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http://math.stackexchange.com/questions/591389/question-involving-cauchy-sequences | # Question involving Cauchy sequences
Suppose $\left \{ a_n \right \}$ is a Cauchy sequence, and $\left \{ x_n \right \}$ is a sequence with a number $k>0$ such that $|x_n - x_m|\leq k|a_n - a_m|$ for all $n,m\in \mathbb{N}$. Is $\left\{ x_n \right\}$ necessarily a Cauchy sequence? Either prove or give a counter-example.
My attempt: I think the question is true. So since $\left \{ a_n \right \}$ is a Cauchy sequence, then for $\forall \epsilon >0$, there is an $N$ so that for all $n,m>N$ $|a_n - a_m| \leq \frac{\epsilon}{k}$.
So for any $n,m$, we get $|x_n - x_m|<\epsilon \Rightarrow |x_n - x_m|\leq k|a_n - a_m|$.
Is that it to the proof? Looks quite simple to me.
-
Did you mean to say that there is a number $k>0$ such that $|x_{n}-x_{m}|\leq k|a_{n}-a_{m}|$ for all $n,m\in\mathbb{N}$? If so your proof is almost correct -- you just need to switch the direction of the last implication. That is, for any $n,m\geq N$ we have $|x_{n}-x_{m}|\leq k|a_{n}-a_{m}|\Rightarrow |x_{n}-x_{m}|<\epsilon$. – Eric Dec 3 '13 at 19:35
Simple facts have simple proofs. – Carsten S Dec 3 '13 at 19:37
So is {$x_n$} necessarily a Cauchy? – user87274 Dec 3 '13 at 20:44
Yeah, that's right. The fact that $|a_n-a_m| \leq \frac{\epsilon}{k}$ is important: by transitivity, we then have $|x_n - x_m| \leq |a_n - a_m | \leq \frac{\epsilon}{k}$, so $|x_n - x_m| \le \epsilon$. | 2015-08-29 23:51:07 | {"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": 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": 0.9636200666427612, "perplexity": 141.71939829094407}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064590.32/warc/CC-MAIN-20150827025424-00301-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://mathoverflow.net/revisions/80986/list | 2 Endollared the LaTeX.
I want to know the following is well-known or not:
Let X be a metric space with Hausdorff dimension \alpha. $\alpha$. Then for any \beta $\beta < \alpha, alpha$, X contains a closed subset whose Hausdorff dimension is \beta.$\beta$.
1
# Question on geometric measure theory
I want to know the following is well-known or not:
Let X be a metric space with Hausdorff dimension \alpha. Then for any \beta < \alpha, X contains a closed subset whose Hausdorff dimension is \beta. | 2013-05-23 10:40:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8740335702896118, "perplexity": 479.4349116808992}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703227943/warc/CC-MAIN-20130516112027-00042-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1677.0 | NTNUJAVA Virtual Physics LaboratoryEnjoy the fun of physics with simulations! Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
July 23, 2019, 05:59:24 am
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ahmedelshfie
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This applet is Solution for two linear equations
Created by prof Hwang Modified by Ahmed
Original project Solution for two linear equations
Assume there are two linear equations:
$a_1 x + b_1 y +c_1=0$
$a_2 x + b_2 y +c_2=0$
The solution is $x=\frac{b1*c2-c1*b2}{a1*b2-a2*b1}$, $y=\frac{a2*c1-a1*c2}{a1*b2-a2*b1}$
You can drag the circle to change the slope of the linear equation or drag the square to change the offset of the linear equations.
Embed a running copy of this simulation
Embed a running copy link(show simulation in a popuped window)
Full screen applet or Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list
• Please feel free to post your ideas about how to use the simulation for better teaching and learning.
• Post questions to be asked to help students to think, to explore.
• Upload worksheets as attached files to share with more users.
Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!
Solution for two linear equations.gif (20.41 KB, 557x564 - viewed 316 times.) Logged
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Never underestimate others. Never overestimate oneself. ...Wisdom
Related Topics Subject Started by Replies Views Last post THE FINAL QUANTUM SOLUTION Wave Janus20 0 14954 November 29, 2005, 03:22:23 pm by Janus20 ejrconsole file does not run Information and Download Fred Chuit 6 14234 January 12, 2015, 06:51:35 pm by whitecrow4 Ejs Open Source Superposition of 2 Waves generated by equations Collaborative Community of EJS lookang 3 9767 August 14, 2012, 01:24:26 pm by lookang Solving linear equations misc Fu-Kwun Hwang 0 6750 March 24, 2009, 08:02:50 am by Fu-Kwun Hwang Solution for two linear equations misc Fu-Kwun Hwang 0 7082 June 18, 2009, 03:37:19 pm by Fu-Kwun Hwang
Page created in 0.366 seconds with 24 queries.since 2011/06/15 | 2019-07-22 22:59:07 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1740562617778778, "perplexity": 11322.100881037946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528290.72/warc/CC-MAIN-20190722221756-20190723003756-00512.warc.gz"} |
https://plainmath.net/pre-algebra/103001-what-is-the-reciprocal-of-4-11 | Alan Wright
2023-02-24
What is the reciprocal of $\frac{4}{11}$?
A. $\frac{4}{11}$
B. 11
C. 4
D. $-\frac{4}{11}$
Darien Jennings
A fraction's reciprocal is created by switching the numerator and denominator.
Reciprocal of $\frac{4}{11}=\frac{11}{4}$ | 2023-03-28 02:26:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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": 0.9798338413238525, "perplexity": 8094.151629342262}, "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/1679296948756.99/warc/CC-MAIN-20230328011555-20230328041555-00371.warc.gz"} |
https://alacaze.net/publication/handbook-prob/ | Frequentism in probability theory
Type
Publication
The Oxford Handbook of Probability and Philosophy | 2021-09-18 19:39:27 | {"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": 0.9867475628852844, "perplexity": 14180.471580657155}, "config": {"markdown_headings": false, "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-2021-39/segments/1631780056572.96/warc/CC-MAIN-20210918184640-20210918214640-00361.warc.gz"} |
https://imathworks.com/tex/tex-latex-last-visited-url-in-apa-style/ | # [Tex/LaTex] Last visited URL in apa style
apa-stylebibliographiesurls
I'm using the apa-good.bst file to typeset my bibliography in APA style. I need to include something like "Last visited…" (using the urldate variable) when I cite a webpage but I don't know how I can do this. Can anyone help me?
Your referenced bibliography style isn't available at CTAN. So I guess You are using the following file:
ucbthesis -- LaTeX template for typesetting UCB thesis -- apa-good.bst
The style support the following entries:
address author booktitle chapter edition
editor howpublished institution journal
key month note number organization pages
publisher school series title type url
volume year
In relation to my previous answer
URL of cited web site in bibliography
You can simple add to the field note:
note="Last visited..." | 2023-03-26 12:35:05 | {"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": 0.5059475302696228, "perplexity": 10118.29231538858}, "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/1679296945472.93/warc/CC-MAIN-20230326111045-20230326141045-00781.warc.gz"} |
http://www.physicsforums.com/showpost.php?p=3804951&postcount=3 | View Single Post
Ok thanks. I think I have understood how to find the selections rules. Could you explain why the vibrational modes only describes the exited modes and not the ground state. I guess it is like that because A1g is not contained in the vibrational modes of graphite (2 * E1u + 2 * E2g + 2 * A2u + 2 * B1g). I thinks it's is logical as you say that the ground state is fully symmetrical (guess you could think of it as all the atoms being at their equilibrium sites, maybe with some caution), but as i said I'm not quit sure why the ground state is not in the problem, let me explain: If I count the dimensions of the representations 2 * E1u + 2 * E2g + 2 * A2u + 2 * B1g i get 12, which I expected because there are 4 atoms in the unit cell each with three degrees of freedom. The representations tells me that I can devide these eigenfunction into sets that transform among each other, but the fully symmetric representation is not present, that is no of the eigenfunctions of the problem has the full symmetry of the problem, and hence is not the ground state. This is what i mean by it seems like the ground state has to be treated seperately. I guess somehow that the representation theory approach only describes exited modes, but i fail to see why that is? Hope that explains my problem a bit clearer. | 2013-05-24 16:26:14 | {"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": 0.8195869326591492, "perplexity": 281.04108135755587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704752145/warc/CC-MAIN-20130516114552-00053-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://gradestack.com/Review-CFA-Level-1-CFA/Time-Value-of-Money/IRR/14402-2904-975-study-wtw | IRR
Discount rate that makes NPV of all cash flows equal to zero.
For mutually exclusive projects, NPV and IRR can give conflicting rankings. NPV is a better measure in such cases.
Â
Â
Q: If I have to invest today $2,000 for a project which gives me$100 next year, $200 the next, and$250 after that till perpetuity, should I make this investment?
Cost of Capital = 10%. | 2017-05-26 21:17:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3144790828227997, "perplexity": 5529.378977914971}, "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/1495463608684.93/warc/CC-MAIN-20170526203511-20170526223511-00199.warc.gz"} |
https://sites.google.com/site/dlhquantum/bell-s-theorem-and-quantum-realism | ### "Bell's Theorem and Quantum Realism" Correction
The following corrections are to be made to the book "Bell's Theorem and Quantum Realism: Reassessement in Light of the Schrödinger Paradox" ( See "Springer" website here: http://www.springer.com/physics/quantum+physics/book/978-3-642-23467-5?changeHeader)In chapter four, 4.3.1 ( pp 67 ), 4.3.2 ( 68-footnote 13 ), and 4.5.2 ( 90 ), the notation "script-M ( O)" is offered for experimental measurement procedure of quantum observable O.A more-appropriate notation "script-E ( O )" was utilized in chapter 2. ( And also makes a brief appearance at the end of chapter 4 in the book summary section 4.7.) The notion behind "script-E(O)" is to emphasize experimental procedure (of which there might be several distinct possibilites, even when one is "measuring" the same quantum observable. See chapter 2 of the book.) The appropriate "LaTeX" command for a "script" variable is "{\cal }". Ideally, one would also prefer not to utilize the term "measurement locality" (4.3.2 (p 68 footnote 13) and 4.5.2 (p 90 in text and in footnote 57) ). Instead, a better apellation would be "procedural locality," which term emphasizes the experimental procedure brought to bear in "measuring" some observable (perhaps making use of the initials PL rather than ML).For those who would like something more explicit and exact, below are attempts at corrected versions of the pages requiring changes. Unfortunately, I was not able to completely match the fonts, size and style used by the typesetter. Therefore, these pages are imperfect in that they do not match up perfectly with the pages in the actual book insofar as the flow of the text. In particular, the end-points of the pages are not the same as those in the book.Nevertheless, here are .jpg files of the pages in question, if you would care to download or just take a look:Page 67 The point of quantum contextuality is that measurement is an *ambiguous* concept. Moreover, this is not some special result that follows from analysis of hidden variables, but from the quantum formalism itself (see chapter 2 of the book). The notation "script-M( O )" and the term "measurement locality" do not really reflect this insight very well.I hope that any resulting confusion will be minimal.Thank you.DLH January 2012
Subpages (3): | 2015-05-05 22:35:24 | {"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": 0.87385094165802, "perplexity": 1839.007167047546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430457008123.23/warc/CC-MAIN-20150501051008-00057-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://chemistry.stackexchange.com/questions/9012/phase-stability-of-alcohols | # Phase stability of alcohols
Tert-butyl alcohol seems unusual among alcohols in that its melting point is high (25°C) while its boiling point is also still low (82°C). I am looking for more materials with phase-unstable liquid regions like this so I'm curious what makes the liquid phase so unstable relative to the solid and gas phases?
Do the methyl groups align and act like alkanes to stabilize the solid but the molecule is still small enough to have a low boiling point?
To my larger point, any advice on characteristics of materials that exhibit low liquid phase stability?
Chromium, molybdenum, and tungsetn metal versus their respective hexacarbonyls. $\ce{-SiMe3}$ and $\ce{-CF3}$ plus symmetry confer remarkable volatility. $\ce{I(CF3)7}$ melts and boils around 0 C. That is molecular weight 609.95 - and it has no static molecular structure (Bartell mechanism). | 2020-02-27 06:08:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43905457854270935, "perplexity": 2554.9281708499334}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00427.warc.gz"} |
https://tex.stackexchange.com/questions/191848/centering-list-of-x-and-following-with-text/191850 | # Centering List of X and Following with Text
With the tocloft package, I can add text under the title of a "List of Z" at the beginning of a latex document:
\renewcommand{\cftafterZtitle}{\par\noindent \textnormal{Z} \hfill \textnormal{PAGE}}
Using the following I can center the title "List of Z":
\renewcommand{\cftZtitlefont}{\hfill\bfseries}
\renewcommand{\cftafterZtitle}{\hfill}
But when I try to combine the two commands, it moves the text to the right margin instead of the center:
\renewcommand{\cftloftitlefont}{\hfill\bfseries}
\renewcommand{\cftafterloftitle}{\hfill\par\noindent \textnormal{Z} \hfill \textnormal{PAGE}}
Does anyone know how to both center the title "List of Z" and have text below the title?
• Please help us to help you and add a minimal working example (MWE) that illustrates your problem. It will be much easier for us to reproduce your situation and find out what the issue is when we see compilable code, starting with \documentclass{...} and ending with \end{document}. – cfr Jul 17 '14 at 1:59
• Don't know the package but usually centring is done with things like \centering or \begin{center} rather than \hfill which does not usually make a good solution. – cfr Jul 17 '14 at 2:00
You can add an empty \hbox after the second \hfill (See egreg's answer to What is \null and when do we need to use it?):
\documentclass{article}
\usepackage{tocloft}
\renewcommand{\cftloftitlefont}{\hfill\bfseries}
\renewcommand{\cftafterloftitle}{\hfill\null\par\noindent\textnormal{Z}\hfill \textnormal{PAGE}}
\begin{document}
\listoffigures
\noindent X\hrulefill Y% for coparison only
\end{document}
Another option is to use \hfil instead:
\renewcommand{\cftloftitlefont}{\hfil\bfseries}
\renewcommand{\cftafterloftitle}{\hfil\par\textnormal{Z}\hfill \textnormal{PAGE}} | 2020-06-03 23:35:43 | {"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": 0.8906961679458618, "perplexity": 1850.7375715033286}, "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/1590347436466.95/warc/CC-MAIN-20200603210112-20200604000112-00589.warc.gz"} |
https://mattermodeling.stackexchange.com/questions/4138/are-different-eigensolvers-consistent-within-vasp-algo-normal-vs-fast | Are different eigensolvers consistent within VASP (Algo=Normal vs Fast)
I tried to relax a 4x4x1 supercell of ferromagnetic monolayer material using the default settings (ALGO = Normal) but it didn't converge. So, I switched to ALGO = Fast and the results are converging normally now. Is this setting safe? Will this affect the accuracy of the results? The used INCAR file is below :
ENCUT = 600 eV
PREC = Accurate
LREAL = Auto
EDIFFG = -0.001
EDIFF = 1E-8
LCHARG = .FALSE.
LWAVE = .FALSE.
ISMEAR = 0
SIGMA = 0.03
NSW = 299
IBRION = 2
ISIF = 3
ISPIN = 2
MAGMOM = 16*2.0 32*0.0
ALGO = Fast # This was Normal before editing
#Mixer
AMIX = 0.2
BMIX = 0.00001
AMIX_MAG = 0.8
BMIX_MAG = 0.00001
LASPH = .TRUE.
NCORE = 2
Changing ALGO should make no difference in an ideal world. However, when you invoke spin polarization, you may find a different magnetic state from both algorithms. The best practice would be to ensure that you converge to the right solution.
That being said, the NORMAL algo is normally more robust than Fast. This in general might be a bad sign for your system. You can also try the ALL algo and see what that gives.
I see you have also added an incar, here is some general advice that might influence convergence.
• ADDGRID is a spooky keyword, I would say never use it but sometimes it helps. I suggest leaving it off, convergence issues tend not to be fixed by it in general in these magnetic systems
• You are using a small sigma value, I would suggest using 0.2 and reduce it to your desired value after convergence. It will not influence geometry much but will make convergence much easier.
• Leave the mixing settings at their defaults most of the time. You can try this approach as a first attempt, but if it doesn't fix the problem do not keep it.
• Consider running a spin paired calculation first as a single point calculation, save the WAVECAR/CHGCAR, then add magnetization. This often helps as well.
• EDIFF = 1e-8 is insanely accurate, use something more like 1e-4 or 1e-5 for geometry optimization. If you find that you cannot converge the geometry you can raise it or switch to a VTST geometry optimizer which uses forces which are less sensitive to this.
• Good point about the magnetic moments. That's a real subtlety. – Andrew Rosen Jan 15 at 18:57
• It has given me many angry noises at my desk in the past few days – Tristan Maxson Jan 15 at 19:02
• I have added my iNCAR file could you please have a look at it? Don't you think that the mixing tags are the source of the problem? – Chi Kou Jan 15 at 19:04
• @ChiKou I have added some additional advice based on prior experience. Maybe some can be applied. – Tristan Maxson Jan 15 at 19:14 | 2021-03-08 20:22:25 | {"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": 0.44507643580436707, "perplexity": 1608.3807677948005}, "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/1614178385389.83/warc/CC-MAIN-20210308174330-20210308204330-00376.warc.gz"} |
https://www.doubtnut.com/question-answer/if-i-int-sin-2x-3-4cosx3dx-then-i-equals-642546099 | # If I= int (sin 2x)/((3+4cosx)^(3))dx, then I equals
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Updated On: 3-5-2021
Apne doubts clear karein ab Whatsapp par bhi. Try it now.
Get Answer to any question, just click a photo and upload the photo
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Text Solution
(3cos x+8)/((3+4cosx)^(2))+C(3+8cos x)/(16(3+4cosx)^(2))+C(3+cos x)/((3+4cosx)^(2))+C(3-8cos x)/(16(3+4cosx)^(2))+C
B
Solution :
I= int (sin 2x)/((3+4cosx)^(3))dx <br> Put 3+4cosx=t," so that " -4sinx dx=dt. Then <br> I=(-1)/(8)int((t-3))/(t^(3))dt=(1)/(8)((1)/(t)-(3)/(2)(1)/(t^(2)))+C <br> =(2t-3)/(16t^(2))=(8cosx+3)/(16(3+4cosx)^(2))+C
Transcript
TimeTranscript
00:00 - 00:59welcome to doctor days is called the question I to integration sin 2x upon 3 + 4 cos x dx is equal to equal to integration to sin x cos x upon 1 + 4 cos x + 4 cos x = 25 - 4 sin x dx is equal to duty so we can purchase value above so it become to outside this is -1 by School this value becomes minus 3 by 4 upon this becomes
01:00 - 01:59- 12 integration t minus 3 upon 4 cube minus 1 by 2 integration of 1 by 4 p square DTE energy + 3 by 2 installation and bi fore u so this becomes minus 1 by 8 management + kids for minus 1 + 3 by 2 into 4 into 10 power minus 2 1 -2 School Tum so we have won by 80 upon 16 p square +
02:00 - 02:592 x minus 3 X square + so heavy put the value of cos x minus 16 cos square x + cos square x + 3 k we get the value of 4 cos x + 3 so we put it here it becomes 8cosx | 2022-01-20 11:53:39 | {"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": 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": 0.5233868360519409, "perplexity": 3980.970235799485}, "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/1642320301737.47/warc/CC-MAIN-20220120100127-20220120130127-00144.warc.gz"} |
https://skyandtelescope.org/online-gallery/3-years-saturn/ | Photographer:
Peter Wienerroither
Email:
[email protected]
Location of Photo:
near Vienna, Austria
3/13/2007
Equipment:
Canon EOS 5D, Sigma 50mm Macro, mount Astro 5. Exposure 4x 4 min. at ISO 400.
Description:
A photo/graph that shows the way of Saturn through Cancer and Leo from Aug. 2005 until Sep. 2008 in steps at 1st and 15th of each month. A animated GIF see at http://homepage.univie.ac.at/~pw/pwafop/20070313-004d.gif
Comments
You must be logged in to post a comment. | 2020-07-06 02:17:58 | {"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": 0.8216764330863953, "perplexity": 14944.211193896297}, "config": {"markdown_headings": false, "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/1593655890092.28/warc/CC-MAIN-20200706011013-20200706041013-00353.warc.gz"} |
https://hal.archives-ouvertes.fr/hal-00911140 | # Improvements on the accelerated integer GCD algorithm
1 Computer Science Institute, University of Oran Es-Senia. Algeria
LIPN - Laboratoire d'Informatique de Paris-Nord
Abstract : The present paper analyses and presents several improvements to the algorithm for finding the $(a,b)$-pairs of integers used in the $k$-ary reduction of the right-shift $k$-ary integer GCD algorithm. While the worst-case complexity of Weber's ''Accelerated integer GCD algorithm'' is $\cO\l(\log_\phi(k)^2\r)$, we show that the worst-case number of iterations of the while loop is exactly $\tfrac 12 \l\lfloor \log_{\phi}(k)\r\rfloor$, where $\phi := \tfrac 12 \l(1+\sqrt{5}\r)$.\par We suggest improvements on the average complexity of the latter algorithm and also present two new faster residual algorithms: the sequential and the parallel one. A lower bound on the probability of avoiding the while loop in our parallel residual algorithm is also given.
Keywords :
Document type :
Journal articles
Domain :
Cited literature [7 references]
https://hal.archives-ouvertes.fr/hal-00911140
Contributor : Christian Lavault <>
Submitted on : Monday, February 10, 2014 - 4:19:10 PM
Last modification on : Thursday, February 7, 2019 - 5:53:12 PM
Document(s) archivé(s) le : Saturday, May 10, 2014 - 11:15:10 PM
### Files
Improvtsgcd97.pdf
Files produced by the author(s)
### Identifiers
• HAL Id : hal-00911140, version 1
• ARXIV : 1402.2266
### Citation
Sidi Mohamed Sedjelmaci, Christian Lavault. Improvements on the accelerated integer GCD algorithm. Information Processing Letters, Elsevier, 1997, 61 (1), pp.31--36. ⟨hal-00911140⟩
Record views | 2019-04-23 00:18:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.3543654680252075, "perplexity": 3990.2924207792867}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578583000.29/warc/CC-MAIN-20190422235159-20190423021159-00201.warc.gz"} |
https://www.maths.usyd.edu.au/s/scnitm/lachlans-SydneyDynamicsGroup-Burns | SMS scnews item created by Lachlan Smith at Mon 10 Feb 2020 1713
Type: Seminar
Distribution: World
Expiry: 13 Mar 2020
Calendar1: 13 Feb 2020 1600-1700
CalLoc1: Carslaw 175
Auth: [email protected] (lsmi9789) in SMS-WASM
# Sydney Dynamics Group: Burns -- Flexible spectral methods and high-level programming for PDEs
Dear All,
This week, Thursday February 13, Keaton Burns (MIT) will give a talk at USyd
in Carslaw 175 (note unusual time and place), at 4pm on
Title: Flexible spectral methods and high-level programming for PDEs
Abstract:
The large-scale numerical solution of PDEs is an essential part of scientific
research. Decades of work have been put into developing fast numerical schemes for
specific equations, but computational research in many fields is still largely
software-limited. Here we will discuss how algorithmic flexibility and composability
can enable new science, as illustrated by the Dedalus Project. Dedalus is an
open-source Python framework that automates the solution of general PDEs using spectral
methods. High-level abstractions allow users to symbolically specify equations,
parallelize and scale their solvers to thousands of cores, and perform arbitrary
analysis with the computed solutions. These features are enabling us to perform novel
simulations of astrophysical, geophysical, and biological fluids with modern
mathematical techniques. We will discuss applications using new bases for tensor-valued
equations in spherical domains, immersed boundary methods for multiphase flows, and
multi-domain simulations interfacing Dedalus with other PDE and integral equation
solvers.
Hope to see you all there, Lachlan
Actions: | 2022-12-07 10:11:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3040563762187958, "perplexity": 11291.822140343957}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00284.warc.gz"} |
https://gamedev.stackexchange.com/questions/69145/how-can-i-extract-the-geometry-from-a-j3o-file/69153 | # How can I extract the Geometry from a j3o file?
I created a blender file and then converted it into the j3o file. The only way to load the 3d structure in the game is through a Spacial object:
Spatial towerModel = assetManager.loadModel("Textures/tower.j3o");
Initially the tower in the scene was composed by a simple Geometry:
new Geometry("Tower." + index, new Box(X_SIZE, Y_SIZE, Z_SIZE));
To substitute this implementation with a proper 3d tower I need to use the Gemetry object from the 3jo.
How can I extract the Geometry from the j3o file?
The Spatial given to you from the loadModel method is most likely a Node. You'll have to traverse that node's children (and possibly grand-children) to get to the Geometry, which you will have to cast from one of the child Spatials.
I've not got the code before me right now, so I can't show you, but looking at the Javadoc it should be pretty simple (a bit of recursion should help).
• I found the way to get the geometry, but once I attach it to the scene it doesn't show up; on the contrary in the "scene composer" windows I can see it. (In the blender file there's just the mesh object, I removed the camera and the lights). – Fab Jan 22 '14 at 20:02 | 2021-06-24 11:49:47 | {"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": 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": 0.2562948167324066, "perplexity": 1139.793155255033}, "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-2021-25/segments/1623488553635.87/warc/CC-MAIN-20210624110458-20210624140458-00328.warc.gz"} |
https://studyadda.com/sample-papers/clat-sample-paper-2_q149/118/252499 | • # question_answer Direction: Each question contains a statement or relationship and a question regarding relationship based on the statement, select the correct option. If 'A + B' means A is the mother of B, 'A - B' means A is the brother of B, 'A % B' means A is the father of B and 'A x B' means A is the sister of B, which of the following shows that P is the maternal uncle of Q? A) $Q-N+M\times P$ B) $P+S\times N-Q$ C) $P-M+N\times Q$ D) $Q-S\,%\,P$
P - M $\to$ P is the bother of M. M + N $\to$ M is the mother of N. N x Q $\to$ N is the maternal uncle of Q. Therefore, P is the maternal uncle of Q | 2022-01-19 04:53:16 | {"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": 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": 0.5345596075057983, "perplexity": 1463.8804647511893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301263.50/warc/CC-MAIN-20220119033421-20220119063421-00174.warc.gz"} |
https://www.cis.upenn.edu/~danroth/Teaching/CIS-700-006/index.html | ### Course Description
Making decisions in natural language processing problems often involves assigning values to sets of interdependent variables where the expressive dependency structure can influence, or even dictate, what assignments are possible. Structured learning problems such as semantic role labeling provide one such example, but the setting is broader and includes a range of problems such as name entity and relation recognition and co-reference resolution. The setting is also appropriate for cases that may require a solution to make use of multiple models (possible pre-designed or pre-learned components) as in summarization, textual entailment and question answering.
This semester, we will devote the course to the study of structured learning problems in natural language processing. We will start by recalling the standard” learning formulations as used in NLP, move to formulations of multiclass classification and from then on focus on models of structure predictions and how they are being used in NLP.
Through lectures and paper presentations the course will introduce some of the central learning frameworks and techniques that have emerged in this area over the last few years, along with their application to multiple problems in NLP and Information Extraction. The course will cover:
Models: We will present both discriminative models such as structured Perceptron and Structured SVM, Probabilistic models, and Constrained Conditional Models.
Training Paradigms: Joint Learning models; Decoupling learning from Inference; Constrained Driven Learning; Semi-Supervised Learning of Structure; Indirect Supervision
Inference: Constrained Optimization Models, Integer Linear Programming, Approximate Inference, Dual Decomposition.
### Prerequisites
Machine Learning class; CIS 419/519/520 or equivalent. Knowledge of NLP is recommended but not mandatory.
There will be
• Course Projects (40%) - The project will be done in teams of sizes 2 or 3; teams will proposed projects and consult us. We will have milestones along define a few intermediate stages and results will be reported and presented at the end of each stage.
• Critical Surveys ( 6 + 6 + 6 + 12 = 30% ) - Four (4) times a semester you will write a short critical essay on one of the additional readings.
• Presentations ( 20% ) - Once or twice you will present a paper from the additional readings (30 minutes, focusing on the mathematical/technical details of the paper). The presentations will be prepared in groups, whenever possible, and a group of presentations will form a coherent tutorial, whenever possible (more on that later).
• Class Participation ( 10% )
There is no final exam.
#### Expectations
This is an advanced course. I view my role as guiding you through the material and helping you in your first steps as an researcher. I expect that your participation in class, reading assignments and presentations will reflect independence, mathematical rigor and critical thinking. | 2021-10-28 12:26:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.2646293640136719, "perplexity": 1708.8550363955428}, "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/1634323588284.71/warc/CC-MAIN-20211028100619-20211028130619-00098.warc.gz"} |
https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.lapacklin.dgttrf.html | naginterfaces.library.lapacklin.dgttrf¶
naginterfaces.library.lapacklin.dgttrf(n, dl, d, du)[source]
dgttrf computes the factorization of a real tridiagonal matrix .
For full information please refer to the NAG Library document for f07cd
https://www.nag.com/numeric/nl/nagdoc_27.3/flhtml/f07/f07cdf.html
Parameters
nint
, the order of the matrix .
dlfloat, array-like, shape
Must contain the subdiagonal elements of the matrix .
dfloat, array-like, shape
Must contain the diagonal elements of the matrix .
dufloat, array-like, shape
Must contain the superdiagonal elements of the matrix .
Returns
dlfloat, ndarray, shape
Is overwritten by the multipliers that define the matrix of the factorization of .
dfloat, ndarray, shape
Is overwritten by the diagonal elements of the upper triangular matrix from the factorization of .
dufloat, ndarray, shape
Is overwritten by the elements of the first superdiagonal of .
du2float, ndarray, shape
Contains the elements of the second superdiagonal of .
ipivint, ndarray, shape
Contains the pivot indices that define the permutation matrix . At the th step, row of the matrix was interchanged with row . will always be either or , indicating that a row interchange was not performed.
Raises
NagValueError
(errno )
On entry, error in parameter .
Constraint: .
Warns
NagAlgorithmicWarning
(errno )
Element of the diagonal is exactly zero. The factorization has been completed, but the factor is exactly singular, and division by zero will occur if it is used to solve a system of equations.
Notes
dgttrf uses Gaussian elimination with partial pivoting and row interchanges to factorize the matrix as
where is a permutation matrix, is unit lower triangular with at most one nonzero subdiagonal element in each column, and is an upper triangular band matrix, with two superdiagonals.
References
Anderson, E, Bai, Z, Bischof, C, Blackford, S, Demmel, J, Dongarra, J J, Du Croz, J J, Greenbaum, A, Hammarling, S, McKenney, A and Sorensen, D, 1999, LAPACK Users’ Guide, (3rd Edition), SIAM, Philadelphia, https://www.netlib.org/lapack/lug | 2021-10-19 08:21:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9545109868049622, "perplexity": 3362.7185142320254}, "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-2021-43/segments/1634323585246.50/warc/CC-MAIN-20211019074128-20211019104128-00466.warc.gz"} |
https://math.stackexchange.com/questions/497415/z-mapsto-sin-overlinez-is-not-holomorphic | # $z\mapsto\sin (\overline{z})$ is not holomorphic
I have to prove that the function $f:\mathbb{C}\to\mathbb{C}$ defined by $f(z)=\sin(\overline{z})$ is not holomorphic at any point of $\mathbb{C}$.
Now, I want to show that $f$ does not satisfy the Cauchy-Riemann equations, but first I must write $f(z)$ in the form $u(z)+iv(z)$.
How can I find $u(z)$ and $v(z)$?
Thanks.
• $\sin (a+b) = \sin a \cos b + \sin b \cos a$. Let $a = x$, $b = -iy$. But it's probably better to use the Wirtinger derivatives and compute $\frac{\partial}{\partial\overline{z}}\sin \overline{z}$. – Daniel Fischer Sep 18 '13 at 11:20
• $\sin(x-iy)=\sin(x)\cos(-iy)+\sin(-iy)\cos(x)=\sin(x)\cos(iy)-\sin(iy)\cos(x)$... What can we do now? Btw, I don't know what it is a Wirtinger derivative. – Talexius Sep 18 '13 at 11:29
• $\cos (iy) = \cosh y$, and $\sin (iy) = i\sinh y$. If you haven't yet learned about the Wirtinger derivatives, ignore that for the moment, the real form of the CR equations is simple enough here. – Daniel Fischer Sep 18 '13 at 11:34
• ... even if the C-R equations are satisfied at an isolated point, still the function is not holomorphic there ... – GEdgar Sep 18 '13 at 12:19
$$\sin\overline z:=\frac{e^{\overline z}-e^{-\overline z}}{2i}=\frac{e^xe^{-iy}-e^{-x}e^{iy}}{2i}=\frac1{2i}\left(e^x(\cos y-i\sin y)-e^{-x}(\cos y+i\sin y)\right)=$$
$$=\frac1{2i}\left[\cos y(e^x-e^{-x})-i\sin y(e^x+e^{-x})\right]=\frac12\left[-\sin y(e^x+e^{-x})-\cos y\left(e^x-e^{-x}\right)i\right]=$$
$$=-\sin y\cosh x-i\cos y\sinh x=u(x,y)+iv(x,y)$$
$$u_x=\sin y\sinh x\;,\;\;v_y=\sin y\sinh x\;\ldots$$ | 2020-02-21 10:32:24 | {"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": 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": 0.8435946106910706, "perplexity": 170.40401005040073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145500.90/warc/CC-MAIN-20200221080411-20200221110411-00067.warc.gz"} |
https://oatao.univ-toulouse.fr/19971/ | Asymptotic stability of the linearised Euler equations with long-memory impedance boundary condition
Monteghetti, Florian and Matignon, Denis and Piot, Estelle and Pascal, Lucas Asymptotic stability of the linearised Euler equations with long-memory impedance boundary condition. (2017) In: 13th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2017), 15 May 2017 - 19 May 2017 (Minneapolis, United States).
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Abstract
This work focuses on the well-posedness and stability of the linearised Euler equations (1) with impedance boundary condition (2,3). The first part covers the acoustical case ($u_0 = 0$), where the complexity lies solely in the chosen impedance model. The existence of an asymptotically stable $C_0$-semigroup of contractions is shown when the passive impedance admits a dissipative realisation; the only source of instability is the time-delay $\tau$. The second part discusses the more challenging aeroacoustical case($u_0 \neq 0$), which is the subject of ongoing research. A discontinuous Galerkin discretisation is used to investigate both cases.
Item Type: Conference or Workshop Item (Paper) International conference proceedings Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE) ONERA and DGA download 13 Jun 2018 11:09
Repository Staff Only: item control page | 2021-04-17 09:24:06 | {"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": 0.48569774627685547, "perplexity": 3665.0995774321336}, "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-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00284.warc.gz"} |
https://www.physicsforums.com/threads/uniform-circular-motion-need-help-with-deriving-equations.596631/ | Uniform Circular Motion; Need help with deriving equations.
1. Apr 14, 2012
n3w ton
1. The problem statement, all variables and given/known data
Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension.
(A & B) I did
(C,D, E) I need help
(a) What variables are being measured / manipulated in this lab? What type of relationship is being tested? (radius, mass, force tension/force causing centripetal force)
(b) Graph the relationship between the frequency of revolution and each of the following:
• the magnitude of the tension force [force causing the circular motion(centripetal force)]
• the radius of the circular path
• the mass of the object
**■→(c) Find the proportionalities between frequency of revolution and the variables in radius, mass, and force of tension/centripetal force.
**■→(d) Derive an equation for the frequency in terms of the tension, the radius, and the mass by combining your results from (c) and using your results from (b) to verify.
**■→(e) The following relationship gives the magnitude of the net force causing the acceleration of an object in uniform circular motion:
Fc = 4π²mrf²
Rearrange this equation to isolate the frequency. Compare this result with the equation you derived in (d). Indicate the likely causes for any discrepancies.
Data: http://i.imgur.com/dLpyP.png
Frequency vs Force Graph: http://i.imgur.com/fyFci.png
Frequency vs Mass Graph: http://i.imgur.com/GJ2ms.png
2. Relevant equations
Fc = 4π²mrf²
3. The attempt at a solution
C) and D) Im stuck at
E)
Fc = 4π²mrf²
$\sqrt{}\frac{Fc}{4π²mr}$
2. Apr 14, 2012
PeterO
Your graphs are not extensive enough - they must include the origin (0,0) - not necessarily as a point, but with the axes long enough for them to show up.
With graphical analysis, the only line you can confidently interpret is a straight line passing through the origin.
if y vs x is not straight, you can try y vs 1/x or y vs x2 or or y vs 1/x2 or y vs x2 of y vs √x or y vs 1/√x to see if any of them are a straight line through the origin [or close - there may be uncertainties in your measurements]
suppose y vs 1/√x was such a straight line.
That means y is proportional to 1/√x or y = k/√x or y2x = k
3. Apr 15, 2012
MrWarlock616
uhmm.. time for one cycle is 1/frequency.
4. Apr 15, 2012
PeterO
Looking at your results, I am not sure the figure you call frequency is in fact frequency.
It looks more like the Period to me - ie the time for one cycle.
You possibly need to follow the step you mention above.
5. Apr 15, 2012
MrWarlock616
Yes exactly, that's what I said. The graphs are obviously wrong because he has used time period instead of frequency.
peter, I didn't ask this question..n3w ton did. :P | 2018-01-19 21:47:13 | {"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": 0.4204109013080597, "perplexity": 1461.076149976633}, "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-2018-05/segments/1516084888135.38/warc/CC-MAIN-20180119204427-20180119224427-00733.warc.gz"} |
https://www.youdict.com/ciyuan/s/mayoralty | punter
• n. 船夫，用篙撑船的人
• n. (Punter)人名；(英)庞特；(西)蓬特尔
«
1 / 10
»
punter 顾客，主顾，赌马的人
punter (n.)
1888 in football, agent noun from punt (v.).
1. Your average punter ( ie The ordinary uncultured person ) does not go to the opera.
2. Your average punter does not go to the opera.
3. You can write what you like, as long as it keep the punter happy.
4. Such a description aa euphemism for a club milkman, or a punter an SW 6 pub. | 2021-09-24 21:29:59 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8471381068229675, "perplexity": 12057.353038045061}, "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-2021-39/segments/1631780057580.39/warc/CC-MAIN-20210924201616-20210924231616-00138.warc.gz"} |
https://mikespivey.wordpress.com/2012/12/04/dualitylp/ | ## Some Uses of Duality in Linear Programming
For most of my students, the first time they see duality in linear programming their first reaction is “What’s the big deal?” There was a recent post on math.SE asking the same question. Duality in linear programming seems to me analogous to eigenvalues and eigenvectors in linear algebra, in the sense that at first the concept doesn’t seem like there’s much there, but as you learn more and more you realize how fundamental it is to the entire subject.
This post will describe some of the uses of duality in linear programming. There are others, of course. The post draws heavily on my answer to the math.SE question about the uses of duality.
1. Any feasible solution to the dual problem gives a bound on the optimal objective function value in the primal problem. This is how I motivate the dual problem in class, in fact. The formal statement of this is the weak duality theorem.
2. Understanding the dual problem leads to specialized algorithms for some important classes of linear programming problems. Examples include the transportation simplex method, the Hungarian algorithm for the assignment problem, and the network simplex method. Even column generation relies partly on duality.
3. The dual can be helpful for sensitivity analysis. Changing the primal’s right-hand side constraint vector or adding a new constraint to it can make the original primal optimal solution infeasible. However, this only changes the objective function or adds a new variable to the dual, respectively, so the original dual optimal solution is still feasible (and is usually not far from the new dual optimal solution).
4. Sometimes finding an initial feasible solution to the dual is much easier than finding one for the primal. For example, if the primal is a minimization problem, the constraints are often of the form $A {\bf x} \geq {\bf b}$, ${\bf x} \geq {\bf 0}$, for ${\bf b} \geq {\bf 0}$. The dual constraints would then likely be of the form $A^T {\bf y} \leq {\bf c}$, ${\bf y} \geq {\bf 0}$, for ${\bf c} \geq {\bf 0}$. The origin is feasible for the latter problem but not for the former.
5. The dual variables give the shadow prices for the primal constraints. Suppose you have a profit maximization problem with a resource constraint i. Then the value $y_i$ of the corresponding dual variable in the optimal solution tells you that you get an increase of $y_i$ in the maximum profit for each unit increase in the amount of resource i (absent degeneracy and for small increases in resource i).
6. Sometimes the dual is easier to solve. A primal problem with many constraints and few variables can be converted into a dual problem with few constraints and many variables. Fewer constraints are nice in linear programs because the basis matrix is an $n \times n$ matrix, where n is the number of constraints. Thus the fewer the constraints, the smaller the size of the basis matrix, and thus the fewer computations required in each iteration of the simplex method.
7. The dual can be used to detect primal infeasibility. This is a consequence of weak duality: If the dual is a minimization problem whose objective function value can be made as small as possible, and any feasible solution to the dual gives an upper bound on the optimal objective function value in the primal, then the primal problem cannot have any feasible solutions. | 2017-10-22 15:45:38 | {"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": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9181774258613586, "perplexity": 194.08806985092468}, "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/1508187825308.77/warc/CC-MAIN-20171022150946-20171022170946-00161.warc.gz"} |
https://www.snapsolve.com/solutions/Whyshould-we-conserve-forests-and-wildlife--1672370209732609 | Home/Class 10/Science/
Why should we conserve forests and wildlife?
Speed
00:00
03:52
## QuestionScienceClass 10
Why should we conserve forests and wildlife?
We should conserve forest and wildlife because of the following reasons:
$$1$$ Forest provides us with oxygen.
$$2$$ Forest causes rain.
$$3$$ Forest prevents soil erosion.
$$4$$ Destruction of forest would lead to destruction of wildlife.
$$5$$ Wildlife are also the members of food web and any gaps in the food web would lead to the destruction of every surface or organism on earth. | 2022-07-04 03:21:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22190003097057343, "perplexity": 7693.874571822896}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104293758.72/warc/CC-MAIN-20220704015700-20220704045700-00353.warc.gz"} |
https://www.transtutors.com/questions/question-30-4-points-capital-profit-loss-partners-balances-sharing-scotty-i-400-000--2567355.htm | # Question 30 (4 points) Capital Profit Loss Partners Balances Sharing Scotty I$400,000 25% Riley ... Question 30 (4 points) Capital Profit Loss Partners Balances Sharing Scotty I$ 400,000 25% Riley I$700,000 45% Dee Dee 900,000 30% Marnee is going to buy into the SRD Partnership by paying$1,000,000 to the partners in exchange for a 30% ownership in the partnership. The partnership uses the Book Value Method when admitting new partners. Answer the following questions using the information in the table above. 1. What is Marnee's balance after joining the partnership? 2. What is Scotty's's balance after Marnee joins the partnership? abo
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• Most Viewed | 2019-01-22 06:39:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26291999220848083, "perplexity": 11550.213066320815}, "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-2019-04/segments/1547583829665.84/warc/CC-MAIN-20190122054634-20190122080634-00111.warc.gz"} |
https://www.maths.cam.ac.uk/research/talk/134725 | # Mathematical Research at the University of Cambridge
In mirror symmetry, points in a variety correspond to Lagrangian tori in the mirror symplectic manifold. In the absence of "quantum corrections" the Ext-algebra of a point is equated with the cohomology algebra of the corresponding torus - both are simply exterior algebras - but in general one has to consider deformations of this picture. In this talk I'll introduce the localised mirror functor of Cho, Hong and Lau, which translates deformations of this sort into the algebro-geometric language of matrix factorisations, and show how this leads to an easy proof that local mirror symmetry near a (monotone) Lagrangian torus is essentially tautological.
29Jan
Jan 29th 2020
14:15 to 15:15
CMS MR13
## Speaker:
Jack Smith, University of Cambridge
## Series:
Algebraic Geometry Seminar | 2020-01-20 14:48:32 | {"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": 0.8686271905899048, "perplexity": 1149.48604653536}, "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/1579250598800.30/warc/CC-MAIN-20200120135447-20200120164447-00157.warc.gz"} |
https://www.cableizer.com/documentation/K_E/ | Surface conductance between the ground surface and the external ambient.
Symbol
$K_{\mathrm{E}}$
Unit
W/m²
Formulae
$9.0$
Used in
$R_{\mathrm{q12}}$
$R_{\mathrm{q22}}$
$R_{\mathrm{q32}}$ | 2019-01-20 22:23:05 | {"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": 0.949983537197113, "perplexity": 6182.07440002795}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583739170.35/warc/CC-MAIN-20190120204649-20190120230649-00187.warc.gz"} |
http://gradestack.com/Circuit-Theory-and/Fourier-Series-and/Solved-Problems-16/19351-3926-40726-revise-wtw | # Solved Problems-16
Problems-16
Find the Fourier transform of the existing voltage,
v(t) = V0e–tt ≥ 0
= 0, t ≤ 0
and sketch approximately its amplitude and phase spectrum.
Solution
The amplitude and phase are
Spectra | 2016-10-28 06:37:17 | {"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": 0.9805207848548889, "perplexity": 1858.8686339868168}, "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/1476988721558.87/warc/CC-MAIN-20161020183841-00531-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://anthonymorris.dev/second-brain/moon | # Moon
• A moon is a large object revolving around a planet
• Roughly $\frac{1}{3}$ of the moons in the outer solar system are in direct orbits
• Regular orbit
• Revolve west --> east
• Major of the moons are irregular
• Retrograde orbit (east --> west)
• Orbit has high eccentricity
• More elliptical than circular
• High inclination
• Moving in and out of the planet's equatorial plane
• Irregular moons are mostly located relatively far from their planet
• Probably formed elsewhere and were captured by the planet | 2022-06-28 10:22:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5250692367553711, "perplexity": 5178.325161174797}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00576.warc.gz"} |
http://www2.math.technion.ac.il/~techm/20110602160020110602bru.html | ===========================================================================
Technion
SPECIAL MATHEMATICS COLLOQUIUM
Please note the unusual day and unusual time.
(In fact we will have two special colloquia on this day.
See a separate announcement for details of Prof. Pesenson's
talk earlier, at 14:30.)
Speaker: Alexander Brudnyi, University of Calgary
Title: Stein-like theory for Banach-valued holomorphic functions on the maximal
ideal space of H^\infty and new developments in the Sz-Nagy operator corona problem.
Date: Thursday June 2 at 16:00.
Place: Technion. Amado 232 is now definitely reserved for this colloquium.
Apology: Because of some rather special circumstances we are not entirely sure at this
stage that Prof. Brudnyi will be available to give this talk.
Abstract: In this talk I describe a new approach to the study of the
Banach algebra H^\infty of bounded holomorphic functions on the unit disk
D with pointwise multiplication and supremum norm. It is based on a new
method for solving Banach-valued d-bar equations on D which allows one to
develop a Stein-like theory for Banach-valued holomorphic functions
defined on open subsets of the maximal ideal space of H^\infty.
Specifically, as in the classical theory of Stein spaces, I establish the
vanishing of the cohomology of sheaves of germs of such functions, solve
the second Cousin problem and prove Runge-type approximation theorems for
them. Then I apply the developed technique to the study of the algebra of
holomorphic functions on D with relatively compact images in a commutative
unital complex Banach algebra A. In particular, solving a Banach-valued
corona problem, I prove that the maximal ideal space of such algebra is
the direct product of maximal ideal spaces of H^\infty and A. This
generalizes the famous Carlseson Corona theorem and solves a major problem
posed in the mid of 60th. The same result would also follow if we knew
that H^\infty has the Grothendieck approximation property (which is still
an open problem). In the second part of my talk I apply the developed
technique to establish the following version of the Oka principle: if a
Banach holomorphic vector bundle on the maximal ideal space of H^\infty is
topologically trivial, then it is holomorphically trivial as well. This
leads to new positive results in the area of the Sz.-Nagy operator valued
corona problem (a noncommutative analog of the Carleson theorem) posed in
1978.
This talk does not require any preliminary specialized knowledge because
all basic definitions and results will be formulated there.
---------------------------------------------------------
Technion Math. Net (TECHMATH)
Editor: Michael Cwikel <[email protected]>
Announcement from: Michael Cwikel <[email protected]> | 2018-01-23 10:07:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8199228644371033, "perplexity": 2016.154733577237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891886.70/warc/CC-MAIN-20180123091931-20180123111931-00129.warc.gz"} |
https://socratic.org/questions/why-are-equilateral-triangles-equiangular | # Why are equilateral triangles equiangular?
Nov 24, 2015
Equal sides implies equal angles
#### Explanation:
Take an example ...
A 30-60-90 triangle will have its smallest side opposite the ${30}^{o}$. The largest side will be opposite the ${90}^{o}$. Finally, the side opposite the ${60}^{o}$ will fall somewhere in between.
As another example, the sides opposite the base angles of an isosceles triangle have sides that are equal because the base angles are equal .
Finally, if all the sides of the triangle are equal, then the angles opposite those sides must also be equal. This is a equilateral or equiangular triangle!
Nov 24, 2015
We can prove this using the law of cosines with the SSS case.
$a = b = c$
So...
${c}^{2} = {a}^{2} + {b}^{2} - 2 a b \cos \angle C$
becomes
${a}^{2} = {a}^{2} + {a}^{2} - 2 a \cdot a \cdot \cos \angle A$
$- {a}^{2} = - 2 {a}^{2} \cos \angle A$
$1 = 2 \cos \angle A$
$\frac{1}{2} = \cos \angle A$
$\textcolor{b l u e}{\angle A = {60}^{\circ}}$
Notice how on every triangle you draw, a side is opposite to an angle. That means only one side corresponds to one particular angle.
Since only one side $c$ corresponds to only one $\angle C$, and since sides $a = b = c$, we have $\angle A = \angle B = \angle C$. | 2021-12-06 14:57:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 14, "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": 0.8902894258499146, "perplexity": 412.0788612966528}, "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/1637964363301.3/warc/CC-MAIN-20211206133552-20211206163552-00441.warc.gz"} |
https://mathsmadeeasy.co.uk/ks3-revision/ks3-substitution/ | Substitution Algebra Revision | KS3 Maths Resources
## What you need to know
Things to remember:
• Substitution just means replacing a letter with a number.
• We don’t write $\times$ when there is a number before a letter, so you need to remember that it is hiding there!
• A fraction is another way of writing a division question.
So, what is substitution? Well, it just means to “replace” one thing with another. So, in maths, this usually means replacing a letter with a number.
Use substitution to find the value of $x+7$ when x = 12
Here we are told that $x=12$, so all we have to do is replace the $x$ in the expression with 12!
$$x+7=12+7=19$$
Easy peasy! We do the same with our other operations too!
Use substitution to find the value of $x-4$ when x = 15
$$x-4=15-4=11$$
Multiplication questions are a little different, because we need to remember that there is a hidden $\times$ symbol between the number and letter.
Use substitution to find the value of $5x$ when x = 13
$$5x=5\times x=5\times13=65$$
Divisions questions could either appear as a division:
Use substitution to find the value of $x\div3$ when x=9
$$x\div3=9\div3=3$$
Or as a fraction that we have to change:
Use substitution to find the value of $\frac{20}{x}$ when x=5
$$\frac{20}{x}=20\div x=20\div5=4$$
## KS3 Maths Revision Cards
(77 Reviews) £8.99
## Example Questions
$$12x=12\times x=12\times7=84$$
$$\dfrac{x}{9}=x\div9=54\div9=6$$
## KS3 Maths Revision Cards
(77 Reviews) £8.99
• All of the major KS2 Maths SATs topics covered
• Practice questions and answers on every topic | 2020-09-26 21:41:07 | {"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": 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": 18, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9168930649757385, "perplexity": 795.8186696175138}, "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-2020-40/segments/1600400245109.69/warc/CC-MAIN-20200926200523-20200926230523-00241.warc.gz"} |
https://www.biostars.org/p/372351/ | How to detect outliers from either (a) SNP-Fst or (b) Window-Fst distributions?
0
0
Entering edit mode
2.7 years ago
serpalma.v ▴ 70
Hello
I want to find the SNPs that could be responsible for the phenotype differences observed between three populations. For that I computed Fst (weir and cockerham) using vcftools.
One population reflects the founder population (line0) from which the two populations were selected (line1 and line2), each one for a different trait. The phenotypes for each line are highly divergent.
Computing per-SNP Fst produces the following representative .
Computing windowed (window = 500kb; slide = 250kb; min #SNPs=20) Fst produces the following representative .
First, line1 vs line2 yields a different Fst distribution compared to (line1 | line2) vs line0.
Second, window Fst calculation (mean) yields smoother distributions.
I would like to seek advise on the following:
(1) how to define outliers considering the two types of observed Fst distributions?
(2) Is windowed Fst more suitable to identify outliers?
(3) How to define the size and step of a sliding window? (what I choose for this example is based on a similar study, but I guess it might require optimization)
(4) Do I need to do some type of SNP pruning (these SNPs are derived from WGS variant discovery analysis following GATK best practices)?
Fst vcftools • 1.4k views
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Powered by the version 2.3.6 | 2021-12-03 07:02:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2197932004928589, "perplexity": 7902.211284533626}, "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-2021-49/segments/1637964362605.52/warc/CC-MAIN-20211203060849-20211203090849-00630.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/cpaa.2007.6.983 | Article Contents
Article Contents
# Regularity properties of a cubically convergent scheme for generalized equations
• We consider the perturbed generalized equation $v \in f(x) +G(x)$ where $v$ is a perturbation parameter, $f$ is a function acting from a Banach space $X$ to a Banach space $Y$ while $G: X \rightarrow Y$ is a set-valued mapping. We associate to this generalized equation the following iterative procedure:
$v \in f(x_n)+ \nabla f(x_n)(x_{n+1}-x_n) +\frac{1}{2}\nabla^2 f(x_n) (x_{n+1}-x_n)^2 +G(x_{n+1}).$ $\quad$ (*)
We investigate some stability properties of the method (*) and we study the behavior of the sequences that it generates, more precisely, we show that they inherit some regularity properties from the mapping $f+G$.
Mathematics Subject Classification: Primary: 49J53, 49J40, 90C48.
Citation:
• on this site
/ | 2023-02-08 03:07:06 | {"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.5446809530258179, "perplexity": 485.6635890447457}, "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-2023-06/segments/1674764500671.13/warc/CC-MAIN-20230208024856-20230208054856-00608.warc.gz"} |
http://www.ck12.org/physics/Electrostatics/lesson/Electrostatics-PPC/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Electrostatics
## Electrons are the fundamental unit of charge.
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Electrostatics
Opposite charges attract and like charges repulse. The electron (and proton) is the fundamental charge unit. The charge of an electron and proton is \begin{align*} 1.6 \times 10^{-19} \end{align*} C. One can determine the number of excess electrons (or protons if positive charge) by dividing the objects charge by the fundamental charge. Most objects are electrically neutral (equal numbers of electrons and protons) and that's why gravity dominates on a macro scale.
Key Equations
\begin{align*}q = Ne \text{ }\end{align*} Any object's charge is an integer multiple of an electron's charge.
#### Example
If an object has +0.003 C of charge, how many excess protons does the object have?
\begin{align*}q = Ne \text{ }\end{align*} \begin{align*} 0.003 \text{C} = N \times 1.6 \times 10^{-19} \end{align*} N = \begin{align*} 1.875 \times 10^{16} \end{align*} ; protons
### Review
1. After sliding your feet across the rug, you touch the sink faucet and get shocked. Explain what is happening.
2. What is the net charge of the universe? Of your toaster?
3. As you slide your feet along the carpet, you pick up a net charge of \begin{align*}+4 \;\mathrm{mC}\end{align*}. Which of the following is true?
1. You have an excess of \begin{align*}2.5 \times 10^{16}\end{align*} electrons
2. You have an excess of \begin{align*}2.5 \times 10^{19}\end{align*} electrons
3. You have an excess of \begin{align*}2.5 \times 10^{16}\end{align*} protons
4. You have an excess of \begin{align*}2.5 \times 10^{19}\end{align*} protons
4. You rub a glass rod with a piece of fur. If the rod now has a charge of \begin{align*}-0.6\ \mu C\end{align*}, how many electrons have been added to the rod?
1. \begin{align*}3.75 \times 10^{18}\end{align*}
2. \begin{align*}3.75 \times 10^{12}\end{align*}
3. \begin{align*}6000\end{align*}
4. \begin{align*}6.00 \times 10^{12}\end{align*}
5. Not enough information
1. The net electric charge you collected from the rug gets discharged when you come in contact with the sink faucet.
2. Neutral
3. c
4. b
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes | 2017-03-24 04:30:56 | {"extraction_info": {"found_math": true, "script_math_tex": 15, "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": 0.9995675683021545, "perplexity": 4765.868296942684}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218187690.11/warc/CC-MAIN-20170322212947-00014-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://lists.debian.org/debian-user/1996/11/msg00231.html | # Re: LaTeX cannot find Greek characters
[email protected] (Zebedee Mason) writes:
> LaTeX runs fine on all my documents apart from the fact that it cannot
> find the Greek alphabet resulting in some strange looking equations, I
> have included part of the log file and several days back tried the TeX
> newsgroup:
> (nomenclature.tex
> Missing character: There is no ^^O in font cmmi12!
> Missing character: There is no u in font cmmi12!
> Missing character: There is no u in font cmmi12!
> Missing character: There is no = in font cmmi12!
> Missing character: There is no ^^W in font cmmi12!
> Missing character: There is no ^^O in font cmmi12!
I'm not a LaTeX user, but I see two possibilities here:
1. Some font configuration file for LaTeX is corrupted. (.fd files)
2. cmmi12.tfm is corrupted.
#2 is easy to check, run the following through plain TeX and see if it
works:
% start of file
This is a test: $\alpha\beta\gamma\epsilon$
\end
% end of file
If this doesn't work, replace cmmi12.tfm (either reinstall the Debian
package or delete the file and make a new one with metafont.) If does
work replace LaTeX (whatever package the latex files come in).
Steve
[email protected]
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[email protected] . Trouble? e-mail to [email protected] | 2013-12-13 21:37:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.9762964248657227, "perplexity": 10919.864654349203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164997874/warc/CC-MAIN-20131204134957-00063-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://codereview.stackexchange.com/questions/80596/gathering-response-from-a-pagable-service | # Gathering response from a pagable service
I'm wondering how this code could be improved. I especially don't like the use of mutable Buffer but not sure what the best way to get it out cleanly.
def find(service: Service): Traversable[Long] = {
def loop(lastId: Option[Long])
(acc: mutable.Buffer[Long])
(quota: Int): Traversable[Long] = {
val response = service.call(lastId.getOrElse(-1))
if (response.size() > 0 && quota > 0) {
loop(response.last.getId)(acc ++ response)(quota - 1)
} else {
(acc ++ response).toList
}
}
loop(None)(mutable.Buffer())(3)
}
You might want to try Scala Streams.
val Quota = 3
def find(service: Service) = {
def chunks(lastIdOption: Option[Long]): Stream[Stream[Int]] = {
Stream.cons(response, chunks(response.last.id))
}
chunks(None).take(Quota).flatten
}
The chunks function returns an infinite stream of pages. The take(3) limits it to three pages. The flatten method joins the inner list in a large stream.
Stream is lazy, so it should fetch only the data that are needed. However, you should not expect some artificial intelligence in the Streams. For example this will always fetch the first page even if quota is zero. I hope this is not an issue in your case. If you are in doubt with the laziness, you can add some print in the chunks function to check (or falsify) your assumptions. | 2019-09-18 19:10:25 | {"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": 0.24390166997909546, "perplexity": 3671.397508229458}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573323.60/warc/CC-MAIN-20190918172932-20190918194932-00094.warc.gz"} |
https://homework.zookal.com/questions-and-answers/suppose-i-offered-you-the-following-bond-the-bond-pays-520978632 | Suppose I offered you the following Bond. The bond pays out $200 per year for ten years, then pays the principal payment$5000 at the end of the contract period. If I offered, you this bond for \$3,156.63. What is the rate of return on this bond? | 2021-03-05 23:50:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6433024406433105, "perplexity": 1109.8479963573093}, "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/1614178373761.80/warc/CC-MAIN-20210305214044-20210306004044-00540.warc.gz"} |
https://forum.dynare.org/t/coefficient-of-variation/163 | # Coefficient of Variation
Dear Professor:
I used Dynare to simulate my model and shows below:
THEORETICAL MOMENTS
VARIABLE MEAN STD. DEV. VARIANCE
C 0.0000 133.8372 17912.3833
Cd 0.0000 133.6476 17861.6923
My question:
the variable C’s STD.DEV.=133.8372,
Does the “STD.DEV” equal “Coefficient of Variation”?
Because I have real economy’s data, I deal the the data step by step.
step1. I count the “a”(assume endogeous variable) from 1961 to 2004 's standerd deviation.
step2. I count the “a”(assume endogeous variable)from 1961 to 2004 's average value.
step3. step1.'s standerd deviation was divided by average value.
step4. I get the “a”'s “Coefficient of Variation”.
Finally, I would like to compare this “Coefficient of Variation” with “C’s STD.DEV.=133.8372”
Can I compare these two ?
thanks
sincerely
You can’t compute the coefficient of variation of the variables in the model, because they have mean zero.
Usually, one compares variances or standard deviation, not coefficients of variation
Best
Michel | 2022-05-17 07:20:47 | {"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": 0.8259472250938416, "perplexity": 12875.232568842346}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662517018.29/warc/CC-MAIN-20220517063528-20220517093528-00304.warc.gz"} |
https://blender.stackexchange.com/questions/81694/how-to-connect-end-and-beginning-of-a-ring-with-a-cutout/81718 | # How to connect end and beginning of a “ring” with a cutout?
I am an absolute beginner in blender and failing at a very simple thing. I have a line lying in a plane. I want this line to have an extension in that plane, i.e. I want to make it a two-dimensional object. I do so by increasing the extrude parameter in the section geometry of the menu to 0.1. What I then get is the following:
I now want to connect the end and the beginning of that object, i.e. to close the cutout of it. From other questions I know that I can achieve this by marking the field U in the section Active spline of the menu. The problem is that the shape of the whole object changes in a very undesired way...
How can I perform the aformentioned connection in a way that preserves the shape shown in the first picture, i.e. in a way in which the extension of the the object stays in the plane defined by the original line etc.?
I attached a blend-file of this minimal-example:
• Apply rotation and scale to your curve object – Mr Zak Jun 19 '17 at 13:30
• @MrZak Although I figured it out how to do it pressing F (thanks to your comment below @Lukasz-40sth post), could you explain for a beginner how to do this? More precisely what exact do you mean by "apply roation and scale"? – DonkeyKong Jun 19 '17 at 14:12
• See manual article on that. Tl;dr is: press Ctrl+A in Object mode and choose Scale and then Rotation. After that no more edits will be needed for curve, just pressing Alt+C will be enough to close it, – Mr Zak Jun 19 '17 at 15:01
Select all vertices at the "start"-edge and all vertices at the "end"-edge, after pressing ALT + C and selecting Mesh from Curve/Meta/Surf/Text. Then press F. | 2021-01-26 22:00:23 | {"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": 0.44750097393989563, "perplexity": 697.6148594547259}, "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/1610704803737.78/warc/CC-MAIN-20210126202017-20210126232017-00628.warc.gz"} |
http://etna.mcs.kent.edu/volumes/2011-2020/vol41/abstract.php?vol=41&pages=93-108 | ## The block preconditioned steepest descent iteration for elliptic operator eigenvalue problems
Klaus Neymeyr and Ming Zhou
### Abstract
The block preconditioned steepest descent iteration is an iterative eigensolver for subspace eigenvalue and eigenvector computations. An important area of application of the method is the approximate solution of mesh eigenproblems for self-adjoint elliptic partial differential operators. The subspace iteration allows to compute some of the smallest eigenvalues together with the associated invariant subspaces simultaneously. The building blocks of the iteration are the computation of the preconditioned residual subspace for the current iteration subspace and the application of the Rayleigh-Ritz method in order to extract an improved subspace iterate. The convergence analysis of this iteration provides new sharp estimates for the Ritz values. It is based on the analysis of the vectorial preconditioned steepest descent iteration which appeared in [SIAM J. Numer. Anal., 50 (2012), pp. 3188–3207]. Numerical experiments using a finite element discretization of the Laplacian with up to $5\cdot 10^7$ degrees of freedom and with multigrid preconditioning demonstrate the near-optimal complexity of the method.
Full Text (PDF) [800 KB]
### Key words
subspace iteration, steepest descent/ascent, Rayleigh-Ritz procedure, elliptic eigenvalue problem, multigrid, preconditioning
### AMS subject classifications
65N12, 65N22, 65N25, 65N30
### Links to the cited ETNA articles
[9] Vol. 7 (1998), pp. 104-123 Andrew V. Knyazev: Preconditioned eigensolvers - an oxymoron?
### ETNA articles which cite this article
Vol. 46 (2017), pp. 424-446 Ming Zhou and Klaus Neymeyr: Sharp Ritz value estimates for restarted Krylov subspace iterations
< Back | 2019-02-16 03:39:46 | {"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": 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": 0.616066038608551, "perplexity": 1350.0374357826508}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479838.37/warc/CC-MAIN-20190216024809-20190216050809-00447.warc.gz"} |
https://www.albert.io/ie/gmat/sum-of-positive-integers | Free Version
Moderate
# Sum of Positive Integers
GMAT-VULZAW
What is the sum of all two-digit, positive, integers that do not contain a $5$?
A
$3920$
B
$4465$
C
$4905$
D
$4360$
E
$545$ | 2017-01-21 15:43:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.4384133219718933, "perplexity": 2781.0531538646323}, "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-2017-04/segments/1484560281151.11/warc/CC-MAIN-20170116095121-00272-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3094899/if-k-1-k-2-are-disjoint-nonempty-compact-sets-show-that-there-exist-k-i | # If $K_1$ & $K_2$ are disjoint nonempty compact sets ,show that there exist $k_i$ $\in$ $K_i$
If $$K_1$$ & $$K_2$$ are disjoint nonempty compact sets ,show that there exist $$k_i$$ $$\in$$ $$K_i$$ such that
$$|k_1 - k_2|$$=inf{$$|x_1 - x_2|$$: $$x_i$$ $$\in$$ $$K_i$$}.
They are all subsets of $$\mathbb R$$
I am able to proof that the set is bounded but I am trying to proof that the set is closed using sequence but I can't. Give me some hint.
• Hint: Use the Extreme Value Theorem – YuiTo Cheng Jan 31 at 13:52
Hint: $$d:\mathbb R\times \mathbb R\to \mathbb R:(x,y)\mapsto |x-y|$$ is continuous, and $$K_1\times K_2$$ is compact.
Here is a proof using sequences: in fact, we can prove a stronger result: assume $$K$$ is compact and $$C$$ is closed.
The $$\inf$$ exists because $$S=\{|x-y|:x\in K;\ y\in C\}$$ is bounded below. Therefore, there is a sequence $$(x_k,y_k)\in K\times C$$ such that $$|x_k-y_k|\to \inf S=s$$. Without loss of generality, $$|x_k-y_k|. Since $$K$$ is compact, we get a subsequence $$x_{k_i}\to p\in K.$$ On the other hand, $$K$$ is bounded so it lies in some ball of radius $$R$$, so $$|y_k|\le |y_k-x_k|+|x_k|\le s+1+R$$. Then, $$y_{k_i}$$ is bounded, so it also has a convergent subsequence, $$y_{k_{i_j}}\to q\in C\$$ (because $$C$$ is closed.) But then $$s=\lim |x_{k_{i_j}}-y_{k_{i_j}}|=|p-q|.$$ | 2019-08-19 22:43:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 29, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9766344428062439, "perplexity": 237.5049659343566}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315132.71/warc/CC-MAIN-20190819221806-20190820003806-00456.warc.gz"} |
https://orbit.dtu.dk/en/publications/plasticity-size-effects-in-voided-crystals-2 | # Plasticity size effects in voided crystals
M. I. Hussein, Ulrik Borg, Christian Frithiof Niordson, V. S. Deshpande
Research output: Book/ReportReportpeer-review
## Abstract
The shear and equi-biaxial straining responses of periodic voided single crystals are analysed using discrete dislocation plasticity and a continuum strain gradient crystal plasticity theory. In the discrete dislocation formulation the dislocations are all of edge character and are modelled as line singularities in an elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Over the range of length scales investigated, both the discrete dislocation and strain gradient plasticity formulations predict a negligible size effect under shear loading. By contrast, under equi-biaxial loading both plasticity formulations predict a strong size dependence with the flow strength scaling approximately inversely with the void-spacing. Excellent agreement is obtained between predictions of the two formulations for all crystal types and void volume fractions considered when the material length scale in the non-local plasticity model chosen to be $0.325\mu m$ (around ten times the slip plane spacing in the discrete dislocation models).
Original language English
Publisher Technical University of Denmark Published - 2006
## Fingerprint
Dive into the research topics of 'Plasticity size effects in voided crystals'. Together they form a unique fingerprint. | 2022-05-21 01:55:17 | {"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": 0.27082762122154236, "perplexity": 5689.207382074111}, "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/1652662534773.36/warc/CC-MAIN-20220521014358-20220521044358-00697.warc.gz"} |
https://www.mathalino.com/forum/algebra/mathematics | # Mathematics
2 posts / 0 new
shthd
Mathematics
A diet must provide exactly 580 mg of protein and 290 mg or iron. These nutrients will be obtained by eating meat and spinach. Each kg of meat contains 900 mg of protein and 200 mg of iron. Each kg of spinach contains 400 mg of protein and 1700 mg of iron. How many kgs of meat and spinach should be eaten in order to provide the proper amounts of nutrients?
Jhun Vert
Let m = amount of meat in kg and s = amount of spinach in kg
For protein
$900x + 400y = 580$ ← equation (1)
For iron
$200x + 1700y = 290$ ← equation (2)
From equations (1) and (2)
$x = 0.6 ~ \text{kg}$
$y = 0.1 ~ \text{kg}$
• Mathematics inside the configured delimiters is rendered by MathJax. The default math delimiters are $$...$$ and $...$ for displayed mathematics, and $...$ and $...$ for in-line mathematics. | 2023-02-03 00:52:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "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": 0.22679932415485382, "perplexity": 6100.76855464136}, "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/1674764500041.2/warc/CC-MAIN-20230202232251-20230203022251-00197.warc.gz"} |
https://www.transtutors.com/questions/3-17-an-insurance-company-s-losses-of-a-particular-type-per-year-are-to-a-reasonable-1328539.htm | # 3.17 An insurance company’s losses of a particular type per year are to a reasonable...
3.17 An insurance company’s losses of a particular type per year are to a reasonable approximation normally distributed with a mean of $150 million and a standard deviation of$50 million. (Assume that the risks taken on by the insurance company are entirely nonsystematic.) The one-year risk-free rate is 5% per annum with annual compounding. Estimate the cost of the following:
a. A contract that will pay in one-year’s time 60% of the insurance company’s costs on a pro rata basis
b. A contract that pays $100 million in one-year’s time if losses exceed$200 million. | 2018-07-19 23:24:50 | {"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": 0.24474579095840454, "perplexity": 1306.0876292627759}, "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/1531676591332.73/warc/CC-MAIN-20180719222958-20180720002958-00333.warc.gz"} |
http://www.gradesaver.com/textbooks/math/precalculus/precalculus-mathematics-for-calculus-7th-edition/chapter-1-review-exercises-page-134/69 | Chapter 1 - Review - Exercises: 69
$x=11$ and $x=3$
Work Step by Step
$|x-7|=4$ By the definition of absolute value, solving this equation is equivalent to solving two separate equations, which are: $x-7=4$ and $x-7=-4$ Solve both equations for $x$: $x-7=4$ $x=4+7$ $x=11$ $x-7=-4$ $x=-4+7$ $x=3$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2017-12-15 06:36:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.737525224685669, "perplexity": 426.6370924436465}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948567042.50/warc/CC-MAIN-20171215060102-20171215080102-00269.warc.gz"} |
http://openstudy.com/updates/4f28a0cce4b049df4e9d6748 | ## anonymous 4 years ago Number 8 please
1. anonymous
2. saifoo.khan
Perimeter = outer boundary.
3. anonymous
yes that know but how would it be including the circular part?
4. saifoo.khan
Circumfrence of semi circle = $$\Huge \pi*r$$
5. saifoo.khan
So, 3.142 * 2
6. anonymous
so that plus the perimeter of the square should give me the answer right?
7. saifoo.khan
Right.
8. anonymous
OK thank you | 2016-10-24 12:22:13 | {"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": 0.23751546442508698, "perplexity": 7455.575082557517}, "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-2016-44/segments/1476988719566.74/warc/CC-MAIN-20161020183839-00323-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://socratic.org/questions/clock-takes-8mins-for-1round-so-in-18mins-how-many-round-it-takes | # clock takes 8mins for 1round so in 18mins how many round it takes???
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
1
Feb 8, 2018
color(purple)(2(1/4) rounds or $\textcolor{p u r p \le}{2.25} r o u n \mathrm{ds}$
#### Explanation:
In 8 minutes -> 1 round
In 18 minutes -> (18/8) * 1 rounds
$\implies \frac{18}{8} = \frac{3 \cdot 3 \cdot \cancel{2}}{2 \cdot 2 \cdot \cancel{2}} = \frac{9}{4} = 2 \left(\frac{1}{4}\right) r o u n \mathrm{ds}$
$\implies 2 \left(\frac{1 \cdot {\cancel{100}}^{25}}{\cancel{4} \cdot 100}\right) = 2 \left(\frac{25}{100}\right) = 2.25 r o u n \mathrm{ds}$
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
1
Kashish Share
Feb 8, 2018
2.25 rounds
#### Explanation:
This question can be easily solved by applying unitary method.
No. of rounds made by the clock in 8 minutes = $1$
No. of rounds made by the clock in 1 minute = $\frac{1}{8}$
No. of rounds made by the clock in 18 minutes = $\frac{1}{8}$ x $18$ = 2.25
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• 31 minutes ago | 2018-02-17 23:18:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.519882321357727, "perplexity": 10160.137696065729}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891808539.63/warc/CC-MAIN-20180217224905-20180218004905-00145.warc.gz"} |
https://stats.stackexchange.com/questions/176124/what-is-the-proper-test-to-use-for-this-study/176130 | # What is the proper test to use for this study?
It's been too long since I have taken a stats course, and I'm struggling to figure out what the proper test is for this experiment I'm designing.
• There are two conditions: A and B
• There is one continuous dependent variable that is measured as the outcome of each trial (each trial is of condition A or condition B)
• There are approx. 30 subjects
• Each subject will do 5 trials with condition A, and 5 trials with condition B
• The order in which the subject does the trials is randomized
• I'm trying to show that the value of the dependent variable is significantly higher with condition A than it is with condition B
The main issue for me is trying to figure out how to handle each subject doing each condition multiple times. Would this be some sort of one-way ANOVA with blocking by subject? Or maybe repeated measures within subjects? Any tips would be great!
Secondary question: for whatever the correct answer to the above is, what would be the closest equivalent non-parametric test?
• Could you please add some information about the number of participants. Is many 20, 50, 100, or even more? This will impact the methods available to you. – Marcus Morrisey Oct 8 '15 at 21:41
• @MarcusMorrisey Sorry about that, OP is updated (roughly 30 subjects) – Jordan Oct 8 '15 at 21:51
lmer(dependentVariable ~ FactorAB + (1|participant), data=yourData) | 2020-04-08 22:16:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5629310607910156, "perplexity": 674.6159672024044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371824409.86/warc/CC-MAIN-20200408202012-20200408232512-00101.warc.gz"} |
http://mathoverflow.net/revisions/18062/list | I think the decisive point is continuity with respect to different topologies. Let $C$ be the space of continuous functions of compact support and $D$ the space of smooth functions of compact support. The inclusion $D\hookrightarrow C$ is a continuous map when you give both spaces the corresponding inductive limit topology. That means, that every continuous linear functional of $C$, i.e., each Radon-measure, defines a continuous linear functional on $D$, i.e., a distribution. But not every distribution extends to a continuous linear map on $C$. Examples are the derivatives of the Dirac distribution. The line in Wikipedia relates to an important property of linear functionals on $C$: if such a functional is positive, i.e., if it maps functions $f\ge 0$ to numbers $\ge 0$, then it is AUTOMATICALLY CONTINUOUS! . This is an a very important and highly non-trivial fact, though it is not hard to prove.
I think the decisive point is continuity with respect to different topologies. Let $C$ be the space of continuous functions of compact support and $D$ the space of smooth functions of compact support. The inclusion $D\hookrightarrow C$ is a continuous map when you give both spaces the corresponding inductive limit topology. That means, that every continuous linear functional of $C$, i.e., each Radon-measure, defines a continuous linear functional on $D$, i.e., a distribution. But not every distribution extends to a continuous linear map on $C$. Examples are the derivatives of the Dirac distribution. The line in Wikipedia relates to an important property of linear functionals on $C$: if such a functional is positive, i.e., if it maps functions $f\ge 0$ to numbers $\ge 0$, then it is AUTOMATICALLY CONTINUOUS! This is an important and highly non-trivial fact. | 2013-05-23 17:17:06 | {"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": 0.9772512912750244, "perplexity": 93.58042565890253}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703635016/warc/CC-MAIN-20130516112715-00064-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.transtutors.com/questions/presented-below-is-a-list-of-possible-transactions-amp--2565389.htm | # Presented below is a list of possible transactions. · &...
Presented below is a list of possible transactions.
· 1. Purchased inventory for $80,000 on account (assume perpetual system is used). · 2. Issued an$80,000 note payable in payment on account (see item 1 above).
· 3. Recorded accrued interest on the note from item 2 above at 10%. Assume the note is a one-year note and 3 months have passed.
· 4. Signed a $100,000 note from the bank by signing a 6-month, zero-interest-bearing note. Prevailing annual interest rate is 10%. · 5. Recognized 4 months' interest expense on the note from item 4 above. · 6. Recorded sales revenue of$75,260 on account, which includes 5% sales tax.
· 7. Incurred a contingency loss of $45,000 on a lawsuit. The company’s lawyer believes there is a reasonable possibility that the company could lose. · 8. Accrued warranty expense of 15,000 on sales. · 9. Paid warranty costs that were accrued in item 8 above. · 10. Purchased goods for$85,000 subject to a cash discount, terms of 2/10, n/30. Purchases and accounts payable are recorded at net amounts after cash discounts (assume perpetual system is used).
· 11. Paid the invoice from 10. above, thirty days later.
Required: Record the journal entries (if needed) for the above transactions | 2018-12-14 01:59:41 | {"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": 0.28633615374565125, "perplexity": 10407.27393768781}, "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/1544376825123.5/warc/CC-MAIN-20181214001053-20181214022553-00580.warc.gz"} |
https://www.physicsforums.com/threads/proving-a-function-is-a-bijection-and-isomorphic.864180/ | # Homework Help: Proving a function is a bijection and isomorphic
1. Mar 28, 2016
### RJLiberator
1. The problem statement, all variables and given/known data
If G is a group and a ∈ G, let π: G--> G be the function defined as π(g) = ag, for all g ∈G.
a) Show that π is a bijection
b) Show that if π is an isomorphism, then a is the identity element of G.
2. Relevant equations
I think to show that pi is a bijection we have to show that it is surjective and injective.
To show that it is an isomorphism we have to show that π(xy) = π(x)π(y).
3. The attempt at a solution
First, I do part a and show that it is one to one:
Suppose π(g) = π(g')
then ag = ag'
Since a ∈G we know a^(-1) exists in G.
a^(-1)ag = a^(-1)ag'
g = g'
and so π is one to one.
I am not sure how to prove that this is onto... any hints here would help.
For onto can I just say
Let x,y ∈ G and x = a^(-1)y
since a is a part of the group we know that a^(-1) exists.
And thus it follows that π(x) = y
To show part b)
if x,y ∈G, then we observe
π(xy) = axy
π(x)π(y) = axay
Here, a must equal the identity element of G for this function to be an isomorphism.
2. Mar 28, 2016
### Samy_A
Mainly correct.
Only the last point needs some explanation.
You have that, for π to be an isomorphism, axy = axay, for all x,y ∈ G.
Why does that imply that a is the identity element of G?
3. Mar 28, 2016
### RJLiberator
Hm, well, it implies that a is the identity element of G as it would mean that a=aa
the only thing that works here is the identity element.
4. Mar 28, 2016
### RJLiberator
Maybe you want it more explicit?
axy = axay
y^(-1) exists as y is a part of G so multiple both sides by it
axy*y^(-1) = axay*y^(-1)
ax = axa
a^(-1) exists as a is a part of G
a^(-1)ax = a^(-1)axa
x = xa
so now a has to be the identity element
5. Mar 28, 2016
Voila! | 2018-07-19 22:15:10 | {"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": 0.858245313167572, "perplexity": 1341.4440366688846}, "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/1531676591296.46/warc/CC-MAIN-20180719203515-20180719223515-00355.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/draw-equilateral-abc-side-62-cm-construct-its-circumcircle-construction-triangle-if-base-angle-opposite-it-either-median-altitude-given_1118 | # Draw an Equilateral ΔABC with Side 6.2 cm and Construct Its Circumcircle - Geometry
Draw an equilateral ΔABC with side 6.2 cm and construct its circumcircle
#### Solution
Steps of construction:
1. Construct the equilateral ΔXYZ of side equal to 6.2 cm.
2. Draw the perpendicular bisectors PR and QS of sides bar(XY) and bar(YZ) respectively.
3. Mark the point of intersection as O.
4. Draw a circle with centre O and radius OX or OY or OZ.
This is the required circumcircle.
Concept: Construction of Triangle If the Base, Angle Opposite to It and Either Median Altitude is Given
Is there an error in this question or solution? | 2021-10-27 10:40:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6978539228439331, "perplexity": 1768.642576970843}, "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/1634323588113.25/warc/CC-MAIN-20211027084718-20211027114718-00516.warc.gz"} |
https://www.studyadda.com/sample-papers/neet-sample-test-paper-50_q10/431/331638 | • # question_answer 10) A triangular prism of glass is shown in figure, A ray incident normal to one face is totally reflected. If $\theta$ is $45{}^\circ$, then index of refraction of the glass is- A) less than 1.41 B) equal to 1.41 C) greater than 1.41D) None of these
$45{}^\circ >{{\theta }_{c}}$ | 2019-07-21 00:41:23 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5991686582565308, "perplexity": 1742.203725081696}, "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/1563195526799.4/warc/CC-MAIN-20190720235054-20190721021054-00233.warc.gz"} |
https://askdev.io/questions/54035/why-exists-a-substantial-distribution-hold-up-when-sending | # Why exists a substantial distribution hold-up when sending out from my Gmail account to an Earthlink account?
Recently I've been having a significant trouble with distribution hold-ups when sending out Gmail to an individual that has an Earthlink account. Sending out the email is great yet the mail does not get here in the recipient is mail box for several hrs, and also occasionally days. Sometimes, I receive an email back from the mail daemon that claims:
Mail Delivery Subsystem to me show information 2:17 PM (5 mins ago) This is an instantly created Delivery Status Notification
THIS IS A WARNING MESSAGE ONLY.
YOU DO NOT NEED TO RESEND YOUR MESSAGE.
Distribution to the adhering to recipient has actually been postponed:
[email protected]
Message will certainly be retried for 2 even more day (s)
Technical information of short-lived failing: The recipient web server did decline our demands to connect. Discover more at http://mail.google.com/support/bin/answer.py?answer=7720 [mx00 - dom.earthlink.net. (10): Connection break ] [mx01 - dom.earthlink.net. (10): Connection break ]
I'm not exactly sure why this is taking place, specifically given that I've been emailing he or she for several years with no hold-ups-- today it takes place virtually every single time I email her.
0
2019-05-18 22:27:08
Source Share | 2021-12-09 10:17:16 | {"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": 0.19238948822021484, "perplexity": 6501.517720225559}, "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/1637964363791.16/warc/CC-MAIN-20211209091917-20211209121917-00482.warc.gz"} |
https://mathhelpforum.com/threads/identity-in-number-theory.284686/ | # Identity in number theory
Is the following statement correct?
If gcd$$\displaystyle (a, m)=m$$, then $$\displaystyle a^m\equiv 0$$ (mod $$\displaystyle m$$)
$$\displaystyle a^m = km$$, which implies
$$\displaystyle k = a^{m-1} * \frac{a}{m}$$ | 2020-02-17 10:44:50 | {"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": 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": 0.9954642057418823, "perplexity": 2990.8658774471387}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141806.26/warc/CC-MAIN-20200217085334-20200217115334-00529.warc.gz"} |
https://www.statsmodels.org/stable/generated/statsmodels.genmod.families.links.CDFLink.deriv2.html | # statsmodels.genmod.families.links.CDFLink.deriv2¶
CDFLink.deriv2(p)[source]
Second derivative of the link function g’’(p)
implemented through numerical differentiation | 2020-04-04 17:32:26 | {"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": 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": 0.6690959930419922, "perplexity": 11584.53198203224}, "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-2020-16/segments/1585370524604.46/warc/CC-MAIN-20200404165658-20200404195658-00095.warc.gz"} |
http://math.iisc.ac.in/seminars/2020/2020-11-04-vishvesh-kumar.html | #### APRG Seminar
##### Venue: Microsoft Teams (online)
In his seminal paper (Acta Math. 1960), H"ormander established the $L^p$-$L^q$ boundedness of Fourier multipliers on $\mathbb{R}^n$ for the range $1<p \leq 2 \leq q<\infty.$ Recently, Ruzhansky and Akylzhanov (JFA, 2020) extended H"ormander’s theorem for general locally compact separable unimodular groups using group von Neumann algebra techniques and as a consequence, they obtained the $L^p$-$L^q$ boundedness of spectral multipliers for general positive unbounded invariant operators on locally compact separable unimodular groups.
In this talk, we will discuss the $L^p$-$L^q$ boundedness of global pseudo-differential operators and Fourier multipliers on smooth manifolds for the range $1<p\leq 2 \leq q<\infty$ using the nonharmonic Fourier analysis developed by Ruzhansky, Tokmagambetov, and Delgado. As an application, we obtain the boundedness of spectral multipliers, embedding theorems, and time asymptotic the heat kernels for the anharmonic oscillator.
This talk is based on my joint works with Duván Cardona (UGent), Marianna Chatzakou (Imperial College London), Michael Ruzhansky (UGent), and Niyaz Tokmagambetov (UGent).
Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ; E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 01 Dec 2020 | 2020-12-02 03:02:15 | {"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": 0.7337964177131653, "perplexity": 3713.5469695173565}, "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/1606141686635.62/warc/CC-MAIN-20201202021743-20201202051743-00662.warc.gz"} |
https://flaviocopes.com/fix-parse-failure-unterminated-string-constant/ | I ran into this error with a student of mine, running Astro on Windows (could not replicate on macOS), after running npm run dev.
After much 🤔 we solved by renaming the parent folder, which apparently had a strange character, perhaps non-ASCII.
If you run into this problem, try renaming the folder you are running (or perhaps a parent folder in the path) to just ASCII text, like “test” | 2022-10-04 04:29:46 | {"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": 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": 0.5415846705436707, "perplexity": 3744.759459555315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337473.26/warc/CC-MAIN-20221004023206-20221004053206-00688.warc.gz"} |
https://www.ideals.illinois.edu/handle/2142/111489 | ## Files in this item
FilesDescriptionFormat
application/pdf
5682.pdf (21kB)
(no description provided)PDF
## Description
Title: An ab Initio Study Of Electronically Excited States Of Sin And So Author(s): Kim, Gap-Sue Contributor(s): Yurchenko, Sergei N.; Semenov, Mikhail; Somogyi, Wilfrid; Clark, Nicholas; Brady, Ryan Subject(s): Linelists Abstract: CASSCF + MRCI calculations for the diatomic molecules, SiN and SO, have been performed using the C$_{2v}$ point group symmetry. For SiN, five lowest bound electronic have been were considered, $X$~$^2\Sigma^+$, $A$~$^2\Pi$, $B$~$^2\Sigma^+$, $a$~$^4\Pi$, $b$~$^4\Sigma^+$, while for SO, 9 electronic states were selected, $X$~$^3\Sigma^-$, $A$~$^3\Pi$, $A'$~$^3\Delta$, $A''$~$^3\Sigma^+$, $B$~$^3\Sigma^-$, $C$~$^3\Pi$, $a$~$^1\Delta$, $b$~$^1\Sigma^+$ and $c$~$^1\Sigma^-$, due to their importance for the spectroscopic applications in the IR, Visible and UV regions. For all the excited states potential energy, electronic angular momenta, spin orbit and (transition) dipole moment curves were generated. We use these \textit{ab initio} curves to predict rovibronic spectra of SO and SiN as well as their lifetimes. We aim to construct accurate molecular line lists for these molecules, which will require an empirical refinement of the \textit{ab initio} curves in order to improve the quality of the predictions of experimental spectra. Issue Date: 2021-06-22 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/111489 Date Available in IDEALS: 2021-09-24
| 2021-10-25 15:08:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6461456418037415, "perplexity": 5054.285003858029}, "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/1634323587711.69/warc/CC-MAIN-20211025123123-20211025153123-00018.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/what-is-the-surface-area-produced-by-rotating-f-x-x-2lnx-x-in-0-3-around-the-x-a-1 | # What is the surface area produced by rotating f(x)=x^2lnx, x in [0,3] around the x-axis?
Oct 20, 2016
$\approx 311.4$
#### Explanation:
If we consider a small strip width $\mathrm{dx}$, it will have radius $y \left(x\right)$ as it is revolved about the x axis, and thus circuference $2 \pi y$.
The arc length $\mathrm{ds}$ of the tip of strip $\mathrm{dx}$ is:
$\mathrm{ds} = \sqrt{1 + {\left(y '\right)}^{2}} \mathrm{dx}$
With $y ' = x \left(1 + 2 \ln x\right)$#
and so the surface area of the element is
$\mathrm{dS} = 2 \pi y \mathrm{ds}$
$= 2 \pi {x}^{2} \ln x \sqrt{1 + {\left(x \left(1 + 2 \ln x\right)\right)}^{2}} \mathrm{dx}$
For $x \in \left[1 , 3\right]$, the surface area $S$ is therefore:
$S = 2 \pi {\int}_{1}^{3} \setminus {x}^{2} \ln x \sqrt{1 + {\left(x \left(1 + 2 \ln x\right)\right)}^{2}} \mathrm{dx}$
However because $y < 0$ for $x \in \left[1 , 3\right]$, which would generate a negative radius, we need to be sure to place a negative number on the integration.
The surface area in total is therefore
$S = 2 \pi \left({\int}_{1}^{3} \setminus {x}^{2} \ln x \sqrt{1 + {\left(x \left(1 + 2 \ln x\right)\right)}^{2}} \mathrm{dx} - {\int}_{0}^{1} \setminus {x}^{2} \ln x \sqrt{1 + {\left(x \left(1 + 2 \ln x\right)\right)}^{2}} \mathrm{dx}\right)$ | 2021-11-27 15:19:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 16, "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": 0.9794442057609558, "perplexity": 489.27506762585125}, "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-2021-49/segments/1637964358189.36/warc/CC-MAIN-20211127133237-20211127163237-00054.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/chapter-3-section-3-1-functions-3-1-assess-your-understanding-page-211/20 | ## College Algebra (10th Edition)
domain: $\left\{\text{Bob, John, Chuck}\right\}$ range: $\left\{\text{Beth, Dianne, Linda, Marcia}\right\}$
The domain is the set of the first coordinates while the range is the set of second coordinates. Thus, the given relation has: domain: $\left\{\text{Bob, John, Chuck}\right\}$ range: $\left\{\text{Beth, Dianne, Linda, Marcia}\right\}$ | 2018-09-25 03:09:02 | {"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": 0.8889200091362, "perplexity": 792.3090023635357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267160923.61/warc/CC-MAIN-20180925024239-20180925044639-00516.warc.gz"} |
https://answers.ros.org/answers/220304/revisions/ | # Revision history [back]
There is a solution. Create a class that has a MoveGroup attribute, initialized with the constructor. Moreover you can implement several service functions in that class which are acting on the same move_group attribute.
This is my post and answer related how to do it.
Here is my working example for a cyton gamma 1500 robot arm.
There is a solution. Create a class that has a MoveGroup attribute, initialized with the constructor. Moreover you can implement several service functions in that class which are acting on the same move_group attribute.
This is my post and answer related how to do it.
Here is my working example for a cyton gamma 1500 robot arm.
EDIT
If you really want to share objects through applications have a look at this (not really related to ROS but c++). | 2020-01-22 21:14:13 | {"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": 0.19375889003276825, "perplexity": 1864.5178082447744}, "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/1579250607407.48/warc/CC-MAIN-20200122191620-20200122220620-00521.warc.gz"} |
http://www.ipam.ucla.edu/abstract/?tid=15168&pcode=QLAWS1 | Approximating freeness under constraints
Sorin PopaUniversity of California, Los Angeles (UCLA)Math
I will discuss a method for constructing unitary elements $u$ in a subalgebra $B$ of a II$_1$ factor $M$ that are as independent as possible’’
(approximately) with respect to a given finite set of elements in $M$. This technique had most surprising applications over the years, e.g., to Kadison-Singer type problems, to proving vanishing cohomology results for II$_1$ factors (like compact valued derivations, or L\$^2^-cohomology), as well as to subfactor theory (notably, to the discovery of the proper axiomatisation of the group-like objects arising from subfactors). After explaining this method, which I call {\it incremental patching}, I will comment on all these applications and its potential for future use.
Back to Workshop I: Expected Characteristic Polynomial Techniques and Applications | 2021-10-23 22:57:06 | {"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": 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": 0.8021883368492126, "perplexity": 1050.836713819768}, "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/1634323585828.15/warc/CC-MAIN-20211023224247-20211024014247-00679.warc.gz"} |
https://zbmath.org/?q=an:0865.68090 | # zbMATH — the first resource for mathematics
Landmarks in graphs. (English) Zbl 0865.68090
Summary: Navigation can be studied in a graph-structured framework in which the navigating agent (which we assume to be a point robot) moves from node to node of a “graph space”. The robot can locate itself by the presence of distinctively labeled “landmark” nodes in the graph space. For a robot navigating in Euclidean space, visual detection of a distinctive landmark provides information about the direction to the landmark, and allows the robot to determine its position by triangulation. On a graph, however, there is either the concept of direction nor that of visibility. Instead, we assume that a robot navigating on a graph can sense the distances to a set of landmarks.
Evidently, if the robot knows its distances to a sufficiently large set of landmarks, its position on the graph is uniquely determined. This suggests the following problem: given a graph, what are the fewest number of landmarks needed, and where should they be located, so that the distances to the landmarks uniquely determine the robot’s position on the graph? This is actually a classical problem about metric spaces. A minimum set of landmarks which uniquely determine the robot’s position is called a “metric basis”, and the minimum number of landmarks is called the “metric dimension” of the graph. We present some results about this problem. Our main new results are that the metric dimension of a graph with $$n$$ nodes can be approximated in polynomial time within a factor of $$O(\log n)$$, and some properties of graphs with metric dimension two.
##### MSC:
68R10 Graph theory (including graph drawing) in computer science | 2021-02-28 12:47:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.541144609451294, "perplexity": 374.54819863851145}, "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/1614178360853.31/warc/CC-MAIN-20210228115201-20210228145201-00185.warc.gz"} |
http://lumberjacksystem.com/ibc-signup.html | t
IBC 2018 Meet with the developers
During IBC 2018, Dr Gregory Clarke and Philip Hodgetts will be available to meet with anyone interested in Lumberjack but uncertain how it might apply to their specific workflow and production technology. (Remember Lumberjack System is for FCP X.)
Meeting times:
Friday September 14: 10:00, 11:00, 14:00, 15:00. 16:00 and 17:00
Saturday September 15: 10:00, 11:00, 14:00, 15:00. 16:00 and 17:00
Sunday September 16 10:00, 11:00, 14:00, 15:00. 16:00 and 17:00
Monday September 17: 10:00, 11:00, 14:00, 15:00. 16:00 and 17:00
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The server encountered an error. | 2018-11-15 01:39:26 | {"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": 0.9631307125091553, "perplexity": 9085.41020357141}, "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/1542039742338.13/warc/CC-MAIN-20181115013218-20181115035218-00092.warc.gz"} |
https://statistics.berkeley.edu/tech-reports/346 | Partition structures derived from Brownian motion and stable subordinators
Report Number
346
Authors
Jim Pitman
Citation
Bernoulli 3, 79-96, 1997
Abstract
Explicit formulae are obtained for the distribution of various random partitions of a positive integer $n$, both ordered and unordered, derived from the zero set $M$ of a Brownian motion by the following scheme: pick $n$ points uniformly at random from $[0,1]$, and classify them by whether they fall in the same or different component intervals of the complement of $M$. Corresponding results are obtained for $M$ the range of a stable subordinator and for bridges defined by conditioning on $1 \in M$. These formulae are related to discrete renewal theory by a general method of discretizing a subordinator using the points of an independent homogeneous Poisson process.
PDF File
Postscript File | 2021-05-18 23:21:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.7305176258087158, "perplexity": 297.1459044396867}, "config": {"markdown_headings": false, "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-2021-21/segments/1620243989874.84/warc/CC-MAIN-20210518222121-20210519012121-00163.warc.gz"} |
https://danflath.com/math-237-multivariable-calculus/vector-fields/ | # Vector fields
Learning objectives
• Interpret functions $f: {\bf R}^2 \longrightarrow {\bf R}^2$ as vector fields in the plane
• Use Mathematica to survey basic linear vector fields: sources, sinks, circles, spirals
• Work with flow lines (stream lines) of a vector field
Before class
• Read Hughes-Hallett sections 7.3, 17.4
• Ponder Hughes-Hallett problems: 17.3: 5, 6, 7, 13, 17; 17.4: 4, 10, 15.
• Post to Piazza
• Write solutions to problems 17.1: 58 and 17.2: 38 to turn in at the beginning of class.
• Complete HW9 on WeBWork
• Remember to bring your laptop to class | 2020-04-02 00:31:02 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8088911771774292, "perplexity": 10680.027028665076}, "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-2020-16/segments/1585370506477.26/warc/CC-MAIN-20200401223807-20200402013807-00171.warc.gz"} |
http://mathhelpforum.com/discrete-math/137509-arithmetic-proof.html | # Math Help - Arithmetic proof
1. ## Arithmetic proof
Prove that, for all n, n^3 + 2n^2 - n - 1 is not divisible by 3.
I hate to ask a question like this...but how do I get started here? I don't even know where to start. Could anyone just tell me the first starting steps in order to prove this and/or the concept that would prove this true? Any help would be appreciated.
2. Originally Posted by SterlingM
Prove that, for all n, n^3 + 2n^2 - n - 1 is not divisible by 3.
I hate to ask a question like this...but how do I get started here? I don't even know where to start. Could anyone just tell me the first starting steps in order to prove this and/or the concept that would prove this true? Any help would be appreciated.
You need only check it for the cases $n=0,1,2$ where you get $-1,1,13$ respectively. | 2016-06-29 00:50:46 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5215314626693726, "perplexity": 166.41920869726542}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783397428.37/warc/CC-MAIN-20160624154957-00116-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://trac-hacks.org/ticket/6406 | Opened 7 years ago
Closed 7 years ago
Let PrivateTicketsPlugin act only on certain "marked" tickets
Reported by: Owned by: HeX Noah Kantrowitz low PrivateTicketsPlugin trivial 0.12
Description
Just came across this plugin it is almost what I'm looking for. On our trac system we got a customisation for the access policies pretty much like the SensitiveTicketsPlugin. But this lacks the feature of PrivateTicketsPlugin to allow reporters and other dedicated groups to view the ticket. So integrating a checkbox and letting PrivateTicketsPlugin act only on "private" tickets would be a nice extension.
comment:1 Changed 7 years ago by Noah Kantrowitz
Resolution: → wontfix new → closed
This is something far too custom to ever see in a general-use plugin, it would be pretty easy for you to add though, probably just use a special keyword and add an if 'private' in tkt['keywords']: in the right place.
comment:2 Changed 7 years ago by HeX
Fair enough, as for too custom I don't think so. The user case is probably quite common. One would like to have some private tickets that only reporters and a special group can see and others that are commonly "public". But I can live with your decision ;) and thanks for the hint.
comment:3 Changed 7 years ago by Noah Kantrowitz
The need might be generic, but the implementation wouldn't be. Some might want it to be per-reporter, others per-component, etc etc. Too hard to predict all the possible conditions.
Modify Ticket
Change Properties | 2017-03-29 21:42:54 | {"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": 0.17687368392944336, "perplexity": 3151.4298996952543}, "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-2017-13/segments/1490218191396.90/warc/CC-MAIN-20170322212951-00172-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Module_is_Submodule_of_Itself | # Module is Submodule of Itself
## Theorem
Let $\left({G, +_G, \circ}\right)_R$ be an $R$-module.
Then $\left({G, +_G, \circ}\right)_R$ is a submodule of itself.
## Proof
Follows directly from the fact that a group is a subgroup of itself.
$\blacksquare$ | 2020-08-06 07:48:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.4073050618171692, "perplexity": 605.68654311997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439736883.40/warc/CC-MAIN-20200806061804-20200806091804-00536.warc.gz"} |
https://www.math.uni-potsdam.de/en/professuren/geometry/publications/ansicht/supersymmetric-path-integrals-i-differential-forms-on-the-loop-space | # Supersymmetric Path Integrals I: Differential Forms on the Loop Space
#### Autoren: Florian Hanisch, Matthias Ludewig (2017)
In this paper, we construct an integral map for differential forms on the loop space of Riemannian spin manifolds. In particular, the even and odd Bismut-Chern characters are integrable by this map, with their integrals given by indices of Dirac operators. We also show that our integral map satisfies a version of the localization principle in equivariant cohomology. This should provide a rigorous background for supersymmetry proofs of the Atiyah-Singer Index theorem.
zur Übersicht der Publikationen | 2021-02-26 22:38:09 | {"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": 0.8906384110450745, "perplexity": 745.822920839372}, "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/1614178357984.22/warc/CC-MAIN-20210226205107-20210226235107-00307.warc.gz"} |
https://mathoverflow.net/questions/330974/weyl-group-element-w-fixing-a-root-and-its-presentation-as-product-of-simple | # Weyl Group Element $w$ fixing a root, and its presentation as product of simple reflections $w=s_1\dots s_n$
Let $$\Phi$$ be a root system and $$\gamma \in \Phi$$ a root. Let $$W$$ be the Weyl group and $$\Delta$$ a set of simple roots. Let $$w \in W$$ such that $$w(\gamma)=\gamma$$. Is it true that if $$w=s_1\dots s_n$$ with $$s_i$$ simple reflections, then $$s_i(\gamma)=\gamma$$ for $$i=1\dots n$$?
I can't see a reason why this shouldn't be true, but am unable to prove it.
Thanks!
This is definitely not true. For instance, already in $$\Phi=B_2$$, each root has a root orthogonal to it, so for every root there is some nontrivial element (in fact, a reflection) of the Weyl group fixing it. But e.g. a simple root in $$B_2$$ is not fixed by any simple reflection.
However, what you might want to know is the following. If we choose any point $$v$$ in the dominant chamber of our root system, then the stabilizer of $$v$$ is exactly the parabolic subgroup of $$W$$ generated by simple reflections that fix $$v$$. For a proof of this see Lemma 10.3B of Humphreys' "Introduction to Lie Algebras and Representation Theory" (https://www.springer.com/us/book/9780387900537). | 2020-05-26 12:25:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 16, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8559864163398743, "perplexity": 87.19010669502286}, "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/1590347390758.21/warc/CC-MAIN-20200526112939-20200526142939-00024.warc.gz"} |
https://www.hepdata.net:443/record/ins1280745 | Dielectron azimuthal anisotropy at mid-rapidity in Au + Au collisions at $\sqrt{s_{_{NN}}} = 200$ GeV
The collaboration
Phys.Rev.C 90 (2014) 064904, 2014.
Abstract
We report on the first measurement of the azimuthal anisotropy ($v_2$) of dielectrons ($e^{+}e^{-}$ pairs) at mid-rapidity from $\sqrt{s_{_{NN}}} = 200$ GeV Au+Au collisions with the STAR detector at RHIC, presented as a function of transverse momentum ($p_T$) for different invariant-mass regions. In the mass region $M_{ee}\!<1.1$ GeV/$c^2$ the dielectron $v_2$ measurements are found to be consistent with expectations from $\pi^{0}$, $\eta$, $\omega$ and $\phi$ decay contributions. In the mass region $1.1\!<M_{ee}\!<2.9$ GeV/$c^2$, the measured dielectron $v_2$ is consistent, within experimental uncertainties, with that from the $c\bar{c}$ contributions.
• #### Figure 19 (exp. data)
Experimental data from Figure 19
10.17182/hepdata.96269.v1/t1
The dielectron $v_2$ in the $\pi^0$ Dalitz decay region as a function of $p_T$ in different centralities from Au +...
• #### Figure 19 (sim. data)
Simulated data from Figure 19
10.17182/hepdata.96269.v1/t2
Expected dielectron $v_2$ from $\pi^0$ Dalitz decay as a function of $p_T$ in different centralities from Au + Au collisions...
• #### Figure 21 a (exp. data)
Experimental data from Figure 21 a
10.17182/hepdata.96269.v1/t3
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for...
• #### Figure 21 b (exp. data)
Experimental data from Figure 21 b
10.17182/hepdata.96269.v1/t4
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for...
• #### Figure 21 c (exp. data)
Experimental data from Figure 21 c
10.17182/hepdata.96269.v1/t5
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for...
• #### Figure 21 d (exp. data)
Experimental data from Figure 21 d
10.17182/hepdata.96269.v1/t6
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for...
• #### Figure 21 e (exp. data)
Experimental data from Figure 21 e
10.17182/hepdata.96269.v1/t7
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for...
• #### Figure 21 f (exp. data)
Experimental data from Figure 21 f
10.17182/hepdata.96269.v1/t8
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV for...
• #### Figure 21 a (sim. data)
Simulated data from Figure 21 a
10.17182/hepdata.96269.v1/t9
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV expected...
• #### Figure 21 b (sim. data)
Simulated data from Figure 21 b
10.17182/hepdata.96269.v1/t10
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV expected...
• #### Figure 21 c (sim. data)
Simulated data from Figure 21 c
10.17182/hepdata.96269.v1/t11
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV expected...
• #### Figure 21 d (sim. data)
Simulated data from Figure 21 d
10.17182/hepdata.96269.v1/t12
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV expected...
• #### Figure 21 e (sim. data)
Simulated data from Figure 21 e
10.17182/hepdata.96269.v1/t13
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV expected...
• #### Figure 21 f (sim. data)
Simulated data from Figure 21 f
10.17182/hepdata.96269.v1/t14
The dielectron $v_2$ as a function of $p_T$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV expected...
• #### Figure 22 (exp. data)
Experimental data from Figure 22
10.17182/hepdata.96269.v1/t15
The $p_T$-integrated dielectron $v_2$ as a function of $M_{ee}$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
• #### Figure 22 (hadron data)
10.17182/hepdata.96269.v1/t16
The $v_2$ of hadrons $\pi$, $K$, $p$, $\phi$ and $\Lambda$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200...
• #### Figure 22 (sim. data)
Simulated data from Figure 22
10.17182/hepdata.96269.v1/t17
The $p_T$-integrated dielectron $v_2$ as a function of $M_{ee}$ in minimum-bias Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV,... | 2022-09-27 16:33:17 | {"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": 0.9723423719406128, "perplexity": 5336.040435615013}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335054.79/warc/CC-MAIN-20220927162620-20220927192620-00638.warc.gz"} |
https://www.gnotomista.com/ancillary/the_best_is_not_there/ | # The best is not there
Published:
My favorite interpretation of Eduardo Scarpetta’s play “Miseria e nobiltà” (“Poverty and Nobility”) is the one by Totò, the Prince of laughter. The video above shows an extract from the comedy film taken from the play at the end of which Totò pronounces the words “la migliore non c’è” (“the best is not there”), speaking about chairs in his house. I find this line hilarious for its spectacular absurdity.
It is evident that, among the chairs of a house, there must be the best one, although this might not be unique. In fact, if we let $S$ be the non-empty finite set of chairs in a house, we can show by induction that it contains its supremum, $\sup S$, namely there is a best chair.
• If $S$ contains a single chair $x$, then $\sup S = x \in S$.
• Suppose that, if $S$ contains $n$ chairs, then $\sup S = \max S \in S$. Now, assume $S$ contains $n+1$ chairs and let $x$ be an element of $S$. By the induction hypothesis, as $S^\prime = S \setminus {x}$ contains $n$ chairs, it contains its supremum, let’s call it $x^\prime \in S^\prime$. Then:
$$\sup S = \sup \left( S^\prime \cup \{x\} \right) = \sup \{x^\prime, x\} = \max \{x^\prime, x\} \in S$$
as $x^\prime \in S^\prime \subseteq S$ and $x \in S$.
Would the line “la migliore non c’è” still sound spectacularly absurd if Totò lived in the Grand Hilbert Hotel assuming there is a chair in each room? | 2020-09-25 03:08:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.7049376368522644, "perplexity": 993.5142526627573}, "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/1600400221980.49/warc/CC-MAIN-20200925021647-20200925051647-00109.warc.gz"} |
https://www.guyrutenberg.com/tag/lyx/page/2/ | # LaTeX Error: Command \textquotedbl unavailable in encoding HE8
I was testing today the SVN version of LyX 1.6.0 and 1.5.7. Due to a change in the way the double quotation mark (“) is handled, adding it to Hebrew text resulted in the following LaTeX error:
`LaTeX Error: Command \textquotedbl unavailable in encoding HE8` | 2017-02-22 21:55:35 | {"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": 0.9565393328666687, "perplexity": 7605.5621664836035}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171053.19/warc/CC-MAIN-20170219104611-00646-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/find-surface-area-sphere-radius-7-cm-concept-of-surface-area-volume-and-capacity_50331 | # Find the Surface Area of a Sphere of Radius 7 Cm. - Geometry
Sum
Find the surface area of a sphere of radius 7 cm.
#### Solution
Radius of the sphere, r = 7 cm
∴ Surface area of the sphere, S = $4\pi r^2 = 4 \times \frac{22}{7} \times \left( 7 \right)^2$ = 616 cm2
Thus, the surface area of sphere is 616 cm2.
Concept: Concept of Surface Area, Volume, and Capacity
Is there an error in this question or solution?
#### APPEARS IN
Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 7 Mensuration
Practice set 7.1 | Q 4 | Page 145 | 2022-05-16 04:56:28 | {"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": 0.6588051915168762, "perplexity": 1847.77278623493}, "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-20220516041337-20220516071337-00080.warc.gz"} |
https://brilliant.org/problems/gamma-of-put-from-call/ | # Gamma of Put from Call
Ford stock is trading around 16.40 . The call option on the $16 strike has a gamma of 0.617. What is the gamma of the put on the$16 strike?
× | 2020-01-29 22:19:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4459661543369293, "perplexity": 11321.764585649173}, "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/1579251802249.87/warc/CC-MAIN-20200129194333-20200129223333-00387.warc.gz"} |
https://cs.stackexchange.com/questions/118514/is-it-decidable-whether-a-given-turing-machine-moves-its-head-more-than-481-cell | # Is it decidable whether a given Turing machine moves its head more than 481 cells away from the left-end marker, on input ε?
So, while reading some problems on decidability, I came across the following resource: https://www.isical.ac.in/~ansuman/flat2018/tm-more-undecidable.pdf
Here, on page no 12, it is written that the problem is decidable and with the following argument:
"Yes, Simulate M on for upto m^481 · 482 · k steps. If M visits the 482nd cell, accept, else reject."
I am quite confused with the step count. Can anyone please explain what does this mean, or maybe point to some resources where I can find a proper explanation!!!! Image of the slide
In particular, if a configuration $$c$$ yields a runs that gets back to $$c$$, at some point, then the run is stuck in a loop (note that this is not a necessary condition, a run might not halt while never repeating a configuration!).
Now, consider all the possible configurations that use up to 481 cells. There is a finite amount of those, namely $$m^{481} \cdot 482 \cdot k$$ (where $$m$$ is the size of the alphabet, and $$k$$ is the number of states). | 2020-02-28 15:05:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5524351000785828, "perplexity": 348.89233121241114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875147234.52/warc/CC-MAIN-20200228135132-20200228165132-00536.warc.gz"} |
http://en.wikipedia.org/wiki/Bateman_transform | # Bateman transform
In the mathematical study of partial differential equations, the Bateman transform is a method for solving the Laplace equation in four dimensions and wave equation in three by using a line integral of a holomorphic function in three complex variables. It is named after the English mathematician Harry Bateman, who first published the result in (Bateman 1904).
The formula asserts that if ƒ is a holomorphic function of three complex variables, then
$\phi(w,x,y,z) = \oint_\gamma f\left((w+ix)+(iy+z)\zeta,(iy-z)+(w-ix)\zeta,\zeta\right)\,d\zeta$
is a solution of the Laplace equation, which follows by differentiation under the integral. Furthermore, Bateman asserted that the most general solution of the Laplace equation arises in this way. | 2015-03-01 08:45:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9523475170135498, "perplexity": 230.41329769677944}, "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-2015-11/segments/1424936462313.6/warc/CC-MAIN-20150226074102-00172-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/urgent-help-in-friction.53637/ | # Urgent Help in Friction
1. Nov 22, 2004
### primarygun
Imagine there is an object on the surface.
The surface is uniform smooth(with same friction over the all surface and friction is greater than 0).
Let's define the friction be f.
Act a f force to horizontally to the object continuously, it is continuous added.
It is obviously stationary.
I'm quite confused of here then. If there is 1N force pushed to it in the same direction to the f force added by hand.
What will be observed?
a.Move with acceleration first, then remains the velocity later on.
b.1.If f>kinetic friction, then the object accelerates first then decelerates to stop.
b.2. If f> kinetic friction, then the object will accelerates continuously forward.
Which one is correct?
2. Nov 22, 2004
### maverick280857
Okay I think I see what you mean but you've not worded it correctly. First off, the friction coefficient is defined differently for zero and nonzero relative motion. In the former case, it is called the coefficient of static friction $$\mu_{s}$$ and in the latter, the coefficient of kinetic friction $$\mu_{k}$$. Usually $$\mu_{k} < \mu_{s}$$.
For the simple case described by you, the actual static frictional force f and the maximum possible static frictional force are related by the inequality,
$$f \leq f_{s,max} = \mu_{s}N$$
where N (=mg for zero vertical motion of the block) is the normal reaction on the block.
You need to know that for as long as f is less than fsmax, friction is a readjusting force..it equals itself to the applied force so that the net force on the body is zero and there is zero relative motion. Now if F is the applied force which is gradually increased from 0 to f, no motion will occur. At F = f, motion is "just" about to occur. As soon as F > f however, motion occurs but now f equals $$f_{k} = \mu_{k}N$$ which is less than its original value (and therefore also less than F). Hence there is a net force on the body.
This explanation can be made clearer if you draw a graph of the friction force versus applied force. At F = fsmax, there is a kink in the graph (which consists of a straight line of slope = 1 for F < fsmax and a horizontal line for F > fsmax) which corresponds to this dynamic switch from static to kinetic friction (in mathematical terminology the frictional force is not a continuous function of applied force). This graph of course can be obtained through experiment but since it holds for most simple pairs of surfaces you can find it in your physics textbook.
Now attempt your question again. Hope that helps...
Cheers
Vivek
3. Nov 22, 2004
### primarygun
b2? right?
4. Nov 22, 2004
### maverick280857
Yup. Good luck! :-)
5. Nov 23, 2004
### primarygun
How can we prove the presence of kinetic friction?
6. Nov 27, 2004
### maverick280857
Well its not something that can be proved mathematically but it can be proved logically using an argument such as the one that follows:
Suppose we exert a force F on an object that is resting on a surface whose coefficient of static friction is known (perhaps through tables or a measurement carried out using more advanced methods than the simple theoretical ones). As mentioned earlier the body will not move for as long as F is less than the maximum static frictional force. Now if F is gradually increased to a point where it "just" exceeds the maximum static frictional force, motion "just" begins and if the force F is kept constant in magnitude and direction, the acceleration vector of the body is constant (assuming no nonlinear behavior of the friction force). The net acceleration of the body is given by
$$a_{net} = \frac{F_{net}}{M}$$
and the acceleration that the applied force F would alone impart the body is
$$a_{F} = \frac{F}{M}$$
If $$a_{F} < a_{net}$$ (as will be the case) there must be some force which reduces the effect of F and that force can be safely thought of as the kinetic frictional force. Upon subsequent measurements you will find that it is less (usually) than the static frictional force.
Again, this "argument" depends on a LOT of assumptions some of which are implicit and so cannot be taken as an experimental or theoretical proof of friction, which is already known to exist. What you can prove however, through this approach is that kinetic friction exists after motion starts and not before it. And taking this a bit further you can plot the graph I had mentioned earlier.
Hope that helps...
Cheers
Vivek | 2018-03-18 08:32:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6975638270378113, "perplexity": 439.4914589637537}, "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/1521257645550.13/warc/CC-MAIN-20180318071715-20180318091715-00303.warc.gz"} |
https://encyclopediaofmath.org/wiki/Nottingham_group | # Nottingham group
The subgroup of automorphisms of the field of formal power series $\mathbf{F_p}[[t]]$ consisting of those automorphisms of the form $f(t) \mapsto f(g(t))$ where $g(t) \in t + O(t^2)$.
It is a finitely generated, just infinite pro-$p$ group of finite width. However, every separable pro-$p$ group can be embedded in it as a closed subgroup. | 2023-02-05 05:05:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9831767678260803, "perplexity": 157.9296785264544}, "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/1674764500215.91/warc/CC-MAIN-20230205032040-20230205062040-00600.warc.gz"} |
https://dynasor.materialsmodeling.org/tutorials/time_convergence.html | # Time convergence¶
Here, a short demonstration on how time-correlation typically converges with total simulation time is provided for FCC Al at $$T =$$ 300 K. To get a converged correlation function, e.g. in order to extract a phonon lifetime, one require on the order 100-1000 times longer simulation than the lifetime itself. Rather than running a single long MD simulation one can also many shorter simulations and average their correlation functions.
In the figure below, the decay time of the correlation function is about 1-2 ps. The $$C_L(q, t)$$ is pretty well-converged after 200 ps and very well converged after 2000 ps.
Current correlation $$C_L(q, t)$$ for simulations of varying lengths. | 2023-02-06 23:27:54 | {"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": 0.8808660507202148, "perplexity": 1275.6256844504214}, "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/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00828.warc.gz"} |
https://en.x-mol.com/paper/article/1356347058825838592 | Find Paper, Faster
Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
On topological Hochschild homology of the K(1)‐local sphere
Journal of Topology (IF1.582), Pub Date : 2021-02-01, DOI: 10.1112/topo.12182
Gabriel Angelini‐Knoll
We compute mod $( p , v 1 )$ topological Hochschild homology of the connective cover of the $K ( 1 )$‐local sphere spectrum for all primes $p ⩾ 3$. This is accomplished using a May‐type spectral sequence in topological Hochschild homology constructed from a filtration of a commutative ring spectrum. | 2022-01-21 23:11:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "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": 0.9488117694854736, "perplexity": 2779.3996588087302}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303717.35/warc/CC-MAIN-20220121222643-20220122012643-00164.warc.gz"} |
https://www.physicsforums.com/threads/divergence-what-am-i-doing-wrong.115853/ | # Homework Help: Divergence what am I doing wrong
1. Mar 29, 2006
I don't understand what I am doing wrong here.
I'm supposed to show that this function is divergence free.
$$\vec v = \left( \frac{x}{x^2+y^2}, \frac{y}{x^2+y^2} \right)$$
I ran the divergence through with my TI-89 at it equals 0. But, I want to calculate it by hand, so it would be easier to do this in polar coordinates (and this is my problem).
$$\vec v(r,\theta) = \left ( \frac{\cos \theta}{r}, \frac{\sin \theta}{r} \left)$$
Standard divergence in cylindrical coordinates (dropping the z component)
$$div\,\, \vec u = \frac{1}{r} \left( \frac{\partial}{\partial r} (rF_r) +\frac{\partial}{\partial \theta} (F_\theta) \right)$$
$$div\,\, \vec v = \frac{1}{r}\left( \frac{\partial}{\partial r} (\cos \theta ) + \frac{\partial}{\partial \theta}\left (\frac{\sin \theta}{r} \right) \right)$$
Now this is obviously not 0, since the $\sin \theta$ is not going anywhere with the partials. So what am I doing wrong?
Thanks,
2. Mar 29, 2006
### Tom Mattson
Staff Emeritus
You made a subtle mistake here. Your vector above is still just $\vec{v}=(v_x,v_y)$. You just changed the expressions for the components. You do not have $\vec{v}=(v_r,v_{\theta})$ yet. To get that you have to transform the basis vectors from $\hat{e}_x$ and $\hat{e}_y$ to $\hat{e}_r$ and $\hat{e}_{\theta}$.
3. Mar 29, 2006
I'm pretty sure I follow what you are saying. Well, I at least understand it. I am unfortunatly too tired to tackle it, so I will do it in the morning... But I should be good with what you said :)
thanks man
4. Mar 29, 2006
### J77
...but I think he's pretty much there.
Since the $$\cos$$ and $$\sin$$ are bounded, and $$1/r\rightarrow 0$$ as $$r\rightarrow\infty$$
(with the exception at $$r=0$$)
5. Mar 29, 2006
### Tom Mattson
Staff Emeritus
No, he is not even close. This has nothing to do with taking a limit. The divergence should vanish identically in polar coordinates, just as it does in rectangular coordinates. His mistake is exactly what I said it was: He is plugging the rectangular components of $\vec{v}$ into the polar form of $\vec{\nabla}$.
$v_x=\frac{x}{x^2+y^2}=\frac{\cos(\theta)}{r}$
Note that this is still just $v_x$
$v_y=\frac{y}{x^2+y^2}=\frac{\sin(\theta)}{r}$
Note that this is still just $v_y$
He needs to find the components $v_r$ and $v_{\theta}$, which both contain contributions from $v_x$ and $v_y$. This is done by transforming the basis vectors, just like I said.
6. Mar 29, 2006
### J77
I'm having a very bad brain day | 2018-06-20 14:06:46 | {"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": 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": 0.8222988843917847, "perplexity": 439.9513782855161}, "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/1529267863519.49/warc/CC-MAIN-20180620124346-20180620144346-00242.warc.gz"} |
https://math.stackexchange.com/questions/683294/determining-linear-independence-dependence-non-trivial-solution | # Determining Linear Independence/Dependence & non-trivial solution.
I put the vectors in a matrix and reduced it, solved the determinant and got 0. This tells me that the vectors are linearly dependent. I am not sure how to figure out the non-trivial relation. This is my reduced matrix.
$$\begin{pmatrix} 1& 0&-1/4 \\ 0& 1& 1\\ 0& 0& 0 \end{pmatrix}$$
$$A = \left\{\begin{matrix} -60\\ -4\\ -72 \end{matrix}\right. : B = \left\{\begin{matrix} -5\\ -1\\ -5 \end{matrix}\right. : C = \left\{\begin{matrix} 10\\ 0\\ 13 \end{matrix}\right.$$
__A +__B +___C = 0
Find coefficients.
• Your reduced matrix corresponds to the system of equations, $a+b-(1/4)c=0,b+c=0$. Find a non-zero solution to that system. That solution will be the coefficients in the relation. – Gerry Myerson Feb 20 '14 at 8:42
• Since they're dependent, can I set A = 1? – KnowledgeGeek Feb 20 '14 at 8:47
• Also, shouldn't your equation just read a - (1/4)c? – KnowledgeGeek Feb 20 '14 at 8:48
• How can you set $A=1$, when $A=\pmatrix{-60\cr-4\cr-72\cr}$? Or do you mean $a$ when you write $A$? In that case, set $a=1$, and see what happens. – Gerry Myerson Feb 20 '14 at 8:49
• My 1st equation comes from the first row. The first row is $(1,1,-1/4)$. So, my 1st equation is $a+b-(1/4)c=0$. – Gerry Myerson Feb 20 '14 at 8:50 | 2020-07-07 15:33:33 | {"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": 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": 0.8229999542236328, "perplexity": 469.4956201569432}, "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-2020-29/segments/1593655893487.8/warc/CC-MAIN-20200707142557-20200707172557-00483.warc.gz"} |
https://global.ihs.com/doc_detail.cfm?document_name=ISO%206932&item_s_key=00042045 | # Cold-reduced carbon steel strip with a maximum carbon content of 0,25 %
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This International Standard describes cold-reduced carbon steel strip with a maximum mass fraction of carbon of 0,25 %, furnished to two levels of closer tolerances than cold-reduced carbon steel sheet, with specific quality, specific hardness requirements or mechanical properties, specific edge, and specific finish.
NOTE This International Standard does not apply to the product in narrow widths known as cold-reduced carbon steel sheet slit from wider widths (see ISO 3574), nor does it include cold-reduced carbon steel strip with a mass fraction of carbon over 0,25 % (see ISO 4960).
Cold-reduced carbon steel strip is produced with a maximum mass fraction of the specified carbon not exceeding:
- 0,15 % for material specified to mechanical properties;
- 0,25 % for material specified to temper (hardness) requirements | 2018-02-22 09:01:14 | {"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": 0.9503539204597473, "perplexity": 11738.233607123657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891814079.59/warc/CC-MAIN-20180222081525-20180222101525-00585.warc.gz"} |
https://www.clutchprep.com/physics/practice-problems/137145/consider-the-wire-loop-you-used-in-part-a-for-the-lab-you-placed-the-bottom-sect | Force and Torque on Current Loops Video Lessons
Concept
# Problem: Consider the wire loop you used in part A. For the lab, you placed the bottom section of the loop in the magnetic field (between two magnets in a box with opening in between for loop to go in) and measured the force upon it when current was flowing through the wire. Imagine instead that both the bottom and one side of the loop were placed in the magnetic field (but not the top or other side). What would be the net direction of the force upon this loop? Explain carefully and refer back to equations if needed. Please specify the NET direction!
###### FREE Expert Solution
Force on a current-carrying conductor:
$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{B}}{\mathbf{i}}{\mathbf{L}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta }}}$
The angle between the current and the magnetic field is 90°. Thus:
$\overline{){\mathbf{F}}{\mathbf{=}}{\mathbf{B}}{\mathbf{i}}{\mathbf{L}}}$
Right-hand rule for currents in B-fields: Fingers→ field direction, Thumb→ current direction, and palm→ force direction.
FAD is directed in the positive x-axis.
FAB is directed in the positive y-axis.
83% (435 ratings)
###### Problem Details
Consider the wire loop you used in part A. For the lab, you placed the bottom section of the loop in the magnetic field (between two magnets in a box with opening in between for loop to go in) and measured the force upon it when current was flowing through the wire. Imagine instead that both the bottom and one side of the loop were placed in the magnetic field (but not the top or other side). What would be the net direction of the force upon this loop? Explain carefully and refer back to equations if needed. Please specify the NET direction! | 2021-09-20 10:58:44 | {"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": 0.5998536944389343, "perplexity": 635.3769099868879}, "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-20210920101029-20210920131029-00220.warc.gz"} |
https://tldr.dendron.so/notes/common.moro.html | # moro
• Invoke moro without parameters, to set the current time as the start of the working day:
moro
• Specify a custom time for the start of the working day:
moro hi {{09:30}}
• Invoke moro without parameters a second time, to set the current time at the end of the working day:
moro
• Specify a custom time for the end of the working day:
moro bye {{17:30}}
• Add a note on the current working day:
moro note {{3 hours on project Foo}}
• Show a report of time logs and notes for the current working day:
moro report
• Show a report of time logs and notes for all working days on record:
moro report --all | 2021-06-22 14:37:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7643957734107971, "perplexity": 3521.619069241706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488517820.68/warc/CC-MAIN-20210622124548-20210622154548-00044.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-7a-3-5b-and-2a-b-0 | # How do you solve 7a=3-5b and 2a+b=0?
May 9, 2016
The solution for the system of equations is:
color(green)(a = -1
color(green)(b = 2
#### Explanation:
$7 a = 3 - 5 b$..........equation $\left(1\right)$
$2 a + b = 0$
color(green)(b = -2a..............equation $\left(2\right)$
Solving by substitution:
Substituting equation $2$ in $1$:
$7 a = 3 - 5 b$
$7 a = 3 + \left(- 5\right) \cdot \textcolor{g r e e n}{\left(- 2 a\right)}$
$7 a = 3 + 10 a$
$7 a - 10 a = 3$
$- 3 a = 3$
$a = \frac{3}{- 3}$
color(green)(a = -1
Finding $b$ from equation $2$ :
$b = - 2 a$
$b = - 2 \cdot \left(- 1\right)$
color(green)(b = 2 | 2019-09-18 03:01:42 | {"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": 0.2534559667110443, "perplexity": 10444.350766528974}, "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-2019-39/segments/1568514573176.51/warc/CC-MAIN-20190918024332-20190918050332-00030.warc.gz"} |
http://mathhelpforum.com/statistics/124100-marbles-bags.html | 1. ## Marbles in Bags
Bag A contains 3 black marbles and 1 white marble and Bag B contains 1 black marble and 3 white marbles. If two marbles are randomly taken from Bag A and placed in Bag B, then a marble is randomly selected from Bag B, what is the probability that the marble selected from Bag B is black?
I've tried to draw a tree, but I must be doing something wrong cause I can't get the correct answer. Could someone give me some guidance?
2. Hello mneox
Originally Posted by mneox
Bag A contains 3 black marbles and 1 white marble and Bag B contains 1 black marble and 3 white marbles. If two marbles are randomly taken from Bag A and placed in Bag B, then a marble is randomly selected from Bag B, what is the probability that the marble selected from Bag B is black?
I've tried to draw a tree, but I must be doing something wrong cause I can't get the correct answer. Could someone give me some guidance?
The number of ways of selecting $2$ marbles from the four in bag A is $\binom42=6$.
The number of ways of selecting the white marble and one of the black marbles from bag A $= 3$.
Therefore the probability that one of the marbles chosen from bag A is white is $\tfrac36 = \tfrac12$; and the probability that both are black is also $\tfrac12$.
So, when a marble is drawn from bag B, half the time it will be chosen from a total of $2$ black and $4$ white, and half the time from $3$ black and $3$ white. So the probability that it is black is
$\frac12\times \frac26 + \frac12\times \frac36 = \frac{5}{12}$ | 2013-05-19 15:11:24 | {"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": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9202381372451782, "perplexity": 107.84652900784478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697745221/warc/CC-MAIN-20130516094905-00043-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/52023-optimum-turning-point.html | # Thread: Optimum Turning Point
1. ## Optimum Turning Point
Time to pull in the big guns. This is a frustrating twist on a classic problem:
A cop is chasing a burglar, both running east along an east-west shore line. (The water is to the north; land is to the south.) When the cop is 50m behind him, the burglar jumps into the water and begins swimming in a straight line 30 degrees north of the shore (a bearing of 60 degrees from North). The burglar swims at a rate of 2m/s. The cop runs along the shore for a short time, then jumps in the water and swims in a straight line on a course that will intercept the burglar. The cop can run 5m/s along the shore, and can swim at a rate of 3m/s. How many meters should the cop run before jumping in the water in order to apprehend the burglar in the shortest amount of time? At what angle from the shore should he turn?
I can get as far as drawing a picture, and coming up with times for three specific points along the shore. Creating a general equation to optimize, though, has me stumped. Any help would be appreciated.
2. I began with the assumption that the shortest time would be obtained in such a way that the cop passes the point at which the burglar leaves the shore, and then some time after that, begins to swim in order to intercept the burglar. So I stated:
$t_1$ is the time between the cop reaching the point where the burglar left the shore (B) and the point at which he begins to swim (A).
$t_2$ is the time the cop takes after he begins to swim before he catches the burglar.
It takes the cop 10 seconds to reach B. Using the law of cosines,
$(3t_2)^2 = [20 + 2(t_1 + t_2)]^2 + (5t_1)^2 - 2[20 + 2(t_1 + t_2)](5t_1)\cdot \frac{\sqrt{3}}{2}$.
Does that make sense or did I lose you?
3. Your equation makes sense- over the weekend I came up with a similar equation, though I had assumed the turning point was before the 50m, and used the cosine of 150.
Now the hard part: how do I find the optimum point off of that? I know I want to minimize the quantity (t1+t2), but...
I guess I'm not sure how to take this derivative, and what I should take it with respect to. | 2017-12-13 15:12:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6567341685295105, "perplexity": 598.5177561365563}, "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/1512948527279.33/warc/CC-MAIN-20171213143307-20171213163307-00184.warc.gz"} |
https://mathemerize.com/the-distribution-below-gives-the-weights-of-30-students-of-a-class-find-the-median-weight-of-the-students/ | # The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
## Solution :
We prepare the following table to compute the median :
We have : n = 30, So, $$n\over 2$$ = 15
The cumulative frequency just greater than $$n\over 2$$ is 19 and the corresponding the class is (55 – 60).
Thus, (55 – 60) is the median class such that $$n\over 2$$ = 15, l = 55, f = 6, cf = 13 and h = 5.
Substituting these values in the formula,
Median = l + ($${n\over 2} – cf\over f$$)(h)
= 55 + ($$15 – 13\over 6$$)(5) = 55 + $$2\over 6$$(5) = 55 + 1.67 = 56.67
Hence, the median weight is 56.67 kg | 2023-01-29 21:26:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5897144675254822, "perplexity": 609.4785709838025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499768.15/warc/CC-MAIN-20230129211612-20230130001612-00830.warc.gz"} |
https://socratic.org/questions/562f9459581e2a4299123973 | # Question 23973
Nov 17, 2015
"Be: " ["He"] 2s^2
#### Explanation:
The first thing to do when trying to write an atom's electron configuration is to figure you exactly how many electrons must be accounted for.
To do that, grab a periodic table and look for that atom's atomic number.
In your case, beryllium, $\text{Be}$, is located in period 2, group 2 of the periodic table, and has an atomic number equal to $4$. This means that a neutral beryllium atom will contain $4$ protons in its nucleus and $4$ electrons surrounding its nucleus.
Therefore, your electron configuration must account for $4$ electrons. The complete electron configuration for beryllium will be
$\text{Be: } 1 {s}^{2} 2 {s}^{2}$
Now, in order to use the noble gas shorthand notation, you must first identify which noble gas comes immediately before beryllium in the periodic table.
In this case, the only option available is helium, $\text{He}$. Helium has $2$ electrons surrounding its nucleus, so its electron configuration will look like this
$\text{He: } \textcolor{b l u e}{1 {s}^{2}}$
Notice that the configuration that accounts for the first two electrons is identical for both atoms. This means that you can replace it in beryllium's configuration to get
$\text{Be: } \textcolor{b l u e}{1 {s}^{2}} 2 {s}^{2}$
The electron configuration of helium is written like this, $\left[\text{He}\right]$, which means that the noble gas shorthand for beryllium will be
"Be: " ["He"] 2s^2# | 2020-08-11 07:40:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "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": 0.6347415447235107, "perplexity": 892.0297114555267}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738735.44/warc/CC-MAIN-20200811055449-20200811085449-00294.warc.gz"} |
https://physics.stackexchange.com/questions/122235/critical-temperature-difference-between-ising-and-xy-model | # Critical temperature difference between Ising and XY model
The following formula gives the critical coupling (more precisely the ratio of the spin-spin coupling over the temperature) for $O(n)$ models on a triangular lattice:
$$\text{e}^{-2K}=\frac{1}{\sqrt{2+\sqrt{2-n}}}$$
with $K=\beta J$
Numerically, it says that:
Ising model (n = 1) has $K \approx 0.27$
XY model (n=2) has $K \approx 0.17$
Thus, the critical temperature for the XY model is higher than the Ising model. I've been thinking about it but I can't come out with a reason of why allowing the order parameter to take continuous values means that we need to go higher in temperature to destroy order. Is there a (semi) intuitive reason for that?
• Your intuition is correct. It is not difficult to prove that the 2-point function of the Ising model is always an upper bound on the corresponding quantity for the XY model. In particular, if $\beta_c^{XY}$ denotes the inverse temperature at which the Kosterlitz-Thouless phase transition occurs, then $\beta_c^{XY}\geq 2\beta_c^{I}$, where $\beta_c^I$ is the inverse critical temperature for the Ising model. You can find the proof here. Note that the formula you give above is not for the $O(n)$ spin model, but for the $O(n)$ loop model. – Yvan Velenik Jun 28 '14 at 17:37
• No, the loop model is an approximation of the O(n) spin model. You can look, for example, at the explanations in Nienhuis' Les Houches lectures on Loop models, which can be downloaded from his homepage. – Yvan Velenik Jul 1 '14 at 8:30
• ps: In the Ising case, I managed to very precisely check the critical coupling value given by the formula above. That's why it's even more puzzling for me. – Learning is a mess Jul 1 '14 at 15:41
• The value of the critical points of the spin and loop models should not be related at all. However, the critical behaviors are expected to be the same (they should belong to the same universality class). – Yvan Velenik Jul 1 '14 at 16:53
• I have no idea what the value of the coupling constant of the spin O(2) model on the triangular lattice is. There are very efficient cluster methods for this model (as far as I know, I am not a specialist in the numerical aspects) which should provide precise estimates. – Yvan Velenik Jul 1 '14 at 16:56 | 2020-02-21 16:30:08 | {"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": 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": 0.7687211036682129, "perplexity": 300.6286811762453}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145533.1/warc/CC-MAIN-20200221142006-20200221172006-00376.warc.gz"} |
http://www.solutioninn.com/cond-nast-traveler-conducts-an-annual-survey-in-which-readers | # Question
Condé Nast Traveler conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service.
A sample of 37 ships that carry fewer than 500 passengers resulted in an average rating of 85.36, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.40 (Condé Nast Traveler, February 2008). Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers.
a. What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?
b. At 95% confidence, what is the margin of error?
c. What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?
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• CreatedSeptember 20, 2015
• Files Included | 2016-10-27 09:54:40 | {"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": 0.8654350638389587, "perplexity": 1590.9795418897456}, "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-2016-44/segments/1476988721174.97/warc/CC-MAIN-20161020183841-00401-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://dharmath.blogspot.com/2014/09/inspired-by-problem-from-brilliant.html | ## Friday, September 5, 2014
### Rotating projected ball
Inspired by a problem from brilliant.org A solid spherical ball with radius $R$ is projected from a rough ground with a velocity $v$ at angle $\theta$ with the horizontal, traveling to the right. At the same time it is given an angular velocity of $\omega$ clockwise such that the axis of rotation is perpendicular to the plane of projection.
At some point, the ball bounced on the ground, with coefficient of restitution $\frac{1}{2}$ and coefficient of friction is enough so that the ball did not slip while touching the ground. Find the initial angle such that the horizontal distance traveled by the ball to the point of second bounce be maximized.
### Solution
The initial velocity components are $v_x = v\cos\theta,v_y = v \sin \theta$. When the ball first touches the ground again, it will do so after a $t = 2v_y/g$ time, covering a distance of $d_1=tv_x = 2v_xv_y/g$.
At that point, the new velocity will have components $v'_x,v'_y$ respectively. We will calculate each component separately.
The vertical velocity is affected by the coeff. of restitution. Since the ground is assumed to be stationary (mass of the ball << mass of the Earth), then $v'_y = v_y / 2$
The horizontal velocity is affected by the friction. At the point of contact, the ball tends to go to the left, so the friction tends to go to the right. Suppose that the impulse caused by friction is $I$, then we have the following:
Linearly, the friction helps the linear motion: $$I = M(v'_x - v_x)$$ Rotationally, the torque caused by the friction slows down the angular motion: $$IR = \frac{2}{5}MR^2 (\omega - \frac{v'_x}{R})$$ (the last term is because we're assuming that the ball doesn't slip when it touches the ground). Solving for $v'_x$ we have: $$MR(v'_x - v_x) = \frac{2}{5}MR^2 (\omega - \frac{v'_x}{R})$$ $$v'_x - v_x = \frac{2}{5}R (\omega - \frac{v'_x}{R})$$ $$v'_x - v_x = \frac{2}{5}R\omega - \frac{2v'_x}{5}$$ $$v'_x = \frac{5}{7}( v_x+\frac{2}{5}R\omega ) = \frac{5v_x+2R\omega}{7}$$ Similar to the distance to the first bounce, the distance between first and second bounce is $$d_2 = 2v'_x v'_y/g = \frac{v_y(5v_x+2R\omega)}{7g}$$ Total distance is therefore: $$d_1+d_2 = \frac{2v_xv_y}{g} + \frac{v_y(5v_x+2R\omega)}{7g} = \frac{19v_xv_y + 2Rv_y\omega}{7g}$$ $$= \frac{v}{7g}(19v\sin\theta\cos\theta + 2R\sin\theta\omega)$$ Now we wish to find $\theta$ that maximizes: $$19v\sin\theta\cos\theta + 2R\omega\sin\theta$$ which can be done in various ways (calculus, double-angle formula etc). | 2018-03-22 15:53:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8952020406723022, "perplexity": 210.74392948372832}, "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/1521257647892.89/warc/CC-MAIN-20180322151300-20180322171300-00564.warc.gz"} |