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https://blog.theleapjournal.org/2011/06/freedom-of-speech-in-pakistan-and-india.html | ## Monday, June 06, 2011
### Freedom of speech in Pakistan and India
One of Pakistan's more remarkable journalists, Syed Saleem Shahzad, was tortured and murdered, probably by Pakistan's ISI.
In one view of the world, freedom of speech is something that you are gifted by your founding fathers. As an example, if you have the good fortune of having a well drafted Constitution, it would say Congress shall make no law ... abridging the freedom of speech, or of the press;. This would block the ability of politicians to enact legislation that is inimical to freedom of speech. Then, as long as rule of law prevails, we get freedom of speech. This seems like a palace coup, it seems rather easy, as long as you have the right intellectual capabilities in the hands of those who draft the Constitution of a country.
We in India or Pakistan are not blessed thusly. The Indian Constitution is not clear-headed about freedom of speech, and anti-defamation law of colonial vintage continues to be on the books. This is an important tool for harassment and intimidation. And then, there is the question of rule of law. What is going on in Pakistan is way beyond questions of how the Constitution should be drafted.
It is, instead, more useful to think that democracy and freedom are made of a million battles, small and large. Freedom of speech is won, piece by piece, through a million mutinies. It is important to constantly think, and speak, and write. Each little act of writing about troublesome issues pushes the envelope of freedom of speech, and creates a culture of honest discussion and discourse.
I feel the media in India has become quite complacent about the tawdry condition of free speech in India. All too often journalists can be warned off a seamy story by a tiny exercise of power or influence. All too often, the crooks are able to buy the loyalty of a journalist quite easily. There isn't enough intellectualism going around, among the men and women in the media. Eshwar Sundaresan, writing in Dawn, says that India badly needs more journalists of the character of Pakistan's Najam Sethi. This is one of many areas where India's success in the last 20 years is leading to an erosion of the very foundations of that success.
LaTeX mathematics works. This means that if you want to say $10 you have to say \$10. | 2019-08-24 13:47:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18215738236904144, "perplexity": 2664.595533681326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027321140.82/warc/CC-MAIN-20190824130424-20190824152424-00019.warc.gz"} |
https://hocatt.com/technology/ozone/ | Call Us Today! 1-844-696-9663
Ozone2018-08-24T13:18:56+00:00
# Ozone
## Ozone Sauna
The HOCATT has an Oxygen concentrator that sends pure Oxygen (O2) to its two Ozone generators. The Ozone generators then use this Oxygen to make pure Ozone (O3), so you can think of Ozone as a Super-Oxygen. The Ozone is infused into the HOCATT chamber (as shown above), where it then mixes with the steam (H2O) to form Ozone products. This creates a relaxing sauna experience with all the benefits of Transdermal Ozone.
The second Ozone generator in the HOCATT is dedicated to delivering pure Ozone to the auxiliary attachments for Ozone Cupping or Vaginal Ozone Insufflations. With the HOCATT, you can save time by using these auxiliary features during a HOCATT sauna session. Alternatively, they can also be used as stand-alone applications.
## Ozone Cupping
You can use a cup, or set of cups, and enjoy Ozone Cupping over specific areas, such as the breasts (as shown above). Cupping is also a form of Transdermal Ozone.
## Vaginal Ozone Insufflations
You can use a disposable catheter for Vaginal Ozone Insufflations (as shown above). | 2018-10-22 20:59:16 | {"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": 0.8106736540794373, "perplexity": 10223.565871879946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1539583515539.93/warc/CC-MAIN-20181022201445-20181022222945-00336.warc.gz"} |
https://cs.stackexchange.com/questions/10245/lookahead-set-determining-minimum-k-such-that-g-is-a-strong-llk-grammar | # Lookahead set: Determining minimum $k$ such that $G$ is a strong $LL(k)$ grammar
How do we determine minimum $k$ such that $G$ is a strong $LL(k)$ Grammar
Like for grammar $G$ with the following rules $S\rightarrow aAcaa \mid bAbcc,A\rightarrow a \mid ab \mid \epsilon$
I do not believe one can obtain directly a minimum $k$ such that $G$ is a strong $LL(k)$ grammar. However, as it is possible to (dis)prove that a grammar is strong $LL(k)$, one can iterate the proof over $k$.
A grammar $G$ is strong $LL(k)$ iff for every pair of distinct production rules $A \to \alpha$ and $A \to \beta$ (with $\alpha \neq \beta$), we have:
$$First_k( \alpha \; Follow_k(A) ) \; \cap \; First_k( \beta \; Follow_k(A) ) = \emptyset$$
The steps to obtain a $k$ for a certain grammar $G$ are thus as follows:
• For each $n > 0$:
1. Check wether $G$ is $LL(n)$
2. If so, try proving $G$ is $LL(n)$
3. If not, we have found our $k = n - 1$
Some documents that might help with the actual proof: | 2020-01-17 20:23:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8714144825935364, "perplexity": 282.9974024743674}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250590107.3/warc/CC-MAIN-20200117180950-20200117204950-00008.warc.gz"} |
http://www.thestudentroom.co.uk/showthread.php?t=2055349 | You are Here: Home
# Daniel Tammet on the Late Show with David Letterman Tweet
Maths and statistics discussion, revision, exam and homework help.
Announcements Posted on
1. Daniel Tammet on the Late Show with David Letterman
Towards the end of this video, Tammet tells Letterman his date of birth. Letterman acts like he's trying to figure out the day, and guesses (?) Wednesday - and he's right!
There are 2 possibilities: Letterman made a lucky guess or he had looked up Tammet's birth-date and day before the show. What is the probability that Letterman made a lucky guess?
Is that correct?
Last edited by thomaskurian89; 12-07-2012 at 15:06.
2. Re: Daniel Tammet on the Late Show with David Letterman
There's a 1 in 7 chance. There are 7 days per week. So the probability of randomly picking the correct one is 1/7.
Due to the nature of the show, it's likely there was a script or a plan, so Letterman probably did not guess.
3. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by Llewellyn)
There's a 1 in 7 chance. There are 7 days per week. So the probability of randomly picking the correct one is 1/7.
While that's true, that's not what I asked. My question was: Given that we know that Letterman got it right, what is the probability that he guessed?
Last edited by thomaskurian89; 12-07-2012 at 16:28.
4. Re: Daniel Tammet on the Late Show with David Letterman
Towards the end of this video, Tammet tells Letterman his date of birth. Letterman acts like he's trying to figure out the day, and guesses (?) Wednesday - and he's right!
There are 2 possibilities: Letterman made a lucky guess or he had looked up Tammet's birth-date and day before the show. What is the probability that Letterman made a lucky guess?
Is that correct?
I got the same answer as you. But I'm no expert.
(Original post by Llewellyn)
There's a 1 in 7 chance. There are 7 days per week. So the probability of randomly picking the correct one is 1/7.
Due to the nature of the show, it's likely there was a script or a plan, so Letterman probably did not guess.
1/7 is P(Correct | Guess) but the OP is asking for P(Guess | Correct).
(This is all assuming that the initial probability that Letterman took a lucky guess is the same as the initial probability that he cheated).
Last edited by notnek; 12-07-2012 at 16:29.
5. Re: Daniel Tammet on the Late Show with David Letterman
While that's true, that's not what I asked. My question was: Given that we know that Letterman got it right, what is the probability that he guessed?
You are assuming that the probability of guessing is 1/2 or 0.5 . How do you know that this is true? No evidence has been given to suggest this.
6. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by Llewellyn)
You are assuming that the probability of guessing is 1/2 or 0.5 . How do you know that this is true? No evidence has been given to suggest this.
It's an assumption made by thomaskurian. While it may not be true, you can still do the maths.
7. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by Llewellyn)
You are assuming that the probability of guessing is 1/2 or 0.5 . How do you know that this is true? No evidence has been given to suggest this.
I think you have a point.
8. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by notnek)
It's an assumption made by thomaskurian. While it may not be true, you can still do the maths.
I would have preferred him to have stated that the general answer is where p is the probability that Letterman guessed.
Stating your assumptions is vital, especially in Statistics.
9. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by Llewellyn)
I would have preferred him to have stated that the general answer is where p is the probability that Letterman guessed.
Stating your assumptions is vital, especially in Statistics.
p is not the probability that Letterman guessed. (We are trying to find that out.) p is the probability that Letterman guesses in such situations.
10. Re: Daniel Tammet on the Late Show with David Letterman
p is not the probability that Letterman guessed. (We are trying to find that out.) p is the probability that Letterman guesses in such situations.
p is the probability that Letterman guessed before any additional information is given. You're trying to use this to work out the probability that Letterman guessed once we know that his answer was correct.
Is this what you meant? I didn't really understand your post.
11. Re: Daniel Tammet on the Late Show with David Letterman
p is not the probability that Letterman guessed. (We are trying to find that out.) p is the probability that Letterman guesses in such situations.
Yes but you don't know the probability that Letterman guessed or the probability that letterman guesses in such situations. Don't you see the problem?
Analogy:
2y = x
Find x without knowing what y is.
12. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by Llewellyn)
Yes but you don't know the probability that Letterman guessed or the probability that letterman guesses in such situations. Don't you see the problem?
Analogy:
2y = x
Find x without knowing what y is.
13. Re: Daniel Tammet on the Late Show with David Letterman
I thought Llewellyn described it fine:
P(Guess)=p
Last edited by notnek; 12-07-2012 at 17:52.
14. Re: Daniel Tammet on the Late Show with David Letterman
(Original post by notnek)
I thought Llewwellyn described it fine:
P(Guess)=p
He said that p is the probability that Letterman guessed. If that were true, our answer would be p.
15. Re: Daniel Tammet on the Late Show with David Letterman
He said that p is the probability that Letterman guessed. If that were true, our answer would be p.
No, our answer would be p/ (7-6p), because you want to find the probability that he guessed given that he got it correct. | 2013-06-19 11:07:27 | {"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": 0.8614379167556763, "perplexity": 2206.206303212563}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368708711794/warc/CC-MAIN-20130516125151-00067-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/187762/equation-of-line-and-its-points | # Equation of line and its points
In the xy coordinate system if (a,b) and (a+3,b+k) are two points on the line defined by equation (the equation is kind of faded in text , but it seems to be like x=3y-7) then k =
A)9 , B)3 , C)1 , D)1 (Ans is 1)
Any suggestions on how that answer was calculated ?
-
The slope of the line through $(a,b)$ and $(a+3, b+k)$ is $\frac{b+k-b}{a+3-a}$, which is $\frac{k}{3}$.
The slope of the line $x=3y-7$ is $\frac{1}{3}$. This is because the equation can be rewritten as $3y=x+7$, and then in standard slope-intercept form as $y=\frac{1}{3}x+\frac{7}{3}$.
These slopes are equal $\frac{k}{3}$ and $\frac{1}{3}$ are equal.
Another way: Because $(a,b)$ is on the line, we have $a=3b-7$. Because $(a+3,b+k)$ is on the line, we have $a+3=3(b+k)-7$, that is, $a+3=3b+3k-7$.
Since $a=3b-7$, we conclude that $3=3k$.
-
so the answer was obtained by comparing the two slopes , right ? – MistyD Aug 28 '12 at 5:14
I was having difficulty computing the slope from the equation. Thanks for clearing that out – MistyD Aug 28 '12 at 5:16
@MistyD: Yes. I added another way of doing it. You are probably at this time learning about equations of lines and slopes, so probably the slope way is the way you are intended to do it. But the second way works fine too. – André Nicolas Aug 28 '12 at 5:18 | 2015-08-03 19:32:09 | {"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": 0.9513847827911377, "perplexity": 342.68179606111903}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042990112.92/warc/CC-MAIN-20150728002310-00234-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://clay6.com/qa/67137/shweta-ate-large-frac-of-a-pizza-and-her-friend-george-ate-large-frac-of-th | Answer
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# Shweta ate $\large\frac{3}{11}$ of a pizza and her friend George ate $\large\frac{13}{22}$ of the pizza. How much total pizza did they eat altogether?
( A ) $\large\frac{19}{11}$
( B ) $\large\frac{22}{19}$
( C ) $\large\frac{11}{19}$
( D ) $\large\frac{19}{22}$ | 2020-08-10 19:36:58 | {"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": 0.7830217480659485, "perplexity": 5529.938304302237}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737168.97/warc/CC-MAIN-20200810175614-20200810205614-00037.warc.gz"} |
https://docs.scipy.org/doc/scipy-1.2.3/reference/generated/scipy.optimize.rosen_hess_prod.html | # scipy.optimize.rosen_hess_prod¶
scipy.optimize.rosen_hess_prod(x, p)[source]
Product of the Hessian matrix of the Rosenbrock function with a vector.
Parameters
xarray_like
1-D array of points at which the Hessian matrix is to be computed.
parray_like
1-D array, the vector to be multiplied by the Hessian matrix.
Returns
rosen_hess_prodndarray
The Hessian matrix of the Rosenbrock function at x multiplied by the vector p.
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scipy.optimize.rosen_hess
#### Next topic
scipy.optimize.fmin | 2021-05-16 19:09:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5917137265205383, "perplexity": 1338.1599541045841}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991178.59/warc/CC-MAIN-20210516171301-20210516201301-00496.warc.gz"} |
https://plainmath.net/other/47895-a-large-grinding-wheel-in-the-shape-of-a-solid-cylinder-of-radius-0-33 | fertilizeki
2021-12-24
A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 250 N applied to its edge causes the wheel to have an angular acceleration of 0.940 rad/s. What is the mass of the wheel?
Travis Hicks
Expert
The information below pertains to solid cylinder wheels rotating on a vertical axis without any friction.
$\alpha =0.94\frac{rad}{{s}^{2}}$
Torque is given by:
$\tau =F\cdot r=I\cdot \alpha$
Addressing the issue of moment of inertia
$I=\frac{F\cdot r}{\alpha }=\frac{250\cdot 0.33}{0.94}=87.8$
Inertia moment is determined by:
$I=\frac{1}{2}\cdot m\cdot {r}^{2}$
Solving it for mass:
$m=\frac{2\cdot I}{{r}^{2}}=\frac{2\cdot 87.8}{{0.33}^{2}}=1612.5$ kg
Do you have a similar question? | 2023-01-31 20:06:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 31, "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": 0.49400654435157776, "perplexity": 846.5132642913285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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-20230131190543-20230131220543-00171.warc.gz"} |
https://math.stackexchange.com/questions/1956394/harmonic-functions-with-positive-boundary-data | # Harmonic functions with positive boundary data
Let $\Omega \subset \mathbb{R}^n$ be a open bounded domain, and let $g$ be a positive smooth function defined on $\partial \Omega$. Let $v$ be the unique harmonic function in $\Omega$ with boundary data $g$. Does $v$ necessarily need to be positive everywhere, or can it be negative?
• It has to be positive by the maximum principe. Indeed $\inf g\le v\le \sup g$. – user99914 Oct 6 '16 at 11:15
## 1 Answer
By the maximum principle, $v$ does indeed have to be positive. If it were non-positive, it'd have a strict local minimum not on the boundary, thus it wouldn't be harmonic. | 2020-01-19 10:33:51 | {"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": 0.942535400390625, "perplexity": 138.2787335378516}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250594391.21/warc/CC-MAIN-20200119093733-20200119121733-00065.warc.gz"} |
https://fe-physics.eu/?page_id=96 | # Magnetic Flux
The magnetic flux is proportional to the number of
field lines that pass through the surface.
Φ = Bn A
• Φ magnetic flux in Wb (Weber). Also : T m2 of Vs
• Bn the component of B perpendicular to the surface in T(esla)
• A area of the surface in m2
Example
See the drawing above.
B = 1.5 x 10-3 T
A = 500 cm2
α = 40 o
Resolve B in both components and calculate Bn
sin α = Bn/B
Bn = B sin 40 o = (1.5 x 10-3)( 0.643) = 9.642 x 10-4 T
Φ = Bn A
Φ = (9.642 x 10-4 )( 500 x 10-4)= 4.82 x 10-5 Wb | 2022-11-28 03:58:33 | {"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": 0.8639705181121826, "perplexity": 14607.711369343933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1669446710473.38/warc/CC-MAIN-20221128034307-20221128064307-00452.warc.gz"} |
https://forum.allaboutcircuits.com/threads/moore-finite-state-machines-in-programming.121444/ | # Moore Finite state machines in programming
#### Vindhyachal Takniki
Joined Nov 3, 2014
593
Explains use of Moore FSM in embedded. Who else use Moore FSM or any other FSM like Mealey?
2. I am used to superloop concept in which I design my own state, step by step. I had tried to put this Morre FSM in my ealier written code for ECG code. I found it extremely difficult by Moore FSM. Since there are so many tasks running, interconnections with ISR, multiple inputs , multiple outputs & other things, I got stuck. What is better method in these kind of situation.
#### Papabravo
Joined Feb 24, 2006
19,873
I have used both types on numerous occasions in hardware and in pure software. It is a very powerful technique.
#### JohnInTX
Joined Jun 26, 2012
4,713
FWIW I use state machines in virtually everything I write unless the chip supports a proper RTOS. After you get the hang of it, it makes coordinating many tasks much easier.
#### Vindhyachal Takniki
Joined Nov 3, 2014
593
Made a code from his course for street light.
Code:
enum
{
goN = 0U, waitN, goE, waitE
};
typedef const struct
{
uint32_t output;
uint32_t wait;
uint32_t next[4];
}street_light;
street_light sl_fsm[4] = {
{
0x21U,
100U,
{goN, waitN, goN, waitN},
},
{
0x31U,
100U,
{goE, goE, goE, goE},
},
{
0x41U,
100U,
{goE, goE, waitE, waitE},
},
{
0x51U,
100U,
{goN, goN, goN, goN},
},
};
{
uint32_t state = goN;
uint32_t input;
uint32_t output;
while(1)
{
output = sl_fsm[state].output; /* set tthe output */
wait_delay_us(sl_fsm[state].wait); /* delay for spcified time */
input = goN; /* input is goN for testing, otherwise input is from pins */
state = sl_fsm[state].next[input]; /* determine next state */
/* to remove compilre warming */
if(output)
{
__nop();
}
}
} /* function ends here */
#### WBahn
Joined Mar 31, 2012
28,191
Explains use of Moore FSM in embedded. Who else use Moore FSM or any other FSM like Mealey?
2. I am used to superloop concept in which I design my own state, step by step. I had tried to put this Morre FSM in my ealier written code for ECG code. I found it extremely difficult by Moore FSM. Since there are so many tasks running, interconnections with ISR, multiple inputs , multiple outputs & other things, I got stuck. What is better method in these kind of situation.
I prefer Moore machines, but sometimes a Mealy machine is simply a much better match to the application.
You can use an informal, ad-hoc design approach, which is often just find for small machines, or you can adopt a more formal, standardized approach, which can be needlessly cumbersome on small machines but can make the design of larger machines much more robust.
If doing it in software, FSM implementations lend themselves to switch() statements (if your language supports that). I find that I can implement the machine with more confidence if I set all of the relevant actions, including the next-state assignment, within every case. In and HDL this helps eliminate inferred latches, but in an MCU or other software it tends to slow down the machine because it has to do a lot of assignments that serve no purpose. But you can always go in and comment out the ones that you determine are truly redundant (I don't delete them because they serve as good documentation for what I expect those signals to have in that state.
#### xennar
Joined Jul 10, 2013
1
I'd been working on a table based state machine framework for Arduino when I read your discussion. The idea is that each state machine is its own object which can be shared like any Arduino library. It comes with a number of reusable state machines.
I'd be interested to hear your thoughts.
The code and doumentation are on Github:
https://github.com/tinkerspy/Automaton
https://github.com/tinkerspy/Automaton/wiki
Regards,
Tinkerspy | 2023-03-31 19:15:22 | {"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": 0.3070032298564911, "perplexity": 3943.127829175044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1679296949678.39/warc/CC-MAIN-20230331175950-20230331205950-00593.warc.gz"} |
https://math.stackexchange.com/questions/3476992/tangents-from-2-sqrt3-2-to-hyperbola-y2-x2-4-determine-a-chord-of-conta | # Tangents from $(-2\sqrt3,2)$ to hyperbola $y^2-x^2=4$ determine a chord of contact subtending angle $\theta$ at the center. Find $12\tan^2\theta$.
Tangents are drawn from a point $$(-2\sqrt 3 ,2)$$ to the hyperbola $$y^2-x^2=4$$ and the chord of contact subtends an angle $$\theta$$ at center of hyperbola. Find the value of $$12 \tan^2 \theta$$.
My attempt:
The equation of chord of contact is $$\sqrt 3 x+y=2$$. Solving it with hyperbola we get the intersection points as $$(0,2)$$ and $$(2\sqrt 3,-4)$$. So calculating the angle gives me as $$\frac{\pi}{2} + \tan^{-1}{(\frac{2}{\sqrt 3})}$$. Which is wrong according to answer key. Where am I wrong?
• What is the answer according to the key?
– Blue
Dec 15 '19 at 12:42
• Answer is 9 according to answer key. Dec 15 '19 at 12:45
• Given your value of $\theta$, what is the corresponding value of $12\tan^2\theta$?
– Blue
Dec 15 '19 at 12:46
• Moreover we want to this without a calculator. Dec 15 '19 at 12:50
• Your calculation involves an inverse tangent, so taking the tangent isn't really a calculator exercise. (Indeed, you didn't really even have to find $\theta$ itself. You just need the value of $\tan\theta$ to complete the problem.)
– Blue
Dec 15 '19 at 12:52
$$\cos\theta = {(0,2)\cdot(2\sqrt3,-4) \over \lVert(0,2)\rVert \lVert(2\sqrt3,-4)\rVert} = {-8 \over 2 \cdot 2\sqrt7} = -\frac2{\sqrt7},$$ then use $$\tan^2\theta+1=\sec^2\theta$$ to obtain $$\tan^2\theta = \frac34$$. Since one of the points is on the $$y$$-axis, we can also compute $$\tan\theta$$ directly from the other point: $$\tan\theta = {2\sqrt3\over-4} = -\frac{\sqrt3}2$$. So, it appears that you’ve gotten a numerator and denominator swapped somewhere along the way.
As Blue noted in a comment, you don’t need to compute $$\theta$$ explicitly since you already have $$\tan^2\theta$$. Now, just multiply that by $$12$$.
• OP's numerator and denominator are swapped because the $\pi/2$ term effectively turns the inverse tangent expression into an inverse cotangent (and changes a sign). (BTW: since one ray of the angle coincides with the $y$-axis, the angle's trig values are easily calculated from the coordinates of the point $(2\sqrt{3},-4)$.) | 2022-01-17 01:42:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9139817357063293, "perplexity": 242.02954683627598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320300253.51/warc/CC-MAIN-20220117000754-20220117030754-00399.warc.gz"} |
http://mathhelpforum.com/trigonometry/7853-trigonometric-identities-print.html | # Trigonometric Identities
• Nov 21st 2006, 01:42 PM
asiankatt
Trigonometric Identities
Hi there .
I'm not sure on how to do this question so I wondering if I could get some help . I'd greatly appreciate it :
Create a trigonometric identity that requires at least 3 steps in the solution to prove it is an identity. The identity must also include cosecant, secant or cotangent. Provide solution .
HUGE Thank you in advance .
• Nov 21st 2006, 02:14 PM
Jameson
This isn't as hard as it sounds.
Take something simple like $\sec(x)$
Well $\sec(x)=\frac{1}{\cos(x)}$
And $\sin^2(x)+\cos^2(x)=1$, so $\sec(x)=\frac{1}{\sin^2(x)\cos(x)+\cos^3(x)}$
Take it one more step. :) | 2017-08-23 21:53:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9369117617607117, "perplexity": 1111.031798672729}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886124563.93/warc/CC-MAIN-20170823210143-20170823230143-00017.warc.gz"} |
http://legisquebec.gouv.qc.ca/en/showversion/cs/I-8.1?code=se:103_4&pointInTime=20210906 | ### I-8.1 - Act respecting offences relating to alcoholic beverages
103.4. In proceedings for contravention of section 103.1 or 103.2, the permit holder shall incur no penalty if he proves that he used reasonable diligence to ascertain the age of the person and that he had reasonable ground for believing that that person was of full age or if he proves that he had reasonable ground for believing that it was a case contemplated in the second paragraph of section 103.2.
1979, c. 71, s. 128. | 2021-10-25 08:46:39 | {"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": 0.8366407155990601, "perplexity": 2790.266276743814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1634323587655.10/warc/CC-MAIN-20211025061300-20211025091300-00139.warc.gz"} |
https://blender.stackexchange.com/questions/28991/straighten-camera-in-blender | # Straighten Camera in Blender
If I have a camera at 0/0/0 of the x/y/z and its heading is unknown.
How do I make it point in the direction of 1/0/0 quickly?
• Rotate it 90 degrees, R X 90 – iKlsR Apr 26 '15 at 16:10
• I updated the question to clarify. The camera is located a 0/0/0 but the direction in which it points ("heading") is unknown. I want it to point towards 1/0/0. – qubodup Apr 26 '15 at 16:15
The fastest way if you haven't applied any transforms on the camera is to reset the rotation with AltR to 0/0/0 and then rotate it 90° on the X and -90° on the Z, RX 90, RZ -90. | 2020-12-03 04:34:38 | {"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": 0.2234036922454834, "perplexity": 1528.2336414136678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141718314.68/warc/CC-MAIN-20201203031111-20201203061111-00107.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-4-polynomials-4-7-polynomials-in-several-variables-4-7-exercise-set-page-286/106 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$$=P-2Pr+Pr^2$$
In order to find a polynomial that gives the amount after two years, we plug in 2 for t and multiply out the expression to obtain: $$P\left(1-r\right)^2 \\ P\left(r^2-2r+1\right) \\ =P-2Pr+Pr^2$$ | 2019-10-21 08:17:58 | {"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": 0.4987066388130188, "perplexity": 394.7427045666538}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570987763641.74/warc/CC-MAIN-20191021070341-20191021093841-00317.warc.gz"} |
https://www.elibm.org/article/10011498 | Bounds for the dimensions of $p$-adic multiple $L$-value spaces
Summary
First, we will define $p$-adic multiple $L$-values ($p$-adic MLV's), which are generalizations of Furusho's $p$-adic multiple zeta values ($p$-adic MZV's) in Section 2. Next, we prove bounds for the dimensions of $p$-adic MLV-spaces in Section 3, assuming results in Section 4, and make a conjecture about a special element in the motivic Galois group of the category of mixed Tate motives, which is a $p$-adic analogue of Grothendieck's conjecture about a special element in the motivic Galois group. The bounds come from the rank of $K$-groups of ring of $S$-integers of cyclotomic fields, and these are $p$-adic analogues of Goncharov-Terasoma's bounds for the dimensions of (complex) MZV-spaces and Deligne-Goncharov's bounds for the dimensions of (complex) MLV-spaces. In the case of $p$-adic MLV-spaces, the gap between the dimensions and the bounds is related to spaces of modular forms similarly as the complex case. In Section 4, we define the crystalline realization of mixed Tate motives and show a comparison isomorphism, by using $p$-adic Hodge theory.
Mathematics Subject Classification
11G55, 11R42, 14F42, 14F30
Keywords/Phrases
p-adic multiple zeta values, mixed Tate motives, algebraic K-theory, p-adic Hodge theory | 2021-07-25 16:41:43 | {"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": 0.8989747762680054, "perplexity": 422.1410648794187}, "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-2021-31/segments/1627046151699.95/warc/CC-MAIN-20210725143345-20210725173345-00702.warc.gz"} |
https://indico.cern.ch/event/1109611/contributions/4821358/ | 10th Edition of the Large Hadron Collider Physics Conference
May 16 – 20, 2022
Europe/Zurich timezone
Constraining Deep Neural Network classifiers’ systematic uncertainty via input feature space reduction
May 17, 2022, 7:00 PM
1h
Experimental poster Performance and Tools
Speaker
Mr Andrea Di Luca (Universita degli Studi di Trento and INFN (IT))
Description
In current and future high-energy physics experiments, the sensitivity of selection-based analysis will increasingly depend on the choice of the set of high-level features determined for each collision. The complexity of event reconstruction algorithms has escalated in the last decade, and thousands of parameters are available for analysts. Deep Learning approaches are widely used to improve the selection performance in physics analysis.
In many cases, the development of the algorithm is based on a brute force approach where all the possible combinations of available neural network architectures are tested using all the available parameters. A crucial aspect is that the results from a model based on a large number of input variables are more difficult to explain and understand. This point becomes relevant for neural network models since they do not provide uncertainty estimation and are often treated as perfect tools, which they are not.
In this work, we show how using a sub-optimal set of input features can lead to higher systematic uncertainty associated with classifier predictions. We also present an approach to selecting an optimal set of features using ensemble learning algorithms. For this study, we considered the case of highly boosted di-jet resonances produced in $pp$ collisions decaying to two $b$-quarks to be selected against an overwhelming QCD background. Results from a Monte Carlo simulation with HEP pseudo-detectors are shown.
Primary author
Mr Andrea Di Luca (Universita degli Studi di Trento and INFN (IT))
Presentation materials
LHCP2022 Poster.jpg LHCP2022 Poster.pdf poster_preview.jpg | 2022-10-02 22:15:19 | {"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": 0.5682007074356079, "perplexity": 994.9538819372901}, "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/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00225.warc.gz"} |
https://math.stackexchange.com/questions/2912995/actions-of-c-dynamical-systems-on-primitive-ideals | # Actions of $C^*$-dynamical systems on primitive ideals
Reading about induced Systems of $C^*$-Algebras, I found this one statement that I can't figure out.
Let $G$ be a compact Group and $(A,G,\alpha)$ a $C^*$-dynamical System, such that for some closed subgroup $H$ of $G$ there exists a $G$-equivariant map $\varphi$ between $(\text{Prim}(A),G,\alpha)$ and $(G/H,G,\text{lt})$, where lt denotes the left-translation. Let $I:= \bigcap \{P\in \text{Prim}(A) \colon \varphi(P)=eH\}$.
Now it is stated that $\bigcap\{\alpha_s(I) : s\in G\}$ equals $\{0\}$. I don't really get. I know that $I$ is an $H$-invariant ideal in $A$, since $\varphi$ is equivariant and all the $\alpha_s$ are *-automorphisms. | 2019-02-17 01:35:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9510607719421387, "perplexity": 134.90038538630404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481428.19/warc/CC-MAIN-20190217010854-20190217032854-00545.warc.gz"} |
https://proofwiki.org/wiki/Mathematician:David_Borwein | # Mathematician:David Borwein
## Mathematician
Canadian mathematician of Lithuanian origin, best known for his research in the summability theory of series and integrals.
Also working in measure theory and probability theory, number theory, and approximate subgradients and coderivatives, and the properties of single- and many-variable sinc integrals.
Father of Jonathan Michael Borwein and Peter Benjamin Borwein. | 2020-08-03 17:30:12 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8455008864402771, "perplexity": 5322.153834313859}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1596439735823.29/warc/CC-MAIN-20200803170210-20200803200210-00322.warc.gz"} |
https://www.encyclopediaofmath.org/index.php/Median_(of_a_triangle) | Median (of a triangle)
A straight line (or its segment contained in the triangle) which joins a vertex of the triangle with the midpoint of the opposite side. The three medians of a triangle intersect at one point, called the centre of gravity, the centroid or the barycentre of the triangle. This point divides each median into two parts with ratio $2:1$ if the first segment is the one that starts at the vertex. The centroid lies on the Euler line. | 2020-02-23 20:47:24 | {"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": 0.6273155808448792, "perplexity": 110.41766501903172}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145839.51/warc/CC-MAIN-20200223185153-20200223215153-00116.warc.gz"} |
https://socratic.org/questions/how-do-you-write-an-equation-for-a-hyperbola-with-vertices-1-3-and-5-3-and-foci- | How do you write an equation for a hyperbola with vertices (1, 3) and (-5, 3), and foci (3, 3) and (-7, 3)?
Oct 30, 2016
The equation is:
${\left(x - - 2\right)}^{2} / {3}^{2} - {\left(y - 3\right)}^{2} / {4}^{2} = 1$
Explanation:
Please notice that the vertices are of the forms:
$\left(h - a , k\right)$ and $\left(h + a , k\right)$ specifically $\left(- 5 , 3\right)$ and $\left(1 , 3\right)$
The same information can be deduced from the foci, which have the forms:
$\left(h - c , k\right)$ and $\left(h + c , k\right)$ specifically $\left(- 7 , 3\right)$ and $\left(3 , 3\right)$
The standard form for the equation of a hyperbola, where the vertices and foci have these properties, is the horizontal transverse axis form:
${\left(x - h\right)}^{2} / {a}^{2} - {\left(y - k\right)}^{2} / {b}^{2} = 1$
$k = 3$ by observation:
${\left(x - h\right)}^{2} / {a}^{2} - {\left(y - 3\right)}^{2} / {b}^{2} = 1$
Compute h and a:
$- 5 = h - a$ and $1 = h + a$
$2 h = - 4$
$h = - 2$
$a = 3$
${\left(x - - 2\right)}^{2} / {3}^{2} - {\left(y - 3\right)}^{2} / {b}^{2} = 1$
To complete the equation, we only need the value of b but, to find the value of b, we must, first, find the value of c:
Using the $\left(h + c , k\right)$ form for the focus point, $\left(3 , 3\right)$, we substitute -2 for h, set the right side equal to 3, and then solve for c:
$- 2 + c = 3$
$c = 5$
Solve for b, using the equation ${c}^{2} = {a}^{2} + {b}^{2}$:
${5}^{2} = {3}^{2} + {b}^{2}$
$b = 4$
${\left(x - - 2\right)}^{2} / {3}^{2} - {\left(y - 3\right)}^{2} / {4}^{2} = 1$ | 2019-09-24 08:39:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 26, "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": 0.8898777365684509, "perplexity": 390.52071445791717}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514572896.15/warc/CC-MAIN-20190924083200-20190924105200-00511.warc.gz"} |
https://port.sas.ac.uk/mod/book/view.php?id=593&chapterid=416 | ### 3. Regular expressions
#### 3.3 Back references
Back references are a very powerful part of regular expressions because they remember matches from your find expression and put them back where you specify in your replacement expression: this allows text to be moved around and copied.
The part to be remembered normally goes in round brackets, and the back reference is $1,$2 etc, where the numbers refer to the order of sets of brackets
Find:
(Ebeneezer) (Scrooge)
Replace:
$2,$1
Gives you Scrooge, Ebeneezer.
A real-world example, which shows how you can begin to automate XML markup with regular expressions
Remember the Houndsditch example from the Parish Clerks' Memoranda? We kept the original spelling of Houndsditch but put the modern, standardised spelling into an attribute:
<place loc=”Houndsditch, London”>Hounsditch</place>
We could automate the markup of things like this, using regular expressions:
Find:
(Ho[^ ]+ch)
Replace
<place loc=”Houndsditch, London”>$1</place> The find part here is looking for Ho followed by any character other than a space (this ensures that we don’t match across multiple words), followed by ch. The brackets mean that everything found will be remembered. Then we use the back reference,$1, to replace the match with itself, this time with the requisite tagging placed around it.
The danger here, you may have spotted, is that we might be inadvertently matching things which are not Houndsditch but which fit the requested pattern, such as Hooch. We could narrow the expression by adding more letters, for example:
Find:
(Hou[^ ]+tch)
But then the opposite risk is run: of not matching enough. The above expression would not find, say, Houndsdich or Hondsditch. The judgement is best made by the person who knows the data best, which on your project will be you, but in general it is best to match too much than too little – false positives are easier to find than false negatives. You can always use your text editor to extract all of the matches and look through the list for false positives. | 2022-01-23 06:32:54 | {"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": 0.6600520014762878, "perplexity": 2027.1011879549858}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304134.13/warc/CC-MAIN-20220123045449-20220123075449-00341.warc.gz"} |
https://socratic.org/questions/an-object-with-a-mass-of-4-kg-is-acted-on-by-two-forces-the-first-is-f-1-3-n-2-n-3 | # An object with a mass of 4 kg is acted on by two forces. The first is F_1= < 3 N , 2 N> and the second is F_2 = < 7 N, 6 N>. What is the object's rate and direction of acceleration?
Dec 21, 2016
The answer is $= 3.2 m {s}^{- 2}$ at 38.7º
#### Explanation:
The resulting force is
$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$
vecF=〈3,2〉+〈7,6〉=〈10,8〉
The magnitude of $\vec{F}$ is
=∥vecF∥ =∥〈10,8〉∥=sqrt(100+64)=sqrt164N
The rate of acceleration is =(∥vecF∥ )/m
$= \frac{\sqrt{164}}{4} = \frac{\sqrt{41}}{2} = 3.2 m {s}^{- 2}$
The direction is =arctan(8/10)=38.7º | 2021-09-24 03:30:30 | {"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": 0.5429803133010864, "perplexity": 2111.794544661796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1631780057496.18/warc/CC-MAIN-20210924020020-20210924050020-00153.warc.gz"} |
https://escholarship.org/uc/item/4r29w8q5 | Open Access Publications from the University of California
## Quantum oscillations in cuprates and Cooper pairing in half filled Landau level
• Author(s): Wang, Zhiqiang
The observation of quantum oscillations in hole under-doped cuprate is a big breakthrough to reveal its normal state nature. To understand the observed oscillation frequencies, in chapter 2, we consider the normal state to be a Fermi liquid and in a symmetry broken phase, whose order parameter is a novel period$-8$ $d-$density wave. This order gives rise to a complex Fermi surface consisting of not only an electron pocket, which can explain the major observed oscillation frequency $F\sim 530 \, \mathrm{T}$, but also a small hole pocket, which corresponds to a newly predicted slower oscillation. This slower oscillation has received some experimental supports recently.
In chapter 3, we study how superconductivity fluctuations, which exist in the form of random vortices, could affect the normal state quasiparticle quantum oscillation. We find that the Onsager rule, which connects extremal normal state Fermi surface areas to quantum oscillation frequencies, remains intact to an excellent approximation in the mixed-vortex state. We also show that the oscillations of the magnetic field $B$ dependent density of states, $\rho(B)$, ride on top of a field independent background in the high field quantum oscillation regime. This feature appears to agree with the most recent specific heat measurement on $\mathrm{YBa_2Cu_3O_{6+\delta}}$. At lower fields the superconductivity fluctuations are quenched and form an ordered vortex lattice. We show that the density of states follows $\rho(B)\propto \sqrt{B}$ as $B\rightarrow 0$, in agreement with the semiclassical results by Volovik.
In chapter 4, we turn to the Cooper pairing problem of composite fermions in the half-filled Landau level. We apply a new pairing mechanism from repulsive forces to the Halperin-Lee-Read composite fermion liquid. This mechanism takes advantage of the dynamical screening at finite frequency from the finite density composite fermions and makes a net attraction possible. We show that the transition from the composite fermion liquid state to a chiral Cooper pairing state, with odd angular momentum channels, is continuous, in disagreement with the previous conclusion that the transition is discontinuous if the bare interaction is short-ranged. We also construct the phase diagrams for different angular momentum channels $\ell$ and show that the $\ell=1$ channel is quite different from higher channels $\ell\ge 3$. Similar analysis has been carried out for the bilayer Hall system with a total filling fraction $\nu=\frac{1}{2}+\frac{1}{2}$ and it is found that the previously established results remain qualitatively unaltered.
Finally, in chapter 5 we apply the above pairing mechanism to the recently proposed particle-hole symmetric Dirac composite fermion liquid theory for the half-filled Landau level. We find that a continuous transition to different chiral pairing states, with angular momentum channels $|\ell|\ge 1$, is possible. These include the Moore-Read Pfaffian and the anti-Pfaffian state. However, the $\ell=0$ channel particle-hole symmetric pairing state, turns out to be energetically impossible although it is symmetry allowed. | 2019-10-20 09:40:37 | {"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": 0.7635565400123596, "perplexity": 794.3332382004705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570986705411.60/warc/CC-MAIN-20191020081806-20191020105306-00145.warc.gz"} |
http://math.stackexchange.com/questions/258741/why-cant-i-interchange-integration-and-differentiation-here | # Why can't I interchange Integration and Differentiation here?
Consider $f(x,y)=y^3e^{-y^2x}$ and define $F(y) =\int_0^{\infty}f(x,y)dx$
We have that $F'(0)\not = \int_0^{\infty} \frac{\partial f}{\partial y}(x,0)dx$
in the spoiler there is how I got this, in case I made a mistake there
We calculate $F'(0)$ essentially using Monotone convergence theorem we can show that, for $y\in \mathbb{R}\setminus\{0\}$, $F(y)=y$ moreover $F(0)=0$ so $F'(0)=1$
Now, I want to understand which hypothesis of Theorem 2 at this page does not hold. Instead of the third hypothesys at the link, though, I use this weacker hypothesis, which is still enough:
"For each $b \in \mathbb{R}$, there exists an open interval $b\in J$ and an integrable function over $(0, \infty)$ , $g(x)$ such that $| \frac{\partial f}{\partial y}(x,y)| \leq g(x)$ for every $y\in J$ and $\forall x$"
Now, the first hypothesis certainly holds as $\forall y, \ x\rightarrow f(x,y)$ is integrable $(0,\infty)$ by comparison with $e^{-kx}$ for appropriate positive value of $k$
Moreover $\frac{\partial f}{\partial y}(x,y)$ exists everywhere...
So is the last hypothesis to be problematic but I can't see how as I can bound $y$ in $J$ and then just use some linear combination of $e^{-kx}$ and $xe^{-lx}$ for suitable $k,l$ as they are both integrable over $(0,\infty)$...
Thank you very much!
-
The theorem says if you can bound $f_y(x,y)$ with an integrable function $g(x)$, that is $$|f_y(x,y)|\leq |g(x)|,$$ then you can change the order of differentiation and integration.
yes but I think you can weacken this condition by bounding $f_y$, for each $b \in \mathbb{R}$ on an open interval containing $b$ (and for all values of x)! – Moritzplatz Dec 14 '12 at 16:13
or do you think I can just say that my $f$ does not respect this condition and hence why the theorem doesn't work? it feels like cheating! – Moritzplatz Dec 14 '12 at 16:50 | 2015-07-29 12:26:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9634621143341064, "perplexity": 130.81636797962042}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042986423.95/warc/CC-MAIN-20150728002306-00220-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://tagoos.readthedocs.io/en/latest/ | # TAGOOS : associated tag SNP boosting¶
TAGOOS is a nucleotide scoring tool for non-coding (Intronic and intergenic) regions. There are two underlying models trained with the XGBOOST algorithm using intronic and intergenic associated SNPs (GWAS P-value < $$5\cdot10^{-8}$$) from the GRASP database. The predictive variables have been selected by the learning algorithm among 4684 gene regulation related annotations such as histone modifications, eQTLs or transcription factors in different tissues from these databases: | 2020-08-09 02:23:29 | {"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": 0.414657324552536, "perplexity": 11779.324014536705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1596439738380.22/warc/CC-MAIN-20200809013812-20200809043812-00030.warc.gz"} |
https://www.mysciencework.com/publication/show/hilbert-space-valued-gabor-frames-weighted-amalgam-spaces-886dd782?search=1 | # Hilbert space valued Gabor frames in weighted amalgam spaces
Authors
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Aug 23, 2018
Volume
10
Issue
4
Pages
377–394
Identifiers
DOI: 10.1515/apam-2018-0067
Source
De Gruyter
Keywords
License
Yellow
## Abstract
Let ℍ {\mathbb{H}} be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the ℍ {\mathbb{H}} -valued Gabor frame operator on ℍ {\mathbb{H}} -valued weighted amalgam spaces W ℍ ( L p , L v q ) {W_{\mathbb{H}}(L^{p},L^{q}_{v})} , 1 ≤ p , q ≤ ∞ {1\leq p,q\leq\infty} . Also, we show that the frame operator is invertible on W ℍ ( L p , L v q ) {W_{\mathbb{H}}(L^{p},L^{q}_{v})} , 1 ≤ p , q ≤ ∞ {1\leq p,q\leq\infty} , if the window function is in the Wiener amalgam space W ℍ ( L ∞ , L w 1 ) {W_{\mathbb{H}}(L^{\infty},L^{1}_{w})} . Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multi-window Gabor frames on W ℍ ( L p , L v q ) {W_{\mathbb{H}}(L^{p},L^{q}_{v})} , 1 ≤ p , q ≤ ∞ {1\leq p,q\leq\infty} , as a special case by choosing the appropriate Hilbert space ℍ {\mathbb{H}} .
Seen <100 times | 2020-10-27 05:41:15 | {"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": 0.9397975206375122, "perplexity": 5285.392791016216}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107893402.83/warc/CC-MAIN-20201027052750-20201027082750-00659.warc.gz"} |
https://ora.ox.ac.uk/objects/uuid:69850c3f-048d-4b90-a276-13d9ce3872c0 | Journal article
### Measurement of the Z/gamma* plus b-jet cross section in pp collisions at root s=7 TeV
Abstract:
The production of b jets in association with a Z/γ*boson is studied using proton-proton collisions delivered by the LHC at a centre-of-mass energy of 7TeV and recorded by the CMS detector. The inclusive cross section for Z/γ*+b-jet production is measured in a sample corresponding to an integrated luminosity of 2.2 fb -1. The Z/γ*+b-jet cross section with Z/γ*→ℓℓ (where ℓ ℓ = ee or μ μ) for events with the invariant mass 60 < M ℓ ℓ < 120 GeV, at least one b jet at the hadron level with p...
Publication status:
Published
### Access Document
Publisher copy:
10.1007/JHEP06(2012)126
### Authors
Chatrchyan, S More by this author
Khachatryan, V More by this author
Sirunyan, AM More by this author
Tumasyan, A More by this author
Journal:
JOURNAL OF HIGH ENERGY PHYSICS
Volume:
2012
Issue:
6
Publication date:
2012-06-05
DOI:
EISSN:
1029-8479
ISSN:
1029-8479
URN:
uuid:69850c3f-048d-4b90-a276-13d9ce3872c0
Source identifiers:
348866
Local pid:
pubs:348866
Keywords: | 2020-10-21 07:26:53 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9318522810935974, "perplexity": 5437.194074104764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107876136.24/warc/CC-MAIN-20201021064154-20201021094154-00355.warc.gz"} |
https://www.smr.ch/doc/B2000++/user_manual/re02.xhtml | ## Name
atemperatures — Ambient temperatures block
## Synopsis
atemperatures id
value v dof list nodes...
...
end
## Description
atemperatures specifies ambient temperature values at nodes for defining convective conditions in heat analysis in conjunction with the heat convection 'overlay' elements (Elements for Heat Transfer Analysis), id defining the set number (a positive integer). To specify temperatures at nodes inducing thermal strains in stress analysis, please refer to the temperatures command. An atemperatures set is identified by id, a non-negative integer which must be unique for the atemperatures conditions of the current model. id is the number which is referenced by the atemperatures option of the case definition. Sets with an id of 0 will be active for all analysis cases.
## Specifying Ambient Temperatue Values
value v
Specifies the current ambient temperature assigned to subsequently specified nodes.
## Assigning Ambient Temperature Values
The following directives are available to assign the specified ambient temperature value(s) to individual nodes and to collections of nodes:
allnodes
Assign the ambient temperature values to all defined nodes of the current branch.
branch br
For models that consist of several branches. Specifies the external branch number br. To be used in conjunction with the allnodes and nodes directives.
epatch id p1-p8|e1-e12|f1-f6|b
When the discretization of a part of the discretization was created by means of the epatch command, a number of pre-defined nodelists are available for use with the nbc command. The epatch is identified by id.
Individual patch vertex nodes are specified with p1 to p8.
The collection of nodes that are located at a patch edge are specified with e1 to e12.
The collection of nodes that are located at a patch face are specified with f1 to f6.
The collection of nodes of the whole patch body are specified with b.
nodes list
Specifies a list of nodes (of the current branch) to which the ambient temperature value will be assigned.
nodelist name
Specifies the name of the node list to which the ambient temperature value will be assigned.
nodeset name
Specifies the name of the node set to which the ambient temperature value will be assigned. | 2021-07-28 23:05:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42751002311706543, "perplexity": 2524.7973903282664}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153803.69/warc/CC-MAIN-20210728220634-20210729010634-00706.warc.gz"} |
https://ask.sagemath.org/answers/13409/revisions/ | # Revision history [back]
The range function needs an actual integer, not a symbolic expression with an additional attribute assigned by the assume function. Is there a reason you need to be working with symbolic expressions at all instead of Python functions? Consider the following:
def pc(p,W):
return 1-(1-p)^W
def prc(p,M,W,C):
return 1 - sum(binomial(M,i)*pc(p,W)^i*(1-pc(p,W))^(M-i) for i in range(C))
def pcol(p,N,M,W,C):
return 1 - (1-prc(p,M,W,C))^N
These are Python functions, so you don't need to declare the variables. The return expressions will be evaluated when you supply actual numbers for the arguments (as is done by the plot function). One difference is that
print pcol
will return
<function pcol at 0x4325500>
instead of a symbolic expression indicating the arithmetic the function performs. But I don't see why this would matter if you just want to plot a graph. On that note, to plot the graph you just need to declare the variable that you're plotting:
var('p')
plot(pcol(p/2.0^33,2^20,2^10,8,1),p,0,1000) | 2020-05-26 10:41:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40254563093185425, "perplexity": 1218.4234156785958}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1590347390755.1/warc/CC-MAIN-20200526081547-20200526111547-00157.warc.gz"} |
https://www.physicsforums.com/threads/vectors-question.107218/ | # Vectors Question
1. Jan 18, 2006
### BigCountry
A plane with a still air speed of 250 km/h is flying due NorthWest. At the same time a wind is blowing toward the South at 50 km/h. In what direction should the pilot head to continue travelling due North West? (The plane must continue with a 250 km/h velocity)
Velocity of plane (Vp) = 250
Velocity of wind (Vw) = 50
sin y = y/x = 50/250
y = 11.5 degrees
90 degrees - 11.5 degrees = 78.5 degrees
The plane must head 78.5 degrees N of W to continue in a 45 degree
N of W line.
Is this correct? Any help is much appreciated.
2. Jan 20, 2006
### Tom Mattson
Staff Emeritus
Your method looks wrong. You need to write down a vector for the velocity of the plane with respect to the air (call it $\vec{v}_{PA}$) and a vector for the velocity of the air with respect to the Eart (call it $\vec{v}_{AE}$. Then you add them up to get the velocity of the plane with respect to the Earth (call it $v_{PE}$).
$$\vec{v}_{PE}=\vec{v}_{PA}+\vec{v}_{AE}$$
3. Jan 20, 2006
### lightgrav
You draw the vectors in the right directions, added tail-to-tip!
your triangle doesn't have a 90-degree in it, but you can use
the law of cosines since you do know two legs and the 135 angle.
4. Jan 21, 2006
### abhijitlohiya
i think use the formula for resultsnt
R=sq.root(p*p+Q*Q+2pqcos135)
find the resultant.
for direction use tan x=p cos 135/p+qsin135
5. Jan 21, 2006
### andrevdh
The resulting motion, $\vec r$, of the plane is the vector sum of is still air speed, $\vec s$, and the wind speed, $\vec w$. The plane has to fly in the direction of the $\vec s$ vector in order to have a resultant motion in the direction of the $\vec r$ vector. Since the $\vec r$ vector is making an angle of $45_o$ with the "x-axis" its x- and y-components have the same magnitude. Assuming that the $\vec s$ vector makes an angle $\theta$ with the x-axis we can therefore say that:
$$r_x\ =\ r_y$$
which gives
$$s\cos(\theta)\ =\ s\sin(\theta)\ -\ 50$$
Last edited: Nov 29, 2006
6. Jan 22, 2006
### andrevdh
If my previous relation is a bit too challenging try solving for the angle between $\vec r$ and $\vec s$, say angle $x$, via the sine rule:
$$\frac{\sin(x)}{w}=\frac{\sin(135^o)}{s}$$ | 2018-01-22 18:51:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6036401391029358, "perplexity": 799.9787398675969}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1516084891530.91/warc/CC-MAIN-20180122173425-20180122193425-00691.warc.gz"} |
https://learn.careers360.com/engineering/question-help-me-please-magnetic-effects-of-current-and-magnetism-neet/ | # Two similar coils of radius r are lying concentrically with their planes at right angles to each others. The currents flowing in them are $I \ and\ 2 I$, respectively. The resultant magnetic field induction at the centre will be: Option 1) $\frac{\sqrt{5}\mu_{o}I}{2R}$ Option 2) $\frac{{3}\mu_{o}I}{2R}$ Option 3) $\frac{\mu_{o}I}{2R}$ Option 4) $\frac{\mu_{o}I}{R}$
Magnetic field due to cCrcular Current Carrying arc -
$B=\frac{\mu_{o}}{4\pi}\:\frac{2\pi i}{r}=\frac{\mu_{o}i}{2r}$
- wherein
$B_{1}=\frac{\mu _{oI}}{2r } \:\:\:\:\:B=\sqrt{B_{1}^{2}+B_{2}^{2}}=\sqrt{5}\frac{\mu ^oI}{2r}\\ B_{2}=\frac{\mu_{o}.2I}{2r}$
Option 1)
$\frac{\sqrt{5}\mu_{o}I}{2R}$
This option is correct
Option 2)
$\frac{{3}\mu_{o}I}{2R}$
This option is incorrect
Option 3)
$\frac{\mu_{o}I}{2R}$
This option is incorrect
Option 4)
$\frac{\mu_{o}I}{R}$
This option is incorrect
Exams
Articles
Questions | 2020-06-05 10:15:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9420980215072632, "perplexity": 5449.385198469425}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1590348496026.74/warc/CC-MAIN-20200605080742-20200605110742-00056.warc.gz"} |
http://intarch.ac.uk/journal/issue8/huggett/jhproc1.html | ## <!-- navbuttons("jhtoc.html","jhproc.html","jhtoc.html","jhproc2.html") writesectionheader(99,'4.1','Automated structures from basic primitives'); // --> Automated structures from basic primitives
The timber palisade and wall-walk surrounding the bailey and motte lend themselves to automated construction since they consist of a repetitive sequence of timber uprights (see Figure ). Information about the topography is held in an XYZ co-ordinate file and used to locate the palisade posts correctly in relation to the ground surface. The timbers between the main uprights are then filled in by 'walking' from post to post, filling in the spaces between. Basic box and cylinder primitives are used for the structural elements, with the only parameters other than the XYZ co-ordinates being the physical dimensions of the timbers.
A variant of this approach was used in the construction of the bridge (Figure ). Here, a profile was generated between the two endpoints of the bridge which, together with a direction vector, was used to extrude the profile across the ditch. A series of direction vectors are similarly used to construct the bridge supports.
URL: http://intarch.ac.uk/journal/issue8/huggett/jhproc1.html | 2018-07-19 11:35:29 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8685978651046753, "perplexity": 1831.6319333460494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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-20180719105750-20180719125750-00132.warc.gz"} |
https://zbmath.org/?q=an:0856.08004 | # zbMATH — the first resource for mathematics
Semi-implication algebra. (English) Zbl 0856.08004
The author generalizes the concept of an implication algebra to that of a semi-implication algebra $$(A,\cdot)$$. $$A$$ induces naturally a $$q$$-semilattice. Let $$(a, b)\in R$$ for $$a, b\in A$$ iff $$(ab)b= 1b$$ and $$B_p= \{a\in A\mid (p, a)\in R\}$$ for $$p\in A$$. Then every $$B_p$$ is a $$q$$-algebra. Further results are on the nilpotent shift of the variety of semilattices and implication algebras.
Reviewer: G.Kalmbach (Ulm)
##### MSC:
08A62 Finitary algebras 06A12 Semilattices 08B99 Varieties | 2021-09-22 04:56:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7367268204689026, "perplexity": 1207.481079391783}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1631780057329.74/warc/CC-MAIN-20210922041825-20210922071825-00130.warc.gz"} |
http://clay6.com/qa/48630/a-parallel-plate-capacitor-with-air-between-the-plates-has-a-capacitance-of | Browse Questions
# A parallel plate capacitor with air between the plates has a capacitance of $9 \;pF$. The separation between its plates is d. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1 = 3$ and thickness $\large\frac{d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\large\frac{2d}{3}$ . Capacitance of the capacitor is now
$(C) 40.5 pF$ | 2017-06-25 19:02:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8954192996025085, "perplexity": 260.8015353927952}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1498128320570.72/warc/CC-MAIN-20170625184914-20170625204914-00527.warc.gz"} |
http://clay6.com/qa/70333/count-the-number-of-parallelogram-in-the-given-figure- | Comment
Share
Q)
# Count the number of parallelogram in the given figure.
$(A) 8 \\ (B) 11 \\(C)12 \\ (D)15$ | 2019-09-20 16:50:20 | {"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": 0.5495256781578064, "perplexity": 4031.3458501672376}, "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-2019-39/segments/1568514574050.69/warc/CC-MAIN-20190920155311-20190920181311-00123.warc.gz"} |
https://www.sparrho.com/item/two-dimensional-relativistic-hydrogenic-atoms-a-complete-set-of-constants-of-motion/87aa15/ | # Two-dimensional relativistic hydrogenic atoms: A complete set of constants of motion
Research paper by A. Poszwa, A. Rutkowski
Indexed on: 11 Sep '08Published on: 11 Sep '08Published in: Quantum Physics
#### Abstract
The complete set of operators commuting with the Dirac Hamiltonian and exact analytic solution of the Dirac equation for the two-dimensional Coulomb potential is presented. Beyond the eigenvalue $\mu$ of the operator $j_{z}$, two quantum numbers $\eta$ and $\kappa$ are introduced as eigenvalues of hermitian operators $P=\beta\sigma_{z}'$ and $K=\beta(\sigma_{z}'l_{z}+1/2)$, respectively. The classification of states according to the full set of constants of motion without referring to the non-relativistic limit is proposed. The linear Paschen-Back effect is analyzed using exact field-free wave-functions as a zero-order approximation. | 2021-05-16 21:09:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8014273643493652, "perplexity": 653.5409670967356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989914.60/warc/CC-MAIN-20210516201947-20210516231947-00011.warc.gz"} |
http://chronos.msu.ru/en/updates/avtorskij-ukazatel/geometrization-of-radial-particles-in-non-empty-space-complies-with-tests-of-general-relativity | Site search: .ya-page_js_yes .ya-site-form_inited_no { display: none; }
Geometrization of radial particles in non-empty space complies with tests of General Relativity
Булыженков И.Э. (Bulyzhenkov I.E.) Geometrization of radial particles in non-empty space complies with tests of General Relativity // Journal of Modern Physics. 2012. 3(10): 1465. doi: 10.4236/jmp.2012.310181
Категории: Исследование, Авторский указатель
## Geometrization of radial particles in non-empty space complies with tests of General Relativity 0.0/5 rating (0 votes)/*<![CDATA[*/jQuery(function($) {$('#c4aab8cf-bd11-4dce-bfe9-a2fdc567666a-62fed42099411').ElementRating({ url: '/en/updates?task=callelement&format=raw&item_id=8843&element=c4aab8cf-bd11-4dce-bfe9-a2fdc567666a' }); });/*]]>*/
### Аннотация
Curved space-time 4-interval of any probe particle does not contradict to flat non-empty 3-space which, in turn, as-sumes the global material overlap of elementary continuous particles or the nonlocal Universe with universal Euclidean geometry. Relativistic particle's time is the chain function of particles speed and this time differs from the proper time of a motionless local observer. Equal passive and active relativistic energy-charges are employed to match the universal free fall and the Principle of Equivalence in non-empty (material) space, where continuous radial densities of elemen-tary energy-charges obey local superpositions and mutual penetrations. The known planetary perihelion precession, the radar echo delay, and the gravitational light bending can be explained quantitatively by the singularity-free metric without departure from Euclidean spatial geometry. The flatspace precession of non-point orbiting gyroscopes is non- Newtonian one due to the Einstein dilation of local time within the Earth's radial energy-charge rather than due to un-physical warping of Euclidean space.
Keywords: Euclidean Material Space; Metric Four-Potentials; Radial Masses; Energy-To-Energy Gravitation; Nonlocal Universe
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You have no rights to post comments | 2022-08-19 00:06:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2603108584880829, "perplexity": 9997.540876197801}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882573533.87/warc/CC-MAIN-20220818215509-20220819005509-00130.warc.gz"} |
https://socratic.org/questions/how-do-you-write-the-nth-term-rule-for-the-sequence-4-1-2-5-8 | # How do you write the nth term rule for the sequence 4,1,-2,-5,-8,...?
Aug 22, 2016
${n}^{t h}$ term in given sequence is $7 - 3 n$.
#### Explanation:
This is an arithmetic sequence as the difference $d$ between a term and its preceding term is always $- 3$ as $- 3 = 1 - 4 = - 2 - 1 = - 5 - \left(- 2\right) = - 8 - \left(- 5\right)$.
If first term is ${a}_{1}$ and common difference in such arithmetic sequence is $d$,
${n}^{t h}$ term is given by a_1+(n-1)×d. Hence ${n}^{t h}$ term in given series is
4+(n-1)×(-3)
= $4 - 3 n + 3$
= $7 - 3 n$ | 2020-09-21 00:38:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9641698598861694, "perplexity": 743.2472900393176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600400198868.29/warc/CC-MAIN-20200920223634-20200921013634-00425.warc.gz"} |
https://proofwiki.org/wiki/Mathematician:Mathematicians/Sorted_By_Nation/Norway | # Mathematician:Mathematicians/Sorted By Nation/Norway
Jump to: navigation, search
For more comprehensive information on the lives and works of mathematicians through the ages, see the MacTutor History of Mathematics archive, created by John J. O'Connor and Edmund F. Robertson.
The army of those who have made at least one definite contribution to mathematics as we know it soon becomes a mob as we look back over history; 6,000 or 8,000 names press forward for some word from us to preserve them from oblivion, and once the bolder leaders have been recognised it becomes largely a matter of arbitrary, illogical legislation to judge who of the clamouring multitude shall be permitted to survive and who be condemned to be forgotten.'
-- Eric Temple Bell: Men of Mathematics, 1937, Victor Gollancz, London
## Norway
##### Caspar Wessel (1745 – 1818)
Norwegian–Danish mathematician and cartographer who, in $1799$, was the first person to describe the geometrical interpretation of complex numbers as points in the complex plane.
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##### Niels Henrik Abel (1802 – 1829)
Norwegian mathematician who died tragically young.
Made significant contributions towards algebra, analysis and group theory.
Best known for proving the impossibility of solving the general quintic in radicals (Abel-Ruffini Theorem).
show full page
##### Peter Ludwig Mejdell Sylow (1832 – 1918)
Ludwig Sylow was a Norwegian mathematician who established some important facts on the topic of subgroups of prime order.
show full page
##### Marius Sophus Lie (1842 – 1899)
Sophus Lie (pronounced Lee) was a Norwegian mathematician famous for his study of continuous transformation groups.
Such objects are now called Lie groups.
show full page
##### Viggo Brun (1885 – 1978)
Norwegian mathematician best known for his work in number theory.
show full page
##### Thoralf Albert Skolem (1887 – 1963)
Norwegian mathematician who worked mainly in the fields of mathematical logic and set theory.
show full page
##### Trygve Nagell (1895 – 1988)
Norwegian mathematician known for his work on Diophantine equations.
show full page
##### Øystein Ore (1899 – 1968)
Norwegian mathematician whose work was mainly in graph theory, although also known for his work in ring theory and Galois theory.
One of the early founders of lattice theory.
Also known for writing and editing several books, including a few on various aspects of the history of mathematics.
show full page
##### Ingebrigt Johansson (1904 – 1987)
Norwegian mathematician and logician best known for inventing minimal logic.
show full page
##### Wilhelm Ljunggren (1905 – 1973)
Norwegian mathematician, specializing in number theory.
show full page
##### Atle Selberg (1917 – 2007)
Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms.
Instrumental in developing a proof of the Prime Number Theorem. Engaged in a bitter dispute with Paul Erdős over priority.
show full page | 2018-05-24 12:02:43 | {"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": 0.8720799088478088, "perplexity": 4282.5171872145565}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866276.61/warc/CC-MAIN-20180524112244-20180524132244-00598.warc.gz"} |
https://www.yourdictionary.com/dissolved | #### Sentence Examples
• Dr Maitland (essay on" The Universal Ordinary ") thinks, but without very much foundation, that great numbers especially of the more important causes were tried before these delegates; although the records have largely perished, since they were the records of courts ' which were dissolved as soon as their single cause had been decided.
• Lodphenol is obtained by the action of iodine a.nd iodic acid on phenol dissolved in a dilute solution of caustic potash.
• The residue is dissolved in alcohol and to the cold saturated solution a cold alcoholic solution of picric acid is added.
• The cobaltous salts are formed when the metal, cobaltous oxide, hydroxide or carbonate, are dissolved in acids, or, in the case of the insoluble salts, by precipitation.
• Submerged leaves are usually filamentous or narrowly ribbonshaped, thus exposing a large amount of surface to the water, some of the dissolved gases of which they must absorb, and into which they must also excrete certain gases. | 2020-02-17 13:12:26 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8189578652381897, "perplexity": 6946.178668337446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1581875142323.84/warc/CC-MAIN-20200217115308-20200217145308-00343.warc.gz"} |
https://socratic.org/questions/how-do-you-factor-15x-3-21x-2-20x-28 | # How do you factor 15x^3-21x^2+20x-28?
$\left(5 x - 7\right) \left(3 {x}^{2} + 4\right)$
$15 {x}^{3} - 21 {x}^{2} + 20 x - 28$ | 2021-12-08 15:35:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 2, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25450748205184937, "perplexity": 8523.29417067636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1637964363515.28/warc/CC-MAIN-20211208144647-20211208174647-00601.warc.gz"} |
https://astronomy.stackexchange.com/questions/39851/did-mercury-clear-its-neighborhood?noredirect=1 | # Did Mercury clear its neighborhood?
For a body to qualify as a planet according to the IAU definition it must have "cleared its neighborhood". What evidence is there Mercury indeed cleared its neighborhood? Perhaps it migrated there afterwards, when the neighborhood had already been cleared. Does the Grand Tack hypothesis impact our definition of the inner planets as planets?
https://en.m.wikipedia.org/wiki/IAU_definition_of_planet
The present definition of a planet is vulnerable as it seems connected to a model of formation of the solar system. The answer below states that in practice an operational definition used that I believe is adequate.
• Can you explain that the "Grand Tack Hypothesis" is? – fasterthanlight Nov 15 '20 at 13:17
• If we take the 2006 definition literally (which seemingly noone does) no planet 'cleared its neighbourhood'. en.wikipedia.org/wiki/List_of_Mercury-crossing_minor_planets – John Nov 15 '20 at 13:59
• That's because the IAU are scientists not lawyers. – James K Nov 15 '20 at 16:38
• @JamesK Scientists could have easily come up with a definition that would exclude Pluto, include 8 planets, and not state anything different or contradictory. – John Nov 15 '20 at 17:02
• I know. They did. – James K Nov 15 '20 at 17:23
• -1 because all the "we call" and "we don't look" language is unsupported with authoritative sources. In Stack Exchange we supply information, we do not generate it ourselves. We are not the authority here. We are merely a service provider. Currently there is no way to tell if this is authoritative and correct or purely guesswork because you don't cite any supporting sources. This is Stack Exchange not Quora. – uhoh Nov 17 '20 at 3:41 | 2021-04-22 18:36:20 | {"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": 0.44289612770080566, "perplexity": 1929.1903120927984}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039594341.91/warc/CC-MAIN-20210422160833-20210422190833-00559.warc.gz"} |
https://www.physicsforums.com/threads/equal-area-question.163658/ | # Equal area question
## Homework Statement
"Find a horizontal line y=k that divides the area between y=x^2 and y=9 into two parts"
## The Attempt at a Solution
Found intersection at (-3,9), (3,9)
Found total area to be 36, half(the area needed for each portion) to be 18. Don't know where to go from here.
Find the two areas as a function of k.
Find the two areas as a function of k.
Can you elaborate more on that? I'm not quite sure what you mean.
y=k divides the total area into two parts, A1=A1(k) and A2=A2(k). You need to find an expression for each area as a function of k and then find the value of k for which A1(k)=A2(k)
Hurkyl
Staff Emeritus
Gold Member
Don't be intimidated by the variable k -- the fact it's there changes nothing. You know how to compute areas, so compute the area of one of the portions.
HallsofIvy | 2021-03-02 05:42:39 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8095378875732422, "perplexity": 863.251999345691}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363217.42/warc/CC-MAIN-20210302034236-20210302064236-00435.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/p-two-blocks-b-mass-ma-mb-respectively-are-kept-contact-frictionless-table-experimenter-pushes-block-newton-s-second-law-motion_66476 | # P Two Blocks a and B of Mass Ma and Mb , Respectively, Are Kept in Contact on a Frictionless Table. the Experimenter Pushes Block a from - Physics
Sum
Two blocks A and B of mass mA and mB , respectively, are kept in contact on a frictionless table. The experimenter pushes block A from behind, so that the blocks accelerate. If block A exerts force F on block B, what is the force exerted by the experimenter on block A?
#### Solution
Let F' = force exerted by the experimenter on block A and F be the force exerted by block A on block B.
Let a be the acceleration produced in the system.
For block A,
$F' - F = m_A a$ ...(1)
For block B,
F = mBa ...(2)
Dividing equation (1) by (2), we get:
$\frac{F'}{F} - 1 = \frac{m_A}{m_B}$
$\Rightarrow F' = F\left( 1 + \frac{m_A}{m_B} \right)$
∴ Force exerted by the experimenter on block A is
$F\left( 1 + \frac{m_A}{m_B} \right)$
Concept: Newton’s Second Law of Motion
Is there an error in this question or solution?
#### APPEARS IN
HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 5 Newton's Laws of Motion
Q 7 | Page 79 | 2022-05-16 11:57:35 | {"extraction_info": {"found_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": 0.49228689074516296, "perplexity": 941.1581508380973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662510117.12/warc/CC-MAIN-20220516104933-20220516134933-00049.warc.gz"} |
https://www.physicsforums.com/threads/3rd-isomorphism-theory.118252/ | # 3rd Isomorphism Theory
1. Apr 21, 2006
### moo5003
Problem:
" Prove (Third Isomorphism THeorem) If M and N are normal subgroups of G and N < or = to M, that (G/N)/(M/N) is isomorphic to G/M."
Work done so far:
Using simply definitions I have simplified (G/N)/(M/N) to (GM/N). Now using the first Isomorphism theorem I want to show that a homomorphism Phi from GM to G/M exists. Such that the Kernal of Phi is N.
I constructed phi such that GM -> G/M
where it sends all x |----> xN.
My problem is as follows: How do I know xN is actually in the set G/M. It may just be that I'm going about the proof in a way that is very complicated then it should be. Any help would be greatly appreciated.
2. Apr 21, 2006
### moo5003
Alright I've been looking at some online proofs and I can see were I went wrong. I should have constructed a phi from G/N to G/M.
My only question is how to show that phi from a gN to a gM is onto G/M. I was looking at the proofs online and they didnt seem to make any sense on this part.
3. Apr 21, 2006
### matt grime
The map is I presume the on induced by sending g to [g] its coset in G/M. This is surjective. N is in the kernel so it factors as G-->G/N-->G/M. And the second map must also be surjective.
THinking more concretely, each and every coset of M is a union of cosets of N, so your map from G/N to G/M just identifies these cosets of N. | 2017-06-26 15:52:05 | {"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": 0.877776563167572, "perplexity": 914.3090342400291}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1498128320823.40/warc/CC-MAIN-20170626152050-20170626172050-00628.warc.gz"} |
https://manual.q-chem.com/5.4/subsec_dual-dyn.html | # 4.7.2 Dual-Basis Dynamics
(May 16, 2021)
The ability to compute SCF and MP2 energies and forces at reduced cost makes dual-basis calculations attractive for ab initio molecular dynamics simulations, which are described in Section 9.9. Dual-basis BOMD has demonstrated savings of 58%, even relative to state-of-the-art, Fock-extrapolated BOMD. Savings are further increased to 71% for dual-basis RI-MP2 dynamics. Notably, these timings outperform estimates of extended Lagrangian (“Car-Parrinello”) dynamics, without detrimental energy conservation artifacts that are sometimes observed in the latter.
Two algorithm improvements make modest but worthwhile improvements to dual-basis dynamics. First, the iterative, small-basis calculation can benefit from Fock matrix extrapolation. Second, extrapolation of the response equations (“$Z$-vector” equations) for nuclear forces further increases efficiency. (See Section 9.9.) Q-Chem automatically adjusts to extrapolate in the proper basis set when DUAL_BASIS_ENERGY is activated. | 2021-06-24 17:50:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "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": 0.7006650567054749, "perplexity": 11359.832620924002}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1623488556482.89/warc/CC-MAIN-20210624171713-20210624201713-00498.warc.gz"} |
http://www.r-bloggers.com/2011/12/page/25/ | # Monthly Archives: December 2011
## Comparing model selection methods
December 2, 2011
By
The standard textbook analysis of different model selection methods, like cross-validation or validation sample, focus on their ability to estimate in-sample, conditional or expected test error. However, the other interesting question is to compare the...
## O’Reilly’s Data Science Kit – Books
December 2, 2011
By
It is not as if I don't have enough books (and material on the web) to read. But this list compiled by the O'Reilly team should make any data analyst salivate.http://shop.oreilly.com/category/deals/data-science-kit.doThe Books and Video included in the...
## Easy cell statistics for factorial designs
December 2, 2011
By
A common task when analyzing multi-group designs is obtaining descriptive statistics for various cells and cell combinations. There are many functions that can help you accomplish this, including aggregate() and by() in the base installation, summaryBy() in the doBy package, and … Continue reading →
December 2, 2011
By
## Wasting away again in Martingaleville
December 1, 2011
By
Alright, I better start with an apology for the title of this post. I know, it’s really bad. But let’s get on to the good stuff, or, perhaps more accurately, the really frightening stuff. The plot shown at the top of this post is a simulation of the martingale betting strategy. You’ll find code for
## Backtesting with Short positions
December 1, 2011
By
I want to illustrate Backtesting with Short positions using an interesting strategy introduced by Woodshedder in the Simple, Long-Term Indicator Near to Giving Short Signal post. This strategy was also analyzed in details by MarketSci in Woodshedder’s Long-Term Indicator post. The strategy uses the 5 day rate of change (ROC5) and the 252 day rate
## Interviews on Revolution R Enterprise 5.0
December 1, 2011
By
For those looking for more background behind the updates in Revolution R Enterprise 5.0, there are now a couple of interviews online where I talk about the new release. At IT Business Edge ("Revolution Analytics' Goal: Make R Analysis Enterprise-Friendly"), I had a chat with Loraine Lawson about how Revolution R Enterprise fits within the analytics stack, its big-data...
## A Friday round-up
December 1, 2011
By
Just a brief selection of items that caught my eye this week. Note that this is a Friday as opposed to Friday, lest you mistake this for a new, regular feature. 1. R/statistics ggbio A new Bioconductor package which builds on the excellent ggplot graphics library, for the visualization of biological data. R development master | 2014-10-31 04:09:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23491410911083221, "perplexity": 4203.883156355222}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637898844.3/warc/CC-MAIN-20141030025818-00065-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://core.ac.uk/display/2183933 | Skip to main content
Location of Repository
## $J/\psi$ production and elliptic flow parameter $v_2$ at LHC energy
### Abstract
We apply the recombination model to study $J/\psi$ production and its elliptic flow in the region of $10<p_T<20$ GeV/$c$ at LHC energy. We show the distribution of $J/\psi$ as function of the transverse momentum $p_T$ and the azimuthal angle $\phi$. If the contribution from the recombination of shower partons from two neighboring jets can not be ignored due to the high jet density at LHC, the elliptic flow parameter $v_2$ of $J/\psi$ is predicted to decrease with $p_T$.Comment: 8 pages; 6 figure
Topics: High Energy Physics - Phenomenology
Year: 2011
DOI identifier: 10.1088/0031-8949/84/03/035202
OAI identifier: oai:arXiv.org:1103.3346
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
• http://arxiv.org/abs/1103.3346 (external link)
• ### Suggested articles
To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request. | 2018-12-14 20:33:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.60209059715271, "perplexity": 1906.5084717030284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826306.47/warc/CC-MAIN-20181214184754-20181214210754-00358.warc.gz"} |
https://www.physicsforums.com/threads/recoiling-inclined-plane.663865/ | # Recoiling Inclined Plane
1. Jan 12, 2013
### WannabeNewton
1. The problem statement, all variables and given/known data
A block of mass m is on an inclined plane of mass M, inclined at angle θ, and slides on the plane without friction. Find the acceleration of the plane.
3. The attempt at a solution
I am using the usual cartesian coordinate system with no rotations and letting up and forward be the positive directions. Let A be the acceleration of the plane as it accelerates backwards from the recoil due to the moving block. Define a non - inertial reference frame that is co - moving with the plane. The equations of motion for the block in this frame are $m\ddot{y} = Ncos\theta - mg$,$m\ddot{x} = F_{apparent} = Nsin\theta - mA$ and we have, in this co - moving frame, the constraint $\ddot{y} = -tan\theta \ddot{x}$. The equation of motion for the plane in this frame is $0 = F'_{apparent} = -Nsin\theta - MA$. Combining the equations for the block we get that $N = mgcos\theta + mAsin\theta$ so $MA = -Nsin\theta = -mgcos\theta sin\theta - mAsin^{2}\theta$ therefore $A = -(\frac{mgcos\theta sin\theta }{M + msin^{2}\theta })$. The book has the same answer except it is positive. I'm not sure why mine is negative. They don't really list if they are taking the backwards direction to be positive or not so I don't know if that is all there is to the issue. Thanks.
2. Jan 12, 2013
### oli4
Hi Isaac
There is nothing in the statement that would give you a preferred direction, I read it as finding the magnitude of the acceleration of the plane. Otherwise, since the acceleration is a vector in the end, you could as well wonder about which component is which.
So I don't think there is any issue at all, you solved the problem :)
3. Jan 12, 2013
### haruspex
Assuming you have exactly reproduced the statement of the problem from the book, I would guess you are supposed to take the positive direction as being whichever way the wedge moves. You say you let "up and forward be the positive directions", but you don't say forward for which object. If you meant forward for the block then you would expect a negative result for the wedge.
(Good job getting the right answer - easy to go wrong with a question like this.) | 2017-10-20 07:25:35 | {"extraction_info": {"found_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": 0.6391015648841858, "perplexity": 226.52545589209353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1508187823839.40/warc/CC-MAIN-20171020063725-20171020083725-00075.warc.gz"} |
https://villasenor-derbez.com/publication/006_peake2018/ | # Feeding ecology of invasive lionfish (Pterois volitans and Pterois miles) in the temperate and tropical western Atlantic
### Abstract
Numerous location-based diet studies have been published describing different aspects of invasive lionfish (Pterois volitans and Pterois miles) feeding ecology, but there has been no synthesis of their diet composition and feeding patterns across regional gradients. 8125 lionfish stomachs collected from 10 locations were analyzed to provide a generalized description of their feeding ecology at a regional scale and to compare their diet among locations. Our regional data indicate lionfish in the western Atlantic are opportunistic generalist carnivores that consume at least 167 vertebrate and invertebrate prey species across multiple trophic guilds, and carnivorous fish and shrimp prey that are not managed fishery species and not considered at risk of extinction by the International Union for Conservation of Nature disproportionately dominate their diet. Correlations between lionfish size and their diet composition indicate lionfish in the western Atlantic transition from a shrimp-dominated diet to a fish-dominated diet through ontogeny. Lionfish total length (TL) (mm) was found to predict mean prey mass per stomach (g) by the following equation $\text{mean prey mass}= 0.0002 \times TL^{1.6391}$, which can be used to estimate prey biomass consumption from lionfish length-frequency data. Our locational comparisons indicate lionfish diet varies considerably among locations, even at the group (e.g., crab) and trophic guild levels. The Modified Index of Relative Importance developed specifically for this study, calculated as the frequency of prey $a \times$ the number of prey $a$, can be used in other diet studies to assess prey importance when prey mass data are not available. Researchers and managers can use the diet data presented in this study to make inference about lionfish feeding ecology in areas where their diet has yet to be described. These data can be used to guide research and monitoring efforts, and can be used in modeling exercises to simulate the potential effects of lionfish on marine food webs. Given the large variability in lionfish diet composition among locations, this study highlights the importance of continued location-based diet assessments to better inform local management activities.
Type
Publication
Biological Invasions
Date | 2022-11-29 17:57:37 | {"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": 0.4024953544139862, "perplexity": 7314.683493706306}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1669446710710.91/warc/CC-MAIN-20221129164449-20221129194449-00826.warc.gz"} |
https://www.physicsforums.com/threads/about-the-action-s-in-quantum-field-theory.6535/ | # About the action S in quantum field theory
1. Sep 30, 2003
### eljose79
Let,s suppose we have a Hamiltonian H so we can construct the action by H+dS/dt then why no use the action to solve the problem of quantization of non renormalizable theories?..
2. Sep 30, 2003
### jeff
I think you probably meant ∂S/∂t + H = 0. In any event, nonrenormalizability is no longer viewed as a problem. A theory is renormalizable if it's lagrangian need only contain a finite number of terms to absorb the different types of divergences that occur in it's perturbation theory. But now we know that it's perfectly alright to allow theories which require an infinite number of terms as long as their contribution to the theory are suppressed at higher energies.
Last edited: Sep 30, 2003
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Have something to add? | 2017-02-25 00:42:03 | {"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": 0.8532383441925049, "perplexity": 884.309744768816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171632.91/warc/CC-MAIN-20170219104611-00253-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://dsp.stackexchange.com/questions/23143/adaptive-filter-gradient-descent | • @user1832413: If you have a quadratic form $x^TAx+b^Tx$, and if the matrix $A$ is positive (semi-)definite (as is the case with an autocorrelation matrix), then the function defined by the quadratic form is convex and has a minimum. A saddle point can only occur if the matrix $A$ is indefinite. – Matt L. May 3 '15 at 20:00 | 2019-09-18 12:23:37 | {"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": 0.9716269969940186, "perplexity": 145.443954643754}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573284.48/warc/CC-MAIN-20190918110932-20190918132932-00475.warc.gz"} |
https://socratic.org/questions/5900bd8f11ef6b57e2faceb0 | # What are examples of a "polar, aprotic solvent"?
Some examples are $\text{methylene chloride}$, $\text{diethyl ether}$, $\text{chloroform.......}$
A polar aprotic solvent is a molecule with significant charge separation (hence a $\text{polar solvent}$) that can be used as a solvent, which does undergo any acid-base equilibrium. And thus water and hydrogen fluoride, while they are certainly polar molecules, do not fall under this umbrella because they are protic, and readily exchange ${H}^{+}$ in their solutions. | 2019-09-23 20:11:50 | {"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": 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": 0.8071701526641846, "perplexity": 2059.5599623771946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1568514578201.99/warc/CC-MAIN-20190923193125-20190923215125-00158.warc.gz"} |
https://boisemathcircles.org/bmc-sessions/fibonacci | This special discussion was led by Zach Teitler and concerned patterns in the famous Fibonacci sequence of numbers. This sequence begins with 1,1 and then each successive number is obtained by taking the sum of the previous two. Here are the next few in the list:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169
Which Fibonacci numbers are even? Which ones are odd? Which Fibonacci numbers are divisible by 3? In this discussion we answered these questions and many more.
Here were the core problems we discussed:
• Which Fibonacci numbers are divisible by 2? By 3? By 5?
• What patterns do you notice?
• Next try the sequence $2^n-1$. This one begins 1, 3, 7, 15, 31, 63, 127, 255, 511, .... Which of these numbers are divisible by 3? By 7? By 15?
• How does this pattern compare with the patterns in the fibonacci numbers? Can you explain why the pattern works?
We also worked on some fun graphical problems:
• We have some bricks that are 1 unit by 2 units. We want to make a wall 2 units high, and n units wide. How many ways can it be done? The bricks can be vertical or horizontal.
• Now you have a row of n chairs and you want to put students in some of the chairs. The students are taking an exam so they are not allowed to sit right next to each other. How many ways are there to do this?
Finally we looked at some more fun patterns:
• Look at the “running totals” of the Fibonacci numbers. Here are the first few:
1+1 = 2
1+1+2 = 4
1+1+2+3 = 7
1+1+2+3+5 = 12
...
Do you see any patterns in this new sequence? Can you explain it?
• What if you only add up every other Fibonacci number
1+2 =
1+2+5 =
1+2+5+13 =
1+2+5+13+34 =
...
What do you get? Can you explain this pattern?
• Look at the "diagonals" in Pascal's triangle:
Can you explain this pattern? | 2019-09-19 15:46:07 | {"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": 0.4096117317676544, "perplexity": 308.4211169300965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1568514573533.49/warc/CC-MAIN-20190919142838-20190919164838-00197.warc.gz"} |
http://math.stackexchange.com/tags/divisibility/info | Tag Info
This tag is for questions about divisibility, that is, determining when one thing is a multiple of another thing.
If $a$ and $b$ are integers, $a$ divides $b$ if $b=ca$ for some integer $c$. This is denoted $a\mid b$. It is usually studied in introductory courses in number theory, so add (elementary-number-theory) tag, if appropriate.
A common notation used for the phrase "$a$ divides $b$" is $a|b$. It is also common to negate the notation by adding a slash like this: "$c$ does not divide $d$" written as $c\nmid d$. Note that the order is important: for example, $2|4$ but "$4\nmid 2$".
This notion can be generalized to any ring. The definition is the same: For two elements $a$ and $b$ of a commutative ring $R$, $a$ divides $b$ if $ac=b$ for some $c$ in $R$.
Divisibility in commutative rings corresponds exactly to containment the poset of principal ideals. That is, $a$ divides $b$ if and only if $aR\subseteq bR$. For commutative rings like principal ideal rings, this means that divisibility mirrors exactly the poset of all ideals of the ring.
The topics appropriate for this tag include, for example:
• Questions about the relation $\mid$.
• Questions about g.c.d and l.c.m. | 2016-02-09 06:39:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7741363644599915, "perplexity": 242.43344512306166}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701156520.89/warc/CC-MAIN-20160205193916-00057-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/790847/a-consistent-first-order-theory-whose-impredicative-second-order-variant-is-inco | # A consistent first-order theory whose impredicative second-order variant is inconsistent
Let's assume that we have a consistent first-order theory, which was derived from a second order theory by replacing universal quantification over second order variables by axiom schemes for first-order definable predicates. Now let's compare this theory to two different second-order theories using Henkin semantics with suitable comprehension axiom schemes.
1. If the comprehension axiom scheme allows quantification only over the first-order variables, can the resulting second-order theory be inconsistent? I guess the answer is no, and the resulting theory will be equivalent to the first-order theory with respect to provability of first-order formulas.
2. If the comprehension axiom scheme allows quantification over both first and second-order variables, we can no longer be sure that the resulting second order theory is consistent. Is there a simple example, where the first-order theory is "provably consistent", and the second-order theory is "provably inconsistent"?
As already clarified in the comments, "provably (in)consistent" just means that assuming ZFC (or any other foundation) is fine, there is no need to restrict answers to syntactic derivations.
• If "the second-order theory is" inconsistent then "the second-order theory is 'provably inconsistent'". $\hspace{.49 in}$ – user57159 May 11 '14 at 21:15
• @RickyDemer By "provably inconsistent", I just mean that I don't insist on a possibly extremely long syntactic derivation of $\phi\land\lnot\phi$, but that a "short" proof (possibly assuming ZFC) that such a derivation exist is also sufficient. – Thomas Klimpel May 11 '14 at 21:21
• While I don't know the answer to your question, here's a nice example. Consider that we work in the theory $\sf ZFC$ augmented by the assumptions of $\rm Con\sf (ZFC)$ and $\lnot\rm Con\sf (ZFC+\rm Con\sf (ZFC))$. Then there is a model of $\sf ZFC$, therefore there is a model of $\sf NBG$; but there is no model of $\sf MK$ since that would imply much more in terms of consistency strength (and there's also no model of $\sf ZFC_2$, since that would require an inaccessible cardinal to exist). – Asaf Karagila May 16 '14 at 5:21
• @AsafKaragila Thanks, this really helped. I see now that the main obstacle to the second part of my question is the word "simple". If I drop it, I can just fix a Gödel numbering, and add $\lnot\mathsf{Con(PA)}$ as a single axiom to $\mathsf{PA}$. My best guess for an answer is then probably that either a "simple" independent statement for PA like Goodstein's theorem can be expressed as a single formula (so that I can add the negation of that formula as an axiom), or to see whether Robinson arithmetic $\mathsf{Q}$ allows for a simple formula (provably) independent of $\mathsf{Q}$. – Thomas Klimpel May 17 '14 at 12:27
• $(\forall y)(\exists x)(x+x = y \: \lor \: S(x+x) = y) \;\;$ is a simple formula that is provably independent of Q. $\hspace{1.01 in}$ – user57159 Aug 11 '14 at 6:27 | 2019-05-19 10:20:07 | {"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": 0.8971373438835144, "perplexity": 423.0283282640497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1558232254751.58/warc/CC-MAIN-20190519101512-20190519123512-00334.warc.gz"} |
https://math.stackexchange.com/questions/661177/clarification-for-this-combinations-permutations-problem | # Clarification for this combinations/permutations problem?
I've been going through a list of poker hands and their descriptions, and then attempting to calculate their probabilities by first calculating the number of possible hands for the given hand.
I tried to do the Two Pair hand, which is a hand where you have 2 cards of the same value, and another 2 cards of the same value but different from the previous pair, and one card of a value different from the pairs(e.g. $3\heartsuit3\spadesuit \space 4\clubsuit$ $4\spadesuit \space10\heartsuit$); I got the wrong answer:
But why is my approach wrong? I thought of it as choosing a value out of 13 possible values(A,K,J,10,...), then choose 2 cards; choose another value from the remaining 12 values, then another 2 cards. But this isn't the same as choosing a pair out of 13 values, and then choose 4 cards as it appears in the correct answer. I can't see how that makes a difference intuitively... what's the difference here?
Your first way double counts. It counts two Jacks, and two $5$'s, and some useless card, as different from two $5$'s, and two Jacks, and some useless card.
For Jack is one of the $\binom{13}{1}$ kinds that you chose "first," and $5$ is among the $\binom{12}{1}$ kinds that you chose "second." But $5$ is among the $\binom{13}{1}$ kinds that you chose "first," and Jack is among the $\binom{12}{1}$ kinds that you chose "second."
Note that this issue does not arise with a full house, for three Jacks and two $5$'s is a different hand than three $5$'s and two Jacks. | 2019-06-26 14:44:19 | {"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": 0.7976263761520386, "perplexity": 346.20804710479206}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000353.82/warc/CC-MAIN-20190626134339-20190626160339-00412.warc.gz"} |
http://theory.cs.uni-bonn.de/Zope/csreports/report_1991/paper_8561/abstract.html | Institut für Informatik Abteilung V
Universität Bonn -> Institut für Informatik -> Abteilung V CS-Reports 1991 Copyright 1991 Universität Bonn, Institut für Informatik, Abt. V 8561 Some Computational Problems in Linear Algebra as Hard as Matrix Multiplication Peter Buergnisser, Marek Karpinski, Thomas Lickteig [Download PostScript] [Download PDF] We define the complexity of a computational problem given by a relation using the model of a computation tree with Ostrowski complexity measure. To a sequence of problems we assign an exponent similar as for matrix multiplication. For the complexity of the following computational problems in linear algebra \begin{itemize} \item $KER_n$: Compute a basis of the kernel for a given $n \times n$--matrix. \item $OGB_n$: Find an invertible matrix that transforms a given symmetric $n \times n$--matrix to diagonal form. \item $SPR_n$: Find a sparse representation of a given $n \times n$--matrix. \end{itemize} we prove relative lower bounds of the form $aM_n - b$ and absolute lower bounds $dn^2$, where $M_n$ denotes the complexity of matrix multiplication and $a,b,d$ are suitably chosen constants. We show that the exponent of the problem sequences $KER,\;OGB,\;SPR$ is the same as the exponent $\omega$ of matrix multiplication. Last Change: 08/18/99 at 13:00:38 English Universität Bonn -> Institut für Informatik -> Abteilung V | 2017-10-19 14:21:15 | {"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": 0.98879075050354, "perplexity": 973.3190529090813}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1508187823309.55/warc/CC-MAIN-20171019141046-20171019161046-00360.warc.gz"} |
https://proofwiki.org/wiki/Electric_Charge/Quantum/Examples | Electric Charge/Quantum/Examples
$60 \ \mathrm W$ Bulb at $200 \ \mathrm V$
Consider a $60 \ \mathrm W$ light bulb running at $200 \ \mathrm V$.
Approximately $2 \times 10^{18}$ units of elementary charge flow along the filament of the light bulb every second. | 2022-01-20 20:55:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8943676948547363, "perplexity": 1439.10177809967}, "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-2022-05/segments/1642320302622.39/warc/CC-MAIN-20220120190514-20220120220514-00640.warc.gz"} |
https://www.physicsforums.com/threads/interpret-current-density-in-plasma-as-material-property.888560/ | # Interpret current density in plasma as material property?
Tags:
1. Oct 10, 2016
### lampCable
1. The problem statement, all variables and given/known data
An electromagnetic wave propagates through a gas of N free electrons per unit volume. Neglecting damping, show that the index of refraction is given by
$$n^2 = 1 - \frac{\omega_P^2}{\omega^2},$$
where the plasma frequency
$$\omega_P = \sqrt{\frac{Ne^2}{\epsilon_0m_e}}.\quad(1)$$
We assume that the incident wave is a plane wave, and that on each electron $F = qE$.
2. Relevant equations
Maxwell's fourth equation in vacuum where there exist charges and current:
$$\nabla\times\textbf{B} = \mu_0\textbf{J} + \mu_0\epsilon_0\frac{\partial\textbf{E}}{\partial t}.$$
3. The attempt at a solution
Integrating Newtons second law and neglecting any source velocity we get
$$\textbf{v} = \frac{iq}{m\omega}\textbf{E}_0e^{i(kz-\omega t)}.$$
The current density, then, is
$$\textbf{J} = Nq\textbf{v} = -\frac{Nq^2}{m\omega^2}\frac{\partial\textbf{E}}{\partial t}.\quad(2)$$
Using now Maxwell's fourth equation in vacuum together with (1) and (2) we get
$$\nabla\times\textbf{B} = \mu_0\epsilon_0\bigg(1-\frac{\omega_P^2}{\omega^2}\bigg)\frac{\partial\textbf{E}}{\partial t}.$$
Question: Is it legit to here define $$\epsilon_r\mu_r = 1 - \frac{\omega_p^2}{\omega^2}$$ for the purpose of calculating the refractive index?
My argument for this is as follows. Since
$$n = \sqrt{\epsilon_r\mu_r}$$
it doesn't matter really (for the purpose of determining the refractive index) how $\epsilon_r$ and $\mu_r$ are chosen per se, so long as their product satisfy the above definition. In this sense it is then possible to convert a case where we have a region with current density, to one where we simply have a material with $\epsilon_r\epsilon_r\neq1$ instead. But since we are free to choose $\epsilon_r$ and $\mu_r$, the analogy could not go further to where the two are used separately.
2. Oct 10, 2016
Your derivation looks quite legitimate. The next step in deriving the E-M wave (at least the $B$ part) is to take the curl of both sides of your equation. With a vector identity $\nabla \times \nabla \times B=\nabla (\nabla \cdot B)-\nabla^2 B$, and using Faraday's law on the other side, you have the wave equation for $B$ and the wave velocity is determined precisely by what you have already presented. editing... Alternatively you could begin with Faraday's law $\nabla \times E=-dB/dt$ and again take the curl of both sides of the equation and proceed in a similar fashion to get the wave equation for the electric field $E$. | 2017-10-22 20:27:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "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": 0.83647620677948, "perplexity": 236.43778574787228}, "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-2017-43/segments/1508187825436.78/warc/CC-MAIN-20171022184824-20171022204824-00782.warc.gz"} |
https://math.stackexchange.com/questions/1875649/volumes-of-revolution-cosine-function | # Volumes of Revolution- cosine function
How do you find the volume of the solid of revolution formed by revolving this function around the $x$-axis: $y=2.33 \cos\left(\frac{25\pi}{119}\left(x-2.47\right)\right)$ between the limits $x=2.47$ and $x=4.85$?
Full working would be greatly appreciated!
• Are you familiar with any standard methods for this? You want to use what is called "disc method" (en.wikipedia.org/wiki/Solid_of_revolution#Disc_method). – Carser Jul 30 '16 at 3:52
• Yes I am familiar with that method. That is what I am trying to use but I am just unsure with how to expand the brackets when you have to square the entire function: (2.33cos(25π119(x−2.47)))^2. Could you please show me how to expand the bracket? Does the 2.33 become squared and the cos become squared or does something happen to inside the cos bracket as well – Emma Jul 30 '16 at 4:11
The volume is given by $$V = \pi \int_{2.47}^{4.85} \left( 2.33 \cos \left( \frac{25 \pi}{119}(x-2.47) \right) \right)^2 \ dx$$ $$= \pi (2.33)^2 \int_{2.47}^{4.85} \cos^2 \left(\frac{25 \pi}{119} (x-2.47) \right) \ dx$$ Letting $u=(x-2.47)$, then $du= dx$ and we can substitute to get $$= \pi (2.33)^2 \int_{2.47}^{4.85} \cos^2 \left(\frac{25 \pi}{119}u\right) \ du$$ and if we can use $$\int \cos^2(a x) dx = \frac{2ax+\sin(2ax)}{4a}$$ then we have $$= \pi (2.33)^2 \left[ \frac{2\frac{25 \pi}{119}u+\sin(2\frac{25 \pi}{119}u)}{4 \frac{25 \pi}{119}} \right]_{2.47}^{4.85}$$ which I'll happily leave for you to simplify. | 2020-01-17 13:27:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8770497441291809, "perplexity": 193.36507246572404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250589560.16/warc/CC-MAIN-20200117123339-20200117151339-00088.warc.gz"} |
http://www.euro-math-soc.eu/node/4003 | ## Riemann, Einstein and geometry
Sep 18 2014 - 09:00
Sep 20 2014 - 12:30
Venue:
Institut de Recherche Mathématique Avancée, University of Strasbourg (France)
Short description of the event:
The conference is part of a series of bi-annual conferences "Encounter between Mathematicians and Theoretical Physicists" and it is addressed to a large audience.
Athanase Papadopoulos : athanase.papadopoulos$math.unistra.fr Sumio Yamada : yamada$math.gakushuin.ac.jp | 2014-03-07 09:00:25 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7580703496932983, "perplexity": 13252.943875181329}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999639602/warc/CC-MAIN-20140305060719-00025-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/850029/rayleigh-quotient-variant | # Rayleigh Quotient variant?
If $A$ is a covariance matrix and I want to get
$\max X^TAX$ where each value of $x$ is between -1 and 1.
Is there a closed-form solution for this?
I understand when $X^TX = 1$ this becomes the original Rayleigh quotient problem.
• Is $X$ a random column vector? – Omnomnomnom Jun 28 '14 at 4:33
• @Omnomnomnom: Right, X is an n x 1 vector – user40923 Jun 28 '14 at 4:45 | 2019-05-25 23:12:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9404663443565369, "perplexity": 434.59922249905475}, "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-2019-22/segments/1558232258453.85/warc/CC-MAIN-20190525224929-20190526010929-00023.warc.gz"} |
http://math.stackexchange.com/questions/99068/how-to-write-x-iff-y-in-cnf-form | # How to write $X \iff Y$ in CNF form?
I know that $X \iff Y$ is true when
1. $X$ is True and $Y$ is True
2. $X$ is False and $Y$ is False
I know that there is a simple algorithm to convert to CNF form, but I don't remember it...
-
How about $(X \land Y) \lor (\lnot X \land \lnot Y) = (\lnot X \lor Y) \land (X \lor \lnot Y)$ – Sasha Jan 14 '12 at 18:38
$$(x \leftrightarrow y) \Leftrightarrow (x \rightarrow y) \land (y \rightarrow x) \Leftrightarrow (\lnot x \lor y) \land (\lnot y \lor x)$$
There is a distinction between $\rightarrow$ and $\Rightarrow$, the former is a connective between propositions within the language, while the latter is in the meta-language. This also made your post somewhat easier to read :-) – Asaf Karagila Jan 14 '12 at 19:47
$(\neg X \vee Y)\wedge(X\vee\neg Y)$ | 2015-11-28 02:58:18 | {"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": 0.8233608603477478, "perplexity": 339.3597344852603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1448398450745.23/warc/CC-MAIN-20151124205410-00250-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/fundamentals-of-physics-extended-10th-edition/chapter-3-vectors-questions-page-56/13e | ## Fundamentals of Physics Extended (10th Edition)
$\vec{A}$ is a vector $\vec{B}\cdot\vec{C}$ is a scalar. (vector) + (scalar) has no meaning as we can not add scalars and vectors. | 2019-03-18 17:50:57 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6945178508758545, "perplexity": 1013.3542255497701}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1552912201521.60/warc/CC-MAIN-20190318172016-20190318194016-00028.warc.gz"} |
https://tex.stackexchange.com/questions/554226/label-figrabbitmq-ha-policyfig-multiply-defined-in-mac-os-catalina-using-late | # Label fig:rabbitmq-ha-policyfig' multiply defined in Mac OS Catalina using latexmk to compile
When I compile my latex doc using this command in Mac OS Catalina:
/Library/TeX/texbin/latexmk -pdfxe -pvc -xelatex -interaction=nonstopmode ./dolphin-book-2020.tex
it give me tips:
Label fig:rabbitmq-ha-policyfig' multiply defined
and I searching my docs and find only one places to define this like this:
另一种避免的方式是RabbitMQ HA，做镜像队列(Mirror Queue)，如图\ref{fig:rabbitmq-ha-policyfig}所示。
\begin{figure}[htbp]
\centering
\includegraphics[scale=0.25]{rabbitmq-ha-policy}
\caption{RabbitMQ添加高可用策略}
\label{fig:rabbitmq-ha-policyfig}
\end{figure}
why still give me tips mutidefined label and what should I do to fix this?
• In terms of label defintions, the code shown in the question is fine. It should only define the label fig:rabbitmq-ha-policyfig once. Double check that there is no other figure (or something else) in your document that uses the label fig:rabbitmq-ha-policyfig. – moewe Jul 20 '20 at 5:40
• no,only this place defined this and ref this label in the whole document.@moewe – Dolphin Jul 20 '20 at 6:00
• Then I'm out of ideas. Is there a chance you can turn the code you have shown so far into a fully compilable example document that reproduces the warning (tex.meta.stackexchange.com/q/228/35864)? It is tricky to diagnose problems like this with only a part of the code, especially if the code on its own (if embedded into a simple document) is unproblematic. – moewe Jul 20 '20 at 6:03 | 2021-06-12 21:11:12 | {"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": 0.6990429162979126, "perplexity": 1843.0685745208511}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1623487586390.4/warc/CC-MAIN-20210612193058-20210612223058-00057.warc.gz"} |
https://paperswithcode.com/paper/bandit-pam-almost-linear-time-k-medoids | # BanditPAM: Almost Linear Time $k$-Medoids Clustering via Multi-Armed Bandits
Clustering is a ubiquitous task in data science. Compared to the commonly used $k$-means clustering, $k$-medoids clustering requires the cluster centers to be actual data points and support arbitrary distance metrics, which permits greater interpretability and the clustering of structured objects... Current state-of-the-art $k$-medoids clustering algorithms, such as Partitioning Around Medoids (PAM), are iterative and are quadratic in the dataset size $n$ for each iteration, being prohibitively expensive for large datasets. We propose BanditPAM, a randomized algorithm inspired by techniques from multi-armed bandits, that reduces the complexity of each PAM iteration from $O(n^2)$ to $O(n \log n)$ and returns the same results with high probability, under assumptions on the data that often hold in practice. As such, BanditPAM matches state-of-the-art clustering loss while reaching solutions much faster. We empirically validate our results on several large real-world datasets, including a coding exercise submissions dataset, the 10x Genomics 68k PBMC single-cell RNA sequencing dataset, and the MNIST handwritten digits dataset. In these experiments, we observe that BanditPAM returns the same results as state-of-the-art PAM-like algorithms up to 4x faster while performing up to 200x fewer distance computations. The improvements demonstrated by BanditPAM enable $k$-medoids clustering on a wide range of applications, including identifying cell types in large-scale single-cell data and providing scalable feedback for students learning computer science online. We also release highly optimized Python and C++ implementations of our algorithm. read more
PDF Abstract | 2021-12-05 11:52:43 | {"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": 0.28359660506248474, "perplexity": 1576.4348101323621}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363157.32/warc/CC-MAIN-20211205100135-20211205130135-00549.warc.gz"} |
https://testbook.com/question-answer/a-collapsible-soil-sub-grade-sample-was-tested-usi--5ee23cdb258a5a0d0e491ec8 | # A collapsible soil sub-grade sample was tested using Standard California Bearing Ratio apparatus, and the observations are given below: Sl. No Load Penetration 1 60.55 kg 2.5 mm 2. 80.55 kg 5.0 mm Taking the standard assumptions regarding the load penetration curve, the CBR value of the sample will be taken as
This question was previously asked in
ESE Civil 2016 Paper 2: Official Paper
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1. 39%
2. 40%
3. 4.4%
4. 5.5%
Option 3 : 4.4%
Free
ST 1: Building Material and Concrete Technology
16847
20 Questions 20 Marks 12 Mins
## Detailed Solution
Concept:
CBR test is a strength test conducted on the soil by introducing a surcharge load at the compaction rate of 1.25 mm per minute on a completely soaked soil sample passing through 20 mm sieve size.
$${\rm{CB}}{{\rm{R}}_{\rm{\delta }}} = \frac{{{{\rm{P}}_{\rm{\delta }}}{\rm{\;of\;soil}}}}{{{{\rm{P}}_{\rm{\delta }}}{\rm{\;of\;standard\;crushed\;aggregate}}}} \times 100$$
δ = displacement in mm
Pδ = Load corresponding to ‘δ’ settlement
Ps = Load for standard crushed aggregate\
For standard aggregate at 2.5 mm penetration, Load is 1370 kg
For standard aggregate at 5 mm penetration, Load is 2055 kg
Calculation:
Given:
Sl. No Load Penetration 1 60.55 kg 2.5 mm 2. 80.55 kg 5.0 mm
$$CBR = \;\frac{{{\rm{Load\;carried\;by\;specimen}}}}{{{\rm{load\;carried\;by\;standard\;specimen}}}} \times 100$$
At 2.5 mm penetration, $$CBR = \;\frac{{60.5}}{{1370}} \times 100 = 4.4\%$$
At 5 mm penetration, $$CBR = \;\frac{{80.55}}{{2055}} \times 100 = 3.9\%$$
CBR is the maximum of the above two ratios i.e. 4.4% | 2021-09-18 10:19:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6494185924530029, "perplexity": 8871.156582927944}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056392.79/warc/CC-MAIN-20210918093220-20210918123220-00249.warc.gz"} |
http://mail-index.netbsd.org/port-vax/2012/12/21/msg001408.html | Port-vax archive
# Re: DEC Video Connector
On Thu, 20 Dec 2012 16:27:58 -0700
emanuel stiebler <emu%e-bbes.com@localhost> wrote:
> So I finally wanted to do it right and make some cables which go
> directly from the 3W3 to VGA ...
Cut off the BNC connectors and solder a DE15 to that end?
> And the solder-able version was just an idea to make a framerate
> converter box, because most of the TFT-panels just deal with 60Hz,
> and DEC had many, many other ideas about resolutions & frequencies
> back then ;-)
I have a crappy consumer grade 27" LCD. Yet it accepted the sync on
green output with 66 Hz or 72 Hz Vsync from my VS4k90 without any
problems. The same with an older 19" LCD.
--
\end{Jochen}
\ref{http://www.unixag-kl.fh-kl.de/~jkunz/}
Home | Main Index | Thread Index | Old Index | 2014-03-15 21:22:15 | {"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": 0.3423660695552826, "perplexity": 12318.264625963555}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394678699721/warc/CC-MAIN-20140313024459-00071-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://lists.gnu.org/archive/html/lilypond-devel/2007-08/msg00158.html | lilypond-devel
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## \bar "|:" - wrong position in the first misure
From: Mattia Giovanetti Subject: \bar "|:" - wrong position in the first misure Date: Wed, 29 Aug 2007 11:42:36 +0200
Hi,
first of all I must thank you for your wonderful program, Lilypond it's fantastic and you did a marvellous work, really super. I'm an intalian classical musician, my intrument is the guitar, I study at Conservatorio, actually I'm at the last year. I think that your program got a notation bug. This involve the command \bar "|:" in the first misure, I attach some files at this mail, so you can take a look of and get what I mean. But in a simple word the problem/bug is that: "the repeat double line with dots, must be after the time signature not befoure in the first misure". Please take a look at 120 Arpeggi di Mauro Giuliani, it's a true example.
I hope you will fix that bug as soon as possible!
Thanks to you.
Salute e Prosperità.
Mattia Giovanetti.
http://xoomer.virgilio.it/naturaljazz
quite right.jpg
Description: JPEG image
quite right.ly
Description: Text Data
wrong.jpg
Description: JPEG image
wrong.ly
Description: Text Data | 2019-05-26 12:34:44 | {"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": 0.863027811050415, "perplexity": 7511.2335802724065}, "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-2019-22/segments/1558232259126.83/warc/CC-MAIN-20190526105248-20190526131248-00441.warc.gz"} |
https://www.eduzip.com/ask/question/in-figure-a-b-c-are-collinear-points-and-angle-dbaangle-eba-name-521033 | Mathematics
# In figure, A, B, C are collinear points and $\angle DBA=\angle EBA$. Name two pairs of supplementary angles.
##### SOLUTION
Supplementary angles are two angles whose sum is $180^{0}$.
According to question, $\angle DBA=\angle EBA$
And $line\ AC$ is a straight line.
So, $\angle DBA+\angle DBC=180^0$ .
So, they satisfy condition for supplementary angles.
Similarly,$\angle EBA+\angle EBC=180^0$ .
So, they also satisfy condition for supplementary angles.
$\therefore \angle DBA$ and $\angle DBC$ as well as $\angle EBA$ and $\angle EBC$ are supplementary angles.
You're just one step away
Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 87
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1 Verified Answer | Published on 09th 09, 2020 | 2022-01-28 20:31:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6124204993247986, "perplexity": 9438.175635691154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320306335.77/warc/CC-MAIN-20220128182552-20220128212552-00422.warc.gz"} |
https://puzzling.stackexchange.com/questions/80400/get-2-liters-from-4-and-5-liter-buckets/80402 | # Get 2 liters from 4 and 5 liter buckets [duplicate]
You have a 4 liter bucket and a 5 liter bucket and an (infinite) supply of liquid.
How do you get 2 liters? | 2020-04-09 05:13:05 | {"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": 0.8790210485458374, "perplexity": 1853.674623205523}, "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-2020-16/segments/1585371829677.89/warc/CC-MAIN-20200409024535-20200409055035-00520.warc.gz"} |
https://www.semanticscholar.org/paper/Lecture-notes-on-Mather's-theory-for-Lagrangian-Sorrentino/95d22cc6d101e6b180becda123c6067b48a0138f | Corpus ID: 118946546
# Lecture notes on Mather's theory for Lagrangian systems
@article{Sorrentino2010LectureNO,
title={Lecture notes on Mather's theory for Lagrangian systems},
author={Alfonso Sorrentino},
journal={arXiv: Dynamical Systems},
year={2010}
}
• Alfonso Sorrentino
• Published 2010
• Mathematics
• arXiv: Dynamical Systems
• These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\a degli Studi di Napoli "Federico II" (April 2009), at University of Cambridge (academic year 2009-2010) and at Universitat Polit\ecnica de Catalunya (June 2010).
27 Citations | 2021-01-23 02:24:44 | {"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": 0.37438589334487915, "perplexity": 10155.141681525849}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703531702.36/warc/CC-MAIN-20210123001629-20210123031629-00227.warc.gz"} |
https://math.stackexchange.com/questions/2537995/windowed-fourier-transform | # Windowed Fourier Transform
I am having some difficulties with this question.
We define the windowed Fourier transform of $f \in L^2(\mathbb{R})$ as $$Sf(\mu,\xi)=\int_\mathbb{R}f(t)g(t-\mu)e^{-i\xi t}dt$$
where $g$ is some real, symmetric and finite supported function such that it vanishes outside a finite interval. Prove that for $f=e^{i\eta_0t}$, we have $$Sf(\mu,\eta)=e^{-i\mu(\eta-\eta_0)}\hat{g}(\eta-\eta_0)$$
Could someone also provide me with the integral definition of the windowed Fourier transform? For instance the Fourier transform is defined as, $$\hat{f}(\omega)=\int_\mathbb{R}f(x)e^{-ixw}dx$$
• For $f$ a single complex sine then $Sf$ is what you wrote, this is obvious from the integral definition. – reuns Nov 26 '17 at 14:21
• Substitute $t'=t-\mu$, pull out the exponential factor that is independent of $t,$ and then recognize the remaining integral as the Fourier transform of $g$ at $\eta-\eta_{0}$. – RideTheWavelet Nov 26 '17 at 14:33 | 2019-06-18 07:17:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.97188401222229, "perplexity": 147.160088067887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1560627998690.87/warc/CC-MAIN-20190618063322-20190618085322-00315.warc.gz"} |
https://crazyproject.wordpress.com/2012/01/03/properties-of-the-derivative-of-a-matrix-power-series/ | ## Properties of the derivative of a matrix power series
Let $G(x)$ be a formal power series on $\mathbb{C}$ having an infinite radius of convergence and fix an $n \times n$ matrix $A$ over $\mathbb{C}$. The mapping $t \mapsto G(At)$ carries a complex number $t$ to a complex matrix $G(At)$; we can think of this as the ‘direct sum’ of $n \times n$ different functions on $\mathbb{C}$, one for each entry of $G(At)$.
We now define the derivative of $G(At)$ with respect to $t$ to be a mapping $\mathbb{C} \rightarrow \mathsf{Mat}_n(\mathbb{C})$ as follows: $\left[\frac{d}{dt} G(At)\right]_{i,j} = \frac{d}{dt} \left[ G(At)_{i,j}\right]$. In other words, thinking of $G(At)$ as a matrix of functions, $\frac{d}{dt} G(At)$ is the matrix whose entries are the derivatives of the corresponding entries of $G(At)$.
We will use the limit definition of derivative (that is, $\frac{d}{dt} f(t) = \mathsf{lim}_{h \rightarrow 0} \dfrac{f(t+h) - f(t)}{h}$, where it doesnt matter how $h$ approaches 0 in $\mathbb{C}$) and will assume that all derivatives exist everywhere.
Prove the following properties of derivatives:
1. If $G(x) = \sum_{k \in \mathbb{N}} \alpha_kx^k$, then $\frac{d}{dt} G(At) = A \sum_{k \in \mathbb{N}} (k+1)\alpha_{k+1}(At)^k$.
2. If $V$ is an $n \times 1$ matrix with constant entries (i.e. not dependent on $t$) then $\frac{d}{dt} (G(At)V) = \left( \frac{d}{dt} G(At) \right) V$.
[My usual disclaimer about analysis applies here: as soon as I see words like ‘limit’ and ‘continuous’ I become even more confused than usual. Read the following with a healthy dose of skepticism, and please point out any errors.]
Note the following.
$\left[ \dfrac{d}{dt} G(At) \right]_{i,j}$ = $\dfrac{d}{dt} G(At)_{i,j}$ = $\mathsf{lim}_{h \rightarrow 0} \dfrac{G(A(t+h)_{i,j}) - G(At)_{i,j}}{h}$ = $\mathsf{lim}_{h \rightarrow 0} \left[ \dfrac{G(A(t+h)) - G(At)}{h} \right]_{i,j}$ = $\mathsf{lim}_{h \rightarrow 0} \left[ \dfrac{\sum_k \alpha_k(A(t+h))^k - \sum_k \alpha_k(At)^k}{h} \right]_{i,j}$ = $\mathsf{lim}_{h \rightarrow 0} \left[ \dfrac{\sum_k \alpha_k A^k ((t+h)^k - t^k)}{h} \right]_{i,j}$ = $\mathsf{lim}_{h \rightarrow 0} \left[ \dfrac{\sum_{k > 0} \alpha_k A^k \left( \sum_{m=0}^k {k \choose m} t^m h^{k-m} - t^k \right)}{h} \right]_{i,j}$ = $\mathsf{lim}_{h \rightarrow 0} \left[ \dfrac{\sum_{k > 0} \alpha_k A^k \left( \sum_{m=0}^{k-1} {k \choose m} t^m h^{k-m} \right)}{h} \right]_{i,j}$ = $\mathsf{lim}_{h \rightarrow 0} \displaystyle\sum_{k > 0} \alpha_k A^k \sum_{m=0}^{k-1} {k \choose m} t^m h^{k-1-m}$ (Now we can substitute $h = 0$.) = $\displaystyle\sum_{k > 0} \alpha_k A^k {k \choose {k-1}} t^{k-1}$ (All terms but $m=k-1$ vanish.) = $\displaystyle\sum_{k > 0} k \alpha_k A^k t^{k-1}$ = $\displaystyle\sum_k (k+1) \alpha_{k+1}A^{k+1}t^k$ = $A \sum_k (k+1)\alpha_{k+1}(At)^k$
As desired.
Now say $V = [v_i]$ and $G(At) = [c_{i,j}(t)]$; we then have the following.
$\dfrac{d}{dt} \left( G(At)V \right)$ = $\dfrac{d}{dt} \left( [c_{i,j}(t)][v_{i,j}] \right)$ = $\dfrac{d}{dt} [\sum_k c_{i,k}(t)v_k]$ = $[\frac{d}{dt} \sum_k c_{i,k}(t)v_k]$ = $[\sum_k (\frac{d}{dt} c_{i,k}(t)) v_k]$ = $[\frac{d}{dt} c_{i,j}(t)][v_i]$ = $\left(\frac{d}{dt} G(At) \right)V$
As desired. | 2017-03-28 06:13:29 | {"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": 0, "mathjax_asciimath": 0, "img_math": 51, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.966854989528656, "perplexity": 91.77483104989716}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1490218189680.78/warc/CC-MAIN-20170322212949-00037-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-1-equations-and-graphs-section-1-10-modeling-variation-1-10-exercises-page-164/17 | College Algebra 7th Edition
$\displaystyle R= \frac{kP^{2}t^{2}}{b^{3}}$
Since $R$ is directly (jointly) proportional to the squares of $P$ and $t$, but inversely proportional to the cube of $b$, we have: $\displaystyle R= \frac{kP^{2}t^{2}}{b^{3}}$ (where $k$ is a constant.) | 2018-07-19 14:09:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9953418374061584, "perplexity": 221.88575288996975}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590901.10/warc/CC-MAIN-20180719125339-20180719145339-00033.warc.gz"} |
https://www.electro-tech-online.com/threads/ir-receiver.93558/ | Status
Not open for further replies.
#### GatorGnet
##### New Member
I posted this in an earlier post:
Remote Controlling Your PC
What does the 78L05 do? I assumed it was a normal transistor but it looks to be something else? Sorry to be such a newb...
#### blueroomelectronics
##### Well-Known Member
It's a 5V regulator.
#### GatorGnet
##### New Member
The only ones I found with the part number 78L05 are hard to find. I assume the normal 7805 will work?
#### blueroomelectronics
##### Well-Known Member
Yes. The L = 100mA rated.
##### Banned
Try google first, the 7805 is WELL documented on the net.
#### GatorGnet
##### New Member
This schematic uses the three pin IR module. What is the difference between them and the two pin IR detectors?
#### blueroomelectronics
##### Well-Known Member
You need the three pin, it's has a small IC demodulator inside.
#### GatorGnet
##### New Member
Well I got one built. After debugging some things I got it working. Now I have an issue with incoming data.
When I push a button on the remote I get random data coming in:
Code:
Outputting raw mode2 data.
space 1382017
pulse 9026
space 4443
pulse 571
space 4418
pulse 562
space 4430
pulse 566
space 2177
pulse 564
space 4427
pulse 568
space 4421
pulse 567
space 4425
pulse 565
space 2179
pulse 575
space 2170
pulse 567
space 2177
pulse 567
space 2179
pulse 569
space 2175
pulse 571
space 2172
pulse 576
space 2170
pulse 575
space 4414
pulse 576
space 2170
pulse 573
space 2170
pulse 571
space 28222
pulse 9052
space 2199
pulse 574
btw, this is from one button push.
When I push the same button again, I get different data coming in.
Could this be the remote or is it something with my board?
Last edited:
#### blueroomelectronics
##### Well-Known Member
What remote are you using? What's it set for?
#### GatorGnet
##### New Member
One is a Toshiba CT-852 and the other is for our comcast cable box. Both give random data when pushing one button. The software I am using states that the remote is using a special repeat code. I just wanted to make sure that my receiver I spent some good time building is working right.
#### Pommie
##### Well-Known Member
That is the raw data. You need different software to interpret it. Your hardware appears to be working correctly.
Mike.
#### GatorGnet
##### New Member
Why would the electronic companies that make those want to use data that changes each time you send it? | 2020-09-26 12:03:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.237917959690094, "perplexity": 12279.385152047118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400241093.64/warc/CC-MAIN-20200926102645-20200926132645-00268.warc.gz"} |
https://www.physicsforums.com/threads/solve-for-salary-given-averages-of-other-salaries.900651/ | # Homework Help: Solve for salary given averages of other salaries
1. Jan 17, 2017
### Mindscrape
My wife is working on problems to study for the GMAT, and asks her fellow math nerd (me) to help on some of them. Originally I had an error and wanted to see if any of you could help me find it, but as I was typing I found it myself! Can I still put this up in case someone stumbles on it and it helps them out? The problem is:
The average weekly salary of 12 workers and 3 managers in a factory was $600. A manager whose salary was$720 was replaced with a new manager, then the average salary of the team fell to $580. What is the salary of the new manager? So basically we start with (from the first sentence) $$\frac{tw+tm}{15}=600$$ where tw represents total worker salary and tm represents total manager salary. Now the second sentence says $$tm=m1+m2+720$$ so the first equation is now (having multiplied out the 15 from before) -- also label this eqn1 $$tw+m1+m2+720=9000$$ continuing with info from the second sentence, we get the second equation for the newly decreased average as $$\frac{tw+m1+m2+m3}{15}=580$$ now simplifying gives -- and labeling this eqn2 $$tw+m1+m2+m3=8700$$ subtract the two equations (eqn1-eqn2) $$720-m3=300$$ for the grand finale... $$m3=420$$ 2. Jan 17, 2017 ### RUber Nicely done. Since standardized tests often encourage shortcuts, I'll add a supplemental method which cuts through many of the steps. In general, if you wanted to affect a change of -$20 in the average of 15 salaries, you have to have a total change of
15(-$20)=-$300 to the sum.
This could be done by reducing one salary by $300, or reducing all salaries by$20, or anywhere in between.
Since the only thing you are changing is the salary starting at $720, you can apply the -$300 to that. | 2018-07-17 08:19:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.35606104135513306, "perplexity": 745.5504241314281}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1531676589618.52/warc/CC-MAIN-20180717070721-20180717090721-00093.warc.gz"} |
http://physics.stackexchange.com/questions/82476/can-i-usefully-interpret-a-non-unital-completely-positive-cp-map-as-a-cooling?answertab=votes | # Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?
Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily decreases its von Neumann entropy and, depending on how you define it, reduces its temperature.
Can a stronger connection be made between thermodynamics and CP maps? To what extent do non-unital CP maps reliably cool states that aren't infinite temperature?
- | 2014-04-20 21:32:50 | {"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": 0.871918797492981, "perplexity": 1355.0096147827135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00440-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://optimization-online.org/tag/constrained-weighted-ell_r-ell_1-minimization/ | ## A new sufficient condition for non-convex sparse recovery via weighted $\ell_r\!-\!\ell_1$ minimization
In this letter, we discuss the reconstruction of sparse signals from undersampled data, which belongs to the core content of compressed sensing. A new sufficient condition in terms of the restricted isometry constant (RIC) and restricted orthogonality constant (ROC) is first established for the performance guarantee of recently proposed non-convex weighted $\ell_r-\ell_1$ minimization in recovering … Read more | 2023-03-27 14:24:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.835136353969574, "perplexity": 427.74037469756263}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1679296948632.20/warc/CC-MAIN-20230327123514-20230327153514-00290.warc.gz"} |
https://forum.math.toronto.edu/index.php?PHPSESSID=1u0iucfle60t5k23oom8iace62&topic=385.0 | ### Author Topic: Writing the quiz with another section (Read 1496 times)
#### Victor Ivrii
• Administrator
• Elder Member
• Posts: 2563
• Karma: 0
##### Writing the quiz with another section
« on: September 15, 2014, 10:57:17 AM »
Students of one evening section are allowed to write Quiz with another evening section but not with a day section.
Students of the day section are allowed to write a Quiz with one of the evening sections. | 2021-09-28 01:42:50 | {"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": 0.9002169370651245, "perplexity": 13565.537339092305}, "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-2021-39/segments/1631780058589.72/warc/CC-MAIN-20210928002254-20210928032254-00582.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php/Nichomauss%27_Theorem | # Nichomauss' Theorem
## Nichomauss' Theorem
Nichomauss' Theorem states that $n^3$ can be written as the sum of $n$ consecutive integers, thus giving us $1^3+2^3+...+n^3=(1+2+...+n)^2$.
## A Visual Proof
Imagine a cuboid with a height of $1$, and length and width of $n$. Divide it into unit cubes. Now, starting from the bottom right of the cuboid (when it's flat on the ground), imagine the first cube to have $l=w=h=1$ (call this $a_1$). Now, extend its length and width by $2$ to get another cuboid with $l=w=3$ and $h=1$ (call this $a_2$). Color $a_1$ yellow and $a_2$ blue. Now, it's easy to see that $a_2$ has $(3 \cdot 3 \cdot 1)-(1 \cdot 1 \cdot 1)=8$ unit cubes and $a_1$ has $1 \cdot 1 \cdot 1=1$ unit cube. We can then rearrange the $8$ unit cubes into a $2 \cdot 2 \cdot 2$ cube. Thus, we clearly have $(1+2)^2=1^3+2^3$. And we can continue this process to $n$ unit cubes and $n$ cuboids with $l=w=n$, $h=1$, which gets us to $(1+2+...+n)^2=1^3+2^3+...+n^3$. | 2020-12-04 17:20:57 | {"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": 25, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9618394374847412, "perplexity": 184.58118279998646}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1606141740670.93/warc/CC-MAIN-20201204162500-20201204192500-00232.warc.gz"} |
https://byjus.com/question-answer/a-man-sold-two-articles-at-375-each-on-the-first-article-he-gains-25/ | Question
# A man sold two articles at $$375$$ each. On the first article, he gains $$25$$% and on the other, he loses $$25$$%. How much does he gain or lose in the whole transaction? Also, find the gain or loss percent in the whole transaction.
Solution
## First article$$SP =375$$Gain$$\% =25\%$$CP $$=\cfrac{ 100 \times 375}{125} = 300$$Second article$$SP =375$$Loss $$\% =25\%$$CP $$=\cfrac{ 100 \times 375}{75} = 500$$Total CP $$= 500+300 = 800$$Total SP $$= 375+375=700$$Loss $$=$$ CP $$-$$ SP Loss $$= 800 - 750 = 50$$Loss $$\%= \cfrac{50 \times 100}{800} = 6.25$$%Mathematics
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View More | 2022-01-29 01:47:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.21889102458953857, "perplexity": 10185.39589293157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320299894.32/warc/CC-MAIN-20220129002459-20220129032459-00673.warc.gz"} |
http://absolutewrite.com/forums/showthread.php?333364-Blinding-the-inner-editor&p=10319145 | I also highlight font with another color when I know that work is needed on a section. It allows me to keep writing without dwelling on the issue needing more research , fleshing out, or editing. I just get the idea down and keep going.
But, I do also get stuck reading and re-reading what I've written. I like the idea of a font that I can't quite read. Although I cringe to think about how many typos I'd find after changing the color back! Flubby fingers are what get me stuck the most. I stop to fix something silly and forget where I was going. | 2018-08-21 09:41:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9142418503761292, "perplexity": 911.6639843828328}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221218101.95/warc/CC-MAIN-20180821092915-20180821112915-00530.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-exact-value-of-the-six-trigonometric-functions-of-the-angle--6#420773 | # How do you find the exact value of the six trigonometric functions of the angle whose terminal side passes through (x, 4x)?
May 10, 2017
$\sin \theta = \frac{4}{\sqrt{17}}$, $\cos \theta = \frac{1}{\sqrt{17}}$, $\tan \theta = 4$,
$\cot \theta = \frac{1}{4}$, $\sec \theta = \sqrt{17}$, $\csc \theta = \frac{\sqrt{17}}{4}$
#### Explanation:
As the terminal side passes through $\left(x , 4 x\right)$, we have $y = 4 x$ and hence its distance from origin is $\sqrt{{x}^{2} + {\left(4 x\right)}^{2}} = \sqrt{{x}^{2} + 16 {x}^{2}} = x \sqrt{17}$
Now consider the diagram below for a typical $\theta$, whose six trigonometrical ratios are
$\sin \theta = \frac{y}{r}$, $\cos \theta = \frac{x}{r}$, $\tan \theta = \frac{y}{x}$ and
$\cot \theta = \frac{x}{y}$, $\sec \theta = \frac{r}{x}$, $\csc \theta = \frac{r}{y}$
As we have $y = 4 x$ and $r = x \sqrt{17}$,
the six trigonometric ratios are
$\sin \theta = \frac{4 x}{x \sqrt{17}} = \frac{4}{\sqrt{17}}$, $\cos \theta = \frac{x}{x \sqrt{17}} = \frac{1}{\sqrt{17}}$,
$\tan \theta = \frac{4 x}{x} = 4$, $\cot \theta = \frac{x}{4 x} = \frac{1}{4}$,
$\sec \theta = \frac{x \sqrt{17}}{x} = \sqrt{17}$, $\csc \theta = \frac{x \sqrt{17}}{4 x} = \frac{\sqrt{17}}{4}$ | 2022-06-29 09:36:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 24, "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": 0.9755913019180298, "perplexity": 345.02685077691183}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103626162.35/warc/CC-MAIN-20220629084939-20220629114939-00653.warc.gz"} |
https://stats.stackexchange.com/questions/488176/multivariate-jensen-shannon-divergence | # Multivariate Jensen-Shannon divergence
This paper says multivariate Jensen-Shannon divergence is
$$JS(\mathbf{p}_1,\dots,\mathbf{p}_K) = \frac{1}{m} \sum KL(\mathbf{p}_i || \bar{\mathbf{p}})$$ with $$KL$$ being the KL-divergence of the multiple probability distributions. Is it accurate compared to bivariate JS-divergence?
Would a matrix of bivariate JS-divergences feasible (like the correlation matrix), and what would its diagonal consist of?
Besides these, if t-distributed Stochastic Neighbor Embedding (t-SNE) in sklearn.manifold.tsne can be used to form a representation of multivariate KL-divergence for minimization (multivariate rather than one pair at a time), can the same or another algorithm do the same for a multivariate version of Jensen-Shannon divergence? | 2021-08-02 15:49:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6122899651527405, "perplexity": 1647.5308847879478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154321.31/warc/CC-MAIN-20210802141221-20210802171221-00261.warc.gz"} |
https://web2.0calc.com/questions/i-need-help-pleaseeee | +0
0
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+64
The five circles making up this archery target have diameters of length and. What is the total red area?
Simplify your answer as much as you can. You can use pi in your answer if necessary (for example, if the answer were, you could enter "3pi" or "3*pi" or "$3\pi$").
Apr 7, 2019
#1
+102417
0
You didn't specify the diameters but.....if memory serves from answering this problem before....I believe that the diameters were 2, 4, 6, 8 and 10
So....the radiuses are 1, 2, 3, 4 and 5
The inner red area is easy = pi (1)^2 = 1pi
The next red area = area of 3rd circle - area of second circle = pi (3^2 - 2^2) = pi (9 - 4) = 5pi
The outer red area is = area of 5th circle - area of 4th circle = pi (5^2 - 4^2) = pi (25 - 16) = 9pi
So....the total of the red areas = [ 1 + 5 + 9 ] = 15 pi [units^2 ]
Apr 7, 2019
#2
+64
0
thanks!
donkey Apr 13, 2019 | 2019-08-25 02:04:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8780478239059448, "perplexity": 6064.895326839017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027322160.92/warc/CC-MAIN-20190825000550-20190825022550-00521.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/drawing-shows-three-square-surfaces-one-lying-xyplane-one-xz-plane-one-yz-plane-sides-ofth-q219517 | The drawing below shows three square surfaces, one lying in the xyplane, one in the xz plane, and one in the yz plane. The sides ofthe square each have length 2.810-2 m. A uniform magnetic field exists inthis region, and its components are: Bx = 0.53 T, By = 0.88 T, and Bz = 0.29 T. Determine the magnetic flux that passesthrough the surface that lies in:
(a) the xy plane
xy = wb
(b) the xz plane
xz = wb
(c) the yz plane
yz = wb
### Get this answer with Chegg Study
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Q:
The drawing below shows three square surfaces, one lying in the xyplane, one in the xz plane, and one in the yz plane. The sides ofthe square each have length 2.810-2 m. A uniform magnetic field exists inthis region, and its components are: Bx = 0.40 T, By = 0.74 T, and Bz = 0.23 T. Determine the magnetic flux that passesthrough the surface that lies in:(a) the xy planexy = wb(c) the yz planeyz = | 2016-07-23 11:22:14 | {"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": 0.9179928302764893, "perplexity": 2122.9293915870144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257822172.7/warc/CC-MAIN-20160723071022-00248-ip-10-185-27-174.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/143882/how-many-n-2-cycles-can-a-cubic-graph-have | # How many n/2-cycles can a cubic graph have
Given a simple cubic graph with $n$ vertices (which implies that $n$ is even), what is a good upper bound on the number of cycles of length $n/2$ it can have?
A random cubic graph has $\Theta((4/3)^n/n)$ cycles of length $n/2$, if I did my sums right. So do random cubic bipartite graphs. Also the whole cycle space has size $2^{n/2+1}$, so twice that is a (silly) upper bound.
Where's the truth?
ADDED: Counts for n=4,6,...,24: 0,2,6,12,20,20,48,48,132,118,312 (not in OEIS). All these are unique except that for 20 vertices there are two graphs.
-
How about (3n/2) choose (n/2)? Another silly bound, but it might lead somewhere. You could also divide the graph into connected groups of 5 edges and note that a cycle can intersect each group of edges in only 8 ways. (I assume each group is acyclic, perhaps a bad move.) Gerhard "Spins Me Round Right Round" Paseman, 2013.10.03 – Gerhard Paseman Oct 3 '13 at 18:16
Interesting question! I communicated it to Michael Krivelevich. He does not know, but suggests that the methods from ams.org/mathscinet-getitem?mr=2520275 might be useful – Boris Bukh Oct 3 '13 at 18:20
The related integer sequence appears to be $4,12,24,40,40,96,96$ – Jernej Oct 3 '13 at 23:21
@Jernej: Agreed if you count oriented cycles. I'm posting counts for unoriented cycles. – Brendan McKay Oct 4 '13 at 2:02 | 2016-02-13 13:01:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8151482343673706, "perplexity": 1066.1969420418593}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1454701166650.78/warc/CC-MAIN-20160205193926-00073-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://ringtheory.herokuapp.com/keywords/keyword/15/ | # Keyword: matrix ring
Description: Given a ring $R$ and a natural number $n$, the set $M_n(R)$ with ordinary matrix operations. | 2018-11-19 06:12:25 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9416454434394836, "perplexity": 394.02314774324077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1542039745281.79/warc/CC-MAIN-20181119043725-20181119065725-00375.warc.gz"} |
https://zbmath.org/?q=an%3A1092.68676 | ## Approximate entropy reducts.(English)Zbl 1092.68676
Summary: We use information entropy measure to extend the rough set based notion of a reduct. We introduce the Approximate Entropy Reduction Principle (AERP). It states that any simplification (reduction of attributes) in the decision model, which approximately preserves its conditional entropy (the measure of inconsistency of defining decision by conditional attributes) should be performed to decrease its prior entropy (the measure of the model’s complexity). We show NP-hardness of optimization tasks concerning application of various modifications of AERP to data analysis.
### MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence 94A17 Measures of information, entropy | 2022-08-15 07:21:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8390934467315674, "perplexity": 1843.3836240205612}, "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-2022-33/segments/1659882572161.46/warc/CC-MAIN-20220815054743-20220815084743-00785.warc.gz"} |
https://brilliant.org/problems/again-a-good-problem/ | # This can't be that Short!
Algebra Level 4
$\displaystyle \sum_{k=1}^m \left [ (k^2 + 1) \ k! \right ] = 1999 \times 2000!$
What value of $$m$$ satisfies the above summation?
× | 2017-10-23 15:42:33 | {"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": 0.9432784914970398, "perplexity": 4574.029062233722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1508187826114.69/warc/CC-MAIN-20171023145244-20171023165244-00190.warc.gz"} |
https://brilliant.org/discussions/thread/needs-solution/ | ×
# Needs solution
My problem Deflection needs a solution and rating.
Note by Nishant Sharma
2 years, 8 months ago
## Comments
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Also try this challenging question Challenges in mechanics by Ronak Agarwal(Part1) · 2 years, 8 months ago
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I have posted the solution.You can check it out · 2 years, 8 months ago
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It is quite an easy question . I want to write a solution but I don't know how to upload a diagram can you please tell me how to upload a diagram.Then I will put up the solution · 2 years, 8 months ago
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You can use these sites: postimage.org, imgur.com. · 2 years, 8 months ago
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! [alt text] (the link)...delete the spaces.. · 2 years, 8 months ago
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The link of what "an uploaded image on facebook" or what · 2 years, 8 months ago
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Can you please give an example of an image upload · 2 years, 8 months ago
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upload your diagram on imgur or any other similar website. Then copy the link of that image from that website onto here. · 2 years, 8 months ago
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Ok · 2 years, 8 months ago
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@Pranav Arora , @jatin yadav , @Sudeep Salgia , @Maharnab Mitra , @David Mattingly , @Anish Puthuraya Care to read this post... · 2 years, 8 months ago
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I have posted the solution. Kindly, check it. · 2 years, 8 months ago
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Set Loading... | 2017-03-23 02:31:18 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9436647295951843, "perplexity": 11518.304161743317}, "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-2017-13/segments/1490218186608.9/warc/CC-MAIN-20170322212946-00146-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://mathematica.stackexchange.com/questions/255577/including-literals-into-compiled-c-code?noredirect=1 | # Including literals into compiled C code
I have a function that I want to Compile into C for speed. Inside this function is a certain long expression called x, which has been computed earlier in a Mathematica session. However, if you call x naively inside the code, then you are referring to an "external variable" and so ordinary Wolfram Language code is used instead.
See below. The second version is 100 times faster because it got properly compiled into C. How can I include x in the code without literally copying-and-pasting a huge expression, which muddies up my notebook?
x = Sin[i^2]*Cos[i] (* A fairly long complicated expression *);
compiledsum1 = Compile[{{NumPoints, _Integer}},
Block[
{i, sum = 0.0},
For[i = 0, i < NumPoints, i++, sum += x;];
sum
], CompilationTarget -> "C"];
compiledsum2 = Compile[{{NumPoints, _Integer}},
Block[
{i, sum = 0.0},
For[i = 0, i < NumPoints, i++, sum += Sin[i^2]*Cos[i];];
sum
], CompilationTarget -> "C"];
Timings:
compiledsum1[100000] // Timing
{0.841049, 223.296}
compiledsum2[100000] // Timing
0.006448, 223.296
• Sep 12, 2021 at 13:35
• Externals are inlined by "InlineExternalDefinitions" -> True, see CompilationOptions in Compile
– I.M.
Sep 12, 2021 at 22:55
x = Sin[i^2]*Cos[i] (*A fairly long complicated expression*);
compiledsumtest1 =
Hold@Compile[{{NumPoints, _Integer}},
Block[{i, sum = 0.0}, For[i = 0, i < NumPoints, i++, sum += x;];
sum], CompilationTarget -> "C"] /. OwnValues@x // ReleaseHold;
Of course the solution above isn't the simplest for your specific problem. Henrik and I.M. have already shown two simpler solutions, I'd like to add one more based on pure function:
x = Sin[i^2]*Cos[i] (*A fairly long complicated expression*);
compiledsumtest2 =
Compile[{{NumPoints, _Integer}},
Block[{i, sum = 0.0}, For[i = 0, i < NumPoints, i++, sum += #;];
sum], CompilationTarget -> "C"] &@x;
But do remember the pattern-matching-based method is more general, here's an example.
• Thank you! Can you point me to the best reference to understand all of this wizardry? The documentation is quite tricky for me to properly grasp. Sep 12, 2021 at 13:04
• @BruceBartlett You may have a look at Leonid Shifrin's book, that's where I first learned about @, OwnValues, etc. These days Stephen Wolfram's book is a good choice, too. Sep 12, 2021 at 13:17
• Thank you very much!! Sep 12, 2021 at 13:35
Even easier with With.
compiledsum3 = With[{x = x},
Compile[{{NumPoints, _Integer}},
Block[{i, sum = 0.0},
For[i = 0, i < NumPoints, i++, sum += x;];
sum
],
CompilationTarget -> "C"]
]
(This is certainly a duplicate, but I have no time to look it up...) | 2022-07-04 11:22:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3842426538467407, "perplexity": 5238.122163425825}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656104375714.75/warc/CC-MAIN-20220704111005-20220704141005-00072.warc.gz"} |
https://www.physicsforums.com/threads/a-set-of-measure-0.304220/ | # A set of measure 0
1. Apr 1, 2009
### e(ho0n3
1. The problem statement, all variables and given/known data
Let $(X_n)$ be a sequence of measurable subsets of $\mathbb R$ such that
$$\sum_{i=1}^\infty m(X_i) < \infty$$
Define
$$X = \bigcap_{i=1}^\infty \left( \bigcup_{j=i}^\infty X_j \right)$$
Prove that m(X) = 0.
2. Relevant equations
Theorem. Let $(E_n)$ be a sequence of measurable sets such that $E_{n+1} \subseteq E_n$ and $m(E_1) < \infty$. Then
$$m\left(\bigcap_{i=1}^\infty E_i \right) = \lim_{i \to \infty} m(E_i)$$
3. The attempt at a solution
Define $E_i = \bigcup\limits_{j=i}^\infty X_j$. Then by the aforementioned theorem,
$$m(X) = \lim_{i \to \infty} m(E_i)$$
My only problem is showing that the limit is in fact 0. I haven't used that $\sum m(X_i) < \infty$. Any tips?
2. Apr 1, 2009
### johnson12
you can say that m(X) <= m(E_{i}) for each i, and
m(E_{i}) = lim m(X_{j}) = 0 since the sum was finite.
3. Apr 1, 2009
### e(ho0n3
I don't understand why $m(E_i) = \lim m(X_j)$. We have that
$$E_i = \bigcup_{j=i}^\infty X_j$$
so
$$m(E_i) \le \sum_{j=i}^\infty m(X_j)$$
I do agree that $\lim m(X_j) = 0$.
4. Apr 1, 2009
### xaos
are these intervals strictly nested or can there be a smallest interval?
i need clarifying: what exactly is INT(UNION(X_i)) with two indexes i and j?
Last edited: Apr 1, 2009
5. Apr 1, 2009
### johnson12
sorry thats only true if the E_{i} where increasing, but
$$lim_{i\rightarrow\infty}\left(\sum^{\infty}_{j=i}m(X_{j})\right) =lim_{i\rightarrow\infty}m(X_{i})$$.
recall that if an infinite series converges you can make the remainder sum arbitrarily small.
6. Apr 1, 2009
### e(ho0n3
You're right. That didn't occur to me. Thanks for the tip.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook | 2017-08-19 21:17:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8463229537010193, "perplexity": 2388.5006237291077}, "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-2017-34/segments/1502886105922.73/warc/CC-MAIN-20170819201404-20170819221404-00058.warc.gz"} |
https://stat.ethz.ch/pipermail/r-package-devel/2018q1/002481.html | # [R-pkg-devel] Warnings if Carriage Returns in Code Elements of R Documentation
Dario Strbenac dstr7320 at uni.sydney.edu.au
Mon Mar 5 10:00:22 CET 2018
Good day,
The package checking software emits a warning if \cr is used inside \code. The reason I'd like to do that is to avoid a S4 constructor specification being limited to one line and running off the side of the PDF page of the PDF manual, as happens by default. The style of the documentation which I wrote is:
\section{Constructor}{
\describe{
\item{}{
\code{DataClass(parameter1, parameter2, parameter3, parameter4,\cr
parameter5, parameter6)
}
}
} \describe{
\item{\code{parameter1}}{A description of the requirements of the first parameter.}
}
}
How can wrapping be forced without causing a warning during checking?
--------------------------------------
Dario Strbenac
University of Sydney
Camperdown NSW 2050
Australia | 2019-08-24 22:58:20 | {"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": 0.3614930510520935, "perplexity": 7332.885014486553}, "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/1566027321786.95/warc/CC-MAIN-20190824214845-20190825000845-00260.warc.gz"} |
https://gamedev.stackexchange.com/questions/133565/directx-12-and-feature-levels | # DirectX 12 and Feature levels
As far as I know the DirectX12 SDK that comes with the Windows 10 SDK can only be used on a Windows 10 machine. Although I'm not entirely sure about the runtime and the use of future levels (which came with DX11). Considering the radical API changes in DX12, is it possible to initiate a level 11_0 device that will operate on the DX11 runtime on Windows 7 for instance? Or am I getting the feature levels idea wrong?
You are confusing the "Runtime version" with the Direct3D Hardware Feature level. They are not the same thing.
The DirectX 12 API is only supported by the Windows 10 operating system. There is no update for older versions of Windows that would install the DirectX 12 API.
If you need to support Windows 7, either use Direct3D 11 only or provide an alternative codepath that uses Direct3D 11.
The DirectX 12 API supports Feature Level 11.0, 11.1, 12.0, and 12.1 hardware. This also requires WDDM 2.0 drivers. Technically it would be possible for a video card manufacturer to make a driver for DirectX 12 that supported older Direct3D hardware feature levels, but there isn't one or likely to be one.
If you need to support a broad range of video hardware, you should stick with Direct3D 11 which supports 9.1, 9.2, 9.3, 10.0, 10.1, 11.0, or later. Windows 8 or later is required to support Direct3D hardware feature level 11.1, and Windows 10 is required to support Direct3D hardware feature level 12.0 or 12.1.
Any machine that can run DirectX 12 can run your program. | 2019-11-14 22:40:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.23426547646522522, "perplexity": 2092.1769532424482}, "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-2019-47/segments/1573496668539.45/warc/CC-MAIN-20191114205415-20191114233415-00188.warc.gz"} |
http://mathhelpforum.com/differential-geometry/111861-homeomorphism.html | # Math Help - Homeomorphism
1. ## Homeomorphism
Show that (a,b) is homeomorphic to R..
Thank you in advance
2. Originally Posted by math.dj
Show that (a,b) is homeomorphic to R..
Thank you in advance
You've left out a lot! Are we to assume that (a, b) is an interval in R with the "usual topology"? If so, you basically need to find a one-to-one function from (a,b) onto R. You should be able to find a rational function that maps a to $-\infty$ and b to $\infty$. | 2014-04-18 22:59:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6146227121353149, "perplexity": 764.5891418843324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00097-ip-10-147-4-33.ec2.internal.warc.gz"} |
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