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https://www.computer.org/csdl/trans/td/2008/08/ttd2008081099-abs.html | Issue No. 08 - August (2008 vol. 19)
ISSN: 1045-9219
pp: 1099-1110
ABSTRACT
Peer-to-peer (P2P) networks often demand scalability, low communication latency among nodes, and low system-wide overhead. For scalability, a node maintains partial states of a P2P network and connects to a few nodes. For fast communication, a P2P network intends to reduce the communication latency between any two nodes as much as possible. With regard to a low system-wide overhead, a P2P network minimizes its traffic in maintaining its performance efficiency and functional correctness. In this paper, we present a novel tree-based P2P network with low communication delay and low system-wide overhead. The merits of our tree-based network include: $(i)$ a tree-shaped P2P network which guarantees that the degree of a node is constant in probability regardless of the system size. The network diameter in our tree-based network increases logarithmically with an increase of the system size. Specially, given a physical network with a power-law latency expansion property, we show that the diameter of our tree network is constant. $(ii)$ Our proposal has the provable performance guarantees. We evaluate our proposal by rigorous performance analysis, and validate by extensive simulations.
INDEX TERMS
Distributed networks, Distributed Systems, Multicast
CITATION
H. Hsiao and C. He, "A Tree-Based Peer-to-Peer Network with Quality Guarantees," in IEEE Transactions on Parallel & Distributed Systems, vol. 19, no. , pp. 1099-1110, 2007.
doi:10.1109/TPDS.2007.70798 | 2018-05-28 10:18:54 | {"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": 0.7336714267730713, "perplexity": 1543.3951099112298}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1526794872766.96/warc/CC-MAIN-20180528091637-20180528111637-00313.warc.gz"} |
https://www.transtutors.com/questions/set-up-a-definite-integral-that-represents-the-length-of-the-curve-y-x-cos-x--5375990.htm | # Set up a definite integral that represents the length of the curve y = x + cos x...
Set up a definite integral that represents the length of the curve y = x + cos x for 0 5 x 5 it. Then use your calculator to find the length rounded off to four decimal places. Note: x is given in radians.
Attachments:
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https://eurekamathanswers.com/use-of-integers/ | An integer is a number that includes 0, positive numbers, and negative numbers. It can never be a fraction, decimal, or percent. Integers are mainly used in our day-to-day lives in mathematical terms. Get to know the definition, operations, and use of integers in the below-mentioned sections. Also, get the example questions with solutions for the convenience of grade 6 math students.
Also, Check: Use of Integers as Directed Numbers
## What is an Integer?
Integers are a set of counting numbers (positive and negative) along with zero. Some of the examples of integers are -4, -3, -2, -1, 0, 1, 2, 3. The integers are represented by Z. The types of integers are positive integers, negative integers, and zero.
### Integer Rules
The rules depend on the operations performed on integers given below:
• If the sign of both integers is the same, then the sum will have the same sign.
• If the sign of one integer is positive, the sign of another integer is negative, then the sign of the result is the sign of the larger number.
• Subtraction Rule:
• Convert the operation to addition by changing the sign of the subtrahend.
• Multiplication Rule:
• Multiply the sign of integers to get the result sign.
• Division Rule:
• Divide the signs of two operands and get the resultant sign.
### Real Life Examples of Integers
The examples on using integers are along the lines:
• If profit is represented by positive integers, losses are by negative integers.
• The rise in the price of a product is represented by positive integers and fill in price by negative integers.
• If heights above the sea level are represented by positive integers, then depths below sea level by negative integers, and so on.
### Integers as Directed Numbers
If a number represents direction, then the number is called a directed number. The below-given examples explain it in detail.
Example:
If +4 represents 4 m towards East, then -5 represents 5 m towards its opposite direction i.e towards west.
If a positive integer shows a particular direction, then the negative integer shows the opposite direction.
### Example Questions on Use of Integers
Question 1:
Write an integer to describe a situation
(i) Losing Rs 100
(ii) Owing Rs 1500
(iii) Depositing $500 in a bank Solution: (i) An integer representing a loss of Rs 100 is -100. (ii) An integer representing an owing of Rs 1500 is -1500 (iii) An integer representing depositing$500 in a bank is +500
Question 2:
Write an appropriate integer for each of the following:
(i) earned Rs 800 interest
(ii) a decrease of 5 members
(iii) an increase of 3 inches
Solution:
(i) Earned Rs 800 interest is represented by +800
(ii) Decrease of 5 members is represented by -5
(iii) An increase of 3 inches is represented by +3
### Frequently Asked Question’s on Using Integers
1. What are the applications of integers?
Integers are used to signify two contradicting situations. The positive and negative integers have different applications. Integers can compare and measure changes in temperature, credits, debits calculation by the bank.
2. What are the integer rules?
The integer rules are the sum of two integers is an integer, a difference of two integers is an integer. Multiplication of two or more integers is an integer. The division of integers may or may not be an integer.
3. What are the integer properties?
The main properties of integers are closure property, commutative property, associative property, identity property, and distributive property.
4. What are the 5 integer operations?
The operations with integers are addition, subtraction, multiplication, and division. | 2022-01-22 09:07:35 | {"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": 0.48777544498443604, "perplexity": 961.7523615772751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00002.warc.gz"} |
https://www.transtutors.com/questions/consider-the-following-multilayer-perceptron-network-the-transfer-function-of-the-hi-2011189.htm | Consider the following multilayer perceptron network. (The transfer function of the hidden layer...
Consider the following multilayer perceptron network. (The transfer function of the hidden layer is
The initial weights and biases are:
Perform one iteration of the standard steepest descent backpropagation (use matrix operations) with learning rate a = 0.5 for the following input/ target pair:
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Free Plagiarism Checker | 2021-04-21 06:04:06 | {"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": 0.8393312692642212, "perplexity": 3066.8290442374864}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039508673.81/warc/CC-MAIN-20210421035139-20210421065139-00105.warc.gz"} |
https://www.effortlessmath.com/math-puzzles/algebra-puzzle-challenge-50/ | # Algebra Puzzle – Challenge 50
This is another math puzzle and brain teaser that is interactive, challenging, and entertaining for those who love Math challenges!
## Challenge:
If 11 workers can build 11 cars in 11 days, then how many days would it take 7 workers to build 7 cars?
A- 7
B- 9
C- 11
D- 14
E- 18
### The Absolute Best Book to challenge your Smart Student!
If, 11 workers can build one car per day, then, one worker can make a car in 11 days. (Each worker can build $$\frac{1}{11}$$ of a car per day. So, it takes 11 days for a worker to make a car) | 2022-01-20 08:06:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1920827031135559, "perplexity": 1741.780503342366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00023.warc.gz"} |
https://matholympiad.org.bd/forum/viewtopic.php?f=13&t=3730&p=17063&hilit=weird+angle | ## BdMO National 2016 Secondary 3: Weird angle condition
Thanic Nur Samin
Posts: 176
Joined: Sun Dec 01, 2013 11:02 am
### BdMO National 2016 Secondary 3: Weird angle condition
In $\triangle ABC$, $AB=AC$. $P$ is a point inside the triangle such that $\angle BCP=30^{\circ}$ and $\angle APB=150^{\circ}$ and $\angle CAP=39^{\circ}$. Find $\angle BAP$
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Thanic Nur Samin
Posts: 176
Joined: Sun Dec 01, 2013 11:02 am
### Re: BdMO National 2016 Secondary 3: Weird angle condition
My solution is quite bash-y, so I am omitting the details. You can work them out by yourselves.
Let $\angle BAP=2x$ and $\angle CAP=2y$. Now, use the isosceles condition and other informations and use trig ceva to arrive at the conclusion,
$\sin 2x \sin (60^{\circ}-x-y) \sin (60^{\circ}+x-y)=\sin 2y \sin 30^{\circ} \sin(30^{\circ}-2x)$
From there, with enough manipulation with product to sum formulas, we can show that,
$2x=\dfrac{2y}{3}$
Since $2y=39^{\circ}$, we can conclude that $\angle BAP=13^{\circ}$
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
Thanic Nur Samin
Posts: 176
Joined: Sun Dec 01, 2013 11:02 am
### Re: BdMO National 2016 Secondary 3: Weird angle condition
On second thought, I am showing my calculation. Not that it is too long.
Hammer with tact.
Because destroying everything mindlessly isn't cool enough.
joydip
Posts: 48
Joined: Tue May 17, 2016 11:52 am
### Re: BdMO National 2016 Secondary 3: Weird angle condition
A synthetic solution :
The first principle is that you must not fool yourself and you are the easiest person to fool. | 2021-04-15 16:36:12 | {"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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7562976479530334, "perplexity": 7402.702806485073}, "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-2021-17/segments/1618038087714.38/warc/CC-MAIN-20210415160727-20210415190727-00288.warc.gz"} |
http://www.logic.univie.ac.at/2014/Talk_10-09_a.html | # 2014 seminar talk: Maximal pseudocompactness and maximal countable compactness in the class of Tychonoff spaces
Talk held by Vladimir V. Tkachuk (Universidad Autónoma Metropolitana de México, Mexico City, Mexico) at the KGRC seminar on 2014-10-09.
### Abstract
This is a presentation of results obtained in 2013-2014 jointly with O.T. Alas and R.G. Wilson. Given a property $\mathcal P$, say that a space $X$ is maximal $\mathcal P$ in the class of Tychonoff spaces if $X$ has $\mathcal P$ but any stronger Tychonoff topology on $X$ does not have $\mathcal P$. It turns out that maximal pseudocompactness and maximal countable compactness in the class of Tychonoff spaces have more interesting properties than maximal pseudocompactness and maximal countable compactness in the class of all spaces so we will call the respective spaces maximal pseudocompact and maximal countably compact. Our presentation will include the following results (all spaces are assumed to be Tychonoff):
1) Any dyadic maximal pseudocompact space is metrizable.
2) Any Fréchet-Urysohn compact space is a retract of a Fréchet-Urysohn maximal pseudocompact space; since there are Fréchet-Urysohn compact spaces which are not maximal pseudocompact, maximal pseudocompactness is not preserved by continuous images even in compact spaces.
3) If $\kappa$ is strictly smaller than the first weakly inaccessible cardinal, then the Tychonoff cube $I^\kappa$ is maximal countably compact.
4) If $\lambda$ is the first measurable cardinal, then the Tychonoff cube $I^\lambda$ does not even embed in a maximal countably compact space.
5) If a space $X$ is maximal countably compact, then every $\omega$-continuous real-valued function on $X$ is continuous.
6) If $X$ is a countably compact space with the Mazur property, i.e., every sequentially continuous real-valued function on $X$ is continuous, then $X$ is maximal countably compact.
7) If $X$ is an $\omega$-monolithic compact space, then $C_p(X)$ has the Mazur property if and only if $C_p(X)$ is Fréchet-Urysohn. | 2021-12-05 20:33:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.7821134328842163, "perplexity": 566.0800088675012}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1637964363216.90/warc/CC-MAIN-20211205191620-20211205221620-00169.warc.gz"} |
http://www.solutioninn.com/an-experiment-consists-of-rolling-a-pair-of-six-sided | # Question
An experiment consists of rolling a pair of (six- sided) dice and observing the sum. This experiment is repeated until the sum of 7 is observed at which point the experiment stops. Let be the random variable which represents the number of times the experiment is repeated. That is, if the first occurrence of {sum= 7} happens on the 5th roll of the dice, then N =5.
(a) Find the probability mass function for the random variable N. That is, find PN (k) = Pr (N= k) for all k.
(b) What is the probability that the experiment proceeds for at least 4 rolls? That is, find Pr (N ≥ 4).
Sales0
Views13 | 2016-10-26 06:40:31 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.828967809677124, "perplexity": 349.1102873342359}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720737.84/warc/CC-MAIN-20161020183840-00337-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://soriavazquez.github.io/publication/hss-17/ | # Low cost constant round MPC combining BMR and oblivious transfer
### Abstract
In this work, we present two new actively secure, constant round multi-party computation (MPC)protocols with security against all-but-one corruptions. Our protocols both start with an actively secure MPC protocol, which may have linear round complexity in the depth of the circuit, and compile it into a constant round protocol based on garbled circuits, with very low overhead.
1. Our first protocol takes a generic approach using any secret-sharing-based MPC protocol for binary circuits, and a correlated oblivious transfer functionality.
2. Our second protocol builds on secret-sharing-based MPC with information-theoretic MACs. This approach is less flexible, being based on a specific form of MPC, but requires no additional oblivious transfers to compute the garbled circuit.
In both approaches, the underlying secret-sharing-based protocol is only used for one actively secure $F_2$ multiplication per AND gate. An interesting consequence of this is that, with current techniques,constant round MPC for binary circuits is not much more expensive than practical, non-constant round protocols.
We demonstrate the practicality of our second protocol with an implementation, and perform ex-periments with up to 9 parties securely computing the AES and SHA-256 circuits. Our running times improve upon the best possible performance with previous protocols in this setting by 60 times.
This paper was accepted to the Journal of Cryptology.
Type
Publication
ASIACRYPT 2017 | 2021-02-27 07:14:37 | {"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": 0.30279138684272766, "perplexity": 2609.663671227325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1614178358203.43/warc/CC-MAIN-20210227054852-20210227084852-00607.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/suppose-planet-reported-orbiting-sun-like-stariota-horologii-period-345days-find-radius-pl-q473794 | Suppose that a planet was reported to be orbiting the sun-like starIota Horologii with a period of 345days. Find the radius of the planet's orbit, assuming that IotaHorologii has twice the mass as theSun. (This planet is presumably similar to Jupiter, but it may havelarge, rocky moons that enjoy a pleasant climate.) (Use 2.00 1030 kg for themass of the Sun.)
I just can't get it right. I change the days to seconds andmultiplied the suns mass by two for the mass of iota horologii.Then i used the equation I thought was right? Can someonehelp!?
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Q:
Suppose that a planet was reported to be orbiting the sun-like star Iota Horologii with a period of 300.0 days. Find the radius of the planet's orbit, assuming that Iota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, but it may have large, rocky moons that enjoy a pleasant climate. Use 2.00 ✕ 1030 kg for the mass of the Sun.)
A: See answer | 2016-07-27 20:44:19 | {"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": 0.857894241809845, "perplexity": 2561.187281406086}, "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-2016-30/segments/1469257827077.13/warc/CC-MAIN-20160723071027-00123-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://quantiki.org/journal-article/tunneling-transform-arxiv14112586v2-physicsgen-ph-updated | # The Tunneling Transform. (arXiv:1411.2586v2 [physics.gen-ph] UPDATED)
We supplement the Lorentz transform $L(v)$ with a new "Tunneling" transform
$T(v)$. Application of this new transform to elementary quantum mechanics
offers a novel, intuitive insight into the nature of quantum tunneling; in
particular, the so called "Klein Paradox" is discussed. | 2019-05-22 22:50:09 | {"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": 0.7238902449607849, "perplexity": 4295.650084933255}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1558232256980.46/warc/CC-MAIN-20190522223411-20190523005411-00169.warc.gz"} |
http://math.stackexchange.com/questions/228112/how-to-show-that-closed-subset-of-mathbbr-is-not-compact-if-restricted-to | # How to show that closed subset of $\mathbb{R}$ is not compact if restricted to $\mathbb{Q}$
Basicly I need to show that $\mathbb{R}\cap[0,1]\cap\mathbb{Q}$ is not compact. I was looking at some posts on this topic and all, that I found, used the finite subcover definition of compact set. I wonder if it could be done this way:
A compact set is closed and bounded. So showing that the set is not closed would be enough to see that it's not compact. To show that this set is not closed I could choose any irational number in the interval $[0,1]$ and construct a sequence of rationals that converge to it. So it would be a limit point of the set $\mathbb{R}\cap[0,1]\cap\mathbb{Q}$ that is not contained in it.
-
your approach of showing that the set is not closed is right – La Belle Noiseuse Nov 3 '12 at 12:31
thankyou @Flute – Mykolas Nov 3 '12 at 12:33
Your title asks to show a closed set is not compact, but then the set you are trying to prove is not compact is not closed. – Thomas Andrews Nov 3 '12 at 12:49
@Thomas Andrews thankyou. Ya that was kind of strange, :) – Mykolas Nov 3 '12 at 13:52
To show that $\mathbb{Q} \cap [0,1]$ is not closed, it is sufficient to construct a sequence of rational numbers converging to an irrational one. See here for example.
$F=\mathbb{Q} \cap [0,1]$ is dense in $[0,1]$; so if $F$ is compact, it is closed whence $\mathbb{Q} \cap [0,1]= [0,1]$. However, $[0,1]$ contains irrational numbers. | 2016-07-02 09:52:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8464019298553467, "perplexity": 130.97705550101824}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783396222.11/warc/CC-MAIN-20160624154956-00121-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://www.wptricks.com/question/ajax-wordpress-json-return-unknown-characters-fo-non-english-characters/ | ## ajax – WordPress JSON return unknown characters fo non English characters
Question
for a project i create an endpoint something like wp-json/HSE/v1/reports which return json file
everything is okey , also Engligh words , but for non English words i have real problem that its bring back something like u0645u0627u0647u0627u0646 u0633u06ccu0631u062cu0627u0646
its confusing me at all .
i also check the wp-json/wp/v2/posts and watch the same problem .English words are fine but non English words are not readable .
what should i do to fix this ?
anyone can help me please ?
0
2 months 2021-05-06T02:33:02-05:00 0 Answers 0 views 0 | 2021-06-23 14:46:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17664790153503418, "perplexity": 6012.408967222791}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1623488539480.67/warc/CC-MAIN-20210623134306-20210623164306-00248.warc.gz"} |
http://www.homermultitext.org/chsseminar/2018/scholion-markers/ | Indexing scholion markers
For the Upsilon 1.1 or Venetus B manuscripts, scholion markers within the Iliad text link passages in the Iliad to scholia. We need to record these after editing the scholia.
Create an index file
1. In your repository, please create a directory (folder) named scholion-markers
2. In the scholion-markers directory, create a file with a name ending in .cex
3. Add this heading line to the cex file:
reading#image#scholion#linked text
Each line represents one entry, with four pieces of information.
1. The reading of the marker. Use HMT XML markup as you would in your edition. For example, if the marker is a Greek numeral 1, you should record <num>α</num>
2. A region of interest on an image illustrating the marker and the Iliadic word it is placed over.
3. The CTS URN for the scholion this marker links to.
4. A CTS URN for the Iliad line that is linked, including a subreference (beginning @) identifying the word that is marked.
Example
Here is a valid entry:
<num>Θ</num>#urn:cite2:hmt:vbbifolio.v1:vb_128v_129r@0.5227,0.6307,0.03371,0.03202#urn:cts:greekLit:tlg5026.vb:129r_9#urn:cts:greekLit:tlg0012.tlg001.vb:10.1@παρὰ
Breaking out each part:
1. <num>Θ</num> is the reading (numeric 9)
2. urn:cite2:hmt:vbbifolio.v1:vb_128v_129r@0.5227,0.6307,0.03371,0.03202 is the image reference (illustrated below)
3. urn:cts:greekLit:tlg5026.vb:129r_9 is the URN for the scholion linked to this passage
4. urn:cts:greekLit:tlg0012.tlg001.vb:10.1@παρὰ is the Iliad passage
website © 2018, the Homer Multitext project | 2019-07-16 04:34:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2620265483856201, "perplexity": 12329.63351654443}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195524502.23/warc/CC-MAIN-20190716035206-20190716061206-00196.warc.gz"} |
https://stats.stackexchange.com/questions/246488/does-the-proportional-hazards-assumption-still-matter-if-the-covariate-is-time-d | # Does the proportional hazards assumption still matter if the covariate is time-dependent?
If I estimate a Cox Proportional Hazards model and my covariate of interest is dependent (continuous or categorical), does the proportional hazards assumption still matter? I recently went to a presentation where the speaker said that when using a time-dependent covariate, the importance of satisfying this assumption didn't matter but didn't really offer any justification for this, nor did he offer a reference.
You are still assuming that the effect of the value at each covariates/factor at each timepoint is the same, you simply allow the covariate to vary its value over time (but the change in the log-hazard rate associated with a particular value is still exactly the same across all timepoints). Thus, it does not change the assumption. Or was the presenter perhaps talking about also putting the covariate by time (or log(time)) interaction in the model as a time-dependent covariate? If you do that (for all covariates), then you have a model that might possibly approximate (a linear interaction cannot fully capture the possibly more complex things that may be going on in any one dataset, but may be okay for approximately capturing it) a model that does not make such an assumption.
I may be wrong but I believe that Björn's answer is not completely correct. The proportional hazards assumption means that the ratio of the hazard for a particular group of observations (determined by the values of the covariates) to the baseline hazard (when all covariates are zero) is constant over time. If there are time-varying covariates this is not true, and therefore the Cox model no longer assumes proportional hazards.
Here is a quote I have recently come across from David Collett's book, Modelling Survival Data in Medical Research (2nd ed., 2003, p. 253), that may be helpful:
It is important to note that in the model given in equation $h_i(t) = \exp \left\{ \sum_{j=1}^p \beta_j x_{ji}(t) \right\} h_o(t)$, the values of the variables $x_{ji}(t)$ depend on the time $t$, and so the relative hazard $h_i(t)/h_0(t)$ is also time-dependent. This means that the hazard of death at time $t$ is no longer proportional to the baseline hazard, and the model is no longer a proportional hazards model.
The accepted answer to this question on CV may also be relevant.
• This might, however, be more of a terminological rather than a practical distinction. Even if the presence of time-dependent covariate values means that the proportional hazards (PH) assumption does not hold, approaches based on partial likelihood for analyzing Cox PH models still can be used reliably with time-dependent covariates, as references linked from the CV question you cite make clear. The underlying assumption with time-dependent covariate values is as Björn stated: "the change in the log-hazard rate associated with a particular value is still exactly the same across all timepoints." – EdM Jul 9 '18 at 15:20
• Thank you for your comment. I think you raise a good point. Perhaps one practical aspect where this question could be important is in whether or not one would need to test the assumption in an applied setting. In a model with only fixed-time covariates I believe it is advisable to test the proportional hazards assumption, for instance by checking that the Schoenfeld residuals for the different variables are approximately constant over time. I think, however, that this would not make sense with time-varying covariates, though I may be wrong. – George Costanza Jul 9 '18 at 19:14
• You can test the assumption that "the change in the log-hazard rate associated with a particular value [of a covariate] is still exactly the same across all timepoints," which for Cox models with time-dependent covariates (assuming that the current value of the covariate determines the instantaneous hazard versus baseline) is the analog of the strict PH assumption. For example, this document (linked from the CV page you cite) shows how to do so by testing the significance of adding a type of covariate*time interaction term to the model. – EdM Jul 9 '18 at 22:08 | 2021-02-25 17:12:24 | {"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": 0.7743350863456726, "perplexity": 527.5740441844674}, "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-2021-10/segments/1614178351374.10/warc/CC-MAIN-20210225153633-20210225183633-00632.warc.gz"} |
https://cs.stackexchange.com/questions/83784/geometric-intuition-behind-vc-dimension | # Geometric intuition behind VC-dimension
Recently, I learnt about VC-dimension and how its boundedness assures PAC learnability on uncountable range spaces (let's assume that hypothesis class is the same as the family of concepts we want to learn).
My question is simple: What is/are the geometric intuition(s) behind the concept of VC dimension?
The VC dimension is a complexity measure for a family of boolean functions over some domain $\mathcal{X}$. Families who allow "richer" behavior have a higher VC dimension. Since $\mathcal{X}$ can be arbitrary, there isn't a general geometric interpretation.
However, if you think of $\mathcal{X}$ as $\mathbb{R}^d$, then you can think of binary functions as manifolds, whose boundary is what's separating positive and negative labels. Families with more "complex" boundaries have a high VC dimension, whereas simple manifolds do not, e.g. the dimension of linear separators is $O(d)$, while convex polygons (with unbounded number of edges) have infinite VC dimension. The more complex you allow the boundary to be, the more likely it is that you can find a large set for which you can agree with any labeling, by avoiding the negative labels in a "snake like" shape.
• Suppose the range space is $(\mathbb{R}^d, \mathcal{M})$, where $\mathcal{M}$ is a family of manifolds. To each $M \in \mathcal{M}$ you are associating the canonical indicator function $\mathbb{1}_M$, right? Nov 12 '17 at 10:01 | 2021-11-29 17:04:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8254061341285706, "perplexity": 447.83611037023746}, "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/1637964358786.67/warc/CC-MAIN-20211129164711-20211129194711-00063.warc.gz"} |
https://study.com/academy/answer/a-circular-coil-has-500-turns-and-a-radius-14-cm-the-coil-is-moved-in-0-35-seconds-from-an-area-where-there-is-no-magnetic-field-into-an-area-with-a-magnetic-field-of-strength-6-7-times-10-2-t.html | # A circular coil has 500 turns and a radius 14 cm. The coil is moved in 0.35 seconds from an area...
## Question:
A circular coil has 500 turns and a radius 14 cm. The coil is moved in 0.35 seconds from an area where there is no magnetic field into an area with a magnetic field of strength {eq}6.7 \times 10^{-2}\ T {/eq}. The coil remains perpendicular to the magnetic field at all times.
a) Find the magnitude of the induced EMF in the coil.
b) If the coil has a resistance of 2.7 Ω, find the current in the coil.
c) After moving into the field, the coil now remains stationary in the field for 3 seconds. Find the current induced in the coil during this interval.
Faraday's Law states that the magnitude of the emf induced in a loop is directly proportional to the rate of change of the magnetic flux linked with the loop, mathematically
{eq}\begin{align} \epsilon = \frac{N\Delta \Phi}{\Delta t} \end{align} {/eq}
Where {eq}\Delta \Phi {/eq} is the change in the magnetic flux, N is the number of turns in the loop, and {eq}\Delta t {/eq} is the time taken.
Data Given
• Number of turns in the coil {eq}N = 500 {/eq}
• Radius of the coil {eq}r = 14 \ \rm cm = 0.14 \ \rm m {/eq}
• The final magnetic field linked with the coil {eq}B_f = 6.7 \times 10^{-2} \ \rm T {/eq}
• Time elapsed {eq}\Delta t = 0.35 \ \rm s {/eq}
• Resistance of the coil {eq}R = 2.7 \ \Omega {/eq}
Part A) Let us use the Faraday's law to calculate the emf induced in the loop
{eq}\begin{align} \epsilon = \frac{N\Delta \Phi}{\Delta t} \end{align} {/eq}
{eq}\begin{align} \epsilon = \frac{NA \Delta B)}{\Delta t} \end{align} {/eq}
{eq}\begin{align} \epsilon = \frac{500 \times \pi \times (0.14\ \rm m)^2 \times (6.7 \times 10^{-2} \ \rm T-0 \ \rm T)}{0.35 \ \rm s} \end{align} {/eq}
{eq}\begin{align} \color{blue}{\boxed{ \ \epsilon = 5.89 \ \rm V \ }} \end{align} {/eq}
Part B) Currnt in the coil, using Ohm's law
{eq}\begin{align} I = \frac{V}{R} \\ I = \frac{ 5.89 \ \rm V}{2.7 \ \rm \Omega} \\ \color{blue}{\boxed{ \ I = 2.2 \ \rm A \ }} \end{align} {/eq}
Part C) As the coil is stationary in the field for the 3 s it means the flux linked with coil remains constant and induced emf and hence induced current during this interval will be zero.
{eq}\begin{align} \color{blue}{\boxed{ \ I' =0 \ \rm A \ }} \end{align} {/eq} | 2020-04-10 13:51:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 7, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9997798800468445, "perplexity": 1550.3443033067285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1585371896913.98/warc/CC-MAIN-20200410110538-20200410141038-00199.warc.gz"} |
https://www.transtutors.com/questions/the-following-account-appears-in-the-ledger-after-only-part-281493.htm | # The following account appears in the ledger after only part
The following account appears in the ledger after only part of the postings has been completed for January:
Work in Process
Balance, January 1 …. $15,500 Direct materials ……… 86,200 Direct labor ………….. 64,300 Factory overhead …….. 93,700 Jobs finished during January are summarized as follows: Job 320 …$57,600
Job 326 ….. 75,400
Job 327 … \$26,100
Job 350 ….. 94,800
a. Journalize the entry to record the jobs completed.
b. Determine the cost of the unfinished jobs at January 31. | 2020-01-25 12:24:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.226205512881279, "perplexity": 8282.999327008545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1579251672440.80/warc/CC-MAIN-20200125101544-20200125130544-00231.warc.gz"} |
https://physics.stackexchange.com/questions/384111/scattering-absorption-emission-and-virtual-photons | # Scattering, absorption, emission and virtual photons
From reading many questions on this site I have the following conclusions:
1. Interaction of a photon and a free electron is an instantaneous process of scattering (transfer of momentum) between said particles.
2. Interaction of a photon and an electron bound in atom is a very fast but not instantaneous (electron cloud has to restructure itself via resonant oscillation) process of absorption in which the photon is annihilated and atom ends up in excited state. Later another photon can be emitted from the atom taking away the excitation. This is not scattering as scattering happens for free electrons and absorption for bound.
3. Virtual photons (and other virtual particles) don't exist and are only a mathematical tool. Any view that they are "real virtual photons" is wrong.
Now to the questions:
1. I was told that spontaneous emissions is a stimulated emission, stimulated by a vacuum fluctuation photon coming from $\frac{\hbar\omega}{2}$ in the photon field hamiltonian. How do I connect this with the fact that virtual photons don't exist?
2. In a process of second harmonic generation, are photons absorbed or scattered, as there is no real absorption? Is "virtual energy level" also only a mathematical tool? If so, why SHG is stronger if there is a real energy level nearby? How would SHG look on a Feynman diagram? How would it look on a Bloch sphere? | 2021-02-27 19:32:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5664388537406921, "perplexity": 726.1975933139533}, "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-2021-10/segments/1614178359082.48/warc/CC-MAIN-20210227174711-20210227204711-00497.warc.gz"} |
https://www.transtutors.com/questions/only-one-firm-produces-and-sells-soccer-balls-in-the-country-of-wiknam-and-as-the-st-3388736.htm | # Only one firm produces and sells soccer balls in the country of Wiknam, and as the story begins,... 1 answer below »
Only one firm produces and sells soccer balls in the country of Wiknam, and as the story begins, international trade in soccer balls is prohibited. The following equations describe the monopolist’s demand, marginal revenue, total cost, and marginal cost: Demand: P = 10 – Q Marginal Revenue: MR = 10 – 2Q Total Cost: TC = 3 + Q + 0.5Q2 Marginal Cost: MC = 1 + Q Where Q is quantity and P is the price measured in Wiknamian dollars. a. How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist’s profit? b. One day, the King of Wiknam decrees that henceforth there will be free trade—either imports or exports— of soccer balls at the world price of $6. The firm is now a price taker in a competitive market. What happens to domestic production of soccer balls? To domestic consumption? Does Wiknam export or import soccer balls? c. In our analysis of international trade in Chapter 9, a country becomes an exporter when the price without trade is below the world price and an importer when the price without trade is above the world price. Does that conclusion hold in your answers to parts (a) and (b)? Explain. d. Suppose that the world price was not$6 but, instead, happened to be exactly the same as the domestic price without trade as determined in part (a). Would allowing trade have changed anything in the Wiknamian economy? Explain. How does the result here compare with the analysis in Chapter 9?
Kandregula S
Date MR=MC for monopoly lo-2Q = 1tQ 9=3Q Q=3] P= 10-Q z 10-3 = 7 (P=7& = 7(3) - 3- Q -0.502 21-3-3-0.5 (9) 21-3-3 -4.5 =...
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Looking for Something Else? Ask a Similar Question | 2021-05-14 07:29:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24462628364562988, "perplexity": 4179.141779401999}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1620243991648.40/warc/CC-MAIN-20210514060536-20210514090536-00569.warc.gz"} |
https://dls.westcollegescotland.ac.uk/mod/glossary/showentry.php?eid=22 | Question:
#### Can I use the College library and PCs?
(Last edited: Thursday, 29 April 2021, 12:43 PM) | 2022-06-24 22:08:05 | {"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": 0.8628464341163635, "perplexity": 12097.522480961019}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103033816.0/warc/CC-MAIN-20220624213908-20220625003908-00571.warc.gz"} |
https://learn.saylor.org/course/view.php?id=67§ionid=636 | • ### Unit 5: Set Theory
Computer scientists often find themselves working with sets of homogeneous or heterogeneous values. Scientists have devised set theory in order to respond to these situations. In this unit, we will learn the basics of set theory, taking a look at definitions and notations and using the proof methods and counterexample means we introduced earlier to establish set properties.a
Set theory is a fundamental tool of mathematics and often used as the starting point for its study and to define basic concepts, such as functions, numbers, and limits.
Completing this unit should take you approximately 15 hours. | 2019-09-19 17:55:45 | {"extraction_info": {"found_math": true, "script_math_tex": 36, "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": 0.9139756560325623, "perplexity": 682.0173338337926}, "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/1568514573561.45/warc/CC-MAIN-20190919163337-20190919185337-00466.warc.gz"} |
https://proofwiki.org/wiki/Equal_Angles_in_Equal_Circles | # Equal Angles in Equal Circles
## Theorem
In equal circles, equal angles stand on equal arcs, whether at the center or at the circumference of those circles.
In the words of Euclid:
In equal circles equal angles stand on equal circumferences, whether at the center or at the circumferences.
## Proof
Let $ABC$ and $DEF$ be equal circles.
Let $\angle BGC = \angle EHF$ and $\angle BAC = \angle EDF$.
Let $BC$ and $EF$ be joined.
Since the circles $ABC$ and $DEF$ are equal, their radii are equal.
So $BG = EH$ and $CG = FH$.
We also have by hypothesis that $\angle BGC = \angle EHF$.
So from Triangle Side-Angle-Side Equality it follows that $BC = EF$.
Since $\angle BAC = \angle EDF$ we have from Book $\text{III}$ Definition $11$: Similar Segments that segment $BAC$ is similar to segment $EDF$.
Moreover, these segments have equal bases.
So from Similar Segments on Equal Bases are Equal, segment $BAC$ is equal to segment $EDF$.
But as $ABC$ and $DEF$ are equal circles, it follows that arc $BKC$ equals arc $ELF$.
$\blacksquare$
## Historical Note
This theorem is Proposition $26$ of Book $\text{III}$ of Euclid's The Elements.
It is the converse of Proposition $27$: Angles on Equal Arcs are Equal. | 2021-01-19 03:07:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8096537590026855, "perplexity": 767.512434061121}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610703517559.41/warc/CC-MAIN-20210119011203-20210119041203-00104.warc.gz"} |
https://eips.ethereum.org/ | # EIPs
Ethereum Improvement Proposals (EIPs) describe standards for the Ethereum platform, including core protocol specifications, client APIs, and contract standards. Network upgrades are discussed separately in the Ethereum Project Management repository.
## Contributing
First review EIP-1. Then clone the repository and add your EIP to it. There is a template EIP here. Then submit a Pull Request to Ethereum's EIPs repository.
## EIP status terms
• Idea - An idea that is pre-draft. This is not tracked within the EIP Repository.
• Draft - The first formally tracked stage of an EIP in development. An EIP is merged by an EIP Editor into the EIP repository when properly formatted.
• Review - An EIP Author marks an EIP as ready for and requesting Peer Review.
• Last Call - This is the final review window for an EIP before moving to FINAL. An EIP editor will assign Last Call status and set a review end date (last-call-deadline), typically 14 days later. If this period results in necessary normative changes it will revert the EIP to Review.
• Final - This EIP represents the final standard. A Final EIP exists in a state of finality and should only be updated to correct errata and add non-normative clarifications.
• Stagnant - Any EIP in Draft or Review if inactive for a period of 6 months or greater is moved to Stagnant. An EIP may be resurrected from this state by Authors or EIP Editors through moving it back to Draft.
• Withdrawn - The EIP Author(s) have withdrawn the proposed EIP. This state has finality and can no longer be resurrected using this EIP number. If the idea is pursued at later date it is considered a new proposal.
• Living - A special status for EIPs that are designed to be continually updated and not reach a state of finality. This includes most notably EIP-1.
## EIP Types
EIPs are separated into a number of types, and each has its own list of EIPs.
### Standard Track (454)
Describes any change that affects most or all Ethereum implementations, such as a change to the network protocol, a change in block or transaction validity rules, proposed application standards/conventions, or any change or addition that affects the interoperability of applications using Ethereum. Furthermore Standard EIPs can be broken down into the following categories.
#### Core (185)
Improvements requiring a consensus fork (e.g. EIP-5, EIP-101), as well as changes that are not necessarily consensus critical but may be relevant to “core dev” discussions (for example, the miner/node strategy changes 2, 3, and 4 of EIP-86).
#### Networking (13)
Includes improvements around devp2p (EIP-8) and Light Ethereum Subprotocol, as well as proposed improvements to network protocol specifications of whisper and swarm.
#### Interface (41)
Includes improvements around client API/RPC specifications and standards, and also certain language-level standards like method names (EIP-6) and contract ABIs. The label “interface” aligns with the interfaces repo and discussion should primarily occur in that repository before an EIP is submitted to the EIPs repository.
#### ERC (215)
Application-level standards and conventions, including contract standards such as token standards (ERC-20), name registries (ERC-137), URI schemes (ERC-681), library/package formats (EIP190), and wallet formats (EIP-85).
### Meta (18)
Describes a process surrounding Ethereum or proposes a change to (or an event in) a process. Process EIPs are like Standards Track EIPs but apply to areas other than the Ethereum protocol itself. They may propose an implementation, but not to Ethereum's codebase; they often require community consensus; unlike Informational EIPs, they are more than recommendations, and users are typically not free to ignore them. Examples include procedures, guidelines, changes to the decision-making process, and changes to the tools or environment used in Ethereum development. Any meta-EIP is also considered a Process EIP.
### Informational (6)
Describes a Ethereum design issue, or provides general guidelines or information to the Ethereum community, but does not propose a new feature. Informational EIPs do not necessarily represent Ethereum community consensus or a recommendation, so users and implementers are free to ignore Informational EIPs or follow their advice. | 2022-08-18 07:27:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17713262140750885, "perplexity": 7361.758274434757}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882573172.64/warc/CC-MAIN-20220818063910-20220818093910-00267.warc.gz"} |
http://koreascience.or.kr/article/JAKO199429464761872.page | # 가스분사반응기에서의 SO2 흡수 특성
• 최병선 (한국전력공사 기술연구원) ;
• 박승수 (한국전력공사 기술연구원) ;
• 김영환 (한국전력공사 기술연구원)
The optimum design conditions of gas sparger pipe and the effects of operating variables on $SO_2$ removal efficiency have been examined in Jet Bubbling Reactor. Geometry of gas sparser pipe of Jet Bubbling Reactor is a very important factor to obtain a effective gas-liquid contact. Test results revealed that Reynolds numbers at sparger and slot have to be kept greater than 12,000 identically at a given gas velocity. $SO_2$ removal efficiency was a function of ${\Delta}P$, pH, inlet $SO_2$ concentration and particle size of limestone and was more sensitive to the change of ${\Delta}P$ than to the changes of others. The ${\Delta}P$ of at least 230mmAq must be maintained to acheive the above 90% $SO_2$ removal at pH of 4.0 which is considered as adequate operating pH. Higher $SO_2$ removal efficiency was obtained even at lower pH ranges, which resulted from the complete oxidation of the absorbed $SO_2$ to sulfates by adding air and consequently from the reduction of $SO_2$ equillibrium partial pressure in the gas-liquid interface The 99.5% of the limestone utilization was attained in pH range from 3.0 to 5.0 with regardless to the particle size of limestone employed. | 2021-03-06 17:12:44 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5989185571670532, "perplexity": 3685.4891429204727}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1614178375274.88/warc/CC-MAIN-20210306162308-20210306192308-00424.warc.gz"} |
https://math.stackexchange.com/questions/319532/angle-preserving-transformation | # Angle preserving transformation
I've been working on a problem where I need to know the angle between the tangent vectors of two curves at their intersection point in a flat torus...
Then I thought: Consider two geodesics $\gamma(t)$ and $\beta(t)$ in a flat torus, such that: $\gamma(0)=p=(\varphi _1,\theta_1)$, $\gamma(1)=(\varphi _2,\theta_2)$, $\beta(0)=p$ and $\beta(1)=(\varphi _3,\theta_3)$; wouldn't the angle between their tangent vectors at $p$ the same as the angle between the two "straight lines" that connect those points in this rectangle? If so, I could just get the angle from the usual Euclidean dot product...Is this right?
On a related question: How can I know if in a given riemannian 2-manifold the angles are preserved in the sense I've stated before?
A smooth map $f:M\to N$ between two Riemannian manifolds $(M,g_M)$ and $(N,g_N)$ is conformal if the pullback metric $f_* g_N$ is of the form $e^u g_M$ where $u$ is some smooth function. This condition expresses the angle-preserving behavior because the scalar multiple $e^u$ cancels out when we calculate angles.
In your case, you are dealing with the quotient map $f:\mathbb R^2\mapsto \mathbb R^2/\mathbb Z^2$ which is a local isometry. Such a map is conformal with $u\equiv 0$. This justifies your computation of angles. | 2019-06-19 17:31:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9361504912376404, "perplexity": 66.42631082747472}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1560627999003.64/warc/CC-MAIN-20190619163847-20190619185847-00262.warc.gz"} |
https://www.doubtnut.com/question-answer/find-the-coordinates-of-the-point-which-divides-the-line-segment-joining-the-points-2-3-5and-1-4-6in-644361779 | # Find the coordinates of the point which divides the line segment joining the points ( 2, 3, 5)and (1, 4, 6)in the ratio (i) 2 : 3internally, (ii) 2 : 3externally.
Updated On: 17-04-2022
Get Answer to any question, just click a photo and upload the photo
and get the answer completely free, | 2022-05-18 20:40:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30074360966682434, "perplexity": 1193.9043119590842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652662522309.14/warc/CC-MAIN-20220518183254-20220518213254-00548.warc.gz"} |
https://webwork.libretexts.org/webwork2/html2xml?answersSubmitted=0&sourceFilePath=Library/270/setDerivatives12MVT/c3s2p1.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&showSummary=1&displayMode=MathJax&problemIdentifierPrefix=102&language=en&outputformat=libretexts | Consider the function Find the average slope of this function on the interval $( 0 , 2 )$.
By the Mean Value Theorem, we know there exists a $c$ in the open interval $( 0, 2 )$ such that $f'(c)$ is equal to this mean slope. Find the two values of $c$ in the interval which work, enter the smaller root first: $\le$ | 2022-08-14 01:13:12 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8870619535446167, "perplexity": 57.327270125208855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571989.67/warc/CC-MAIN-20220813232744-20220814022744-00294.warc.gz"} |
https://mathoverflow.net/questions/261708/numerical-analysis-of-parabolic-obstacle-problem | # Numerical analysis of parabolic obstacle problem
I want to solve a parabolic obstacle problem, written as a variational inequality: For almost all $t\in [0,T]$
\begin{align*} \langle u'(t), v - u(t)\rangle +a(u(t),v-u(t)) \geq \langle f(t),v-u(t)\rangle \quad \forall v \in K \end{align*}
with $K = \{v \in H^1_0(\Omega) ~\vert ~ v \geq \chi ~ \text{ f.a.a }~ x \in \Omega\}$ and $u(0) = u_0$. Now we will discretize this inequality in time using, for instance, the explicit Euler Scheme. After this we need to solve an elliptic problem in each timestep. This will be done by a primal-dual-active-set method following Bartels book "Numerical methods for Nonlinear Partial Differential Equations". Can someone give me a hint or literature, how to prove the convergence of this "method" to a solution of the obstacle problem?
Thanks in advance, FFoDWindow
## 1 Answer
There's an overview of available schemes in chapter III of
Roland Glowinski, MR 737005 Numerical methods for nonlinear variational problems, ISBN: 0-387-12434-9.
(of which there is also reprint from 2008). The schemes are presented and a few references for their behaviour are given. In particular, this book references chapter 6 of
Roland Glowinski, Jacques-Louis Lions, and Raymond Trémolières, MR 1333916 Numerical analysis of variational inequalities, ISBN: 0-444-86199-8.
which might take you further, even though at a first glance I didn't see the explicit Euler method covered.
• Thank you for your answer. Unfortunately he just 'lists' the algorithms, but doesn't provides proves for convergence... – FredTheBread Feb 8 '17 at 18:49
• It gives an overview but also provides references for proofs. I've added the one that seems most important to me to my answer. Now, I have to admit that I don't see the explicit Euler scheme covered there right away, although other schemes are covered. It sounded to me like you were interested in having a starting point were not very much constrained on the precise method that is used. Does this help you? – anonymous Feb 8 '17 at 18:58
• Yeah, I took a brief look into the book and it looks helpful. Thanks! – FredTheBread Feb 8 '17 at 19:04 | 2021-05-11 13:21:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9107178449630737, "perplexity": 228.81000678903504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989614.9/warc/CC-MAIN-20210511122905-20210511152905-00292.warc.gz"} |
https://www.ideals.illinois.edu/handle/2142/96923 | ## Files in this item
FilesDescriptionFormat
application/vnd.openxmlformats-officedocument.presentationml.presentation
833824.pptx (4MB)
PresentationMicrosoft PowerPoint 2007
application/pdf
2272.pdf (14kB)
AbstractPDF
## Description
Title: A MOLECULAR FOUNTAIN Author(s): Cheng, Cunfeng Contributor(s): Bethlem, Hendrick; Ubachs, Wim; van der Poel, Aernout P.P. Subject(s): Small molecules Abstract: The resolution of any spectroscopic experiment is limited by the coherent interaction time between the probe radiation and the particle that is being studied. The introduction of cooling techniques for atoms and ions has resulted in a dramatic increase of interaction times and accuracy, it is hoped that molecular cooling techniques will lead to a similar increase. Here we demonstrate the first molecular fountain, a development which permits hitherto unattainably long interrogation times with molecules. In our experiment, beams of ammonia molecules are decelerated, trapped and cooled using inhomogeneous electric fields and subsequently launched. Using a combination of quadrupole lenses and buncher elements, the beam is shaped such that it has a large position spread and a small velocity spread (corresponding to a transverse temperature of less than 10$mu$K and a longitudinal temperature of less than 1$mu$K) while the molecules are in free fall, but strongly focused at the detection region. The molecules are in free fall for up to 266 milliseconds, making it possible, in principle, to perform sub-Hz measurements in molecular systems and paving the way for stringent tests of fundamental physics theories. Issue Date: 6/19/2017 Publisher: International Symposium on Molecular Spectroscopy Citation Info: APS Genre: CONFERENCE PAPER/PRESENTATION Type: Text Language: English URI: http://hdl.handle.net/2142/96923 DOI: 10.15278/isms.2017.MH04 Date Available in IDEALS: 2017-07-272018-01-29
| 2018-02-18 07:12:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5697906017303467, "perplexity": 3970.3717925185765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891811794.67/warc/CC-MAIN-20180218062032-20180218082032-00127.warc.gz"} |
https://brilliant.org/problems/inspired-by-myself-3/ | # Mirrored Functions
Calculus Level 2
Find the shortest distance between the two curves $f(x)=\ln(x)$ and $g(x)=e^x$.
× | 2021-06-16 09:07:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "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": 0.23986899852752686, "perplexity": 2462.889377386647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487622234.42/warc/CC-MAIN-20210616063154-20210616093154-00085.warc.gz"} |
https://www.mypractice-page.com/content/c/s01/c_s01_ex07.php | ## Exercise 07: VTBI And Infusion Rate Calculator
Date completed: 02/09/2019
Hospitals use programmable pumps to deliver medications and fluids to intra-venous lines at a set number of milliliters per hour. Write a program to output information for the labels the hospital pharmacy places on bags of I.V. medications indicating the volume of medication to be infused and the rate at which the pump should be set. The program should prompt the user to enter the quantity of fluid in the bag and the number of minutes over which it should be infused. Output the VTBI (volume to be infused) in $ml$ and the infusion rate in $ml/hr$.
### Sample run:
Volume to be infused (ml) => 100
Minutes over which to infuse => 20
VTBI: 100 ml
Rate: 300 ml/hr
### The Created Code
The created source code can be found . It has been compressed in to a 7-Zip file.
### Some screen prints
Description Screen Print Out
The output as seen in the command prompt | 2020-09-29 14:24:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.19431348145008087, "perplexity": 4365.010619377651}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600401643509.96/warc/CC-MAIN-20200929123413-20200929153413-00694.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-10th-edition/appendix-graphing-utilities-3-using-a-graphing-utility-to-locate-intercepts-and-check-for-symmetry-3-exercises-page-a6/4 | ## College Algebra (10th Edition)
Using the ZERO function of a graphing utility we get: $ZERO(3x^2+5x+1)=-1.4343\approx-1.43$ | 2019-11-22 17:36:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9834896326065063, "perplexity": 2131.9264952512067}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1573496671411.14/warc/CC-MAIN-20191122171140-20191122200140-00037.warc.gz"} |
https://blender.stackexchange.com/questions/126493/how-to-shift-foward-actions-using-python/126494 | How to shift foward actions using python
I have two sequential actions, and I want to shift them both foward. I can list the actions with bpy.data.actons, but I don't know how to modify them.
While you can list the actions with bpy.data.actions, once they are in the NLA Editor you need to access them slightly differently.
Once in the NLA Editor they are classed as strips on nla_tracks which are stored in the animation_data for that object.
For example, in the case of the image you have shown you will use this to access an individual strip:
bpy.data.objects['sash_KIN_TYPE_S'].animation_data.nla_tracks['KIN_TYPE_SL'].strips['KIN_TYPE_SL_close']
From there you can access the frame_start and frame_end properties of the strip. Increasing both of these by the same amount will move the strip. For example:
strip.frame_start += 10
strip.frame_end += 10
To shift multiple strips you can loop over the strips collection in the same way you would loop over actions:
strips = bpy.data.objects['sash_KIN_TYPE_S'].animation_data.nla_tracks['KIN_TYPE_SL'].strips
for strip in strips:
strip.frame_start += 10
strip.frame_end += 10
I found all of this out by hovering my mouse over the properties in the NLA Editor and looking in the tooltip (because I enabled Python Tooltips in the User Preferences). | 2021-12-06 02:40:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17524874210357666, "perplexity": 1959.3343696755092}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363229.84/warc/CC-MAIN-20211206012231-20211206042231-00009.warc.gz"} |
https://infoscience.epfl.ch/record/82964 | Confidence Measures in Multiple pronunciations Modeling For Speaker Verification
This paper investigates the use of multiple pronunciations modeling for User-Customized Password Speaker Verification (UCP-SV). The main characteristic of the UCP-SV is that the system does not have any {\it a priori} knowledge about the password used by the speaker. Our aim is to exploit the information about how the speaker pronounces a password in the decision process. This information is extracted automatically by using a speaker-independent speech recognizer. In this paper, we investigate and compare several techniques. Some of them are based on the combination of confidence scores estimated by different models.In this context, we propose a new confidence measure that uses acoustic information extracted during the speaker enrollment and based on {\it log likelihood ratio} measure. These techniques show significant improvement ($15.7\%$ relative improvement in terms of equal error rate) compared to a UCP-SV baseline system where the speaker is modeled by only one model (corresponding to one utterance).
Year:
2003
Publisher:
IDIAP
Keywords:
Note:
in Proceedings of the 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-04), 2004
Laboratories: | 2019-11-19 21:48:40 | {"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": 0.552105188369751, "perplexity": 829.0981307132498}, "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-2019-47/segments/1573496670255.18/warc/CC-MAIN-20191119195450-20191119223450-00100.warc.gz"} |
http://www.mathgoespop.com/2012/11/mathalicious-post-most-expensive-collectibles-ever.html | ## Mathalicious Post: Most Expensive. Collectibles. Ever.
Hey y'all. My most recent post on the Mathalicious blog has been live for a while, but in case you missed it, I’d encourage you to go check it out! Consider it a Simpsons themed cautionary tale for collectors on a budget. Here’s a sample:
One of the more recent trends in the world of Simpsons memorabilia is the advent of the Mini-Figure collections, produced by Kidrobot. Each series (there have been two so far) consists of around 25 small Simpsons figures, each with his or her own accessories. The figures cost around $10 each ($9.95, to be precise), so an avid collector would need to spend something like \$250 to complete each of the two collections, right?
Well, not quite. When you buy one of these figures, you have no idea which one you’ll get, because the box containing the figure doesn’t indicate what’s inside. All you know are the probabilities for each figure, and even those are sometimes missing…
Given this information, here’s a natural question: how many of these boxes should you expect to buy if you want to complete the set, and how much will it cost you? | 2017-01-20 01:37:07 | {"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": 0.47449368238449097, "perplexity": 1543.367280300323}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280763.38/warc/CC-MAIN-20170116095120-00570-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://documen.tv/question/calculate-the-molecular-weight-of-a-dibasic-acid-0-56gm-of-which-is-required-250ml-of-n-20-sodiu-24159433-80/ | ## Calculate the molecular weight of a dibasic acid.0.56gm of which is required 250ml of N/20 sodium hydroxide solution for neutralization.
Question
Calculate the molecular weight of a dibasic acid.0.56gm of which is required 250ml of N/20 sodium hydroxide solution for neutralization.
in progress 0
6 months 2021-07-13T19:43:48+00:00 1 Answers 5 views 0
1. Answer: The molecular weight of the dibasic acid is 89.6 g/mol
Explanation:
Normality is defined as the amount of solute expressed in the number of gram equivalents present per liter of solution. The units of normality are eq/L. The formula used to calculate normality:
….(1)
We are given:
Normality of solution =
Given mass of solute = 0.56 g
Volume of solution = 250 mL
Putting values in equation 1, we get:
Equivalent weight of an acid is calculated by using the equation:
…..(2)
Equivalent weight of acid = 44.8 g/eq
Basicity of an acid = 2 eq/mol
Putting values in equation 2, we get:
Hence, the molecular weight of the dibasic acid is 89.6 g/mol | 2022-06-26 06:16:59 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8250992298126221, "perplexity": 4237.423520984006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103037089.4/warc/CC-MAIN-20220626040948-20220626070948-00229.warc.gz"} |
https://www.physicsforums.com/threads/if-this-is-gaussian-beam.370176/ | # If this is Gaussian beam?
1. Jan 16, 2010
### KFC
In the book "Fundamentals of Photonics", the form of the Gaussian beam is written as
$$I(\rho,z) = I_0 \left(\frac{W_0}{W(z)}\right)^2\exp\left[-\frac{2\rho^2}{W^2(z)}\right]$$
where $$\rho = \sqrt{x^2 + y^2}$$
However, in some books (I forgot which one), the author use the following form
$$I(R) = I_0 \exp\left[-\frac{R^2W_0^2}{W^2}\right]$$
where
$$R = \rho/W_0, \qquad \rho=\sqrt{x^2+y^2}$$
In the second expression, I don't know why there is no $$\left(W_0/W(z)\right)^2$$ in the amplitude and why he want to define R instead of using $$\rho$$ directly? And what about $$W_0$$ and $$W$$ in the second expression? Are they have some meaning as in the first one?
I forgot which book using such form, if you know any information, could you please tell me the title and author of the book? Thanks.
2. Jan 17, 2010
### mathman
Off hand (I'll admit I know nothing about the physics involved) it looks like the two expressions are equivalent, except for the 2 in the numerator of the first expression. W and W0 look like they are the same in both. The coeficient of both is I0. In one case the argument seems to be expressed, while the other may be implicit - again I don't know what any of this is supposed to be physically.
3. Jan 17, 2010
### KFC
Thanks. I am thinking one aspect on physics. Since the energy is conserved (the total energy of the input beam should be conserved after transported to some distance), so if the intensity is not inverse proportional to the waist, how to make the energy conserved? Please show me if I am wrong :)
4. Jan 18, 2010
### Bob S
I would first write the cross section of the beam traveling in the z direction in cartesian coordinates:
I(z) = I0 exp[-x2/2σx(z)2] exp[-y2/2σy(z)2]
where σx(z) and σy(z) are the rms widths of the Gaussian beam in the x and y directions at z.
This may be rewritten as
I(z) = I0 exp[-x2/2σx(z)2-y2/2σy(z)2]
and finally as
I(z) = I0 exp[-ρ2/2σ(z)2]
if σx(z) = σy(z), where ρ2 = x2 + y2.
Bob S | 2018-03-19 04:00:57 | {"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": 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": 0.8168206810951233, "perplexity": 597.9993543605506}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646213.26/warc/CC-MAIN-20180319023123-20180319043123-00778.warc.gz"} |
https://www.zbmath.org/?q=an%3A0962.76012 | ## The sub-harmonic bifurcation of Stokes waves.(English)Zbl 0962.76012
The behaviour of steady periodic water waves on water of infinite depth, that satisfy exactly the kinematic and dynamic boundary conditions on the free surface of water, with or without surface tension, are given by solutions of a nonlinear pseudo-differential operator equation for a $$2\pi$$-periodic function of a real variable. The study is complicated by the fact that the equation is quasilinear, and it involves a non-local operator in the form of a Hilbert transform. Although this equation is exact, it is quadratic with no higher order terms, and the global structure of its solution set can be studied using elements of the theory of real analytic varieties, and using the variational technique. The purpose of this paper is to show that uniquely defined arc-wise connected set of solutions with prescribed minimal period bifurcates from the first eigenvalue of the linearized problem. Although the set is not necessarily maximal as a connected set of solutions, and may possibly self-intersect, it has a local real analytic parametrization that contains a wave of greatest height in its closure. The authors also examine the dependence of the solution on the Froude number in relation to Stokes waves.
### MSC:
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76E99 Hydrodynamic stability
Full Text: | 2022-07-07 13:15:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7586178183555603, "perplexity": 264.3216301021908}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00422.warc.gz"} |
http://aas.org/archives/BAAS/v27n4/aas187/S058006.html | Session 58 - Gamma Rays & Cosmic Rays.
Oral session, Tuesday, January 16
Salon del Rey South, Hilton
## [58.06] EGRET Observations of Radio Bright Supernova Remnants
J. A. Esposito, P. Sreekumar (USRA NASA/GSFC), S. D. Hunter (NASA/GSFC), G. Kanbach (MPE)
Data from Phase 1 through Phase 3 of EGRET observations have been analyzed for gamma-ray emission near supernova remnants (SNRs) with radio flux greater than 1 Jy at 1 GHz. Comparision of the position of unidentified gamma ray sources from the second EGRET catalog (Thompson et al. 1995, ApJS, in press) with fourteen SNRs near the Galactic plane, |b| < 10\deg, indicates a statistically significant correlation, with a probability of chance coincidence better than 2 \times 10^-5 for five of thirty-two unidentified EGRET gamma ray sources being spatially consistant with radio bright SNRs.
Four of the unidentified EGRET sources studied have strong spatial correlations with radio bright SNRs associated with nearby medium mass (\sim 5000\rm\ M_ødot) molecular clouds. In these cases the mass of the molecular cloud is substantially greater than the mass of the SNR. If the gamma-ray emission is assumed to originate from cosmic rays accelerated in the SNR and interacting with the molecular cloud then, the inferred cosmic ray density in the vicinity of the SNRs is significantly enhanced compared to the average Galactic cosmic ray density in the Solar neighborhood (Esposito et al. 1996, ApJ, in press). This result supports the explanation of SNRs being the dominant acceleration site, and possibly the source, of Galactic cosmic rays.
Spectral analysis has been performed on two unidentified EGRET sources, 2EG J2020-4026 and 2EG J0618+2234, which are spatially correlated with \gamma\rm\, Cygni and IC443 respectively. The spectral index of both sources is consistant with a cosmic ray source spectral index \sim2. However, the spectral analysis is photon limited above 2 GeV.
The gamma-ray intensity or upper limit for all fourteen SNRs and spectra of 2EG J2020-4026 and 2EG J0618+2234 will be presented along with interpretation of the results. | 2015-03-31 00:19:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8032026290893555, "perplexity": 5038.7281531728795}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131300031.99/warc/CC-MAIN-20150323172140-00136-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://www.examfriend.in/Forum/Arithmetic-aptitude/Chain-Rule/1140 | 1)
A contractor employed 30 men to do a piece of work in 38 days. After 25 days, he employed 5 men more and the work was finished one day earlier. How many days he would have been behind, if he had not employed additional men ?
A) $1$
B) $1\frac{1}{4}$
C) $1\frac{1}{2}$
D) $1\frac{3}{4}$
$\therefore$ 30 men can do it in $\frac{12\times 35}{30}$ = 14 days, which is 1 day behind. | 2023-02-06 02:09:18 | {"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": 0.5923280119895935, "perplexity": 409.8025445424311}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500303.56/warc/CC-MAIN-20230206015710-20230206045710-00607.warc.gz"} |
http://mymathforum.com/algebra/45465-exponent-2.html | My Math Forum Exponent
Algebra Pre-Algebra and Basic Algebra Math Forum
July 27th, 2014, 11:25 AM #11
Senior Member
Joined: Nov 2013
From: Baku
Posts: 502
Thanks: 56
Math Focus: Geometry
Quote:
Originally Posted by bml1105 Can anyone tell me how to make the subscripts for the log formulas when writing on the forum? Thanks!
\log_x y => $\displaystyle \log_x y$
July 27th, 2014, 11:31 AM #12 Newbie Joined: Jul 2014 From: Seattle Posts: 16 Thanks: 0 Hmmm that actually isn't working for me. It's just staying in the same format \log_x y log_x y => Last edited by bml1105; July 27th, 2014 at 11:35 AM.
July 27th, 2014, 11:40 AM #13 Newbie Joined: Jul 2014 From: Seattle Posts: 16 Thanks: 0 Nevermind I figured it out!
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2019-08-19 05:27:07 | {"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": 0.6166505813598633, "perplexity": 14198.882527981425}, "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-2019-35/segments/1566027314667.60/warc/CC-MAIN-20190819052133-20190819074133-00051.warc.gz"} |
http://cloud.originlab.com/doc/en/OriginC/ref/Curve-Class | # 2.2.3.4 Curve
Curve
## Remark
An Origin C Curve is comprised of a Y Dataset and typically (but not necessarily) an associated X Dataset. For example, a data set plotted against row numbers will not have an associated X data set. An Origin C Curve object can easily be plotted using methods of the GraphLayer class. The Curve class is derived from the curvebase, and vectorbase classes from which it inherits methods and properties.
## Examples
EX1
// Assumes Book1_A and Book1_B exist and contain data
void Curve_ex1()
{
Dataset ds1("Book1_A"), ds2("Book1_B");
Curve crvCopy( ds1, ds2 );
crvCopy.Sort(); // Does not effect ds1, ds2
} | 2022-05-26 14:41:58 | {"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": 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": 0.437033087015152, "perplexity": 7565.535887469524}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662606992.69/warc/CC-MAIN-20220526131456-20220526161456-00444.warc.gz"} |
https://www.all-dictionary.com/sentences-with-the-word-Small%20intestine | # Sentence Examples with the word Small intestine
The salts of sodium resemble potassium in their action on the alimentary tract, but they are much more slowly absorbed, and much less diffusible; therefore considerable amounts may reach the small intestine and there act as saline purgatives.
Internally they are found to consist of a lamina twisted upon itself, and externally they generally exhibit a tortuous structure, produced, before the cloaca was reached, by the spiral valve of a compressed small intestine (as in skates, sharks and dog-fishes); the surface shows also vascular impressions and corrugations due to the same cause.
Among mammals, o, oesophagus; st, stomach; p, pylorus; ss, small intestine breviated); c, caecum; ll, large intestine colon, ending in r, the rectum.
View more
With few exceptions tapeworms select the small intestine for their station, and in this situation execute active movements of extension and contraction. | 2017-07-22 19:11:36 | {"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": 0.800742506980896, "perplexity": 13080.55431516353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424090.53/warc/CC-MAIN-20170722182647-20170722202647-00237.warc.gz"} |
https://www.physicsforums.com/threads/irreducible-representation-and-ir-stretching-bands.536288/ | # Irreducible Representation and IR stretching bands
After you find the irreducible representation of a molecule, how do you determine the number of IR active bands?
For example, in methane, the pointgroup is Td , then you found that the irreducible representation is A1 + T2.
How do you find the number of IR active and Raman active bands?
Thanks
Btw, a friend of mine said there are 2 IR active bands but I am not sure how to figure that out. Also, I know that T is triple degenerate and A is nondegenerate. But not sure how that relates to the number of IR active bands. | 2021-01-27 03:12:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8521255850791931, "perplexity": 507.4194899349721}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610704820894.84/warc/CC-MAIN-20210127024104-20210127054104-00664.warc.gz"} |
https://mathoverflow.net/questions/157117/real-analytic-variant-of-theorem-4-2-5-of-duistermaats-fio-1996 | # Real-analytic variant of theorem 4.2.5 of Duistermaat's “FIO”, 1996
Theorem 4.2.5 of Duistermaat's "Fourier Integral Operators", 1996, states:
Let $A \in I^m(X,Y,C)$ be an elliptic Fourier Integral Operator of order $m$, associated to a bijective canonical homogeneous transformation $C$ from an open cone $\Gamma \subset T^\ast Y \setminus 0$ into $T^\ast X \setminus 0$. Then for any closed (in $T^\ast Y \setminus 0$) cone $\Gamma_0 \subset \Gamma$ such that $C(\Gamma_0)$ is closed in $T^\ast X \setminus 0$ one can find a properly supported Fourier Integral Operator $B \in I^{-m}(Y,X,C^{-1})$ such that for any $u \in \mathscr E'(Y)$, for any $v \in \mathscr E'(X)$ the following relations are valid: $$WF(BAu - u) \cap \Gamma_0 = \varnothing,\quad WF(ABv - v) \cap C(\Gamma_0) = \varnothing.$$
The proof of the theorem involves multiplications by smooth functions with compact supports. This is why I can't directly generalize the proof of the abovementioned theorem to the case of the real-analytic category (the only real analytic function with compact support is zero). On the other hand, I think that the theorem is still valid for real-analytic Fourier Integral Operators and for analytic wavefronts but uses some more subtle proof. Please tell me, if you have encountered the mentioned theorem (or some variants) in the real-analytic case in some paper. | 2019-11-14 19:50:35 | {"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": 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": 0.9625563621520996, "perplexity": 89.21902607573853}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1573496668534.60/warc/CC-MAIN-20191114182304-20191114210304-00142.warc.gz"} |
https://lists.webkit.org/pipermail/webkit-dev/2016-March/028064.html | # [webkit-dev] Proposal: remove menclose notation radical
Frédéric WANG fred.wang at free.fr
Thu Mar 10 03:45:04 PST 2016
Hi everyone,
As said in a previous message, MathML layout refactoring is in progress
[1] and I'd like to use this opportunity to propose removing support for
More context:
In MathML3 there are three ways to write roots:
1) <msqrt> child1 child2 ... child3 </msqrt>, equivalent to the LaTeX
expression \sqrt{child1 child2 ... child3} i.e. square root of "child1
child2 ... child3".
2) <mroot> child1 child2 </mroot>, equivalent to the LaTeX expression
\sqrt[child2]{child1} i.e. "child2"-th root of "child1".
3) <menclose notation="radical"> child1 child2 ... child3 </menclose>,
equivalent to 1)
Currently 1) and 2) share an implementation in the RenderMathMLRoot
class. That implementation relies on anonymous renderers and flexbox
layout and has many issues with dynamic changes of child list, style,
zoom etc. However, I've uploaded a patch to do a complete refactoring of
RenderMathMLRoot in bug 153987 [2] which solves these issues.
The menclose element definitely needs a clean rewriting too. In
particular, 3) is implemented by appending an anonymous RenderMathMLRoot
child in which we put all the other children ; and again dynamic changes
are not handled very well . I have uploaded a patch to bug 155019 [3] in
order to completely rewrite the menclose implementation and I decided to
reuse RenderMathMLRoot.
I expect this removal to be safe for the users given that (except in
examples and tests) I've always seen 1) preferred over 3) in math
documents. The only rationale for 3) would be to write overlapping
notations (e.g. <menclose notation="radical circle horizontalstrike">)
but again I'm not aware of any concrete use case for that and it's
always possible to nest <msqrt> and <menclose> to get similar rendering.
Finally, note that the accessibility code does expose the radical
notation and my patch for bug 155019 does not affect that code.
I plan to ask the same to Mozilla developers (FYI in Gecko, 1) and 3)
are implemented in the same class but 2) is implemented in a separate
class with duplicate code ; so it would also make sense for them to do a
simplification). In the future, I also plan to ask to the Math WG to
deprecate this notation and this is already done in the current draft of
the MathML in HTML5 implementation note I wrote [4]. Anyway, the MathML
"Conforming renderers may ignore any value they do not handle, although
renderers are encouraged to render as many of the values listed below as
possible" [5].
Frédéric Wang
[1] https://lists.webkit.org/pipermail/webkit-dev/2015-December/027840.html
[2] https://bugs.webkit.org/show_bug.cgi?id=153987
[3] https://bugs.webkit.org/show_bug.cgi?id=155019
[4] http://www.mathml-association.org/MathMLinHTML5/
[5] https://www.w3.org/TR/MathML3/chapter3.html#presm.menclose
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URL: <https://lists.webkit.org/pipermail/webkit-dev/attachments/20160310/00dda7da/attachment.sig> | 2022-08-14 14:49:15 | {"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": 0.4758663773536682, "perplexity": 9432.233925146636}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882572043.2/warc/CC-MAIN-20220814143522-20220814173522-00110.warc.gz"} |
http://architectradure.blogspot.com/2007/08/usb-rechargeable-batteries.html | # USB - rechargeable batteries
Nice idea. Knowing that many of us carry a laptop everyday, it makes sense to use it for charging batteries!
UsbCell can be found here.
Brent said...
hi cati, wow, nice find. :)
Luciano Bove said...
Ciao! This is a real useful gadget.
Bob Johnson said...
Great Idea.
dt said...
Its interesting, but I was told that the USB power is not enough for recharging? Perhaps my source was wrong.
Joanne said...
Whoa, neat idea. I like the whole multi-tasking energy use! | 2014-09-16 23:26:12 | {"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": 0.8433843851089478, "perplexity": 10630.06821393985}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657120057.96/warc/CC-MAIN-20140914011200-00035-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://irzu.org/research/video-conversion-ffmpeg-command-what-is-the-best-config-to-re-encode-vidoe-youtube/ | # video conversion – ffmpeg command, what is the “best” config to re-encode vidoe youtube?
Let’s say we have a video generated with matplotlib.animation with the code below (while can’t figure how to have the mp4 file with HD 1080p, but we can re-encode with Final cut pro HD 1080p)
Writer = animation.writers['ffmpeg']#code to save the example.mp4
writer = Writer(fps=0.9, codec="h264", bitrate=1000000, metadata=dict(artist="me"))
animator.save('example.mp4', writer=writer)
When this mp4 file is imported into Final Cut, we have the option to make it HD 1080p.
Q: How can “convert” an mp4 file with HD 1080P as planned for youtube use with ffmpeg command?
enter image description here | 2023-02-08 05:08:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.35586071014404297, "perplexity": 9112.085170817138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500671.13/warc/CC-MAIN-20230208024856-20230208054856-00277.warc.gz"} |
https://socialcar-project.eu/en/a-central-angle-thata-of-a-circle-with-radius-16-inches-intercepts-an-arc-of-1936-inches-find-th.11757.html | CorneliusFurtado414
14
# A central angle, thata, of a circle with radius 16 inches intercepts an arc of 19.36 inches. Find thata.
(1) Answers
Skyheart
Theta* $\theta=\frac{19.36}{16}=1.21$ radians.
Add answer | 2023-02-08 17:45:24 | {"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": 0.7366499304771423, "perplexity": 7781.187639970789}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00321.warc.gz"} |
https://socratic.org/questions/what-is-the-remainder-when-the-function-f-x-x-3-4x-2-12-is-divided-by-x-2 | # What is the remainder when the function f(x)=x^3-4x^2+12 is divided by (x+2)?
Jan 11, 2018
$\textcolor{b l u e}{- 12}$
#### Explanation:
The Remainder theorem states that, when $f \left(x\right)$ is divided by $\left(x - a\right)$
$f \left(x\right) = g \left(x\right) \left(x - a\right) + r$
Where $g \left(x\right)$ is the quotient and $r$ is the remainder.
If for some $x$ we can make $g \left(x\right) \left(x - a\right) = 0$, then we have:
$f \left(a\right) = r$
From example:
${x}^{3} - 4 {x}^{2} + 12 = g \left(x\right) \left(x + 2\right) + r$
Let $x = - 2$
$\therefore$
${\left(- 2\right)}^{3} - 4 {\left(- 2\right)}^{2} + 12 = g \left(x\right) \left(\left(- 2\right) + 2\right) + r$
$- 12 = 0 + r$
$\textcolor{b l u e}{r = - 12}$
This theorem is just based on what we know about numerical division. i.e.
The divisor x the quotient + the remainder = the dividend
$\therefore$
$\frac{6}{4} = 1$ + remainder 2.
$4 \times 1 + 2 = 6$
Jan 11, 2018
$\text{remainder } = - 12$
#### Explanation:
$\text{using the "color(blue)"remainder theorem}$
$\text{the remainder when "f(x)" is divided by "(x-a)" is } f \left(a\right)$
$\text{here } \left(x - a\right) = \left(x - \left(- 2\right)\right) \Rightarrow a = - 2$
$f \left(- 2\right) = {\left(- 2\right)}^{3} - 4 {\left(- 2\right)}^{2} + 12 = - 12$ | 2020-09-23 23:21:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 23, "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": 0.916348934173584, "perplexity": 1169.2717199977835}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600400212959.12/warc/CC-MAIN-20200923211300-20200924001300-00546.warc.gz"} |
https://www.biostars.org/p/9464010/ | Does a smaller value of F from PLINK --het represent higher heterozygosity?
0
0
Entering edit mode
5 days ago
curious ▴ 500
Running command plink --het gives a column "F".
I read that F is essentially "1 - (HI/HS), where HI represents the individual's heterozygosity, and HS the subpopulation's heterozygosity".
From this definition it would seem that the lower the F value for a sample the higher the heterozygosity (eg maybe contamination if low enough, inbreeding if high enough). Is it right?
I am also wondering what a "normal" range of F is for a randomly sampled population. Here they say to remove samples that are 3 standard deviation (SD) units from the mean, but what is a typical mean? 0.018?
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Use of this site constitutes acceptance of our User Agreement and Privacy Policy. | 2021-04-13 09:46:27 | {"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": 0.4323251247406006, "perplexity": 3454.4495940251577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038072180.33/warc/CC-MAIN-20210413092418-20210413122418-00305.warc.gz"} |
https://www.transtutors.com/questions/exercise-8-13-contrasting-traditional-and-abc-product-costs-86851.htm | # Exercise 8-13 Contrasting Traditional and ABC Product Costs 1 answer below »
Exercise 8-13 Contrasting Traditional and ABC Product Costs [LO1, LO5] Model X100 sells for $120 per unit whereas Model X200 offers advanced features and sells for$500 per unit. Management expects to sell 50,000 units of Model X100 and 5,000 units of Model X200 next year. The direct material cost per unit is $50 for Model X100 and$220 for Model X200. The company's total manufacturing overhead for the year is expected to be $1,995,000. A unit of Model X100 requires 2 direct labor-hours and a unit of Model X200 requires 5 direct labor-hours. The direct labor wage rate is$20 per hour.
Requirement 1:
(a) Calculate the predetermined overhead rate. (Round your answer to 2 decimal places. Omit the "$" sign in your response.) (b) Using this traditional approach, compute the product margins for X100 and X200. (Negative amounts should be indicated by a minus sign. Omit the "$" sign in your response.)
2.) Management is considering an activity-based costing system and would like to know what impact this would have on product costs. Preliminary analysis suggests that under activity-based costing, a total of $1,000,000 in manufacturing overhead cost would be assigned to Model X100 and a total of$600,000 would be assigned to Model X200. In addition, a total of $150,000 in nonmanufacturing overhead would be applied to Model X100 and a total of$350,000 would be applied to Model X200. Using the activity-based costing approach, compute the product margins for X100 and X200. (Negative amounts should be indicated by a minus sign. Omit the "$" sign in your response.) ## 1 Approved Answer kanika b 5 Ratings, (9 Votes) 1 Under the traditional direct labor-hour based costing system, manufacturing overhead is applied to products using the predetermined overhead rate computed as follows: Predtermined overhead rate= Total manufacturing overhead / total direct labor hours *50,000 units of Model X100 @ 2.0 DLH per unit + 5,000 units of Model X200 @ 5.0 DLH per unit = 100,000 DLHs + 25,000 DLHs = 125,000 DLHs Predtermined overhead rate=$1,995,000/125,000 labor hours Predtermined overhead rate $15.96 2 Consequently, the product margins using the traditional approach would be computed as follows: Model X100 Model X200 Total Sales (50000 units*$120), (5000 units *$500) 60,00,000 25,00,000 85,00,000 Direct materials (50000 units*$50), (5000 units *$220) 25,00,000 11,00,000 36,00,000 Direct labor (50000 units*2 DLH*$20) , (5000 units*5DLH*$20) 20,00,000 5,00,000 25,00,000 Manufacturing overhead applied @$15.96 per direct labor-hour 1,596,000 399,000 1,995,000 Total manufacturing cost...
Looking for Something Else? Ask a Similar Question | 2021-08-05 09:31:26 | {"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": 0.45572781562805176, "perplexity": 6450.26323341899}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1627046155458.35/warc/CC-MAIN-20210805063730-20210805093730-00191.warc.gz"} |
https://psychopy.org/api/visual/simpleimagestim.html | # SimpleImageStim¶
class psychopy.visual.SimpleImageStim(*args, **kwargs)[source]
A simple stimulus for loading images from a file and presenting at exactly the resolution and color in the file (subject to gamma correction if set).
Unlike the ImageStim, this type of stimulus cannot be rescaled, rotated or masked (although flipping horizontally or vertically is possible). Drawing will also tend to be marginally slower, because the image isn’t preloaded to the graphics card. The slight advantage, however is that the stimulus will always be in its original aspect ratio, with no interplotation or other transformation, and it is slightly faster to load into PsychoPy. | 2021-04-22 22:26:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5918710231781006, "perplexity": 2793.5053546278677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1618039563095.86/warc/CC-MAIN-20210422221531-20210423011531-00441.warc.gz"} |
https://socratic.org/questions/the-sum-of-two-consecutive-odd-integers-is-124-what-are-the-integers | # The sum of two consecutive odd integers is 124, what are the integers?
Feb 7, 2016
$61$ and $63$
#### Explanation:
An odd integer can be written as:
$\left(2 n + 1\right)$
If the odd integers are consecutive, then the next odd integer will be:
$\left(2 \left(n + 1\right) + 1\right) = \left(2 n + 3\right)$
Given that the sum of these integers comes to $124$ we can write an equation and then solve for $n$:
$\left(2 n + 1\right) + \left(2 n + 3\right) = 124$
$4 n + 4 = 124$
$4 n = 120$
$\to n = 30$.
That would mean that our odd integers are:
$2 \left(30\right) + 1$ =61
and #2(30)+3 = 63
And of course $61 + 63 = 124$. | 2019-10-22 16:28:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "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": 0.670746386051178, "perplexity": 591.7684921037103}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00135.warc.gz"} |
http://aperiodical.com/2012/04/laziest-torus-identified/ | # Laziest torus identified
Or, in similarly simplified headlinese, “Math finds the best doughnut”. A little bit more precisely, Fernando C. Marques and André Neves claim in a preprint on the arXiv to have proved the Willmore conjecture, that the minimum achievable mean curvature of a torus is $\frac{2}{\pi^2}$.
The article I linked to is some surprisingly non-stupid coverage from the Huffington Post. It seems they have a maths professor writing a column. I will never understand that site. I don’t know if there’s a Serious Business way of framing this, but the result is nice to know.
Richard Elwes has written a very short post on Google+ with some more real-maths information about what’s going on. | 2013-05-24 08:36:40 | {"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": 0.5300264954566956, "perplexity": 1222.6773353530828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368704392896/warc/CC-MAIN-20130516113952-00032-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://blender.stackexchange.com/questions/36691/how-to-use-propertygroupitem | # How to use PropertyGroupItem
I was browsing the docs when I ran into something interesting: bpy.types.propertyGroupItem
This is what the doc says about it:
Property that stores arbitrary, user defined properties
I did a little digging around but couldn't find anything else about it. It sounds very interesting but I have absolutely no idea how to use it. Could someone give an explanation of what this is and when to use it?
• example is in the DOC – Chebhou Aug 29 '15 at 22:18
• Instances of MyPropertyGroup as seen in that example can store two properties, custom_1 and custom_2. The instances of these properties are PropertyGroupItems. You don't use that type however, it's handled internally. See here for properties in general: blender.org/api/blender_python_api_2_75_release/bpy.props.html – CoDEmanX Aug 29 '15 at 22:57
• @CoDEmanX That makes a lot of sense, thanks! – Isaac Aug 30 '15 at 0:14 | 2019-10-15 13:21:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3166322112083435, "perplexity": 878.3088035637152}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986659097.10/warc/CC-MAIN-20191015131723-20191015155223-00393.warc.gz"} |
https://math.stackexchange.com/questions/4299984/evaluate-int-frac-pi8-frac-7-pi8-frac-ln-left-1 | # Evaluate $\int_{{\frac {\pi}{8}}}^{{\frac {7\,\pi}{8}}}\!{\frac {\ln \left( 1- \cos \left( t \right) \right) }{\sin \left( t \right) }}\,{\rm d}t$
I'm interested in this integral: $$\int_{{\frac {\pi}{8}}}^{{\frac {7\,\pi}{8}}}\!{\frac {\ln \left( 1- \cos \left( t \right) \right) }{\sin \left( t \right) }}\,{\rm d}t$$
I found this particular closed form with Maple and finally : $$-{\frac { \left( \ln \left( 2-\sqrt {2+\sqrt {2}} \right) \right) ^{ 2}}{2}}-{\frac {{\pi}^{2}}{12}}+{\frac {11\, \left( \ln \left( 2 \right) \right) ^{2}}{8}}-{\frac { \left( \ln \left( 1+\sqrt {2} \right) \right) ^{2}}{2}}+{\frac {3\, \left( \ln \left( 2+\sqrt {2} \right) \right) ^{2}}{4}}+{\it {Li_2}} \left( -{\frac {\sqrt {2+ \sqrt {2}}}{4}}+{\frac{1}{2}} \right)$$, where \Li_2 is the dilogarithm function.
Please, can someone prove it ?
• Start with the property of definite integrals that $\int_{a}^{b}f(x)dx=\int_{a}^{b}f(a+b-x)dx$ Nov 8, 2021 at 8:23
$$I=\int{\frac {\log \left( 1- \cos \left( t \right) \right) }{\sin \left( t \right) }}\,dt=\int \sin(t){\frac {\log \left( 1- \cos \left( t \right) \right) }{1-\cos^2\left( t \right) }}\,dt$$
Let $$x=\cos(t)\implies I=\int \frac{\log(1-x)}{x^2-1} \,dx=-\frac12\int\frac{\log(1-x)}{ 1-x}\,dx-\frac12\int\frac{\log(1-x)}{ x+1}\,dx$$
$$\int\frac{\log(1-x)}{ 1-x}\,dx=-\frac{1}{2} \log ^2(1-x)$$ For the second integral, integration by parts gives $$\int\frac{\log(1-x)}{x+1}\,dx=\text{Li}_2\left(\frac{1-x}{2}\right)+\log (1-x) \log \left(\frac{x+1}{2}\right)$$ Combining the results
$$I=\int \frac{\log(1-x)}{x^2-1} \,dx=\frac{1}{4} \left(\log (1-x) (\log (4(1-x))-2 \log (x+1))-2 \text{Li}_2\left(\frac{1-x}{2}\right)\right)$$ Go back to $$t$$ if you wish and use bounds.
• So great and thanks !
– Dens
Nov 8, 2021 at 10:40
• @Dens. Glad to help ! In fact the problem is simple if you think about the first trick $$\frac 1 {\sin(x)}=\frac {\sin(x)}{\sin^2(x)}=\frac {\sin(x)}{1-\cos^2(x)}$$ Nov 8, 2021 at 10:49
• Merci bien pour le conseil !
– Dens
Nov 8, 2021 at 10:50
• If I may ask, where are you located ? I am in Pau. Cheers :-) Nov 8, 2021 at 10:52
• Je suis francais et je me trouve en Saône et Loire.D'ailleurs, je vous avais écris au sujet d'une publication sur Vixra << values of barnes function >>. C'est moi !
– Dens
Nov 8, 2021 at 10:55 | 2022-08-14 17:21:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6979813575744629, "perplexity": 3059.7579588616127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882572043.2/warc/CC-MAIN-20220814143522-20220814173522-00062.warc.gz"} |
https://mathoverflow.net/questions/398088/period-map-for-partial-bar-partial-manifolds | # Period map for $\partial\bar\partial$-manifolds
When we talk about the theory of variation of Hodge structures, we always assume that the central fiber is a Kähler manifold $$X$$, then consider a family of deformations $$\pi:\mathcal X\to B$$ and the period map $$\mathcal P:B\to Grass(b^{p,k},H^k(X,\mathbb C))$$, $$b^{p,k}=dim F^pH^k(X,\mathbb C)$$.
What if we replace the Kähler manifold by a $$\partial\bar\partial$$-manifold and consider a holomorphic family of $$\partial\bar\partial$$-manifolds $$\pi:\mathcal X\to B$$?
Recall a $$\partial\bar\partial$$-manifold is a compact complex manifold which satisfies for any $$\partial$$, $$\bar\partial$$-closed $$d$$ exact $$(p,q)$$ form $$\alpha$$, there this a $$(p-1,q-1)$$ form $$\beta$$ such that $$\alpha=\partial\bar\partial \beta$$.
Is the theory of variation of Hodge structures remains the same? And is there also a period map $$\mathcal P:B\to Grass(b^{p,k},H^k(X,\mathbb C))$$? If so, is the period map holomorphic and the Griffiths transversality still holds?
In my opinion, first we should define what $$F^pH^k(X,\mathbb C)$$ means for a non-Kähler manifold, since for a Kähler manifold, we have the Kähler identity $$\Delta=2\Delta_{\bar\partial}=2\Delta_{\partial}$$ from which we deduce the Hodge decomposition: $$H^k(X,\mathbb C)=\oplus_{p+q=k}H^{p,q}(X)$$, so we can define $$F^pH^k(X,\mathbb C)=H^{p,k-p}(X)\oplus H^{p+1,k-p-1}(X)\oplus...\oplus H^{k,0}(X)$$ which is obviously a subspace of $$H^k(X,\mathbb C)$$, but for a non-Kähler manifold, there is no Kähler identities. But from AT13, we know that the Bott-Chern cohomology $$H^{p,q}_{BC}(X,\mathbb C):=\frac{ker\partial\cap ker\bar\partial}{im\partial\bar\partial}$$ is isomorphic to Dolbeault cohomology $$H_{\bar\partial}^{p,q}(X)$$ and $$H_{\partial}^{p,q}(X)$$, so if we define $$F^pH^k(X,\mathbb C)=H^{p,k-p}_{BC}(X,\mathbb C)\oplus H^{p+1,k-p-1}_{BC}(X,\mathbb C)\oplus...\oplus H^{k,0}_{BC}(X,\mathbb C)$$, is it reasonable to treat is as a subspace of $$H^k(X,\mathbb C)$$ and define a period map as in the Kähler case?
Let me start with a disclaimer that I think the following facts are true, but I'm doing this over coffee and I haven't checked the details carefully. First, I'll redefine $$F^pH^k(X,\mathbb{C})$$ to be the space of de Rham classes represented by the sum of $$(p', p'-k)$$ forms with $$p'\ge p$$, or equivalently as $$F^pH^k(X,\mathbb{C})= im(H^k(\Omega_X^{\ge p})\xrightarrow{\iota} H^k(X,\Omega_X^\bullet))$$ Then the $$\partial\bar\partial$$-lemma is sufficient to guarantee the filtration is strict in the sense that the maps above are injective (or equivalently that the Hodge to de Rham spectral sequence degenerates); edit see remark 5.21 of Deligne, Griffiths, Morgan, Sullivan, Real homotopy theory of Kähler manifolds. Then, if I understand the notation of the paper you linked, this should probably give decomposition in terms of BC cohomology as you wrote. The other thing I want to remark is that if $$\mathcal{X}\to B$$ is a smooth proper family such that the fibres satisfy $$\partial\bar\partial$$-lemma, then usual arguments should imply that $$F^p R^kf_*\Omega_{\mathcal{X}/B}^\bullet= im(R^kf_*\Omega_{\mathcal{X}/B}^{\ge p}\xrightarrow{\iota}R^kf_*\Omega_{\mathcal{X}/B}^\bullet)$$ satisfies Griffiths transversality etc. So in this sense, things work. However, you would be missing the polarization, which need for most of the deeper results about the Griffiths period map.
• Do you mean you define $F^pH^k(X,\mathbb C)=ker(d:F^pA^k\to F^{p+1}A^k)/im(d:F^{p-1}A^k\to F^pA^k)$?
• Almost, but there is no shift because $d(F^p)\subset F^p$ Jul 24 at 14:50
• Sorry that I made a mistake, I mean $F^pH^k(X,\mathbb C)=ker(d:F^pA^k\to F^pA^{k+1})/im(d:F^pA^{k-1}\to F^pA^k)$. If we define the filtration like this, I don't think it obvious that we will have of decompostion of this filtration in BC cohomology, since for the Kahler case, it takes p158-159 for Voisin in her book<Hodge theory and...> to prove the corresponding decomposition.
• Technically, it gives an isomorphism $F^pH^k(X)= H^{p,k-p}\oplus\ldots$ with Dolbeault cohomology. Now use the fact, you stated, that BC and Dolbeault cohomologies are isomorphic. Jul 25 at 14:36 | 2021-10-24 00:21:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9728434085845947, "perplexity": 145.52912438173652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585828.15/warc/CC-MAIN-20211023224247-20211024014247-00009.warc.gz"} |
https://mailman.ntg.nl/pipermail/ntg-context/2022/104845.html | # [NTG-context] How to let a macro check the previous value of #1 the last time the same macro was called?
Joel uaru99 at yahoo.com
Sun Jan 9 15:16:37 CET 2022
```Is there a way for a macro to check the previous value of #1, the last time that same macro was called?
Here is a minimum working example, pretending that `\previousvalue` is equal to #1 from the last time the same macro was called:
\define[1]\mymacro{
\if\previousvalue=#1
same as last time
\else
it is different from last time
\fi
}
\starttext
\mymacro{cat}
\mymacro{cat}
\mymacro{mouse}
\mymacro{mouse}
\mymacro{cat}
\stoptext
This would print:
it is different from last time <--it was never called previously
same as last time
it is different from last time
same as last time
it is different from last time
--Joel
-------------- next part --------------
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URL: <http://mailman.ntg.nl/pipermail/ntg-context/attachments/20220109/bc12b74b/attachment.htm>
```
More information about the ntg-context mailing list | 2022-08-15 04:37:47 | {"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": 0.9640842080116272, "perplexity": 8466.422430811563}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572127.33/warc/CC-MAIN-20220815024523-20220815054523-00109.warc.gz"} |
https://unapologetic.wordpress.com/2008/05/20/matrices-i/?like=1&source=post_flair&_wpnonce=8cb43e0c56 | # The Unapologetic Mathematician
## Matrices I
May 20, 2008 - Posted by | Algebra, Linear Algebra
1. […] Einstein Summation Convention Look at the formulas we were using yesterday. There’s a lot of summations in there, and a lot of big sigmas. Those get really tiring to […]
Pingback by The Einstein Summation Convention « The Unapologetic Mathematician | May 21, 2008 | Reply
2. […] Matrices II With the summation convention firmly in hand, we continue our discussion of matrices. […]
Pingback by Matrices II « The Unapologetic Mathematician | May 22, 2008 | Reply
3. […] compose two morphisms by the process of matrix multiplication. If is an matrix in and is a matrix in , then their product is a matrix in (remember the […]
Pingback by The Category of Matrices I « The Unapologetic Mathematician | June 2, 2008 | Reply
4. […] satisfies ), we construct the column vector (here ). But we’ve already established that matrix multiplication represents composition of linear transformations. Further, it’s straightforward to see that the linear transformation corresponding to a […]
Pingback by The Category of Matrices III « The Unapologetic Mathematician | June 23, 2008 | Reply
5. […] vector space comes equipped with a basis , where has a in the th place, and elsewhere. And so we can write any such transformation as an […]
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6. […] Okay, back to linear algebra and inner product spaces. I want to look at the matrix of a linear map between finite-dimensional inner product […]
Pingback by Matrix Elements « The Unapologetic Mathematician | May 29, 2009 | Reply
7. […] the space of -tuples of complex numbers — and that linear transformations are described by matrices. Composition of transformations is reflected in matrix multiplication. That is, for every […]
Pingback by Some Review « The Unapologetic Mathematician | September 8, 2010 | Reply | 2015-05-07 06:42:18 | {"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": 0.9997219443321228, "perplexity": 1171.8522152991104}, "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-2015-18/segments/1430460544953.41/warc/CC-MAIN-20150501060904-00026-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://www.gamedev.net/forums/topic/408891-arrive-function/ | Arrive Function
This topic is 4175 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
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Hi, so I have this code for my AI's Arrive function.
Vector2D EGsoldier::Arrive(Vector2D TargetPos) //Need to improve on this function
{
Vector2D ToTarget = TargetPos - Pos();
double dist = ToTarget.Length();
if( dist > 0 )
{
double speed = dist/( 1.3 );
speed = min(speed, e_dMaxSpeed);
Vector2D DesiredVelocity = ToTarget*speed/dist;
Vector2D FinalVelocity = DesiredVelocity - Velocity();
return FinalVelocity;
}
return Vector2D(0,0);
}
It returns the 2D vector where my EGsoldier should go. The problem is, that if there is an obstacle in the way, the soldier has no idea what to do (and subsequently runs into the obstacle and stays there). Can someone help me figure out how to improve this function so that the EGsoldier can get to his destination w/o running into an object?
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Create a vector that resembles the difference between the obstacle.pos and the current unit.pos, This should be normalized and converted to appropriate size.
Then add this vector to the current unit.pos
You may want to add a random number to the new direction vector before adding it, since if the collision is head-on, it might get stuck (pinball-style) trying to repell in direct opposite direction.
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Quote:
Original post by bballmitchCan someone help me figure out how to improve this function so that the EGsoldier can get to his destination w/o running into an object?
Rather than change this function, design a function for 'Avoid', which will generate a movement vector to avoid the object. The resulting movement should be a weighted sum of the outputs of the Arrive and Avoid functions. This weight would be changed depending on the proximity of the object. So, when the soldier is moving toward the object but is still some distance from it, there would be a small perturbation to the path to take it around the object. If the object suddently appeared right in front of it, the Avoid behaviour would dominate and the Arrive behaviour would be minimised, so that the soldier first avoided the object and then went back to heading to the goal. Make sense?
I suggest you look at the full set of steering behaviours available for reactive pathing.
Cheers,
Timkin | 2018-01-21 07:20:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3903544843196869, "perplexity": 1151.0663263383453}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084890314.60/warc/CC-MAIN-20180121060717-20180121080717-00673.warc.gz"} |
https://planetmath.org/AscendingChainCondition | # ascending chain condition
A partially ordered set $S$ (for example, a collection of subsets of a set $X$ when ordered by inclusion) satisfies the or ACC if there does not exist an infinite ascending chain $s_{1} of elements of $S$. | 2019-09-21 17:42:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 4, "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": 0.7975494265556335, "perplexity": 210.78382455256903}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1568514574588.96/warc/CC-MAIN-20190921170434-20190921192434-00265.warc.gz"} |
https://socratic.org/questions/how-do-you-evaluate-cos-arcsin-1-4 | # How do you evaluate cos(arcsin (1/4))?
Sep 10, 2015
$\frac{\sqrt{15}}{4} \approx 0.968$
#### Explanation:
By the fact that ${\cos}^{2} \left(\theta\right) + {\sin}^{2} \left(\theta\right) = 1$ for all $\theta$, when we know the value of $\sin \left(\theta\right)$, there are two possible corresponding values for $\cos \left(\theta\right)$, namely $\cos \left(\theta\right) = \pm \sqrt{1 - {\sin}^{2} \left(\theta\right)}$.
Next note that $\arcsin \left(x\right)$ always gives an answer between $- \frac{\pi}{2}$ and $\frac{\pi}{2}$ radians, where the cosine function is positive. Hence, $\cos \left(\arcsin \left(\frac{1}{4}\right)\right) \ge q 0$.
Thus, $\cos \left(\arcsin \left(\frac{1}{4}\right)\right) = \sqrt{1 - {\sin}^{2} \left(\arcsin \left(\frac{1}{4}\right)\right)}$
$= \sqrt{1 - {\left(\frac{1}{4}\right)}^{2}} = \sqrt{1 - \frac{1}{16}} = \sqrt{\frac{15}{16}} = \frac{\sqrt{15}}{4} \approx 0.968 .$
It's also possible to solve this problem by drawing a right triangle, labeling one of the non-right angles as $\arcsin \left(\frac{1}{4}\right)$, using the Pythagorean Theorem and SOH, CAH, TOA to label and find possible side lengths and ultimately the final answer.
Jul 19, 2016
Less formal style of solution
$\frac{\sqrt{15}}{4} \approx 0.9682$ to 4 decimal places
#### Explanation:
arcsin of some value gives you the angle that was used derive the that value of the sine
$\textcolor{b r o w n}{\text{sin, cos and tangent are just another way of defining ratios}}$
The value given can be used in conjunction with the properties of sine to determine a related triangle.
From this and using Pythagoras we can determine the length of the adjacent.
${x}^{2} + {1}^{2} = {4}^{2}$
$\implies x = \sqrt{15}$
so $\cos \left(\theta\right) = \frac{x}{4} = \frac{\sqrt{15}}{4} \approx 0.9682$ to 4 decimal places | 2020-02-22 17:27:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 18, "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": 0.9176129102706909, "perplexity": 393.23275111022895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1581875145708.59/warc/CC-MAIN-20200222150029-20200222180029-00459.warc.gz"} |
https://math.stackexchange.com/questions/2788894/projection-of-a-measurable-cylinder-of-the-product-sigma-algebra | # Projection of a measurable cylinder of the product $\sigma$-algebra
Take some set $A \subset \mathbb{R}$ such that $A \times \mathbb{R}$ is measurable in $\mathrm{B}(\mathbb{R}) \times \mathrm{B}(\mathbb{R})$, the product $\sigma$-algebra of the borel $\sigma$-algebra of $\mathbb{R}$ by itself (which is also $\mathrm{B}(\mathbb{R^2})$, the borel $\sigma$-algebra of $\mathbb{R}^2$ for its product topology). Then must $A$ be measurable in $\mathrm{B}(\mathbb{R})$?
I know the converse is true, and that the image of a measurable set for the product $\sigma$-algebra by a projection isn't necessary measurable, but what happens for a just cylinder $A \times \mathbb{R}$?
Alright, it turns out that it was true, $A$ needs to be measurable. Someone posted on another page here a link to the solution: | 2022-07-03 09:47:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9773464798927307, "perplexity": 126.57047644347833}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104215805.66/warc/CC-MAIN-20220703073750-20220703103750-00169.warc.gz"} |
https://tug.org/pipermail/macostex-archives/2005-November/018642.html | # [OS X TeX] tex files and mdimport
Mon Nov 14 20:56:16 CET 2005
```
On Monday, November 14, 2005, at 11:51AM, Gary L. Gray <gray at engr.psu.edu> wrote:
>
>On Nov 14, 2005, at 2:42 PM, Adam Maxwell wrote:
>
>>
>> On Monday, November 14, 2005, at 09:05AM, Herbert Schulz
>> <herbs at wideopenwest.com> wrote:
>>
>>> I don't know how many folks here also look at the TeXShop Forum
>>> <http://www.apfelwiki.de/forum/viewforum.php?f=6> but there is an
>>> interesting note there about Spotlight and .tex files. It seems that,
>>> at least after the 10.4.3 update, .tex files are no longer searched
>>> for meta-data. I just checked this and it seems to be true: looking
>>> for some information (the word abbreviations which I know is in at
>>> least one of my .tex files) within on of my .tex files doesn't list
>>> that file. Apparently the file type for .tex files is dyn.... and
>>> those files aren't searched.
>>
>> I don't think they should have been searched in the first place, so
>> Spotlight is probably working (more) correctly now. I wrote up a
>> trivial importer that indexes .tex files by file content, \author,
>> and \title. Any other LaTeX commands that would be worth trying to
>> parse for metadata? If this would be useful, I'll release it under
>> a BSD license as part of the mactextoolbox (if Maarten is agreeable).
>
>Maybe I am crazy (actually, I know I am, but that is for another
>topic), but I would like to see it index everything in the .tex file.
>Is there a reason this shouldn't be done?
That was the "file content" part of my message above. | 2023-01-31 16:47:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9719028472900391, "perplexity": 5571.919327032817}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1674764499888.62/warc/CC-MAIN-20230131154832-20230131184832-00717.warc.gz"} |
http://www.linyekexue.net/CN/10.11707/j.1001-7488.20030611 | • 论文及研究报告 •
### 辽西半干旱地区栎树人工造林技术的研究
1. 沈阳农业大学林学院,沈阳110161；辽宁省凌源市五家子国合造林站,凌源122507；辽宁省凌源市河东国合造林站,凌源122500；辽宁省朝阳县朝阳林场,朝阳122000
• 收稿日期:2000-05-12 修回日期:2003-02-27 出版日期:2003-11-25 发布日期:2003-11-25
### STUDIES ON THE AFFORESTATION TECHNIQUES FOR THREE OAK SPECIES INTHE SEMIARID AREAS OF WESTERN LIAONING PROVINCE
Cui Jianguo,Cui Wenshan,Bai Ruixing,Li Demin Lan,Xianzhen
1. College of Forestry, Shenyang Agricultural University Shenyang 110161;Wujiazi Afforestation Station of Lingyuan,Liaoning Province Lingyuan122507;Hedong Afforestation Station of Lingyuan, Laioning Province Lingyuan122500;Chaoyang Forest Farm of Chaoyang County,Liaoning Province Chaoyang122000
• Received:2000-05-12 Revised:2003-02-27 Online:2003-11-25 Published:2003-11-25
Abstract:
Pinus tabulaeformis forest mixed with deciduous oak species such as Quercus mongolica and Q.liaotungensis is the zonal native vegetation in Western Liaoning Province. However, the present artificial vegetation dominated in Western Liaoning Province is monocultures of P.tabulaeformis. It is of great significance to introduce oak species into the pure P.tabulaeformis plantations to promote the restoration of P.tabulaeformis forest mixed with oak species and the sustainable management of the pure P.tabulaeformis plantations. The objective of this study was to investigate the afforestation techniques for Q.mongolica, Q.liaotungensis and Q.acutissima under the semiarid conditions in Western Liaoning Province. In view of the natural conditions in Western Liaoning Province, a series of direct seeding and planting experiments for oak species under different shading conditions such as in the cutting strip of P.tabulaeformis stand, under the canopy of P.tabulaeformis stand and in the open stand of P.tabulaeformis were carried out. The results showed that oak growth was characterized by growth of root system during the first 3～4 years after seeding or planting. However, it was dominated by the elongation of the taproot while the absorptive root was too less to maintain balance of water contents between the above and below ground parts of the oak seedlings and saplings. This was the main reason for the failure of oak afforestation in wild land in Western Liaoning Province. Under shading conditions, transpiration rate of oak seedlings decreased greatly because of the drastic reduction of light intensity, which reduced the waste of water in summer, while in winter and at the end of winter and at the beginning of spring, seedling death rate resulted from top_drying or withered stem after physiological drought was greatly reduced. Both situations contributed to the high survival rate and satisfactory growth of oak seedlings and saplings. The survival rate could be as high as 100% in the first few years when afforestation was done under closed canopy of P.tabulaeformis stand, but the growth increment of height and diameter was less. This phenomenon became more obvious with increase of age of the seedlings. The survival rate of oak saplings at the age of 6 years was more than 90%; the average basal diameter of trees ranged from 0.45 to 0.95 cm; the average tree height from 19.5 to 32.3 cm; the root system reached a depth of 70.5 cm, the width in diameter was 1.728 cm, and the width in diameter where the root was broken was 0.344 cm. With the increase in number of lateral and fibrous roots and the enhancement of their adsorptive capability, the oak saplings was at a stage of stable growth from 6～7 years onwards. Based on this study, it was concluded that the following set of techniques should be followed to guarantee the success of artificial oak afforestation in Western Liaoning Province:(1)Afforestation under shelter such as in the cutting strip of P.tabulaeformis stand, under the canopy of P.tabulaeformis stand and in the open stand of P.tabulaeformis, but afforestation under closed canopy of P.tabulaeformis stand should be avoided; (2) Direct seeding in autumn with careful site preparation, seed screening and classification before seeding, and a favorable mulching soil layer depth of 5～8 cm, but places where were heavily damaged by mouse or hare should be avoided; (3)Selection of site with a thick soil layer depth; and (4) Careful tending, particularly stumping of saplings.
Key words: Semiarid areas, Quercus mongolica, Q.liaotungensis, Q.acutissima, Afforestation techniques | 2022-06-29 03:05:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.1874714344739914, "perplexity": 8449.468893172356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103620968.33/warc/CC-MAIN-20220629024217-20220629054217-00530.warc.gz"} |
https://bitbucket.org/smileychris/southwest | southwest
A quick way to alter the database schema based on model changes for an app which doesn't (yet) need the power of full south migrations.
Usage
Initially, you'll need to set up the initial definitions for all (non-south) apps:
manage.py syncdb
Then after making a model change to an app you can see the changes, and optionally apply them (requires confirmation) by using the new alterdb command:
manage.py alterdb myapp
If you'd rather just see the SQL than alter the database directly:
manage.py alterdb myapp --sql
If you have manually altered the database and would like to forget the old model definition for an app, you can reset the definition:
manage.py alterdb myapp --reset | 2017-06-25 12:50:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.1903262585401535, "perplexity": 4104.492361059811}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320491.13/warc/CC-MAIN-20170625115717-20170625135717-00545.warc.gz"} |
https://brilliant.org/problems/confusion-5/ | # Confusion
Logic Level 1
$\large 3 \square 3=1$
which sign $$(+ \ , \times \ , -)$$ to make the equation above true?
× | 2017-03-26 11:32:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7596665024757385, "perplexity": 12850.172899426581}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1490218189214.2/warc/CC-MAIN-20170322212949-00561-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/87985/quadratic-fields-and-solving-diophantine-equations | # Quadratic fields and solving Diophantine equations
I would like to learn to solve Diophantine equations and I think my next step would be quadratic fields or number fields. What are kind of methods there are to use those on solving equations? And what kind of Diophantine equation can be solved using quadratic fields? Are there just few methods one can list here or should I read some book?
-
You should read a book on algebraic number theory, e.g. Stewart and Tall or Neukirch. – Alex B. Dec 3 '11 at 12:16
Two books that explicitly deal with the connection: Cox's Primes of the Form $x^2 + ny^2$ and Frölich-Taylor's Algebraic Number Theory. – Dylan Moreland Dec 3 '11 at 22:24 | 2013-12-18 20:04:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.496285617351532, "perplexity": 465.3095572344739}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1387345759442/warc/CC-MAIN-20131218054919-00031-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://mathhelpforum.com/calculus/86709-damped-harmonic-oscillation-question-print.html | Damped Harmonic Oscillation Question
• Apr 30th 2009, 08:21 PM
nosh
Damped Harmonic Oscillation Question
If a marble is placed on the end of a horizontal oscillating spring and the harmonic horizontal position of the marble as a function of time is given as :
If x = A ( 2 pi f t)
where A is amplitude
f is frequency
and t is time in seconds
If the spring oscillates every 0.5 seconds and has a maximum displacement of 0.2 m
what is the frequency?
what is the velocity as a function of time ?
how do you write the equation in the form given above for the position of the marble as a function of time ?
• May 1st 2009, 04:34 AM
Showcase_22
Isn't it $x=A \cos ( 2 \pi ft)$?
If the spring oscillates every 0.5 seconds, then isn't the frequency just $\frac{1}{0.5}=2$Hz?
The velocity is $v=\frac{dx}{dt}=-2 \pi Af \sin (2 \pi f t)$.
From here you can normally use the initial conditions to find A. When $t=0, v=0$. | 2018-01-19 08:03:57 | {"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": 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": 0.8657012581825256, "perplexity": 653.2137378565465}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887832.51/warc/CC-MAIN-20180119065719-20180119085719-00292.warc.gz"} |
https://alanzed.wordpress.com/2009/02/13/mit-1803-lecture-6/ | ## MIT 1803 lecture 6
This lecture introduced complex numbers – most of which I knew. But useful to me was the reminder that, when presented with an integral like $\int e^{-x} \cos x dx$ one can solve it by passing to the complex domain, or complexifying the integral, that is, noting that the integrand is the Re part of a complex expression, solving the integral and pulling off the Re part of the answer.
$\int e^{-x} \cos x dx = Re [ \int e^{-x} { e^{ix} + e^{-ix} \over 2} dx ] = {1 \over -2e} ( \cos x - \sin x)$ | 2017-07-21 14:45:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9509959816932678, "perplexity": 465.95655329563346}, "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-2017-30/segments/1500549423785.29/warc/CC-MAIN-20170721142410-20170721162410-00414.warc.gz"} |
End of preview. Expand
in Dataset Viewer.
Dataset Card for "open-web-math-minhash"
An attempt at a "high quality sample" of open-web-math/open-web-math by aggressively applying minhash from text-dedup. The result is 1.82M rows down from the original 6M:
DatasetDict({
train: Dataset({
features: ['url', 'text', 'date', 'metadata'],
num_rows: 1820241
})
})
Usage
Unless you need the metadata, load the text-only config which is only 1.4 GB/5 shards:
from datasets import load_dataset
dataset_config = "text-only"
dataset = load_dataset("BEE-spoke-data/open-web-math-minhash", dataset_config)
making of
On a high-RAM colab TPU (40 cores)
from pathlib import Path
from tqdm.auto import tqdm
ds_name = "open-web-math/open-web-math"
dataset_config = "default"
data_split = 'train'
text_column = 'text'
out_dir = Path(f"output/minhash/{ds_short_name}/{data_split}")
!mkdir -p $out_dir
!python -m text_dedup.minhash \
--path $ds_name \
--name $dataset_config \
--split $data_split \
--cache_dir "./cache" \
--output $out_dir \
--column $text_column \
--ngram 5 --threshold 0.5 \
--hash_func xxh3 --hash_bits 16 --num_perm 64 \
--batch_size 10000
print(f"output dir is:\n\t{out_dir}")
!ls $out_dir
Console:
Resolving data files: 100% 114/114 [00:11<00:00, 9.79it/s]
Fingerprinting... (num_proc=40): 100% 6315233/6315233 [15:27<00:00, 6806.11 examples/s]
Iterating MinHashes...: 100% 632/632 [05:37<00:00, 1.87it/s]
Clustering...: 100% 14/14 [01:13<00:00, 5.22s/it]
Finding clusters... (num_proc=40): 100% 6315233/6315233 [10:57<00:00, 9602.90 examples/s]
Filtering clusters... (num_proc=40): 100% 6315233/6315233 [03:53<00:00, 27069.61 examples/s]
Saving the dataset (33/33 shards): 100% 1820241/1820241 [07:07<00:00, 4260.38 examples/s]
[10/11/23 23:41:46] INFO Loading :
citation
@misc{paster2023openwebmath,
title={OpenWebMath: An Open Dataset of High-Quality Mathematical Web Text},
author={Keiran Paster and Marco Dos Santos and Zhangir Azerbayev and Jimmy Ba},
year={2023},
eprint={2310.06786},
archivePrefix={arXiv},
primaryClass={cs.AI}
}
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