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https://chemistry.stackexchange.com/questions/75396/why-add-acid-to-rid-of-soluble-carbonate-or-hydroxide-impurities-will-it-not-al | # Why add acid to rid of soluble carbonate or hydroxide impurities? Will it not also react with halide I'm testing for
When identifying metal halides with silver ions, the positive ion $\ce{Ag+}$ will form $\ce{AgX}$ with halide in a solution. However, $\ce{H+}$ is added (typically in the form of an acid like $\ce{HNO3}$) to solution to get rid of $\ce{OH-}$ and $\ce{CO3^{2-}}$ ions first. Will the $\ce{H+}$ not also react with the halide $\ce{X-}$?
Hydrogen halides are strong acids, meaning that their conjugate bases $\ce{X-}$ are extremely weak. Thus, adding $\ce{H+}$ will neutralize stronger bases such as $\ce{OH-}$ first before $\ce{X-}$. | 2019-07-21 06:56:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6663104891777039, "perplexity": 2399.689378819202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1563195526931.25/warc/CC-MAIN-20190721061720-20190721083720-00521.warc.gz"} |
https://mathoverflow.net/questions/214830/extension-by-zero-in-sobolev-spaces/214833 | # Extension by zero in Sobolev spaces
Let $\Omega$ be an open bounded set of $R^n$, and let $\omega$ be an open subset of $\Omega$ s.t $\overline{\omega} \subset \Omega.$
For $f\in H_0^1(\omega)$, it is known that the extension of $f$ to $\Omega$ by $0$ is an element of $H_0^1(\Omega).$
I wonder if the result remains true when we replace $H_0^1$ with $H_0^1\cap H^2$.
It does not remain true. If $\omega=B(0,1)$ and $\Omega=B(0,2)$ and $f(x)=1-|x|^2$, then $f\in H^1_0(\omega)\cap H^2(\omega)$ but the extension by zero is not in $H^2(\Omega)$. | 2019-04-23 12:51:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9133818745613098, "perplexity": 31.438010304811165}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578602767.67/warc/CC-MAIN-20190423114901-20190423140901-00312.warc.gz"} |
https://pos.sissa.it/396/293/ | Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
An update on QCD+QED simulations with C* boundary conditions
J. Luecke*, L. Bushnaq, I. Campos, M. Catillo, A. Cotellucci, M.E.B. Dale, P. Fritzsch, M.K. Marinkovic, A. Patella and N. Tantalo
Full text: pdf
Pre-published on: May 16, 2022
Published on:
Abstract
We present two novelties in our analysis of fully dynamical QCD+QED ensembles with C* boundary conditions. The first one is the explicit computation of the sign of the Pfaffian. We present an algorithm that provides a significant speedup compared to traditional methods. The second one is a reweighting of the mass in the context of the RHMC. We have tested the techniques on both pure QCD and QCD+QED ensembles with pions at $m_{\pi^\pm}\approx400$ MeV, a lattice spacing of $a\approx0.05$ fm, a fine-structure constant of $\alpha_{\mathrm{R}}=0$ and $0.04$.
DOI: https://doi.org/10.22323/1.396.0293
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2022-06-28 05:37:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.334401398897171, "perplexity": 1830.6569644033973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103355949.26/warc/CC-MAIN-20220628050721-20220628080721-00089.warc.gz"} |
https://lifemath.wordpress.com/2007/05/12/on-the-size-of-shoe-racks/ | # On the size of shoe racks
On a web discussion board, I conjectured the following:
The diversity of the size of women’s shoe-racks can be expressed in mathematical fashion as a distribution of a particular form, called a “power law“, meaning that the probability of a woman’s shoe-rack attaining a certain size $x$ is proportional to $(1/x)^y$, where $y \ge 1$.
When a distribution of some property has a power law form, the system looks the same at all length scales. Therefore, if one were to look at the distribution of rack-sizes for one arbitrary range, say, just racks with 100 to 1000 shoes, it would look the same as for a different range, say, 1 to 10 shoes. In other words, “zooming” in or out in the distribution, one keeps obtaining the same result. It also means that if one can determine the distribution of shoes per rack for a range of shoes, one can then predict the distribution for many other ranges.
Equally interesting, power law distributions have very long tails, meaning there is a non-zero probability of finding racks extremely large compared to the average. This finite probability of finding large racks is quite striking and can be illustrated by the example of the heights of individuals following the familiar normal distribution. It would be very surprising to find someone measuring two or three times the average human height of 5’10”. On the other hand, a power law distribution makes it possible to find a rack many times larger than average. Power laws also imply that the system’s average behavior is not typical. A typical size is one that is encountered most frequently; the average is the sum of all the sizes divided by the number of women. If one were to select a group of shoe-racks at random and count the number of shoes in each of them, the majority would be smaller than average.
A similar analysis can be carried out for women’s cloth cupboards, with $y \in [3, \infty)$.
Men don’t have shoe-racks! So an analogy between the show-rack size and the size of the cupboard would not be possible. But here is one fact that gives you the basic idea: I’ve two pairs of jeans, one is torn at several places. I have a few Ts, a few bought and a few won in different competitions held at my place. Apart from these prized possessions, I also have a couple of shorts and a track suite, a couple of towels, a few pairs of rotten socks and a few undies. | 2017-06-28 07:17:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7185444831848145, "perplexity": 460.5978236388218}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128322873.10/warc/CC-MAIN-20170628065139-20170628085139-00098.warc.gz"} |
https://www.expii.com/t/use-of-polynomials-over-zpz-in-number-theory-10926 | Expii
# Use of Polynomials over Z/pZ in Number Theory - Expii
Polynomials over Z/pZ are quite useful for encoding various kinds of information in number theory. Applications include the proofs of Wilson's theorem, Euler's criterion, and the existence of primitive roots mod p; as well as the determination of the sign of the quadratic Gauss sum. | 2021-01-23 17:51:46 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9467962980270386, "perplexity": 321.7914219774014}, "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-2021-04/segments/1610703538226.66/warc/CC-MAIN-20210123160717-20210123190717-00055.warc.gz"} |
https://www.physicsforums.com/threads/inverse-matrix.559196/ | # Inverse Matrix
1. Dec 11, 2011
### AlonsoMcLaren
Is it always true that (see the attachment)?
#### Attached Files:
• ###### Untitled.png
File size:
2 KB
Views:
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2. Dec 11, 2011
### AlonsoMcLaren
I am assuming that phi is a matrix and its elements depend on t, another variable.
3. Dec 12, 2011
### HallsofIvy
In order for this to make sense, $\phi$ would have to be a one-to-one function from a set of matrices onto itself. And it asks if the inverse function, appled to matrix x, is the same as the inverse of $\phi(x)$. | 2018-02-24 16:49:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7652836441993713, "perplexity": 1444.7961800954595}, "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/1518891815843.84/warc/CC-MAIN-20180224152306-20180224172306-00218.warc.gz"} |
https://quantumcomputing.stackexchange.com/questions/12966/given-a-channel-phix-sum-k-c-kx-sigma-k-are-there-always-f-k-ge0-such | # Given a channel $\Phi(X)=\sum_k c_k(X)\sigma_k$, are there always $F_k\ge0$ such that $\Phi(X)=\sum_k \operatorname{tr}(F_k X)\sigma_k$?
Fix a finite number of states $$\sigma_k$$, and consider a channel of the form $$\Phi(X)=\sum_k c_{k}(X)\sigma_k.$$
For $$\Phi$$ to be linear and trace-preserving we must have: $$c_k(X+X') = c_k(X) + c_k(X'), \qquad \sum_k c_k(X)=1.$$ In other words, the coefficients must be linear functionals $$c_k\in\mathrm{Lin}(\mathcal X)^*$$ for all $$k$$.
Does this imply that there must be some positive operators $$F_k\ge0$$ such that $$c_k(X)=\operatorname{Tr}(F_k X)$$ for all $$k$$ (which in turn would imply $$\sum_k F_k=I$$ and thus that $$\{F_k\}_k$$ is a POVM)? What's a good way to show this?
To this end, pick a linearly independent set $$\{\sigma_k\}$$ which spans the full matrix space (over $$\mathbb C)$$, that is, a basis. (This is always possible, as the positive operators span the hermitian ones over $$\mathbb R$$.)
Then pick a dual basis $$\sigma'_\ell$$ such that $$\mathrm{tr}[\sigma'_\ell \sigma_k]=\delta_{k\ell}\ .$$
Then, $$\Phi(X) = \sum_k \mathrm{tr}[\sigma'_k X]\,\sigma_k$$ is the identity channel, which cannot be written as a POVM $$F_k\ge0$$ followed by a preparation of $$\sigma_k$$ (as that channel would be entanglement breaking).
(Note that this shows that the dual basis $$\sigma'_\ell$$ has non-positive elements. This is not surprising, since otherwise the scalar product $$\mathrm{tr}[\sigma'_\ell\sigma_k]\ge0$$ for all $$k,\ell$$.)
• by "identity channel" you mean $\Phi(X)=X$? But if there are such states $\sigma_k\ge0$ s.t. $\Phi(X)=X=\sum_k c_k(X)\sigma_k$ for all $X$, then $c_k(X)=\operatorname{Tr}(\sigma_k X)$ and thus $\sum_k\sigma_k=I$ if $\Phi$ is trace-preserving (assuming these are an orthonormal basis... but if they are not, are we ensured that they can be used to decompose any $X$?) – glS Jul 19 '20 at 16:51
• ah, I think I got it. There is a (non-orthogonal) basis of states $\sigma_k$ such that we can write $X=c_k(X)\sigma_k$ for all $X$. However, it is not true that $c_k(X)=\operatorname{Tr}(\sigma_k X)$ because the basis is not made of orthogonal operators (and now I understand why you used the notion of dual basis here). So I guess the hypothesis is true only as long as restrict $\sigma_k$ to be orthogonal operators. – glS Jul 19 '20 at 17:07
• @glS The hypothesis is true if and only if the channel is entanglement breaking. I would have to look up myself whether an entanglement breaking channel can always be written with $\sigma_k$ an orthogonormal basis. On the spot, I don't see why. Just because this is not the case in my example does not mean it is required. – Norbert Schuch Jul 19 '20 at 17:25 | 2021-04-17 21:16:01 | {"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": 22, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9322410225868225, "perplexity": 141.75496553395274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1618038464045.54/warc/CC-MAIN-20210417192821-20210417222821-00412.warc.gz"} |
https://www.physicsforums.com/threads/verifying-this-trigonometric-identity.457034/ | # Verifying this Trigonometric Identity
Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :)
## Homework Statement
Verify (1-cos^2 (a))(1+cos^2(a)) = 2sin^2 (a) -sin^4 (a). I cant simplify the (1+cos^2(a)). Also can not tell if I can simplify the other side as well.
## Homework Equations
sin^2 a + cos^2 a = 1
## The Attempt at a Solution
So using the Pythagorean identity, I have been able to simplify this to:
(sin^2 (a))(1+cos^2) ) = 2sin^2 (a) -sin^4 (a).
I am just stuck in simplifying the part after sin^2 (a). Also cant seem to simplify the other side. Any assistance is awesome. | 2020-08-07 01:57:14 | {"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": 0.8796271681785583, "perplexity": 1746.2421378797922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1596439737050.56/warc/CC-MAIN-20200807000315-20200807030315-00144.warc.gz"} |
https://docs.openstack.org/tripleo-docs/latest/install/post_deployment/build_single_image.html | # Building a Single Image¶
The openstack overcloud image build --all command builds all the images needed for an overcloud deploy. However, you may need to rebuild a single one of them. Use the following commands if you want to do it:
openstack overcloud image build --type {agent-ramdisk|deploy-ramdisk|fedora-user|overcloud-full}
If the target image exist, this commands ends silently. Make sure to delete a previous version of the image to run the command as you expect.
Moreover, you can build the image with an extra element of your choice using the --builder-extra-args argument:
openstack overcloud image build --type overcloud-full \
--builder-extra-args overcloud-network-midonet
Note
Make sure the element is available in the \$ELEMENTS_PATH environment variable
After the new image is built, it can be uploaded using the same command as before, with the --update-existing flag added:
openstack overcloud image upload --update-existing
Note that if the new image is a ramdisk, the Ironic nodes need to be re-configured to use it. This can be done by re-running:
openstack overcloud node configure --all-manageable
Note
If you want to use custom images for boot configuration, specify their names in --deploy-kernel and --deploy-ramdisk options.
Now the new image should be fully ready for use by new deployments. | 2018-10-23 21:07:22 | {"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": 0.5578268766403198, "perplexity": 4691.159018265891}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583517376.96/warc/CC-MAIN-20181023195531-20181023221031-00487.warc.gz"} |
https://www.gradesaver.com/textbooks/math/applied-mathematics/elementary-technical-mathematics/chapter-15-section-15-6-other-average-measurements-and-percentiles-exercise-page-518/25 | ## Elementary Technical Mathematics
$0.05\times50=2.5$. 2.5 rounds up to 3, so the 5th percentile is the 3rd piece of data in this ordered set of 50 numbers. The 5th percentile is 23. | 2022-08-07 17:06:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6517664790153503, "perplexity": 736.5755169750513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882570651.49/warc/CC-MAIN-20220807150925-20220807180925-00067.warc.gz"} |
http://cvgmt.sns.it/paper/4558/ | # Rectifiability of the jump set of locally integrable functions
created by delnin on 08 Jan 2020
[BibTeX]
Preprint
Inserted: 8 jan 2020
Last Updated: 8 jan 2020
Year: 2020
Abstract:
In this note we show that for every measurable function on $\mathbb{R}^n$ the set of points where the blowup exists and is not constant is $(n-1)$-rectifiable. In particular, for every $u\in L^1_{loc}(\mathbb{R}^n)$ the jump set $J_u$ is $(n-1)$-rectifiable.
Keywords: Rectifiability, bounded variation, jump set, Blowup | 2020-06-04 12:00:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9151849746704102, "perplexity": 1255.1234664631847}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347439928.61/warc/CC-MAIN-20200604094848-20200604124848-00230.warc.gz"} |
http://www.lastfm.com.br/user/froggafiend/library/music/Elvis+Presley/_/You+Gave+Me+A+Mountain?setlang=pt | # Biblioteca
Música » Elvis Presley »
## You Gave Me A Mountain
39 execuções | Ir para página da faixa
Faixas (39)
Faixa Álbum Duração Data
You Gave Me A Mountain 3:15 Jan 23 2013, 17h49
You Gave Me A Mountain 3:15 Jan 16 2013, 12h46
You Gave Me A Mountain 3:15 Jan 3 2013, 9h32
You Gave Me A Mountain 3:15 Jan 2 2013, 9h40
You Gave Me A Mountain 3:15 Jan 1 2013, 11h03
You Gave Me A Mountain 3:15 Jan 1 2013, 10h01
You Gave Me A Mountain 3:15 Jan 1 2013, 9h22
You Gave Me A Mountain 3:15 Dez 23 2012, 11h48
You Gave Me A Mountain 3:15 Dez 23 2012, 10h08
You Gave Me A Mountain 3:15 Dez 19 2012, 2h08
You Gave Me A Mountain 3:15 Dez 18 2012, 9h53
You Gave Me A Mountain 3:15 Dez 18 2012, 9h22
You Gave Me A Mountain 3:15 Dez 15 2012, 9h55
You Gave Me A Mountain 3:15 Out 21 2012, 11h42
You Gave Me A Mountain 3:15 Out 19 2012, 22h39
You Gave Me A Mountain 3:15 Out 2 2012, 12h36
You Gave Me A Mountain 3:15 Ago 29 2012, 8h07
You Gave Me A Mountain 3:15 Ago 25 2012, 15h44
You Gave Me A Mountain 3:15 Abr 6 2012, 10h38
You Gave Me A Mountain 3:15 Mar 14 2012, 19h10
You Gave Me A Mountain 3:15 Mar 14 2012, 16h11
You Gave Me A Mountain 3:15 Mar 9 2012, 13h34
You Gave Me A Mountain 3:15 Mar 1 2012, 3h07
You Gave Me A Mountain 3:15 Mar 1 2012, 1h36
You Gave Me A Mountain 3:15 Fev 29 2012, 14h38
You Gave Me A Mountain 3:15 Fev 19 2012, 9h33
You Gave Me A Mountain 3:15 Fev 4 2012, 10h05
You Gave Me A Mountain 3:15 Fev 4 2012, 9h51
You Gave Me A Mountain 3:15 Jan 25 2012, 16h11
You Gave Me A Mountain 3:15 Jan 2 2012, 0h44
You Gave Me A Mountain 3:15 Dez 25 2011, 14h59
You Gave Me A Mountain 3:15 Dez 25 2011, 13h33
You Gave Me A Mountain 3:15 Dez 24 2011, 9h27
You Gave Me A Mountain 3:15 Dez 9 2011, 12h41
You Gave Me A Mountain 3:15 Dez 9 2011, 11h27
You Gave Me A Mountain 3:15 Dez 3 2011, 3h15
You Gave Me A Mountain 3:15 Set 14 2011, 17h11
You Gave Me A Mountain 3:15 Set 12 2011, 9h02
You Gave Me A Mountain 3:15 Set 12 2011, 8h58 | 2014-07-22 13:10:33 | {"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": 0.9453175663948059, "perplexity": 14484.703741340441}, "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-2014-23/segments/1405997858581.26/warc/CC-MAIN-20140722025738-00217-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-sum-of-the-infinite-geometric-series-sigma-2-2-3-n-from-n-0--1 | How do you find the sum of the infinite geometric series Sigma 2(-2/3)^n from n=0 to oo?
Apr 14, 2017
$\frac{6}{5}$
Explanation:
First, take the $2$ out of the sigma so it's easier to deal with:
$2 \sum {\left(- \frac{2}{3}\right)}^{n}$
This is in the form:
$\sum {\left(u\right)}^{n}$ where $| u | < 1$. That means, that $\sum {u}^{n} = \frac{1}{1 - u}$
Our $u$, in this case, is $- \frac{2}{3}$. Simply plug into the formula.
$2 \left(\frac{1}{1 - \left(- \frac{2}{3}\right)}\right) = 2 \left(\frac{1}{\frac{5}{3}}\right) = 2 \left(\frac{3}{5}\right) = \frac{6}{5}$ | 2019-03-23 02:16:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "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": 0.9850311875343323, "perplexity": 261.8952801757185}, "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-2019-13/segments/1552912202711.3/warc/CC-MAIN-20190323020538-20190323042538-00251.warc.gz"} |
https://www.bizone.se/2014/05/14/understanding-your-customer-base-churn/ | # Understanding Your Customer Base: Churn
Churn is a means to understanding change in a business’s customer base due to loss of customers. Since keeping customers is generally cheaper than gaining new customers, then preventing the loss of customers is a profitable endeavor. The purpose of measuring churn, and similar metrics, is to evaluate actions taken by the business to retain customers or to identify weak points in the business.
Churn rate is a measure of churn in a given time period. Churn rate can be defined in multiple ways; here we’ll define churn rate as the ratio of customers lost in a given time period compared to the number of customers that could have been lost.
We can look at the extremes to understand churn rate better,
1. If the churn rate is 0, then we have not lost any customers in the time period
2. If the churn rate is 1, then we have lost all our customers in the time period
Below we can see the population at risk for each time period as green smiley faces, with red X’s over the population lost, i.e. the churned customers. On the lower axis, we display the calculated churn rate for each time period, $\frac{\text{customers lost}}{\text{customers at risk to be lost}}.$
#### Basic consideration for tracking churn rate:
1. Define the moment a person becomes a customer (or user)
2. Define when a customer has churned and is no longer a customer
• deciding when a customer has churned can be subtle in some environments, such as eCommerce
3. Determine the appropriate time period
• the smallest gradient of time to track flux of customers; if you choose weeks it’s possible to aggregate up from weeks to months or years, but not down from weeks to days.
###### A Simple Example
Consider a subscription based business, where the customer pays in advance of receiving the service. Online services, phone companies, gyms and many other companies work in this way.
1. A person becomes a customer on the date the service agreement is signed, and the first payment is received.
2. The lost of a customer is set at the next billing date after the customer cancels the subscription, or the immediately after no payment is received.
3. Since the billing cycle is monthly, a monthly time frame makes sense to record churn. A monthly period would imply there is a set billing date that is the same for all customers and likely a prorating of the first payment.
###### A More Subtle Example
A Swedish grocery store is an example of a commerce based business. It’s easy to understand grocery stores have repeat customers; it may be you buy all your groceries as the same store.
1. A person becomes a customer when they sign up for a loyalty card.
2. The customer is lost when there is zero spending on the loyalty card for a set amount of time. This amount of time can only be set by knowing and understanding your customer base, and your plan of action for preventing churn. A typical time period is 90 days.
3. The time period for recording churn in this case is dependent on the set amount of time for zero spending. If 90 days is the limit for zero spending observing churn monthly is reasonable, however it may be advisable to consider shorter time periods to understand the effect of churn prevention programs.
##### Summary
Churn is flux in a customer base due to loss. Churn rate is a measure of the amount of churn in a predetermined time period. Calculating and recording churn rate is a fundamental steps in measuring, understanding, and reducing churn. Churn rate in this format is lets us look back and evaluate past actions, which leads to the question how do we look forward?
###### And Beyond
Looking forward with churn rate, we can calculate the expected churn rate for time period. Once we have the expected value of churn we can determine when churn is too high, or churn is reducing. One simple way to approach this is to use at averages and t-test, but a more accurate way is to apply some basic Bayesian analysis.
Going beyond churn rate, we can start look at calculating, measuring, and leveraging insight from tenure, hazard, and survival analysis. In future posts, we’ll review the fundamentals and some basic insights that can be gained form tenure, hazard and survival analysis. These three will give us insights on how and when churn is happening in the customers life cycle. | 2019-09-22 23:27:06 | {"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": 0.3661184310913086, "perplexity": 1363.106713681875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575751.84/warc/CC-MAIN-20190922221623-20190923003623-00346.warc.gz"} |
http://openstudy.com/updates/4f2fc4c5e4b0571e9cbb5b51 | ## anonymous 4 years ago 2nd question: Find lim (sin2xcot4x) X->0.
1. anonymous
are you allowed to use l'hopital's rule?
2. anonymous
assuming this is $\lim_{x\rightarrow 0}\sin(2x)\cot(4x)$ $\lim_{x\rightarrow 0}\frac{\sin(2x)\cos(4x)}{\sin(4x)}$
1/2
4. anonymous
in any case the answer is $\frac{1}{2}$
5. anonymous
but if you need to show your work your answer will depend on what you are allowed to use. l'hopital's rule is the simplest, otherwise it will be some work
6. anonymous
i dont know the hospital rule that you have said :(
7. anonymous
you mean you do not know it or you are not allowed to use it? i assume this is calc class, so hve you covered deriviatives yet or are you just starting out?
|dw:1328531016861:dw|
without using l'hopital rule
10. anonymous
any computation as a long the answer will be the same in a long method
11. anonymous
i dont know it sorry :(
12. anonymous
there is a nice neat answer above. i think you can also use $\frac{sin(2x)\cos(4x)}{\sin(4x)}=\frac{\sin(2x)(\cos^2(2x)-\sin^2(2x))}{2\sin(2x)\cos(2x)}$
13. anonymous
here i used the double angle formula for sine and cosine
14. anonymous
can i post the 3rd question too?
15. anonymous
then cancel the sin(2x) top and bottom, get $\frac{\cos^2(2x)-\sin^2(2x)}{2\cos(2x)}$ replace x by zero, get $\frac{1}{2}$
16. anonymous
no limit to the amount you can post
17. anonymous
yes i will write your solution :)
18. anonymous
if f(x)=tanx-x and g(x)=x^3, evaluate the limit of f(x) over g(x) as x approaches 0. -3rd question.
19. anonymous
@nenadmatematica if you can do this without l'hopital or power series i will be impressed
haha I just wanted to ask you the same thing :D ....
21. anonymous
lol well, i guess we cannot give an elementary reason for this. the answer is $\frac{1}{3}$ but i cannot think of a gimmick to simplify this expression. are you sure you have not covered l'hopital? because i am stumped. in particular you have a trig fuction combined in combination with x and x^3 so there is no simple trig identity that will change the form of this for you
22. anonymous
@nenadmatematika tahnks for helping us too :)
well you're welcome....I agree with satellite that this example is very convenient for using L'Hopital rule.....I can't think of any other way now :D
24. anonymous
i really dont know but if both of you wants to use L'hopital rule. then i will agree to both of you
25. anonymous
4th question: Evaluate the lim x^2-16 over x+4 as x->4. | 2017-01-17 07:16:59 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9024730920791626, "perplexity": 1196.3956434689862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279489.14/warc/CC-MAIN-20170116095119-00430-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://bojjenclon.com/about/ | # bojjenclon
## tl;dr
I'm a Calculating... year old nerd with a passion for programming. I graduated from Stetson University in 2017, with a B.S. in Computer Information Systems (CIS).
## FAQ
### How did you start programming?
The origin of my interest in programming can potentially be traced back to a couple of different (but ultimately similar) places. Regardless of what you consider the "starting location" of my interest, I was around 14 or 15 when said interest cropped up. I used to mess around with a program called RPG Maker XP, which could be used to make GameBoy-style games without any coding knowledge. However, if you wanted your game to be unique or to have features beyond what the program came with, you needed to be able to extend it with the software's varient of Ruby. This is probably where the spark began, but it wasn't until I started using GameMaker that I actually tried to learn to code seriously. From there it was simply a matter of realizing that relying on pre-built systems such as RMXP or GM was incredibly limiting. I wanted more, and I knew I'd have to learn to code properly in order to reach my newfound goals. I followed tutorials online and taught myself as much as I could, and my passion for coding grew as a I did so.
### Have you always wanted to code for a living?
Since I didn't really start programming until I was about 14/15, I certainly didn't always want to be a programmer. That isn't to say I wasn't interested in general computing concepts; I've always love computers and the various tasks they can perform. Despite this, when I was young my goal was to become a scientist one day. I didn't know much about the various "types" of scientists (chemists, biologists, physists, etc.), I just knew I wanted to do something in that realm. After all, Bill Nye the Science guy was practically my hero. The middle school science fair was when I realized that science as a career just wasn't going to work. To put it bluntly, I hated the science fair. Fortunately, it was soon after the fair that I began experimenting with coding. After taking a couple of programming classes in highschool (one of which being AP Computer Science), I knew I wanted to code professionally. | 2019-06-25 17:44:44 | {"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": 0.30283135175704956, "perplexity": 1048.2143221296576}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1560627999876.81/warc/CC-MAIN-20190625172832-20190625194832-00160.warc.gz"} |
https://www.transtutors.com/questions/2-10-express-the-given-equations-without-using-and-gates-a-x-a-b-3-10-using-a-simila-3297895.htm | # 2. (10) Express the given equations without using AND gates (a) X = A-B 3. (10) Using a similar...
2. (10) Express the given equations without using AND gates (a) X = A-B 3. (10) Using a similar method to when we proved NAND was a complete logic set, prove that NOR is also a complete set. (a) Construct a NOT gate using only NOR gates (b) Construct an AND gate using only NOR gates (c) Construct an OR gate using only NOR gates
Attachments: | 2019-08-23 02:49:23 | {"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": 0.8701302409172058, "perplexity": 1495.0400474856947}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027317817.76/warc/CC-MAIN-20190823020039-20190823042039-00106.warc.gz"} |
http://www.ck12.org/geometry/Triangle-Sum-Theorem/exerciseint/Find-The-Measure-of-the-Third-Angle/ | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Triangle Sum Theorem ( Assessments ) | Geometry | CK-12 Foundation
# Triangle Sum Theorem
%
Progress
Practice Triangle Sum Theorem
Progress
%
Find The Measure of the Third Angle
Teacher Contributed
The measures of two angles of a triangle are 70$70^\circ$ and 45$45^\circ$. What is the measure of the third angle?
qid: 100158 | 2014-12-19 10:15:43 | {"extraction_info": {"found_math": true, "script_math_tex": 2, "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": 0.2299450784921646, "perplexity": 10320.305132799538}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1418802768397.103/warc/CC-MAIN-20141217075248-00066-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Definition:Weakly_Locally_Connected_at_Point/Definition_2 | # Definition:Weakly Locally Connected at Point/Definition 2
## Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $x \in S$.
The space $T$ is weakly locally connected at $x$ if and only if every open neighborhood $U$ of $x$ contains an open neighborhood $V$ of $x$ such that every two points of $V$ lie in some connected subset of $U$.
## Also known as
If $T$ is weakly locally connected at $x$, it is also said to be connected im kleinen at $x$.
Some sources refer to a space which is weakly locally connected at $x$ as locally connected at $x$. | 2021-09-23 00:24:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9715273380279541, "perplexity": 69.58415362633157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057403.84/warc/CC-MAIN-20210922223752-20210923013752-00487.warc.gz"} |
http://docs.prophesee.ai/metavision_designer/modules/core/samples/raw_to_video.html | # Metavision Designer RAW to Video Sample¶
The sample in <install-prefix>/share/metavision/designer/core/samples/metavision_raw_to_video.py shows how to generate an AVI video from a RAW file.
## Expected Output¶
Metavision RAW to Video sample generates an AVI file and by default saves it to the same directory and with the same name as the input RAW file.
## How to start¶
To start the sample based on recorded data, provide the full path to a RAW file (here, we use the file from Metavision Dataset):
Linux
python3 /usr/share/metavision/designer/core/samples/metavision_raw_to_video.py -i spinner.raw
Windows
python "C:\Program Files\Prophesee\share\metavision\designer\core\samples\metavision_raw_to_video.py" -i spinner.raw
python3 /usr/share/metavision/designer/core/samples/metavision_raw_to_video.py -h
python "C:\Program Files\Prophesee\share\metavision\designer\core\samples\metavision_raw_to_video.py" -h | 2021-02-24 17:58:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.28887638449668884, "perplexity": 14707.131618576424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1614178347293.1/warc/CC-MAIN-20210224165708-20210224195708-00345.warc.gz"} |
https://www.semanticscholar.org/paper/An-arithmetic-enrichment-of-B%5C'ezout's-Theorem-McKean/a9366c30e6d1d8dc0ad900546ee55ef3976fa941 | Corpus ID: 212736956
# An arithmetic enrichment of B\'ezout's Theorem
@article{McKean2020AnAE,
title={An arithmetic enrichment of B\'ezout's Theorem},
author={S. McKean},
journal={arXiv: Algebraic Geometry},
year={2020}
}
• S. McKean
• Published 2020
• Mathematics
• arXiv: Algebraic Geometry
• The classical version of Bezout's Theorem gives an integer-valued count of the intersection points of hypersurfaces in projective space over an algebraically closed field. Using work of Kass and Wickelgren, we prove a version of Bezout's Theorem over any perfect field by giving a bilinear form-valued count of the intersection points of hypersurfaces in projective space. Over non-algebraically closed fields, this enriched Bezout's Theorem imposes a relation on the gradients of the hypersurfaces… CONTINUE READING
6 Citations | 2021-01-23 03:03:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.5277272462844849, "perplexity": 1716.5613396847166}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610703531702.36/warc/CC-MAIN-20210123001629-20210123031629-00015.warc.gz"} |
https://www.esaral.com/q/how-many-linear-equations-in-x-and-y-can-be-satisfied-by-x-2-y-3-24184 | # How many linear equations in x and y can be satisfied by x = 2, y = 3?
Question:
How many linear equations in x and y can be satisfied by x = 2, y = 3?
(a) Only one
(b) Only two
(c) Infinitely many
(d) None of these
Solution:
(c) Infinitely many
Infinite linear equations are satisfied by $x=2, y=3$. | 2023-03-22 22:42:43 | {"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": 0.7697863578796387, "perplexity": 784.0599962135916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296944452.97/warc/CC-MAIN-20230322211955-20230323001955-00318.warc.gz"} |
http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/statug_genmod_details22.htm | # The GENMOD Procedure
### Predicted Values of the Mean
Subsections:
#### Predicted Values
A predicted value, or fitted value, of the mean corresponding to the vector of covariates is given by
where g is the link function, regardless of whether corresponds to an observation or not. That is, the response variable can be missing and the predicted value is still computed for valid . In the case where does not correspond to a valid observation, is not checked for estimability. You should check the estimability of in this case in order to ensure the uniqueness of the predicted value of the mean. If there is an offset, it is included in the predicted value computation.
#### Confidence Intervals on Predicted Values
Approximate confidence intervals for predicted values of the mean can be computed as follows. The variance of the linear predictor is estimated by
where is the estimated covariance of . The robust estimate of the covariance is used for in the case of models fit with GEEs.
Approximate confidence intervals are computed as
where is the th percentile of the standard normal distribution and g is the link function. If either endpoint in the argument is outside the valid range of arguments for the inverse link function, the corresponding confidence interval endpoint is set to missing. | 2019-04-26 00:15:17 | {"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": 0.8202362656593323, "perplexity": 375.5037727243213}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1555578743307.87/warc/CC-MAIN-20190425233736-20190426014904-00070.warc.gz"} |
http://openstudy.com/updates/4d8b6b9d012f8b0b824f1b0a | ## anonymous 5 years ago 3x + 5 – 2x – 4 ------ ------ = 3 6 5
1. anonymous
$(3x+5)/6$is $(3/6)x +(5/6)$ you can figure out the rest.
2. anonymous
ahhh i'm confused :/
3. anonymous
first, u have to diminish the fraction such that: $1\div x + 1 \div y = t$ this equal to $1\div x \times xy + 1\div y \times xy = t \times xy$ thus $y + x = txy$ | 2016-10-28 08:45:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9429520964622498, "perplexity": 1405.5363295957459}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721595.48/warc/CC-MAIN-20161020183841-00433-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=08-216 | 08-216 Denis Gaidashev, Hans Koch
Period doubling in area-preserving maps: an associated one-dimensional problem (4063K, Postscript) Nov 16, 08
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers
Abstract. It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of $\field{R}^2$. A renormalization approach has been used in a computer-assisted proof of existence of an area-preserving map with orbits of all binary periods by J.-P. Eckmann, H. Koch and P. Wittwer (1982 and 1984). As it is the case with all non-trivial universality problems in non-dissipative systems in dimensions more than one, no analytic proof of this period doubling universality exists to date. We argue that the period doubling renormalization fixed point for area-preserving maps is almost one dimensional, in the sense that it is close to the following Henon-like map: $$H^*(x,u)=(\phi(x)-u,x-\phi(\phi(x)-u )),$$ where $\phi$ solves $$\phi(x)={2 \over \lambda} \phi(\phi(\lambda x))-x.$$ We then give a proof'' of existence of solutions of small analytic perturbations of this one dimensional problem, and describe some of the properties of this solution. The proof'' consists of an analytic argument for factorized inverse branches of $\phi$ together with verification of several inequalities and inclusions of subsets of $\field{C}$ numerically. Finally, we suggest an analytic approach to the full period doubling problem for area-preserving maps based on its proximity to the one dimensional. In this respect, the paper is an exploration of a possible analytic machinery for a non-trivial renormalization problem in a conservative two-dimensional system.
Files: 08-216.src( 08-216.keywords , Doubling.ps ) | 2018-07-20 19:54:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9265276193618774, "perplexity": 853.9063959017118}, "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-2018-30/segments/1531676591831.57/warc/CC-MAIN-20180720193850-20180720213850-00363.warc.gz"} |
https://tug.org/pipermail/tex-hyphen/2010-June/000676.html | # [tex-hyphen] Latin Hyphenation when using utf8
Mojca Miklavec mojca.miklavec.lists at gmail.com
Wed Jun 23 09:29:36 CEST 2010
On Tue, Jun 22, 2010 at 23:16, Andrew Gollan wrote:
> grātiās plūrimās vōbīs agō
>
> This almost completely solved my problem (though I confess I haven't looked
> through for nasty hyphenations yet). I ran xelatex on my input file with
> only a couple of minor mods for font handling:
> \usepackage{palatino} => \usepackage{fontspec}\setromanfont{Palatino
> Linotype}.
>
> But xelatex seems to just happily proceed when it doesn't have a glyph. In
> the old scheme I could put a macon on 'y' to make 'ȳ' and it came out in the
> wash even though the font did not directly contain it. My new book had gaps
> where the 'ȳ' should be. Any quick hints on how to understand/control glyph
> substitution in the brave new (to me) world of XeTeX?
You have a few options:
a) Use Gentium or some other complete font (I vote for that)
b) You could use TeX Gyre Pagella, but that font doesn't have ȳ
either, at least not yet; however, you may request that glyph at
Polish font gurus and then you'll have the support in all the fonts
they are covering (8 TeX Gyre families, Latin Modern, Antykwa
Torunska, Antykwa Poltawskiego, Iwona, Kurier, ...)
c) The following works in ConTeXt to make a fallback for a missing
glyph in the font:
\catcode\ȳ=\active
\defȳ{\buildtextaccent\textmacron y}
The same should work in plain TeX/LaTeX, but it must be some other
command (\accent or something ... maybe even \defȳ{\=y} works fine).
However, while the option "c" is "it always works", you'll get exactly
the same problems with hyphenation as in pdfTeX. So the best option is
to take the font that does have that glyph (or request its addition to
TeX fonts). You can do the "b" independent of whether you choose to go
with the first option for now.
> My first reaction would be just to say:
> amacron = abreve = a
> Amacron = Abreve = A
> ...
Sure. You just need a complete list. If what Arthur say is true (that
there's no more way to use \savehyphencodes or however it is spelled),
the easiest way to implement the patterns is to "duplicate" all the
patterns or rather: replace each patterns with all the possible
substitutions of "a" with abreve and amacron (all possible
combinations).
If you are able to buy or borrow the TeXBook, read appendix H. (For a
shortcut see pages 36-45 in
http://tug.org/tex-hyphen/pdf/hyphenator.pdf for a nice visual
explanation of how patterns work.)
Mojca
` | 2019-08-23 04:54:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.940554678440094, "perplexity": 8080.195618349452}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027317847.79/warc/CC-MAIN-20190823041746-20190823063746-00215.warc.gz"} |
https://askthetask.com/1249/whats-the-area-of-the-sector | 0 like 0 dislike
What’s the area of the sector=
$$(\pi)\left(\frac{60}{360} \right)(9^{2})=\boxed{13.5\pi}$$ | 2022-12-09 14:57:49 | {"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": 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": 0.6457981467247009, "perplexity": 9090.914383495236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711417.46/warc/CC-MAIN-20221209144722-20221209174722-00684.warc.gz"} |
https://www.ipht.fr/en/Phocea/Vie_des_labos/Seminaires/index.php?type=29&id=993857 | Separated variables and wave functions for rational GL(N) spin chains
Dmytro Volin
Nordita Stockholm and Uppsal U.
Thu, Apr. 25th 2019, 11:30
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
\noindent Integrability meeting ENS/IPhT'' \\ \\ We present a basis in which wave functions of integrable XXX spin chain factorise into a product of Slater determinants of Baxter Q-functions. We furthermore show that this basis is formed by eigenvectors of the B[good]-operator and it is naturally labelled by Gelfand-Tsetlin patterns. The discussion is valid for spin chains in any rectangular representation and arbitrary rank of the GL(N) symmetry group. For symmetric powers of the defining representation, one also observes a corollary that B[good]-operator acting on a suitably chosen vacuum constructs the eigenstates of the Bethe algebra. \\ \\ (IPhT organizers: Ivan Kostov and Didina Serban)
Contact : lbervas | 2022-06-25 23:23:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.999937891960144, "perplexity": 2596.210682334338}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103036176.7/warc/CC-MAIN-20220625220543-20220626010543-00795.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/amy-lloyd-is-interested-in-leasing-a-new-saab-and-has-contacted-three-automobile-dealers-f-q3163488 | ## Quantitative Methods
Amy Lloyd is interested in leasing a new Saab and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mil basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow: Dealer Monthly Cost Mileage Allowance Cost per Additional Mile Forno Saab $299 36,000$0.15 Midtown Motors $310 45,000$0.20 Hopkins Automotive $325 54,000$0.15 Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options. For example, she figures that the Forno Saab lease will cost her $10,764 is she drives 12,000 miles per year,$12,114 if she drives 15,000 miles per year, or \$13, 464 if she drives 18,000 miles per year. a. What is the decision, and what is the chance event? b. Construct a payoff table for Amy’s problem. c. If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches? d. Suppose that the probabilities that Amy drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What option should Amy choose using the expected value approach? e. Develop a risk profile for the decision selected in part (d). What is the most likely cost, and what is its probability? f. Suppose that after further consideration Amy concludes that the probabilities that she will drive 12,000, 15,000, and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What decision should Amy make using the expected value approach? | 2013-05-19 04:31:15 | {"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": 0.41927671432495117, "perplexity": 2999.4024931887925}, "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-2013-20/segments/1368696383259/warc/CC-MAIN-20130516092623-00080-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://mathshistory.st-andrews.ac.uk/OfTheDay/oftheday-02-10/ | ## Mathematicians Of The Day
### 10th February
#### Quotation of the day
##### From Sofia Kovalevskaya
Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination. | 2020-07-06 13:40:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8550671339035034, "perplexity": 2327.4605270054126}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1593655880616.1/warc/CC-MAIN-20200706104839-20200706134839-00415.warc.gz"} |
http://mathhelpforum.com/differential-geometry/159835-distance-between-normed-spaces.html | # Thread: Distance between normed spaces
1. ## Distance between normed spaces
Hi, I need to solve this problem, can someone help me?
Let c be the space of convergent scalar sequences and c0 the spaces of the null scalar sequences. Prove that the distance between them is less or equal than 3.
Thanks.
2. Originally Posted by felixgotti
Hi, I need to solve this problem, can someone help me?
Let c be the space of convergent scalar sequences and c0 the spaces of the null scalar sequences. Prove that the distance between them is less or equal than 3.
Thanks.
What is the ambient space? What norm is this ambient space given?. Also isn't $c\cap c_0 \neq \emptyset$, so which is your definition of distance between normed spaces? (maybe this last one is the only one relevant?) | 2017-03-27 23:08:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.8948801755905151, "perplexity": 361.3430442150632}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1490218189534.68/warc/CC-MAIN-20170322212949-00509-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Definition:Sum_of_Ideals_of_Ring | # Definition:Sum of Ideals of Ring
## Definition
Let $R$ be a ring.
### Two ideals
Let $I$ and $J$ be ideals of $R$.
Their sum is the ideal equal to their subset sum:
$I + J = \{i + j : i \in I \land j \in J\}$ | 2019-11-19 12:10:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9083125591278076, "perplexity": 2259.6901544032785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1573496670135.29/warc/CC-MAIN-20191119093744-20191119121744-00382.warc.gz"} |
https://bioinformatics.stackexchange.com/questions/2783/5utr-and-3utr-annotation-in-yeast | # 5'UTR and 3'UTR annotation in yeast
I am working on a project in which I need to compute several parameters (such GC content and length) of 5'UTR and 3'UTR sequences of Saccharomyces cerevisiae yeast genes.
The problem is finding a proper annotation for these regions in yeast. I have tried with BiomaRt and these sequences are not available for yeast. I have also tried with UCSC table browser to obtain a BED file with 5'UTR or 3'UTR sequences but it is returning only coordinates of tRNAs, pseudogenes, ncRNAs.
In summary, is there a straight-forward way to obtain an annotation for 5'UTR and 3'UTR regions in Saccharomyces cerevisiae yeast?
• Sorry, is for Saccharomyces cerevisiae. I am going to edit the question just in case.
– plat
Nov 6 '17 at 12:58
• isn't there an equivalent of AceView for Yeast ? ncbi.nlm.nih.gov/IEB/Research/Acembly/index.html Nov 6 '17 at 17:15
I am unaware of any "official" or gold-standard UTR annotations in S. cerevisiae.
One option is to use the annotations from the TIF-Seq publication (Pelechano et al. 2013).
The GSE39128_tsedall.txt.gz file contains the major isoforms identified. It would be up to you to computational associate each transcript with a given gene. It is also up to you to determine which major isoforms are present in your dataset. Furthermore based on my own experience there is often a significant number of discrepancies between what I see in an NGS dataset (e.g. RNA-Seq) and what is called as a possible isoform in these annotations. However, a lot of this could be related to the inherent technological limitations of the method.
If you look at the SGD genome browser they provide some additional UTR annotations. Derived from Nagalakshmi et al. 2008.
You can find the relevant annotations for those UTR's in their supplemental data section. The file is 1158441_tables_s2_to_s6.zip and inside you will find TableS4 which seems to contain what you seek.
There might be more resources but these are the two main ones I'm aware of.
According to the README files in the same directory, these are (the README for the 5' file is equivalent): | 2022-01-18 05:09:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47564268112182617, "perplexity": 2377.3048052727218}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320300722.91/warc/CC-MAIN-20220118032342-20220118062342-00417.warc.gz"} |
https://techutils.in/blog/2021/01/01/stackbounty-normal-distribution-conditional-expectation-intuition-multivariate-distribution-interpretation-of-multivariate-condit/ | # #StackBounty: #normal-distribution #conditional-expectation #intuition #multivariate-distribution Interpretation of multivariate condit…
### Bounty: 50
I’ve been reading over this Multivariate Gaussian conditional proof, trying to make sense of how the mean and variance of a gaussian conditional was derived. I’ve come to accept that unless I allocate a dozen or so hours to refreshing my linear algebra knowledge, it’s out of my reach for the time being.
that being said, I’m looking for a conceptual explanation for that these equations represent:
$$mu_{1|2} = mu_1 + Sigma_{1,2} * Sigma^{-1}_{2,2}(x_2 – mu_2)$$
I read the first as "Take $$mu1$$ and augment it by some factor, which is the covariance scaled by the precision (measure of how closely $$X_2$$ is clustered about $$mu_2$$, maybe?) and projected onto the distance of the specific $$x_2$$ from $$mu_2$$."
$$Sigma_{1|2} = Sigma_{1,1} – Sigma_{1,2} * Sigma^{-1}_{2,2} * Sigma_{1,2}$$
I read the second as, "take the variance about $$mu_1$$ and subtract some factor, which is covariance squared scaled by the precision about $$x_2$$."
In either case, the precision $$Sigma^{-1}_{2,2}$$ seems to be playing a really important role.
A few questions:
• Am I right to treat precision as a measure of how closely observations are clustered about the expectation?
• Why is the covariance squared in the latter equation? (Is there a geometric interpretation?) So far, I’ve been treating $$Sigma_{1,2} * Sigma^{-1}_{2,2}$$ as a ratio, (a/b), and so this ratio acts to scale the (second) $$Sigma_{1,2}$$, essentially accounting for/damping the effect of the covariance; I don’t know if this is valid.
• Anything else you’d like to add/clarify?
Get this bounty!!!
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2021-11-27 18:14:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.7186129093170166, "perplexity": 1024.6825714355432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00583.warc.gz"} |
https://brilliant.org/problems/squares-and-roots-i/ | # Squares and Roots I
Algebra Level 1
Having a number n, we can make this relation:
$$\frac { \sqrt { n } }{ n } =m\quad \Rightarrow \quad \frac { 1 }{ m } =\sqrt { n }$$
If n=2, what is the m value?
× | 2018-06-22 21:18:22 | {"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": 0.5049037933349609, "perplexity": 8132.440943757804}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864795.68/warc/CC-MAIN-20180622201448-20180622221448-00472.warc.gz"} |
https://www.doubtnut.com/question-answer/the-coordinates-ofi-as-point-p-are-123-find-the-coordinates-fothe-seven-pints-such-that-the-absolute-8495651 | Home
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# The coordinates ofi as point P are (1,2,3). Find the coordinates fothe seven pints such that the absolute vaues of their coordinates are the same as those of coordinates of P.
Updated On: 27-06-2022 | 2022-11-30 13:47:59 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9405695796012878, "perplexity": 8059.87057947582}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1669446710764.12/warc/CC-MAIN-20221130124353-20221130154353-00478.warc.gz"} |
http://acscihotseat.org/index.php?qa=474&qa_1=proof-for-long-forward-price-at-time-t&show=478 | # Proof for long-forward price at time t
55 views
asked Apr 28, 2017
I tried to rigorously prove the value of long-forward price at time t. The outline of the proof is given on slide 22 of "The introduction the derivatives" slides.
I am quite close to the correct answer except that my answer has the incorrect sign. I have attached my workings as a pdf. Proof.pdf (0,3 MB)
Any idea of where I went wrong?
answered May 2, 2017 by (3,390 points)
selected May 9, 2017 by Rowan
Hi Conor
In the your proof, the amount of money you wish to borrow at time $$t$$ should be the present value of the difference between what you are going to receive from the long Forward and what you are going to pay for the short Forward.
i.e. The present value of $$F_{0,T} - F_{t,T}$$.
That should then give you the correct answer.
commented May 13, 2017 by (1,120 points)
If we borrow the PV of $$F_{0,T} - F_{t,T}$$. then surely we would have to pay back $$F_{0,T} - F_{t,T}$$. i.e. have a cashflow of -($$F_{0,T} - F_{t,T}$$)=$$F_{t,T} - F_{0,T}$$? which would then make our overall cashflow at T 2($$F_{t,T} - F_{0,T}$$)? which is then non-zero and makes the arbitrage argument not work?
commented May 14, 2017 by (3,390 points)
Hi Dean
Thanks for pointing out my error.
I have relooked at the proof. The amount which is borrowed is indeed supposed to be $$F_{t,T} - F_{0,T}$$ .
From what I can see, the reason why Conor was getting the wrong sign in the final step is because he was adding the cashflows at time $$t$$ to get zero instead equating them to each other. If the cashflows at all other times are equal, then the values of each component at time $$t$$ should be equal to each other. They should not add up to zero. | 2018-05-21 08:50:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6414092779159546, "perplexity": 531.8587846877901}, "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-2018-22/segments/1526794863972.16/warc/CC-MAIN-20180521082806-20180521102806-00020.warc.gz"} |
https://math.stackexchange.com/questions/1911089/in-french-mathematics-what-does-hypoth%C3%A8se-mean | # In French mathematics, what does “hypothèse” mean?
Of course, it seems the answer is obviously "hypothesis". However, that translation does not seem right in the following context, taken from a paper by Bernard Host.
Désormais, $p > 1$ est un entier et $\mu$ une mesure de probabilité sur $\mathbb{T}$; on ne fait pour l'instant aucune hypothèse d'invariance.
Using Google Translate, my best translation is the following.
Henceforth, let $p>1$ be an integer and let $\mu$ be a probability measure on $\mathbb{T}$; As of yet we do not have an invariance hypothesis."
But isn't a hypothesis the same as a conjecture (e.g. Riemann hypothesis)? "Conjecture" doesn't seem to fit here. My gut tells me that the last part should read "As of yet we do not make any assumption about invariance." So, in this context, does "hypothèsis" mean "assumption"?
• hypothèse is the same as assumption – Gabriel Romon Sep 1 '16 at 16:07
• @John: English hypothesis can mean ‘conjecture’, but it can also mean ‘assumption’: we speak of the hypotheses of a given theorem, meaning the assumptions. However, I would translate the second clause as for now we do not assume invariance. – Brian M. Scott Sep 1 '16 at 16:18
• The normal meaning, in English as well as in French is one of the meanings of the Greek word ̔υπόθεσις : supposition. – Bernard Sep 1 '16 at 18:25
Suppose I say "Let $P$ be a probability measure on $\mathbb R^2$ that is invariant under rotations about the origin. Then we can conclude that..."
Then rotation-invariance is a hypothesis. That $P$ is a probability measure is a hypothesis. | 2020-02-19 01:33:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8754816651344299, "perplexity": 252.60819699908868}, "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/1581875143963.79/warc/CC-MAIN-20200219000604-20200219030604-00409.warc.gz"} |
http://cpr-nuclth.blogspot.com/2013/08/13080031-j-hooker-et-al.html | ## Efficacy of crustal superfluid neutrons in pulsar glitch models [PDF]
J. Hooker, W. G. Newton, Bao-An Li
Within the framework of recent hydrodynamic models of pulsar glitches, we explore systematically the dependence on the stiffness of the nuclear symmetry energy at saturation density $L$, of the fractional moment of inertia of the pinned neutron superfluid in the crust $G$ and the initial post-glitch relative acceleration of the crust $K$, both of which are confronted with observational constraints from the Vela pulsar. We allow for a variable fraction of core superfluid neutrons coupled to the crust on glitch rise timescales, $Y_{\rm g}$. We assess whether the crustal superfluid neutrons are still a tenable angular momentum source to explain the Vela glitches when crustal entrainment is included. The observed values $G$ and $K$ are found to provide nearly orthogonal constraints on the slope of the symmetry energy, and thus taken together offer potentially tight constraints on the equation of state. However, when entrainment is included at the level suggested by recent microscopic calculations, the model is unable to reproduce the observational constraints on $G$ and $K$ simultaneously, and is limited to $L>100$ MeV and $Y_{\rm g} \approx 0$ when $G$ is considered alone. One solution is to allow the pinned superfluid vortices to penetrate the outer crust, which leads to a constraint of $L\lesssim 45$ MeV and $Y_{\rm g} \lesssim 0.04$ when $G$ and $K$ are required to match observations simultaneously. When one allows the pinned vortices to penetrate into the crust by densities of up to 0.082 fm$^{-3}$ above crust-core transition density (a total density of 0.176 fm$^{-3}$) for L=30 MeV, and 0.048 fm$^{-3}$ above crust-core transition density (a total density of 0.126 fm$^{-3}$) for L=60 MeV, the constraint on $G$ is satisfied for \emph{any} value of $Y_{\rm g}$. We discuss the implications of these results for crust-initiated glitch models.
View original: http://arxiv.org/abs/1308.0031 | 2017-10-19 01:46:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.671958327293396, "perplexity": 1510.4788957639034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1508187823214.37/warc/CC-MAIN-20171019012514-20171019032514-00096.warc.gz"} |
https://2022.congresso.sif.it/talk/254 | Relazione su invito
# Nuclear astrophysics: A review of the most interesting recent results.
##### Palmerini S.
Giovedì 15/09 09:00 - 13:00 Aula B - Maria Goeppert-Mayer I - Fisica nucleare e subnucleare
Measuring neutron capture cross-sections on unstable nuclei and their half-lives in stellar plasma is the ultimate frontier of experimental nuclear astrophysics. However, many other pivotal results have been achieved so far. Among the most recent ones we review 4 cases. The $^{12}C+\,^{12}C$ reaction, whose measurements by an indirect technique has been extensively debated and turned out to deeply affect the exploitability of the SN progenitors. The $^{7}Be+{n}$ reaction, involved the cosmological lithium problem, whose rate has been measured by two different approaches demonstrating the feasibility of investigating neutron capture cross-sections on unstable nuclei at astrophysical energies. The $^{13}C({a}, {n})^{16}O$ and $^{22}Ne({a}, {n})^{25}Mg$ reactions that are the neutron sources for the $s$-process and have been measured with high precision in order to provide constraints to both the $s$- and the $r$-process nucleosynthesis. The $^{17}O({p}, {a})^{14}N$ and $^{17}O({p}, {g})^{18}F$ reactions, whose roles in the radiative H-burning are well known, but whose nucleosynthesis yields vary significantly according with the reaction rate recommended by the different authors, defining different scenarios for the nucleosynthesis of $^{17}O$ and $^{18}O$. | 2022-10-04 00:49:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5993736982345581, "perplexity": 2192.857991696151}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1664030337446.8/warc/CC-MAIN-20221003231906-20221004021906-00285.warc.gz"} |
http://www.ni.com/documentation/en/labview-comms/2.0/m-ref/sort/ | # sort
Version:
Sorts the input elements in ascending or descending order.
## Syntax
c = sort(a)
c = sort(a, b)
c = sort(a, order)
c = sort(a, b, order)
[c, d] = sort(a)
[c, d] = sort(a, b)
[c, d] = sort(a, order)
[c, d] = sort(a, b, order)
## a
Real or complex scalar or array of any dimension.
## b
Dimension of a across which to sort if a is an array. b can be in a range of 1 to the maximum supported array dimension (32). If you do not specify b, the function sorts the first dimension whose size is not equal to 1.
## order
Direction by which to sort elements. order is a string that accepts the following values.
Name Description
'ascend' (default)
Sorts the elements in ascending order.
'descend'
Sorts the elements in descending order.
## c
Elements of a in ascending or descending order, depending on the value of order. MathScript sorts complex vectors by magnitude and angle, in that order. If a is an array, c returns a sorted by the dimension specified in b. c is an array of the same size as a.
## d
Indexes in a of the elements in c. d is a double array of the same size as a.
A = [-1+2i, 3, -1-2i, -4]
[C, D] = sort(A)
Where This Node Can Run:
Desktop OS: Windows
FPGA: Not supported | 2018-03-23 10:33:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2309042066335678, "perplexity": 3346.7086644011947}, "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-2018-13/segments/1521257648207.96/warc/CC-MAIN-20180323102828-20180323122828-00511.warc.gz"} |
https://socratic.org/questions/1-if-the-ph-of-a-solution-is-the-solution-is-basic-a-2-b-5-c-7-d-10-can-someone- | # 1. If the pH of a solution is ….. the solution is basic. a. 2 b. 5 c. 7 d. 10 Can someone help me?
Aug 28, 2017
[H_2O] → [H^+] + [OH^1] where $p H = - \log \left[{H}^{+}\right]$,
The neutral point, where $\left[{H}^{+}\right] = \left[O {H}^{1}\right]$ is 7. Anything lower means that there are more $\left[{H}^{+}\right]$ than $\left[O {H}^{1}\right]$ ions, so the solution is acidic. Anything lower means that there are more $\left[O {H}^{1}\right]$ than $\left[{H}^{+}\right]$ ions, so the solution is basic. | 2019-11-19 10:01:49 | {"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": 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": 0.8669497966766357, "perplexity": 1005.6732002729226}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1573496670135.29/warc/CC-MAIN-20191119093744-20191119121744-00352.warc.gz"} |
http://mathoverflow.net/revisions/8685/list | 3 Acknowledged error.
Hey Joel, long time etc. It looks to me like blowing down your knotted $S^2$ will only produce a homology 4-sphere. And one could presumably produce examples by taking some known 2-knot in $S^4$ and connect-summing it with the line in $\mathbb{CP}^2$, distinguishing the resulting 2-knots in $\mathbb{CP}^2$ from the line via $\pi_1$ of their complements.
[EDIT: I fell into Joel's heffalump trap. Still, at least there's company down here...]
You could rephrase the question (with a bit of help from Gromov) as asking whether a 2-knot in $\mathbb{CP}^2$ with self-intersection $1$ and simply connected complement is isotopic to a symplectic sphere. You could invoke Taubes too, and see that, to produce a diffeo with the line, it's enough to extend a symplectic form on the image of $S^2$ to one on $\mathbb{CP}^2$. Well, the complement of a neighbourhood of $S^2$ is then a homotopy 4-ball, bounding $S^3$ with its usual contact structure, and the goal is to build a symplectic form which is a convex filling of the contact boundary... Yep, that's probably an open problem.
2 corrected "concave" to "convex"
Hey Joel, long time etc. It looks to me like blowing down your knotted $S^2$ will only produce a homology 4-sphere. And one could presumably produce examples by taking some known 2-knot in $S^4$ and connect-summing it with the line in $\mathbb{CP}^2$, distinguishing the resulting 2-knots in $\mathbb{CP}^2$ from the line via $\pi_1$ of their complements.
You could rephrase the question (with a bit of help from Gromov) as asking whether a 2-knot in $\mathbb{CP}^2$ with self-intersection $1$ and simply connected complement is isotopic to a symplectic sphere. You could invoke Taubes too, and see that, to produce a diffeo with the line, it's enough to extend a symplectic form on the image of $S^2$ to one on $\mathbb{CP}^2$. Well, the complement of a neighbourhood of $S^2$ is then a homotopy 4-ball, bounding $S^3$ with its usual contact structure, and the goal is to build a symplectic form which is a concave convex filling of the contact boundary... Yep, that's probably an open problem.
1
Hey Joel, long time etc. It looks to me like blowing down your knotted $S^2$ will only produce a homology 4-sphere. And one could presumably produce examples by taking some known 2-knot in $S^4$ and connect-summing it with the line in $\mathbb{CP}^2$, distinguishing the resulting 2-knots in $\mathbb{CP}^2$ from the line via $\pi_1$ of their complements.
You could rephrase the question (with a bit of help from Gromov) as asking whether a 2-knot in $\mathbb{CP}^2$ with self-intersection $1$ and simply connected complement is isotopic to a symplectic sphere. You could invoke Taubes too, and see that, to produce a diffeo with the line, it's enough to extend a symplectic form on the image of $S^2$ to one on $\mathbb{CP}^2$. Well, the complement of a neighbourhood of $S^2$ is then a homotopy 4-ball, bounding $S^3$ with its usual contact structure, and the goal is to build a symplectic form which is a concave filling of the contact boundary... Yep, that's probably an open problem. | 2013-05-19 17:39:11 | {"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": 0.8870279788970947, "perplexity": 399.54963190854505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368697917013/warc/CC-MAIN-20130516095157-00038-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://arxiver.moonhats.com/2017/12/08/the-apostle-simulations-rotation-curves-derived-from-synthetic-21-cm-observations-ga/ | The APOSTLE simulations: Rotation curves derived from synthetic 21-cm observations [GA]
The APOSTLE cosmological hydrodynamical simulation suite is a collection of twelve regions $\sim 5$ Mpc in diameter, selected to resemble the Local Group of galaxies in terms of kinematics and environment, and re-simulated at high resolution (minimum gas particle mass of $10^4\,{\rm M}\odot$) using the galaxy formation model and calibration developed for the EAGLE project. I select a sample of dwarf galaxies ($60 < V{\rm max}/{\rm km}\,{\rm s}^{-1} < 120$) from these simulations and construct synthetic spatially- and spectrally-resolved observations of their 21-cm emission. Using the $^{3{\rm D}}$BAROLO tilted-ring modelling tool, I extract rotation curves from the synthetic data cubes. In many cases, non-circular motions present in the gas disc hinder the recovery of a rotation curve which accurately traces the underlying mass distribution; a large central deficit of dark matter, relative to the predictions of cold dark matter N-body simulations, may then be erroneously inferred.
K. Oman
Fri, 8 Dec 17
12/70
Comments: To appear in the proceedings of IAUS 334: Rediscovering our Galaxy, July 10-14 2017, Telegrafenberg, Potsdam, Germany, Eds. C. Chiappini, I. Minchev, E. Starkenburg & M. Valentini | 2017-12-13 05:36:09 | {"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": 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": 0.48355358839035034, "perplexity": 5310.552733040826}, "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-2017-51/segments/1512948521292.23/warc/CC-MAIN-20171213045921-20171213065921-00119.warc.gz"} |
https://electronics.stackexchange.com/questions/305821/how-do-i-solve-this-circuit-with-thevenins/305826 | How do i solve this circuit with Thevenin's?
I am not sure how to place my voltage source after i combine the 2 parallel resistors R1 and R2. Can someone please help me with this?
Method1 (specific method for voltage divider):
After you simplified the parralel resistors $R_{23} = R_2 || R_3$ you got a voltage source with voltage divider formed by $R_{23}$ and $R_1$.
The Thevenin Equivalent of a voltage source $V_{src}$ with voltage divider is a Thevenin source with $V_{th}=V_{src}\frac{R_{23}}{R_1+R_{23}}$ and $R_{th}= R_1 || R_{23}$
Method2 (general method that works always):
If you don't know this shortcut above: do what you should have learned in the lessons:
• find open circuit voltage $V_{oc}$ between a and b
• find short circuit current $I_{sc}$ between a and b
• use both results to derive $V_{th}=V_{oc}$ and $R_{th}=\frac{V_{oc}}{I_{sc}}$.
First, r2//r3 so you find the equivalent resistance Req1. Then you see that R1 and Req1 are in series so you find the equivalent resistance between r1 an Req1 and i think it's good. you have your equivalent schema.
• The OP asked about using Thevenin. – Chu May 17 '17 at 14:18
• i should have said it was the beginning of method to find equivalent schema. After you just had to as @curd said. Sorry i wasn't explicit. – Dipo May 17 '17 at 14:39 | 2019-12-16 08:14:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49432462453842163, "perplexity": 814.6566278036485}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541318556.99/warc/CC-MAIN-20191216065654-20191216093654-00024.warc.gz"} |
https://community.ptc.com/t5/Windchill-Systems-Software/Integrity-create-field-that-is-a-computed-sum/td-p/260382 | cancel
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## Integrity - create field that is a computed sum
Hello -
In Integrity 10.9, I'm trying to create a new field for my documents that is a computed sum of all "Verified By Trace Count" entries in a document.
The field "Verified By Trace Count" related to each requirement is calculated by:
isEmpty(RelCount("Verified By"),0);
So, at the document level, I was hoping the sum of all these values would simply be:
sum("Verified By Trace Count");
but that always gave me the error:
"An error occurred parsing the computation expression "sum("Verfied By Trace Count");": MKS124539: sum: Function is an aggregate function, but a non-aggregate computation is being evaluated."
I tried using the aggregate function, but couldn't quite get the syntax right.
Any help would be appreciated.
Is there a document that gives examples on how to use all these computational functions and operators?
Thanks!
John
Tags (2)
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Hi John, | 2020-09-21 03:57:39 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8660068511962891, "perplexity": 4290.634380903315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198887.3/warc/CC-MAIN-20200921014923-20200921044923-00724.warc.gz"} |
http://orzhtml.com/benefits-of-ovopdj/43dc57-log-of-exponential-distribution | Spraying Zinsser 123 Primer With Hvlp, Duane And Barbara Island Hunters, B2200 Mazda Pickup, Qualcast Abp118lz Battery, Quizizz Dependent And Independent Clauses, Super Seal 30 Vs Eagle, Sherwin-williams Resinous Flooring, Synonyms Of Nippy, ">
# log of exponential distribution
1℃
| 2021-10-26 22:07:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.917448878288269, "perplexity": 398.100238560316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1634323587926.9/warc/CC-MAIN-20211026200738-20211026230738-00205.warc.gz"} |
http://radiodmg.com/?p=549 | # Radio DMG Episode 041: “Uniquely Random”
Click on through.
You know what to do.
Make it happen.
In This Episode: We have Raj Ramayya, Tia Ballard, and David Vincent. The middle interview with Tia Ballard is weirdly chaotic and bizarre. There is audio I had to censor and then ridiculous klaxons. My apologies and maybe you could enjoy it. Actually, you will enjoy it. Just be warned. Okay?
MP3(68MB): Thank you for your co-operation.
Time Stamps are just something we feel we need because of White Guilt.
This entry was posted in Radio Dmg Shows and tagged , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink. | 2019-08-24 05:01:39 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8290758728981018, "perplexity": 4837.940673200972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027319724.97/warc/CC-MAIN-20190824041053-20190824063053-00182.warc.gz"} |
https://www.transtutors.com/questions/32-net-present-value-graph-and-indifference-cost-of-capital-specialized-consulting-s-1384532.htm | # 32. Net present value graph and indifference cost of capital. Specialized Consulting Service...
32. Net present value graph and indifference cost of capital. Specialized Consulting Service Company’s after-tax net cash flows associated with two mutually exclusive projects, Alpha and Beta, are as follows:
Cash Flow, End of Year
Project 0 1 2 Alpha $(100)$125 --- Beta (100) 50 \$84
a. Calculate the net present value for each project using discount rates of 0, 0.04, 0.08, 0.12, 0.15, 0.20, and 0.25.
b. Prepare a graph as follows. Label the vertical axis ‘‘Net Present Value in Dollars’’ and the horizontal axis ‘‘Discount Rate in Percent per Year.’’ Plot the net present value amounts calculated in part a. for project Alpha and project Beta.
c. State the decision rule for choosing between projects Alpha and Beta as a function of the firm’s cost of capital.
d. What generalizations can you draw from this exercise? | 2018-11-18 23:08:15 | {"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": 0.35093778371810913, "perplexity": 5676.537389851214}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1542039744750.80/warc/CC-MAIN-20181118221818-20181119003818-00257.warc.gz"} |
http://math.stackexchange.com/questions/68148/big-o-of-polynomial-functions | # Big O of polynomial functions
I am required to identify if $\log{(f(x))}$ is a subset of $O(\log{n})$ holds true for all polynomial functions. If I try with $f(x) = x^2$, then I am able to prove it to be correct. But, with $f(x) = -2(x+2)(x-7)$, I am unable to prove it.
Am I missing something? Please advise.
Thanks
-
I assume that $f$ is supposed to be positive for sufficiently large $x$? – JavaMan Sep 28 '11 at 6:01
Note that $x^m\le x^n$ for $m\le n,x\ge1$ implies that $P(x)=a_dx^d+\cdots+a_0\le(a_d+\cdots+a_0)x^d$ for $x\ge1$ which is obviously $O(x^d)$. – anon Sep 28 '11 at 6:19
## 1 Answer
Assuming $\lim_{x\to\infty} p(x) = \infty$ as otherwise it doesn't make sense.
First, if $p(x)=a_nx^n+\cdots+a_0$ then there exists $C$, such that for all sufficiently large $x$, $p(x) \leq C x^n$ (a suitable $C$ would be $a_n+1$).
Second, $\forall D,E$ exists $F$, such that $D\log x+E \leq F\log x$ for all sufficiently large $x$ (you can take $F$ to be $D+1$ for example).
Now, for sufficiently large $x$: $$\log p(x) \leq \log (C x^n) = \log C + n\log x \leq D \log x .$$
If $\lim_{x\to\infty} p(x) = -\infty$ a sensible question to ask would be if $\log |p(x)|\in O(\log x)$.
-
Thanks for that mate. – Prasanna K Rao Sep 28 '11 at 20:58 | 2015-05-30 02:34:48 | {"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": 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": 0.9255517721176147, "perplexity": 148.5313010097186}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930866.66/warc/CC-MAIN-20150521113210-00128-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://blender.stackexchange.com/questions/94355/how-to-unwrap-multiple-planes-and-have-them-exactly-overlap/94358#94358 | # How to unwrap multiple planes and have them exactly overlap?
I'm currently modeling a stadium for a game and am trying to find a quick way to get all the rows of seating to share a UV image. Each plane is the same height but differs in length, but I can just have the UV image repeat itself for longer planes.
Here you can see how I'd like each plane to land on the UV map, obviously differing in length.
I've just did a smart unwrap, but it lays them all out without overlapping. Is there a way to have them all overlap in the UV without having to painstakingly move each one by hand into the correct area? Even if they were all along the same X plane, not overlapping, that would work fine. Just now, they're stacked with spacing in between them which throws off most of the rows of seats, making them cut in half or floating and other issues.
Any help is greatly appreciated!
I found a work around. If I unwrapped in as a Smart UV Project, it placed all the unwrapped planes tightly together, as in no space between them. So, if I aligned one of the planes to the corresponding UV image, the rest of them repeated correctly.
You can do this by using magic UV addon.
After enable addon go to edit mode, select one plane, unwrap it how you need, than press U -> copy/paste UV -> Copy UV
Next select all planes with same size and U -> copy/paste UV -> Paste UV
In this case you need to repeat this operation as many times as you have variations in length. | 2021-09-26 03:53:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2050204575061798, "perplexity": 1104.0372567955199}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057796.87/warc/CC-MAIN-20210926022920-20210926052920-00240.warc.gz"} |
http://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/chapter-3-section-3-2-the-graph-of-a-function-3-2-assess-your-understanding-page-223/54 | ## College Algebra (10th Edition)
$y=\frac{2}{3}x+8$
We find a line with a slope of $2/3$ that passes through $(-6,4)$ using the point-slope form: $y-y_{1}=m(x-x_{1})$ $y-4=\displaystyle \frac{2}{3}(x- -6)$ $y-4=\displaystyle \frac{2}{3}(x+6)$ $y-4=\frac{2}{3}x+4$ $y=\frac{2}{3}x+8$ | 2018-04-20 13:02:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8667599558830261, "perplexity": 229.74758275690567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1524125937780.9/warc/CC-MAIN-20180420120351-20180420140351-00539.warc.gz"} |
https://phys.libretexts.org/Courses/College_of_the_Canyons/Physci_101_Lab%3A_Physical_Science_Laboratory_Investigations_(Ciardi)/29%3A_Investigation_28__The_Electromagnetic_Connection/29.6%3A_General_Questions | Skip to main content
# 29.6: General Questions
1. Describe any correlation between number of coils and magnetic strength.
2. Describe any differences between the nail electromagnets and the bolt electromagnets. Explain why any differences may occur.
## Contributors and Attributions
29.6: General Questions is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.
• Was this article helpful? | 2023-02-03 04:21:49 | {"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": 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": 0.9816486835479736, "perplexity": 1813.3291730013136}, "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-2023-06/segments/1674764500042.8/warc/CC-MAIN-20230203024018-20230203054018-00691.warc.gz"} |
https://platonicrealms.com/encyclopedia/cone | cone
A cone is an infinite surface of revolution generated as shown:
Figure 1: Generating a cone.
The term also refers to the solid bounded by one of the nappes and a flat elliptical base. If in this case the base is circular (at right angles to the axis), the cone is called a right circular cone.
Figure 2: The cone as a solid.
The surface area S (excluding the base) and volume V of a right circular cone are given by
$\begin{eqnarray*} S & = & \pi r \sqrt{r^2+h^2} \\ & & \\ V & = & \frac{\pi r^2h}{3} \end{eqnarray*}$ | 2021-01-17 16:21:43 | {"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": 0.8228099346160889, "perplexity": 611.0887331832707}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703513062.16/warc/CC-MAIN-20210117143625-20210117173625-00178.warc.gz"} |
http://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/chapter-5-section-5-2-properties-of-rational-functions-5-2-assess-your-understanding-page-351/18 | ## College Algebra (10th Edition)
All real numbers; $x\ne -3, x\ne 4$
The domain of the function is all real numbers, except for when the denominator is 0. Thus, we let the denominator equal 0: $$(x+3)(4-x)=0 \\ x=-3, 4$$ Thus, we know that x cannot equal -3 or 4. | 2018-04-20 03:32:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9461999535560608, "perplexity": 326.5833084313023}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1524125937113.3/warc/CC-MAIN-20180420022906-20180420042906-00160.warc.gz"} |
http://web.math.rochester.edu/news-events/events/single/1861 | # Algebra/Number Theory Seminar
## An upper bound for image set sizes of iterated quadratic maps
George Grell, U Rochester
Wednesday, April 3rd, 2019
1:00 PM - 2:00 PM
Hylan 1106A
Let $f(x)$ be a quadratic rational map defined over the field $\mathbb{F}_q$. Then work of Pink (2013) and Juul, Kurlberg, Madhu, and Tucker (2015) classifies the possible Galois groups that arise from considering $f^n(x)-t$ over the function field $\mathbb{F}_q(t)$. For one class of Galois groups we describe the proportion of elements of with fixed points, and use a lesser known generalization of Burnside’s Lemma to show this is an upper bound across all classes. The Chebotarev Density Theorem translates this result to a bound on image set sizes.
Event contact: dinesh dot thakur at rochester dot edu | 2019-08-21 00:21:38 | {"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": 0.8745911717414856, "perplexity": 1573.757273051088}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027315695.36/warc/CC-MAIN-20190821001802-20190821023802-00112.warc.gz"} |
http://formula.s21g.com/formulae/help/latex | # LaTeX Format
This service uses a subset of LaTeX format. It includes most of mathematical functions of the LaTeX, but others are not.
## Examples
The source of LaTeX below is converted into the image which follows it.
f(x)=\int_0^{x}g(t)\,dt
## Chemical Structural Formulae
You can also get images of chemical structural formulae by using XyMTeX format.
\purinev{4==NH$\mathrm{_2}$;6==H;2==H;1==H}
The source above is converted into the image below. | 2019-03-24 14:17:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.9878514409065247, "perplexity": 3372.534718270498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1552912203448.17/warc/CC-MAIN-20190324124545-20190324150545-00006.warc.gz"} |
http://mathoverflow.net/questions/91601/fx-1-x-2-x-3-ldots-x-n-maximum-how-many-different-results-can-have-with-all | # $f(x_1,x_2,x_3,\ldots,x_n)$ Maximum how many different results can have with all permutation of inputs?
$\alpha _n=e^{2 \pi i/n}$
$$f(x_1,x_2,x_3,\ldots,x_n)=(x_1+\alpha _n x_2+ \alpha _n ^2 x_3+\cdots+\alpha _n ^{n-1} x_n)^n$$
Maximum how many different results can have with all permutation of inputs? I have read in Jim Brown's paper on page 5. http://www.math.caltech.edu/~jimlb/abel.pdf
Lagrange showed that If n=3 then $f(x_1,x_2,x_3)$ Maximum can have 2 different results with all permutations of $(x_1,x_2,x_3)$
If n=4 then $f(x_1,x_2,x_3,x_4)$ Maximum can have 3 different results with all permutations of $(x_1,x_2,x_3,x_4)$
If n=5 then $f(x_1,x_2,x_3,x_4,x_5)$ Maximum can have 6 different results with all permutations of $(x_1,x_2,x_3,x_4,x_5)$
Is there any general formula for n and which method is used to find the general formula? | 2015-09-04 12:29:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8836606740951538, "perplexity": 188.99825586730114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645348533.67/warc/CC-MAIN-20150827031548-00347-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.studyadda.com/notes/kvpy/physics/mathematical-tools-units-dimensions/fundamental-and-derived-quantities/7131 | # 11th Class Physics Physical World / भौतिक जगत Fundamental and Derived Quantities
Fundamental and Derived Quantities
Category : 11th Class
(1) Fundamental quantities : Out of large number of physical quantities which exist in nature, there are only few quantities which are independent of all other quantities and do not require the help of any other physical quantity for their definition, therefore these are called absolute quantities. These quantities are also called fundamental or basic quantities, as all other quantities are based upon and can be expressed in terms of these quantities.
(2) Derived quantities : All other physical quantities can be derived by suitable multiplication or division of different powers of fundamental quantities. These are therefore called derived quantities. If length is defined as a fundamental quantity then area and volume are derived from length and are expressed in term of length with power 2 and 3 over the term of length. Note : q In mechanics, Length, Mass and Time are arbitrarily chosen as fundamental quantities. However this set of fundamental quantities is not a unique choice. In fact any three quantities in mechanics can be termed as fundamental as all other quantities in mechanics can be expressed in terms of these. e.g. if speed and time are taken as fundamental quantities, length will become a derived quantity because then length will be expressed as Speed ´ Time. and if force and acceleration are taken as fundamental quantities, then mass will be defined as Force / acceleration and will be termed as a derived quantity.
#### Other Topics
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https://www.physicsforums.com/threads/differential-equations-2.381724/ | # Homework Help: Differential Equations (2)
1. Feb 25, 2010
### der.physika
I'm having trouble setting up this solution can anyone give me a hint, or set it up, so I can see if what i'm doing is right?
$$xy\prime=y=e^x^y$$
using the substitution
$$u\equiv(xy)$$
Last edited: Feb 25, 2010
2. Feb 26, 2010
### kosovtsov
$$xy\prime=y=e^x^y$$
What do you mean with two = in "equation"?
3. Feb 26, 2010
### Redbelly98
Staff Emeritus
Moderator's note:
Thread moved to "Calculus and Beyond" in the https://www.physicsforums.com/forumdisplay.php?f=152" area.
Homework assignments or any textbook style exercises for which one is seeking assistance are to be posted in the appropriate forum in our Homework & Coursework Questions area. This should be done whether the problem is part of one's assigned coursework or just independent study.
Last edited by a moderator: Apr 24, 2017
4. Feb 26, 2010
### der.physika
Sorry about that, I wrote that wrong the actual problem is
$$xy\prime+y=e^x^y$$
using the substitution
$$u\equiv(xy)$$
Last edited: Feb 26, 2010 | 2018-12-19 16:33:10 | {"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": 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": 0.5082540512084961, "perplexity": 3549.569582119065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376832559.95/warc/CC-MAIN-20181219151124-20181219173124-00414.warc.gz"} |
https://www.physicsforums.com/threads/related-rates.72928/ | # Homework Help: Related Rates
1. Apr 24, 2005
### scorpa
Hi Again,
I am doing a question on related rates that I have become stuck on.
The height (h) of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5cm?
I know that the area of a triangle is bh/2, but after that I am stuck I tried deriving it using the chain rule so that I could substitute h and the rate of h, but I don't think that i was doing it the right way. If anyone could direct me here I would really appreciate the help.
2. Apr 24, 2005
### Jameson
Here are some things to consider, the height "h" of an equilateral triangle is
$$\frac{1}{2}\sqrt{3}s$$
where "s" is the length of one side.
The area of this triangle is equal to
$$\frac{1}{2}sh$$
See any substitutions?
3. Apr 24, 2005
### futb0l
$$\frac{dA}{dt} = \frac{dh}{dt} * \frac{dA}{dh}$$ | 2018-04-23 19:40:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7913756370544434, "perplexity": 481.90920041299887}, "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-2018-17/segments/1524125946165.56/warc/CC-MAIN-20180423184427-20180423204427-00152.warc.gz"} |
https://za.limehousetownhall.org.uk/21132-removing-frameplot-borders-from-plotim-output.html | # Removing frame/plot borders from plot.im output
I am plotting point density using theplot.imcommand in spatstat, and my output always has a frame around the plotted image that becomes thicker when I increase resolution for export. I triedframe=F,axes=F,plot.frame=FALSE,bty='n'but none of them seem to fix the issue. Anyone know a solution to this?
Usebox=FALSE(see?plot.im: argument box, a logical value specifying whether a box should be drawn.):
Z <- setcov(owin()) tc <- colourmap(rainbow(128), breaks=seq(-1, 2, length=129)) plot(Z, col=tc)
plot(Z, col=tc, box=FALSE) | 2021-10-16 21:50:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48065418004989624, "perplexity": 13783.061790294269}, "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-2021-43/segments/1634323585025.23/warc/CC-MAIN-20211016200444-20211016230444-00510.warc.gz"} |
https://math.stackexchange.com/questions/2249988/closed-form-expressions-for-harmonic-sums-i | # Closed form expressions for harmonic sums I.
This question is a continuation of the topic in Closed form expressions for harmonic sums . By using the integral representation of harmonic numbers and by induction we have derived the following integral representation of an infinite harmonic sum. We have: $${\mathfrak S}^{(p)}_n(t):=\sum\limits_{m=0}^\infty H_m^p \cdot \frac{t^{m+1}}{(m+1)^n} = \int\limits_{[0,1]^p} \prod\limits_{\eta=0}^{p-1} \log\left(1-\xi_\eta\right) \cdot \frac{\left(\sum\limits_{l=0}^{p}(-1)^l \binom{p}{l} Li_{n-l}(t\prod\limits_{\eta=0}^{p-1} \xi_\eta )\right)}{\prod\limits_{\eta=0}^{p-1} \xi_\eta^2} \prod\limits_{\eta=0}^{p-1} d \xi_\eta$$ Here $Li_n()$ are poly-logarithms, $p$ and $n$ are strictly positive integers and $t\in (-1,1)$. Now the question is how can we use the result above to calculate those sums at unity,i.e. how do we calculate ${\mathfrak S}^{(n)}_p(1)$ ? Does the result always depend only on certain values of the zeta function (as it does in case $p=1$ as shown in the question quoted above) or instead does it also depend on something else?
• For $p+m$ is odd it is reducible to zeta values and there is a general formula. For the other case I have never seen one. – Zaid Alyafeai Apr 24 '17 at 17:08
• – Zaid Alyafeai Apr 24 '17 at 17:12
• @Zaid Alyafeai: Thank you for this document and for the comments. I am interested in this topic because those Euler sums appear to be related to solutions to certain recurrence relations with time dependent coefficients. Again, ${\mathfrak S}^{(1)}_n(1)$ is known -- you posted it yourself some time ago. I was thinking that the integral I gave above could help us to derive the result for $p=2$ or maybe $p=3$. I will be working on this and I will post results if I achieve any. – Przemo Apr 24 '17 at 17:20
• It seems difficult to work with $\mathrm{Li}_q(xy)$. Moreover in the link I provided they claim that Euler sums with large even weight should be considered as 'new' constants. Perhaps the best someone can do is consider ${\mathfrak S}^{(2)}_4(1)$. I guess you already know that ${\mathfrak S}^{(p)}_p(1)$ is trivial. – Zaid Alyafeai Apr 25 '17 at 6:45
• If you like working with Euler sums. You can take a look at my latest question math.stackexchange.com/questions/2169507/… – Zaid Alyafeai Apr 25 '17 at 6:50 | 2019-07-23 13:20:45 | {"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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.8864536881446838, "perplexity": 204.83289474507686}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1563195529406.97/warc/CC-MAIN-20190723130306-20190723152306-00050.warc.gz"} |
https://admin.clutchprep.com/physics/practice-problems/138396/when-two-or-more-capacitors-are-connected-in-series-across-a-potential-differenc | # Problem: When two or more capacitors are connected in series across a potential difference:a) the potential difference across the combination is the algebraic sum of the potential differences across the individual capacitors.b) the equivalent capacitance of the combination is less than the capacitance of any of the capacitors.c) each capacitor carries the same amount of charge.d) All of the above choices are correct.e) None of the above choices are correct.
###### FREE Expert Solution
Equivalent capacitance of series capacitors.
$\overline{)\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{e}\mathbf{q}}}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{3}}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{n}}}}$
The equivalent capacitance of the combination is less than the capacitance of any of the capacitors.
###### Problem Details
When two or more capacitors are connected in series across a potential difference:
a) the potential difference across the combination is the algebraic sum of the potential differences across the individual capacitors.
b) the equivalent capacitance of the combination is less than the capacitance of any of the capacitors.
c) each capacitor carries the same amount of charge.
d) All of the above choices are correct.
e) None of the above choices are correct. | 2020-09-19 02:29:04 | {"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": 0.8289346694946289, "perplexity": 428.7820514103739}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400189928.2/warc/CC-MAIN-20200919013135-20200919043135-00693.warc.gz"} |
http://openstudy.com/updates/50903b6be4b0ad6205377c21 | • anonymous
Suppose that limit x-> a f(x)= infinity and limit x-> a g(x) = c, where c is a real number. Prove each statement. (a) lim x-> a [f(x) + g(x)] = infinity (b) lim x-> a [f(x)g(x)] = infinity if c > 0 (c) lim x-> a [f(x)g(x)] = negative infinity if c < 0 I need to prove it using the precise definition of a limit (i.e. no limit laws). Thanks so much!!!!!! I actually only need the proofs for a) and c)... if it helps, here's the link to the proof of a problem to (b): http://imageshack.us/photo/my-images/190/unledmkd.png/
Calculus1
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Not the answer you are looking for? Search for more explanations. | 2017-04-23 14:07:00 | {"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": 0.9100618958473206, "perplexity": 947.4057875335227}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1492917118707.23/warc/CC-MAIN-20170423031158-00259-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.yaclass.in/p/mathematics-state-board/class-9/geometry-3173/geometry-of-circles-and-construction-of-incircle-and-centroid-16087/re-6d1d7809-23cf-4213-9faa-236f7f26a471 | PUMPA - THE SMART LEARNING APP
AI system creates personalised training plan based on your mistakes
Circle through a point
Given a point $$O$$, it is always possible to draw infinitely many circles through the given point.
In other words, an infinite number of circles can be drawn through a given point.
Illustration:
Circle through two points
Given any two points, it is always possible to draw infinitely many circles through the given points.
In other words, an infinite number of circles can be drawn, passing through a pair of points.
Illustration:
Circle through three points
Case 1: Collinear points
If the three points are collinear, then it is impossible to draw a circle using all three points.
Any set of points are said to be collinear if all the points lie on the same line.
Illustration:
Case 2: Non-collinear points
If the three points are non-collinear, then it is possible to draw only one circle using all the three points.
Any set of points are said to be non-collinear if all the points do not lie on the same line.
Illustration:
Theorem: There is one and only one circle passing through three non-collinear points. | 2022-09-29 03:56:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7265254855155945, "perplexity": 682.4729842622191}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335304.71/warc/CC-MAIN-20220929034214-20220929064214-00231.warc.gz"} |
http://math.stackexchange.com/questions/194301/is-a-sigma-compact-hausdorff-space-normal | # Is a $\sigma$ - compact Hausdorff space normal?
Are $\sigma$ -compact Hausdorff spaces normal?
-
Yes. Every $\sigma$-compact space is Lindelöf, every $\sigma$-compact Hausdorff space is $T_3$ (regular and $T_1$), and every $T_3$ Lindelöf space is $T_4$ (normal and $T_1$).
Correction: I was apparently not yet awake when I wrote that. There are countable Hausdorff spaces that are not regular, so the result is actually false in general. However, if you have any property that ensures regularity, you do get normality for free.
For an example of a countable Hausdorff space that isn’t regular, see this answer to an earlier, related question.
-
There may be some confusion based on definitions. Engelking's text, in particular, defines $\sigma$-compact spaces to be regular (T$_3$) spaces which are the countable union of compact subspaces. With this Brian's (original) answer works. (I cannot stress enough that his current answer works perfectly well.)
However if you remove regularity from the definition of $\sigma$-compactness, you can get counterexamples, as Brian mentions above. Another example is the following: Let $A = \{ \frac{1}{n} : n \in \mathbb{N} \}$, and give $\mathbb{R}$ the topology by declaring the open sets to be of the form $U \setminus B$ where $U \subseteq \mathbb{R}$ is open in the usual metric topology and $B \subseteq A$.
• As this topology is finer than the usual metric topology, it follows that this space is Hausdorff.
• It is $\sigma$-compact since you can cover $\mathbb{R}$ by countably many closed (bounded) intervals which each contain only finitely many elements of $A$.
• However this space is not regular because $A$ is closed in the new topology, but there is no pair of disjoint open sets around $0$ and $A$, respectively.
- | 2014-11-28 12:37:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9763342142105103, "perplexity": 258.9235346183049}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931010166.36/warc/CC-MAIN-20141125155650-00213-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/160264 | ## Closedness of the Tangent Spaces to the Orbits of Proper Actions
In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence, for each free proper action on a Hilbert manifold, the quotient M/G carries a natural manifold structure.
Published in:
Journal Of Lie Theory, 18, 517-521
Year:
2008
Keywords:
Laboratories: | 2018-07-19 12:07:24 | {"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": 0.9601660966873169, "perplexity": 412.6809213818093}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590866.65/warc/CC-MAIN-20180719105750-20180719125750-00014.warc.gz"} |
http://math.iisc.ac.in/all-courses/ma339.html | MA 339: Geometric Analysis
Pre-requisites :
1. A first course on manifolds (MA 338 should do).
2. Analysis (multivariable calculus, some measure theory, function spaces).
3. Functional analysis (The Hahn-Banach theorem, Riesz representation theorem, Open mapping theorem. Ideally, the spectral theory of compact self-adjoint operators too, but we will recall the statement if not the proof)
Basics of Riemannian geometry (Metrics, Levi-Civita connection, curvature, Geodesics, Normal coordinates, Riemannian Volume form), The Laplace equation on compact manifolds (Existence, Uniqueness, Sobolev spaces, Schauder estimates), Hodge theory, more general elliptic equations (Fredholmness etc), Uniformization theorem.
Suggested books :
1. Do Carmo, Riemannian Geometry .
2. Griffiths and Harris, Principles of Algebraic Geometry .
3. S. Donaldson, Lecture Notes for TCC Course “Geometric Analysis” .
4. J. Kazdan, Applications of Partial Differential Equations To Problems in Geometry .
5. L. Nicolaescu, Lectures on the Geometry of Manifolds .
6. T. Aubin, Some nonlinear problems in geometry .
7. C. Evans, Partial differential equations .
8. Gilbarg and Trudinger, Elliptic partial differential equations of the second order .
9. G. Szekelyhidi, Extremal Kahler metrics .
All Courses
Contact: +91 (80) 2293 2711, +91 (80) 2293 2265
E-mail: chairman.math[at]iisc[dot]ac[dot]in | 2018-05-24 15:38:48 | {"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": 0.8617571592330933, "perplexity": 2835.8057501582257}, "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-2018-22/segments/1526794866511.32/warc/CC-MAIN-20180524151157-20180524171157-00254.warc.gz"} |
http://icmp.lviv.ua/en/preprints/2000/00-01e | 00-01E
# 00-01E
By - Posted on 08 February 2012
UDC:
536.432.1; 536.44.
PACS:
05.70.Jk
Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture
O.V. Patsahan
M.P. Kozlovskii
R.S. Melnyk
A microscopic approach to the investigation of the behaviour of a symmetrical binary fluid mixture in the vicinity of the vapour-liquid critical point is proposed. It is shown that the problem can be reduced to the calculation of the partition function of a 3D Ising model in an external field. For a square-well symmetrical binary mixture we calculate the parameters of the critical point (critical temperature and critical density) as functions of the microscopic parameters: the parameter $r$ measuring the relative strength of interactions between the particles of dissimilar and similar species and the parameter $\lambda$ measuring the width of the potential well. The obtained results agree well with the ones of computer simulations.
Year:
2000
Pages:
24 | 2019-08-21 00:33:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6871815323829651, "perplexity": 456.57911744433085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315695.36/warc/CC-MAIN-20190821001802-20190821023802-00328.warc.gz"} |
http://mathcentral.uregina.ca/QQ/database/QQ.09.11/h/rahul1.html | SEARCH HOME
Math Central Quandaries & Queries
Question from Rahul: I want to know about limit proofs of composite functions. Like limit of log of a function equals log of limit of the function
Hi Rahul,
I think the result you want is
If $f$ is continuous at $b$ and $\lim_{x \rightarrow a} \; g(x) = b$ then
$\lim_{x \to a} f(g(x)) = f(b) = f\left(\lim_{x \to a} \; g(x) \right)$
Penny
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. | 2022-10-04 14:30:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45223212242126465, "perplexity": 839.7571767066229}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337504.21/warc/CC-MAIN-20221004121345-20221004151345-00300.warc.gz"} |
https://bitbucket.org/spookylukey/django-selectable/src/dbe91d1afb4e8a2008dd7e3cafd86164bd84abfc/docs/lookups.rst?at=version-0.2.0 | # Defining Lookups
## What are Lookups?
Lookups define the corresponding ajax views used by the auto-completion fields and widgets. They take in the current request and return the JSON needed by the jQuery auto-complete plugin.
## Defining a Lookup
django-selectable uses a registration pattern similar to the Django admin. Lookups should be defined in a lookups.py in your application's module. Once defined you must register in with django-selectable. All lookups must extend from selectable.base.LookupBase which defines the API for every lookup.
from selectable.base import LookupBase
from selectable.registry import registry
class MyLookup(LookupBase):
def get_query(self, request, term):
data = ['Foo', 'Bar']
return filter(lambda x: x.startswith(term), data)
registry.register(MyLookup)
## Lookups Based on Models
Perhaps the most common use case is to define a lookup based on a given Django model. For this you can extend selectable.base.ModelLookup. To extend ModelLookup you should set two class attributes: model and search_field.
The syntax for search_field is the same as the Django field lookup syntax. You may optionally define a third class attribute filters which is a dictionary of filters to be applied to the model queryset. The keys should be a string defining a field lookup and the value should be the value for the field lookup. | 2016-02-06 21:36:53 | {"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": 0.20603734254837036, "perplexity": 5940.547007417868}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701147841.50/warc/CC-MAIN-20160205193907-00328-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://blender.stackexchange.com/questions/6608/how-to-get-3d-view-grid-properties | # How to get 3d view grid properties?
I am trying to store the grid scale, but keep getting an error for being in the text editor view.
I have tried
bpy.context.area.type = "VIEW_3D"
print(bpy.context.space_data.grid_scale)
but am getting an attribute error for "SpaceTextEditor" not having a "grid_scale". However, the space does change to the 3d view, so the first line is going through.
Any help is appreciated.
Your code works for me in 2.69, but there might be timing issues (grid_scale accessed but the view has not finished changing).
To get all 3D Views' grid_scale as a list, use:
grid_scales = [area.spaces[0].grid_scale for area in bpy.context.screen.areas if area.type == 'VIEW_3D'] | 2020-01-25 17:56:11 | {"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": 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": 0.20996201038360596, "perplexity": 3647.358747183806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251678287.60/warc/CC-MAIN-20200125161753-20200125190753-00358.warc.gz"} |
http://www.maths.ox.ac.uk/node/33054 | # Exact functors on perverse coherent sheaves
Koppensteiner, C
September 2015
## Journal:
COMPOSITIO MATHEMATICA
## Last Updated:
2020-07-12T22:08:21.707+01:00
9
151
## DOI:
10.1112/S0010437X15007265
1688-1696
## abstract:
Inspired by symplectic geometry and a microlocal characterizations of
perverse (constructible) sheaves we consider an alternative definition of
perverse coherent sheaves. We show that a coherent sheaf is perverse if and
only if $R\Gamma_Z(\mathcal{F})$ is concentrated in degree 0 for special
subvarieties Z of X. These subvarieties Z are analogs of Lagrangians in the
symplectic case.
1037510 | 2020-12-01 05:54:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8812204003334045, "perplexity": 4603.909564445412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1606141652107.52/warc/CC-MAIN-20201201043603-20201201073603-00537.warc.gz"} |
http://mathematica.stackexchange.com/questions/13675/symbolic-findinstance | # Symbolic FindInstance
I'm wondering if there is any way of doing something like the following: FindInstance[x < y, {x}, Reals] and getting, as a possible return value, {x -> y - 1}.
Currently FindInstance will complain that y is a non-constant expression..
-
I am assuming you would not be satisfied with FindInstance[x - y < 0, {x, y}, Reals] (* {x->0,y->1} *) – chris Oct 26 '12 at 9:59
At this point, I think that I will just implement a function which uses CylindricalDecomposition. If I do successfully do that, I'll post it as an answer here. – jnhnum1 Oct 27 '12 at 16:33 | 2014-09-19 01:55:50 | {"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": 0.4348122775554657, "perplexity": 1229.6217460853677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657129431.12/warc/CC-MAIN-20140914011209-00030-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://isfana.ru/calculating-profitability-index-in-excel/ | Learn finance, banking, risk, data science and fintech
# Calculating Profitability Index in Excel
Profitability index is an important measure in project finance to decide whether to invest in a project or not. It is calculated as the ratio of present value of a project cash flows and the initial investment.
$Profitability\ Index = \frac{PV\ of\ Future\ Cash\ Flows}{Initial\ Investment}$
If the profitability index is greater than 1, the project is accepted, and if it is less than 1, the project is rejected.
Let’s see how profitability index can be calculated in excel. Let us say that we are examining a project, which requires an initial investment of $10,000, and after the will give us cash flow of$3,000, $4,000,$2,000, 41,500, and \$1,800 in the next five years.
To calculate the profitability index:
Step 1: Assume a required rate of return, or cost of capital for the project. Let’s say the cost of capital is 10%.
Step 2: Calculate the present value of all future cash flows. You can use the PV() function in excel for this calculation.
Step 3: Take the total of PV of all future cash flows. In our example, the total is 9677.87.
Step 4: Calculate profitability Index as follows:
Profitability Index = 9677.87/10,000 = 0.97
Since the profitability index is less than one, this project should not be accepted. The cash flows and calculations are shown below: | 2018-01-19 21:05:22 | {"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": 1, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.501107394695282, "perplexity": 980.8095871197239}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084888135.38/warc/CC-MAIN-20180119204427-20180119224427-00494.warc.gz"} |
https://thermtest.com/papers_author/takeshi-okutani | # Thermal Conductivity Paper Database
## Recommended Papers for: Takeshi Okutani
Total Papers Found: 3
#### Thermophysical properties of Zr–Cu–Al metallic glasses during crystallization
Zr-Cu-Al metallic glasses were formulated with differing compositions to determine their thermophysical properties. It was determined that by decreasing the zirconium content of the metallic glass, the thermal conductivity can be increased. The maximum value of thermal conductivity was found for the metallic glass with ...
Author(s):
#### Thermal conductivity measurement of molten indium antimonide in short-duration microgravity
In this study, a sensor measured the thermal conductivity of molten indium antimonide (InSb) using the transient plane source (TPS) method. The measurements were taken during a 10 m short-duration microgravity drop. Results showed that the thermal conductivities of molten InSb were higher in normal gravity ...
Author(s):
#### Development of Sensor for Molten Metal, and the Thermal Conductivity Measurement of Molten Bismuth and Tin
The authors measured the thermal conductivity of a couple molten metals, namely bismuth and tin. This was accomplished by using a molybdenum sensor placed in between two aluminum nitride plates (to protect the molybdenum sensor from the high temperature of the molten metals. The thermal ...
Author(s): | 2023-03-30 20:45:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9010862708091736, "perplexity": 5632.381525302644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1679296949387.98/warc/CC-MAIN-20230330194843-20230330224843-00583.warc.gz"} |
https://open.kattis.com/problems/smartphone | Kattis
# Smart Phone
You have a very smart phone. Here is the user experience when entering a word:
1. You decide on the word you want to write.
2. You start typing it.
3. At some point, three suggestions appear. The list of suggestions never changes after it has first been presented, even if you keep typing.
You always only get three suggestions. This would mean that the suggestions would not always fit on the screen. However, when this happens they are read aloud by a text to speech plugin that cost $9.99. Yes, it reads all the suggestions for every character you enter until you take one of the suggestions. Since it’s a very smart phone, you can only do the following: • Replace what you have written so far with one of the suggestions. • Hit the backspace button. • Enter a letter. Each of these options takes one keypress. An example: you want to enter the text CAKEEATER. When the suggestions appear, you had gotten to CAK. Let’s say you decide to take the suggestion CAKEMONSTER, remove MONSTER and enter EATER. This would mean that you used 1+7+5=13 keypresses to get to the word CAKEEATER. The only time you would want to do this is when you want to annoy the cookie monster. Also, a lot of keypresses could have been avoided here if we had made different decisions. Write a program that minimize the amount of keypresses given the current input, the desired word and the three suggestions from your very smart phone. ## Input The first line of the input consists of a single integer,$T$, the number of test cases. For each test case there will be five lines: • The word you want to type. • What has been written so far. • Suggestion 1 • Suggestion 2 • Suggestion 3. •$1 \leq T \leq 50\$
• All line lengths will be greater than zero, and less than or equal to 25.
• All lines consist of only uppercase characters from the English alphabet (AZ).
## Output
For each test case, output the minimum number of keypresses needed to get to the desired word.
Sample Input 1 Sample Output 1
2
CAKEEATER
CAK
CAKEMONSTER
CARNIVAL
CAKEEATUR
IDIOPEN
HODOR
KEG
IPHONE
FLUXCAPACITATOR
5
11 | 2019-06-25 21:33:56 | {"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": 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": 0.6804103851318359, "perplexity": 1296.1785739310178}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1560627999948.3/warc/CC-MAIN-20190625213113-20190625235113-00312.warc.gz"} |
https://www.varsitytutors.com/isee_middle_level_math-help/how-to-find-a-square-on-a-coordinate-plane | # ISEE Middle Level Math : How to find a square on a coordinate plane
## Example Questions
### Example Question #1 : How To Do Coordinate Geometry
Which of the following is a vertex of the square?
Explanation:
The coordinates of a point are determined by the distance from the origin. The first point in the ordered pair is the number of units to the left or right of the origin. Negative numbers indicate the number of units to the left while positive numbers indicate the number of units to the right. The second number indicates the number of units above or below the origin. Positive numbers indicate the number of units above while negative numbrs indicate the number of units below the origin. The vertices of the square are: | 2017-09-22 03:02:16 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8285579681396484, "perplexity": 217.58674561192254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688158.27/warc/CC-MAIN-20170922022225-20170922042225-00281.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/driving-home-school-one-day-spot-ball-rolling-street-see-figure--brake-130-s-slowing-980-r-q937376 | Driving home from school one day, you spot a ball rolling out into the street (see the figure ). You brake for 1.30 s, slowing your 980-{\rm kg} car from 16.0 \rm m/s to 9.50 \rm m/s.
What was the magnitude of the average force exerted on your car during braking?
F =
\rm N
Part B
What was the direction of the average force exerted on your car during braking?
To the direction of motion.
Opposite to the direction of motion. | 2015-12-01 06:30:58 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8284506797790527, "perplexity": 1888.613929366175}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398464536.35/warc/CC-MAIN-20151124205424-00020-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://brilliant.org/explorations/probability/math-of-poker/b-premium/?element_id=clicked_locked_chapter_btn_from_explorations_topic_page | Back to all chapters
# Math of Poker
You aren't a true card shark unless you know your probabilities.
# A preview of "Math of Poker"Join Brilliant Premium
What is the probability of drawing a Heart or a King from a shuffled poker deck?
4 cards are drawn from a shuffled poker deck. How many possible combinations of these cards (without regard to order) are there?
You are playing a game of Five-Card Draw poker. You are dealt the following hand:
During the draw phase, you discard the $$2\clubsuit$$ and $$\text{Q}\spadesuit$$ cards and request two new cards.
What is the probability that you will improve your hand to a straight?
Note: You have no knowledge of the cards the other players have.
× | 2017-04-30 01:10:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.3312603533267975, "perplexity": 927.6658358756872}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1492917123635.74/warc/CC-MAIN-20170423031203-00547-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://en.m.wikibooks.org/wiki/Probability_Theory/Independence | # Probability Theory/Independence
note to self: in the case of indep., the rules of the kind ${\displaystyle P(\sum \prod )=\sum \prod P}$ should be derived.
Definition (independence of events):
Let ${\displaystyle (\Omega ,{\mathcal {F}},P)}$ be a probability space and let ${\displaystyle A,B\in {\mathcal {F}}}$. ${\displaystyle A}$ and ${\displaystyle B}$ are said to be independent iff ${\displaystyle P(A\cap B)=P(A)P(B)}$.
Remark (independence and conditional probability):
Using the definition of conditional probability, if e.g. ${\displaystyle P(A)\neq 0}$ we may rephrase the independence of ${\displaystyle A}$ and ${\displaystyle B}$ as ${\displaystyle P(B)=P(B|A)}$. | 2023-02-06 20:17:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 10, "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": 0.9582842588424683, "perplexity": 296.4673494361743}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1674764500357.3/warc/CC-MAIN-20230206181343-20230206211343-00114.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/how-do-you-solve-log-x-15-2-logx | How do you solve log(x-15)=2-logx?
Sep 18, 2015
$x = 20$
Explanation:
Put everything that's a log on the same side
$\log \left(x - 15\right) + \log \left(x\right) = 2$
Remember that $\log \left(m\right) + \log \left(n\right) = \log \left(m n\right)$
$\log \left(x \left(x - 15\right)\right) = 2$
If ${\log}_{a} \left(b\right) = c$, then $b = {a}^{c}$
$x \left(x - 15\right) = {10}^{2}$
Expand and solve the quadratic equation
${x}^{2} - 15 x = 100 \rightarrow {x}^{2} - 15 x - 100 = 0$
$x = \frac{15 \pm \sqrt{225 - 4 \cdot 1 \left(- 100\right)}}{2} = \frac{15 \pm \sqrt{225 + 400}}{2}$
$x = \frac{15 \pm \sqrt{625}}{2} = \frac{15 \pm 25}{2}$
${x}_{1} = \frac{15 + 25}{2} = \frac{40}{2} = 20$
${x}_{2} = \frac{15 - 25}{2} = - \frac{10}{2} = - 5$
Remember that since we were dealing with logarithms, we can't have null or negative arguments, so
$x - 15 > 0 \rightarrow x > 15$
$x > 0$
We conclude that any answers must follow $x > 15$, which only of the two answers do, thus, the answer is $x = 20$ | 2021-10-26 11:37:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 16, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7330345511436462, "perplexity": 887.2703697119332}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587877.85/warc/CC-MAIN-20211026103840-20211026133840-00315.warc.gz"} |
http://mathoverflow.net/revisions/74859/list | Post Made Community Wiki by S. Carnahan
3 added 1 characters in body
The theorem of "friends and strangers": the Ramsey number $R(3,3)=6$. Not only can the proof be understood by high-school students, proofs a proof can be discovered by students at that level via something akin to the Socratic method. First students can establish the bound $R(3,3) > 5$ by 2-coloring the edges of $K_5$:
Then they can reason through that a 2-coloring of the edges of $K_6$ must contain a monochromatic triangle, and so $R(3,3)=6$: in every group of six, three must be friends or three must be strangers.
After this exercise, an inductive proof of the 2-color version of Ramsey's theorem is in reach.
An added bonus here is that one quickly reaches the frontiers of mathematics: $R(5,5)$ is unknown! It can be a revelation to students that there is a frontier of mathematics. And then one can tell the Erdős story about $R(6,6)$, as recounted here. :-)
2 deleted 8 characters in body
The theorem of "friends and strangers": the Ramsey number $R(3,3)=6$. Not only can the proof be understood by high-school students, proofs can be discovered by students at that level via something akin to the Socratic method. First students can establish the bound $R(3,3) > 5$ by 2-coloring the edges of $K_5$:
Then they can reason through that a 2-coloring of the edges of $K_6$ must contain a monochromatic triangle, and so $R(3,3)=6$. And so R(3,3)=6$: in every group of six, three must be friends or three must be strangers. After this exercise, an inductive proof of the 2-color version of Ramsey's theorem is in reach. An added bonus here is that one quickly reaches the frontiers of mathematics:$R(5,5)$is unknown! It can be a revelation to students that there is a frontier of mathematics. And then one can tell the Erdős story about$R(6,6)\$, as recounted here. :-)
1 | 2013-05-23 15:47:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6401820182800293, "perplexity": 720.5630944410638}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703532372/warc/CC-MAIN-20130516112532-00010-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://harrypotter.wikia.com/wiki/Pullus | # Pullus Jinx
## Redirected from Pullus
14,896pages on
this wiki
The Pullus Jinx (Pullus) is a transforming jinx used to transfigure the target into a chicken or a goose; in particular, Erklings appear to be rather vulnerable to this jinx
## History
This jinx was used in 1754 by an unknown wizard on Silvio Astolfi, an Italian broom racer.[1]
## Etymology
Pullus is Latin for the young of animals, particularly chickens (i.e. chicks). | 2017-05-29 22:54:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8541455864906311, "perplexity": 10085.173621129594}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463613135.2/warc/CC-MAIN-20170529223110-20170530003110-00324.warc.gz"} |
https://www.albert.io/ie/ap-chemistry/ionization-energy-data | Free Version
Difficult
# Ionization Energy Data
APCHEM-GIQ7UO
Consider the following ionization energy data (kJ/mol):
Element Ionization Energy (kJ/mol)
$N$ 1402
$O$ 1314
$F$ 1681
$Ne$ 2081
$\$
Which of the following is the BEST explanation for why the ionization energy for oxygen is the lowest for these elements?
A | 2017-03-24 02:18:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5025390982627869, "perplexity": 3158.8761524376737}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1490218187519.8/warc/CC-MAIN-20170322212947-00367-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.cymath.com/blog/2021-11-08 | # Problem of the Week
## Updated at Nov 8, 2021 3:57 PM
How can we find the derivative of $${x}^{7}+4x$$?
Below is the solution.
$\frac{d}{dx} {x}^{7}+4x$
1 Use Power Rule: $$\frac{d}{dx} {x}^{n}=n{x}^{n-1}$$.$7{x}^{6}+4$Done7*x^6+4 | 2021-11-27 22:50:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46743741631507874, "perplexity": 2845.4096216989983}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1637964358323.91/warc/CC-MAIN-20211127223710-20211128013710-00411.warc.gz"} |
https://math.stackexchange.com/questions/416031/greatest-common-divisor-of-two-numbers | Greatest Common Divisor of two numbers
If $ab=600$ how large can the greatest common divisor of $a$ and $b$ be?
I am not sure if I should check for all factor multiples of $a$ and $b$ for this question. Please advise.
We have $600=2^3\cdot 5^2\cdot 3$. To make the gcd large, we give a $2$ to each of $a$ and $b$, also a $5$. So the largest possible gcd is $10$.
Remark: The idea generalizes. Let $n$ have prime power factorization $$n=p_1^{d_1}p_2^{d_2}\cdots p_k^{d_k}.$$ Let $e_i=\lfloor d_i/2\rfloor$, where $\lfloor x\rfloor$ is the greatest integer that is $\le x$. Then the greatest possible gcd of $a$ and $b$, where $ab=n$, is $$p_1^{e_1}p_2^{e_2}\cdots p_k^{e_k}.$$
• You are welcome. For the maximum, we distribute the power of any prime $p$ as evenly as possible between $a$ and $b$. – André Nicolas Jun 10 '13 at 2:00
$$ab=600=2^3\cdot 3\cdot 5^2$$ The greatest common divisor of $a,b$ will have the greatest number of common prime factors that you can arrange. | 2019-10-22 14:26:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9121160507202148, "perplexity": 94.30818004161397}, "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-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00417.warc.gz"} |
https://rpg.meta.stackexchange.com/questions/8752/should-the-wfrp-4-tag-be-renamed-to-wfrp-4e | Should the [wfrp-4] tag be renamed to [wfrp-4e]?
Pretty straightforward stuff. We generally use the -[#]e tag suffix to denote different editions (presumably because that's how those editions of those games are commonly abbreviated) - and the tags for the previous three editions of Warhammer Fantasy Roleplay follow this trend: , , and . (There's also a general tag, but that's not relevant here.)
The tag was created a little over a month ago; I'm guessing the person who created it wasn't aware of the convention for edition tags.
Should the tag be renamed to ? | 2020-01-24 05:13:53 | {"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": 0.26437655091285706, "perplexity": 2522.894628870971}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250615407.46/warc/CC-MAIN-20200124040939-20200124065939-00366.warc.gz"} |
https://math.stackexchange.com/questions/2414647/help-in-solving-pde-heat-problem-with-ffct | # help in Solving PDE heat problem with FFCT
solve the following heat problem using Finite Fourier Coseine Transform(FFCT): A metal bar of length $L$, is at constant temperature of $U0$, at $t=0$ the end $x=L$ is suddenly given the constant temperature of $U_1$ and the end $x=0$ is insulated. Assuming that the surface of the bar is insulated, find the temperature at any point $x$ of the bar at any time $t>0$ , assume $k=1$
Equations used: 1. Heat equation: $$\frac {\partial^2 u} {\partial x^2} = \frac 1 k \frac {\partial u} {\partial t}$$ 2. the following FFCT Equations ( as in the attached pic): FFCT Equations
My attempt at solutions goes like this: $$\frac {\partial^2 u} {\partial x^2} = \frac 1 k \frac {\partial u} {\partial t}$$ $$\mathcal{F}_{fc} \left[ \frac {\partial u} {\partial t} \right] = \mathcal{F}_{fc} \frac {\partial^2 u} {\partial x^2}$$ $$\frac {dU} {dt} = {-\left( \frac {{n} {\pi}} L \right)}ˆ{2} * F(x,t) + \left( {-1} \right)ˆn \frac {\partial{f(L,t)}} {\partial x} - \frac {\partial{f(0,t)}} {\partial x}$$ $$\frac {dU} {dt} = - \left( \frac {{n} {\pi}} L \right)ˆ(2) * F(x,t) + \left( {-1} \right)ˆn \frac {\partial{f(L,t)}} {\partial x}$$
and i don't know how to continue, can you provide the rest of the solution in details please, regards.
• Hello Mr. @Harry49 , here is my complete problem. – aows61 Sep 14 '17 at 16:24
• i just want to make sure you got the problem @Harry49 – aows61 Sep 14 '17 at 16:30
• Hello Mr Harry @Harry49 – aows61 Sep 14 '17 at 16:31
• Please stop the spam! The most straightforward way to solve this PDE problem is separation of variables (see e.g. [1]). – Harry49 Sep 14 '17 at 16:32
• dear Mr. @Harry49 , i already solve it using separation of variables, but am required solve it using the Finite Fourier Cosine Transform (FFCT), and i tried but stopped somewhere. – aows61 Sep 14 '17 at 16:37 | 2019-07-23 15:40:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8326833844184875, "perplexity": 672.5894205777159}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1563195529480.89/warc/CC-MAIN-20190723151547-20190723173547-00122.warc.gz"} |
https://answers.opencv.org/answers/225744/revisions/ | # Revision history [back]
After some search, I think I can now answer my own questions.
What is the fast pyramids approach?
On browsing the OpenCV source code, in optflowgf.cpp, I found the following lines:
// Crop unnecessary levels
double scale = 1;
int numLevelsCropped = 0;
for (; numLevelsCropped < numLevels_; numLevelsCropped++)
{
scale *= pyrScale_;
if (size.width*scale < min_size || size.height*scale < min_size)
break;
}
The above lines crop the pyramid levels which are smaller than min_size x min_size. Furthermore, min_size is defined, still in optflowgf.cpp, as
const int min_size = 32;
Finally, again in optflowgf.cpp, I found
if (fastPyramids_)
{
// Build Gaussian pyramids using pyrDown()
pyramid0_.resize(numLevelsCropped + 1);
pyramid1_.resize(numLevelsCropped + 1);
pyramid0_[0] = frames_[0];
pyramid1_[0] = frames_[1];
for (int i = 1; i <= numLevelsCropped; ++i)
{
pyrDown(pyramid0_[i - 1], pyramid0_[i]);
pyrDown(pyramid1_[i - 1], pyramid1_[i]);
}
}
I would then say that fast pyramids skip too small pyramid levels.
In which way are we smoothing derivatives?
From Farneback's paper "Two-Frame Motion Estimation Based on Polynomial Expansion", my understanding is that the window function involved in eq. (12) is a Gaussian. From this point of view, polyN x polyN is the size of the window, while polySigma is the standard deviation of the Gaussian. | 2021-01-24 23:08:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30583620071411133, "perplexity": 8030.247328972492}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610703557462.87/warc/CC-MAIN-20210124204052-20210124234052-00023.warc.gz"} |
https://juliadocs.github.io/Documenter.jl/latest/lib/internals/anchors/ | # Anchors
Documenter.Anchors.AnchorType
Stores an arbitrary object called .object and it's location within a document.
Fields
• object – the stored object.
• order – ordering of object within the entire document.
• file – the destination file, in build, where the object will be written to.
• id – the generated "slug" identifying the object.
• nth – integer that unique-ifies anchors with the same id.
source
Documenter.Anchors.AnchorMapType
Tree structure representating anchors in a document and their relationships with eachother.
Object Hierarchy
id -> file -> anchors
Each id maps to a file which in turn maps to a vector of Anchor objects.
source | 2022-08-16 01:42:49 | {"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": 0.2707662582397461, "perplexity": 6545.207119222927}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882572215.27/warc/CC-MAIN-20220815235954-20220816025954-00173.warc.gz"} |
https://www.bbc.co.uk/bitesize/guides/zkfwxnb/revision/6 | Acids are neutralised by bases
A neutralisation reaction is one in which an acid reacts with a base to form water. A salt is also formed in this reaction.
Bases are metal oxides, metal hydroxides and metal carbonates.
In the neutralisation reaction between an acid and a metal carbonate, there are three products, a salt, water and also carbon dioxide gas.
$\begin{array}{l} \text{Hyrdrochloric acid} + \text{calcium carbonate} \to \\ \text{calcium chloride} + \text{water} + \text{carbon dioxide} \end{array}$
The salt is named in the same way as before, taking the metal's name from the metal carbonate and the ending from the type of acid used.
Carbon dioxide can be tested for using lime water (turns from colourless to chalky white). | 2021-06-23 19:18:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41042041778564453, "perplexity": 4757.076524283937}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488539764.83/warc/CC-MAIN-20210623165014-20210623195014-00210.warc.gz"} |
https://www.physicsforums.com/threads/find-minimum-value-of-the-expression.753528/ | # Find minimum value of the expression
1. May 13, 2014
### utkarshakash
1. The problem statement, all variables and given/known data
Let n be a positive integer. Determine the smallest possible value of $$|p(1)|^2+|p(2)|^2 + .........+ |p(n+3)|^2$$ over all a monic polynomials p with degree n.
3. The attempt at a solution
Let the polynomial be $x^n+c_{n-1} x^{n-1} +.........+ c_1x+c_0$
p(1) = $c_0+c_1+c_2+........+1$
Similarly I can write p(2) and so on, square them and add them together to get a messy expression. But after this, I don't see how to find its minimum value. The final expression is itself difficult to handle. I'm sure I'm missing an easier way to this problem.
2. May 13, 2014
### Staff: Mentor
You don't need the full expressions to find derivatives with respect to the coefficients.
3. May 13, 2014
### utkarshakash
Derivative wrt to which coefficient? There are so many.
4. May 13, 2014
### Ray Vickson
Yo have n variables $c_0,c_1, \ldots, c_{n-1}$ and a function
$$f(c_0,c_2, \ldots, c_{n-1}) = \sum_{k=1}^{n+3} [k^n + c_{n-1} k^{n-1} + \cdots + c_1 k + c_0]^2$$
You minimize $f$ by setting all its partial derivatives to zero; that is, by setting up and solving the equations
$$\frac{\partial f}{\partial c_i} = 0, \: i = 0, 1, 2, \ldots, n-1$$ | 2017-11-18 22:08:55 | {"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": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49237239360809326, "perplexity": 431.03176555266657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805049.34/warc/CC-MAIN-20171118210145-20171118230145-00454.warc.gz"} |
https://gaurish4math.wordpress.com/tag/radicals/ | I have figured out that $\sqrt{1- \sqrt{1+ \sqrt{1- \sqrt{\ldots } }}}$ is a diverging series. But now I am struck with another problem: | 2020-01-28 15:05:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7358754277229309, "perplexity": 89.7378794963236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1579251778272.69/warc/CC-MAIN-20200128122813-20200128152813-00181.warc.gz"} |
https://stats.stackexchange.com/questions/32340/negative-binomial-irr-interpretation-for-predictors | # Negative binomial — IRR interpretation for predictors
I have a zero-inflated negative binomial model. I have used incidence rate ratios and I'm trying to interpret the coefficients in relation to my predictors. Most of my predictors are continuous variables of census data -- ie: % of the population that is Hispanic; % of the population less than age 18, etc. I know that the IRR is normally interpreted as the rate ratio for a 1-unit increase in the independent variable, but what does this mean in terms of these continuous predictors -- does this mean the IRR is the estimated rate ratio for a 1% increase in % Hispanic. Is there a way I can scale this so it can be interpreted to be the estimated rate ratio for a 10% increase in the % Hispanic? Also, one of my IRR's is 20. Does that seem unusually high?
• The last question cannot be answered without knowing more about your outcome and the predictors. A factor of 20 increase for 1 percentage point increase in X could make sense in some contexts. You might also find the second example useful: ats.ucla.edu/stat/stata/output/stata_nbreg_output.htm – Dimitriy V. Masterov Jul 9 '13 at 17:26 | 2019-10-21 01:20:37 | {"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": 0.8783987164497375, "perplexity": 581.7283208309217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570987750110.78/warc/CC-MAIN-20191020233245-20191021020745-00293.warc.gz"} |
https://socratic.org/questions/how-do-you-sketch-a-graph-with-x-intercept-of-1-and-y-intercept-of-5 | # How do you sketch a graph with x-intercept of 1 and y-intercept of -5?
Assuming that the function is a line, the graph is immediately obatined: the $x$ intecept is $1$, so the point $\left(1 , 0\right)$ belongs to the line. The same goes for the $y$ intercept: it says us that the point $\left(0 , - 5\right)$ belongs to the line. | 2019-10-22 10:50:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7580963969230652, "perplexity": 254.29241240763005}, "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-2019-43/segments/1570987817685.87/warc/CC-MAIN-20191022104415-20191022131915-00363.warc.gz"} |
https://www.boost.org/doc/libs/1_80_0/libs/hana/doc/html/structboost_1_1hana_1_1detail_1_1nested__than.html | Boost.Hana 1.7.1 Your standard library for metaprogramming
boost::hana::detail::nested_than< Algorithm > Struct Template Reference
## Description
### template<typename Algorithm> struct boost::hana::detail::nested_than< Algorithm >
Provides a .than static constexpr function object.
When creating a binary function object of type Algo whose signature is A x B -> Return, nested_than<Algo> can be used as a base class of Algo. Doing so will provide a static constexpr member called than, which has the following signature:
B -> A -> Return
times A(T_1) \times \cdots \times A(T_n) \to A(U) @f\$. const expr auto ap
Lifted application.
Note that the function object Algo must be default-constructible, since it will be called as Algo{}(arguments...).
Note
This function object is especially useful because it takes care of avoiding ODR violations caused by the nested static constexpr member. | 2023-01-31 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": 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": 0.541082501411438, "perplexity": 10331.072628917322}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1674764499890.39/warc/CC-MAIN-20230131190543-20230131220543-00554.warc.gz"} |
https://math.stackexchange.com/questions/2058616/how-to-find-the-solution-to-this-system-of-integer-variables/2058622 | # How to find the solution to this system of integer variables?
Let $x_i$ be nonnegative integer variables in $\mathbb{N}$. The system is to find $x_i$ in
$$\sum_{i=1}^nx_i=3n,\\\quad \quad \quad \quad \;\;\,x_i\leqslant3,\,\forall\, i\in\{1,\ldots,n\}.$$
I find the solution to be $x_i=3$ for all $i$ but I cannot prove that it is the unique solution.
• If there was a different soluion, some of the $x_i$ would be smaller and some of them larger than $3$, but the second condition says they can't be larger. – Henrik Dec 14 '16 at 16:01
Suppose that some $x_j <3$. Wlog we can assume $j=1$. Then $$\sum_{i=1}^{n} x_i = x_1 + \sum_{i=2}^{n}x_i \le 2 + 3(n-1) < 3n.$$ So we have a contradiction.
$$\sum_{i=1}^nx_i \leq \sum_{i=1}^n3=3n$$ and the equality holds only when $x_i=x_j$ for all $i,j$.
So the only solution is $x_i=3$ for all $i$
Suppose at least $1 \ x_i$ is less than $3$. Then there must be at least one $x_j$ strictly greater than $3$ to make up for $3n$ . Hence a contradiction
Assume there is an other solution $(y_i)_{i=1,2...n}$ . then
$$S=\sum_{i=1}^n|3-y_i|=0 \implies$$
$$\forall i\in\{1,2,...n\}\;\;S\geq |3-y_i|\geq 0$$
$$\implies \forall i\in\{1,2,...n\}\;\;y_i=3$$ | 2019-07-20 08:14:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.936028003692627, "perplexity": 90.3100079552393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1563195526489.6/warc/CC-MAIN-20190720070937-20190720092937-00110.warc.gz"} |
http://lara.epfl.ch/w/cartesianproducts?rev=1429631101&do=diff | • English only
# Differences
This shows you the differences between two versions of the page.
cartesianproducts [2015/04/21 17:44]
cartesianproducts [2015/04/21 17:45] (current)
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...in a system with only two positions can be seen as the constraint: ...in a system with only two positions can be seen as the constraint:
-$p_i = ENode \times ]2;\infty[$+\begin{equation*}p_i = ENode \times ]2;\infty[ \end{equation*}
This works well for .isInstanceOf checks as well, but not for stuff like if i > j, as our cartesian products have no way to represent dependencies between members. This works well for .isInstanceOf checks as well, but not for stuff like if i > j, as our cartesian products have no way to represent dependencies between members. | 2019-05-24 10:17:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9569936990737915, "perplexity": 1531.6316994390234}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257601.8/warc/CC-MAIN-20190524084432-20190524110432-00292.warc.gz"} |