could think of is polling, or subscribing to /tf and filtering myself - both sounds bad to me.
This depends on what metric you want to use to define "bad" are you looking for minimum latency, minimum computational resources, minimal network resources. What are the rates of all components in your system? In most scenarios low rate polling will be by far the lowest CPU overhead, but will have higher latency.
Similarly do you really want an update every time that a transform updates? /tf topics may come in at 1000Hz. Is there not a minimum threshold for the update etc? An example of doing something like this is already implemented in the tf2_web_republisher
more
In TF "changes" are distributed by broadcasting frames, which are essentially publications on the /tf topic.
There is no update of the TF tree inbetween transforms (which I get the feeling you are somewhat expecting). Lookups for frames at timepoints which fall between two updates are interpolated (but of course: only when actually requested).
So a naive approach would indeed be to subscribe to /tf yourself and then pick out the frames you're interested in.
There is no infrastructure that could do the filtering for you available afaik, but tf/tfMessage is relatively trivial: it consists of a list of geometry_msgs/TransformStamped, which have child_frame_id and frame_id (in the header).
more
Thanks. Just making sure - tf is a pretty high rate topic, so subscribing to it directly will be quite wasteful right?
( 2020-01-14 09:58:05 -0600 )edit
It'll be no different from instantiating a tf2_ros::TransformListener.
( 2020-01-14 10:09:49 -0600 )edit
I think subscribing to the TF topic is the right answer. The Listeners are also doing that and then dumping the results into a buffer used to get transforms and interpolate. If you want to trigger something based on an update of a specific frame, this seems to be the clearest way to handle it.
( 2020-01-14 15:41:48 -0600 )edit | 2020-01-21 20:54:05 | {"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": 0.22256307303905487, "perplexity": 1470.549738688166}, "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-2020-05/segments/1579250605075.24/warc/CC-MAIN-20200121192553-20200121221553-00096.warc.gz"} |
http://openstudy.com/updates/55f9ba6de4b0b96d8936c3d1 | ## anonymous one year ago Y=6/(3x-2) Find the gradient of the curve at the point where x = 2.
1. IrishBoy123
for this? $y = \frac {6}{3x-2}$ how did you try to do this?!
2. anonymous
actually i have a diagram wait .
3. anonymous
4. IrishBoy123
so what are you actually learning? some context would be great :p | 2016-10-23 06:29:34 | {"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": 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": 0.569854736328125, "perplexity": 1670.766079253182}, "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/1476988719155.26/warc/CC-MAIN-20161020183839-00290-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.tutorialspoint.com/delete-function-in-php | # delete() function in PHP
The delete() function deletes a file. The path of the file to be deleted is to be specified as a parameter.
## Syntax
delete(file_path)
## Parameters
• file_path − Specify the path of the file to be deleted.
## Return
The delete() function returns.
• True, on success
• False, on failure
## Example
The following is an example. This deletes the file “amit.txt” specified as a parameter.
<?php
echo delete("E:/list/amit.txt");
?>
## Output
true
karthikeya Boyini
I love programming (: That's all I know | 2023-03-22 06:05:42 | {"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": 0.3495207726955414, "perplexity": 14064.499144365931}, "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/1679296943750.71/warc/CC-MAIN-20230322051607-20230322081607-00477.warc.gz"} |
https://escholarship.org/uc/item/12z3z7vg | Nearly Linear-Work Algorithms for Mixed Packing/Covering and Facility-Location Linear Programs
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Open Access Publications from the University of California
## Nearly Linear-Work Algorithms for Mixed Packing/Covering and Facility-Location Linear Programs
• Author(s): Young, Neal E
• et al.
## Published Web Location
https://arxiv.org/pdf/1407.3015.pdf
No data is associated with this publication.
Abstract
We describe the first nearly linear-time approximation algorithms for explicitly given mixed packing/covering linear programs, and for (non-metric) fractional facility location. We also describe the first parallel algorithms requiring only near-linear total work and finishing in polylog time. The algorithms compute $(1+\epsilon)$-approximate solutions in time (and work) $O^*(N/\epsilon^2)$, where $N$ is the number of non-zeros in the constraint matrix. For facility location, $N$ is the number of eligible client/facility pairs.
Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.
Item not freely available? Link broken?
Report a problem accessing this item | 2021-05-15 11:02:24 | {"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": 0.7636702656745911, "perplexity": 5069.721831490336}, "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-2021-21/segments/1620243991801.49/warc/CC-MAIN-20210515100825-20210515130825-00303.warc.gz"} |
https://www.studyadda.com/ncert-solution/11th-chemistry-the-p-block-elements_q21/500/32422 | • # question_answer 21) Rationalise the given statements and give chemical reactions. (i) Lead (II) chloride reacts with $C{{l}_{2}}$ to give$PbC{{l}_{4}}$. (ii) Lead (IV) chloride is highly unstable towards heat. (iii) Lead is known not to form an iodide, $Pb{{l}_{4}}$.
(i) On account of inert pair effect, $PbC{{l}_{2}}$ is more stable than$PbC{{l}_{4}}$. Thus, $PbC{{l}_{2}}$ does not react with chlorine to form$Pb{{I}_{4}}$. (ii) On account of greater stability of +2 state over +4 state, $PbC{{l}_{4}}$decomposes on heating into$PbC{{I}_{2}}$. $PbC{{l}_{4}}\xrightarrow{Heat}PbC{{l}_{2}}+C{{l}_{2}}$ (iii) As $P{{b}^{4+}}$ is an oxidising agent while ${{I}^{-}}$ ion is a reducing agent, the formation of $Pb{{I}_{4}}$ is not possible. $P{{b}^{4+}}+4{{I}^{-}}\to Pb{{I}_{2}}+{{I}_{2}}$ Thus, $Pb{{I}_{4}}$ does not exist. | 2020-09-21 03:20:26 | {"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": 0.5762506723403931, "perplexity": 2796.813386938983}, "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/1600400198887.3/warc/CC-MAIN-20200921014923-20200921044923-00270.warc.gz"} |
http://mathhelpforum.com/number-theory/59701-congruence-print.html | # congruence
Printable View
• November 15th 2008, 11:04 AM
bill77
congruence
Is there anyone who can help me where to start. I'm having a hard time to figure this problem out. Thanks
Show that if a, b, and m are integers such that m ≥ 2 and a ≡ b( mod m), then gcd(a,m) = gcd(b,m).
• November 15th 2008, 11:30 AM
o_O
$a \equiv b \ (\text{mod } m) \ \Leftrightarrow a = b + km$ for some integer k.
Let $d = (a,m)$. Since $d \mid a$ and $d \mid m$, it follows from $a = b+km$ that $d \mid b$ and is thus a common divisor of $b$ and $m$.
Let $c$ be any common divisor of $b$ and $m$. With a similar argument, we have that $c \mid a$. By definition, since $d$ is the greatest common divisor of $a$ and $m$, we have that $c \leq d$.
This means that any common divisor of $b$ and $m$ is less than $d$. Can you conclude?
• November 15th 2008, 12:14 PM
bill77
thanks for the help, i now know what to conclude:) | 2015-04-25 06:54:33 | {"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": 19, "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": 0.9414550065994263, "perplexity": 135.40336901314816}, "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-2015-18/segments/1429246647589.15/warc/CC-MAIN-20150417045727-00135-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/geometry/CLONE-df935a18-ac27-40be-bc9b-9bee017916c2/chapter-4-section-4-1-properties-of-a-parallelogram-exercises-page-190/44 | ## Elementary Geometry for College Students (7th Edition)
We consider a rectangle. where the sides are a, b, c, and d and where the diagonals are A and B. Thus, we obtain: $A^2 = a^2 + b^2$ And: $B^2 = c^2 + d^2$ Adding these gives: $A^2 + B^2 = a^2 + b^2 +c^2 + d^2$ Thus, the proof is completed. | 2021-01-25 08:03:47 | {"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": 0.563818633556366, "perplexity": 338.19665236608745}, "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/1610703565376.63/warc/CC-MAIN-20210125061144-20210125091144-00452.warc.gz"} |
https://hackage.haskell.org/package/hex-text-0.1.0.4/docs/Text-Hex.html | hex-text-0.1.0.4: ByteString-Text hexidecimal conversions
Text.Hex
Synopsis
# Encoding and decoding
Encodes a byte string as hexidecimal number represented in text. Each byte of the input is converted into two characters in the resulting text.
>>> (encodeHex . ByteString.singleton) 192
"c0"
>>> (encodeHex . ByteString.singleton) 168
"a8"
>>> (encodeHex . ByteString.pack) [192, 168, 1, 2]
"c0a80102"
Text produced by encodeHex can be converted back to a ByteString using decodeHex.
The lazy variant of encodeHex is lazilyEncodeHex.
Decodes hexidecimal text as a byte string. If the text contains an even number of characters and consists only of the digits 0 through 9 and letters a through f, then the result is a Just value.
Unpacking the ByteString in the following examples allows for prettier printing in the REPL. >>> (fmap ByteString.unpack . decodeHex . Text.pack) "c0a80102" Just [192,168,1,2]
If the text contains an odd number of characters, decoding fails and produces Nothing.
>>> (fmap ByteString.unpack . decodeHex . Text.pack) "c0a8010"
Nothing
If the text contains non-hexidecimal characters, decoding fails and produces Nothing.
>>> (fmap ByteString.unpack . decodeHex . Text.pack) "x0a80102"
Nothing
The letters may be in either upper or lower case. This next example therefore gives the same result as the first one above:
>>> (fmap ByteString.unpack . decodeHex . Text.pack) "C0A80102"
Just [192,168,1,2]
lazilyEncodeHex is the lazy variant of encodeHex.
With laziness, it is possible to encode byte strings of infinite length:
>>> (LazyText.take 8 . lazilyEncodeHex . LazyByteString.pack . cycle) [1, 2, 3]
"01020301"
# Types
type Text = Text Source #
Strict text
type LazyText = Text Source #
Lazy text
Strict byte string
Lazy byte string | 2022-01-22 22:00:16 | {"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": 0.368380069732666, "perplexity": 13997.033478197418}, "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/1642320303884.44/warc/CC-MAIN-20220122194730-20220122224730-00254.warc.gz"} |
https://www.physicsforums.com/threads/physical-meaning-of-kdv-equation.809586/ | # Physical meaning of KdV equation
1. Apr 20, 2015
### fian
Here is one of the KdV form
u_t + u_x + uu_x + u_{xxx} = 0
Where u is elevation, x is spatial variable, and t is time variable. The first two terms describe the linear water wave, the third term represent the nonlinear effect, and the last term is the dispersion.
From what i understand, the nonlinear term explain the energy focusing that keeps the shape of the wave packet. But, how is u multiplied by u_x represents the energy focusing? For example, like in predator-prey model, the nonlinear term xy explain the interaction between the two species, where x and y are the number of predators and prey respectively.
Also, how does the last term, the third derivative of u with respect to x, explain the dispersion which is the deformation of the waves?
2. Apr 20, 2015
### fian
Sorry, It seems like i accidentally posted it twice, it is because of the low connection.
3. Apr 20, 2015
### fian
Can anybody please help me to understand the physical interpretation of kdv eq.?
4. Apr 23, 2015
### bigfooted
$uu_x = (\frac{1}{2}u^2)_x$
so it represents convection of kinetic energy. There is a link with the (inviscid) Burgers equation.
5. Apr 23, 2015
### fian
Thank you for replying.
It gives me some hints to study more.
This is how i understand it. Let u be the elevetion of wave. u^2 represents the interaction of waves which causes energy transfer among the waves. Am I correct? | 2017-12-17 14:04:17 | {"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": 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": 0.4791027903556824, "perplexity": 911.0461711299955}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948596051.82/warc/CC-MAIN-20171217132751-20171217154751-00139.warc.gz"} |
http://mathoverflow.net/questions/90490/blow-up-along-a-subscheme-and-along-its-associated-reduced-closed-subscheme | # Blow-up along a subscheme and along its associated reduced closed subscheme
Let $X$ be a noetherian scheme and let $Y$ be a closed subscheme of $X$. What relation is there between $\mathrm{Bl} _ {Y}(X)$ and $\mathrm{Bl} _{ Y _{\mathrm{red}}}(X)$ ?
Thanks.
-
There is no map from one blow up to the other, and definitely not an isomorphism. Please see my comments to J.C. Ottems answer.
However, if you replace radical by integral closure, then everything is fine.
Here's what I mean, if $I$ is an ideal and $J$ is its integral closure, then you always have an everywhere defined map
$$Bl_J X \to Bl_I X.$$
This need not be an isomorphism, indeed the integral closure of $(x^2, y^2)$ is $(x^2, xy, y^2)$. The blow up of the latter ideal is the normalization of the blow up of the former.
The other way you can get a map is if $J = \sqrt I$, and also if we can write $I = J \cdot \mathfrak{a}$ for some other ideal $\mathfrak{a}$. Then the blow up of $I$ is always the blow up of $\mathfrak{a}$ pulled back to $Bl_J X$.
In general, you should expect no relation between the blow up of two ideals with the same radical unless there is some integral closure relation between them and/or one ideal is the product of the other (and something else).
-
In fact, this characterises all cases, according to projecteuclid.org/euclid.ijm/1258138260. – Norbert Pintye Nov 26 '14 at 21:44
Thanks, I didn't know about that paper. – Karl Schwede Nov 27 '14 at 15:11
In general they can be very different. For example take the subscheme $Y$ of $\mathbb{A}^2$ given by the ideal $(x^2,y)$. Here the blow up is covered by the two open subsets
$$U = \mbox{Spec} k[x, y][t]/(y − x^2t),\qquad V = \mbox{Spec} k[x, y][s]/(ys − x^2)$$
In particular the blow up of $Y$ is singular, whereas the blow-up of $\mathbb{A}^2$ at a point is not.
In general, even if you assume that both blow-ups are smooth, all sorts of things can happen depending on how complicated the ideal sheaf is. For example the blow-ups can have a different number of exceptional divisors and not even be related by a finite map. Even worse, every birational morphism $X'\to X$ is the blow-up of $X$ along some ideal sheaf.
-
Thanks for the example. But at least, there is a natural map from one to another? – gio Mar 7 '12 at 21:25
I believe there is no map from one to the other. In the example J.C. Ottem gives, the blow up of $(x^2,y)$ can be obtained as follows. Blow up $(x,y)$, then blow up another point on that first blowup (the origin on one of the usual charts), and then contract the first exceptional curve. There's no map between $Bl_{(x^2,y)}X$ and $Bl_(x,y) X$, at least no map over $X$.$$\text{ }$$ Just because you have an inclusion of Rees algebras, does not mean that there is an everywhere defined map of the blow-ups. In the given example, one of the points of the overring contracts to an irrelevant ideal. – Karl Schwede Mar 8 '12 at 4:39
You are right, Karl. Thanks. – J.C. Ottem Mar 8 '12 at 8:06 | 2015-07-07 13:21:07 | {"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": 0.9445434212684631, "perplexity": 180.06218053607466}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375099361.57/warc/CC-MAIN-20150627031819-00250-ip-10-179-60-89.ec2.internal.warc.gz"} |
http://www.motls.blogspot.com/2006/06/superman-explains-double-slit.html | ## Tuesday, June 06, 2006 ... /////
### Superman explains double slit experiment
If you're a reader who does not know how quantum interference works, an old supersymmetric man, also known as superman with a supercharge "Q" on his shirt, explains it in this
If you have two minutes, you can also learn what is string theory from a
Sorry, Steve, I just copied the description at Google's website and of course disagree with it! :-) For those who found the previous videos too complicated or separated from reality, here's a
but it is more physical than this blog, especially in the context of mechanics. Finally, you should certainly avoid searching for
because otherwise you may find a calculus tutorial by an MIT alumnus which could be a problem. ;-)
#### snail feedback (4) :
During a single run of a double-slit experiment (leading to one more detection event), do you think that
(1) the particle actually goes through both slits
(2) the particle actually goes through only one slit
(3) the question is not allowed
(4) something else?
By the way, I do know the rules for making a quantum calculation, e.g. an irreversible interaction at the slit would destroy the quantum interference. This is a conceptual question about how you think of the physical reality between observations.
Dear mitchell,
sorry, these are somewhat verbal games. But the point of 1) and 2) is clearly designed for the reader to imagine a classical "reality" which either has a real, objective object that goes through one slit, or both slits.
But that's not how this world - a quantum world - operates. So answers 1,2) are gone.
Because I support the freedom of speec, I must also reject the answer 3).
Thankfully, you have given us another choice, option 4).
The correct answer is that a single particle must be treated as going through one slit only, but all histories contribute to the probability amplitudes via Feynman's path-integral prescription, and the resulting amplitude that has contributions from all the histories must be squared (in absolute value) and only be interpreted as the probability, and this probability is the only thing that QM (the most complete possible theory) can predict.
So physical laws can only predict statistical properties of many similar experiments, not the outcome of one particular experiment.
I can also describe the situation without Feynman's approach. The most complete knowledge about the particle is described by a wave function that is nonzero in both slits. But the wave function "is not" the particle itself and it is not a real wave. It is a tool to calculate probabilities, and the rest goes just like in the paragraphs above.
Best wishes
Lubos
Lubos:
I didn't quite understand that explanation, it sounds a awful lot like Many Worlds, but at the same time it didn't.
How would that interpretation differ from the Many histories interpretation/decoherent histories interpretation that Hartle and Gell Mann are supporters of where the others worlds are actual?
Dear I Do Not Give a F***,
what I write is true and completely independent of someone's preferred interpretation as long as the interpretation is consistent with the known observations.
The wave functions interfere (i.e. add from both slits); they only determine probabilities that can only be checked when the same experiment is repeated many times; the particle is always seen at one place.
In many worlds, one imagines that all the histories with the final outcome "exist" somewhere in "parallel universes". I personally prefer consistent histories as the most comprehensive interpretation.
But once again, phenomena such as decoherence are real phenomena that exist regardless any interpretation as long as the interpretation takes experimentally verified 25-year-old realizations into account. They can be observed, they can be calculated and predicted, and they describe many things such as the boundary between the classical and quantum intuition.
Physics is not about vacuous philosophical flapdoodle. Physics is about understanding and predicting phenomena. I told you how this should be done properly, what can be done, and what can't be done. Everything you try to add is pure rubbish and you're clearly dissatisfied only because I don't want to add any rubbish of this kind - which is too bad.
Best wishes
Lubos | 2014-12-22 23:22:24 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6712509393692017, "perplexity": 889.9786299382087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802777295.134/warc/CC-MAIN-20141217075257-00101-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://homework.zookal.com/questions-and-answers/use-n-to-write-an-expression-which-computes-the-excess-430344920 | 1. Engineering
2. Computer Science
3. use n to write an expression which computes the excess...
# Question: use n to write an expression which computes the excess...
###### Question details
Use n to write an expression which computes the excess amount for the n-bit excess notation used by the IEEE Standard 754. Hint When n = 8 (single precision), the excess amount is 127; when n = 11 (double precision), the excess amount is 1023. | 2021-04-19 22:51:42 | {"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": 0.9138088822364807, "perplexity": 2416.35215816793}, "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/1618038917413.71/warc/CC-MAIN-20210419204416-20210419234416-00172.warc.gz"} |
https://lu.kattis.com/problems/lu.gorilla | OpenKattis
Lund University
# Gorilla
In biology, a recurring problem is to find optimal alignments between two strings of DNA, RNA, or proteins. One example of this is measuring the similarity of different protein sequences found in different animals to understand how related they are.
Given a set of amino acid sequences belonging to different animals, we want to produce an optimal alignment. An alignment between two strings $X$, $Y$ is a pair of alignment strings $X_ a, Y_ a$ of the same length, where each alignment string consists of the original string, but with zero or more ‘-’ characters (called gaps) inserted. An alignment is considered optimal if it maximises the score. The score is calculated by the sum of each aligned character pair in the two strings. A gap compared to anything always gives the score $-4$. The score of two characters from the set ARNDCQEGHILKMFPSTWYVBZX is determined by a specific BLOSUM-matrix. The matrix and code snippets for generating the matrix are attached.
For example, the strings $\texttt{KATTIS}$ and $\texttt{KATIS}$ can be aligned as:
$\texttt{KATTIS}$
$\texttt{KAT-IS}$
This is an optimal alignment since it produces the maximal score $5 + 4 + 5 - 4 + 4 + 4 = 18$.
## Input
The first line contains integers $N$ and $Q$, such that $1 \leq N \leq 20$ and $1 \leq Q \leq 100$. Then follow $2N$ lines of organism names and their amino acid sequences. For each organism, the first line is their name, and the second line is a string representing the amino acid sequence. Then follow $Q$ lines of queries, where each query is a pair of names separated by a space.
An organism name consists of a unique word of at most 20 characters, using only characters in the range {a—z,A—Z}.
Each amino acid sequence consists of a string of length at most $200$ where each character represents an amino acid (from the set ARNDCQEGHILKMFPSTWYVBZX).
## Output
For each of the $Q$ queries, output two lines containing an optimal alignment for the two amino acid sequences. The first line should contain the alignment string corresponding to the first organism, and the second should contain the alignment string corresponding to the second organism. If there exists multiple optimal alignments output any of them.
Sample Input 1 Sample Output 1
2 1
katis
KATIS
kattis
KATTIS
kattis katis
KATTIS
KAT-IS
Sample Input 2 Sample Output 2
1 1
a
A
a a
A
A
Sample Input 3 Sample Output 3
3 3
Sphinx
KQRK
Bandersnatch
KAK
Snark
KQRIKAAKABK
Sphinx Snark
Sphinx Bandersnatch
Snark Bandersnatch
KQR-------K
KQRIKAAKABK
KQRK
K-AK
KQRIKAAKABK
-------KA-K | 2018-11-14 03:20:28 | {"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": 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": 0.46186065673828125, "perplexity": 958.9013670032706}, "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-2018-47/segments/1542039741578.24/warc/CC-MAIN-20181114020650-20181114042650-00449.warc.gz"} |
https://mathematica.stackexchange.com/questions/184941/understanding-conditional-replacement | # Understanding conditional replacement
I have encountered recently a replacement and I tried to look up documentation but could not quite find anything and hope to get some explanation from experts. The replacement is the following:
Gamma[2*x+c] /. Gamma[t:2*g_ + d_:0 ] -> 1/Sqrt[Pi]*2^(t-1)*Gamma[t/2]*Gamma[(t+1)/2]
I have never seen this way of conditional replacement. This gives correct replacement for any
Gamma[2*x+c].
What I want to know if anyone can explain the piece, what it does:
Gamma[t:2*g_ + d_:0 ]
What I understood is that whenever it sees argument of the type 2*x+c, it replaces and in the replaced output it does the following:
t-> 2*x+c
and +d_:0 is needed to recognise any argument of type
2*x+c
I will be grateful if anyone can explain this type of notations for replacement and what are the scopes and how it will look for multiple variable replacement.
• t:2*g_ + d_ matches 2 x + c, t:2*g_ matches 2 x, and t:2*g_ + d_:0 (or t:2*g_ + d_.) matches both 2x and 2 x +c. – kglr Oct 30 '18 at 17:42
• The symbol t:2*g_ means that “t” is a name that on the right hand side represents 2*g_. In the second example d_:0 means that “0” is a default value that will be used in case “d” is not supplied. – Jack LaVigne Oct 30 '18 at 18:10
Take your expression and wrap it in FullForm[HoldForm[expr]] and it will spell out the details:
FullForm[HoldForm[
Gamma[2*x + c] /.
Gamma[t : 2*g_ + d_: 0] ->
1/Sqrt[Pi]*2^(t - 1)*Gamma[t/2]*Gamma[(t + 1)/2]]]
The construct
t:2*g_
is a shortcut for a named pattern. t represents the pattern object 2*g_ on the right hand side during the replacement.
The construct
d_:0
is a shortcut for Optional. It means that if that part of the pattern is omitted it will use 0 for d during the replacement. | 2020-07-15 01:45:27 | {"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": 0.3292062282562256, "perplexity": 2002.5336789814496}, "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/1593657154789.95/warc/CC-MAIN-20200715003838-20200715033838-00233.warc.gz"} |
http://tug.org/pipermail/texhax/2005-September/004623.html | # [texhax] roman page numbers in acrobat
Fri Sep 9 18:34:43 CEST 2005
```On Sep 9, 2005, at 12:02 PM, Florian Knorn wrote:
> short question. i'm using the hyperref package, together with the
> memoir
> class. i also use \frontmatter, \mainmatter and \backmatter.
>
> now how do i get the cute roman page numbers into acrobat aswell ? like
> in the manual from the memoir-class ?
>
> thanks for your help, i hope it's not jsut some little setup thing i
> oversaw,
Are you using pdftex?
The invocation for this from the memman.tex manual I have handy is:
\ifpdf
\pdfoutput=1
\usepackage[plainpages=false,pdfpagelabels,bookmarksnumbered]{hyperref}
\usepackage{memhfixc}
\fi
William
-- | 2017-10-18 20:33:46 | {"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": 0.9738834500312805, "perplexity": 13752.47247039015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823114.39/warc/CC-MAIN-20171018195607-20171018215607-00385.warc.gz"} |
http://mymathforum.com/topology/4767-discrete-topology-product-topology.html | My Math Forum discrete topology, product topology
Topology Topology Math Forum
December 2nd, 2008, 01:04 PM #1 Newbie Joined: Nov 2008 Posts: 13 Thanks: 0 discrete topology, product topology For each $n \in \omega$, let $X_n$ be the set $\{0, 1\}$, and let $\tau_n$ be the discrete topology on $X_n$. For each of the following subsets of $\prod_{n \in \omega} X_n$, say whether it is open or closed (or neither or both) in the product topology. (a) $\{f \in \prod_{n \in \omega} X_n | f(10)=0 \}$ (b) $\{f \in \prod_{n \in \omega} X_n | \text{ }\exists n \in \omega \text{ }f(n)=0 \}$ (c) $\{f \in \prod_{n \in \omega} X_n | \text{ }\forall n \in \omega \text{ }f(n)=0 \Rightarrow f(n+1)=1 \}$ (d) $\{f \in \prod_{n \in \omega} X_n | \text{ }|\{ n \in \omega | f(n)=0 \}|=5 \}$ (e)$\{f \in \prod_{n \in \omega} X_n | \text{ }|\{ n \in \omega | f(n)=0 \}|\leq5 \}$ Recall that $\omega= \mathbb{N} \cup \{0\}$
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2018-06-25 05:59:28 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 12, "/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": 0.5045293569564819, "perplexity": 2223.9298333757565}, "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-2018-26/segments/1529267867493.99/warc/CC-MAIN-20180625053151-20180625073151-00537.warc.gz"} |
http://stackoverflow.com/questions/1048805/compressing-a-directory-of-files-with-php | # Compressing a directory of files with PHP
I am creating a php backup script that will dump everything from a database and save it to a file. I have been successful in doing that but now I need to take hundreds of images in a directory and compress them into one simple .tar.gz file.
What is the best way to do this and how is it done? I have no idea where to start.
-
If you are using PHP 5.2 or later, you could use the Zip Library
and then do something along the lines of:
$images = '/path/to/images'; //this folder must be writeable by the server$backup = '/path/to/backup';
$zip_file =$backup.'/backup.zip';
if ($handle = opendir($images))
{
$zip = new ZipArchive(); if ($zip->open($zip_file, ZIPARCHIVE::CREATE)!==TRUE) { exit("cannot open <$filename>\n");
}
while (false !== ($file = readdir($handle)))
{
$zip->addFile('path/to/images/'.$file);
echo "$file\n"; } closedir($handle);
echo "numfiles: " . $zip->numFiles . "\n"; echo "status:" .$zip->status . "\n";
$zip->close(); echo 'Zip File:'.$zip_file . "\n";
}
-
Thanks Kev for the answer. I just need to clarify one little thing: did you mean to ask if I had a version of PHP lower than 5.2 or higher than 5.2. I currently have 5.2.6. As I understand your answer, I will not be able to run this because I have a PHP version to high. Is this correct? – VinkoCM Jun 26 '09 at 12:43
He means that you need a PHP version that's 5.2.0 or later, so you'll be fine. – alexn Jun 26 '09 at 13:00
Yeah sorry as Alexander says its for 5.2.0 or later – Paul Dixon Jun 26 '09 at 13:08
I just tried this and I get this error:<br> Fatal error: Class 'ZipArchive' not found in [...] on line 7. <br>What could cause this? I just contacted my web hosting provider to tell me if PHP is installed with the appropriate libraries. – VinkoCM Jun 26 '09 at 13:11
Thank you everybody for all the help. I finally go the script to work. All I had to do was change this line: $zip->addFile($file); to this: $zip->addFile('path/to/images/'.$file); – VinkoCM Jun 26 '09 at 14:43
You can also use something like this:
exec('tar -czf backup.tar.gz /path/to/dir-to-be-backed-up/');
Be sure to heed the warnings about using PHP's exec() function.
-
Is this code runs on a server which is disabled functions exec,system,shell_exec,...? – Amir Jul 1 at 0:46
$archive_name = 'path\to\archive\arch1.tar';$dir_path = 'path\to\dir';
$archive = new PharData($archive_name);
$archive->buildFromDirectory($dir_path); // make path\to\archive\arch1.tar
$archive->compress(Phar::GZ); // make path\to\archive\arch1.tar.gz unlink($archive_name); // deleting path\to\archive\arch1.tar
-
You can easily gzip a folder using this command:
tar -cvzpf backup.tar.gz /path/to/folder
This command can be ran through phps system()-function.
Don't forget to escapeshellarg() all commands.
-
Thank you Alexander for you answer. How would this look like in php? Would it go something along the lines of: system('tar -cvzpf my_backup.tar.gz /images_water/images_rivers/'); – VinkoCM Jun 26 '09 at 12:45
Yes, that would do it. – alexn Jun 26 '09 at 13:00
Unfortunately this does not work for me because my hosting provider has set security restrictions on exec/system commands. – VinkoCM Jun 26 '09 at 13:32 | 2014-07-10 06:30:07 | {"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": 0.704372763633728, "perplexity": 2701.8711798415984}, "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-2014-23/segments/1404776404630.61/warc/CC-MAIN-20140707234004-00002-ip-10-180-212-248.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/160573-rolles-theorem-print.html | # Rolle's Theorem!
• October 21st 2010, 07:26 PM
drewbear
Rolle's Theorem!
Use Rolle's Theorem and argue the case that $f(x)=x^5-7x+c$ has at most one real root in the interval [-1,1]
• October 21st 2010, 07:44 PM
Jhevon
Quote:
Originally Posted by drewbear
Use Rolle's Theorem and argue the case that $f(x)=x^5-7x+c$ has at most one real root in the interval [-1,1]
You can show it is possible to have a root using the intermediate value theorem.
To use Rolle's theorem to argue there is at most one, you can proceed thusly:
Assume, to the contrary, there are two roots (or more, but at least 2 is fine), say for $\displaystyle x = x_1$ and $\displaystyle x = x_2$, both in the interval you are considering. and you may also assume that $x_1 < x_2$. then that means
$\displaystyle f(x_1) = f(x_2) = 0$
and so according to Rolle's theorem, there must be a point $\displaystyle x = x_3$, such that $\displaystyle x_1 < x_3 < x_2$ and $\displaystyle f'(x_3) = 0$.
Where can you get with that?
• October 21st 2010, 08:12 PM
drewbear
i am sorry but i am still a little confused. i understand the IVT and the proving by contradiction, but the c variable is throwing me off. do i have to solve for that ever or is that just a constant of no importance?
• October 21st 2010, 08:50 PM
TheEmptySet
c is a constant so when you take the derivative you get
$f'(x)=5x^4-7$
As Jhevon suggested where are the zero's of $f'(x)$? | 2014-03-15 14:53:28 | {"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": 0, "img_math": 0, "codecogs_latex": 11, "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": 0.9097934365272522, "perplexity": 345.45608655603786}, "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-2014-10/segments/1394678697956/warc/CC-MAIN-20140313024457-00008-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/50355/wanted-a-graph-g-without-bridges-whose-square-is-not-hamiltonian | # Wanted: a graph $G$ without bridges, whose square is not hamiltonian
Construct an example of graph $G$ without bridges, such that its square $G^2$ is non hamiltonian. Note: Since Fleischner's Theorem (the square of each 2-connected graph is Hamiltonian) and bridges are forbidden, the required graph should have at least one cut-vertex.
-
Please see mathoverflow.net/faq#whatnot – Yemon Choi Dec 25 '10 at 17:41
Or, if this is not homework/coursework, see mathoverflow.net/howtoask – Yemon Choi Dec 25 '10 at 17:42
No, the teacher said that this example exists, but he did not remember it. He also said, that as conclusion we obtain that the Fleischner's Theorem does not improve. – Michael Dec 25 '10 at 17:44
I tried to find information on the Internet, but had no success – Michael Dec 25 '10 at 17:51
In this context the square of a graph $G$ has the same vertices but has edges between vertices if their distance in $G$ is 1 or 2. – Aaron Meyerowitz Dec 26 '10 at 6:30 | 2015-10-06 20:23:06 | {"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": 0.9458744525909424, "perplexity": 786.2698793312968}, "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-2015-40/segments/1443736679145.29/warc/CC-MAIN-20151001215759-00113-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://scicomp.stackexchange.com/questions/16179/discrete-optimization-on-a-cartesian-product-with-component-wise-increasing-obje | # Discrete optimization on a cartesian product with component-wise increasing objective function
The set-up is the following:
We have $K$ finite sets of real numbers,
i.e. sets $G_i, i=1 \dotsc, K$ and $|G_i| = n_i < \infty$.
Furthermore, assume that we have a function
$$h: \mathbb R^K \to \mathbb R$$
which is monotonically increasing in each component.
Similarly, there is another function $$g: \mathbb R^K \to \mathbb R$$,which does not necessarily fullfill the monotonicity condition.
The optimization problem I want to solve is the following:
Find $$\max_{(x_1,\dotsc,x_K) \in G_1 \times \dotsc \times G_K} h(x_1,\dotsc, x_K)$$
subject to $$g(x_1,\dotsc, x_K) \leq c$$, where $c$ is a pre-specified constant. The naive approach takes $2\prod_{i=1}^{K}n_i$ function evaluations (evaluate $h$, check condition defined by $g$).
By how much can we improve this by using the componentwise monotonicity of $h$? What if we also assume that $g$ is also increasing in each component?
The monotonicity of $h$ doesn't help you much if you can't say anything about the shape of the feasible set defined by the constraint. Intuitively, for a monotonic objective function, you'd like to "go as far to the right as possible" in each coordinate, but if the constraint function has no properties, in each coordinate direction the feasible set may be disconnected intervals. On the other hand, if $g$ is also increasing in each component, then you know that the feasible set is connected and, I believe, in fact convex. That's a much easier problem to describe.
• "If $g$ is also increasing in each component, then you know that the feasible set is connected and, I believe, in fact convex." It's connected, but not necessarily convex: consider $g(x,y)=\sqrt x+\sqrt y$. – user3883 Nov 21 '14 at 9:52 | 2021-06-16 14:04:12 | {"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": 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": 0.8505187034606934, "perplexity": 206.45366701812847}, "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-2021-25/segments/1623487623942.48/warc/CC-MAIN-20210616124819-20210616154819-00291.warc.gz"} |
https://socratic.org/questions/what-is-the-cross-product-of-3-0-5-and-3-6-4 | # What is the cross product of [3, 0, 5] and [3,-6,4] ?
Feb 19, 2016
$\left[3 , 0 , 5\right] \times \left[3 , - 6 , 4\right] = \left[30 , 3 , - 18\right]$
#### Explanation:
[i j k]
[3 0 5]
[3 -6 4]
To calculate the cross product, cover set the vectors out in a table as shown above. Then cover up the column for which you're calculating the value of (e.g. if looking for the i value cover the first column). Next take the product on the top value in the next column to the right and the bottom value of the remaining column. Subtract from this the product of the two remaining values. This has been carried out below, to show how it's done:
i = (04) - (5(-6)) = 0 - (-30) = 30
j = (53) - (34) = 15 - 12 = 3
k = (3(-6)) - (03) = -18 - 0 = -18
Therefore:
$\left[3 , 0 , 5\right] \times \left[3 , - 6 , 4\right] = \left[30 , 3 , - 18\right]$ | 2020-02-21 07:13:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7034896016120911, "perplexity": 534.4561830528071}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145443.63/warc/CC-MAIN-20200221045555-20200221075555-00236.warc.gz"} |
https://emacs.stackexchange.com/questions/47874/fastest-way-to-draw-pixels-in-emacs/47875 | # Fastest way to draw pixels in Emacs
I'm currently working on a CHIP-8 emulator. This platform requires me to draw 64x32 black/white pixels, ideally at a speed between 30 and 60 frames per second. There's an extension to it that increases the possible resolution to 128x64 black/white pixels. At this speed I've found it necessary to avoid needless consing, this severely limits my options. My experiences so far:
• Generating SVG on the fly. My preferred library for this keeps creating tons of lists. The alternative would be using a template string, however I'm afraid editing it will create new strings, creating a comparable amount of garbage in the process.
• Inserting lines of colored text, then moving across them and deleting/inserting differently colored text if needed. This is my current approach. It works fast enough at 64x32 pixels, but turned out to be too slow at 128x64 pixels. I can imagine that changing the properties of text might help, but haven't tested it yet.
• Inserting a XBM image backed by a bool vector, then changing the bool vector's contents and forcing Emacs to redraw the image. The latter part is particularly painful as you need to (force-window-update BUFFER) and (image-flush SPEC) to make changes happen. Furthermore, not all changes are visible for a yet to be determined reason, the overall experience isn't nearly as smooth as with the previous solution. If drawn at a scale comparable to the text solution, the speed is in fact a bit worse. I've yet to test it at 128x64 pixels.
Are there any other possible solutions or tweaks I've overlooked? I'd prefer to stay within the options of vanilla Emacs before venturing into creating my own C module for creating a canvas I can quickly paint to... | 2019-10-16 10:41:25 | {"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": 0.4740859568119049, "perplexity": 1459.4315524949252}, "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/1570986666959.47/warc/CC-MAIN-20191016090425-20191016113925-00440.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition-blitzer/chapter-p-section-p-4-polynomials-exercise-set-page-56/8 | ## Precalculus (6th Edition) Blitzer
Write the terms polynomial in standard form (descending degree) to obtain $15x^4-8x^3+x^2+91.$ The degree of a polynomial is equal to the degree of the term with the highest degree. The degree of a term with one variable is equal to the exponent of the variable. Thus, the terms of the given polynomial have the following degrees: First term: $4$ Second Term: $3$ Third Term: $2$ Fourth Term: $0$ ( the degree of a constant is 0) The highest degree is 4, therefore the degree of the polynomial is $4$. | 2018-10-18 22:06:26 | {"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": 0.6814751029014587, "perplexity": 176.83201297718747}, "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-2018-43/segments/1539583512015.74/warc/CC-MAIN-20181018214747-20181019000247-00512.warc.gz"} |
http://hal.in2p3.fr/in2p3-00130927 | # Relativistic Transport Theory for Systems Containing Bound States
Abstract : Using a Lagrangian which contains quarks as elementary degrees of freedom and mesons as bound states, a transport formalism is developed, which allows for a dynamical transition from a quark plasma to a state, where quarks are bound into hadrons. Simultaneous transport equations for both particle species are derived in a systematic and consistent fashion. For the mesons a formalism is used which introduces off-shell corrections to the off-diagonal Green functions. It is shown that these off-shell corrections lead to the appearance of elastic quark scattering processes in the collision integral. The interference of the processes $q\bar q\to\pi$ and $q\bar q\to\pi\to q\bar q$ leads to a modification of the $s$-channel amplitude of quark-antiquark scattering.
Document type :
Journal articles
Complete list of metadata
http://hal.in2p3.fr/in2p3-00130927
Contributor : Dominique Girod <>
Submitted on : Wednesday, February 14, 2007 - 2:20:00 PM
Last modification on : Friday, June 22, 2018 - 9:33:10 AM
### Citation
P. Rehberg. Relativistic Transport Theory for Systems Containing Bound States. Physical Review C, American Physical Society, 1998, 57, pp.3299-3313. ⟨in2p3-00130927⟩
Record views | 2021-06-13 06:04:05 | {"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": 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": 0.4211571514606476, "perplexity": 1921.4826820638696}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487600396.21/warc/CC-MAIN-20210613041713-20210613071713-00422.warc.gz"} |
https://csinva.io/blog/compiled_notes/_build/html/intro.html | # overview 👋#
These are a series of notes (see csinva.io) to serve as useful reference for people in machine learning / ai / neuroscience.
Below are the high-level topics of each note, with an auto-generated graph showing their similarities (based on tf-idf).
*Topics labelled with an asterisk are research-level notes, not introductory.
The raw similarities are given in the plot below: | 2023-04-01 16:17:00 | {"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": 0.48343709111213684, "perplexity": 4533.464419536614}, "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-2023-14/segments/1679296950110.72/warc/CC-MAIN-20230401160259-20230401190259-00651.warc.gz"} |
https://web2.0calc.com/questions/help_74853 | +0
# help
0
106
1
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Oct 25, 2019
#1
+195
0
If there are n people, you would count the number of handshakes as nC2.
nC2= $$\frac{n(n-1)}{2\cdot1}$$
If there were 10 people, there would be (10*9)/2=45 handshakes. Thats not enough, so lets try a bigger number. 12 people: (12*11)/2=66 handshakes so there were 12 people.
Oct 25, 2019 | 2020-01-26 23:43:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8025878667831421, "perplexity": 1568.0616428007631}, "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/1579251694071.63/warc/CC-MAIN-20200126230255-20200127020255-00548.warc.gz"} |
https://www.qb365.in/materials/stateboard/12th-computer-science-algorithmic-strategies-two-marks-questions-3061.html | #### Algorithmic Strategies Two Marks Questions
12th Standard EM
Reg.No. :
•
•
•
•
•
•
Computer Science
Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. What is an Algorithm?
2. Define Pseudo code
3. Who is an Algorist?
4. What is Sorting?
5. What is searching? Write its types.
6. Give an example of data structures
7. What in algorithmic strategy? Give an example.
8. What is algorithmic solution?
9. How the efficiency of an algorithm is defined?
10. How the analysis of algorithms and performance evaluation can be divided?Explain.
11. Name the two factors, which decide the efficiency of an algorithm.
12. Give an example. How the time efficiency of an algorithm is measured.
13. What is algorithmetic strategy?
14. Write a note on Big omega asymptotic notation
15. Write a note on memorization. | 2019-10-20 12:26:25 | {"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": 0.8255427479743958, "perplexity": 5147.991555059095}, "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/1570986707990.49/warc/CC-MAIN-20191020105426-20191020132926-00373.warc.gz"} |
https://swmath.org/software/22883 | # Polyhedral
GAP package Polyhedral. The package polyhedral is designed to be used for doing all kinds of computations related to polytopes and use their symmetry groups in the course of the computation. The package Polyhedral is devoted to polytopes and lattices. Its main functionalities are: Computing dual description of polytopes by using symmetries for reducing the size of the computation. Compute the automorphism group of a polytope. Compute the volume of a polytope. Compute the K-skeleton of a polytope. Compute the Wythoff construction of a polytope. Compute the Delaunay tesselation corresponding to a lattice of Rn. Deal with L-type domains, i.e. spaces of lattices. Compute with unimodular vector systems. Recognize affine and spherical Coxeter Dynkin diagrams. Enumerate perfect forms in T-spaces.
## Keywords for this software
Anything in here will be replaced on browsers that support the canvas element
## References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
Sorted by year (citations) | 2019-06-19 06:05:16 | {"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": 0.8134969472885132, "perplexity": 1780.257937351434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998913.66/warc/CC-MAIN-20190619043625-20190619065625-00024.warc.gz"} |
http://class-specific.com/csf/csf_book/node79.html | ### Module
The function software/module_A_chisq.m implements a module for the feature calculation (5.1). The module uses a floating reference hypothesis for normalization (Section 2.3.4). The function software/module_A_chisq_synth.m implements UMS and function software/module_A_chisq_test.m tests both functions.
Example 8 We now provide an example of the application of the SPA to a linear combination of exponentials. We performed an acid test (see Section 2.3.8) by generating 1000 samples of a 100-by-1 vector of independent exponentially distributed RVs. The elements of were scaled such that the expected value of the -th element was , . Let the PDF of under these conditions be denoted by . Although the elements of have different means, they are independent, so is easily obtained from the joint PDF from product of chi-square distributions with 2 degrees of freedom (Section 16.1.2).
Next, we applied the linear transformation , where
Notice that the columns of form a linear subspace which contains both the special scaling function applied to under as well as constant scaling under . We can assume, therefore, that will be approximately sufficient for vs. . We then estimated the PDF using a Gaussian mixture model (Section 13.2.1).
Using the module software/module_A_chisq.m, we obtained the projected PDF:
where
Projected PDF values are plotted against the true values of in Figure 5.1. The agreement is very close. The script software/module_A_chisq_test.m runs the example with the following syntax:
module_A_chisq_test('acid',100,2,2);
We then changed matrix to include only the first column (a constant). This makes a scalar and no longer an approximate sufficient statistic for vs. . The result is shown in Figure 5.2. Note the worsening of the error. The script software/module_A_chisq_test.m runs this test with the following syntax:
module_A_chisq_test('acid',100,1,2);
Baggenstoss 2017-05-19 | 2017-12-17 06:05:18 | {"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": 0.8389829993247986, "perplexity": 823.8750676696621}, "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-2017-51/segments/1512948593526.80/warc/CC-MAIN-20171217054825-20171217080825-00149.warc.gz"} |
https://math.stackexchange.com/questions/3144333/question-about-a-simple-field-extensions-equality | # Question about a Simple Field Extensions Equality
Let $$E\supseteq F$$ be an extension of fields. Show that $$\forall u \in E,$$ and nonzero $$a\in F,$$ $$F(u)=F(au)$$.
My first instinct was to argue with the fact that $$F(u)$$ is the smallest subfield that contains both $$F$$ and $$u$$, so the "$$\subseteq$$" inclusion is clear. Would the same approach work for the reverse inclusion? I'm not so sure if this method would work this time around, so any other suggestions would be appreciated!
You need to show $$F(u)\subseteq F(au)$$ and $$F(au)\subseteq F(u)$$.
Because $$F(au)$$ is the smallest subfield of $$E$$ containing $$F$$ and $$au$$, to show $$F(au)\subseteq F(u)$$ it suffices to show that $$au\in F(u)$$; but $$u\in F(u)$$ and $$a\in F\subseteq F(u)$$, so their product should be in $$F(u)$$ as well.
Now use similar logic to show $$F(u)\subseteq F(au)$$, using the fact that $$a$$ is invertible in $$F$$.
note that $$a^{-1}\in F\subset F(au)$$, so $$a^{-1}au=u\in F(au)$$, therefore $$F(u)=F(au)$$ | 2019-04-19 20:47:47 | {"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": 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": 25, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8569562435150146, "perplexity": 55.283126028994765}, "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-2019-18/segments/1555578528058.3/warc/CC-MAIN-20190419201105-20190419222049-00053.warc.gz"} |
https://socratic.org/questions/58b7a9cbb72cff613541336b | # Question 1336b
Mar 5, 2017
${\text{H"_ 2"C"_ 2"O"_ (4(aq)) + "Ca"("OH")_ (2(aq)) -> "CaC"_ 2"O"_ (4(s)) darr + 2"H"_ 2"O}}_{\left(l\right)}$
#### Explanation:
The unbalanced chemical equation should look like this
${\text{H"_ 2"C"_ 2"O"_ (4(aq)) + "Ca"("OH")_ (2(aq)) -> "CaC"_ 2"O"_ (4(s)) darr + "H"_ 2"O}}_{\left(l\right)}$
This reaction has oxalic acid, ${\text{H"_2"C"_2"O}}_{4}$, and calcium hydroxide, "Ca"("OH")_2#, as the reactants and calcium oxalate, ${\text{CaC"_2"O}}_{4}$, and water as the products.
Calcium hydroxide is not very soluble in water, but the amount that does dissolve dissociates completely to produce calcium cations, ${\text{Ca}}^{2 +}$, and hydroxide anions, ${\text{OH}}^{-}$.
You can thus say that you're dealing with a neutralization reaction between a weak acid and a strong base.
You can balance this equation by taking a look at the ions involved in the reaction.
$2 {\text{H"_ ((aq))^(+) + color(blue)("C"_ 2"O"_ 4)_ ((aq))^(color(blue)(2-)) + color(red)("Ca")_ ((aq))^(color(red)(2+)) + 2"OH"_ ((aq))^(-) -> color(red)("Ca")color(blue)("C"_ 2"O"_ 4) _ ((s)) darr + "H"_ 2"O}}_{\left(l\right)}$
Notice that the $1$ calcium cation and $1$ oxalate anion, ${\text{C"_2"O}}_{4}^{2 -}$, present on the reactants' side are accounted for on the products' side.
This means that all you have to do in order to balance this chemical equation is to balance the hydrogen and oxygen atoms.
Excluding the aforementioned oxalate anion, you have
• $4 \times \text{H}$ on the reactants' side $\to 2 {\text{H"^(+) + 2"OH}}^{-}$
• $2 \times \text{H}$ on the products' side $\to \text{H"_2"O}$
and
• $2 \times \text{O}$ on the reactants 'side $\to 2 {\text{OH}}^{-}$
• $1 \times \text{O}$ on the products' side $\to \text{H"_2"O}$
You can thus balance the hydrogen and oxygen atoms by adding a coefficient of $2$ to the water molecule.
The balanced chemical equation will thus be
$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{H"_ 2"C"_ 2"O"_ (4(aq)) + "Ca"("OH")_ (2(aq)) -> "CaC"_ 2"O"_ (4(s)) darr + 2"H"_ 2"O}}_{\left(l\right)}}}}$ | 2019-09-20 16:10:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 21, "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": 0.8474399447441101, "perplexity": 2804.5137210700673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574050.69/warc/CC-MAIN-20190920155311-20190920181311-00302.warc.gz"} |
http://documenta.sagemath.org/vol-kato/bloch_esnault.dm.html | #### DOCUMENTA MATHEMATICA, Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 131-155
Spencer Bloch and Hélène Esnault
A notion of additive dilogarithm for a field $k$ is introduced, based on the $K$-theory and higher Chow groups of the affine line relative to $2(0)$. Analogues of the $K_2$-regulator, the polylogarithm Lie algebra, and the $\ell$-adic realization of the dilogarithm motive are discussed. The higher Chow groups of $0$-cycles in this theory are identified with the Kähler differential forms $\Omega^*_k$. It is hoped that these results will serve as a guide in developing a theory of contravariant motivic cohomology with modulus, modelled on the generalized Jacobians of Rosenlicht and Serre. | 2017-08-17 15:37:31 | {"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": 0.7218807935714722, "perplexity": 887.6253355326005}, "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/1502886103579.21/warc/CC-MAIN-20170817151157-20170817171157-00049.warc.gz"} |
http://math.stackexchange.com/questions/313306/permutation-strategy-for-sudoku-solver-np-complete | # Permutation Strategy for Sudoku solver NP-complete?
We know that Sudoku itself is $\mathbf{\mathsf{NP}}$-complete, but while trying to implement the "Permutation Rule" strategy in my solver, I was unable to find an efficient algorithm to do so. The problem is essentially:
Given $U=\{1,\ldots,n\}$, $n$ sets $Z_1,\ldots,Z_n$ with $\bigcup Z_i=U$, and an integer $k$, $1\leq k\leq n$, is there a subcollection of $k$ sets $Z_{i_1},\ldots,Z_{i_k}$ such that $\left|\bigcup_{j=1}^k Z_{i_j}\right| = k$?
Clearly we have membership in $\mathbf{\mathsf{NP}}$, and it seems $\mathbf{\mathsf{NP}}$-complete (since it's so similar to Set Cover), but I don't have any proof at the moment.
-
Peter Norvig's approach may help – Ben Feb 24 '13 at 21:10
@Ben, thanks, though my question is a theoretical one about the abstract problem I defined. I already have a fast Sudoku solver implemented. – Nick Feb 24 '13 at 21:42 | 2015-07-28 08:37:39 | {"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": 0.881040632724762, "perplexity": 721.2384044804061}, "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-2015-32/segments/1438042981753.21/warc/CC-MAIN-20150728002301-00313-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://caddellprep.com/subjects/common-core-geometry/rhombuses/ | Watch a video lesson and learn about the properties of rhombuses including properties of sides, angles, diagonals and angles formed by diagonals.
Rhombus: A parallelogram with consecutive sides congruent.
A rhombus has a similar set of rules as a parallelogram does.
The special thing about a rhombus is that all 4 sides are congruent.
The diagonals are perpendicular bisectors to each other. When this happens, four congruent triangles are formed. The diagonals also bisect the angles at each vertex.
Video-Lesson Transcript
Let’s go over a rhombus.
A rhombus is another type of parallelogram.
In a parallelogram, we have opposite sides are parallel. And also opposite sides are congruent.
What’s special about a rhombus is that all four sides are congruent. Not only the opposite sides but all four of them are congruent.
Let’s label these vertices.
When we draw diagonals, they bisect each other.
Something else that happens in a rhombus is when diagonals intersect, we get right angles. The diagonals are perpendicular to each other.
Here, we end up with four congruent right triangles.
This diagonal bisects $\angle A$. So, angle $BAD$ are bisected. Angle $BCD$ also gets bisected.
And also, the second diagonal bisects these two angles. Angle $ABC$ and angle $ADC$ such that these two pairs of angles are congruent. | 2020-02-20 02:49:38 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "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": 0.5327129364013672, "perplexity": 682.4694392331359}, "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-2020-10/segments/1581875144498.68/warc/CC-MAIN-20200220005045-20200220035045-00230.warc.gz"} |
https://itecnotes.com/electrical/electronic-how-to-calculate-the-power-dissipation-in-a-transistor/ | # Electronic – How to calculate the power dissipation in a transistor
bjttransistors
Consider this simple sketch of a circuit, a current source:
I'm not sure how to calculate the power dissipation across the transistor.
I'm taking a class in electronics and have the following equation in my notes (not sure if it helps):
$$P = P_{CE} + P_{BE} + P_{base-resistor}$$
So the power dissipation is the power dissipation across the collector and emitter, the power dissipation across the base and emitter and a mystery factor $$\P_{base-resistor}\$$. Note that the β of the transistor in this example was set to 50.
I'm quite confused overall and the many questions here on transistors have been very helpful. | 2023-02-04 05:27:05 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8392070531845093, "perplexity": 484.16865485574215}, "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-2023-06/segments/1674764500094.26/warc/CC-MAIN-20230204044030-20230204074030-00508.warc.gz"} |
https://mathematica.stackexchange.com/questions/213738/performing-operations-on-lhs-of-assignment?noredirect=1 | # Performing operations on LHS of assignment [duplicate]
Is it possible to first perform an operation on LHS of the = symbol, evaluate that, and then assign the RHS to the new LHS as usual? The following shows the most basic example I could think of.
ToExpression["list" <> ToString[4]] = {1,2,3,4,5});
> Set::write: Tag ToExpression in ToExpression[list4] is Protected.
It looks like Mathematica thinks we want to redefine the functions used on the LHS of =, not first evaluate it first and then assign. I've tried surrounding LHS with brackets and parenthesis, but that doesn't work either. Is there a way to make this work? If yes, with what code?
The reason this arose is because I made a function that takes input n, and makes a list accordingly. Now I wanted to AUTOMATICALLY give that list a name that has n in it. So if I compute f[1209], I want to automatically store whatever list I computed to list1209, without having to type list1209 = computedlist.
• Welcome to MSE. Try Evaluate@ToExpression["list" <> ToString[4]] = {1, 2, 3, 4, 5} Jan 29 '20 at 4:20
• In this case, it's safer to use something like Symbol["list" <> IntegerString[4]]. Jan 29 '20 at 4:44 | 2021-09-20 10:42:38 | {"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": 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": 0.6631941199302673, "perplexity": 1030.1667808442176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057036.89/warc/CC-MAIN-20210920101029-20210920131029-00338.warc.gz"} |
https://dsp.stackexchange.com/questions/62674/adding-white-gaussian-noise-to-a-voice-signal | # Adding White Gaussian noise to a voice signal
I'm trying to add White Gaussian Noise to an audio file. However; the energy of the noise should be 1/10th of that of the signal. My first attempt is as following:
[y,Fs] = audioread('drum.wav');
%sound(y,Fs);
sound(noisy_sig,Fs);
function noisy_sig = addnoise( sig , SNRdb )
sig_power = norm(sig,2) / length(sig);
% noise power is equal to sigma^2
sigma2 = sig_power / 10^(SNRdb/10) ;
noisy_sig = sig + sqrt(sigma2)*randn(size(sig));
end
When I listen the resulting wav, there is no difference between the original and noisy ones. Am I doing something wrong? Any help would be appreciated.
• So, Is it correct to say x = y + 0.1*randn(length(y),1) ? The energy of the noise signal should be 1/10th of the original signal. – Jason Dec 18 '19 at 15:31
Your problem is how you calculate the signal power. You are calling norm which calculates $$\sqrt{\sum_i |x_i|^2}$$ but you want to calculate the sum of the squared values and then divide by the length as you do in your code. Try this instead: sig_power = norm(sig)^2 / length(sig);. This line will calculate $$\frac{1}{N}\sum_{i=1}^N |x_i|^2$$.
• That adds noise with variance $0.1$. But from your comment you don't mention anything about y's power. SNR is signal-to-noise ratio so it is the signal and noise power relative to each other. – Engineer Dec 18 '19 at 17:07 | 2020-05-25 18:21:40 | {"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7830792665481567, "perplexity": 666.7952449021569}, "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-2020-24/segments/1590347389309.17/warc/CC-MAIN-20200525161346-20200525191346-00444.warc.gz"} |
https://proofwiki.org/wiki/Book:I.M._Gelfand/Calculus_of_Variations | Book:I.M. Gelfand/Calculus of Variations
I.M. Gelfand and S.V. Fomin: Calculus of Variations
Published $1963$, Dover Publications
ISBN 0-486-41448-5 (translated by Richard A. Silverman).
Subject Matter
Calculus of Variations
Contents
Authors' Preface (I.M. Gelfand and S.V. Fomin)
Translator's Preface (Richard A. Silverman)
1 Elements of the Theory
2 Further Generalizations
3 The General Variation of a Functional
4 The Canonical Form of the Euler Equations and Related Topics
5 The Second Variation. Sufficient Conditions for a Weak Extremum
6 Fields. Sufficient Conditions for a Strong Extremum
7 Variational Problems Involving Multiple Integrals
8 Direct Methods in the Calculus of Variations
Appendix I: Propagation of Disturbances and the Canonical Equations
Appendix II: Variational Methods in Problems of Optimal Control
Bibliography
Index | 2019-07-17 16:58:31 | {"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": 0.5523819327354431, "perplexity": 8589.922498516247}, "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-2019-30/segments/1563195525355.54/warc/CC-MAIN-20190717161703-20190717183703-00453.warc.gz"} |
https://www.math.sissa.it/publications?f%5Btg%5D=M&f%5Bauthor%5D=1300&s=year&o=asc | MENU
## Publications
Export 2 results:
Filters: First Letter Of Title is M and Author is Francisco Chinesta [Clear All Filters]
2016
. Model Order Reduction: a survey. In: Wiley Encyclopedia of Computational Mechanics, 2016. Wiley Encyclopedia of Computational Mechanics, 2016. Wiley; 2016. Available from: http://urania.sissa.it/xmlui/handle/1963/35194
2017
. Model Reduction Methods. In: Encyclopedia of Computational Mechanics Second Edition. Encyclopedia of Computational Mechanics Second Edition. John Wiley & Sons; 2017. pp. 1-36. | 2020-07-02 05:39:55 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8705775737762451, "perplexity": 7454.915451011577}, "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-2020-29/segments/1593655878519.27/warc/CC-MAIN-20200702045758-20200702075758-00249.warc.gz"} |
https://www.esaral.com/q/the-volume-of-a-right-circular-cone-is-9856-mathrmcm3 | # The volume of a right circular cone is $9856 \mathrm{~cm}^{3}$.
Question.
The volume of a right circular cone is $9856 \mathrm{~cm}^{3}$. If the diameter of the base is $28 \mathrm{~cm}$, find
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone
$\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$
Solution:
(i) Radius of cone $=\left(\frac{28}{2}\right) \mathrm{cm}=14 \mathrm{~cm}$
Let the height of the cone be h.
Volume of cone $=9856 \mathrm{~cm}^{3}$
$\Rightarrow \frac{1}{3} \pi r^{2} h=9856 \mathrm{~cm}^{3}$
$\Rightarrow\left[\frac{1}{3} \times \frac{22}{7} \times(14)^{2} \times h\right] \mathrm{cm}^{2}=9856 \mathrm{~cm}^{3}$
$h=48 \mathrm{~cm}$
Therefore, the height of the cone is $48 \mathrm{~cm}$.
(ii) Slant height ( $l$ ) of cone $=\sqrt{r^{2}+h^{2}}$
$=\left[\sqrt{(14)^{2}+(48)^{2}}\right] \mathrm{cm}$
$=[\sqrt{196+2304}] \mathrm{cm}$
$=50 \mathrm{~cm}$
Therefore, the slant height of the cone is $50 \mathrm{~cm}$.
(iii) CSA of cone $=\pi r$
$=\left(\frac{22}{7} \times 14 \times 50\right) \mathrm{cm}^{2}$
$=2200 \mathrm{~cm}^{2}$
Therefore, the curved surface area of the cone is $2200 \mathrm{~cm}^{2}$.
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Free Study Material | 2023-03-21 14:58:08 | {"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": 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": 0.8923824429512024, "perplexity": 590.0586738954391}, "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-20230321131205-20230321161205-00443.warc.gz"} |
http://mathhelpforum.com/algebra/100520-weights-print.html | # Weights
• Sep 4th 2009, 02:29 AM
travellingscotsman
Weights
Hello all.
I'm trying to work out the total weight of a a bundle of pipe that in total is 4200 feet long, each joint is 40 foot long, so this means that I have 105 joints of pipe. The diameter is 13 3/8" and it's 54.5 pounds per foot. Any ideas?
• Sep 4th 2009, 04:05 AM
HallsofIvy
Quote:
Originally Posted by travellingscotsman
Hello all.
I'm trying to work out the total weight of a a bundle of pipe that in total is 4200 feet long, each joint is 40 foot long, so this means that I have 105 joints of pipe. The diameter is 13 3/8" and it's 54.5 pounds per foot. Any ideas?
Since you have "pounds per foot" the diameter is not relevant. You have 4200 feet of pipe at 54.5 pounds per foot: the total weight is (4200)(54.5)= 228900 pounds or 228900/2000= 114.45 tons.
I hope you are not hoping to lift that yourself!
• Sep 4th 2009, 04:08 AM
aidan
Quote:
Originally Posted by travellingscotsman
Hello all.
I'm trying to work out the total weight of a a bundle of pipe that in total is 4200 feet long, each joint is 40 foot long, so this means that I have 105 joints of pipe. The diameter is 13 3/8" and it's 54.5 pounds per foot. Any ideas?
Yes.
You state that you have 4200 feet of pipe that weighs 54.5 pound per foot.
And that you are trying to work out the total weight of this bundle of pipe.
.
Step 1:
If you had ONLY 1 foot of pipe, how much would 1 foot of pipe weigh?
.
Step 2:
If you had 2 (two) feet of pipe, how much would 2 feet of pipe weigh?
You should be able to provide that answer. (Hint: 54.5+54.5 = 109)
.
Step 3:
If you had 3 feet of pipe, how much would 3 feet of pipe weigh?
Hint: $3 \times 54.5 = 163.5$
.
Step 4:
If you had 4 feet of pipe, how much would 4 feet of pipe weigh?
No hints here. You should be able to provide the answer.
At this point you should see a pattern developing.
You will need to do this step business 4200 more times before the answer for the total weight appears.
DO NOT SKIP ANY INTERMEDIATE STEPS!
. | 2017-05-23 01:19:05 | {"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": 0, "img_math": 0, "codecogs_latex": 1, "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": 0.615361213684082, "perplexity": 1245.9538249554357}, "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-2017-22/segments/1495463607245.69/warc/CC-MAIN-20170523005639-20170523025639-00515.warc.gz"} |
http://mathhelpforum.com/geometry/29916-math.html | 1. ## math
What is the perimeter of a triangle where the sides measure 6,8,and 10 inches? what would be the radius of a circle with a diameter of 8 inches?
2. Originally Posted by shamekagilmore
What is the perimeter of a triangle where the sides measure 6,8,and 10 inches? what would be the radius of a circle with a diameter of 8 inches?
The perimeter is the sum of all of a shapes sides.
The radius of a circle is half the diameter.
3. ## solve this for me.
Originally Posted by shamekagilmore
What is the perimeter of a triangle where the sides measure 6,8,and 10 inches? what would be the radius of a circle with a diameter of 8 inches?
solution
__________
1) p =6+8+10 =24 inches. and
2) r = d/2 = 8/2 = 4inches.
clement okhale
nigeria.
my question:
1) given that matrix s = [3 1] , t = [2 3]
2 4 -1 1
find:
a) 2s-3t
b) s.t
c) s+4t
d) 2s + 3t
send it to cokhale@yahoo.com | 2016-10-28 21:38:55 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8345856070518494, "perplexity": 1034.615404315976}, "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/1476988725475.41/warc/CC-MAIN-20161020183845-00453-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://eprints.iisc.ernet.in/8139/ | # Pressure-induced valence changes in mixed-valent systems
Chandran, Leena and Krishnamurthy, HR and Ramakrishnan, TV (1992) Pressure-induced valence changes in mixed-valent systems. In: Journal of Physics: Condensed Matter, 4 (34). pp. 7067-7094.
PDF Pressure_induced_July20th.pdf Restricted to Registered users only Download (1243Kb) | Request a copy
## Abstract
Mixed-valent systems based on Ce, Sm, Eu and Yb exhibit a wide range of behaviour with respect to valence changes under the application of pressure. We present a semi phenomenological model for this behaviour based on competition effects between the usual elastic energy cost and the magnetic energy gain due to valence fluctuations. For the latter we use a mean-field Andenon lattice description and incorporate the effects of pressure by introducing a volume dependence to the Anderson model parameters $\epsilon_f$ and $\Delta$. In contrast to existing models such as the Kondo Volume Collapse theory of Allen and Martin, which describes magnetic to non-magnetic transitions without sizable valence change $(e.g. \gamma-Ce\rightarrow \alpha-Ce)$, the Anderson lattice model developed here dascribes systems with both small and large valence changes the transition can be continuous $(e.g. EuPd_2Si_2)$ or discontinuous ($EuPd_2Si_2$ alloyed with Au).
Item Type: Journal Article http://dx.doi.org/10.1088/0953-8984/4/34... Copyright of this article belongs to Institute of Physics. Division of Physical & Mathematical Sciences > Physics 05 Sep 2006 19 Sep 2010 04:30 http://eprints.iisc.ernet.in/id/eprint/8139 | 2016-10-26 06:02:17 | {"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": 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": 0.688072919845581, "perplexity": 3090.221788406365}, "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/1476988720737.84/warc/CC-MAIN-20161020183840-00107-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://myknowsys.com/blog/2012/03/316-mathematics.html | # Exponents
Follow the Knowsys Method and remember to read the problem, identify the bottom line, assess your options, and attack the problem. Then loop back to check that you answered the right question. For the vast majority of problems, you do not need to look at the answer choices before this point.
What is the largest possible integer value of n for which $5^{n}$ divides into $50^{7}$?
The bottom line is easy to find here: n=?
Now assess your options. You could look at the answer choices and plug them in, calculate each product, and see whether $50^{7}$ can divide by it evenly. But there must be a faster way! This is an exponent problem, so think about your exponent rules. If you can get the bases to match, finding the appropriate value of n will be easy.
Fortunately, 50 is a multiple of 5. It is also a multiple of 25.
$50=2(5^{2})$
Therefore,
$50^{7}=(2(5^{2}))^{7}$
Now you can apply the distributive property and the exponent rules.
$50^{7}=2^{7}(5^{2^{7}})$
$50^{7}=2^{7}(5^{14})$
Now you know that $(5^{14})$ is a product of $50^{7}$. There's not much you can do from here, so look at the answer choices.
(A) 2
(B) 7
(C) 9
(D) 10
(E) 14 | 2018-03-23 03:32:19 | {"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": 0, "img_math": 0, "codecogs_latex": 9, "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": 0.7964437007904053, "perplexity": 458.57383931883606}, "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-2018-13/segments/1521257648177.88/warc/CC-MAIN-20180323024544-20180323044544-00363.warc.gz"} |
http://mathhelpforum.com/discrete-math/179895-number-functions-one-set-another.html | # Math Help - Number of functions from one set to another?
1. ## Number of functions from one set to another?
How many functions, injections, surjections, bijections and relations from A to B are there, when A = {a, b, c}, B = {0, 1}?
Edit: I know the answer should be 64, but I don't know how to arrive at that.
2. Originally Posted by posix_memalign
How many functions, injections, surjections, bijections and relations from A to B are there, when A = {a, b, c}, B = {0, 1}?
Edit: I know the answer should be 64, but I don't know how to arrive at that.
I have no idea what you mean by 64.
There are $2^3$ functions $A\to B.$
There are no injections $A\to B$.
Therefore, no bijections.
There are 6 surjections.
Because $\|A\times B\|=6$ there are $2^6$ relations from $A\to B$ is you allow the empty relation,
3. Originally Posted by Plato
I have no idea what you mean by 64.
There are $2^3$ functions $A\to B.$
There are no injections $A\to B$.
Therefore, no bijections.
There are 6 surjections.
Because $\|A\times B\|=6$ there are $2^6$ relations from $A\to B$ is you allow the empty relation,
Thanks, but why do you need the $\|$? Why isn't the cartesian product by itself sufficient?
4. Originally Posted by posix_memalign
Thanks, but why do you need the $\|$? Why isn't the cartesian product by itself sufficient?
#(X)= $|X|=$ $\|X\|$ these are all common symbols standing for the number of elements in a given set. | 2015-04-27 14:32:49 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "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": 0.6859612464904785, "perplexity": 334.12671247562747}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246658376.88/warc/CC-MAIN-20150417045738-00016-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1989365/find-square-and-triangular-numbers | Find square and triangular numbers
Square and triangular numbers are expressed as
$n^2=\frac{m(m+1)}{2}$
Further on this can be expressed as
$8n^2=4m(m+1)=4m^2+4m=(2m+1)^2-1$
Taking $a=2m+1$ and $b=2n$ the expression becomes
$2b^2=a^2-1$ or $1=a^2-2b^2$
After a bit of factoring previous equation becomes
$1=(a-\sqrt{2}b)(a+\sqrt{2}b)$
One of the solutions is $(a,b)=(3,2)$ and $(m,n)=(1,1)$. From here additional solutions can be found recursively.
Once there is a solution say $(m,n)$ there is another $(1+im+jn, 1+km+ln)$ for some integers $i,j,k,l$. I need help proving this.
• Why do you say "previous equation has no integer solutions" when it clearly does (because you give the solution $a=3, b=2$ only two lines later)? – Gabriel Burns Oct 28 '16 at 17:46
• @GabrielBurns actually just the polynomial can't be expressed in integer terms – php-- Oct 28 '16 at 17:50
• It has something to do with "triangle" and "square" numbering of the elements of $mathbb N^2$. – hamam_Abdallah Oct 28 '16 at 17:54
• I don't think there are other solutions since the "triangle" numbering is faster than the square . – hamam_Abdallah Oct 28 '16 at 17:56 | 2019-09-18 05:36:38 | {"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": 0.7346562743186951, "perplexity": 467.95395969638116}, "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-2019-39/segments/1568514573184.25/warc/CC-MAIN-20190918044831-20190918070831-00373.warc.gz"} |
https://math.stackexchange.com/questions/3982683/deriving-the-formula-for-calculating-the-length-of-the-project-of-the-vector-a | # Deriving the formula for calculating the length of the project of the vector $a$ onto the vector $b$
My situation: I am currently taking a course in linear algebra and I am quite all the time. I have however miraculously reached projections in 2-dimensions. I am studying and learning both from course material but also from this article and I am stuck about between page 6 and 7. My question is:
My problem: I wanted to know how to derive the formula for projection of a vector $$a$$ onto a linearly independent vector $$b$$, in order to understand because I am so lost. Why is this text, linked above, and my course book defining the dot product between two vectors as:
$$a\cdot b=|a|*|b|*cos(\theta)$$
and then calculating the length of the projection of the vector $$a$$ onto the vector $$b$$ as:
$$|a_b|=\frac{a\cdot b}{|a|}=\frac{a_x*b_x+a_y*b_y}{|a|}$$
However the dot product is defined as being the product of the length of $$|a|$$, $$|b|$$ and $$cos(\theta)$$ where $$\theta$$ is the angle between the two vectors. If I follow my course book, the slideshows provided by my professor and the pdf link above I am not in fact calculating the dot product and using it to calculate the length of the projection. I am in the example in the pdf calculating some random sum of $$a_x*b_x+a_y*b_y$$ instead of $$\sqrt{a_x^2+a_y^2}*\sqrt{b_x^2+b_y^2}*cos(\theta)$$.
How do you derive $$\sqrt{a_x^2+a_y^2}*\sqrt{b_x^2+b_y^2}*cos(\theta) = a_x*b_x+a_y*b_y$$ and why this difficult change? And why is this equation shift not mentioned? Am I missing something?
• The law of cosines explains the equivalence. Jan 12, 2021 at 17:28
• @Randall, you are very correct! I scrolled up and looked at how the author derived the dot product using, among other things, the law of cosines and saw the equivalence at the bottom of the proof. Thanks a lot! You're a life saver Randall! Jan 12, 2021 at 18:06 | 2022-05-16 09:28:23 | {"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": 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": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8406032919883728, "perplexity": 140.5144887420534}, "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/1652662510097.3/warc/CC-MAIN-20220516073101-20220516103101-00699.warc.gz"} |
http://gap-packages.github.io/SingularInterface/ | # SingularInterface
A GAP interface to Singular
Version 0.7.2
This project is maintained by Mohamed Barakat, Max Horn, Frank Lübeck
# GAP Package SingularInterface
The SingularInterface package provides a GAP interface to Singular, enabling direct access to the complete functionality of Singular.
The current version of this package is version 0.7.2. For more information, please refer to the package manual. There is also a README file.
## Dependencies
This package requires at least GAP 4.7.2 as well as Singular 4.0.1.
The following additional GAP packages are not required, but suggested:
## Obtaining the SingularInterface source code
The easiest way to obtain SingularInterface is to download the latest version using one of the download buttons on the left.
If you would like to use the very latest “bleeding edge” version of SingularInterface, you can also do so, but you will need some additional tools:
• git
• autoconf
• automake
• libtool
must be installed on your system. You can then clone the SingularInterface repository as follows:
git clone https://github.com/gap-system/SingularInterface
## Installing SingularInterface
SingularInterface requires Singular 4.0.1 or later, and that Singular and GAP are compiled against the exact same version of the GMP library.
The easiest way to achieve that is to compile Singular yourself, telling it to link against GAP’s version of GMP.
Therefore, usually the first step towards compiling SingularInterface is to build such a special version of Singular. The following instructions should get you going.
1. Fetch the Singular source code. For your convenience, we provide two shell scripts which do this for you. If you want to use Singular 4.0.1, run
./fetchsingular
If you want the development version run
./fetchsingular.dev
2. Prepare Singular for compilation. At this point, you need to know against which version of GMP your GAP library was linked: If it is a GMP version installed globally on your system, simply run:
./configuresingular
If it is the version of GMP shipped with GAP, run this instead:
./configuresingular --with-gmp=GAPDIR/bin/GAPARCH/extern/gmp
where GAPDIR should be replaced with the path to your GAP installation, and GAPARCH by the value of the GAParch variable in GAPDIR/sysinfo.gap
3. Compile Singular by running
./makesingular
4. Now we turn to SingularInterface. If you are using the git version of SingularInterface, you need to setup its build system first. To do this, run this command:
./autogen.sh
5. Prepare SingularInterface for compilation, by running
./configure --with-gaproot=GAPDIR \
--with-libSingular=\$PWD/singular/dst \
CONFIGNAME=default64
where you should replace GAP_DIR as above. If you know what you do, you can change your CONFIGNAME (but note that SingularInterface can only be used with 64 bit versions of GAP).
6. Compile SingularInterface:
make
7. To make sure everything worked, run the test suite
make check
## Contact
You can contact the SingularInterface team by sending an email to
gapsing AT mathematik DOT uni-kl DOT de
Bug reports and code contributions are highly welcome and can be submitted via our GitHub issues tracker respectively via pull requests.
## Feedback
For bug reports, feature requests and suggestions, please use the issue tracker. | 2018-01-18 19:52:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.24736128747463226, "perplexity": 3886.558047016168}, "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-2018-05/segments/1516084887600.12/warc/CC-MAIN-20180118190921-20180118210921-00228.warc.gz"} |
https://getfem.org/python/cmdref_CvStruct.html | # CvStruct¶
class CvStruct(*args)
GetFEM CvStruct object
General constructor for CvStruct objects
basic_structure()
Get the simplest convex structure.
For example, the ‘basic structure’ of the 6-node triangle, is the canonical 3-noded triangle.
char()
Output a string description of the CvStruct.
dim()
Get the dimension of the convex structure.
display()
displays a short summary for a CvStruct object.
face(F)
Return the convex structure of the face F.
facepts(F)
Return the list of point indices for the face F.
nbpts()
Get the number of points of the convex structure. | 2021-08-03 10:23:51 | {"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": 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": 0.6806355714797974, "perplexity": 6103.514179132436}, "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/1627046154457.66/warc/CC-MAIN-20210803092648-20210803122648-00365.warc.gz"} |
https://brilliant.org/problems/properties-of-electric-transformer/ | # Properties of an electric transformer
The above is a schematic diagram of an electric transformer, where the primary AC voltage is $$220\text{ V}$$ and the secondary coil is connected with an electric heating instrument. The secondary voltage and current intensity are $$110\text{ V}$$ and $$8\text{ A},$$ respectively. Which of the following statements is correct?
There is no energy loss in this electric transformer.
$$a)$$ The current intensity flowing in the primary winding is $$4\text{ A}.$$
$$b)$$ The number of turns in the secondary winding is twice as many as that in the primary winding.
$$c)$$ The primary coil always transfers $$880\text{ W}$$ of electric power to the secondary coil without reference to any heating instrument.
× | 2018-12-11 10:12:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6225500702857971, "perplexity": 281.8484571723805}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823614.22/warc/CC-MAIN-20181211083052-20181211104552-00097.warc.gz"} |
https://zbmath.org/?q=an%3A1094.62077 | zbMATH — the first resource for mathematics
Conditional Akaike information for mixed-effects models. (English) Zbl 1094.62077
Summary: This paper focuses on the Akaike information criterion, AIC, for linear mixed-effects models in the analysis of clustered data. We make the distinction between questions regarding the population and questions regarding the particular clusters in the data. We show that the AIC in current use is not appropriate for the focus on clusters, and we propose instead the conditional Akaike information and its corresponding criterion, the conditional AIC, cAIC. The penalty term in cAIC is related to the effective degrees of freedom $$\rho$$ for a linear mixed model proposed by J. S. Hodges and D. J. Sargent [ibid. 88, No. 2, 367–379 (2001; Zbl 0984.62045)]; $$\rho$$ reflects an intermediate level of complexity between a fixed-effects model with no cluster effect and a corresponding model with fixed cluster effects. The cAIC is defined for both maximum likelihood and residual maximum likelihood estimation. A pharmacokinetics data application is used to illuminate the distinction between the two inference settings, and to illustrate the use of the conditional AIC in model selection.
MSC:
62J05 Linear regression; mixed models 62B10 Statistical aspects of information-theoretic topics 62P10 Applications of statistics to biology and medical sciences; meta analysis 62J10 Analysis of variance and covariance (ANOVA)
MEMSS
Full Text: | 2021-03-03 12:54:08 | {"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": 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": 0.4059046804904938, "perplexity": 1287.2689293890508}, "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/1614178366959.54/warc/CC-MAIN-20210303104028-20210303134028-00468.warc.gz"} |
https://puzzling.stackexchange.com/questions/92512/another-picture-problem | # Another picture problem
Another picture puzzle. Replace the question mark. Once again, the information needed is there. So, try replace it!
There are
exactly 26 vertical bands in the "question" image. If we map these to letters of the alphabet in the obvious way and guess that subdivision means multiple copies of a letter, we get AEEEHIIMNNSSTTTTW, an anagram of WHAT IS TEN TIMES TEN. | 2021-10-16 15:23:52 | {"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": 0.8682535886764526, "perplexity": 1616.649916760523}, "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/1634323584886.5/warc/CC-MAIN-20211016135542-20211016165542-00430.warc.gz"} |
https://www.research.ed.ac.uk/en/publications/improved-measurement-of-bto%CF%81%CF%810-and-determination-of-the-quark-mix | # Improved Measurement of $B^+\toρ^+ρ^0$ and Determination of the Quark-Mixing Phase Angle $α$
The BaBar Collaboration, Philip Clark
Research output: Contribution to journalArticlepeer-review
## Abstract
We present improved measurements of the branching fraction ${\cal B}$, the longitudinal polarization fraction $f_L$, and the direct {\ensuremath{CP}\xspace} asymmetry {\ensuremath{{\cal A}_{CP}}\xspace} in the $B$ meson decay channel $B^+\to\rho^+\rho^0$. The data sample was collected with the {{\slshape B\kern-0.1em{\smaller A}\kern-0.1em B\kern-0.1em{\smaller A\kern-0.2em R}}} detector at SLAC. The results are ${\cal B} (\Bp\ra\rprz)=(23.7\pm1.4\pm1.4)\times10^{-6}$, $f_L=0.950\pm0.015\pm0.006$, and $\Acp=-0.054\pm0.055\pm0.010$, where the uncertainties are statistical and systematic, respectively. Based on these results, we perform an isospin analysis and determine the CKM weak phase angle $\alpha$ to be $(92.4^{+6.0}_{-6.5})^{\circ}$.
Original language English Physical Review Letters https://doi.org/10.1103/PhysRevLett.102.141802 Published - 22 Jan 2009
• hep-ex
## Fingerprint
Dive into the research topics of 'Improved Measurement of $B^+\toρ^+ρ^0$ and Determination of the Quark-Mixing Phase Angle $α$'. Together they form a unique fingerprint. | 2022-05-16 04:53:28 | {"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": 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": 0.547146737575531, "perplexity": 3997.8469402491423}, "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/1652662509990.19/warc/CC-MAIN-20220516041337-20220516071337-00067.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-6th-edition/chapter-r-review-of-basic-concepts-r-4-factoring-polynomials-r-4-exercises-page-43/12 | ## Precalculus (6th Edition)
$3(5r-9)$
Note that: $15r=5(3)(r) \\27=3(3)(3)$ Thus, the greatest common factor $3$. Factor out the GCF to obtain: $15r-27=3(5r-9)$ | 2019-12-16 05:02:58 | {"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": 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": 0.5893000364303589, "perplexity": 1680.078405262122}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541317967.94/warc/CC-MAIN-20191216041840-20191216065840-00456.warc.gz"} |
https://www.zbmath.org/?q=an%3A0308.46054 | zbMATH — the first resource for mathematics
Representations of the CAR generated by representations of the CCR. Fock case. (English) Zbl 0308.46054
MSC:
46L05 General theory of $$C^*$$-algebras 46N99 Miscellaneous applications of functional analysis 47D03 Groups and semigroups of linear operators 22D25 $$C^*$$-algebras and $$W^*$$-algebras in relation to group representations
Full Text:
References:
[1] Heisenberg, W.: Introduction to the unified field theory of elementary particles. London: Interscience 1966 · Zbl 0205.57502 [2] Streater, R.F., Wilde, I.F.: Nucl. Phys. B24, 561 (1970) · doi:10.1016/0550-3213(70)90445-1 [3] Kalnay, A.J., MacCotrina, E., Kademova, K.V.: Int. J. Theor. Phys.7, 9 (1973) · doi:10.1007/BF02412656 [4] Rzewuski, J.: Field theory, part II. PWN Warsaw: Illife Books Ltd. 1969 [5] Berezin, F.A.: Methods of second quantization. Moscow: Nauka 1965 (in Russian) · Zbl 0131.44805 [6] Rzewuski, J.: Rep. Math. Phys.1, 195 (1971) [7] Garbaczewski, P., Rzewuski, J.: Rep. Math. Phys.6, 423 (1974) · Zbl 0325.46071 · doi:10.1016/S0034-4877(74)80007-8 [8] Garbaczewski, P.: Rep. Math. Phys.7, 9 (1975) · doi:10.1016/0034-4877(75)90037-3 [9] Emch, G.G.: Algebraic methods in statistical mechanics and quantum field theory. London: Wiley, Interscience 1972 · Zbl 0235.46085 [10] Rohrlich, F.: In: Analytic methods in mathematical physics. Newton, R.G., Gilbert, R.P. (Ed.). New York: Gordon and Breach 1970 · Zbl 0194.29903 [11] Jost, R.: The general theory of quantized fields. Moscow: Mir 1967 (in Russian) · Zbl 0127.19105
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-02-28 13:53:06 | {"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": 0.6663483381271362, "perplexity": 11687.416089788227}, "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/1614178360853.31/warc/CC-MAIN-20210228115201-20210228145201-00135.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/let-a-3-6-9-12-696-699-and-b-7-14-21-287-294-find-no-of-ordered-pairs-of-a-b-such-that-a-a-b-b-a-b-and-a-b-is-odd-number-system-entrance-exam_103018 | # Let a = { 3, 6, 9, 12, ......., 696, 699} and B = {7, 14, 21, .........., 287, 294} Find No. of Ordered Pairs of (A, B) Such that a ∈ A, B ∈ B, a ≠ B and a + B is Odd. - Mathematics
MCQ
Solve the following question and mark the best possible option.
Let A = { 3, 6, 9, 12, ......., 696, 699} & B = {7, 14, 21, .........., 287, 294}
Find no. of ordered pairs of (a, b) such that a ∈ A, b ∈ B, a ≠ b & a + b is odd.
• 4879
• 4893
• 2436
• 2457
#### Solution
A has 699/3 = 233 elements of which 116 are even & 117 are odd.
B has 294/7= 42 elements out of which 21 are even & 21 are odd.
A∩B = { 21, 42, ........, 273, 294}
∴ n(A ∩ B) = 14
For choice of a & b, 2 cases arise:-
Case- I: a is even & b is odd.
No. of possible cases = ""^116C_1 xx ""^21C = 116 xx 21
Case-II: a is odd & b is even:-
No. of possible cases = ""^117C_1 xx ""^21C = 117 x 21
But there are 14 cases where a = b & a, b, x A∩B.
So, required answer = 116 x 21 + 117 x 21 - 14 = 4879.
Concept: Number System (Entrance Exam)
Is there an error in this question or solution? | 2021-05-18 10:23:42 | {"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": 0.1831728219985962, "perplexity": 991.2830867893371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989819.92/warc/CC-MAIN-20210518094809-20210518124809-00180.warc.gz"} |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/169/1/90189/characterizations-of-p-superharmonic-functions-on-metric-spaces | # Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty
## Characterizations of $p$-superharmonic functions on metric spaces
### Tom 169 / 2005
Studia Mathematica 169 (2005), 45-62 MSC: Primary 31C45; Secondary 31C05, 35J60, 49J27. DOI: 10.4064/sm169-1-3
#### Streszczenie
We show the equivalence of some different definitions of $p$-superharmonic functions given in the literature. We also provide several other characterizations of $p$-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also apply to Cheeger $p$-superharmonic functions and in the Euclidean setting to $\cal A$-superharmonic functions, with the usual assumptions on $\cal A$.
#### Autorzy
• Anders BjörnDepartment of Mathematics | 2021-09-18 11:32:13 | {"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": 0.46939006447792053, "perplexity": 1016.2143820126843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056392.79/warc/CC-MAIN-20210918093220-20210918123220-00509.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/how-do-you-evaluate-3-ln0-2 | How do you evaluate 3^ln0.2?
Feb 24, 2017
${3}^{\ln 0.2} = 0.171$
Explanation:
Let ${3}^{\ln 0.2} = x$. Taking natural log on both sides, we get
$\ln 0.2 \ln 3 = \ln x$ and hence
$x = {e}^{\ln 0.2 \ln 3}$
= ${e}^{- 1.609 \times 1.0986}$
= ${e}^{- 1.76815} = 0.171$ | 2021-10-20 07:48:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.7448530197143555, "perplexity": 774.0855958614062}, "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-2021-43/segments/1634323585302.91/warc/CC-MAIN-20211020055136-20211020085136-00134.warc.gz"} |
https://biodynamo.org/notebooks/ST13-dynamic-scheduling.html | # Dynamic scheduling¶
Author: Lukas Breitwieser
This tutorial demonstrates that behaviors and operations can be added and removed during the simulation. This feature provides maximum flexibility to control which functions will be executed during the lifetime of a simulation.
Let's start by setting up BioDynaMo notebooks.
Define a helper variable
We define a standalone operation TestOp which prints out that it got executed and which removes itself from the list of scheduled operations afterwards. The same principles apply also for agent operations.
Let's define a little helper function which creates a new instance of TestOp and adds it to the list of scheduled operations.
Let's define a new behavior b2 which prints out when it gets executed and which adds a new operation with name OP2 to the simulation if a condition is met.
In this scenario the condition is defined as simulation time step == 1.
We define another behavior b1 which prints out when it gets executed, removes itself from the agent, and which adds behavior b2 to the agent.
Now all required building blocks are ready. Let's define the initial model: a single agent with behavior b1.
We also add a new operation to the simulation.
Let's simulate one iteration and think about the expected output.
• Since we initialized our only agent with behavior b1, we expect to see a line B1 0-0
• Furthermore, b1 will print a line to inform us that it removed itself from the agent, and that it added behavior b2 to the agent.
• Because changes are applied immediately (using the default InPlaceExecCtxt) also B2 will be executed. However the condition inside b2 is not met.
• Next we expect an output from OP1 telling us that it got executed.
• Lastly, we expect an output from OP1 to tell is that it removed itself from the simulation.
Let's simulate another iteration.
This time we only expect output from B2. Remember that B1 and OP1 have been removed in the last iteration.
This time the condition in B2 is met and we expect to see an output line to tell us that a new instance of TestOp with name OP2 has been added to the simulation.
Let's simulate another iteration. This time we expect an output from B2 whose condition is not met in this iterations, and from OP2 that it got executed and removed from the simulation.
Let's simulate one last iteration. OP2 removed itself in the last iteration. Therefore, only B2 should be left. The condition of B2 is not met.
In summary: We initialized the simulation with B1 and OP1.
In iteration:
1. B1 removed, B2 added, OP1 removed | 2022-08-15 04:49:43 | {"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": 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": 0.30388718843460083, "perplexity": 1939.1265183352027}, "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/1659882572127.33/warc/CC-MAIN-20220815024523-20220815054523-00315.warc.gz"} |
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### Adding co-author without consent of all co-authors [closed]
I have been collaborating with an individual on a scientific paper. I have documents showing that this individual has shared the paper content with other people. Also, the individual has added co-... | 2021-03-08 18:55:32 | {"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": 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": 0.36005643010139465, "perplexity": 2254.426246951233}, "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-2021-10/segments/1614178385389.83/warc/CC-MAIN-20210308174330-20210308204330-00291.warc.gz"} |
https://www.physicsforums.com/threads/did-i-do-this-integral-right.63953/ | Homework Help: Did I do this integral right?
1. Feb 15, 2005
UrbanXrisis
$$\int \frac {e^x+4}{e^x}dx =?$$
Here's what I did:
$$\int \frac {e^x+4}{e^x}dx = \int e^{-x}(e^x+4)dx$$
$$\int e^{-x}(e^x+4)dx =\int 1+4e^{-x} = x-\frac {4e^{-x+1}}{x+1}$$
Did I do this correctly? Is there a more simplified answer?
2. Feb 15, 2005
Galileo
Rewriting $\frac{e^x+4}{e^x}=1+4e^{-x}$ was correct.
Check the antiderivative of $e^{-x}$. Your answer is not correct. You can easily check it by differentiating it.
Mind the difference between $x^a$ where the base is the variable and $a^x$ where the base is constant and the exponent is the variable.
3. Feb 15, 2005
UrbanXrisis
since $$\int e^{x} = e^{x}+C$$
then...
$$\int 1+4e^{-x} = x+4e^{-x}+C$$
is that correct?
4. Feb 15, 2005
Jameson
When you differentiate $$x + 4e^{-x} + C$$ you get
$$1 - 4e^{-x}$$ , so the integral is actually
$$\int 1 + 4e^{-x} dx = x - 4e^{-x} + C$$
5. Feb 15, 2005
UrbanXrisis
I dont understand where the negative came from
6. Feb 15, 2005
Jameson
The integral of $$e^x dx = {e^x} + C$$
The integral of $$e^{-x}dx = -e^{-x} + C$$.
Differentiating that answer you find that $$\frac {d}{dx} -e ^{-x} = e^{-x}$$
7. Feb 15, 2005
dextercioby
Think of it as an $e^{u}$ and apply the method of substitution:
$$-x=u$$
Daniel.
P.S.That's how u end up with the minus.
8. Feb 15, 2005
UrbanXrisis
$$\int \frac {e^x}{e^x+4}dx =?$$
Here's what I did:
$$= \int e^{x}(e^x+4)^{-1}dx$$
subsitute:
$$u=e^x+4$$
$$du=e^x dx$$
$$\int u^{-1}du =ln(e^x+4)$$
Did I do this correctly? Is there a more simplified answer?
9. Feb 15, 2005
NateTG
Looks good to me.
10. Feb 15, 2005
dextercioby
Don't forget the constant of integration.
Daniel. | 2018-04-25 22:31:28 | {"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": 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": 0.8786009550094604, "perplexity": 1692.0938225022378}, "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-2018-17/segments/1524125947968.96/warc/CC-MAIN-20180425213156-20180425233156-00217.warc.gz"} |
https://cs184.eecs.berkeley.edu/sp20/lecture/4-49/transforms | Lecture 4: Transforms (49)
FLinesse
Another closely connected field in which the Rodriguez Formula is used commonly to express a general rotation is robotics! (movement at rotational joints)
You must be enrolled in the course to comment | 2020-06-04 09:02:47 | {"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": 0.8915998935699463, "perplexity": 3222.782485227368}, "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-2020-24/segments/1590347439213.69/warc/CC-MAIN-20200604063532-20200604093532-00214.warc.gz"} |
https://www.gradesaver.com/textbooks/math/calculus/calculus-3rd-edition/chapter-7-exponential-functions-7-4-exponential-growth-and-decay-exercises-page-349/12 | ## Calculus (3rd Edition)
The decay constant is $4.27\times 10^{-4}$.
The half-life is given by $$\frac{\ln 2}{k}\Longrightarrow 1622= \frac{\ln 2}{k}\Longrightarrow k= \frac{\ln 2}{1622}=4.27\times 10^{-4}.$$ So the decay constant is $4.27\times 10^{-4}$. | 2020-11-24 05:54:01 | {"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": 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": 0.9996469020843506, "perplexity": 841.6006235524046}, "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-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00577.warc.gz"} |
https://arduino.stackexchange.com/questions/26285/attiny44-millis-not-working-with-16-mhz-external-clock | # ATtiny44 millis() not working with 16 MHz external clock
I'm using ATtiny44 with Arduino IDE according to this tutorial: http://highlowtech.org/?p=1695
I have a problem with millis(). When I use an internal 1 MHz clock it works correctly but when I use external 16 MHz clock it takes millis() much more time than one second to be divisible by 1000.
I tested it with LCD and Hello World sketch, modified to correspond ATtiny's pins. Do millis() actually work with Tiny's?
Why does it work properly with 1MHz and not with 16 MHz which is the same as used in Arduino platform.
• Did you forget to unprogram CKDIV8? – Ignacio Vazquez-Abrams Jul 13 '16 at 8:20
• Testing whether millis() is divisible by 1000 is a terrible idea. With a 16 MHz clock millis does not count every millisecond: it is updated only every 1024 µs and occasionally jumps by 2 ms. – Edgar Bonet Jul 13 '16 at 9:41
• Please post the Fuses config – Talk2 Jul 13 '16 at 10:40
• If you are specific about 'much more time', that will help people to explain the specific problem you observed. As you can see, there are several possible interpretations of the problem. – Sean Houlihane Jul 13 '16 at 12:06
When millis() was written, it had to assume what the input clock was. There is no way to detect the speed of the input clock: to do so would require another clock! So the writers of the function defined a starting constant, set it to 1000000, and required anyone that changed the clock would have to change that constant.
Find the constant, and set it to 16000000. Voilà! | 2021-04-22 04:28:49 | {"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": 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": 0.38228005170822144, "perplexity": 1859.6491940045362}, "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/1618039560245.87/warc/CC-MAIN-20210422013104-20210422043104-00139.warc.gz"} |
https://aptitude.gateoverflow.in/4993/cat-2010-question-41 | 234 views
Which of the following statements is wrong ?
1. Depreciation expense is the lowest for food industry
2. Power and fuel expenses are $5$th largest item in the expenditure of diverifies industries.
3. Electricity industry earns more of other income as a percentage of total income compared to other industries.
4. Raw material cost is the largest item of expense in all industry sectors
1 | 2022-12-09 20:01:02 | {"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": 0.33215683698654175, "perplexity": 4589.442401275765}, "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/1669446711475.44/warc/CC-MAIN-20221209181231-20221209211231-00714.warc.gz"} |
https://byjus.com/perimeter-of-an-ellipse-calculator/ | # Perimeter Of An Ellipse Calculator
Perimeter of a Ellipse
Perimeter of an Ellipse Calculator is a free online tool that displays the value of perimeter of ellipse for the given radii. BYJU’S online perimeter of an ellipse calculator tool makes the calculation faster, and it displays the perimeter for the given vertical and horizontal radius in a fraction of seconds.
## How to Use the Perimeter of an Ellipse Calculator?
The procedure to use the perimeter of an ellipse calculator is as follows:
Step 1: Enter the vertical and horizontal radius in the respective input field
Step 2: Now click the button “Calculate” to get the ellipse perimeter
Step 3: Finally, the value of perimeter of the ellipse will be displayed in the output field
### What is Meant by Perimeter of an Ellipse?
In conic sections, an ellipse is one of the important curves that surround two focal points and with two radii, namely the semi-major axis and semi-minor axis. The perimeter of an ellipse is defined as the distance around the boundary of an ellipse. The longest chord of the ellipse is called the major axis, and the chord which perpendicular to it and bisects the major axis is called the minor axis. The perimeter of an ellipse formula is given as:
Perimeter of an ellipse
$$\begin{array}{l}=2\pi\sqrt{\frac{r_1^2+r_2^2}{2}}\end{array}$$
Here,
r1 and r2 represent the radii (i.e. vertical and horizontal axis) | 2022-05-17 19:49:13 | {"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": 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": 0.9018383622169495, "perplexity": 467.94190059817896}, "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/1652662520817.27/warc/CC-MAIN-20220517194243-20220517224243-00233.warc.gz"} |
https://ai.stackexchange.com/questions/7149/how-to-solve-problem-pairwise-grouping-to-maximise-score | # How to solve problem: pairwise grouping to maximise score
Sorry, the title is bad because I don't even know what to call this problem.
I have a set of n objects {obj_0, obj_1, ......, obj_(n-1)}, where n is an even number.
Any two objects can be paired together to produce an output score. So for instance, you might take obj_j and obj_k, and pair them together giving a score of S_j,k. All scores are independent, so the previous example doesn't tell you anything about what the score for combining obj_j and obj_i, S_j,i might be.
There is no ordering in the combination, so S_j,i and S_i,j are the same.
All scores for all pairing possibilities are known.
The whole set of objects is to be taken and organised into pairs (leaving no objects unpaired). The total score, S_tot is the sum of all scores of individual pairs.
What's the most efficient way to find the score-maximising pairing configuration for a large set of such objects? (does this problem have a name?)
Is there a method which works with the version of this problem where objects are grouped into triplets? | 2019-10-14 18:22:05 | {"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": 0.5599978566169739, "perplexity": 900.8536291832637}, "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/1570986654086.1/warc/CC-MAIN-20191014173924-20191014201424-00053.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/simple-problems-single-events-two-dice-are-rolled-together-find-probability-getting-multiple-2-one-die-odd-number-other-die_29821 | Share
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# Two Dice Are Rolled Together. Find the Probability of Getting: a Multiple of 2 on One Die and an Odd Number on the Other Die. - ICSE Class 10 - Mathematics
ConceptSimple Problems on Single Events
#### Question
Two dice are rolled together. Find the probability of getting:
a multiple of 2 on one die and an odd number on the other die.
#### Solution
In throwing a dice, total possible outcomes= {1,2,3,4,5,6}
n(s)
for two dice, n (s)=6xx6=36
E= event of getting a multiple of 2 on one die and an odd number on the othher = (2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5),(1,2),(3,2),(5,2),(1,4),(3,4),(5,4),(1,6),(3,6),(5,6)
n(E)=18
Probability of getting a multiple of 2 one die and an odd number on the other= (n(E))/(n(s))=18/36=1/2
Is there an error in this question or solution?
#### Video TutorialsVIEW ALL [3]
Solution Two Dice Are Rolled Together. Find the Probability of Getting: a Multiple of 2 on One Die and an Odd Number on the Other Die. Concept: Simple Problems on Single Events.
S | 2019-07-19 19:31:13 | {"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": 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": 0.200042262673378, "perplexity": 1009.7988453055764}, "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/1563195526337.45/warc/CC-MAIN-20190719182214-20190719204214-00397.warc.gz"} |