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https://m-sciences.com/index.php/jast/citationstylelanguage/get/associacao-brasileira-de-normas-tecnicas?submissionId=57&publicationId=57 | LAKSHMI HN, K. .; LATHA, S. . A Note on Sufficient Conditions for Sakaguchi Type Functions of Order $$\beta$$. Journal of Advanced Studies in Topology, [S. l.], v. 3, n. 2, p. 59–65, 2022. Disponível em: https://m-sciences.com/index.php/jast/article/view/57. Acesso em: 5 dec. 2022. | 2022-12-06 00:31:07 | {"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": 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": 0.8266324996948242, "perplexity": 13989.976488884628}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711064.71/warc/CC-MAIN-20221205232822-20221206022822-00465.warc.gz"} |
https://picongpu.readthedocs.io/en/0.3.1/usage/workflows/numberOfCells.html | # Setting the Number of Cells¶
Together with the grid resolution in grid.param, the number of cells in our .cfg files determine the overall size of a simulation (box). The following rules need to be applied when setting the number of cells:
Each GPU needs to:
1. contain an integer multiple of supercells
2. at least three supercells
Supercell sizes in terms of number of cells are set in memory.param and are by default 8x8x4 for 3D3V simulations on GPUs. For 2D3V simulations, 16x16 is usually a good supercell size, however the default is simply cropped to 8x8, so make sure to change it to get more performance. | 2019-12-12 23:31:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33542969822883606, "perplexity": 1694.33801313699}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540547536.49/warc/CC-MAIN-20191212232450-20191213020450-00152.warc.gz"} |
https://algorithm-essentials.soulmachine.me/dfs/additive-number/ | # Additive Number
### 描述
Additive number is a string whose digits can form additive sequence.
A valid additive sequence should contain at least three numbers. Except for the first two numbers, each subsequent number in the sequence must be the sum of the preceding two.
For example:
"112358" is an additive number because the digits can form an additive sequence: 1, 1, 2, 3, 5, 8.
1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8
"199100199" is also an additive number, the additive sequence is: 1, 99, 100, 199.
1 + 99 = 100, 99 + 100 = 199
Note: Numbers in the additive sequence cannot have leading zeros, so sequence 1, 2, 03 or 1, 02, 3 is invalid.
Given a string containing only digits '0'-'9', write a function to determine if it's an additive number.
Follow up:
How would you handle overflow for very large input integers?
### 代码
// Additive Number// 多入口深搜// 时间复杂度O(n^3)，空间复杂度O(1)public class Solution { public boolean isAdditiveNumber(String num) { for (int i = 1; i <= num.length() / 2; ++i) { if (num.charAt(0) == '0' && i > 1) continue; for (int j = i + 1; j < num.length(); ++j) { if (num.charAt(i) == '0' && j - i > 1) continue; if (dfs(num, 0, i, j)) return true; } } return false; } // 判断从 [i, j) 和 [j, k) 出发,能否走到尽头 private static boolean dfs(String num, int i, int j, int k) { long num1 = Long.parseLong(num.substring(i, j)); long num2 = Long.parseLong(num.substring(j, k)); final String addition = String.valueOf(num1 + num2); if (!num.substring(k).startsWith(addition)) return false; if (k + addition.length() == num.length()) return true; return dfs(num, j, k, k + addition.length()); }} | 2023-04-02 08:42:07 | {"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": 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": 0.45119914412498474, "perplexity": 1812.00504134766}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00709.warc.gz"} |
https://brilliant.org/problems/sometimes-coefficients-are-scary/ | # Do you know how to multiply?
Algebra Level 4
$\large \displaystyle \prod_{n=1}^{100} (x+n)$
Find the coefficient of $$x^{98}$$ in the above product.
× | 2018-01-22 10:26:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.574849009513855, "perplexity": 947.0435923003122}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891277.94/warc/CC-MAIN-20180122093724-20180122113724-00699.warc.gz"} |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-molecular-science-5th-edition/chapter-4-energy-and-chemical-reactions-questions-for-review-and-thought-topical-questions-page-189d/61d | ## Chemistry: The Molecular Science (5th Edition)
The reaction that is the most exothermic will be the one with the most negative $\Delta H$. Using the calculations from part c, we find that this is the reaction with HF. | 2019-08-18 03:42:23 | {"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": 0.376518577337265, "perplexity": 964.7316986445567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313589.19/warc/CC-MAIN-20190818022816-20190818044816-00251.warc.gz"} |
https://brilliant.org/problems/area-24/ | # Area
Geometry Level pending
Find the area of the region in the $$xy$$ plane consisting of all points in the set $$\{(x,y) | x^2+y^2 \leq 144 \}$$ and satisfy the inequality $$\sin(2x+3y) \leq 0$$.
× | 2018-04-25 12:39:01 | {"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": 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": 0.7360039949417114, "perplexity": 310.87576677023446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947803.66/warc/CC-MAIN-20180425115743-20180425135743-00566.warc.gz"} |
https://www.expii.com/t/converting-units-of-time-9111 | Expii
# Converting Units of Time - Expii
Time can be measured in seconds, minutes, hours, days, or even months. There are no consistent multiples in time measurement. | 2021-11-27 04:22:12 | {"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": 0.8028542399406433, "perplexity": 2220.425129334533}, "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/1637964358078.2/warc/CC-MAIN-20211127013935-20211127043935-00605.warc.gz"} |
https://ask.openstack.org/en/questions/110556/revisions/ | Trying to figure out which one to use and why? They seem very similar and both have ansible directories with the same files and folders. I just want to simply deploy openstack newton services on a few different nodes to have an internal openstack environment. | 2019-08-17 23:44:22 | {"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": 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": 0.33721327781677246, "perplexity": 741.536931279694}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313501.0/warc/CC-MAIN-20190817222907-20190818004907-00216.warc.gz"} |
http://www.physicsforums.com/showthread.php?p=4160171 | # How can I solve this without using integrating factor?
by ktklam9
Tags: factor, integrating, solve
P: 3 Let the Wronskian between the functions f and g to be 3e$^{4t}$, if f(t) = e$^{2t}$, then what is g(t)? So the Wronskian setup is pretty easy W(t) = fg' - f'g = 3e$^{4t}$ f = e$^{2t}$ f' = 2e$^{2t}$ So plugging it in I would get: e$^{2t}$g' - 2e$^{2t}$g = 3e$^{4t}$ Which results in g' - 2g = 3e$^{2t}$ How can I solve for g without using integrating factor? Is it even possible? Thanks :)
Math Emeritus Sci Advisor Thanks PF Gold P: 39,556 It's always possible to solve "some other way" but often much more difficult. This particular example, however, is a "linear equation with constant coefficients" which has a fairly simple solution method. Because it is linear, we can add two solutions to get a third so start by looking at g'- 2g= 0. g'= 2g give dg/g= 2dt and, integrating ln(g)= 2t+ c. Taking the exponential of both sides, $g(t)= e^{2t+ c}= e^{2t}e^c= Ce^{2t}$ where C is defined as ec. Now, we can use a method called "variation of parameters" because we allow that "C" in the previous solution to be a variable: let $g= v(t)e^{2t}$. Then $g'= v'(t)e^{2t}+ 2v(t)e^{2t}$ so the equation becomes $g'- 2g= v'(t)e^{2t}+ 2v(t)e^{2t}- 2v(t)e^{2t}= v'(t)e^{2t}= 3e^{2t}$. We can cancel the "$e^{2t}$" terms to get $v'(t)= 3$ and, integrating, v(t)= 3t+ C. That gives the solution $g(t)= v(t)e^{2t}= 3te^{2t}+ Ce^{2t}$ where "C" can be any number. | 2014-09-01 07:46:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.8783454298973083, "perplexity": 1046.0816066035575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535917463.1/warc/CC-MAIN-20140901014517-00188-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/302076/two-questions-on-foliation-by-geodesics | # Two questions on “foliation by geodesics”
I would appreciate if you consider the following two questions on $1$ dimensional foliations whose leaves are geodesic.
1)Assume that $M$ is a Riemannian manifold which is either an open manifold or is a compact manifold with zero Euler characteristic. Does $M$ admit a foliation by geodesics?
2)Assume that $M$ is a Riemannian surface which admit at least one foliation by geodesics. Does there necessarily exist a foliation of $M$ by geodesics which satisfy the "Isocline Locale property"?
The Isocline local property is defined as follows:
For every $x\in M$ there is locally a geodesic $\alpha$ which is transverse to the foliation and it intersect all leaves with the same angle.
No to the first question. Let $M$ be a Riemannian $2$-manifold whose universal cover is the hyperbolic plane $H$, and whose fundamental group is not cyclic. For any foliation of $H$ by geodesics (lines), it seems to me that the endpoints of these lines on the boundary circle of $H$ will fill up the whole circle except for two points. These two points will have to be preserved by deck transformations, so any discrete group of isometries of $H$ that preserves the foliation must be cyclic.
• @Thiku: The $M$ in this answer is an open manifold. – Lee Mosher Jun 16 '18 at 17:59
• To be honest I can not understand this answer. For example consider $M=H\setminus \{p,q\}$. Then is not $H$ the universal covering space of $M$? But M admit a foliation by geodesic. The vertical foliation. Am I mistaken? – Ali Taghavi Jun 17 '18 at 10:54
• This $M$ is not complete, as it would have to be if its universal covering space were to be metrically isomorphic to $H$. – Tom Goodwillie Jun 17 '18 at 11:44 | 2021-01-22 07:59:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7395037412643433, "perplexity": 138.15826176252443}, "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/1610703529128.47/warc/CC-MAIN-20210122051338-20210122081338-00768.warc.gz"} |
https://www.gradesaver.com/textbooks/math/other-math/CLONE-547b8018-14a8-4d02-afd6-6bc35a0864ed/chapter-4-decimals-review-exercises-page-323/53 | ## Basic College Mathematics (10th Edition)
$3.5^{2}$+8.7(1.95) = 3.5$\times$3.5 + 8.7$\times$1.95 = 12.25 + 16.965 = 29.215 | 2022-09-29 12:16:22 | {"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": 0.7507299780845642, "perplexity": 11932.401750093855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335350.36/warc/CC-MAIN-20220929100506-20220929130506-00326.warc.gz"} |
https://support.atlas-sys.com/hc/en-us/article_attachments/1500007788622/Script-03a_-_The_Tree.html | # The Tree and Ordered Records¶
## The Tree¶
The structure that unites resources and archival objects into the archival hierarchy.
Please note that are are some depreciated tree endpoints as of this presentation, I am using the newer ones
### Explore the Morris Canal Collection tree¶
http://localhost:8080/resources/1#tree::resource_1
These demonstrations used the tree endpoints, such as [:GET] /repositories/:repo_id/resources/:id/tree/node. Dealing with the tree endpoints is not intuitive. I consider them an intermediate-to-advanced skill in your ArchivesSpace toolbox.
By demonstrating the tree endpoints I want your takeaway to be two things, the first of which is more important:
1. The hierarchy essential to archival description is represented in the data by this concept called a tree.
2. There are tree endpoints, but they are not the only way to see and use tree information. Just don’t think you need to use the tree endpoints because I showed them to you in this presentation. Make a distinction between the concept of the tree versus the specific endpoints that say "tree" in them.
Here are other ways to see and use tree information, including one of my favorite endpoints ever.
## /repositories/:repo_id/resources/:id/ordered_records¶
Get the list of URIs of this published resource and all published archival objects contained within. Ordered by tree order (i.e. if you fully expanded the record tree and read from top to bottom) | 2021-05-09 05:02:59 | {"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": 0.4594023823738098, "perplexity": 1850.5835543248513}, "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-2021-21/segments/1620243988955.89/warc/CC-MAIN-20210509032519-20210509062519-00638.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-absolute-value-inequalities-with-absolute-value-variables-on-bo#136260 | # How do you solve absolute value inequalities with absolute value variables on both sides abs(2x)<=abs(x-3)?
Apr 7, 2015
All values of x in the interval [-3,2]
To remove the absolute value sign, square both sides, so that both would be positive only. Accordingly,
4${x}^{2}$ $\le$ x-3)^2
4${x}^{2}$ $\le$ ${x}^{2}$ -6x+9
3${x}^{2}$ +6x - 9 $\le 0$
${x}^{2}$ +2x -3 $\le$0
(x+3)(x-2) $\le 0$.
Now, there can be two options for this inequality to hold good.
Case 1 x+3 is positive, that is x $\ge$-3. and x-2 is negative, that is x$\le$2.
Case 2 x+3 is negative, that is x$\le$ -3 and x-2 is positive, that is x$\ge$2
To understand the solution mark the above inequalities on the number line. The solution to the inequality would be x$\ge$-3 and x$\le$2. In the interval notation it would be [-3,2] | 2022-01-26 11:26:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "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": 0.6833896040916443, "perplexity": 1141.6507443641383}, "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/1642320304947.93/warc/CC-MAIN-20220126101419-20220126131419-00253.warc.gz"} |
https://paperswithcode.com/paper/fair-near-neighbor-search-independent-range | # Fair Near Neighbor Search: Independent Range Sampling in High Dimensions
5 Jun 2019 · , , ·
Similarity search is a fundamental algorithmic primitive, widely used in many computer science disciplines. There are several variants of the similarity search problem, and one of the most relevant is the $r$-near neighbor ($r$-NN) problem: given a radius $r>0$ and a set of points $S$, construct a data structure that, for any given query point $q$, returns a point $p$ within distance at most $r$ from $q$. In this paper, we study the $r$-NN problem in the light of fairness. We consider fairness in the sense of equal opportunity: all points that are within distance $r$ from the query should have the same probability to be returned. In the low-dimensional case, this problem was first studied by Hu, Qiao, and Tao (PODS 2014). Locality sensitive hashing (LSH), the theoretically strongest approach to similarity search in high dimensions, does not provide such a fairness guarantee. To address this, we propose efficient data structures for $r$-NN where all points in $S$ that are near $q$ have the same probability to be selected and returned by the query. Specifically, we first propose a black-box approach that, given any LSH scheme, constructs a data structure for uniformly sampling points in the neighborhood of a query. Then, we develop a data structure for fair similarity search under inner product that requires nearly-linear space and exploits locality sensitive filters. The paper concludes with an experimental evaluation that highlights (un)fairness in a recommendation setting on real-world datasets and discusses the inherent unfairness introduced by solving other variants of the problem.
PDF Abstract
## Datasets
Add Datasets introduced or used in this paper
## Results from the Paper Add Remove
Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers. | 2022-05-21 16:01:48 | {"extraction_info": {"found_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": 0.6905869841575623, "perplexity": 592.0349636874914}, "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/1652662539131.21/warc/CC-MAIN-20220521143241-20220521173241-00367.warc.gz"} |
https://www.physicsforums.com/threads/geometry-problem-involving-dot-cross-product.341248/ | # Geometry problem involving dot/cross product
1. Sep 28, 2009
### hanelliot
1. The problem statement, all variables and given/known data
Let r be a line and pi be a plane with equations
r: P + tv
pi: Q + hu + kw (v, u, w are vectors)
Assume v · (u x w) = 0. Show that either r ∩ pi = zero vector or r belongs to pi.
2. Relevant equations
n/a
3. The attempt at a solution
I get the basic idea behind it but I'm not sure if my "solution" is formally good enough. I know that cross product gives you a normal to a plane, which is u x w here. I also know that the dot product = 0 means that they are perpendicular to each other.. so v and (u x w) are perpendicular to each other. If you draw it out, you can clearly see that r must be either in pi or out of pi. Is this good enough to warrant a good mark? Thanks!
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Sep 28, 2009
### lanedance
if r is parallel to pi, but not "in" pi their intersection will not be the zero vector, it will be the empty set
try the separate cases when P is "in" pi, and when P is not "in" pi and try and see if you can show whether any arbitrary point on r is in, or not in P, knowing that v = a.(uXw) where a is some non-zero constant
3. Sep 29, 2009
### hanelliot
you are right, my mistake
I can show that with intuition and a sketch of plane/line but not sure how I should go about proving it formally.. maybe this Q is that simple and I'm overreacting
4. Sep 29, 2009
### lanedance
as you know
v.(u x w) = 0
then
v = au + bw
for constants a & b - why?
equation of you line is P + vt
now, i haven't tried, but using your equation of a line & the equation of a plane, considering the following cases, should show what you want:
Case 1 - P is a point in pi. Now show any other point on the line, using the line equation, satisfies the equation defining pi.
Case 2 - P is not a point in pi. Now show any other point on the line, using the line equation, does not satisfy the equation defining pi. | 2018-01-24 09:51:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8255792856216431, "perplexity": 620.2501948871325}, "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/1516084893629.85/warc/CC-MAIN-20180124090112-20180124110112-00589.warc.gz"} |
https://socratic.org/questions/does-this-identity-exist-if-so-what-is-it-equivalent-to-sin-2-x-cos-2-x | # Does this identity exist? If so, what is it equivalent to? -sin^(2)x+cos^(2)x = ?
Mar 18, 2018
$\cos \left(2 x\right)$
#### Explanation:
Yes this is an identity:
$- {\sin}^{2} x + {\cos}^{2} x =$
${\cos}^{2} x - {\sin}^{2} x =$
$\cos x \cos x - \sin x \sin x =$
Look familiar yet?
$\cos x \cos x - \sin x \sin x = \cos \left(2 x\right)$
Mar 18, 2018
$- {\sin}^{2} x + {\cos}^{2} x$
$= {\cos}^{2} x - {\sin}^{2} x$
$= {\cos}^{2} x - \left(1 - {\cos}^{2} x\right)$
$= 2 {\cos}^{2} x - 1$
$= \cos \left(2 x\right)$ | 2019-03-19 16:45:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "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": 0.9420083165168762, "perplexity": 13417.622530348952}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202003.56/warc/CC-MAIN-20190319163636-20190319185636-00307.warc.gz"} |
https://www.techwhiff.com/issue/you-want-to-create-a-triangle-with-sides-of-a-b-and--384820 | # You want to create a triangle with sides of a, b, and c. Which of the following inequalities should be true? a+b c a-b>c a-b
###### Question:
You want to create a triangle with sides of a, b, and c. Which of the following inequalities should be true?
a+b c
a-b>c
a-b
### Gas costs $3.05 a gallon, and your car travels at 27 miles for each gallon of gas. How far can you travel in your car with$95 in your pocket? A: 7800 B: 11 miles C: 870 miles D: 840
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### The total investment (GPDI) is for both replacement of destroyed capital (CFC) and new additions which are called ____________..
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### HELP MEEEEEE!!!!!!!!!!!!!!!!!!!!
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### Select all the objective case pronouns. I me my you your he her we us our they them their
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### Which of the following products is both a major import and export of the U.S
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### Which of the following represents the impacts of mining on human health? I. Toxic chemicals can leak into drinking water. II. Air pollution can lead to irritation of eyes, nose, and throat. III. Heavy metal exposure can cause birth defects. (A) III only (B) I and II (C) I and III (D) I, II, and III
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### Emphasize most nearly means
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### Tina placed a 12 meter rope along one side of the bicycle path. She hung a ribbon on each end of the rope and every 3 meters in-between. How many ribbons did she hang? A)4 B)5 C)6 D)7
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### A historian claims massive drought and famine in China caused the Boxer Rebellion. Which of the following historians is making a counterclaim . A historian who claims the Boxer Rebellion followed directly from the actions of external colonial powers B. A historian who shares a diary entry from a Chinese woman who lost her crops to drought C. A historian who offers evidence that Christians were targeted during the Boxer Rebellion D. A historian who shows that harvest yields declined in the years
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### Evaluate 5x-2y;x=2,y=-1
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### 81 people passed and 27 failed their functional skills level 2 exams write this as in its simplest form
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### A prism has an area of 4374 ft3. What is its volume in yd3?
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### Which step can be used when solving x^2-6x-25=0?
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### What is the product written in scientific notation? (5.9*10^-3) * (8.7*10^10) a. 14.61 * 10^-30 b. 5.1417 * 10^8 c. 14.61 * 10^7 d. 5.1417 * 10^7
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### Mountain region is called the area of fruits expalin
mountain region is called the area of fruits expalin... | 2023-02-06 00:04:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3892003893852234, "perplexity": 4846.555726891784}, "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/1674764500294.64/warc/CC-MAIN-20230205224620-20230206014620-00839.warc.gz"} |
http://httpcode.com/2014/04/10/april-fool.html | Last week was Aprils fools day, which means that for the days before and after you tend to be especially skeptical about the things you read on the web. So when I read that Redis had added one of my favorite algorithms the HyperLogLog I was in two minds as to whether this was real or not. The detailed analysis that Salvatore put together was very convincing but the date of the post was really off-putting.
If you haven’t heard of HyperLogLog before, it’s a method to work out the cardinality of some measure. Which in non-set based terms means, being able to efficiently count the number of unique items. One of the best implementations I’ve seen is the HyperLogLog Postgresql extension. This lets you define a new native data type. To use it you must use the various hash methods when inserting data, this is a required part of the HyperLogLog algorithm. The examples used in the readme.md page of the Github repo shows the real power of the extension.
Consider a data warehouse that stores analytic data;
-- Create the destination table
CREATE TABLE daily_uniques (
date date UNIQUE,
users hll
);
-- Fill it with the aggregated unique statistics
INSERT INTO daily_uniques(date, users)
FROM facts
GROUP BY 1;
Imagine that we have inserted a number of items into this table from some fact table. We can then query the table:
SELECT date, hll_cardinality(users) FROM daily_uniques;
Now the queries will look like:
SELECT hll_cardinality(hll_union_agg(users)) FROM daily_uniques WHERE date >= '2012-01-02'::date AND date <= '2012-01-08'::date;
or
SELECT date, #hll_union_agg(users) OVER seven_days
FROM daily_uniques
WINDOW seven_days AS (ORDER BY date ASC ROWS 6 PRECEDING);
Remember as well that the amount of storage space used here is absolutely minimal, Often in the order of bytes.
So as you can see HyperLogLog is really cool and it’s a great credit to the team behind Redis for bringing this into the product. Even if they do publish the announcement on April Fools day
Redis is a fantastic tool, it is so much more than just a memcache replacement, I like to think of it as Comp Sci in a box. It has all of the goodies: Lists with set based operations, sliding caches, queues, single threaded event based goodness. It’s a very exciting tool and I’m very glad to see it evolve. | 2017-04-25 20:12:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22738927602767944, "perplexity": 1768.5735327689338}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917120878.96/warc/CC-MAIN-20170423031200-00320-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://www.ipm.ac.ir/ViewPaperInfo.jsp?PTID=6929&school=Physics | ## “School of Physics”
Back to Papers Home
Back to Papers of School of Physics
Paper IPM / P / 6929
School of Physics
Title: Casimir Energy for Spherical Shell in Schwarzchild Black Hole Background
Author(s):
1 M.R. Setare 2 M.B. Altaie
Status: Published
Journal: Gen. Relat. Gravit.
No.: 2
Vol.: 36
Year: 2004
Pages: 331-341
Supported by: IPM
Abstract:
In this paper, we consider the Casimir energy of massless scalar field which satisfy Dirichlet boundary condition on a spherical shell. Outside the shell, the spacetime is assumed to be described by the Schwarzschild metric, while inside the shell it is taken to be the flat Minkowski space. Using zeta function regularization and heat kernel coefficients we isolate the divergent contributions of the Casimir energy inside and outside the shell, then using the renormalization procedure of the bag model the divergent parts are cancelled, finally obtaining a renormalized expression for the total Casimir energy. | 2022-05-20 10:37:17 | {"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": 0.871445894241333, "perplexity": 1785.4461128288629}, "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/1652662531779.10/warc/CC-MAIN-20220520093441-20220520123441-00055.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/find-distance-point-p-1-4-3-line-l-x-2-t-y-1-t-z-3t-using-following-methods--l-line-2-spac-q1450324 | Find the distance from the point P(1, 4, -3) to the line L: x=2+t, y=-1-t, z=3t by using each of the following methods.
a). If L is a line in 2-space or 3-space that passes through the points A and B, then the distance d from a point P to the line L is equal to the length of the component of the vector that is orthogonal to the vector
b). Show that in 3-space the distance d from a point P to the line L through points A and B can be expressed as
then use this result to find the distance between the point P and line L given at the beginning of this problem. | 2015-12-01 12:57:56 | {"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": 0.8101730346679688, "perplexity": 106.24504761177907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398467979.1/warc/CC-MAIN-20151124205427-00147-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.transtutors.com/questions/create-an-income-statement-64008.htm | # create an income statement
B Corporation had Income from continuing operations of $800,000 (after taxes) in 2010, unadjusted. In addition, the following information, which has not been considered, is as follows. 1. In 2010, the company adopted the double declining-balance method of amortizing equipment. Prior to 2010, Hauser had used the straight-line method. The change decreases income for 2010 by$50,000 (pre-tax) and the cumulative effect of the change on prior years' income was a $200,000 (pre-tax) decrease. 2. A machine was sold for$140,000 cash during the year at a time when its book value was $100,000. (Amortization has been properly recorded.) The company often sells machinery of this type. 3. B Corp decided to discontinue its stereo division in 2010. During the current year, the loss on the disposal of the segment of the business was$150,000 less applicable taxes. Instructions -Present in good form the Income Statement of the Corporation for 2010 starting with "income from continuing operations, unadjusted." (\$800,000). Then deal with the 3 items above as required and complete the income statement. -tax rate is 20% and 100,000 shares of common stock were outstanding during the year. Show calculations separate from the Income Statement as your Income statement must be in Good Form which means it is to look as a formal statement would. Any calculations to arrive at these figures should be shown on a separate sheet, or on the bottom of the page and referenced to the Income Statement. | 2019-07-16 04:04:40 | {"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": 0.2566113770008087, "perplexity": 1951.266585369686}, "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/1563195524502.23/warc/CC-MAIN-20190716035206-20190716061206-00314.warc.gz"} |
http://dmitrybrant.com/2007/10 | Monthly Archives: October 2007
• If you’re using Internet Explorer, the cache folder should be located at “C:\Documents and Settings\yourname\Local Settings\Temporary Internet Files“, where yourname is your Windows login name.
If you’re using Firefox, the cache folder should be located at “C:\Documents and Settings\yourname\Local Settings\Application Data\Mozilla\Firefox\Profiles\default\Cache“.
• It’s a bit complicated to actually find the video you want in the cache folder, since neither Internet Explorer and Firefox give cached items proper file extensions. The best you can do here is sort the files by size, and look for files of a video-worthy size (several megabytes). Under Firefox, the files named _CACHE_nnn_ are special files, and not videos. A good method of doing this would be to clear your browser’s cache, then go to YouTube, view the video you want (and only that video), then go to the cache folder: the largest file in the cache should be the video. Now copy it out of the cache folder and rename it with a “.flv” extension, and you’ve got it! | 2013-12-09 06:08:48 | {"extraction_info": {"found_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": 0.6546091437339783, "perplexity": 4327.265631289907}, "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-2013-48/segments/1386163915534/warc/CC-MAIN-20131204133155-00088-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://mathhelpboards.com/threads/polynomial-types.3618/ | # [SOLVED]Polynomial types
#### karush
##### Well-known member
$2x^{-3}-2x^{2}+3$
Decide whether the function is a polynomial function, If so, states its degree, type, and leading coefficient.
well, I presume it is a polynomial since it the sum of powers in the variable x. Its degree is 2 since that is highest power, but I don't know its type, since it is not quadratic or cubic. and has a vertical asymptote. and of course the leading coefficient is 2
couldn't find the answer in the book?
Last edited:
#### Bacterius
##### Well-known member
MHB Math Helper
Polynomials cannot have negative powers of $x$, so it's not a polynomial. Polynomials are continuous everywhere, differentiable everywhere, are well-behaved and have no asymptotes.
See the Wikipedia article, it says "non-negative integer exponents" | 2020-10-24 17:22:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7263809442520142, "perplexity": 850.4933570126864}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107884322.44/warc/CC-MAIN-20201024164841-20201024194841-00451.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-10th-edition/chapter-5-exponential-and-logarithmic-functions-5-3-one-to-one-functions-inverse-functions-5-3-assess-your-understanding-page-282/79 | ## Precalculus (10th Edition)
Published by Pearson
# Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 79
#### Answer
$x=-4$
#### Work Step by Step
The base is same on the 2 sides of the equation (and it is not 1), hence they will be equal if the exponents are equal. Hence $x=3x+8$, Solve the equation: \begin{align*} x&=3x+8\\ x-3x&=8\\ -2x&=8\\ \frac{-2x}{-2}&=\frac{8}{-2}\\ x&=-4 \end{align*}
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. | 2021-10-28 10:38:45 | {"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": 0.9196843504905701, "perplexity": 2266.669541276298}, "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-2021-43/segments/1634323588284.71/warc/CC-MAIN-20211028100619-20211028130619-00279.warc.gz"} |
https://livrepository.liverpool.ac.uk/516/ | # Three loop anomalous dimension of the second moment of the transversity operator in the (MS)over-bar and RI ' schemes
Gracey, JA ORCID: 0000-0002-9101-2853
(2003) Three loop anomalous dimension of the second moment of the transversity operator in the (MS)over-bar and RI ' schemes. NUCLEAR PHYSICS B, 667 (1-2). 242 - 260. | 2021-10-19 11:33:55 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9253544211387634, "perplexity": 4774.426408092355}, "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/1634323585265.67/warc/CC-MAIN-20211019105138-20211019135138-00409.warc.gz"} |
http://www.maa.org/david-p-robbins-prize?device=mobile | # David P. Robbins Prize
Approved by the Board of Governors, April 2005
In 2005, the family of David P. Robbins gave the Mathematical Association of America funds sufficient to support a prize honoring the author or authors of a paper reporting on novel research in algebra, combinatorics, or discrete mathematics. The prize of $5000 is awarded every third year. David Robbins spent most of his career on the research staff at the Institute for Defense Analyses Center for Communications Research (IDA-CCR) in Princeton. He exhibited extraordinary creativity and brilliance in his classified work, while also finding time to make major contributions in combinatorics, notably to the proof of the MacDonald Conjecture and to the discovery of conjectural relationships between plane partitions and alternating sign matrices. 1. The David P. Robbins Prize in Algebra, Combinatorics, and Discrete Mathematics shall be given to the author or authors of an outstanding paper in algebra, combinatorics, or discrete mathematics. Papers will be judged on quality of research, clarity of exposition, and accessibility to undergraduates. The paper must have been published within six years of the presentation of the prize, and must be written in English. 2. The prize is to be$5000, together with a certificate and a citation prepared by the Selection Committee. In the event of joint authors, the prize shall be divided equally.
3. The prize shall be given every third year at a national meeting of the Association.
4. The recipient need not be a member of the Association.
5. A standing committee on the David P. Robbins Prize shall recommend the recipient of the prize. The recommendation must be confirmed by the Board of Governors.
6. The Committee on the David P. Robbins Prize shall be appointed by the President of the Association. The Committee shall consist of four members, including academic and non-academic mathematicians. The term of appointment is six years and is non-renewable. Former members of the committee are eligible for reappointment after an interim of six yeasr, except that members appointed to fulfill an unexpired term of less than three years may be reappointed, immediately thereafter, for a full term.
## List of Recipients
#### 2011
Mike Paterson, Yuval Peres, Mikkel Thorup, Peter Winkler, and Uri Zwick, "Overhang," American Mathematical Monthly 116, January 2009; and "Maximum Overhang," American Mathematical Monthly 116, December 2009.
#### 2008
Neil J.A. Sloane, "The on-line encyclopedia of integer sequences," Notices of the American Mathematical Society, Vol. 50, 2003, pp. 912-915.
Yuval Peres received the David P. Robbins Prize from the Mathematical Association of America at the 2011 Joint Mathematics Meetings in New Orleans. | 2013-12-08 22:22:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4179303050041199, "perplexity": 2443.014317320889}, "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/1386163824647/warc/CC-MAIN-20131204133024-00050-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://planetmath.org/ProperMap | # proper map
Definition Suppose $X$ and $Y$ are topological spaces, and $f$ is a map $f:X\to Y$. Then $f$ is a proper map if the inverse image of every compact subset in $Y$ of is a compact set in $X$.
Title proper map ProperMap 2013-03-22 13:59:49 2013-03-22 13:59:49 matte (1858) matte (1858) 6 matte (1858) Definition msc 54C10 msc 54-00 PolynomialFunctionIsAProperMap | 2018-03-25 03:33:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 7, "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": 0.9827776551246643, "perplexity": 1336.6356137366733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257651780.99/warc/CC-MAIN-20180325025050-20180325045050-00676.warc.gz"} |
https://ageconsearch.umn.edu/record/62294 | Formats
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### Abstract
A survey was used to gauge consumer preferences toward four fresh pork attributes : juiciness, tenderness, marbling, and leanness. The survey elicited consumer willingness-to-pay a premium for an improvement in these attributes. Approximately one-half of the respondents were willing to pay some premium for the attributes of juiciness, leanness, and tenderness. The average premium size ranged from $0.20/lb. for marbling to$0.37/lb. for tenderness. Neither the choice of a certifying agency nor the use of a cheap talk script influenced premium levels. | 2021-04-23 12:26:16 | {"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": 0.21028967201709747, "perplexity": 11823.745281051817}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039617701.99/warc/CC-MAIN-20210423101141-20210423131141-00599.warc.gz"} |
http://books.duhnnae.com/2017/jun4/149716059569-Well-posedness-of-a-Class-of-Non-homogeneous-Boundary-Value-Problems-of-the-Korteweg-de-Vries-Equation-on-a-Finite-Domain-Eugene-Kramer-Ivonne-Riva.php | # Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain
Download or read this book online for free in PDF: Well-posedness of a Class of Non-homogeneous Boundary Value Problems of the Korteweg-de Vries Equation on a Finite Domain
In this paper, we study a class of initial-boundary value problems for the Korteweg-de Vries equation posed on a bounded domain $0,L$. We show that the initial-boundary value problem is locally well-posed in the classical Sobolev space $H^s0,L$ for $s-\frac34$, which provides a positive answer to one of the open questions of Colin and Ghidalia .
Author: Eugene Kramer; Ivonne Rivas; Bing-Yu Zhang
Source: https://archive.org/ | 2017-10-19 04:02:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42389950156211853, "perplexity": 233.46230112345893}, "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/1508187823220.45/warc/CC-MAIN-20171019031425-20171019051425-00199.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-6-p-s-problem-solving-page-506/9d | ## Algebra and Trigonometry 10th Edition
$80~beats~per~second$
The pulse of the patient is the frequency of the given function. The frequency is the inverse of the period. According to item (b) the period is 0.75 seconds: $f=\frac{1}{0.75}=\frac{4}{3}~beats~per~second=\frac{4}{3}\times60=80~beats~per~second$ | 2020-04-01 15:40:00 | {"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": 0.7001689672470093, "perplexity": 516.1795755016577}, "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/1585370505731.37/warc/CC-MAIN-20200401130837-20200401160837-00499.warc.gz"} |
http://ask.cvxr.com/t/express-log-sum-of-the-squared-exponential-in-cvx/10559 | # Express -log(sum of the squared exponential) in cvx
Hi, I want to express -log(exp(-x.^2)+exp(-2*x.^2)). But I cannot find a way that CVX accepts it. Can anyone help?
log-convex can be added, so log(exp(x^2) + exp(2*x^2)) is allowed.
log-concave can’t be added, so log(exp(-x^2) + exp(-2*x^2)) is not allowed.
Read the answer by mcg at Log of sigmoid function to learn the CVX rules for log-convex and log-concave. This material is not really addressed in the CVX Users’ Guide.
Thanks so much for your reply. But I think **-**log(exp(-x.^2)+exp(-2*x.^2)) is convex at least for x\in [-20, 20].
You think? Or you’ve proved?
I plot it with MATLAB.
Did you read the link in my previous post? That is not a proof. | 2022-10-04 04:12:26 | {"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": 0.8603273034095764, "perplexity": 2862.055177652331}, "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-20221004023206-20221004053206-00668.warc.gz"} |
http://mathoverflow.net/revisions/104685/list | We know it converges for any prime p. I just want to know how to compute its exact value: \prod_{n=1}^{\infty} $$\prod_{n=1}^{\infty} (1-p^{-n})1-p^{-n})$$ | 2013-05-22 11:35:22 | {"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": 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": 0.8969008326530457, "perplexity": 114.76545514645412}, "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/1368701638778/warc/CC-MAIN-20130516105358-00003-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-geometry/120484-image-principal-value-mapping.html | ## image, principal value mapping
Sketch an image under $w = \text{Log} (z)$ of
i) the line $y=x$
ii) the line $x=e$
I have not done many problems with mappings under the principal value mapping of the logarithm. I know that
$\text{Log} (z) := \ln r + i \theta = \ln | z | + i \text{Arg} (z)$.
However, I do not see what these images would look like. I need a few pointers here on what to do. | 2014-12-29 14:11:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6536876559257507, "perplexity": 575.1537981081801}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447563009.126/warc/CC-MAIN-20141224185923-00084-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-10th-edition/chapter-3-chemical-equations-and-reaction-of-stoichiometry-exercises-limiting-reactant-page-108/34 | # Chapter 3 - Chemical Equations and Reaction of Stoichiometry - Exercises - Limiting Reactant - Page 108: 34
(a) $S_8$ is the limiting reactant. (b) 67.5 g of $S_2Cl_2$ (c) 35.6 g of $Cl_2$
#### Work Step by Step
- Calculate or find the molar mass for $S_8$: $S_8$ : ( 32.07 $\times$ 8 )= 256.56 g/mol - Using the molar mass as a conversion factor, find the amount in moles: $$32.0 \space g \times \frac{1 \space mole}{ 256.56 \space g} = 0.125 \space mole$$ - Calculate or find the molar mass for $Cl_2$: $Cl_2$ : ( 35.45 $\times$ 2 )= 70.90 g/mol - Using the molar mass as a conversion factor, find the amount in moles: $$71.0 \space g \times \frac{1 \space mole}{ 70.90 \space g} = 1.00 \space mole$$ Find the amount of product if each reactant is completely consumed. $$0.125 \space mole \space S_8 \times \frac{ 4 \space moles \ S_2Cl_2 }{ 1 \space mole \space S_8 } = 0.500 \space mole \space S_2Cl_2$$ $$1.00 \space mole \space Cl_2 \times \frac{ 4 \space moles \ S_2Cl_2 }{ 4 \space moles \space Cl_2 } = 1.00 \space mole \space S_2Cl_2$$ Since the reaction of $S_8$ produces less $S_2Cl_2$ for these quantities, it is the limiting reactant. - Calculate or find the molar mass for $S_2Cl_2$: $S_2Cl_2$ : ( 35.45 $\times$ 2 )+ ( 32.07 $\times$ 2 )= 135.04 g/mol - Using the molar mass as a conversion factor, find the mass in g: $$0.500 \space mole \times \frac{ 135.04 \space g}{1 \space mole} = 67.5 \space g$$ - Find the amount of $Cl_2$ consumed. $$0.125 \space mole \space S_8 \times \frac{ 4 \space moles \ Cl_2 }{ 1 \space mole \space S_8 } = 0.500 \space mole \space Cl_2$$ $$0.500 \space mole \times \frac{ 70.90 \space g}{1 \space mole} = 35.4 \space g$$ Excess = Initial - Consumed = 71.0 g - 35.4 g = 35.6 g
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. | 2022-05-25 10:26:11 | {"extraction_info": {"found_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": 0.6623057723045349, "perplexity": 1513.3916669929868}, "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-2022-21/segments/1652662584398.89/warc/CC-MAIN-20220525085552-20220525115552-00616.warc.gz"} |
https://www.coin-or.org/CppAD/Doc/parallel_ad.htm | Prev Next Index-> contents reference index search external Up-> CppAD multi_thread parallel_ad CppAD-> Install Introduction AD ADFun preprocessor multi_thread utility ipopt_solve Example speed Appendix multi_thread-> parallel_ad thread_test.cpp parallel_ad Headings-> Syntax Purpose Discussion CheckSimpleVector Example Restriction
Enable AD Calculations During Parallel Mode
Syntax
parallel_ad<Base>()
Purpose
The function parallel_ad<Base>() must be called before any AD<Base> objects are used in parallel mode. In addition, if this routine is called after one is done using parallel mode, it will free extra memory used to keep track of the multiple AD<Base> tapes required for parallel execution.
Discussion
By default, for each AD<Base> class there is only one tape that records AD of Base operations. This tape is a global variable and hence it cannot be used by multiple threads at the same time. The parallel_setup function informs CppAD of the maximum number of threads that can be active in parallel mode. This routine does extra setup (and teardown) for the particular Base type.
CheckSimpleVector
This routine has the side effect of calling the routines CheckSimpleVector< Type, CppAD::vector<Type> >() where Type is Base and AD<Base> .
Example
The files team_openmp.cpp , team_bthread.cpp , and team_pthread.cpp , contain examples and tests that implement this function.
Restriction
This routine cannot be called in parallel mode or while there is a tape recording AD<Base> operations.
Input File: cppad/core/parallel_ad.hpp | 2018-01-19 07:11:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6053341627120972, "perplexity": 7457.073417989129}, "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-2018-05/segments/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00749.warc.gz"} |
https://physics.stackexchange.com/questions/530962/forced-oscillation-and-resonance-formula-for-the-externally-applied-force | # Forced oscillation and resonance: formula for the externally applied force
In forced oscillation the formula for the externally applied force is $$F = \cos(\omega t)$$ in almost every book except one book, which uses $$F = \sin(\omega t)$$.
If the equation for the position is $$x = A\cdot\cos(\omega t+\phi)$$ and velocity is the derivative of position, then the velocity of the oscillator should be proportional to $$\sin(\omega t)$$ (because the derivate of $$\cos$$ is $$-\sin$$), and hence match the function 'drawn' by the applied force which is actually '$$\sin$$' only in one book. But if it's '$$\cos$$' it just doesn't make any sense in terms of the resonance.
Which is correct? Are both of them correct? Why?
• I think you mean "then the velocity of the oscillator should be proportional to $\sin(\omega t +\phi)$." Feb 13, 2020 at 20:36
• Do you know about Fourier transforms? Feb 14, 2020 at 16:02
In general there is a phase difference between the displacement, x, and the applied force, F. The phase difference depends on the frequency of F relative to the natural frequency of the oscillatory system. At resonance (or, more precisely, when the driving force frequency is the same as the system's undamped natural frequency) the displacement lags behind the driving force by $$\tfrac{\pi}{2}$$ (a quarter of a cycle).
It's usual to express both F and x as cosines or both as sines, so that the phase difference is simply the difference in the phase constants that are added to or subtracted from, $$\omega t$$. For example if $$F=F_0 \cos (\omega t)$$ and $$x=x_0 \cos (\omega t +\phi)$$, the displacement will be ahead of the driving force by a phase angle of $$(\phi-0)=\phi$$.
But it's perfectly possible to use $$F=F_0 \sin (\omega t)$$ for the force and $$x=x_0 \cos (\omega t +\phi)$$ for the displacement. Simply remember that $$\sin (\omega t) =\cos (\omega t-\tfrac{\pi}{2})$$. So in this case the displacement will be ahead of the driving force by a phase angle of $$[\phi -(-\tfrac{\pi}{2})]=(\phi+\tfrac{\pi}{2})$$. At resonance this phase angle is $$-\tfrac{\pi}{2}$$, so $$(\phi+\tfrac{\pi}{2})=-\tfrac{\pi}{2}$$, that is $$\phi=-\pi$$, which is indistinguishable from $$\phi=\pi$$. | 2022-07-02 14:22:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 21, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8867750763893127, "perplexity": 217.4193197437529}, "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-2022-27/segments/1656104141372.60/warc/CC-MAIN-20220702131941-20220702161941-00118.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/12/lesson/12.2.2/problem/12-121 | ### Home > PC3 > Chapter 12 > Lesson 12.2.2 > Problem12-121
12-121.
Three thieves in ancient times stole three bags of gold. The gold in the heaviest bag had three times the value of the gold in the lightest bag and twice the value of the gold in the medium bag. All together, the gold amounted to $330$ florins. How much gold was in each bag? Write a system of equations and use matrices to solve the system.
$h = 3l$
$h = 2m$
$h + m + l = 330$ | 2021-10-23 18:09:19 | {"extraction_info": {"found_math": true, "script_math_tex": 4, "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": 0.628598153591156, "perplexity": 1913.7094730849335}, "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/1634323585737.45/warc/CC-MAIN-20211023162040-20211023192040-00677.warc.gz"} |
https://www.houseofmath.com/encyclopedia/numbers-and-quantities/quantities/time/learning-about-the-clock-quarters-of-an-hour | # Learning About the Clock (Quarters of an Hour)
Here you will learn about the time in terms of quarters of an hour. The word quarter means one fourth, so when we talk about a quarter of an hour, we mean one fourth of an hour, which is $15$ minutes.
On a digital clock, we say that the time is a quarter to or past something when the last number is either $15$ or $45$. When the last number is $15$, we say that the time is a quarter past the hour we’re in. If the last number is $45$, we say that the time is a quarter to the next hour.
An analog clock shows a quarter to or past something when the minute hand points at $3$ or $9$. In the same ways as we did with the digital clock, we say that the time is “a quarter to” or “a quarter past” some hour. The time is a quarter past the current hour when the minute hand points at $3$. When the minute hand points at $9$, the time is a quarter to the next hour. Below you can see a couple of examples of times.
Can you see the connection between the images and what you read about quarters of an hour? Here are some examples for you to try.
Example 1
Draw the times on a piece of paper.
Example 2
What time is it?
Example 3
Write down the times and describe the times in words on a piece of paper.
Math Vault
Would you like to solve exercises about quarters of an hour? Try Math Vault! | 2022-12-03 16:50:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "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": 0.35698172450065613, "perplexity": 386.3916335539652}, "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/1669446710933.89/warc/CC-MAIN-20221203143925-20221203173925-00168.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/11/lesson/11.2.5/problem/11-159 | ### Home > PC3 > Chapter 11 > Lesson 11.2.5 > Problem11-159
11-159.
Write and solve an absolute value inequality for the following situation.
The gas consumption of a particular car averages $30$ miles per gallon on the highway, but the actual mileage varies from the average by at most $4$ miles per gallon. How far can the car travel on a $12$-gallon tank of gas?
Let $m = \text{miles}$. Since the information given is in miles per gallon, write an inequality where all terms represent miles per gallon.
$\text{actual mileage − predicted average milage = mpg variance}$ | 2021-03-05 23:14:15 | {"extraction_info": {"found_math": true, "script_math_tex": 5, "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": 0.8634302616119385, "perplexity": 1084.273353990422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373761.80/warc/CC-MAIN-20210305214044-20210306004044-00072.warc.gz"} |
https://www.physicsforums.com/threads/sample-statistics-vs-population-statistics.589204/ | # Homework Help: Sample statistics vs population statistics
1. Mar 21, 2012
### 939
1. The problem statement, all variables and given/known data
My task is to explain why the sample statistics I have obtained differ from the population statistics I have obtained from some data - using "concepts taught in class, if they exist". I have calculated x̄ and s, as well as σ and µ.
2. Relevant equations
First of all, the distribution is not normal, thus the emperical rule is invalid.
3. The attempt at a solution
Part of me thinks it's a trick question because there are very few "concepts" I can think of. The only thing I can come up with is that the mean differs because it is merely one sample, and according to the Central Limit Theorum, if I had a bigger sample space, the mean would be similar. Similarly, the standard deviation differs because it is merely one sample. Is this all there is to it or am I missing something?
2. Mar 22, 2012
### camillio
Sample statistics are obtained by sampling from a population. The idea is that the statistical properties of a population can (usually) be only estimated. In this respect, I slightly doubt about your data-based $\mu, \sigma^2$ :-) | 2018-11-16 22:57:36 | {"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": 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": 0.7906538844108582, "perplexity": 532.1210301925368}, "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/1542039743216.58/warc/CC-MAIN-20181116214920-20181117000920-00555.warc.gz"} |
https://statisfaction.wordpress.com/2010/12/01/ihp-seminar-november/ | # Statisfaction
## IHP seminar – November
Posted in Seminar/Conference by Julyan Arbel on 1 December 2010
Hi,
for those who missed this month IHP seminar organized by Ghislaine Gayraud and Karine Tribouley, below is a very quick summary/introduction of the talks. At closing time, it is not uncommon in that area to pass Field medals, as it happened when we left.
Anne Philippe spoke about long memory time series. For a weak second order stationary time series $X_t$, define its autocovariance $\Gamma(h)=Cov(X_0,X_h)$. Then $X_t$ has long memory if $\sum_h\Gamma(h)=\infty$. The long memory parameter is $d$ such that $\Gamma(h)$ decreases as $h^{2d-1}$. The core of the talk was about tests on long memory parameters for different time series (eg. test of equality), involving fractional Brownian motion…
Then, Judith Rousseau presented results on the Bernstein – von Mises property. It states that the posterior distribution of the parameter is asymptotically Gaussian. A nice consequence of BvM property is that Bayesian credible regions are also frequentist confidence regions, with confidence levels that coincide asymptotically.
Last, Erwan Le Pennec gave a technically involved talk, on a nice subject: the question raised by a group of researchers is to know whether or not Stradivarius violins are varnished differently from other violins. The statisticians’ contribution is to cluster the images of slices of violins, in order to help for their physical analysis. What is found is that the main difference in varnishes is the presence of a red pigment in Stradivarius violins. Which does not really translates as a factor for exceptional sound and quality. | 2017-06-29 12:21:01 | {"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": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49310117959976196, "perplexity": 1678.8243479808514}, "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-2017-26/segments/1498128323970.81/warc/CC-MAIN-20170629121355-20170629141355-00374.warc.gz"} |
http://mathhelpforum.com/differential-geometry/103996-fubini-tonelli-complete-measure-space.html | Thread: Fubini-Tonelli with complete measure space
1. Fubini-Tonelli with complete measure space
So let $(X,M,\mu), (Y,N,\nu)$ be complete $\sigma$-finite measure spaces. Then consider $(X\times Y,L,\lambda)$, the completion of $(X\times Y,M\times N,mu\times\nu)$.
This is the basic set up. I have to show that if $f$ is $L$-measurable and $f=0$ $\lambda$ almost everywhere, then $f_x,f^y$ are integrable and $\int f_xd\nu=\int f^yd\mu=0$ almost everywhere.
Note: $f_x(x,y)=f^y(x,y)=f(x,y)$ for fixed x,y.
I was told that for this part that I need to use the fact that $\mu,\nu$ are both complete but I don't see how.
I am starting out by assuming that $f=\chi_E$ (characteristic function). Then $f_x=E_x$ right? I assume that it is at this point I need to make use of completeness some how.
2. Originally Posted by putnam120
So let $(X,M,\mu), (Y,N,\nu)$ be complete $\sigma$-finite measure spaces. Then consider $(X\times Y,L,\lambda)$, the completion of $(X\times Y,M\times N,mu\times\nu)$.
This is the basic set up. I have to show that if $f$ is $L$-measurable and $f=0$ $\lambda$ almost everywhere, then $f_x,f^y$ are integrable and $\int f_xd\nu=\int f^yd\mu=0$ almost everywhere.
Note: $f_x(x,y)=f^y(x,y)=f(x,y)$ for fixed x,y.
I was told that for this part that I need to use the fact that $\mu,\nu$ are both complete but I don't see how.
I am starting out by assuming that $f=\chi_E$ (characteristic function). Then $f_x=E_x$ right? I assume that it is at this point I need to make use of completeness some how.
I don't see that completeness should be needed for this. According to Halmos, the definition of $\lambda(E)$ is $\lambda(E) = \textstyle\int\nu(E_x)\,d\mu(x) = \int\mu(E^y)\,d\nu(y)$ (of course, he has to show that those two integrals are equal). So the result for $f = \chi_E$ follows straight from that definition. See §36 of Halmos's book, pp.145–148. His results for product measures assume throughout that the measures on the component spaces are σ-finite, but not that they are complete. | 2017-08-22 02:17:48 | {"extraction_info": {"found_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": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9740535616874695, "perplexity": 141.51592405207603}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109803.8/warc/CC-MAIN-20170822011838-20170822031838-00143.warc.gz"} |
https://logtalk.org/symbolic_ai_examples.html | # Classical symbolic AI examples
The Logtalk distribution includes some classical symbolic AI examples, most of them adapted from literature and other logic programming systems (see the example/port notes for credits). These include:
## Reasoning
• many_worlds - Design pattern for reasoning about different worlds, where a world can be e.g. a dataset, a knowledge base, a set of examples | 2019-10-16 10:20:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47778555750846863, "perplexity": 4759.759391934821}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986666959.47/warc/CC-MAIN-20191016090425-20191016113925-00429.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/solve-x-x-3-x-4-x-5-x-6-10-3-x-4-6-solutions-quadratic-equations-factorization_1885 | # Solve for x: (x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6 - Mathematics
Solve for x: (x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6
#### Solution
Solution:
(x-3)/(x-4)+(x-5)/(x-6)=10/3
[(x-3)(x-6)+(x-5)(x-4)]/((x-4)(x-6))=10/3
(x^2-9x+18+x^2-9x+20)/((x-4)(x-6))=10/3
(2x^2-18x+38)/((x-4)(x-6))=10/3
(2(x62-9x+19))/x=10/3(x^2-10x+24)
(x-9x+19)/1=5/3[x^2-10x+24]
3x^2-27x+57=5x^2-50x+120
2x^2-23x+63=0
x=7 or x=9/2
Concept: Solutions of Quadratic Equations by Factorization
Is there an error in this question or solution? | 2021-10-27 19:32:07 | {"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": 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": 0.3086954951286316, "perplexity": 6430.011565926652}, "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/1634323588242.22/warc/CC-MAIN-20211027181907-20211027211907-00533.warc.gz"} |
https://www.findfilo.com/maths-question-answers/sides-of-triangleabc-ab-7-cm-bc-5cm-ca-6cm-a-pole-9pu | Sides of triangleABC, AB=7 cm, BC=5cm, CA=6cm. A pole is stand at | Filo
class 12
Math
Calculus
Curve Sketching
544
150
Sides of . A pole is stand at mid point of side . Angle of elevation of pole from vertex is , find height of pole (a) (b) (c) (d)
544
150
Connecting you to a tutor in 60 seconds. | 2021-08-03 10:50:31 | {"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": 0.9185046553611755, "perplexity": 4957.337995286301}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154457.66/warc/CC-MAIN-20210803092648-20210803122648-00039.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=1996_AJHSME_Problems/Problem_1&oldid=80808 | # 1996 AJHSME Problems/Problem 1
## Problem
How many positive factors of 36 are also multiples of 4?
$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 4 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 6$
## Solution
The factors of $36$ are $1, 2, 3, 4, 6, 9, 12, 18,$ and $36$.
The multiples of $4$ up to $36$ are $4, 8, 12, 16, 20, 24, 28, 32$ and $36$.
Only $4, 12$ and $36$ appear on both lists, so the answer is $3$, which is option $\boxed{B}$.
## See also
1996 AJHSME (Problems • Answer Key • Resources) Preceded by1995 AJHSME Last Question Followed byProblem 2 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
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Login to AoPS | 2020-12-04 02:33:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 12, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8763694167137146, "perplexity": 4271.538095238793}, "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-2020-50/segments/1606141733120.84/warc/CC-MAIN-20201204010410-20201204040410-00072.warc.gz"} |
https://zbmath.org/?q=ai%3Aschroder.karl-heinz+se%3A2413 | ## Semidirect products of locally convex algebras and the three-space-problem.(English)Zbl 0995.46032
An algebra (over $$\mathbb R$$ or $$\mathbb C$$) containing an ideal $$C$$ and a subalgebra $$B$$ such that $$C\cap B= \{0\}$$ and $$A= C+ B$$ is called the semi-direct product of $$C$$ and $$B$$. If $${\mathcal T}$$ is a locally convex topology on $$A$$ and $$(c,b)\mapsto b$$ is a homeomorphism, then the preceding terminology is further amplified with the adjective topological. The authors present a method for constructing such algebras and they show that if both $$C$$ and $$B$$ are locally $$m$$-convex, then so is $$A$$. However, they also construct an example in which $${\mathcal T}$$ is a Banach-space topology, the ideal $$C$$ in the topology $${\mathcal T}\cap C$$, and the quotient space $$A/C$$ in the quotient-topology induced by $${\mathcal T}$$ are both Banach algebras, but $$(A,{\mathcal T})$$ is not a Banach algebra-multiplication in it is not $${\mathcal T}$$-continuous.
### MSC:
46H10 Ideals and subalgebras 46H05 General theory of topological algebras
Full Text: | 2022-08-12 02:15:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6191846132278442, "perplexity": 150.62373015125024}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571538.36/warc/CC-MAIN-20220812014923-20220812044923-00174.warc.gz"} |
https://stdworkflow.com/447/python-matplotlib-subscript-font-setting-problem | # Python matplotlib subscript font setting problem
created at 07-29-2021 views: 23
## subscript font¶
The python code used (first step in your own python):
df_up= pd.read_excel(xlsxFilename)
df_up.index=['Q$_\mathrm{Oct}$','Q$_\mathrm{Nov}$','Q$_\mathrm{Dec}$','Q$_\mathrm{Jan}$']
This mathrm is the first step to make the subscript into the desired font
If you don’t understand, you can copy the above code directly to your document.
## global font settings¶
At this point, you will find that even after using the above, the picture that comes out still looks unsatisfactory, because it is just like the picture below
If I want the above "sou" to also become "Times New Roman" font, what should I do?
plt.rcParams['mathtext.fontset'] = 'stix'# Most similar to Times new roman
Or (I didn't use this, but you can try)
import matplotlib.pyplot as plt
from matplotlib import rcParams
config = {
"font.family":'serif',
"font.size": 20,
"mathtext.fontset":'stix',
"font.serif": ['SimSun'],
}
rcParams.update(config)
Or:
plt.rcParams['font.family'] = "Times New Roman"
plt.rcParams["mathtext.fontset"] = "dejavuserif"
plt.rc('text', usetex=True )
## debug¶
If you show up at this step:
RuntimeError: Failed to process string with tex because latex could not be found
you can
first step:
pip install latex
second step:
The main reason for this problem is the lack of latex, dvipng and ghostscript
Just choose one of the 3 subordinates (anaconda)
conda install -c conda-forge jupyter_latex_envs
conda install -c conda-forge/label/cf201901 jupyter_latex_envs
conda install -c conda-forge/label/cf202003 jupyter_latex_envs
third step
After the above attempts, it doesn’t work, what should I do, download Protext and only install miktex
fourth step
Detect
created at:07-29-2021 | 2022-07-01 07:15:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5570465326309204, "perplexity": 8947.654862560874}, "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/1656103922377.50/warc/CC-MAIN-20220701064920-20220701094920-00128.warc.gz"} |
https://brilliant.org/problems/intersecting-planes/ | # intersecting planes
Level pending
For what value of $$k$$ do the following sets of planes intersect in a line?
$$3x-y+z=0$$
$$kx+2y-z=0$$
$$4x+y+z=0$$
The answer can be represented as $$-\frac { a }{ b }$$. Express the answer as $$a+b$$.
× | 2017-03-25 11:38:04 | {"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": 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": 0.6128813028335571, "perplexity": 970.5488544675563}, "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-2017-13/segments/1490218188924.7/warc/CC-MAIN-20170322212948-00425-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.risk.net/derivatives/2080443/repricing-cross-smile-analytic-joint-density | # Repricing the cross smile: an analytic joint density
## Repricing the cross smile: an analytic joint density
When valuing a derivatives contract whose payout depends on two assets, the correlation between the random processes followed by those two assets must be taken into account. In most asset classes, there is no liquid instrument to determine that correlation. This makes the exposure to correlation hard to hedge, but straightforward from a modelling point of view since a single number, perhaps calculated from a historic time series of spot returns, can be used.
Repricing the cross smile: an | 2019-06-19 20:48:33 | {"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": 0.801415741443634, "perplexity": 2679.318186626933}, "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-2019-26/segments/1560627999041.59/warc/CC-MAIN-20190619204313-20190619230313-00032.warc.gz"} |
http://planetmath.org/EulersConstant | # Euler’s constant
Euler’s constant $\gamma$ is defined by
$\gamma=\lim_{n\rightarrow\infty}\;\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+% \cdots+\frac{1}{n}-\ln{n}\right)$
or equivalently
$\gamma=\lim_{n\rightarrow\infty}\;\sum_{i=1}^{n}\left[\frac{1}{i}-\ln\left(1+% \frac{1}{i}\right)\right]$
Euler’s constant has the value
$0.57721566490153286060651209008240243104\ldots$
It is related to the gamma function by
$\gamma=-\Gamma^{\prime}(1)$
It is not known whether $\gamma$ is rational or irrational.
References.
• Chris Caldwell - “Euler’s Constant”, http://primes.utm.edu/glossary/page.php/Gamma.htmlhttp://primes.utm.edu/glossary/page.php/Gamma.html
Title Euler’s constant EulersConstant 2013-03-22 12:18:27 2013-03-22 12:18:27 akrowne (2) akrowne (2) 10 akrowne (2) Definition msc 40A25 Euler-Mascheroni constant Mascheroni constant | 2018-03-24 04:34:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 6, "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": 0.9484512209892273, "perplexity": 6708.498319951146}, "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/1521257649683.30/warc/CC-MAIN-20180324034649-20180324054649-00118.warc.gz"} |
http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-8-section-8-1-solving-quadratic-equations-by-completing-the-square-exercise-set-page-482/7 | ## Intermediate Algebra (6th Edition)
z=±$\sqrt 10$
Original Equation 3z²-30=0 Add 30 to both sides 3z²=30 Divide both sides by 3 z²=10 Take the square root of both sides z=±$\sqrt 10$ | 2017-03-28 08:24:11 | {"extraction_info": {"found_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": 0.7890872955322266, "perplexity": 2449.5776402372694}, "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/1490218189686.31/warc/CC-MAIN-20170322212949-00444-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://www.tug.org/pipermail/texhax/2009-June/012671.html | # [texhax] fbox in align environment
Philip G. Ratcliffe philip.ratcliffe at uninsubria.it
Mon Jun 15 10:29:06 CEST 2009
> Say you have three equations in an align environment. You
> want to box only one of them, say the last one. How does one
> do this? I want all three equations aligned (at, say the =
> sign). Fancybox.sty wasn't of much help in this regard. I can
> put the first two eqns in an align, and the third eqn in an
> fbox in the equation environment, but the alignment is disturbed.
If you haven't found anything better, here's a not very elegant solution:
\documentclass{article}
\usepackage{amsmath}
\newcommand\alignboxed[2]{\rlap{\boxed{#1#2}}\hphantom{#1\mkern6mu}}
\begin{document}
\begin{align}
f_1(x) &= a+bx, \\
f_2(x) &= a+bx+cx², \\
\alignboxed{f_3(x)}{= a+bx+cx²+dx³.}
\end{align}
\end{document}
This works similarly:
\documentclass{article}
\usepackage{amsmath}
\def\alignboxed#1\endalignboxed{\rlap{\boxed{#1#2}}\hphantom{#1\mkern6mu}
}
\begin{document}
\begin{align}
f_1(x) &= a+bx, \\
f_2(x) &= a+bx+cx², \\
\alignboxed
f_3(x) &= a+bx+cx²+dx³.
\endalignboxed
\end{align}
\end{document}
Cheers, Phil | 2018-02-18 20:06:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999911785125732, "perplexity": 8460.013537190838}, "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/1518891812259.18/warc/CC-MAIN-20180218192636-20180218212636-00427.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/thin-uniform-rectangular-sign-hangs-vertically-doorof-shop-sign-hinged-stationary-horizont-q218021 | A thin, uniform, rectangular sign hangs vertically above the doorof a shop. The sign is hinged to a stationary horizontal rod alongits top edge. The mass of the sign is 2.40 kg and its verticaldimension is 60.0 cm. The sign isswinging without friction, becoming a tempting target for childrenarmed with snowballs. The maximum angular displacement of the signis 25.0° on both sides of the vertical. At a moment when thesign is vertical and moving to the left, a snowball of mass500 g, traveling horizontally with avelocity of 160 cm/s to the right, strikes perpendicularly thelower edge of the sign and sticks there.
(a) Calculate the angular speed of the signimmediately before the impact.
rad/s
(b) Calculate its angular speed immediately after the impact.
rad/s
(c) The spattered sign will swing up through what maximumangle?
°
Best answer: | 2014-08-20 15:01:24 | {"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": 0.8287899494171143, "perplexity": 3030.1857887003607}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500809686.31/warc/CC-MAIN-20140820021329-00306-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://scicomp.stackexchange.com/questions/28204/computing-ifft-for-only-k-samples-in-a-high-dimensional-signal | # Computing IFFT for only $k$ samples in a high dimensional signal
I have a very high dimensional signal, say $15$ dimensions. Across each dimension the width is $N$ points. So total number of points is $N^{15}$. I already have the FFT given to me. Only low frequency coeffs are non zero. The non zero coeffs are the ones inside of the hypercube of width 5. So only $5^{15}$ are non zero.
Now I want to take an IFFT to compute samples in signal domain.But I dont want to compute all samples of signalbut only a $k$ of them. $k$ is much smaller compared to $N^{15}$. The samplesin signal domain are by no means sparse, but its just that I want to compute only a small number $k$ of them. These $k$ samples are distributed arbitrarily and are not confined to any region. How can I compute them efficiently?
I came across Sparse FFT, but here my signal is not sparse but just that i am interested only in a few samples in signal domain. So I am not sure I can use SFFT.
PS : I don't want to take a full IFFT due to memory constraints.
• The sparse FFT isn't really applicable here- it's an algorithm for locating the small number of frequencies with non-zero coefficients, in a single that is sparse in the frequency domain, but your signal is dense in the frequency domain and you already know where you want to compute the IFFT. If $k$ is small enough, then you could do this by direct evaluation of the IFFT sum. It's still going to take $O(kN^{15})$ time to do this, because all of your coefficients in the frequency domain are potentially nonzero. – Brian Borchers Nov 5 '17 at 16:50
• @Brian not all coffs in frequency are non zero but only 5^15 low frequencies. So in this case i cant better than O(k5^15)? Can i use Gortzel algorithm to get any better? – Rajesh D Nov 5 '17 at 22:27
• If you know exactly which of the Fourier coefficients are nonzero than you can just sum over those terms in the inverse Fourier transform. – Brian Borchers Nov 6 '17 at 0:11 | 2021-06-24 12:47:16 | {"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": 0.8108150362968445, "perplexity": 352.58997740077336}, "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/1623488553635.87/warc/CC-MAIN-20210624110458-20210624140458-00605.warc.gz"} |
https://math.stackexchange.com/questions/1356136/delta-2-frac-lambdax4-w2-2-omega-cap-w1-2-0-o | # $\Delta ^2(.)-\frac{\lambda}{|x|^4}(.): W^{2,2}(\Omega) \cap W^{1,2}_0(\Omega) \to W_0^{-2,2}(\Omega) $ is coercive.
I am reading an article and there, author claim that $$L(.)=\Delta ^2(.)-\frac{\lambda}{|x|^4}(.): W^{2,2}(\Omega) \cap W^{1,2}_0(\Omega) \to W_0^{-2,2}(\Omega) $$ is coercive if $0\leq \lambda<\Lambda_N=(\frac{N^2(N-4)^2}{16})$ , because of the following inequality:
For all $u \in W^{2,2}(\Omega) \cap W^{1,2}_0(\Omega)$ و $N>4$ $$\Lambda_N \int_{\Omega}\frac{u^2}{|x|^4}\mathrm{d}x \leq \int_{\Omega} |\Delta u|^2 \mathrm{d}x$$ where $\Lambda_N=(\frac{N^2(N-4)^2}{16})$ is optimal constant.
My question is this that how the inequality with the optimal constant conclude that operator is coercive for $0\leq \lambda<\Lambda_N=(\frac{N^2(N-4)^2}{16})$.
my try:
the norm on the hilbet space $\mathbb{H}=W^{2,2}(\Omega) \cap W^{1,2}_0(\Omega)$ is $$\langle u,v\rangle_{\mathbb{H}}=\int_{\Omega} \Delta u \Delta v dx$$
I must show that $$\langle Lu,u \rangle_{\mathbb H} \geq c ||u||_{\mathbb H}^2$$ for a positive constant $c$.
with simple calculations and using above inequality, I have showed that $$\langle Lu,u \rangle_{L^2} \geq c ||\Delta u||_{L^2}=c||u||_{\mathbb H}^2$$ for a positive $c$
but I must show that $$\langle Lu,u \rangle_{\mathbb H} \geq c||u||_{\mathbb H}^2$$ .
It appears that you are using the notation $\langle \cdot, \cdot \rangle_{\mathbb{H}}$ for the inner product on you Hilbert space $W^{2,2}(\Omega)\cap W^{1,2}_0(\Omega)$ and $\langle \cdot,\cdot\rangle_{L^2}$ for the dual pairing with the space $W^{-2,2}_0(\Omega)$, which is the co-domain of the operator $L$. The term $\langle Lu,u\rangle_{\mathbb{H}}$ then does not make sense unless $u$ has more differentiability and even then will not be coercive.
The appropriate bi-linear form for coercivity, i.e. for existence of solutions via the Lax-Milgram theorem, is $\langle Lu,u\rangle_{L^2}$ which you have already shown is coercive. | 2019-11-12 18:16:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9417932033538818, "perplexity": 136.61636139623081}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665726.39/warc/CC-MAIN-20191112175604-20191112203604-00454.warc.gz"} |
https://www.sarthaks.com/2757061/625-is-related-to-24-in-such-a-way-that-169-is-related-to | # 625 is related to 24 in such a way that 169 is related to:-
29 views
closed
625 is related to 24 in such a way that 169 is related to:-
1. 17
2. 144
3. 12
4. 13
by (55.2k points)
selected
Correct Answer - Option 3 : 12
The logic follows here is:
Number2 : (Number - 1)
252 : (25 - 1)
= 625 : 24
Similarly,
132 : (13 - 1)
= 169 : 12
Hence, "12" is the correct answer. | 2023-03-27 01:35:14 | {"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": 0.8456653952598572, "perplexity": 2416.955714183985}, "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/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00516.warc.gz"} |
https://docs.lib.purdue.edu/dissertations/AAI9314052/ | A process technology for IC compatible micromechanical sensors using merged epitaxial lateral overgrowth of silicon
Abstract
A novel technology for manufacturing thin silicon diaphragm structures is presented. Controllability of thin silicon diaphragm is one of the most important issues in fabricating silicon micromechanical sensors whose sensitivity depends on the diaphragm thickness. This can be accomplished by epitaxial lateral overgrowth (ELO) of single crystal silicon on a patterned layer of masking material, typically SiO$\sb2,$ combined with crystallographic etching of which etching rate depends on the crystal plane. With recent improvement of ELO material, good quality of 10$\mu$m thick, 200$\mu$m x 1000$\mu$m single crystal silicon was obtained with its thickness being precisely controlled by growth rate ($\le$1$\mu$m/min.). The junction leakage of the p-n junction diodes fabricated on merged ELO silicon indicated the material quality is comparable to the substrate silicon. Using this technology, a bridge-type piezoresistive accelerometer with four beams and one proof mass was fabricated successfully. Its sensitivity and resonant frequency were comparable to the accelerometers made by other methods. They were analyzed by comparing the experimental results to a simple analytical solution as well as ANSYS stress simulator using a finite element method. The experimental results showed a potential application of the new technology to silicon sensor fabrication but some further refinement is remaining. ^
Degree
Ph.D.
Major Professor: Gerold W. Neudeck, Purdue University.
Subject Area
Engineering, Electronics and Electrical|Physics, Condensed Matter
Off-Campus Purdue Users: | 2018-03-19 12:31:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7500649094581604, "perplexity": 5670.786384613184}, "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-2018-13/segments/1521257646914.32/warc/CC-MAIN-20180319120712-20180319140712-00517.warc.gz"} |
http://mathhelpforum.com/calculators/180517-integrating-ti-89-a.html | # Math Help - integrating with the ti 89
1. ## integrating with the ti 89
can the ti 89 integrate matrices...
10e^(3t/2) 2e^t/2
3e^(3t/2) e^(t/2)
2. Originally Posted by slapmaxwell1
can the ti 89 integrate matrices...
10e^(3t/2) 2e^t/2
3e^(3t/2) e^(t/2)
You will need to integrate each entry seperately.
3. when i tried to enter the term i got an error message, can you tell me what is the proper format for integrating an e expression...say 10e^(3t/2)
4. Are you typing
" $\int$(10e^(3t/2),t)"
?
TI-89 tutorial
6. Originally Posted by mr fantastic
You will need to integrate each entry seperately.
i should probably further explain why im asking these series of questions....
Im trying to solve a variation of parameters problem on my ti 89, well im trying to do as much of the matrix manipulations as i can on the ti 89.
7. Originally Posted by TheEmptySet | 2016-06-27 07:18:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9603818655014038, "perplexity": 2267.8816738572687}, "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/1466783395621.98/warc/CC-MAIN-20160624154955-00115-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://wu-kan.cn/_posts/2019-09-19-%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD-%E5%85%AD/ | ## What is KRR (Knowledge representation and reasoning)
Symbolic encoding of propositions believed by some agent andtheir manipulation to produce representations of propositions thatare believed by the agent but not explicitly represented.
## Why KRR
• KR hypothesis: any artificial intelligent system isknowledge-based
• Knowledge-based system: system with structures that
• can be interpreted propositionally and
• determine the system behavior such structures are called its knowledge base (KB)
• Knowledge-based system most suitable for open-ended tasks
• Hallmark of knowledge-based system: cognitive penetrability,i.e., actions depend on beliefs, including implicitly representedbeliefs
• KR假设：任何人工智能系统都是基于知识的。
• 基于知识的系统：具有以下结构的系统。
• 可以通过命题和
• 确定系统行为 这样的结构称为其知识库(KB)。
• 基于知识的系统最适合开放式任务
• 基于知识的系统的Hallmark：认知渗透性，即行动依赖于信念，包括隐含表示的信念
## KRR and logic
Logic is the main tool for KRR, because logic studies
• How to formally represent agent’s beliefs
• Given the explicitly represented beliefs, what are the implicitlyrepresented beliefs.
There are many kinds of logics. In this course, we will usefirst-order logic (FOL) as the tool for KRR
## An example (cont’d)
• Intelligence is needed to answer the question
• Can we make machines answer the question?
• A possible approach
• First, translate the sentences and question into FOL formulas
• Of course, this is hard, and we do not have a good way toautomate this step
• Second, check if the formula of the question is logicallyentailed by the formulas of the sentences
• We will show that there are ways to automate this step
## Alphabet
• Logical symbols (fixed meaning and use):
• Punctuation: (,),,,.
• Connectives and quantifiers:=,¬,∧,∨,∀,∃
• Variables:x,x1,x2,…,x′,x′′,…,y,…,z,…
• Non-logical symbols (domain-dependent meaning and use):
• Predicate symbols
• arity: number of arguments
• arity 0 predicates: propositional symbols -Function symbols
• arity 0 functions: constant symbols
## Terms
• Every variable is a term
• If t1,…,tn are terms andfis a function symbol of arityn,then f(t1,…,tn)is a term
## Formulas
• If t1,…,tn are terms andPis a predicate symbol of arityn,thenP(t1,…,tn)is an atomic formula
• Ift1andt2are terms, then(t1=t2)is an atomic formula
• Ifαandβare formulas, andvis a variable, then¬α,(α∧β),(α∨β),∃v.α,∀v.αare formulas
## Notation
• Occasionally add or omit (,)
• Use [,] and {,}
• Abbreviation:(α→β)for(¬α∨β)
• Abbreviation:(α↔β)for(α→β)∧(β→α)
• Predicates: mixed case capitalized,e.g., Person, OlderThan
• Functions (and constants): mixed case uncapitalized,e.g.,john, father,
## Variable scope
• Free and bound occurrences of variables
• e.g.,P(x)∧∃x[P(x)∨Q(x)]
• A sentence: formula with no free variables
• Substitution:α[v/t]meansαwith all free occurrences of thevreplaced by termt
• In general,α[v1/t1,…,vn/tn]
## Interpretations
An interpretation is a pair = <D,I>
• D,Ii D is the domain, can be any non-empty set
• I is a mapping from the set of predicate and function symbols
• If P is a predicate symbol of arity n, I(P) is an n-ary relation over D, i.e., I(P) ⊆ Dn
• If p is a 0-ary predicate symbol, i.e., a propositional symbol, I(p) ∈{true,false}
• If f is a function symbol of arity n, I(f) is an n-ary function over D, i.e., I(f) : Dn → D
• If c is a 0-ary function symbol, i.e., a constant symbol, I(c) ∈ D
wrt: with pespect to | 2020-07-03 23:57:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8408132195472717, "perplexity": 10913.862338705352}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655883439.15/warc/CC-MAIN-20200703215640-20200704005640-00363.warc.gz"} |
https://byjus.com/question-answer/which-of-the-following-oxides-is-not-expected-to-react-with-sodium-hydroxide-cao-b/ | Question
# Which of the following oxides is not expected to react with sodium hydroxide?
A
BeO
B
B2O3
C
CaO
D
SiO2
Solution
## The correct option is A $$CaO$$$$CaO$$ is not expected to react with $$NaOH$$ because $$NaOH$$ is a base and it can only react with either an acidic oxide or an amphoteric oxide. Among given options $$BeO$$ is an amphoteric oxide while $$B_2O_3$$ and $$SiO_2$$ are acidic oxides.Thus, all of them react with $$NaOH$$ to form salts.$$CaO$$, on the other hand, is a basic oxide and hence it will not react with $$NaOH$$.Chemistry
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View More | 2022-01-18 16:02:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6074661612510681, "perplexity": 1418.0420150964508}, "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/1642320300934.87/warc/CC-MAIN-20220118152809-20220118182809-00103.warc.gz"} |
http://en.wikiversity.org/wiki/Talk:Analytic_Maths_for_Olympiads | Welcome to the Brainstorm Forum for Olympiad Algebra and Induction
Part of the School of Olympiads
POST YOUR QUESTIONS ON THIS TALKPAGE AND GET ANSWERS FROM OTHER VIEWERS. ALSO WE CAN DISCUSS SOLUTIONS AND DISAGREEMENTS.
For more Resources visit Analytic Maths for Olympiads
## A picking game (problem on induction)
There is a heap of $n$ matches. 2 players take turns to pick 1 or 2 matches. The winner is the person who picks the last match.
• Who wins for 5 matches (if no player misses a chance to win or draw)?
• Is there a general strategy for any number of matches (to force a win or a tie for either side)?
• What is the strategy if existing?
## A Rootful Question
Prove the following:
• $5<\sqrt{5}+\sqrt[3]{5}+\sqrt[4]{5}$
• $8>\sqrt{8}+\sqrt[3]{8}+\sqrt[4]{8}$
• $9>\sqrt{n}+\sqrt[3]{n}+\sqrt[4]{n},n\geq 9$
## A problem on functions
Find all pairs of real numbers (a,b) such that: f(x)= x2 + ax + b If q is a root of f(x) then q2-2 is also a root | 2013-12-05 01:34:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.4671015441417694, "perplexity": 1447.3496399368842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163037952/warc/CC-MAIN-20131204131717-00092-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-quotient-of-the-sum-of-3-and-a-number-and-6-is-less-than-2-and- | # How do you solve "quotient of the sum of 3 and a number and 6 is less than -2" and graph the solution on a number line?
Jul 10, 2017
$x < - 15$
#### Explanation:
A quotient is the answer to a division.
Let's add the required phrasing to the the statement.
The quotient of (the sum of 3 and a number) and (6) is (less than -2)
$\left(3 + x\right) \div 6 < - 2$ which is easier shown as :
$\frac{3 + x}{6} < - 2 \text{ } \leftarrow \times 6$
$3 + x < - 12$
$x < - 12 - 3$
$x < - 15$
On a number line graph this is shown as an open circle on -15 and an arrow extending to the left.
Any value less then $- 15$ is part of the solution. | 2020-02-19 10:15:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "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": 0.8813871145248413, "perplexity": 679.0372561702833}, "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-2020-10/segments/1581875144111.17/warc/CC-MAIN-20200219092153-20200219122153-00109.warc.gz"} |
https://economics.stackexchange.com/questions/42939/deriving-aggregate-output-from-labor-demand-and-supply | # Deriving aggregate output from labor demand and supply
I was reading the following paper:
http://eml.berkeley.edu//~moretti/growth.pdf
I got stuck at equation (7)
The firm's production function is $$Y_{i}=A_{i}L_{i}^{\alpha}K_{i}^{\eta}T_{i}^{1-\alpha-\eta}$$
Labor supply is $$W_{i}=V\frac{P_{i}^{\beta}}{Z_{i}}=V\frac{\bar{P_{i}}^{\beta}L_{i}^{\beta \gamma_{i}}}{Z_{i}}$$
Labor demand is $$L_{i}=(\frac{\alpha^{1-\eta}\eta^{\eta}}{R^{\eta}}\frac{A_{i}}{W_{i}^{1-\eta}})^{\frac{1}{1-\alpha-\eta}}T_{i}$$
The paper says that if we impose aggregate labor demand is equal to aggregate labor supply (normalized to one), then the aggregate output $$Y=\sum_{i}Y_{i}$$ is
$$Y=(\frac{\eta}{R})^{\frac{\eta}{1-\eta}}[\sum_{i}(A_{i}[\frac{\bar{Q}}{Q_{i}}]^{1-\eta})^{\frac{1}{1-\alpha-\eta}}T_{i}]^{\frac{1-\alpha-\eta}{1-\eta}}$$
This step looks drastic to me. How can the aggregate output be derived from the above conditions?
Use $$W_{i}=V \cdot \frac{P_{i}^{\beta}}{Z_{i}}=VQ_i$$, then $$L_{i}=\left(\frac{\alpha^{1-\eta} \eta^{\eta}}{R^{\eta}} \cdot \frac{A_{i}}{(V_{i} Q_{i})^{1-\eta}}\right)^{\frac{1}{1-\alpha-\eta}} \cdot T_{i}$$ and $$\sum L_i = {\left({\frac{\alpha}{V}}\right)}^{\frac{1-\eta}{1-\alpha-\eta}} {\left({\frac{\eta}{R}}\right)}^{\frac{\eta}{1-\alpha-\eta}} \sum\left(\frac{A_i}{Q_i^{1-\eta}}\right)^{\frac{1}{1-\alpha-\eta}}T_i = 1$$ $$\frac{V}{\alpha} = {\left({\frac{\eta}{R}}\right)}^{\frac{\eta}{1-\eta}} \left(\sum\left(\frac{A_i}{Q_i^{1-\eta}}\right)^{\frac{1}{1-\alpha-\eta}}T_i\right)^{\frac{1-\alpha-\eta}{1-\eta}}$$.
Use the FOC on labor, $$W_i=\alpha \frac{Y_i}{L_i}$$, then $$\sum Y_i = \frac{V}{\alpha}\sum L_iQ_i = \frac{V}{\alpha} \bar{Q}$$, and replace $$\frac{V}{\alpha}$$ with above equation then you get equation (7). | 2021-04-16 17:45:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 12, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8839653730392456, "perplexity": 1319.7475532266747}, "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-2021-17/segments/1618038088245.37/warc/CC-MAIN-20210416161217-20210416191217-00253.warc.gz"} |
https://www.physicsforums.com/threads/economics-elasticity-of-substitution-between-capital-and-labor.626716/ | Economics: Elasticity of substitution between capital and labor
1. Aug 9, 2012
Cinitiator
1. The problem statement, all variables and given/known data
Am I right or wrong on the following?
The more capital is needed to replace one unit of labor to attain the same production level, the lower the elasticity of substitution between capital and labor.
It can measure how productive the capital in question is, and/or how much has been invested given the condition of diminishing returns.
This is the way I understood this concept. However, I'm not completely sure that my understanding of it is right. If it isn't, please tell me.
2. Relevant equations
-
3. The attempt at a solution | 2017-08-17 10:18:32 | {"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": 0.8152912259101868, "perplexity": 637.9422677441356}, "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-2017-34/segments/1502886103167.97/warc/CC-MAIN-20170817092444-20170817112444-00528.warc.gz"} |
http://openstudy.com/updates/500e10f0e4b0ed432e10787e | • anonymous
Nicole spent $32 on shirts at the mall. She spent a total of$80 that day. What percentage of the total did she spend on shirts?
Mathematics
Looking for something else?
Not the answer you are looking for? Search for more explanations. | 2017-04-24 13:25:06 | {"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": 0.24849165976047516, "perplexity": 2691.187801096036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119361.6/warc/CC-MAIN-20170423031159-00402-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.projecteuclid.org/euclid.jdg/1324476750 | ## Journal of Differential Geometry
### Einstein spaces as attractors for the Einstein flow
#### Abstract
In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of $n + 1$-dimensional, spatially compact spacetimes, which generalizes the $k = -1$ Friedmann-Lemaître-Robertson-Walker vacuum spacetime. This work extends the result from Future complete vacuum spacetimes. The background spacetimes we consider are Lorentz cones over negative Einstein spaces of dimension $n \ge 3$.
We use a variant of the constant mean curvature, spatially harmonic (CMCSH) gauge introduced in Elliptic-hyperbolic systems and the Einstein equations. An important difference from the $3+1$ dimensional case is that one may have a nontrivial moduli space of negative Einstein geometries. This makes it necessary to introduce a time-dependent background metric, which is used to define the spatially harmonic coordinate system that goes into the gauge.
Instead of the Bel-Robinson energy used in Future complete vacuum spacetimes, we here use an expression analogous to the wave equation type of energy introduced in Elliptic-hyperbolic systems and the Einstein equations for the Einstein equations in CMCSH gauge. In order to prove energy estimates, it turns out to be necessary to assume stability of the Einstein geometry. Further, for our analysis it is necessary to have a smooth moduli space. Fortunately, all known examples of negative Einstein geometries satisfy these conditions. We give examples of families of Einstein geometries which have nontrivial moduli spaces. A product construction allows one to generate new families of examples.
Our results demonstrate causal geodesic completeness of the perturbed spacetimes, in the expanding direction, and show that the scale-free geometry converges toward an element in the moduli space of Einstein geometries, with a rate of decay depending on the stability properties of the Einstein geometry.
#### Article information
Source
J. Differential Geom., Volume 89, Number 1 (2011), 1-47.
Dates
First available in Project Euclid: 21 December 2011
https://projecteuclid.org/euclid.jdg/1324476750
Digital Object Identifier
doi:10.4310/jdg/1324476750
Mathematical Reviews number (MathSciNet)
MR2863911
Zentralblatt MATH identifier
1256.53035
#### Citation
Andersson, Lars; Moncrief, Vincent. Einstein spaces as attractors for the Einstein flow. J. Differential Geom. 89 (2011), no. 1, 1--47. doi:10.4310/jdg/1324476750. https://projecteuclid.org/euclid.jdg/1324476750 | 2019-12-12 09:41:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8427540063858032, "perplexity": 642.1566953779749}, "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-2019-51/segments/1575540542644.69/warc/CC-MAIN-20191212074623-20191212102623-00108.warc.gz"} |
https://mathoverflow.net/questions/280442/on-unstable-manifold-and-incidence-number-of-novikov-complex | # On unstable manifold and incidence number of Novikov complex
Novikov complex is an extension of Morse theory to (closed) Morse 1-form $\omega$, which is not necessarily exact. Suppose for simplicity, $\omega$ is in the integer cohomology class and the universal covering is infinite cyclic. Then $\omega$ can be lifted to the universal cover $\hat M$, i.e., $\pi^\star \omega=d\hat f$, for some Morse function $\hat f$ on $\hat M$. The Morse 1-form $\omega$ generalizes the Morse function and the zeros of $\omega$ take the place of the critical points of a Morse function. Indices of the zeros (or critical points) of $\omega$ can be defined similarly and we have the stable and unstable manifolds of a critical point. The incidence number between a pair of critical points respectively of index $k$ and $k-1$ of $\omega$ can be defined for a Morse-Smale pair $(\omega, g)$, where $g$ is a Riemann metric on $M$. One can lift the stable and unstable manifolds to $\hat M$ and define the corresponding incidence number in $\hat M$ similarly. One can also define the Novikov complex.
My question is: $\hat M$ is not compact and the unstable manifold (or the descending disc) of a critical point in $\hat M$ in general goes infinitely downwards. Also, for fixed $x$ in $\hat M$, it is possible that the incidence numbers between the critical points $x$ of index $k$ and $y$ of index $k-1$ in $\hat M$ are non-zero for infinitely many $y$. These are different from Morse theory on compact manifolds. Can someone give a (simple) example of an unstable manifold in $\hat M$ going infinitely downwards for some Morse 1-form? Maybe also an example of infinite number of non-zero incidence numbers? I am sorry that I pose the question rather imprecisely. | 2019-10-22 17:43:15 | {"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": 0.8786854147911072, "perplexity": 130.31768613286644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00269.warc.gz"} |
https://www.gradesaver.com/textbooks/science/chemistry/chemistry-9th-edition/chapter-3-stoichiometry-exercises-page-129/51 | ## Chemistry 9th Edition
a. $17.03$ grams b. $30.03$ grams
a. $NH_3$ Molar mass = $1*14.007+3*1.008=17.03$ grams b. $N_2H_4$ Molar mass = $2*14.007+2*1.008=30.03$ grams | 2018-09-26 12:19:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3997398018836975, "perplexity": 13249.008119776778}, "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/1537267164925.98/warc/CC-MAIN-20180926121205-20180926141605-00460.warc.gz"} |
https://www.physicsforums.com/threads/limit-problem.842926/ | # Limit problem
1. Nov 13, 2015
### geoffrey159
1. The problem statement, all variables and given/known data
Let $f$ be piecewise continuous from $[0,+\infty[$ into $V = \mathbb{R}$ or $\mathbb{C}$, such that $f(x) \longrightarrow_{ x\rightarrow +\infty} \ell$.
Show that $\frac{1}{x}\ \int_0^x f(t) \ dt \longrightarrow_{ x\rightarrow +\infty} \ell$
2. Relevant equations
Integration of asymptotic comparisons
3. The attempt at a solution
Can you tell me if this is correct please ?
Since $f - \ell = o_{+\infty}(1)$, and since $u: x \rightarrow 1$ is non-negative, piecewise continuous, and non-integrable on $[0,+\infty[$, then
$\int_0^x f(t) - \ell \ dt = o_{+\infty}(\int_0^x u(t) \ dt)$
which is the same as saying that $\int_0^x f(t) \ dt - x \ell = o_{+\infty}(x)$.
Multiplying left and right by $\frac{1}{x}$, I get that $\frac{1}{x}\ \int_0^x f(t) \ dt - \ell = o_{+\infty}(1)$ which proves that
$\frac{1}{x}\ \int_0^x f(t) \ dt \longrightarrow_{ x\rightarrow +\infty} \ell$.
Is this OK ?
2. Nov 13, 2015
### geoffrey159
Never mind, I've had confirmation. Thanks !
3. Nov 13, 2015
### Staff: Mentor
I think this is nicer notation: $\lim_{x \to \infty} f(x) = \ell$
My LaTeX script is $\lim_{x \to \infty} f(x) = \ell$
4. Nov 13, 2015
### HallsofIvy
Surely you meant "integrable" not "non-integrable" here?
5. Nov 13, 2015
### geoffrey159
:-) Ok thanks, I'll try to follow that notation in the future
No, why do you say that? $u = 1$ is non-integrable on $[0,+\infty[$ since $\int_0^x u(t) \ dt$ does not have a finite limit as $x$ tends to infinity. | 2018-02-24 02:38:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8596652746200562, "perplexity": 1297.3145033363821}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815034.13/warc/CC-MAIN-20180224013638-20180224033638-00727.warc.gz"} |
https://rpg.stackexchange.com/questions/62338/with-street-grimoire-out-are-there-more-ways-by-which-mystic-adepts-can-gain-pow | # With street grimoire out are there more ways by which mystic adepts can gain power points?
As mentioned here: How do mystic adepts gain power points in Shadowrun 5? mystic adepts can gain power points at character creation. Later on they can only gain them by not choosing a metamagic ability during an initiation.
With street grimoire out now are there additional ways / what are the ways now by which (mystic) adepts can gain power points after character creation?
• possible duplicate of How do mystic adepts gain power points in Shadowrun 5? – Thomas E. May 24 '15 at 8:43
• I just saw that there is a question that is essentially the same as mine (the question itself. The answer here though has a few more details to it): rpg.stackexchange.com/questions/27290/… – Thomas E. May 24 '15 at 8:44
• Updated the question so that it shouldn't be a complete duplicate any longer (saw that the other question was out before street grimoire came out so focused on that in the edit) – Thomas E. May 24 '15 at 9:49
• Following a way (Streetgrimoire p. 176ff) can reduce the cost of adept powers, which allows you to buy new ones; but the number of points you can reduce the costs sum up to at most MAG/4 | 2020-01-23 00:11:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26335278153419495, "perplexity": 2685.759781197894}, "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/1579250607596.34/warc/CC-MAIN-20200122221541-20200123010541-00178.warc.gz"} |
https://www.zora.uzh.ch/id/eprint/91829/ | # Amplitude analysis and branching fraction measurement of Bs->J/ψK+K-
LHCb Collaboration; et al; Bernet, R; Müller, K; Steinkamp, O; Straumann, U; Vollhardt, A (2013). Amplitude analysis and branching fraction measurement of Bs->J/ψK+K-. Physical Review D (Particles, Fields, Gravitation and Cosmology), 87(7):072004.
## Abstract
An amplitude analysis of the final state structure in the B¯¯¯0s→J/ψK+K− decay mode is performed using 1.0 fb−1 of data collected by the LHCb experiment in 7 TeV center-of-mass energy pp collisions produced by the LHC. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. Resonant structures are observed in the K+K− mass spectrum as well as a significant nonresonant S-wave contribution over the entire K+K− mass range. The largest resonant component is the ϕ(1020), accompanied by f0(980), f′2(1525), and four additional resonances. The overall branching fraction is measured to be B(B¯¯¯0s→J/ψK+K−)=(7.70±0.08±0.39±0.60)×10−4, where the first uncertainty is statistical, the second systematic, and the third due to the ratio of the number of B¯¯¯0s to B− mesons produced. The mass and width of the f′2(1525) are measured to be 1522.2±2.8+5.3−2.0 MeV and 84±6+10−5 MeV, respectively. The final state fractions of the other resonant states are also reported.
## Abstract
An amplitude analysis of the final state structure in the B¯¯¯0s→J/ψK+K− decay mode is performed using 1.0 fb−1 of data collected by the LHCb experiment in 7 TeV center-of-mass energy pp collisions produced by the LHC. A modified Dalitz plot analysis of the final state is performed using both the invariant mass spectra and the decay angular distributions. Resonant structures are observed in the K+K− mass spectrum as well as a significant nonresonant S-wave contribution over the entire K+K− mass range. The largest resonant component is the ϕ(1020), accompanied by f0(980), f′2(1525), and four additional resonances. The overall branching fraction is measured to be B(B¯¯¯0s→J/ψK+K−)=(7.70±0.08±0.39±0.60)×10−4, where the first uncertainty is statistical, the second systematic, and the third due to the ratio of the number of B¯¯¯0s to B− mesons produced. The mass and width of the f′2(1525) are measured to be 1522.2±2.8+5.3−2.0 MeV and 84±6+10−5 MeV, respectively. The final state fractions of the other resonant states are also reported.
## Statistics
### Citations
Dimensions.ai Metrics
38 citations in Web of Science®
57 citations in Scopus® | 2022-06-25 17:49:54 | {"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": 0.8255130052566528, "perplexity": 2591.0826129140696}, "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/1656103036077.8/warc/CC-MAIN-20220625160220-20220625190220-00311.warc.gz"} |
https://www.clutchprep.com/macroeconomics/average-propensity-to-consume-and-save | Clutch Prep is now a part of Pearson
Ch. 15 - Income and ConsumptionWorksheetSee all chapters
# Average Propensity to Consume and Save
See all sections
Sections
The Consumption Function
The Saving Function
Determinants of Consumption and Saving
Average Propensity to Consume and Save
Multiplier Effect of Investment Spending
Concept #1: Average Propensity to Consume and Save
Practice: If the Keynesian consumption function is C = 10 + 0.8 Yd then, when disposable income is $1000, what is the average propensity to consume? Practice: If the Keynesian consumption function is C = 10 + 0.8 Yd then, when disposable income is$1000, what is the marginal propensity to save? | 2022-06-27 06:32:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.46880781650543213, "perplexity": 13297.849582297173}, "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-2022-27/segments/1656103328647.18/warc/CC-MAIN-20220627043200-20220627073200-00610.warc.gz"} |
https://math.stackexchange.com/questions/357156/cycle-of-length | # Cycle of length
I'm learning permutations and came upon this question which made me freeze. So to say it in my own words, it asks that how many permutations in $S_n$ do not have a cycle of length one in their disjoint cycle notation. My guess at it would be just one but I don't know how to show it.
• Have you tried writing down all the permutations of $S_3$ as products of disjoint cycles? – Paul Gustafson Apr 10 '13 at 14:18
• Tough problem, if you are meeting it fresh. Look at the wikipedia article on Derangements. – André Nicolas Apr 10 '13 at 14:22
• @AndréNicolas I looked at Derangments but it confused me further. I can see the connection to a certain limit but Im not able to solve for this problem. – user65422 Apr 14 '13 at 23:48
• @user66345 Like this? $(a,b,c)=(a,c),(a,b)$ – user65422 Apr 15 '13 at 1:18 | 2019-08-17 10:49:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7766680121421814, "perplexity": 312.7155749588558}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027312128.3/warc/CC-MAIN-20190817102624-20190817124624-00140.warc.gz"} |
https://stats.stackexchange.com/questions/272397/prove-that-the-joint-density-of-independent-multivariate-normal-variables-is-a-m | # Prove that the joint density of independent multivariate normal variables is a matrix-normal
Let $X_1,...,X_n \sim N_p(\mu_i,\Sigma_i)$ be Multivariate Normal a.v. independent.
Show that $W = (X_1,...,X_n) \sim MN(M,\mathbb{I},\Sigma)$ where $M = [\mu_1 \mu_2...\mu_n]$ and $\mathbb{I}$ is the identity nxn.
The density of a matrix-normal variable with independent entries is $$p(W|M,\mathbb{I},\Sigma) =\frac{\exp\left(-\frac{1}{2}tr(\Sigma^{-1}(W-M)^T\mathbb{I}(W-M)\right))}{(2\pi)^{np/2}|\Sigma|^{n/2}}$$
Given that my variables $X_i$ are independent, the joint density will be the product of them, so:
$$f(W|M,\mathbb{I},\Sigma) =\prod^n_{i=1}\left\{\frac{1}{(2\pi)^{p/2}|\Sigma|^{1/2}}\exp\left[-\frac{1}{2}(X_i-\mu_i)^T\Sigma^{-1}(X_i-\mu_i)\right]\right\}$$ $$=\frac{1}{(2\pi)^{np/2}|\Sigma|^{n/2}}\exp\left[-\frac{1}{2}\sum_{i=1}^n(X_i-\mu_i)^T\Sigma^{-1}(X_i-\mu_i)\right]$$
Now, what I have to do is somehow turn the expression within the exp into a diagonal matrix in order to change the expression from a sum to the trace of a matrix. Any tips on how to do that? My professor suggested trying to use kronecker product in order to generate this matrix.
Easier ways to prove it or any books with the solution would also be really apreciated. Thanks in advance. | 2019-07-20 05:23:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.7303915619850159, "perplexity": 179.0036870988933}, "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/1563195526446.61/warc/CC-MAIN-20190720045157-20190720071157-00557.warc.gz"} |
https://askdev.io/questions/36912/what-am-i-missing-out-on-to-get-symlinks-to-collaborate-with | # What am I missing out on to get symlinks to collaborate with CIFS?
Circumstance
I have a brainless Ubuntu 10.10 RC box running a couple of solution applications on my residence network. I have a Windows 2008 Server organizing all my network shares and also disk drives. I am presently placing the network drives at boot - up making use of FSTAB with the adhering to alternatives set:
credentails=/etc/smbcredentials,. iocharset=utf8,uid=1000,gid=1000,file_mode=0777,dir_mode=0777,noserverino,sfu
Question
What alternative do I require to ready to get SYMLINKS to effectively register making use of CIFS? I need to confess the details in man mount.cifs does not appear to give a clear adequate definition of which alternatives I need to be making use of for correct assistance.
Trouble
When running RSYNC from the Ubuntu equipment to support picked folders to the Windows shares, it falls short attempting to recreate the SYMLINKS. I am worried that this will certainly create a trouble when later on attempting to recover these documents back need to I ever before require to.
0
2019-05-13 04:12:24
Source Share
Not certain, yet I are afraid that a cifs share, that in your instance is basically a folder on a ntfs dividing readily available via the network, can not take care of symbolic web links.
Various would certainly hold true if the cifs share were given by a samba web server on a linux equipment.
The remedy that enter your mind is:
• create a massive adequate documents on the share (with dd, as an example)
• create a ext4 filesystem on this documents
• mount the documents as a dividing photo, with - o loop
• usage this ext4 dividing as a location for your back-up
0
2019-05-17 16:50:26
Source | 2021-01-25 00:16:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31159377098083496, "perplexity": 4024.3858678450365}, "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-2021-04/segments/1610703561996.72/warc/CC-MAIN-20210124235054-20210125025054-00198.warc.gz"} |
http://www.math.md/en/publications/basm/issues/y2020-n1/13165/ | RO EN
On self-adjoint and invertible linear relations generated by integral equations
Authors: V. M. Bruk
Abstract
We define a minimal operator $$L_{0}$$ generated by an integral equation with an operator measure and prove necessary and sufficient conditions for the operator $$L_{0}$$ to be densely defined. In general, $$L^{*}_{0}$$ is a linear relation. We give a description of $$L^{*}_{0}$$ and establish that there exists a one-to-one correspondence between relations $$\widehat{L}$$ with the property $$L_{0}\!\subset\widehat{\!L}\!\subset \!L^{*}_{0}$$ and relations $$\theta$$ ente\-ring in boundary conditions. In this case we denote $$\widehat{L}=L_{\theta}$$. We establish conditions under which linear relations $$L_{\theta}$$ and $$\theta$$ together have the following properties: a linear relation $$(l.r)$$ is self-adjoint; $$l.r$$ is closed; $$l.r$$ is invertible, i.e., the inverse relation is an operator; $$l.r$$ has the finite-dimensional kernel; $$l.r$$ is well-defined; the range of $$l.r$$ is closed; the range of $$l.r$$ is a closed subspace of the finite codimension; the range of $$l.r$$ coincides with the space wholly; $$l.r$$ is continuously invertible. We describe the spectrum of $$L_{\theta}$$ and prove that families of linear rela\-tions $$L_{\theta(\lambda)}$$ and $$\theta(\lambda)$$ are holomorphic together.
Saratov State Technical University
77, Politehnicheskaja str., Saratov 410054
Russia
E-mail:
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https://homework.zookal.com/questions-and-answers/find-the-linear-approximation-of-fx--x14-at-x-945169186 | 1. Math
2. Calculus
3. find the linear approximation of fx x14 at x...
# Question: find the linear approximation of fx x14 at x...
###### Question details
Find the linear approximation of f(x) = x1/4 at x = 625 and use this to get an estimate for 4√610. | 2021-03-01 10:24:43 | {"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": 0.9195887446403503, "perplexity": 3010.3685086539635}, "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/1614178362481.49/warc/CC-MAIN-20210301090526-20210301120526-00176.warc.gz"} |
https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=19188&extra=longdesc_idm46461545336336&clicked=1 | This shows a rectangle. The lengths of the sides are marked as 5 m, 4 m, 5 m, and 4 m, working clockwise around the figure starting at the top edge.
2 Perimeters | 2021-02-26 15:19:18 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9167624115943909, "perplexity": 618.8324054219437}, "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/1614178357929.4/warc/CC-MAIN-20210226145416-20210226175416-00442.warc.gz"} |
http://math.stackexchange.com/questions/166560/how-is-i-0-inftyt-defined | # How is $I_{[0,\infty)}(t)$ defined?
How is $I_{[0,\infty)}(t)$ defined? This must be a notation in probabilty theory.
-
It's likely an indicator function: it has value 1 on $[0,\infty)$ and 0 on $(-\infty,0)$. – David Mitra Jul 4 '12 at 12:55
Although indicator functions come up in probability, it doesn't seem that an indicator over an infinite interval would come up. – Michael Chernick Jul 4 '12 at 15:26
You can use the Heaviside Step Function $H(t)$:
$H(0) = 1$ is used when $H$ needs to be right-continuous. For instance cumulative distribution functions are usually taken to be right continuous, as are functions integrated against in Lebesgue–Stieltjes integration. In this case $H$ is the indicator function of a closed semi-infinite interval: $$H(t) = \mathbf{I}_{[0,\infty)}(t).\,$$
...or one could use Iverson brackets as well: $[t \geq 0]$. – J. M. Aug 9 '12 at 10:49 | 2016-07-24 05:16:59 | {"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": 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": 0.8997180461883545, "perplexity": 531.9855047692052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823947.97/warc/CC-MAIN-20160723071023-00305-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3065530/the-expected-value-of-beta-function | The expected value of Beta Function
Estimate the probability of success
Suppose I send 10 tasks to my machine. 6 out of 10 tasks success, and 4 failed. These outcomes is summarized by $$X$$ as a binary variable, 1 is task success, and 0 if task fail. We know that $$X$$ is continuous random variable
The expected value of a continuous random variable is dependent on the probability density function used to model the probability that the variable will have a certain value. Therefor, I exploit Beta distribution to estimate the probability of success for next tasks. I will $${\alpha}$$ as input of the number past success tasks and $${\beta}$$ as the number of past fail tasks
Expected value
$$$$E(x) = \frac{\alpha+1}{\alpha+\beta+2}$$$$
In my example, $$\alpha = 6$$ and $$\beta = 4$$. Thus, the $$E(x)$$ = 0.58.
Does every think looks good? | 2019-06-16 21:10:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 8, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.8516888618469238, "perplexity": 541.2323676835917}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998298.91/warc/CC-MAIN-20190616202813-20190616224813-00130.warc.gz"} |
https://ncatlab.org/nlab/show/arithmetic+D-module | # Contents
## Idea
The theory of arithmetic D-modules was primarily developped by Berthelot to better understand the functoriality properties of rigid cohomology. It gives a theory of coefficients for the cohomology of quasi-projective algebraic varieties over finite fields that are stable by the six Grothendieck operations, after Kedlaya and Caro. This allows a purely p-adic proof of Deligne’s Weil II theorem, that generalized the Riemann hypothesis over finite fields to the category of coefficients for cohomology (i.e., motivic sheaves).
## References
Revised on February 16, 2014 08:11:54 by Urs Schreiber (89.204.155.248) | 2017-02-19 14:19:09 | {"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": 0.8008359670639038, "perplexity": 1029.9389615352463}, "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/1487501169776.21/warc/CC-MAIN-20170219104609-00332-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://www.julia-harz.de/publication/harz-theoretical-2016/ | # Theoretical uncertainty of the supersymmetric dark matter relic density from scheme and scale variations
### Abstract
For particle physics observables at colliders such as the LHC at CERN, it has been common practice for many decades to estimate the theoretical uncertainty by studying the variations of the predicted cross sections with a priori unpredictable scales. In astroparticle physics, this has so far not been possible, since most of the observables were calculated at Born level only, so that the renormalization scheme and scale dependence could not be studied in a meaningful way. In this paper, we present the first quantitative study of the theoretical uncertainty of the neutralino dark matter relic density from scheme and scale variations. We first explain in detail how the renormalization scale enters the tree-level calculations through coupling constants, masses and mixing angles. We then demonstrate a reduction of the renormalization scale dependence through one-loop SUSY-QCD corrections in many different dark matter annihilation channels and enhanced perturbative stability of a mixed on-shell/$barrm DR$ renormalization scheme over a pure $barrm DR$ scheme in the top-quark sector. In the stop-stop annihilation channel, the Sommerfeld enhancement and its scale dependence are shown to be of particular importance. Finally, the impact of our higher-order SUSY-QCD corrections and their scale uncertainties are studied in three typical scenarios of the phenomenological Minimal Supersymmetric Standard Model with eleven parameters (pMSSM-11). We find that the theoretical uncertainty is reduced in many cases and can become comparable to the size of the experimental one in some scenarios.
Type
Publication
Physical Review D | 2021-03-06 05:47:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6374918222427368, "perplexity": 683.8731100580949}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374391.90/warc/CC-MAIN-20210306035529-20210306065529-00027.warc.gz"} |
https://zbmath.org/?q=an:1129.53302 | ## On Chen invariant of CR-submanifolds in a complex hyperbolic space.(English)Zbl 1129.53302
Recently B. Y. Chen [Jap. J. Math., New Ser. 26, No. 1, 105–127 (2000; Zbl 1026.53009)] introduced an invariant for a Riemannian manifold and obtained a sharp inequality between his invariant and the squared mean curvature for a CR-submanifolds $$M$$ in real spaceforms.
In the present paper, by applying the Chen invariant the author has obtained some interesting new results for CR-submanifolds which satisfy $\delta(n_1, ...,n_k) = c(n_1, ..., n_k)H^2 - b(n_1, ..., n_k) -3n + \frac{3}{2} \Sigma^k_{i = 1} n_i$ where $$\delta (n_1, ..., n_k)$$ and $$H^2$$ are the Chen invariant and the square of the mean curvature of $$M$$.
### MSC:
53C40 Global submanifolds
### Keywords:
submanifold; complex hyperbolic space; invariants
Zbl 1026.53009
Full Text: | 2022-07-06 10:33:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7123879790306091, "perplexity": 1052.0111879444057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104669950.91/warc/CC-MAIN-20220706090857-20220706120857-00075.warc.gz"} |
https://www.physicsforums.com/threads/light-and-relativity.363050/ | # Light and Relativity
1. Dec 13, 2009
### Dragohunter
2 questions
Does light have a frame of reference?
Although there is no speed greater than c, can it be said that the change in distance between two identifiable objects changed at a rate greater than c?
For example one person I know said this:
Last edited: Dec 13, 2009
2. Dec 13, 2009
### bcrowell
Staff Emeritus
Are you asking whether it's possible to have a frame of reference that's moving along with a beam of light? If so, then the answer is no. For example, the $\gamma$ factor linking this frame to the frame of any material object would be infinite.
Your friend is correct. What's forbidden by relativity is much more specific. For example, suppose you have an observer who takes measurements in a certain reference frame. Relativity forbids a particle from whizzing right past the observer's location at a speed greater than c. It doesn't forbid distant objects from moving at greater than c relative to the observer. For example, you can say that galaxies beyond the edge of the observable universe are moving away from us at greater than c; however, it's impossible for us to observe those galaxies. | 2018-03-21 13:07:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3748804032802582, "perplexity": 434.6575174328328}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647649.70/warc/CC-MAIN-20180321121805-20180321141805-00280.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=Fermat%27s_Last_Theorem&diff=next&oldid=5095 | # Difference between revisions of "Fermat's Last Theorem"
Fermat's Last Theorem is a long-unproved theorem stating that for non-zero integers $\displaystyle a,b,c,n$ with $n \geq 3$, there are no solutions to the equation: $\displaystyle a^n + b^n = c^n$
## History
Fermat's last theorem was proposed by Pierre Fermat in the margin of his book Arithmetica. The note in the margin (when translated) read: "It is impossible for a cube to be the sum of two cubes, a fourth power to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain." Despite Fermat's claim that a simple proof existed, the theorem wasn't proven until Andrew Wiles did so in 1993. Interestingly enough, Wiles's proof was much more complicated than anything Fermat could have produced himself. | 2021-03-01 14:10:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7989507913589478, "perplexity": 392.924416910229}, "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/1614178362513.50/warc/CC-MAIN-20210301121225-20210301151225-00425.warc.gz"} |
https://socratic.org/questions/how-do-empirical-formulas-and-molecular-formulas-differ | # How do empirical formulas and molecular formulas differ?
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$.
SMARTERTEACHER
Jan 18, 2014
The empirical formula represents the ratio of atoms in a molecule in lowest terms, while the molecular formula is the actual atom number in the molecule.
For instance, carbohydrates have an empirical formula of $C {H}_{2} O$, while the carbohydrate glucose has a molecular formula of ${C}_{6} {H}_{12} {O}_{6}$ and the sugar ribose found in RNA has a molecular formula of ${C}_{5} {H}_{10} {O}_{5}$
Water has an empirical formula of ${H}_{2} O$ which is the same as the molecular formula, but hydrogen peroxide whose molecular formula is ${H}_{2} {O}_{2}$, it has an empirical formula of $H O$. | 2019-04-19 10:36:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 54, "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": 0.8460046052932739, "perplexity": 921.479236461569}, "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/1555578527566.44/warc/CC-MAIN-20190419101239-20190419123239-00344.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=130&t=59290 | ## Irreversible reactions and temperature
$\Delta U=q+w$
Jessica Li 4F
Posts: 115
Joined: Fri Aug 09, 2019 12:16 am
### Irreversible reactions and temperature
Can you have an irreversible reaction that involves no change in temperature or delta U, or could you have a reaction at constant temperature but a nonzero value for delta U?
For instance, 4.17 is at constant temperature but delta U does not equal to 0.
Angela Patel 2J
Posts: 110
Joined: Sat Aug 24, 2019 12:17 am
### Re: Irreversible reactions and temperature
It is possible to have a reaction where the temperature change is 0 but delta U is constant. Work and heat both affect temperature, so if their effects on temperature cancel out you could technically have a situation where there is no temp. change.
005324438
Posts: 51
Joined: Sat Aug 24, 2019 12:16 am
### Re: Irreversible reactions and temperature
An example of this would be solid vs liquid of the same material. Inputting energy into the system will make the solid turn to liquid, but they can be the same temperature.
705302428
Posts: 50
Joined: Sat Aug 24, 2019 12:16 am
### Re: Irreversible reactions and temperature
Yes it is possible. | 2020-08-09 09:30:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6032863259315491, "perplexity": 2705.4376411704407}, "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/1596439738523.63/warc/CC-MAIN-20200809073133-20200809103133-00092.warc.gz"} |
https://docs.opengosim.com/manual/input_deck/thermodynamic_props/eos_water/ | # EOS WATER¶
Defines the water properties such as density, viscosity and enthalpy, and the surface density. For example:
EOS WATER
SURFACE_DENSITY 1000.0 kg/m^3
END
The above is the minimum required input, where the surface density is specified, while the other properties are defaulted to use standard water tables, IFC67.
When the GAS_WATER mode is used, the water viscosity is modelled by default with the Batzle and Wang correlation to account for brine salinity.
The following modelling options are available for the water properties:
Different type of models can be selected for different properties, however mixed selections should be assessed carefully. Properties for which no models have been selected will default to the IFC67 water tables.
## SURFACE_DENSITY specification of water surface density¶
This keyword specifies the density of the aqueous phase at surface conditions. This may include any dissolved salts and the effect of the surface temperature. The surface density value is used to convert fluid flows in the reservoir into surface volume flows. Surface volumes are used to specify required well rates with targets like TARG_WSV, and surface volume rates and totals are reported in the Mass file and in the Eclipse files. The surface density must be entered or the software will return an error. The density units are optional, if not entered are defaulted to kg/m^3.
An example is:
SURFACE_DENSITY 1004.2 kg/m^3 | 2021-07-25 09:00:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5231271386146545, "perplexity": 2592.636540193969}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151641.83/warc/CC-MAIN-20210725080735-20210725110735-00082.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/in-corner-rectangular-field-dimensions-35m-22-m-well-14-m-inside-diameter-dug-8-m-deep-earth-dug-out-spread-evenly-over-remaining-part-concept-of-surface-area-volume-and-capacity_75209 | # In a Corner of a Rectangular Field with Dimensions 35m × 22 M, a Well with 14 M Inside Diameter is Dug 8 M Deep. the Earth Dug Out is Spread Evenly Over the Remaining Part - Mathematics
Sum
In a corner of a rectangular field with dimensions 35m × 22 m, a well with 14 m inside diameter is dug 8 m deep. The earth dug out is spread evenly over the remaining part of the field. Find the rise in the level of the field.
#### Solution
We have,
Length of the field, l = 35 m,
Width of the field, b = 22 m,
Depth of the well, H = 8 m and
Radius of the well, "R" = 14/7 = 7 "m"
Let the rise in the level of the field be h.
Now,
Volume of the earth on remaining part of the field = Volume of earth dug out
⇒ Area of the earth on remaining part of the field = Volume of earth
⇒ (Area of the field - Area of base of the well ) × h = πR2H
⇒ (lb - πR2) × h = πR2
rArr (35xx22-22/7xx7xx7)xx"h" =22/7xx7xx7xx8
⇒ (770 - 154) × h = 1232
⇒ 616 × h = 1232
⇒ "h" = 1232/616
∴ h = 2 m
So, the rise in the level of the field is 2 m.
Is there an error in this question or solution?
#### APPEARS IN
RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise 19B | Q 32 | Page 900 | 2021-04-15 13:59:22 | {"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": 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": 0.7663766145706177, "perplexity": 1474.4211426644931}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038085599.55/warc/CC-MAIN-20210415125840-20210415155840-00144.warc.gz"} |
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https://www.clutchprep.com/physics/practice-problems/142436/assume-the-following-waves-are-propagating-in-aira-calculate-the-wavelength-1-fo | What is an Electromagnetic Wave? Video Lessons
Concept
# Problem: Assume the following waves are propagating in aira) Calculate the wavelength λ1 for gamma rays of frequency f1 = 6.30×1021 Hz.b) Calculate the wavelength λ2 for visible light of frequency f2 = 5.40×1014 Hz.
###### FREE Expert Solution
The wavelength for a wave propagating in air is given by:
$\overline{){\mathbf{\lambda }}{\mathbf{=}}\frac{\mathbf{c}}{\mathbf{f}}}$, where c is the speed of light and f is the frequency of the wave propagation.
79% (65 ratings)
###### Problem Details
Assume the following waves are propagating in air
a) Calculate the wavelength λ1 for gamma rays of frequency f1 = 6.30×1021 Hz.
b) Calculate the wavelength λ2 for visible light of frequency f2 = 5.40×1014 Hz. | 2021-04-16 07:40:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8342364430427551, "perplexity": 1034.4028125980844}, "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-2021-17/segments/1618038088731.42/warc/CC-MAIN-20210416065116-20210416095116-00625.warc.gz"} |
https://www.researching.cn/articles/OJ5491be97ccbad667 | Search by keywords or author
• Chinese Optics Letters
• Vol. 20, Issue 9, 091602 (2022)
Yu Cao, Li Chong, Ke-Hui Wu, Lu-Qian You, Sen-Sen Li, and Lu-Jian Chen*
Author Affiliations
• Department of Electronic Engineering, School of Electronic Science and Engineering, Xiamen University, Xiamen 361005, China
• show less
Yu Cao, Li Chong, Ke-Hui Wu, Lu-Qian You, Sen-Sen Li, Lu-Jian Chen. Dynamic coloration of polymerized cholesteric liquid crystal networks by infiltrating organic compounds[J]. Chinese Optics Letters, 2022, 20(9): 091602 Copy Citation Text show less
Abstract
We demonstrate the dynamic coloration of polymerized cholesteric liquid crystal (PCLC) networks templated by the “wash-out/refill” method in the presence of organic compounds. The reflection colors were modulated by two key approaches, that is, the injection of mutually soluble organic fluids into a microfluidic channel and the diffusion of volatile organic compounds (VOCs). The reversible tuning of reflected colors with central wavelengths between $∼450 nm$ and $∼600 nm$ was achieved by alternative injection of nematic liquid crystal E7 (nav = 1.64) and benzyl alcohol (n = 1.54) using syringe pumps. The fascinating iridescence with reflection centers from $∼620 nm$ to $∼410 nm$ was presented from the volatilization and diffusion of alcohol as a model VOC. Additionally, the flow velocity of fluid and the diffusion time were adjusted to explore the underlying mechanism for the dynamic coloration of cholesteric networks. This work is expected to extend the study of PCLCs as a dynamically tunable optofluidic reflector, visually readable sensor, or compact anti-counterfeit label in response to organic compounds.
1. Introduction
During the past few decades, cholesteric liquid crystals (CLCs) with intrinsic helical configuration of molecular directors have great perspectives towards a wide range of advanced photonic applications such as brightness-enhancement devices of liquid crystal (LC) displays, diffractive optical elements, smart windows, mirrorless lasers, and sensors[15]. Thanks to the Bragg reflection of CLCs, which confers nontrivial optical functionalities, significant structural color can be generated to reflect circularly polarized (CP) light with identical handedness in the visible spectrum. In general, the colors of CLCs, exhibited by the selective reflection wavelength, depend on the helical pitch length ($p$) or/and the average refractive index (average RI, $nav$)[68] in response to the external stimuli, such as temperature, electric field, and light irradiation. Also, some organic compounds can be incorporated into CLCs to alter the optical properties directly. The molecular structure of CLCs can be further modified with recognition fragments and utilized to absorb specific analytes. The uptake of specific analytes will affect $p$ and $nav$ and reveal different reflected colors consequently[911]. This feature is beneficial for the detection of volatile samples such as alcohol, amine, and acetone[1214], providing a versatile sensing platform with several advantages like low cost, being power-free, and naked-eye detection.
Copy Citation Text
Yu Cao, Li Chong, Ke-Hui Wu, Lu-Qian You, Sen-Sen Li, Lu-Jian Chen. Dynamic coloration of polymerized cholesteric liquid crystal networks by infiltrating organic compounds[J]. Chinese Optics Letters, 2022, 20(9): 091602 | 2022-06-25 01:58:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "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": 0.3668203353881836, "perplexity": 8081.021800876956}, "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/1656103033925.2/warc/CC-MAIN-20220625004242-20220625034242-00161.warc.gz"} |
https://homework.cpm.org/category/CON_FOUND/textbook/mc1/chapter/6/lesson/6.1.1/problem/6-4 | ### Home > MC1 > Chapter 6 > Lesson 6.1.1 > Problem6-4
6-4.
On grid paper:
• Draw a square that measures $5$ units on each side.
• Draw a design inside your $5×5$ square.
• Then draw a square that measures $15$ units on each side.
• Enlarge your picture as accurately as possible so that it fits inside of the $15 × 15$ square.
How much wider and how much longer is your new picture?
A simple design will be easiest to enlarge.
How much longer is a $15$ unit number line than a $5$ unit number line? | 2023-02-05 18:21:20 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "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": 0.43649783730506897, "perplexity": 1970.1770628240195}, "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/1674764500273.30/warc/CC-MAIN-20230205161658-20230205191658-00183.warc.gz"} |
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1831 | ## On Geometric Ergodicity of CHARME Models
• In this paper we consider a CHARME Model, a class of generalized mixture of nonlinear nonparametric AR-ARCH time series. We apply the theory of Markov models to derive asymptotic stability of this model. Indeed, the goal is to provide some sets of conditions under which our model is geometric ergodic and therefore satisfies some mixing conditions. This result can be considered as the basis toward an asymptotic theory for our model.
$Rev: 13581$ | 2016-05-29 19:29:49 | {"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": 0.5525369644165039, "perplexity": 392.4398344267837}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281876.4/warc/CC-MAIN-20160524002121-00238-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://www.cje.net.cn/CN/abstract/abstract19983.shtml | • 研究报告 •
### 基于突变级数法的广东省资源环境承载力动态
1. (1广州大学地理科学学院， 广州 510006； 2广东省地理国情监测与综合分析工程技术研究中心， 广州 510006)
• 出版日期:2019-06-10 发布日期:2019-06-10
### Dynamics of resource and environment carrying capacity of Guangdong Province based on catastrophe progression method.
SUN Duan1,2, CHEN Ying-biao1,2*, CAO Zhen1,2, HU Ying-long1,2
1. (1College of Geographical Sciences, Guangzhou University, Guangzhou 510006,China; 2Guangdong Province Engineering Technology Research Center for Geographical Condition Monitoring and Comprehensive Analysis, Guangzhou 510006, China).
• Online:2019-06-10 Published:2019-06-10
Abstract: The carrying capacity of resources and environment is important basis for sustainable development. Effective evaluation of carrying capacity of resources and environment is of great significance to the construction of ecological civilization society. Based on catastrophe progression method in catastrophe theory, we used 14 evaluation indices from four aspects of economy, society, resources and environment to evaluate the carrying capacity of urban comprehensive resources and environment of 21 prefecturelevel cities in Guangdong Province from 2000 to 2015. The results showed that in the 15 years, the index of comprehensive resources and environmental carrying capacity of Guangdong Province slightly decreased on the whole. Guangdong gradually changed from a high bearingcapacity province in most areas to a relatively high comprehensive bearing capacity index in the Pearl River Delta region and relatively weak comprehensive bearing capacity in Dongguan and Shenzhen. Each subsystem had different influence on the comprehensive carrying capacity of the city. The composite system of resources and environment is the supporting foundation of carrying capacity, while the composite system of economy and society is the powerful guarantee of carrying capacity. Among all cities, Jiangmen, Shantou, Huizhou and Foshan had the highest comprehensive carrying capacity index of resources and environment, indicating that the more balanced the economic level and resources and environment, the higher the comprehensive carrying capacity of cities. The bearing capacity index of each subsystem changed with different forms. The economic subsystem highlighted the status of urban economic development. The higher the economic level, the higher the carrying capacity, the smaller the overall growth pattern. Due to the aggravation of floating population, the carrying capacity index of the social subsystem declined slightly. Based on the premise of relative stability of resources, the carrying capacity index of resource subsystem was relatively stable. The carrying capacity index of environmental subsystem showed a downward trend due to environmental pollution. Spatially, the differences of bearing capacity index of the subsystems in Guangdong were significant. The index of carrying capacity of economic and social composite system was basically matched with the economic development level of each city. Meanwhile, the index of carrying capacity of the composite system of resources and environment was roughly consistent with the topography of Guangdong, with the index being high in eastern and western Guangdong, and gradual decline in the Pearl River Delta in Dongguan and Shenzhen. | 2022-01-21 19:47:26 | {"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": 0.5293475389480591, "perplexity": 3485.0012378625747}, "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-2022-05/segments/1642320303709.2/warc/CC-MAIN-20220121192415-20220121222415-00166.warc.gz"} |
http://newartisans.com/2007/11/ready-lisp-for-os-x-leopard/ | Lost in Technopolis
by John Wiegley
# Ready Lisp for OS X Leopard
Posted by John Wiegley on November 9, 2007 with labels: SBCL, SLIME
After upgrading my system to Leopard this weekend, I decided to refresh Ready Lisp as well. It now contains both 32-bit and 64-bit builds of SBCL (which has been bumped to 1.0.11), so if you have a Core 2 Duo machine, you’ll be running Lisp at full 64-bit! Alas, Emacs itself cannot support 64-bit as a Carbon app, because there are no 64-bit Carbon libraries. SLIME has also been updated, to CVS latest as of today. Aquamacs is still the same version at 1.2a.
I did spend several hours trying to build a fully Universal package that would run on PowerPC as well (I have a PowerBook G4 in addition to this MacBook Pro), but it seems Leopard has broken the PowerPC port of SBCL. Some of the core OS structures have changed, such as os_context_t.
Ready Lisp is now being versioned according to the SBCL version it contains, which makes today’s release ReadyLisp-1.0.11-10.5-x86.dmg. The older version, which still works on 10.4, can be downloaded here.
NOTE: The recent loading bug for Leopard users has been fixed. Please re-download. Also, it still does not work on OS X 10.4 (Tiger) at the moment. I will have to create a separate build of SBCL for that version this weekend. | 2015-10-10 19:40:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24036988615989685, "perplexity": 4340.896726409309}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737962531.78/warc/CC-MAIN-20151001221922-00040-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://openstudy.com/updates/4dded6b1ee2c8b0bc3ee45e8 | ## anonymous 5 years ago The formula V=pie r^2h represents the volume of a cylinder where V represents the volume, r represents the radius of the base of the cylinder, and h represents the height of the cylinder. Solve this formula for h. Show all work.
$V=\pi r^2 h$ $h=\frac{V}{\pi r^2}$ | 2017-01-20 20:46:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.918541669845581, "perplexity": 542.2586693422169}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280872.69/warc/CC-MAIN-20170116095120-00470-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1504347/is-there-a-general-formula-to-compute-the-number-of-integer-solutions-of-an-equa | # Is there a general formula to compute the number of integer solutions of an equation?
recently, I asked a question concerning the number of solutions of a diophantine equation that used the rounding function. This question, however, dealt with a linear function, and I was wondering if the method or the answer could be generalized to include larger families of functions. I was trying to use the same technique given to me in the answer of that question to solve: $$\lceil x(\ln (x \ln x))\rceil+ \lceil y(\ln (y \ln y))\rceil = N$$ However, I do not think the same method can be applied, given that this equation is non linear. I have tried but I got stuck in the spot with the minimums and maximums. Is there a function $f(N)$ that counts how many integer solutions this equation has?
Furthermore, is there a function $f(g(x),m,N)$ that counts the number of integer solutions of the following equation? $$\sum_{i=1}^m g(x_i)=N$$
• You know the study of integer or rational solutions of diophantine equations is the major motivating force behind much of modern number theory and arithmetic geometry right? After all, Fermat's last theorem was only settled in the last 20 years and studies solutions to $x^n + y^n = z^n$ (for some fixed $n$). Pretty much as soon as you start considering nonlinear equations you go from linear algebra (easy) to algebraic geometry (hard). I'm sure estimates exist for certain types of equations, but there is pretty much nothing that can be said of nonlinear equations in general – oxeimon Oct 30 '15 at 0:50
• @oxeimon alright, so forget the last part of the question, what about the first? Is there an answer to the question regarding the first equation? – Guacho Perez Oct 30 '15 at 1:00
• @WillJagy why does anyone want to know anything in mathematics? :) – Guacho Perez Oct 30 '15 at 2:04
## 1 Answer
Of course there is such a function: you just defined it. The question is whether there is an algorithm for computing this function.
In general there is no way to tell whether a polynomial Diophantine equation (in several variables) has any solutions: see Hilbert's 10th Problem.
In your case, because the left side is greater than $x + y$ for $x, y \ge 3$, any solution must have $x + y \le N$, so there are only finitely many possibilities to try.
• And are there any methods to be used so I can find an explicit formula or even an algorithm? Maybe even properties of the function, i.e. bounds, asymptotes, etc.? Are there some books I can refer to? – Guacho Perez Oct 30 '15 at 2:05 | 2021-03-02 10:57:24 | {"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": 0.7340121865272522, "perplexity": 126.30563841285931}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363809.24/warc/CC-MAIN-20210302095427-20210302125427-00256.warc.gz"} |
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