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https://www.esaral.com/q/mark-against-the-correct-answer-in-the-following-38990 | # Mark (√) against the correct answer in the following:
Question:
Mark (√) against the correct answer in the following:
If $f(x)=\left(x^{2}-1\right)$ and $g(x)=(2 x+3)$ then $(g \circ f)(x)=?$
A. $\left(2 x^{2}+3\right)$
B. $\left(3 x^{2}+2\right)$
C. $\left(2 x^{2}+1\right)$
D. None of these
Solution:
$f(x)=\left(x^{2}-1\right)$
$g(x)=(2 x+3)$
$\therefore(g \circ f)(x)=g(f(x))$
$\Rightarrow \mathrm{g}(\mathrm{f}(\mathrm{x}))=2 \mathrm{f}(\mathrm{x})+3$
$\Rightarrow g(f(x))=2\left(\left(x^{2}-1\right)\right)+3=2 x^{2}-2+3=2 x^{2}+1$ | 2023-02-06 22:16:54 | {"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": 0.6820907592773438, "perplexity": 1156.2582410926511}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00648.warc.gz"} |
https://bobsegarini.wordpress.com/tag/super-bowl/ | ## Segarini – The Difference Between Women Artists and “Women” Artists
Posted in Opinion, Review with tags , , , , , , , , , , on February 6, 2017 by segarini
Today the Intertoobz are all a-flutter with praise and pronouncements concerning the performance of a Lady named Ga Ga, seen and heard during the pee break in America’s biggest Sportsball Event of the Year.
Back before decorum was even a word, this Event would not be the attraction it has become, but because of civilization’s sloooowly advancing maturity, there came a modicum of sense and reason that resulted in the feeding of the less fortunate (called “Christians” by those in the know), to lions, tigers, and bears (oh my) and the odd angry horde of hostile gibbons, becoming unacceptable, much to the chagrin of the elite classes and Ruling Kings, Emperors, and Early Republicans….
## Roxanne Tellier – Who’s Sorry Now?
Posted in Opinion with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on February 8, 2015 by segarini
Is it just me, or does it seem like every week – every day, even – of 2015 to date has been rife with some new horror, political revelation, or scandal involving everyone from the guy on the street to a British royal? | 2023-04-01 10:45:05 | {"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": 0.884448230266571, "perplexity": 1608.1002077722528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949958.54/warc/CC-MAIN-20230401094611-20230401124611-00120.warc.gz"} |
https://socratic.org/questions/how-do-you-write-a-polynomial-equation-of-least-degree-given-the-roots-5i-i-i-5i | # How do you write a polynomial equation of least degree given the roots -5i, -i, i, 5i?
Jan 15, 2017
${x}^{4} + 26 {x}^{2} + 25 = 0$
#### Explanation:
Each zero $a$ corresponds to a factor $\left(x - a\right)$.
So we can write:
$f \left(x\right) = \left(x - 5 i\right) \left(x + 5 i\right) \left(x - i\right) \left(x + i\right)$
$\textcolor{w h i t e}{f \left(x\right)} = \left({x}^{2} + 25\right) \left({x}^{2} + 1\right)$
$\textcolor{w h i t e}{f \left(x\right)} = {x}^{4} + 26 {x}^{2} + 25$
So a suitable polynomial equation is:
${x}^{4} + 26 {x}^{2} + 25 = 0$ | 2019-02-19 02:19:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9784345626831055, "perplexity": 1392.3465072435101}, "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-2019-09/segments/1550247489304.34/warc/CC-MAIN-20190219020906-20190219042906-00484.warc.gz"} |
http://mathhelpforum.com/geometry/14073-volume.html | Math Help - volume
1. volume
A spherical cap of radius p and height h is cut from a sphere of radius r. Show that the volume V of the spherical cap can be expressed as
A) (1/3)pi h^2 (3r-h)
B) (1/6)pi h (3p^2 + h^2)
2. Could you perhaps illustrate with a picture what you mean?
3. Originally Posted by janvdl
Could you perhaps illustrate with a picture what you mean?
This is what he means:
4. Hello, Csou090490!
I can help with part (A) . . .
A spherical cap of radius p and height h is cut from a sphere of radius r.
Show that the volume V of the spherical cap can be expressed as:
A) (1/3)πh²(3r - h)
B) (1/6)π h(3p² + h²)
Code:
|
* * *
* | *
* | |:*
* | |::*
| |:::
* | |:h:*
--*---------+-----+---*--
* | r-h * r
|
* | *
* | *
* | *
* * *
|
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ._____
We have a circle: .x² + y² .= . . . y .= .√r² - x² | 2016-05-27 16:34:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8784793019294739, "perplexity": 1258.894065217448}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049276964.14/warc/CC-MAIN-20160524002116-00138-ip-10-185-217-139.ec2.internal.warc.gz"} |
http://www.teachmathematics.net/page/11329/2017-puzzle | # 2017 Puzzle
Be creative and find how many ways you can put together 2,0,1 & 7 to make different numbers.
2017 is the year and this brings a new challenge. This activity is the 2017 puzzle. Using ALL the digits in the year 2017 once and only once (you may not use any other numbers except 2, 0, 1, and 7) write down as many different mathematical expressions that give results for the numbers 1 to 100. You should learn many different tricks along the way to help you and you may even surprise yourself how creative you can be to find solutions to ‘difficult’ numbers.
Resources
The manipulative below may help as a stimulus to start this activity.
Student grid can be printed off
Teachers may wish to display this Classroom Poster and get classes to collate their results.
#### Rules
• Use ALL the digits in the year 2017 (you may not use any other numbers except 2, 0, 1, and 7) to write mathematical expressions that give results for the numbers 1 to 100.
• You may use the arithmetic operations + , - , x , / , square root and ! (see below).
• Indices or exponents may only be made from the digits 2, 0, 1, and 7, for example $$2^{7-1}$$= 64 is allowed; it has used the 2, 1 and 7.
• Multi-digit numbers and decimal points can be used such as 20, 102, .02 but you CANNOT make 30 by combining (2+1)0.
• Recurring decimals can be used using the overhead dots or bar e.g. $$2\div0.\overline{1}$$
• Trigonometric functions can be used if you know how to use them, e.g.$$sin^{-1}(\frac{1}{2})=30°$$
Factorials are allowed
n! = nx(n - 1)x(n - 2)x...x2x1
For example
• 3! = 3x2x1 = 6
• 0! = 1
#### Tips for students
• The four digits 2, 0, 1 & 7 can be used ONCE and once only.
• 0! is a very useful result that will help you a good deal. Use it wisely!
• Make good use of brackets. Your solutions should only have one equal sign in them.
• Remember the order of operations: 2+1x7+0=9 , but (2+1)x7+0=21
• Don’t set your mind necessarily on finding the solution to one particular number. Play with the digits and different operations and see what you can make.
• Try to work in clusters of numbers. If you find the solution to one number maybe you could find the solution to a number one more or one less than the number by a simple manipulation.
Description
Here follows an outline of how the task could be run.
• The class could be introduced to an expression and asked to work out the solution. An example is given in the manipulative above.
• It is important to share some solutions early on to clarify the rules and iron out some misconceptions.
• Check students work so that misunderstandings can be corrected.
• A competitive element could be added to the task.
• Students could be asked to choose a solution that they are most proud of and share it with the class. They can learn from each others' clever tricks!
• Students love entering their correct solutions on a classroom poster. They could take it in turns to enter one at a time with their name written beside it for posterity!
• It is often a good idea to set students targets on the number of solutions you think they might be able to get.
• This puzzle can run for weeks and months especially if incentives are set to find solutions to the more elusive numbers.
• Students can do this puzzle year after year. What a great way to bring the New Year in!
All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. Any unauthorised copying or posting of materials on other websites is an infringement of our copyright and could result in your account being blocked and legal action being taken against you.
## Comments
To post comments you need to log in. If it is your first time you will need to subscribe. | 2017-01-24 17:18:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.3142218291759491, "perplexity": 776.2522689764176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560285001.96/warc/CC-MAIN-20170116095125-00457-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://hal.archives-ouvertes.fr/hal-00542185 | # Bounded discrete walks
Abstract : This article tackles the enumeration and asymptotics of directed lattice paths (that are isomorphic to unidimensional paths) of bounded height (walks below one wall, or between two walls, for $\textit{any}$ finite set of jumps). Thus, for any lattice paths, we give the generating functions of bridges ("discrete'' Brownian bridges) and reflected bridges ("discrete'' reflected Brownian bridges) of a given height. It is a new success of the "kernel method'' that the generating functions of such walks have some nice expressions as symmetric functions in terms of the roots of the kernel. These formulae also lead to fast algorithms for computing the $n$-th Taylor coefficients of the corresponding generating functions. For a large class of walks, we give the discrete distribution of the height of bridges, and show the convergence to a Rayleigh limit law. For the family of walks consisting of a $-1$ jump and many positive jumps, we give more precise bounds for the speed of convergence. We end our article with a heuristic application to bioinformatics that has a high speed-up relative to previous work.
Keywords :
Document type :
Conference papers
Domain :
Cited literature [16 references]
https://hal.inria.fr/hal-00542185
Contributor : Coordination Episciences Iam <>
Submitted on : Thursday, August 20, 2015 - 4:33:30 PM
Last modification on : Thursday, March 5, 2020 - 6:31:07 PM
Long-term archiving on: : Wednesday, April 26, 2017 - 10:10:58 AM
### File
dmAM0103.pdf
Publisher files allowed on an open archive
### Identifiers
• HAL Id : hal-00542185, version 2
### Citation
C. Banderier, P. Nicodème. Bounded discrete walks. pp.35-48. ⟨hal-00542185v2⟩
Record views | 2021-01-15 15:58:35 | {"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": 0.5920435786247253, "perplexity": 2451.2747484360902}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610703495901.0/warc/CC-MAIN-20210115134101-20210115164101-00400.warc.gz"} |
http://www.purplemath.com/learning/viewtopic.php?f=5&t=1724 | Solving equations w fractions (not quite getting it, help!)
Simple patterns, variables, the order of operations, simplification, evaluation, linear equations and graphs, etc.
Solving equations w fractions (not quite getting it, help!)
Hi,
Can someone please explain to me how to do this problem step-by-step
Solve for b: H=5/3(a+2ab)
I know the answer is b=3H-5a/10
However, I'm just unsure how to get there, more specifically how H became 3H.
More, more specifically I don't know how to multiply the fraction with the equation... for the right side I know I convert the a and 2ab into fractions by giving them the same denominator as 5/3 (i.e. 5 * a/3 + 2ab/3)
..But, how did 3 get multiplied with H.. shouldn't it be 5/3*H = 5/3 * H/3? (why is H getting multiplied with the denominator??)
please explain to me how this works
thanks!
onmyown
Posts: 18
Joined: Fri Dec 17, 2010 10:16 pm
onmyown wrote:Can someone please explain to me how to do this problem step-by-step
Solve for b: H=5/3(a+2ab)
....But, how did 3 get multiplied with H.. shouldn't it be 5/3*H = 5/3 * H/3? (why is H getting multiplied with the denominator??)
You need to get "b" by itself. It is currently in the denominator:
. . . . .$H\, =\, \frac{5}{3(a\, +\, 2ab)}$
To undo this, you need to multiply through by the current denominator. This will get the "b" up on the left-hand side.
To get the "b" by itself, you need to get rid of the "3" which is now on top, so you'll need to divide through after you subtract off the 3aH term.
stapel_eliz
Posts: 1797
Joined: Mon Dec 08, 2008 4:22 pm
Re:
stapel_eliz wrote:
onmyown wrote:Can someone please explain to me how to do this problem step-by-step
Solve for b: H=5/3(a+2ab)
....But, how did 3 get multiplied with H.. shouldn't it be 5/3*H = 5/3 * H/3? (why is H getting multiplied with the denominator??)
You need to get "b" by itself. It is currently in the denominator:
. . . . .$H\, =\, \frac{5}{3(a\, +\, 2ab)}$
To undo this, you need to multiply through by the current denominator. This will get the "b" up on the left-hand side.
To get the "b" by itself, you need to get rid of the "3" which is now on top, so you'll need to divide through after you subtract off the 3aH term.
Thank you. It all makes sense now!
onmyown
Posts: 18
Joined: Fri Dec 17, 2010 10:16 pm | 2014-03-09 23:04:05 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 2, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8415067195892334, "perplexity": 1097.782205448048}, "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-2014-10/segments/1394010451932/warc/CC-MAIN-20140305090731-00013-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://i.stanford.edu/TR/CS-TN-96-36.html | Report Number: CS-TN-96-36
Institution: Stanford University, Department of Computer Science
Title: Efficient Snapshot Differential Algorithms for Data Warehousing
Author: Garcia-Molina, Hector
Author: Labio, Wilburt Juan
Date: June 1996
Abstract: Detecting and extracting modifications from information sources is an integral part of data warehousing. For unsophisticated sources, in practice it is often necessary to infer modifications by periodically comparing snapshots of data from the source. Although this em snapshot differential problem is closely related to traditional joins and outerjoins, there are significant differences, which lead to simple new algorithms. In particular, we present algorithms that perform (possibly lossy) compression of records. We also present a {\em window} algorithm that works very well if the snapshots are not very different.'' The algorithms are studied via analysis and an implementation of two of them; the results illustrate the potential gains achievable with the new algorithms.
http://i.stanford.edu/pub/cstr/reports/cs/tn/96/36/CS-TN-96-36.pdf | 2018-07-19 02:14:33 | {"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": 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": 0.7136471271514893, "perplexity": 2086.9232472831845}, "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-2018-30/segments/1531676590443.0/warc/CC-MAIN-20180719012155-20180719032155-00517.warc.gz"} |
https://www.physicsforums.com/threads/vector-calculus-question-relating-to-electrical-dipoles-more-of-a-math-question.559667/ | # Vector calculus question relating to electrical dipoles (more of a math question)
1. Dec 12, 2011
### jsund323
The potential for an ideal electric dipole is given by
V(x,y,z)= pz/(4π ε0(x+y^2+z^2))
In rectangular, spherical, and cylindrical coordinates:
a) Find the electric field, E(x,y,z)= -∇V. (E is a vector, can't figure out how to denote that on my computer).
b) By direct Calculation find ∇•E and ∇XE (E is still vector)
this isn't really a physics question and more a vector calc question, but maybe someone is feeling up to flexing their spherical and cylindrical coordinate skills.
Last edited: Dec 12, 2011
2. Dec 12, 2011
### cragar
the gradient in rectangular coordinates should be straight forward, take the derivatives of the components and then add them up. And then for cylindrical and spherical coordinates change x,y , z in terms of (rho)(theta(phi) or the appropriate variables and then take the gradient. but in cylindrical and spherical you have to be more careful with the gradient because their are terms in front, this should be on the inside cover of your book. | 2017-02-27 02:41:58 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9351418018341064, "perplexity": 1156.2817674240748}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501172404.62/warc/CC-MAIN-20170219104612-00497-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://ravensworthsolutions.co.uk/site/article.php?acadf6=multidimensional-poverty-index-calculation | # multidimensional poverty index calculation
The methodology has been mainly, but not exclusively,[3] applied to developing countries. {@C. 1 1/3) then a household is considered to be 'multiply deprived', or simply 'poor'. Mapa mundial que muestra el índice de desarrollo humano basado en el Informe sobre Desarrollo Humano 2011 del Programa de las Naciones Unidas para el… … Wikipedia Español, Tamil Nadu — தமிழ் நாடு State Tamil Nadu Emblem … Wikipedia, Indice de pauvreté multidimensionnelle — L indice de pauvreté multidimensionnel, en anglais Multidimensional Poverty Index (MPI), est un indice statistique évaluant la pauvreté dans les pays en développement, créé par un département de l Université d Oxford en 2010 et utilisé par le… … Wikipédia en Français, We are using cookies for the best presentation of our site. = The Multidimensional Poverty Index (MPI) was developed in 2010 by Oxford Poverty Human Development Initiative and the United Nations Development Programme. If this household deprivation score exceeds a given threshold (e.g. Those who are MPI poor suffer from deprivation in 69.3% of indicators, on average. = MPIs are useful as an analytical tool to identify the most vulnerable people - the poorest among the poor, revealing poverty patterns within countries and over time, enabling policy makers to target resources and design policies more effectively. L�D����T@dn.�d�X$������y$�'����c�� �4; The Multidimensional Poverty Index was launched by the UNDP and the OPHI in 2010.; MPI is based on the idea that poverty is not unidimensional (not just depends on income and one individual may lack several basic needs like education, health etc. multidimensional index or via multiple indicators than about what multidimensional poverty actually is. 1 [1] The method was developed following increased criticism of monetary and consumption based poverty measures, seeking to capture the deprivations in non-monetary factors that contribute towards well-being. %PDF-1.5 %���� 2010. The Alkire-Foster (AF) method[14] is a way of measuring multidimensional poverty developed by OPHI's Sabina Alkire and James Foster. The indicators may be equally weighted or take different weights. The most common way of measuring poverty is to calculate the percentage of the population who are poor, known as the headcount ratio (H). This, amongst other reasons, has led to the MPI only being calculated for just over 100 countries, where data is available for all these diverse indicators, while HDI is calculated for almost all countries. A person is considered poor if they are deprived in at least 30% of the weighted indicators. These are measured using ten indicators. Deprived if the household's sanitation facility is not improved (according to. Deprived if at least one of the three housing materials for roof, walls and floor are inadequate: the floor is of natural materials and/or the roof and/or walls are of natural or rudimentary materials. [5], MPI advocates state that the method can be used to create a comprehensive picture of people living in poverty, and permits comparisons both across countries, regions and the world and within countries by ethnic group, urban/rural location, as well as other key household and community characteristics. OK, "A wealth of data. Deprived if a child under the age of 18 years has died in the family In the 5 years preceding the survey. %%EOF It compares the situation of countries with respect to acute poverty. {\displaystyle 0.667\times 0.417=0.278}. Child poverty refers to the phenomenon of children living in poverty. To identify the poor, the AF method counts the overlapping or simultaneous deprivations that a person or household experiences in different indicators of poverty. 2393 0 obj <>/Filter/FlateDecode/ID[<16A5D3BB5C4F0A4681BE026B3C2B600D>]/Index[2374 30]/Info 2373 0 R/Length 93/Prev 943046/Root 2375 0 R/Size 2404/Type/XRef/W[1 3 1]>>stream It replaced the Human Poverty Index. Multidimensional Poverty Indices used for purposes other than global comparison have sometimes used different dimensions, including income and consumption. El IPM … Wikipedia Español, Oxford Poverty and Human Development Initiative — The Oxford Poverty and Human Development Initiative (OPHI) is an economic research centre within the Oxford Department of International Development at the University of Oxford, England, that was established in 2007. ), rather it is multidimensional. Poverty is not just the absence of income, money and/or money-like resources required to meet needs. % Three measures in this class are of high importance: M0 can be calculated with ordinal as well as cardinal data, which is why it is most often used. 0.417 Der MPI wurde im Jahr 2010 an der Universität von Oxford für das… … Deutsch Wikipedia, Poverty — Street children sleeping in Mulberry Street – Jacob Riis photo New York, United States (1890) Poverty is the state of one who lacks a certain amount of material possessions or money. Each dimension and each indicator within a dimension is equally weighted. Building on the Foster-Greer-Thorbecke poverty measures, it involves counting the different types of deprivation that individuals experience at the same time, such as a lack of education or employment, or poor health or living standards. Jointly developed by the United Nations Development Programme (UNDP) and the Oxford Poverty … Deprived if the household has no electricity. 0.417 [1], The MPI was created for the 20th Anniversary edition of the UNDP Human Development Report and uses different factors to determine poverty beyond income-based lists. It has since been used to measure acute poverty across over 100 developing countries. Y��cc�5�Vɴp�nbhA��g��7ܧ��$�9\Z�/j"U(�$ZҼe[uqd'��r�r�������k\$���V�QC�ɿ%>L�@��z2e">4N����#�cs��������z���| @��! {\displaystyle {\frac {1+1+0}{3}}=0.667}, 33.33 The AF Method is unique in that by measuring intensity it can distinguish between, for example, a group of poor people who suffer two deprivations on average and a group of poor people who suffer five deprivations on average at the same time. | 2022-01-28 22:38:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4422391951084137, "perplexity": 6150.258609457376}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320306346.64/warc/CC-MAIN-20220128212503-20220129002503-00507.warc.gz"} |
https://www.jobilize.com/calculus/section/piecewise-defined-functions-by-openstax?qcr=www.quizover.com | # 1.2 Basic classes of functions (Page 7/28)
Page 7 / 28
Find the domain for each of the following functions: $f\left(x\right)=\left(5-2x\right)\text{/}\left({x}^{2}+2\right)$ and $g\left(x\right)=\sqrt{5x-1}.$
The domain of $f$ is $\text{(−∞, ∞).}$ The domain of $g$ is $\left\{x|x\ge 1\text{/}5\right\}.$
## Transcendental functions
Thus far, we have discussed algebraic functions. Some functions, however, cannot be described by basic algebraic operations. These functions are known as transcendental functions because they are said to “transcend,” or go beyond, algebra. The most common transcendental functions are trigonometric, exponential, and logarithmic functions. A trigonometric function relates the ratios of two sides of a right triangle. They are $\mathrm{sin}x,\mathrm{cos}x,\mathrm{tan}x,\mathrm{cot}x,\mathrm{sec}x,\text{and}\phantom{\rule{0.2em}{0ex}}\mathrm{csc}x.$ (We discuss trigonometric functions later in the chapter.) An exponential function is a function of the form $f\left(x\right)={b}^{x},$ where the base $b>0,b\ne 1.$ A logarithmic function is a function of the form $f\left(x\right)={\mathrm{log}}_{b}\left(x\right)$ for some constant $b>0,b\ne 1,$ where ${\mathrm{log}}_{b}\left(x\right)=y$ if and only if ${b}^{y}=x.$ (We also discuss exponential and logarithmic functions later in the chapter.)
## Classifying algebraic and transcendental functions
Classify each of the following functions, a. through c., as algebraic or transcendental.
1. $f\left(x\right)=\frac{\sqrt{{x}^{3}+1}}{4x+2}$
2. $f\left(x\right)={2}^{{x}^{2}}$
3. $f\left(x\right)=\text{sin}\left(2x\right)$
1. Since this function involves basic algebraic operations only, it is an algebraic function.
2. This function cannot be written as a formula that involves only basic algebraic operations, so it is transcendental. (Note that algebraic functions can only have powers that are rational numbers.)
3. As in part b., this function cannot be written using a formula involving basic algebraic operations only; therefore, this function is transcendental.
Is $f\left(x\right)=x\text{/}2$ an algebraic or a transcendental function?
Algebraic
## Piecewise-defined functions
Sometimes a function is defined by different formulas on different parts of its domain. A function with this property is known as a piecewise-defined function . The absolute value function is an example of a piecewise-defined function because the formula changes with the sign of $x\text{:}$
$f\left(x\right)=\left\{\begin{array}{c}\text{−}x,x<0\\ x,x\ge 0\end{array}.$
Other piecewise-defined functions may be represented by completely different formulas, depending on the part of the domain in which a point falls. To graph a piecewise-defined function, we graph each part of the function in its respective domain, on the same coordinate system. If the formula for a function is different for $x and $x>a,$ we need to pay special attention to what happens at $x=a$ when we graph the function. Sometimes the graph needs to include an open or closed circle to indicate the value of the function at $x=a.$ We examine this in the next example.
## Graphing a piecewise-defined function
Sketch a graph of the following piecewise-defined function:
$f\left(x\right)=\left\{\begin{array}{l}x+3,\phantom{\rule{3em}{0ex}}x<1\\ {\left(x-2\right)}^{2},\phantom{\rule{1.5em}{0ex}}x\ge 1\end{array}.$
Graph the linear function $y=x+3$ on the interval $\left(\text{−∞},1\right)$ and graph the quadratic function $y={\left(x-2\right)}^{2}$ on the interval $\left[1,\infty \right).$ Since the value of the function at $x=1$ is given by the formula $f\left(x\right)={\left(x-2\right)}^{2},$ we see that $f\left(1\right)=1.$ To indicate this on the graph, we draw a closed circle at the point $\left(1,1\right).$ The value of the function is given by $f\left(x\right)=x+2$ for all $x<1,$ but not at $x=1.$ To indicate this on the graph, we draw an open circle at $\left(1,4\right).$
discuss continuity of x-[x] at [ _1 1]
Given that u = tan–¹(y/x), show that d²u/dx² + d²u/dy²=0
find the limiting value of 5n-3÷2n-7
Use the first principal to solve the following questions 5x-1
175000/9*100-100+164294/9*100-100*4
mode of (x+4) is equal to 10..graph it how?
66
ram
6
ram
6
Cajab
what is domain in calculus
nelson
integrals of 1/6-6x-5x²
derivative of (-x^3+1)%x^2
(-x^5+x^2)/100
(-5x^4+2x)/100
oh sorry it's (-x^3+1)÷x^2
Misha
-5x^4+2x
sorry I didn't understan A with that symbol
find the derivative of the following y=4^e5x y=Cos^2 y=x^inx , x>0 y= 1+x^2/1-x^2 y=Sin ^2 3x + Cos^2 3x please guys I need answer and solutions
differentiate y=(3x-2)^2(2x^2+5) and simplify the result
Ga
72x³-72x²+106x-60
okhiria
y= (2x^2+5)(3x+9)^2
lemmor
solve for dy/dx of y= 8x^3+5x^2-x+5
192x^2+50x-1
Daniel
are you sure? my answer is 24x^2+10x-1 but I'm not sure about my answer .. what do you think?
Ga
24x²+10x-1
Ga
yes
ok ok hehe thanks nice dp ekko hahaha
Ga
hahaha 😂❤️❤️❤️ welcome bro ❤️
Ga
y= (2x^2+5)(3x+9)^2
lemmor
can i join?
Fernando
yes of course
Jug
can anyone teach me integral calculus?
Jug
it's just the opposite of differential calculus
yhin
of coursr
okhiria
but i think, it's more complicated than calculus 1
Jug
Hello can someone help me with calculus one...
Jainaba
find the derivative of y= (2x+3)raise to 2 sorry I didn't know how to put the raise correctly
8x+12
Dhruv
8x+3
okhiria
d the derivative of y= e raised to power x
okhiria
rates of change and tangents to curves
how can find differential Calculus
Kyaw
derivative of ^5√1+x
can you help with this f(×)=square roots 3-4
oscar
using first principle, find the derivative of y=cosx^3
Approximate root 4 without a calculator
Approximate root 4.02 without using a calculator
Tinkeu
2.03
temigbe
unit of energy
Safiyo
< or = or >4.00000001
Fufa
2.01
Cajab
+-2
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https://www.fimfiction.net/blog/838904/bbcode-updates | ## Xaquseg525 followers
Xaquseg is the system administrator for FIMFiction, as well as various misc. development, especially related to security. Non-technical problems are probably best asked to other staff members.
# News Archive
• ## 27 weeks Recent Changelog
We've done various unannounced changes of the past few weeks so I thought I'd group up the things we've done so you guys know what's changed.
• Reorganised user toolbar dropdown to better fit more items
• Added new articles system and moved some existing ones into it
• Redesigned PM page a bit to be cleaner
• Increased font size in major places across the site to improve readability
• Recommended groups list on groups page - WIP
• Tooltips in many locations around the site with helpful tips
• ## 27 weeks Help Articles
Something I've worked on the last couple of days is adding the ability for us to add arbitrary "articles" to the site which we can use for various things. Sort of an extension on the manual articles we've added in the past like the bbcode page, writing guide, etc.
So far I've added 3 guides:
I'd love to know if you guys have any idea for articles that would have helped you out when starting out or anything else that comes to mind.
• ## 55 weeks Night Mode
I've been working on it for ages but only really got the impetus to finish all of it off over the last few days. In the "settings" dropdown at the top on desktop, or the bottom of the slide out bar on mobile you'll find a toggle for night mode. Enjoy!
Oh, and although I've tried to cover everything there is a 100% chance I've missed styling some things so apologies in advance for any funky pages.
• ## 56 weeks Additional Search Update
Hey folks,
Over the last few days I've added a few things to the new search system. A lot of people were unhappy with not being able to filter various things as quickly as they used to be able to. To that end, I've added a little filter dropdown to the right of the search box which effectively contains everything the old sidebar used to. It even has some niceties like quick word count filters and a highly rated filter.
• ## 56 weeks December 2017 Update
Hey guys, got a whole bunch of updates for you today.
# Tags
This is a small but important step on our way to the tagging system I envision. The existing way we handled things like characters and genres has all been merged into a single tagging system. That won't result in much difference for you viewing and using the site but it makes it a lot easier to add new tags especially.
We now have a couple of new tag types: series and warnings.
The series tag is for identifying what series (franchise) your fanfiction contains. I've added a whole ton of various TV shows, movies, comics, books and games but clearly we will have to add a ton more in the coming future. Stories must also contain one of the four MLP tags which are FIM, EqG, Movie and Comic, as this is a pony fanfic site after all. Feel free to bug me on Discord if you have a requirement for a series to be added.
• ## 57 weeks Math BBCode tag
I've added [math] and [mathblock] BBCode tags, which can be used to display formatted math. We've had a few requests for this, particularly for group forum threads and blog posts. Most math-related TeX syntax is supported. (We are currently using MathJax to handle the layout.)
The documentation from the BBCode guide is repeated below for your convenience.
• ## 80 weeks Fimfiction API
If you're not a developer you can probably ignore this post.
It's been like 6 years, but hey, things take time. The API is currently very WIP still but it's ready for people to get working on in our development chat room.
API documentation can be found at https://www.fimfiction.net/developers/api/v2/docs and you should join the Discord Chat and PM me to add you to the private API channel and I can help you get started. The functionality is very limited right now but I'm dedicating all my time to it at the moment and would love to have people add their input to the process.
• ## 84 weeks New BBCode Tags
Hey guys,
One of the features in this new update was reader-side paragraph formatting. This helps improve consistency for readers across the site, especially for those of us who can’t stand reading indented text on a computer screen.
However, one thing that wasn’t accounted for was the legitimate need for specific indenting of passages and for certain blocks of text to have no paragraph formatting. Some examples would be lyrics and poetry.
Taking this into account, we have come up with a couple of new tags that remedy this situation which are documented below (copied directly from the bbcode guide)
## [indent] Indent
The indent tag can be used to, unsurprisingly, indent portions of your text.
[indent]The indent tag can be used to, unsurprisingly, indent portions of your text.[/indent]
It also support levels of indenting
• ## 85 weeks Fimfiction 4.0
It’s been a very very long time coming, but we’ve finally updated the site again. this is by far the biggest update we have ever done. There is a cavalcade of new features but the biggest changes are under the hood and affect how easy it is to extend the site and performance. A change log of everything I can remember can be found below.
There are bound to be unforeseen bugs. If you come across anything major please let us know in the comments (or preferably in the #site-help-and-dev discord channel).
# Miscellaneous / Site Wide
• Dropped support entirely for pre-IE11
• Updated inline searching across the site to order much better. Eg. Typing "Ra" into the tag selector actually shows Rainbow Dash first. On shorter lists like bookshelves, we use a different algorithm that lets you type things like "ril" and it’ll prioritise a shelf called "read it Later".
• ## 85 weeks 💩
So, emojis are now supported all over the site. Go have fun and stuff.
oh god what have we done
Dec
21st
2018
# Site Update » BBCode updates · 5:08pm Dec 21st, 2018
## Performance improvements
Over the last few days I've been working on improving the performance of the BBCode parser. I've managed to implement a few major optimizations, reducing the run time in common cases to around 1/4th to 1/20th compared to the older version. This has reduced total server-side render times on some of the more complicated test pages I've been using to around 50ms–70ms, which should be a noticeable improvement.
## New features
### Opacity
The [opacity] tag is similar to [color], except it controls the transparency of text. This is primarily intended as an alternative to setting text to gray to make it "fade out" that works on both dark and light background colors. Keep in mind that fading the text out will reduce the contrast, which may make it difficult for some users to read, so this should be using sparingly. The opacity can be specified as either a percentage or a decimal between 0.0 and 1.0.
This is 75%
This is 50%
This is 25%
[opacity=75%]This is 75%[/opacity]
[opacity=.5]This is 50%[/opacity]
[opacity=25%]This is 25%[/opacity]
### Footnotes
There's also a somewhat incomplete feature: [footnote]. This allows you to declare footnotes inline with your text, which will then be placed in a list at the bottom. This feature still needs a bit of work, the appearance of the list will be adjusted, some issues with formatting tags will be corrected1, and the placement and numbering rules may be adjusted.
The feature should still work for simple cases however, as long as you don't try to do anything too fancy.
This feature still needs a bit of work, the appearance of the list will be adjusted, some issues with formatting tags will be corrected[footnote]Mostly related to inline formatting tags like [code=bbcode][b][/code] being active across the start or end tag.[/footnote], and the placement and numbering rules may be adjusted.
1. Mostly related to inline formatting tags like [b] being active across the start or end tag.
Report Xaquseg · 2,298 views · #bbcode
• Viewing 1 - 50 of 48
I can see potential with the opacity feature, having dialogue fade out or hiding pieces of text. Interested to see what comes out of these new additions.
Nice! I'll have to test this with fimdic2epub! :D
i will admit i have little to no understanding of the coding you have done, but i do know you have helped make my favorite site on the internet better. thank you.
4983780
People were already doing things like that with [color], but it didn't work very well if you had a different background color from what the author expected...
Thank you based Xaquseg!
Footnotes, eh?
I have a feeling Terry Pratchett fans will love that early Christmas present.
Thanks
Good features. Thanks for all you do!
Neat! Although this may require iisaw and Kris Overstreet to completely reformat their stories unless they like where their “footnotes” currently are.... Also, it seems more like they’re endnotes rather than footnotes, if they go at the very bottom of the post, rather than a page/section as in a print book, unless it’s possible to code them to appear right above or below the next
While you’re fixing things, can you fix the comments counter issue (at least in the desktop browser version) where it says there are currently 1-50 of 10 comments, or 51-100 of 73, rather than the correct count?
NIce
Why do websites insist on translating a zillion different variations of BBCode and Markdown into HTML and CSS for the reader, instead of just making the author use HTML and CSS in the first place??
4983807
...Because that's a security risk?
...Okay, after rewatching, I realized the video is only tangentally related, but it's still a fun watch so I'll leave it in.
Thanks much, Xaquseg, for the optimizations as well as the new tags, they're much appreciated!
I gave the footnote tag a test-drive, and it works great. One question: can the footnote number be made a link to the footnote itself? That way the reader can jump to the footnote, and then back to where they were in the text.
4983780
Hiding text was still possible if you changed the font color to white, although this new feature will make it much easier to hide it in dark mode.
4983814
That'll be coming
4983814
We plan to add that, that falls under "somewhat incomplete"
4983794
Positioning footnotes in a more complex way than "all at the end" is a possible improvement, yes, that's why the position of the notes might change.
Woo, footnotes!1
Now we just need to get them working properly with my browser's find function...
1. For what it's worth, I've made good (ab)use of them in the past.
I've never even thought about needing them before, but now, Celestia damn it I want to find a way to use footnotes.
Thanks Xaquseg! 1 Nice work! 2
Having specific support for footnotes is great, although mostly as a step towards more functional display of footnotes than we have right now - the lack of pagination really makes footnotes a pain to read. Personally I'd most like to see them displayed in a pop-up upon clicking the little number, although having links back and forth is a close second best.
I'm not really sure what the point of zero-opacity text is...
4983892
To write secret messages, duh!
4983892
Yeah, I brought this up in Discord. It's to do evil things, naturally.
Time for some Infinity War memes.
Motherfucker
Neat.
I'm going to walk away.
4983812
4983807
Here's a better one:
Thank you so much for your work! Looks great!
There is a site update post that doesn't contain things that make everything go up in flames, for once?
I assume another pending feature will be showing a preview window of the footnote so we can immediately resume reading where we left off without needing to bookmark our place first? Kinda like with the insert snippets that are in my one story?
I know at least one story that makes heavy use of footnotes, but I don't think these would work for them. Partly because the chapters are very, very long and the footnotes at the bottom have turned out to be too faraway to be useful. So they mostly end up before the next section break. They are also numbered from the start of the story on, so being able to set that as part of the footnote would be helpful.
Automatically putting the footnotes at the next section break would be good for this story. Another choice would be to have a special tag for where to put the footnotes, so every footnote before that would be placed there (allowing for more then one in a given chapter).
Are footnotes gonna be hash links in both sides? Or they're gonna be popping-out boxes on hover, like in some wikis?
4983807
Some sites use so-called "limited HTML", and it's just as inconsistent as BBCode. Not to mention all implementations are very inconsistent with html special characters, and some even either eat "<" and ">", or do double-escaping, which result in them display as < and >. Some implementation print out incorrectly typed tags as text, and some hide them instead. Etc, etc.
At least BBCode thousand times better than textile and markdown, where you can accidentally strike-out fifteen paragraphs, and sometimes you can't use spaces, or have to use spaces.
4983812
4983935
You do realize that as long as you use parser, and not filter, it doesn't matter security-wise if you use square brackets [b] or angle brackets <b>.
Cautiously excited about the footnotes! But sharing 4984065's caveat:
I know at least one story that makes heavy use of footnotes, but I don't think these would work for them. Partly because the chapters are very, very long and the footnotes at the bottom have turned out to be too faraway to be useful.
I'll be happy to start using the feature when it doesn't break my readers' experience by making them manually scroll halfway up and down a page to a tiny, arbitrary target in order to read optional content in-line. They work at the bottom of the page in books because there's no scrolling and the bottom is actually the bottom (as opposed to sitting on top of a stack of comments). But having the tag in place is an awesome start to making it useful, and I can tell you're already mindful of the other issues involved, so thank you for moving this forward!
I now wonder what support for text opacity the various epub viewers have. I was reading a story the other day which annoyingly used different colored text in place of grammar, to distinguish thoughts from different personalities residing in a character's head. The viewer doesn't handle text color ideally, in my opinion, for its dark background viewing mode; it just over-writes the color of all text to make it white. Luckily, it leaves color unaltered in the normal white-background viewing mode. But if I could program, and were writing an ebook reader, I would make it convert all text color styles to a linear-HSB colorspace1, then invert the brightness value, then either use that if the display component of the program could understand it, or convert it all again to the sRGB color space (probably in hexadecimal format to save a smidgeon of space). Or maybe “generating an alternative style sheet” for an entire ebook would be an impractical thing to do for an ebook reader, or there's some more practical solution that hasn't crossed the mind of the person who designed the program I use to read my reading collection. Anyway… The point I wanted to originally make, was that ebook readers don't always work ideally. Although I really do like the idea of having the option for opacity.
As for the footnote tag. I could see that coming in really useful for a lot of stories. Although I do have an idea that could improve it a little… Suppose you want a specific footnote to go to a list in the author's notes section at the bottom or top of your chapter. Suppose, even, that no author' notes section exists for that chapter. Could an optional flag be added to the footnote tag, that signals where you want it to be placed? (at the end of story text|at the authors notes at the beginning of the chapter|at the author's notes at the end of the chapter) And if there is no author's note existing already, then create one to hold the footnotes section? Maybe this is a silly suggestion… But maybe it's not?
1. I'm not actually sure if a linear HSB colorspace is possible. I'd need to do a little searching and researching. For all I know, HSB already is linear, to make it more intuitive to use.
Is anyone else having trouble with their views counter? I updated one of my stories and people are commenting on the story, however the views is still the amount it had before the update.
4983892
The downside is that you can't even read it by highlighting the text. Or even see that there is any text, because the text-highlight will ALSO become transparent.
Further linebreak which would otherwise just be replaced by a single linebreak, which is terrible for formatting.
Good for circumventing some of fimfiction's formatting bugs though.
But... where's my meme function?
4984065
Changeling space program?
4984199
Yeah. My favourite solution for that issue with HTML and footnotes is how Sphinx implemented it.
It hyperlinks the footnote markers to the footnotes and vice-versa and even supports referencing the same footnote from multiple places, which will result in multiple reverse links on the same footnote.
4983935
You don't need BBcode for that. In fact, Markdown (as used on GitHub, StackExchange, and so on) is explicitly designed to not be a security sandbox and supports embedding <html>...</html> chunks in among the lightweight markup.
BBcode is basically a holdover from before developers had easy access to good HTML sanitizers and needed a hack to make "escape all literal HTML, then translate special markup into the accepted subset of it" their alternative.
The proper solution (which is what you're supposed to stick on the output end of a Markdown renderer) is to use a whitelist-based HTML sanitizer built on top of a proper HTML parser. For example:
That way, the markup has nothing to do with your site's security and is purely a matter of user convenience independent from the whitelist you feed into the sanitizer. (And it makes WYSIWYG post editors easy to offer to users who prefer them.)
Then, for belt-and-suspenders safety, design your site so none of the CSS or JavaScript which powers it is declared inline or attached by modifying the DOM, and then declare a Content Security Policy to instruct CSP-supporting browsers to ignore any CSS or JavaScript that's either declared inline within the HTML or served from domains you don't control.
Yay, footnotes!
Doesn't look like the opacity tag works on images. Works with colors, tho'. I'll have to play around with it!
--Sweetie Belle
4983819
If it's of any interest, I just whipped up a POC for footnote tooltips: https://gist.github.com/chall8908/93892e1abd437dbae5052c60be62e1cf
Nice; I used to set my text to just a few hexadecimal values short of pure white to hide stuff in my comments. This opacity tag sounds quite useful, especially if it's added the the comment box toolbar (likely under the "Show More" option, or next to the colour wheel) to made it more obvious and readily-accessible.
The footnote feature could be used to show translations, should a different language (real or fictional) be used in a story. It would also likely differentiate that kind of information from the Author's Note stuff, where miscellaneous information is sometimes placed. It might be primitive now, but I do see it potentially becoming quite useful.
So, there's a feature I've been wanting for a while. Would it be possible to implement a tag that converts whatever is in the tag to the username of a logged in user, or if no one is logged in it displays whatever text is in the tagged area instead? It would make second person stories much more enjoyable to read and far more fun to write if we could have "Anon" read as "Meep the Changeling" if I read it while logged in. I know that DOS can do that with the %username% variable, so I dont' see why BB code can't.
• Viewing 1 - 50 of 48 | 2019-01-21 20:41:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2828848958015442, "perplexity": 1850.6055406100722}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583807724.75/warc/CC-MAIN-20190121193154-20190121215154-00283.warc.gz"} |
http://www.austms.org.au/Publ/JAustMS/V81P2/l65.html | J. Aust. Math. Soc. 81 (2006), 253-278
Homomorphisms of the algebra of locally integrable functions on the half line
Sandy Grabiner Department of Mathematics Pomona College 610 North College Avenue Claremont, CA 91711 USA sgrabiner@pomona.edu
Abstract
Let be a continuous nonzero homomorphism of the convolution algebra and also the unique extension of this homomorphism to . We show that the map is continuous in the weak* and strong operator topologies on , considered as the dual space of and as the multiplier algebra of . Analogous results are proved for homomorphisms from to . For each convolution algebra , restricts to a continuous homomorphism from some to some , and, for each sufficiently large , restricts to a continuous homomorphism from some to . We also determine which continuous homomorphisms between weighted convolution algebras extend to homomorphisms of . We also prove results on convergent nets, continuous semigroups, and bounded sets in that we need in our study of homomorphisms.
Download the article in PDF format (size 211 Kb)
Australian Mathematical Publishing Association Inc. © Australian MS | 2019-03-26 12:28:59 | {"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": 0.9410951733589172, "perplexity": 936.4096660853822}, "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-2019-13/segments/1552912205163.72/warc/CC-MAIN-20190326115319-20190326141319-00064.warc.gz"} |
http://www.koreascience.or.kr/article/JAKO199506776295012.page | # Rat에서 설파메타진의 대사 및 약물동태학
We used rats as the experimental animal for the elucidation of metabolic patterns and pharmacokinetic profiles of SMZ in the rat, by use of the urine and plasma from predetermined intervals, respectively. Information herefrom would give some insight into species differences and sex differences in the metabolism and pharamcokinetics of drugs, at least SMZ in particular. Results would be summarized as follows: 1. There were two hydorxy metabolites(5-hydroxysulfamethazine and 6-hydroxyethylsulfamethazine) and an acetyl derivative($N_4$-acetyl sulfamethazine) in the 24h-collected urine, on confirmation with each standard materials. There were also two unknown metabolites therein. 2. In the viewpoint of quantitative aspect, $N_4$-acetylsulfamethazine was the largest, hence it is assumed that the acetyl pathway is the major one in the metabolism of SMZ in the rat. 3. As regards sex difference in the rat, the male had more metabolic capacity than the female in metabolism of SMZ. 4. The concenteration-time curves of sulfamethazine(20mg/kg, po) in the plasma compartment were fitted to a one-compartment open model by use of a computer program(NONLIN). 5. There were significant differences(P<0.05) in the pharmacokinetics of sulfamethazine between two sexes in the rat, with higher disposition rate in the male. 6. The emergence of $N_4AcSMZ$ metabolized from SMZ was fast in the plasma of the rat. Half-life of $N_4AcSMZ$ was also. significantly different(P<0.05) between two sexes, suggesting differences in the eliminatory capacity of $N_4AcSMZ$. | 2021-03-08 15:58:30 | {"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": 0.606773316860199, "perplexity": 7279.889151020015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1614178385378.96/warc/CC-MAIN-20210308143535-20210308173535-00267.warc.gz"} |
https://number.subwiki.org/wiki/Cunningham_chain_of_the_first_kind | # Cunningham chain of the first kind
## Definition
Let be a natural number. A Cunningham chain of the first kind of length is a sequence of primes such that for each .
A complete Cunningham chain of the first kind is a Cunningham chain of the first kind that cannot be extended further in either direction.
Given a Cunningham chain of the first kind of length , the first prime in the chain is a Sophie Germain prime and the second prime in the chain is a safe prime. More generally, in any Cunningham chain of length , the first primes are Sophie Germain primes and the last primes are safe primes.
## Testing/listing
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A005602
This lists, for every , the smallest prime beginning a complete Cunningham chain of length . | 2022-06-25 19:15:07 | {"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": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9244341254234314, "perplexity": 254.47814150562297}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00705.warc.gz"} |
https://email.esm.psu.edu/pipermail/macosx-tex/2007-January/027628.html | # [OS X TeX] Use of nomencl with TeXShop
Christian Burk maillists at gmx.de
Sat Jan 6 10:15:32 EST 2007
```Am 05.01.2007 um 23:30 schrieb Joshua Smith:
>
> On Jan 5, 2007, at 2:23 PM, Herbert Schulz wrote:
>
>> On Jan 5, 2007, at 4:16 PM, Christian Burk wrote:
>>
>>> Thanks a bunch Josh, but I need some help more... ;)
>>>
>>> I would like to oranize it in an extra file called
>>> "nomenclature.tex" and using \include get it into the entire
>>> document.
[snip]
>> I don't believe that is the intention of the nomencl package. You
>> should include the \nomenclature command just after introducing
>> the idea and all of that data is gathered and a Nomenclature is
>> generated at the end of the document with the \printnomenclature
>> command.
>
> I agree with Herb. What you want may be possible, but I don't know
> how you would do it.
>
> Also consider, if you want to get fancy [...]
I am not that fancy guy. ;) I thought a source out of the
nomenclature would be helpfull for maintaining purposes, but may be
it's not.
Thanks
Christian
P.S.: Is there a way to costumize the header "Nomenclature" to the
german expression? | 2020-09-23 00:45:59 | {"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": 0.8279106616973877, "perplexity": 5485.085938255352}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600400208095.31/warc/CC-MAIN-20200922224013-20200923014013-00475.warc.gz"} |
http://gluon.mxnet.io/chapter06_optimization/momentum-scratch.html | # Momentum from scratch¶
As discussed in the previous chapter, at each iteration stochastic gradient descent (SGD) finds the direction where the objective function can be reduced fastest on a given example. Thus, gradient descent is also known as the method of steepest descent. Essentially, SGD is a myopic algorithm. It doesn’t look very far into the past and it doesn’t think much about the future. At each step, SGD just does whatever looks right just at that moment.
You might wonder, can we do something smarter? It turns out that we can. One class of methods use an idea called momentum. The idea of momentum-based optimizers is to remember the previous gradients from recent optimization steps and to use them to help to do a better job of choosing the direction to move next, acting less like a drunk student walking downhill and more like a rolling ball.In this chapter we’ll motivate and explain SGD with momentum.
## Motivating example¶
In order to motivate the method, let’s start by visualizing a simple quadratic objective function $$f: \mathbb{R}^2 \rightarrow \mathbb{R}$$ taking a two-dimensional vector $$\mathbf{x} = [x_1, x_2]^\top$$ as the input. In the following figure, each contour line indicates points of equivalent value $$f(\mathbf{x})$$. The objective function is minimized in the center and the outer rings have progressively worse values.
The red triangle indicates the starting point for our stochastic gradient descent optimizer. The lines and arrows that follow indicate each step of SGD. You might wonder why the lines don’t just point directly towards the center. That’s because the gradient estimates in SGD are noisy, due to the small sample size. So the gradient steps are noisy even if they are correct on average (unbiased). As you can see, SGD wastes too much time swinging back and forth along the direction in parallel with the $$x_2$$-axis while advancing too slowly along the direction of the $$x_1$$-axis.
## Curvature and Hessian matrix¶
Even if we just did plain old gradient descent, we’d expect our function to bounce around quite a lot. That’s because our gradient is changing as we move around in parameter space due to the curvature of the function.
We can reason about the curvature of objective function by considering their second derivative. The second derivative says how much the gradient changes as we move in parameter space. In one dimension, a second derivative of a function indicates how fast the first derivative changes when the input changes. Thus, it is often considered as a measure of the curvature of a function. It is the rate of change of the rate of change. If you’ve never done calculus before, that might sound rather meta, but you’ll get over it.
Consider the objective function $$f: \mathbb{R}^d \rightarrow \mathbb{R}$$ that takes a multi-dimensional vector $$\mathbf{x} = [x_1, x_2, \ldots, x_d]^\top$$ as the input. Its Hessian matrix $$\mathbf{H} \in \mathbb{R}^{d \times d}$$ collects its second derivatives. Each entry $$(i, j)$$ says how much the gradient of the objective with respect to parameter $$i$$ changes, with a small change in parameter $$j$$.
$\mathbf{H}_{i,j} = \frac{\partial^2 f(\mathbf{x})}{\partial x_i \partial x_j}$
for all $$i, j = 1, \ldots, d$$. Since $$\mathbf{H}$$ is a real symmetric matrix, by spectral theorem, it is orthogonally diagonalizable as
$\mathbf{S}^\top \mathbf{H} \mathbf{S} = \mathbf{\Lambda},$
where $$\mathbf{S}$$ is an orthonormal eigenbasis composed of eigenvectors of $$\mathbf{H}$$ with corresponding eigenvalues in a diagonal matrix $$\mathbf{\Lambda}$$: the eigenvalue $$\mathbf{\Lambda}_{i, i}$$ corresponds to the eigenvector in the $$i^{\text{th}}$$ column of $$\mathbf{S}$$. The second derivative (curvature) of the objective function $$f$$ in any direction $$\mathbf{d}$$ (unit vector) is a quadratic form $$\mathbf{d}^\top \mathbf{H} \mathbf{d}$$. Specifically, if the direction $$\mathbf{d}$$ is an eigenvector of $$\mathbf{H}$$, the curvature of $$f$$ in that direction is equal to the corresponding eigenvalue of $$\mathbf{d}$$. Since the curvature of the objective function in any direction is a weighted average of all the eigenvalues of the Hessian matrix, the curvature is bounded by the minimum and maximum eigenvalues of the Hessian matrix $$\mathbf{H}$$. The ratio of the maximum to the minimum eigenvalue is the condition number of the Hessian matrix $$\mathbf{H}$$.
## Gradient descent in ill-conditioned problems¶
How does the condition number of the Hessian matrix of the objective function affect the performance of gradient descent? Let us revisit the problem in the motivating example.
Recall that gradient descent is a greedy approach that selects the steepest gradient at the current point as the direction of advancement. At the starting point, the search by gradient descent advances more aggressively in the direction of the $$x_2$$-axis than that of the $$x_1$$-axis.
In the plotted problem of the motivating example, the curvature in the direction of the $$x_2$$-axis is much larger than that of the $$x_1$$-axis. Thus, gradient descent tends to overshoot the bottom of the function that is projected to the plane in parallel with the $$x_2$$-axis. At the next iteration, if the gradient along the direction in parallel with the $$x_2$$-axis remains larger, the search continues to advance more aggressively along the direction in parallel with the $$x_2$$-axis and the overshooting continues to take place. As a result, gradient descent wastes too much time swinging back and forth in parallel with the $$x_2$$-axis due to overshooting while the advancement in the direction of the $$x_1$$-axis is too slow.
To generalize, the problem in the motivating example is an ill-conditioned problem. In an ill-conditioned problem, the condition number of the Hessian matrix of the objective function is large. In other words, the ratio of the largest curvature to the smallest is high.
### The momentum algorithm¶
The aforementioned ill-conditioned problems are challenging for gradient descent. By treating gradient descent as a special form of stochastic gradient descent, we can address the challenge with the following momentum algorithm for stochastic gradient descent.
\begin{split}\begin{align*} \mathbf{v} &:= \gamma \mathbf{v} + \eta \nabla f_\mathcal{B}(\mathbf{x}),\\ \mathbf{x} &:= \mathbf{x} - \mathbf{v}, \end{align*}\end{split}
where $$\mathbf{v}$$ is the current velocity and $$\gamma$$ is the momentum parameter. The learning rate $$\eta$$ and the stochastic gradient $$\nabla f_\mathcal{B}(\mathbf{x})$$ with respect to the sampled mini-batch $$\mathcal{B}$$ are both defined in the previous chapter.
It is important to highlight that, the scale of advancement at each iteration now also depends on how aligned the directions of the past gradients are. This scale is the largest when all the past gradients are perfectly aligned to the same direction.
To better understand the momentum parameter $$\gamma$$, let us simplify the scenario by assuming the stochastic gradients $$\nabla f_\mathcal{B}(\mathbf{x})$$ are the same as $$\mathbf{g}$$ throughout the iterations. Since all the gradients are perfectly aligned to the same direction, the momentum algorithm accelerates the advancement along the same direction of $$\mathbf{g}$$ as
\begin{split}\begin{align*} \mathbf{v}_1 &:= \eta\mathbf{g},\\ \mathbf{v}_2 &:= \gamma \mathbf{v}_1 + \eta\mathbf{g} = \eta\mathbf{g} (\gamma + 1),\\ \mathbf{v}_3 &:= \gamma \mathbf{v}_2 + \eta\mathbf{g} = \eta\mathbf{g} (\gamma^2 + \gamma + 1),\\ &\ldots\\ \mathbf{v}_\inf &:= \frac{\eta\mathbf{g}}{1 - \gamma}. \end{align*}\end{split}
Thus, if $$\gamma = 0.99$$, the final velocity is 100 times faster than that of the corresponding gradient descent where the gradient is $$\mathbf{g}$$.
Now with the momentum algorithm, a sample search path can be improved as illustrated in the following figure.
### Experiments¶
For demonstrating the momentum algorithm, we still use the regression problem in the linear regression chapter as a case study. Specifically, we investigate stochastic gradient descent with momentum.
In [1]:
def sgd_momentum(params, vs, lr, mom, batch_size):
for param, v in zip(params, vs):
v[:] = mom * v + lr * param.grad / batch_size
param[:] = param - v
In [2]:
import mxnet as mx
from mxnet import ndarray as nd
from mxnet import gluon
import random
mx.random.seed(1)
random.seed(1)
# Generate data.
num_inputs = 2
num_examples = 1000
true_w = [2, -3.4]
true_b = 4.2
X = nd.random_normal(scale=1, shape=(num_examples, num_inputs))
y = true_w[0] * X[:, 0] + true_w[1] * X[:, 1] + true_b
y += .01 * nd.random_normal(scale=1, shape=y.shape)
dataset = gluon.data.ArrayDataset(X, y)
# Construct data iterator.
def data_iter(batch_size):
idx = list(range(num_examples))
random.shuffle(idx)
for batch_i, i in enumerate(range(0, num_examples, batch_size)):
j = nd.array(idx[i: min(i + batch_size, num_examples)])
yield batch_i, X.take(j), y.take(j)
# Initialize model parameters.
def init_params():
w = nd.random_normal(scale=1, shape=(num_inputs, 1))
b = nd.zeros(shape=(1,))
params = [w, b]
vs = []
for param in params:
#
vs.append(param.zeros_like())
return params, vs
# Linear regression.
def net(X, w, b):
return nd.dot(X, w) + b
# Loss function.
def square_loss(yhat, y):
return (yhat - y.reshape(yhat.shape)) ** 2 / 2
In [3]:
%matplotlib inline
import matplotlib as mpl
mpl.rcParams['figure.dpi']= 120
import matplotlib.pyplot as plt
import numpy as np
def train(batch_size, lr, mom, epochs, period):
assert period >= batch_size and period % batch_size == 0
[w, b], vs = init_params()
total_loss = [np.mean(square_loss(net(X, w, b), y).asnumpy())]
# Epoch starts from 1.
for epoch in range(1, epochs + 1):
# Decay learning rate.
if epoch > 2:
lr *= 0.1
for batch_i, data, label in data_iter(batch_size):
output = net(data, w, b)
loss = square_loss(output, label)
loss.backward()
sgd_momentum([w, b], vs, lr, mom, batch_size)
if batch_i * batch_size % period == 0:
total_loss.append(np.mean(square_loss(net(X, w, b), y).asnumpy()))
print("Batch size %d, Learning rate %f, Epoch %d, loss %.4e" %
(batch_size, lr, epoch, total_loss[-1]))
print('w:', np.reshape(w.asnumpy(), (1, -1)),
'b:', b.asnumpy()[0], '\n')
x_axis = np.linspace(0, epochs, len(total_loss), endpoint=True)
plt.semilogy(x_axis, total_loss)
plt.xlabel('epoch')
plt.ylabel('loss')
plt.show()
In [4]:
train(batch_size=10, lr=0.2, mom=0.9, epochs=3, period=10)
Batch size 10, Learning rate 0.200000, Epoch 1, loss 3.4819e-04
Batch size 10, Learning rate 0.200000, Epoch 2, loss 6.6014e-05
Batch size 10, Learning rate 0.020000, Epoch 3, loss 5.0524e-05
w: [[ 1.99991071 -3.39920688]] b: 4.19865 | 2017-12-12 19:39:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.8411380648612976, "perplexity": 1032.1969362162554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948517917.20/warc/CC-MAIN-20171212192750-20171212212750-00699.warc.gz"} |
http://www.physicsforums.com/showthread.php?s=28a84a7ca4081ca846554459aa976347&p=4277546 | ## Quick question about Dirac delta functions
What does the square of a Dirac delta function look like? Is the approximate graph the same as that of the delta function?
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Quote by black_hole Is the approximate graph the same as that of the delta function?
yes
(only more so! )
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Quote by black_hole What does the square of a Dirac delta function look like?
The square of a Dirac delta function is not defined.
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## Quick question about Dirac delta functions
George is right. There is no way that we can make sense of squares of the Dirac Delta function. Distributions are very strange things and their properties are subtle. Nice operations like squaring don't always make sense.
So the square doesn't exist and so the approximate graph also doesn't exist.
often this question comes up in an electrical engineering class when one is faced with convolving an impulse $\delta(t)$ with another impulse. i.e. what would happen if you had a linear, time-invariant system with impulse response $h(t) = \delta(t)$ and you input to that system $x(t) = \delta(t)$. obviously, the output should be $y(t) = \delta(t)$, but how do you get that from the convolution integral?
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Quote by rbj often this question comes up in an electrical engineering class when one is faced with convolving an impulse $\delta(t)$ with another impulse. i.e. what would happen if you had a linear, time-invariant system with impulse response $h(t) = \delta(t)$ and you input to that system $x(t) = \delta(t)$. obviously, the output should be $y(t) = \delta(t)$, but how do you get that from the convolution integral?
It's important for students to realize that the convolution of two delta functions can be well-defined, as the integral contains both a dummy variable and a free variable: ##\int d\tau~\delta(\tau)\delta(t-\tau) = \delta(t)##. One can interpret the integral as being done over one of the delta functions to give the result (there's probably a much more formal and rigorous way to do this). The problem with something like ##\int d\tau~\delta(\tau)\delta(\tau)## is that the result is naively ##\delta(0)##, which doesn't have a well-defined interpretation (though in some contexts, like quantum field theory, for example, you might see it taken to mean the volume a system which is to be taken to grow infinitely large at the end of the calculation).
Although it looks like the convolution integral will generate the squared delta function integral when t = 0, one has to remember that 'functions' like the delta function are meant to exist under integrals, so t has to remain a free variable. Fixing its value doesn't really make much sense.
Of course, this is a physicist's way of looking at the issue, so there are some gaps in the formality and rigor, and mathematicians should feel free to shore it up (or tear it down, as the case may be) with the appropriate rigor.
Quote by Mute Of course, this is a physicist's way of looking at the issue, so there are some gaps in the formality and rigor, and mathematicians should feel free to shore it up (or tear it down, as the case may be) with the appropriate rigor.
Well, first you need to know the actual definition of convolution of distributions
First, let ##f(x)## and ##g(y)## be distributions on ##\Omega \subset \mathbb{R}##. We define the two variable distribution ##f \oplus g## as
##(f \oplus g, \, \phi(x,y)) := (f(x), \, (g(y), \, \phi(x,y)))##.
We now define ##(f * g, \phi) := (f(x) \oplus g(y), \phi(x+y))##.
Now this is well-defined in any of the following cases:
1. f or g has compact support,
2. both have their support bounded from below,
3. both have their support bounded from above.
Dirac has compact support therefore the convolution exists.
Edit: Now that I think about it, the simples method would be a approximation to identity argument. You would still need to show that the identity holds irrespective of your choice of representative though.
Similar discussions for: Quick question about Dirac delta functions Thread Forum Replies Calculus & Beyond Homework 2 Calculus 1 Calculus 2 Calculus & Beyond Homework 3 Calculus 12 | 2013-06-19 02:35:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8032131791114807, "perplexity": 616.3697139906083}, "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-2013-20/segments/1368707440258/warc/CC-MAIN-20130516123040-00085-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://quant.stackexchange.com/questions/20687/multivariate-garch-in-python | # Multivariate GARCH in Python
Is there a package to run simplified multivariate GARCH models in Python? I found the Arch package but that seems to work on only univariate models. I'd like to test out some of the more simple methods described in Bauwends et. al. (2006) like constant conditional correlation.
Python libraries are preferred though I'll play with R as well.
PYTHON
I have found this class from the statsmodels library for calculating Garch models.
Unfortunately, I have not seen MGARCH class/library. Below you can see the basic information about the garch models in mentioned class from the statsmodels. Probably you have to implement it by your own in python, so this class might be used as a starting point.
Slight correction: the package in R is called rmgarch, not mgarch. It works well with rugarch, which provides a variety of univariate GARCH models. Both packages allow for parallelized computation on local cluster and return a nice and full set of fitted parameters, model specs, etc. I provided some additional links in this post. | 2019-07-16 02:02:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4779623746871948, "perplexity": 1363.8931407401062}, "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-2019-30/segments/1563195524475.48/warc/CC-MAIN-20190716015213-20190716041213-00196.warc.gz"} |
http://www.mathworks.com/help/stats/linearmixedmodel.plotresiduals.html?nocookie=true | Accelerating the pace of engineering and science
# plotResiduals
Class: LinearMixedModel
Plot residuals of linear mixed-effects model
## Syntax
• plotResiduals(lme,plottype) example
• plotResiduals(lme,plottype,Name,Value) example
• h = plotResiduals(___)
## Description
example
plotResiduals(lme,plottype) plots the raw conditional residuals of the linear mixed-effects model lme in a plot of the type specified by plottype.
example
plotResiduals(lme,plottype,Name,Value) also plots the residuals of the linear mixed-effects model lme with additional options specified by one or more name-value pair arguments. For example, you can specify the residual type to plot.
plotResiduals also accepts some other name-value pair arguments that specify the properties of the primary line in the plot. For those name-value pairs, see plot.
h = plotResiduals(___) returns a handle, h, to the lines or patches in the plot of residuals.
## Input Arguments
expand all
### lme — Linear mixed-effects modelLinearMixedModel object
Linear mixed-effects model, returned as a LinearMixedModel object.
For properties and methods of this object, see LinearMixedModel.
### plottype — Type of residual plot'histogram' (default) | 'caseorder' | 'fitted' | 'lagged' | 'probability' | 'symmetry'
Type of residual plot, specified as one of the following strings.
'histogram' Default. Histogram of residuals 'caseorder' Residuals versus case (row) order 'fitted' Residuals versus fitted values 'lagged' Residuals versus lagged residual (r(t) versus r(t – 1)) 'probability' Normal probability plot 'symmetry' Symmetry plot
Example: plotResiduals(lme,'lagged')
### Name-Value Pair Arguments
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
### 'ResidualType' — Residual type'Raw' (default) | 'Pearson' | 'Standardized'
Residual type, specified by the comma-separated pair consisting of ResidualType and one of the following.
Residual TypeConditionalMarginal
'Raw'
${r}_{i}^{C}={\left[y-X\stackrel{^}{\beta }-Z\stackrel{^}{b}\right]}_{i}$
${r}_{i}^{M}={\left[y-X\stackrel{^}{\beta }\right]}_{i}$
'Pearson'
$p{r}_{i}^{C}=\frac{{r}_{i}^{C}}{{\sqrt{\left[{\stackrel{^}{Var}}_{y,b}\left(y-X\beta -Zb\right)\right]}}_{ii}}$
$p{r}_{i}^{M}=\frac{{r}_{i}^{M}}{\sqrt{{\left[{\stackrel{^}{Var}}_{y}\left(y-X\beta \right)\right]}_{ii}}}$
'Standardized'
$s{t}_{i}^{C}=\frac{{r}_{i}^{C}}{\sqrt{{\left[{\stackrel{^}{Var}}_{y}\left({r}^{C}\right)\right]}_{ii}}}$
$s{t}_{i}^{M}=\frac{{r}_{i}^{M}}{\sqrt{{\left[{\stackrel{^}{Var}}_{y}\left({r}^{M}\right)\right]}_{ii}}}$
Example: 'ResidualType','Standardized'
## Output Arguments
expand all
### h — Handle to residual plothandle
Handle to the residual plot, returned as a handle.
## Examples
expand all
### Examine Residuals
Navigate to a folder containing sample data.
```cd(matlabroot)
cd('help/toolbox/stats/examples')```
`load weight`
weight contains data from a longitudinal study, where 20 subjects are randomly assigned to 4 exercise programs, and their weight loss is recorded over six 2-week time periods. This is simulated data.
Store the data in a table. Define Subject and Program as categorical variables.
```tbl = table(InitialWeight,Program,Subject,Week,y);
tbl.Subject = nominal(tbl.Subject);
tbl.Program = nominal(tbl.Program);
```
Fit a linear mixed-effects model where the initial weight, type of program, week, and the interaction between the week and type of program are the fixed effects. The intercept and week vary by subject.
`lme = fitlme(tbl,'y ~ InitialWeight + Program*Week + (Week|Subject)');`
Plot the histogram of the raw residuals.
`plotResiduals(lme)`
Plot the residuals versus the fitted values.
```figure();
plotResiduals(lme,'fitted')```
There is no obvious pattern, so there are no immediate signs of heteroscedasticity.
Create the normal probability plot of residuals.
```figure();
plotResiduals(lme,'probability')```
Data appears to be normal.
Find the observation number for the data that appears to be an outlier to the right of the plot.
`find(residuals(lme)>0.25)`
```ans =
101```
Create a box plot of the raw, Pearson, and standardized residuals.
```r = residuals(lme);
pr = residuals(lme,'ResidualType','Pearson');
st = residuals(lme,'ResidualType','Standardized');
X = [r pr st];
boxplot(X,'labels',{'Raw','Pearson','Standardized'});```
All three box plots point out the outlier on the right tail of the distribution. The box plots of raw and Pearson residuals also point out a second possible outlier on the left tail. Find the corresponding observation number.
```find(pr<-2)
```
```ans =
10```
Plot the raw residuals versus lagged residuals.
`plotResiduals(lme,'lagged')`
There is no obvious pattern in the graph. The residuals do not appear to be correlated. | 2014-12-18 10:43:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "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": 0.6473230123519897, "perplexity": 5610.422088268172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802765846.54/warc/CC-MAIN-20141217075245-00122-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://www.studysmarter.us/textbooks/math/precalculus-enhanced-with-graphing-utilities-6th/graphs/q-126-show-that-the-line-containing-the-points-a-b-and-b-a-a/ | Suggested languages for you:
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Q. 126
Expert-verified
Found in: Page 43
### Precalculus Enhanced with Graphing Utilities
Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465
# Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.
We show that the lines are perpendicular to line $y=x$ and also we show that the midpoints lie on the line $y=x$
See the step by step solution
## Step 1: Given information
We are given that a line contains a point $\left(a,b\right),\left(b,a\right)$
## Step 2: We find the slope of line containing points (a,b)(b,a)
We get
Slope$=\frac{a-b}{b-a}\phantom{\rule{0ex}{0ex}}=-1$
Therefore the slope is $-1$
## Step 3: We find the slope of line y=x and compare them
Comparing the slope with standard equation, we get $slope=1$
And on multiplying both the slopes we get $-1$.
Hence the line containing point $\left(a,b\right)\left(b,a\right)$is perpendicular to line $y=x$
## Step 4: Find the midpoint of the points (a,b)(b,a)
We get,
$M=\left(\frac{a+b}{2},\frac{b+a}{2}\right)$
And clearly this point lies on $y=x$
## Step 5: Conclusion
We proved that the two lines are perpendicular and the midpoint of (a,b) (b,a) lie on the line $y=x$ | 2023-03-29 16:39:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 21, "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": 0.6161389946937561, "perplexity": 738.5605846239384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949009.11/warc/CC-MAIN-20230329151629-20230329181629-00605.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php/Zero_ring | Zero ring
A zero ring is a ring with one element, 0 (equal to 1), with the additive and multiplicative structure of the trivial group. Technically speaking, there are infinitely many zero rings (one for each possible element "0"), but they are all trivially isomorphic, so by abuse of language we may refer to the zero ring.
Proposition. If $R$ is a ring in which $0=1$, then $R$ is a trivial ring.
Proof. For any $x \in R$, we have $$x = 1 \cdot x = 0 \cdot x = 0 . \qquad \blacksquare$$
In the category of rings, the zero ring is a terminal object, through the trivial ring homomorphism. However, it is not an initial object. This can be seen by the fact that ring homomorphisms must preserve the identities. Clearly a ring homomorphism, $\varphi(1_0)$ where $\varphi : \mathbf{0} \to R$ cannot be defined as both $1_R$ and $0_R$ since AoPS defines rings to have multiplicative identity (some sources vary here). It can instead be shown that the integers, $\mathbb{Z}$ is initial in $\mathbf{Ring}$.
Note that by convention there is no "trivial field" or "zero field", as we usually require 0 and 1 to be distinct in fields. | 2022-10-04 23:55:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9126848578453064, "perplexity": 192.0115924467208}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337529.69/warc/CC-MAIN-20221004215917-20221005005917-00202.warc.gz"} |
https://www.intechopen.com/online-first/79942 | Open access peer-reviewed chapter - ONLINE FIRST
# Recent Megafires Provide a Tipping Point for Desertification of Conifer Ecosystems
By Daniel G. Neary
Submitted: July 26th 2021Reviewed: November 12th 2021Published: January 7th 2022
DOI: 10.5772/intechopen.101595
## Abstract
Recent megafires and gigafires are contributing to the desertification of conifer forest ecosystems due to their size and severity. Megafires have been increasing in their frequency in the past two decades of the 21st century. They are classed as such because of being 40,469 to 404,694 ha in size, having high complexity, resisting suppression, and producing desertification due to erosion and vegetation type conversion. Increasingly, gigafires (>404,694 ha) are impacting coniferous forest ecosystems. These were once thought of as only pre-20th century phenomena when fire suppression was in its infancy. Climate change is an insidious inciting factor in large wildfire occurrences. Fire seasons are longer, drier, hotter, and windier due to changes in basic meteorology. Conifer forests have accumulated high fuel loads in the 20th and 21st centuries. Ignition sources in conifer forests have increased as well due to human activities, economic development, and population demographics. Natural ignitions from lightning are increasing as a result of greater severe thunderstorm activity. Drought has predisposed these forests to easy fire ignition and spread. Wildfires are more likely to produce vegetation shifts from conifers to scrublands or grasslands, especially when wildfires occur with higher frequency and severity. Severe erosion after megafires has the collateral damage of reducing conifer resilience and sustainability.
### Keywords
• wildfire
• megafires
• gigafires
• desertification
• type conversion
• drought
## 1. Introduction
Wildfires are now the most common disturbance in forest ecosystems other than tree harvesting [1]. Warmer, dryer, and windier weather conditions that are characterizing climate change-related drought in the western USA and elsewhere are driving wildfire occurrence and severity [2]. Future wildfire conditions are most likely to be aggravated in coniferous and boreal biomes, but grasslands are also at risk of serious disturbance [3]. Wildfire size and terrain features have also contributed to a destructive nexus of conditions that have resulted in unprecedented fire disturbances to wildland and urban landscapes. Forested catchments are particularly susceptible to this disturbance [4, 5].
Fire is not new to the planet. It has been a major disturbance force affecting terrestrial ecosystems since vegetation developed as an abundant fuel 450 million years during the Paleozoic Ordovician Period [6]. The sedimentary record indicates that wildfires have been occurring since the Paleozoic, but they increased substantially with the development of plant fuels in a lightning-filled atmosphere of the Carboniferous Period (307 to 359 million years before the present). Fire was one of the environmental and evolutionary pressures that created forest and grassland ecosystems. Humans then used fire as an ecological agent to further sculpt vegetation to suit their needs [6] What was once a relatively stable and predictable tool for use in forest and grassland ecosystems, is now, under the pressure of changes in the climate and human activity, an unpredictable ecological stressor. Wildfires are now burning in meteorological environments that are hotter, windier, and drier than in previous decades [2]. The result has been on fires increasing numbers, size, severity, and complexity. Forest management has been forced to change to adapt to these conditions by placing more resources into fire suppression and management.
One example can be easily viewed in decadal areas burned by wildfire in the southwestern United States (Figure 1). Accurate wildfire records began tallying areas burned at the turn of the 20th century (1910). For the next eight decades, the cumulative area burned in each decade was steady with less than 20,235 ha (<50,000 ac) burned by wildfires that were small in areal extent. An ecological tipping point occurred in the 1990 to 1999 decade when the burned area doubled due to increasing numbers and size [7]. The next decade (2000 to 2009) saw a 69.3-fold increase. The following decade was characterized by an even larger 110.6-fold increase over the average of the 1910 to 1990 decades. In the first year of the 2020–2029 decade so far, wildfires burned over the record sizes of wildland landscapes.
A second example comes from Australia which suffered another devastating, record-smashing bushfire season in 2019–2021. Australia is no stranger to bushfires but climate change is wreaking havoc on the continent [8]. The 2019–2020 season proved to be unprecedented in many ways [9]. The first major bushfires began even before the official arrival of spring in June. Then, new out-of-control fires ignited at the beginning of Sept. 2019. This was followed by even worse fires at the beginning of November 2019 due to a lengthy drought and increasing temperatures. High temperatures, drought, and high winds in the late summer aggravated the bushfire escalated the crisis again over the first weekend in February. The fires in this outbreak were either extinguished or contained in early March after 9 months of raging around the Australian continent. The infrastructure, ecosystem, and human impacts were staggering.
The bushfires burned more than 18.6 million ha, an area the same as the entire State of Washington in the USA, 70% of New Zealand, or 55% of Finland. At least 3500 houses and 5852 other buildings were burned to some degree. A total of 34 people died as a direct consequence of the bushfires between September 2019 and March 2020, but another 445 died due to other fire-related medical co-morbidities. This was much more than the 170 people estimate that died in the 2009 bushfires. Economic losses were initially estimated at the USA$1.3 billion in insured claims. But it may not be possible to completely determine the real economic loss from the bushfires because of: 1) the difficulties in evaluating intangible losses, 2) the confluence of the bushfires and COVID-19 impacts, 3) mortality of a billion native animals [10], and 4) the impacts on Australian fishing and tourism. The real economic effects probably surpass the infamous Black Saturday fires of 2009 that resulted in losses of the USA$2.9 billion to the Australian economy.
On the other side of the Pacific Ocean, the California wildfire season was record-setting with 9639 fires burning 1,779,730 ha [11]. Direct deaths were about the same as in Australia but there were ten times as many fatalities due to indirect air pollution impacts. The economic cost was much higher at over >\$USA 12.1 billion. The number of buildings destroyed was 10,488 which contributed to the high cost. One gigafire, the August Complex, set the California record for size (417,907 ha) [7]. The 2021 fire season is underway and has the potential to eclipse 2020, which was a record year.
## 2. Wildfire, climate change, and drought
The trends in global wildfire potential under climate change was investigated by Liu et al. [12] using drought indices and general circulation models. It is shown that future wildfire potential increases significantly in the United States, South America, Central Asia, southern Europe, southern Africa, and Australia. Expected changes in drought and fire potential are expected to be the largest and smallest in southern Europe and Australia, respectively. The increased fire potential is mainly caused by warming in the U.S., South America, and Australia and by the combination of warming and drying in the other regions. The results of the Liu et al. suggest dramatic increases in wildfire potential that will require increased future investments in human resources, fire suppression infrastructure, and management activities to prevent fire disasters and recover from fire catastrophes. Stephens et al. [13] examined the role of drought-induced tree mortality in fueling wildfires. Their analysis points out that the scale of the western USA tree mortality creates a risk for even greater landscape-scale wildfires in the coming decades.
## 3. Wildfire characteristics
### 3.1 Ignition sources
The types of wildfire ignition are related to natural sources such as lightning, but more importantly human activities (e.g. agriculture, vehicle operations, and forestry activities), infrastructures (e.g. power lines, railways, etc.), or human behavior (e.g. recreation, delinquency, etc.). The main sources of human-caused ignitions vary by country but also at a regional scale [14, 15]. However, despite its importance in the improvement of fire prevention, knowledge of human-induced fire ignitions is still very limited in most parts of the world [16]. Ignitions by lightning are considerably enhanced by long-term drought plaguing forest regions of the world.
### 3.2 Frequency
Wildfire frequency is a key factor in describing a fire regime. It is a useful concept for comparing the relative role of fire between ecosystems and for describing the degree of departure from historical conditions [17, 18]. Brown [19] contains a discussion of the development of fire regime classifications based on fire characteristics and effects, combinations of factors including fire frequency, periodicity, intensity, size, pattern, season, and depth of burn, severity, and fire periodicity, season, and effects [20]. Several investigators have used modal severity and frequency to map fire regimes in the Western United States (Table 1) [21].
Fire regimeFire frequency (Years)Fire type
I0–35Understory Fire
II0–35Stand Replacement
III35–100Mixed
IV35 * 100Stand Replacement
V>200Stand Replacement
### Table 1.
Fire regime classifications according to Hardy [21].
However, a number of the wildfire factors that affect this classification system have changed substantially in the past three decades. Wildfires are occurring over a longer period (season) and the fire climate is hotter, drier, and windier. This trend has been true for the past three decades and is accelerating. An example of the change in frequency and size of wildfires can be seen in the data from the southwestern USA.
Wildfire burned area tracking started in 1910. For the next eight decades, the total burned area remained under 20,000 ha Figure 1. Starting in 1990, fires began to occur at a higher frequency, size, and severity as the regional climate shifted into a mega-drought. Fires in 2020 and 2021, the current decade, are occurring at a record-setting pace.
### 3.3 Severity
#### 3.3.1 Severity definition
At finer spatial and temporal scales the effects of a specific fire can be described at the stand and community level [2, 22]. The fire term is used to describe the ecological effects of fire severity. It describes both the degree of ecosystem disturbance and the amount of change in ecosystem components. Thus, severity integrates the damaging effect of both the heat pulse above ground and the energy transferred into the soil. In essence, it describes the amount of heat that is released by a fire that ultimately affects ecosystem functions. Fire severity is a good descriptive term that categorizes multiple ecosystem impacts [23]. The most important factors which determine the degree of fire severity are the fuel characteristics and the type of combustion. The amounts of flaming versus smoldering combustion that occur when wildland fuels are burned determine the degree of severity.
Wildfire literature is rife with confusion between the terms fire intensity and fire severity. A consistent distinction between the two terms has emerged in the past three decades as fire science has improved and evolved. Fire managers trained in the science of fire behavior prediction systems now use the term fire intensity in a strict thermodynamic sense to describe the rate of energy released [24]. Fire intensity describes the rate of above-ground fuel consumption and, therefore the energy release rate [25]. It can be measured in thermodynamic terms of heat transfer per unit length of the fireline (kW m−1) [2, 26]. The faster a mass of fuel combusts, the greater the fire intensity and the shorter the time that the soil is subjected to heat impact. Fast-moving wildfires typically do not produce complete litter combustion, whereas slower fires can completely combust the litter layer of soils. The rate at which energy can be transmitted through soils is restricted by the thermal properties of the mineral medium. As mentioned earlier, the duration of burning is critically important to the ultimate effect on soils [27].
Fire intensity is often related to the total amount of energy produced during the combustion process, but it is a measure of both small-scale prescribed fires as well as large-scale wildfires. Most energy released by the flaming combustion of above-ground fuels is transmitted upwards, not downward into the soil [28]. For example, Packham and Pompe [29] determined that only about 5 percent of the heat released by a surface fire occurs as heat pulses are transmitted into the ground. Therefore, fire intensity alone is not a good measure of the amount of fire-derived heat transmitted downward into the soil. Changes that occur in the physical, chemical, and biological properties of the soil are better indicators of heat transfer to the ground. For example, a high-intensity, and fast-moving crown fire will consume little of the surface litter because only a small amount of the heat energy released during the combustion of fuels is transferred downward to the litter surface [22]. In this case, the surface litter is identified as severe and presents as blackened, charred litter, but not completely consumed ash. Fire intensity can be quantitatively measured but fire severity can only be described (low, moderate, or high).
In wildfires in Alaska and North Carolina, fast-spreading crown fires were observed to completely consume the forest canopy but did not even scorch all of the surface fuels. However, if the fire also consumes substantial surface and ground fuels as a result of a longer residence time on a site, more energy is transmitted into the soil. Then, damage to the soil system is much greater. In such cases, a white or white-orange ash layer is often the only postfire material left on the soil surface [2, 30, 31].
Because the actual energy release of fire cannot be easily measured across a burned piece of land, the term fire intensity has limited practical application when evaluating ecosystem responses to fire. Increasingly, the term fire severity is used to indicate the ecosystem effects of fire on the landscape and its components [2, 31]. Fire severity was commonly used to describe the magnitude of negative fire impacts on natural ecosystems in the past. Wider usage of the term to include all fire effects is proposed. In this context, severity does not necessarily imply that there are negative consequences. Thus, a low severity fire may be discontinuous in nature, restoring and maintaining a variety of ecological attributes that are generally viewed as positive. For example, in fire-adapted longleaf pine (Pinus palustris) or ponderosa pine (P. ponderosa) ecosystems, fire is viewed as a necessary disturbance for maintaining the ecological characteristics of these forest types. In contrast, a high severity fire may be a dominant, albeit infrequent, disturbance in a non-fire adapted ecosystem. For example, in spruce (Piceaspp.) forests fire is often a destructive disturbance. Frequent low severity fire is normal in a fire-adapted ecosystem. While all high severity fires may have some significant negative social and ecological impacts, only in the case of non-fire adapted ecosystems is the long-term functioning of the ecosystem significantly altered.
#### 3.3.2 Fire severity classification
Judging fire severity solely on ground-based processes ignores the aboveground dimension of severity implied in the ecological definition of the severity of a disturbance. This is especially important because soil heating is commonly shallow even when surface fires are intense [22, 28]. Fire intensity classes were combined with the depth of burn (char) classes by Ryan and Noste [32] to develop a two-dimensional matrix approach to defining fire severity. Their system is based on two components:
1. An above-ground radiation and convection heat pulse associated with flaming combustion, and
2. A below-ground heat pulse due to conduction from smoldering combustion where duff is present, or radiation from flaming combustion where duff is absent on bare mineral soil.
Fire-intensity classes qualify the relative peak energy release rate (kW m−1), whereas depth-of-burn classes qualify the relative duration of fuel combustion [2]. The concept of severity focuses on the ecological impacts of fire both above-ground and below-ground. Ryan [22] revised the Ryan and Noste [32] surface fire characteristic classes and depth of burn classes. By this nomenclature change, two burned areas would be contrasted as having had, for example, an active spreading-light depth of burn fire versus an intense-moderate depth of burn fire, common in high severity wildfires (Figure 2).
### 3.4 Wildfire size: Megafires and Gigafires
Wildfires burn on a number of scales between and within wildfires. Most do not go beyond the Zone of Prescribed Fire (4 to 400 ha) or the low end of Small Wildfires (400 to 4040 ha) (Table 2). All large fires will have components of smaller-scale fires embedded within them. A change that has occurred in the past three decades is the increasing number of wildfires and the scale of those fires. Mega Fires (4060 to 40,469 ha) are now more common and there is a resurgence of Giga Fires (>404,604 ha) [33, 34].
Fire size classFire burned area rangeFire nameState prov.Actual fire size
haha
Micro10−4“A Burning Stump”
Zone of Prescribed Fires……………………………………………………………………………………………………
A<0.1
B, C, D, E121 to 404
Zone of Small Wildfires………………………………………………………………………………………………………
F
G
404 to 2023
2023 to 4049
H4049 to 20,234Schultz Fire 2010
Cerro Grande Fire 2000
AZ
NM
6100
19,425
I20,234 to 40,469Okanagon Park 2003BC25,600
Zone of Megafires………………………………………………………………………………………………………………
J40,469 to 202,347Rim Fire 2013
Chelaslie River 2014
Rodeo-Chediski 2002
CA
BC
AZ
104,135
133,098
189,655
K202,347 to 404,694Wallow Fire 2012
Biscuit Fire 2002
Dixie Fire 2021
AZ
CA
CA
217,741
229,057
384,150
Zone of Gigafires…………………………………………………………………………………………………………………
L>404,694August Complex 2020CA417,907
Taylor Complex 2004AK428,500
Yellowstone Fire 1988MT/ID607,042
Peshtigo Fire 1871WI/MI1,214,083
Great Fire 1910ID/MT1,600,000
Miramichi Fire 1825NB1,700,000
Chinchaga Fire 1950BC/AL2,000,000
Victoria Black Fri. 1939AUST3,000,000
### Table 2.
Modified wildfire size classes and individual fire examples (from [33, 34]).
The largest Giga Fires known in the historical record are from the 19th and 20th Centuries when fire suppression knowledge, technology, and resources were limited or non-existent. Land managers and owners relied on weather changes to dampen fire activity. Both Giga and Megafires (classes J, K, and L) are more prevalent in the first two decades of the 21st Century due to fuel loadings and climate change. Wildfires are burning in hotter, drier, and windier weather conditions than was experienced in much of the 20th century. The sizes and severities of current wildfires are proving to be much more resistant to suppression activities. Consequently, the infrastructure, ecological, and economic costs continue to escalate.
## 4. Erosion
### 4.1 Types of fire induced erosion
Erosion involves three separate processes that are a function of sediment size, transport medium (water, wind, or air), and velocity. These are (1) detachment, (2) transport, and (3) deposition. Erosion occurs when sediments are affected by water, wind, or air and velocities that are sufficient to detach and transport sediments. Erosion is a natural process occurring on landscapes at different rates and scales depending on geology, topography, vegetation, and climate. Natural rates of erosion vary from <0.01 to 15.00 Mg ha−1 [2, 31]. These rates increase as annual precipitation increases, peaking in semiarid ecoregions on the transition desert to wet forest [35]. This occurs because there is sufficient rainfall to produce erosion from the sparser desert and semiarid grassland covers. As precipitation increases, the landscapes start supporting dry and eventually wet forests, which produce increasingly dense plant and litter covers that decrease natural erosion. However, if landscapes are denuded by disturbances (e.g. fire, grazing, timber harvesting, mining, and so forth), then erosion continues to increase with greater precipitation. Surface physical conditions, topography, and soil hydrological status after wildfires and prescribed fires are important for determining post-fire water flows and the magnitude of erosion (Table 3).
Soil surface conditionInfiltrationRunoffErosion
Litter CharredHighLowLow
Littter ConsumedMediumMediumMedium
Bare SoilLowHighHigh
Water RepellentVery LowVery HighSevere
### Table 3.
Soil surface conditions that affect infiltration, runoff, and erosion after wildfires and prescribed fires (from [31]).
Apart from the consumption of vegetation, erosion is certainly the most visible and dramatic impact of fire. Wildfire suppression, prescribed fire, and post-fire watershed rehabilitation also affect erosion processes in wildland ecosystems. Fire management activities such as fireline construction, temporary roads, and new and unpaved roads receiving heavy vehicle traffic will increase erosion. Stormflows after wildfires will also accelerate erosion rates. Burned Area Emergency Response (BAER) activities on watersheds have the potential to decrease some post-fire erosion to varying degrees depending on the timing, amount, and intensity of rainfall, slope, degree of litter combustion, and the presence of water repellent soils [36].
### 4.2 Sheet, rill, and gully erosion
In sheet erosion, slope surfaces erode somewhat uniformly. This type proceeds to rill erosion in which small, linear, rectangular channels cut into the surface of a slope. Further redevelopment of rills leads to the formation of deep, large, rectangular to v-shaped gully [35]. Another type of slope erosion called dry ravel is initiated by a variety of disturbances, including fire. Dry ravel may best be described as a type of dry grain flow. Fires greatly alter the physical characteristics of hillslopes, stripping them of their protective cover of vegetation and organic litter, and removing log barriers that were naturally trapping sediment. Consequently, during and immediately following fires, large quantities of surface material are released and transit downslope as dry ravel even before rainfall events occur [37]. Dry ravel can equal or exceed rainfall-induced hillslope erosion after a fire in semi-arid ecosystems [38]. In the Oregon Coast Range of the United States, prescribed fires in heavy slash after clearcutting produced non-cohesive soils that were less resistant to the force of gravity [39]. Sixty-four percent of post-fire erosion occurred as dry ravel, not water erosion, happening within the first 24 hours after the end of active fire behavior.
### 4.3 Mass failure erosion
Mass failure erosion includes slope creep, falls, topples, rotational and translational slides, lateral spreads, debris flows, and complex movements. The largest, most dramatic, and main form of mass wasting that delivers sediment to streams are debris flows [40]. Most fire-associated debris flows are associated with the development of water repellent conditions in soils [2]. These mass failures are a large source of localized sediment delivered to stream channels. They can account for 50% of the total post-fire sediment yield in some ecoregions). Wells [41] reported that wildfire in chaparral vegetation in coastal southern California can increase average sediment delivery in large watersheds from 7 to 1910 m3 km−2 yr−1. However, individual storm events in smaller basins can produce much greater sediment yields. Single storms have delivered sediment yields as high as 65,238 m3 km2 in unstable terrain.
### 4.4 Channel destabilization erosion
Fire-related sediment yields depend on fire frequency, climate, vegetation, and geomorphic factors such as topography, geology, and soils [41, 42]. In some regions, more than 60% of the total landscape sediment production over the long term is fire-related. Much of the sediment production can occur the first year after a wildfire [2, 43]. However, a risk of increased sediment in streamflow can persist for 10 or more years after a wildfire. Sediment transported from wildfire scars as a result of increased stream peak flows can adversely affect aquatic habitat, recreation areas, roads, buildings, bridges, and culverts. Management of newly deposited sediments is a problem in both the terrestrial and aquatic environment since fire-derived material can block roads, block culverts, alter drainage patterns, and fill in channels, lakes, and reservoirs [44, 45] (Reid 1993, Rinne 1996).
### 4.5 Effect of water repellent soils on post-fire erosion
Fire affects rainwater infiltration in two ways. First, the combustion of soil organic horizons leaves mineral soil unprotected from raindrop impact. The force of rainfall loosens and disperses fine soil and ash particles, causing the soil surface to seal [46]. Second, soil heating during a fire frequently produces a water-repellent layer at or near the soil surface. This process further impedes water infiltration into the soil. The severity of this water repellency in the surface mineral soil layer, however, decreases over time as it is exposed to moisture, freeze–thaw cycles, and animal and insect burrowing. In many cases, water repellency does not substantially affect infiltration beyond the first year. However, fire-induced repellency can persist for several years. Water repellency has a particularly important effect on two post-fire erosion processes, raindrop splash, and rill formation.
The sequence of rill formation as a result of fire-induced water repellency has been documented to follow several well-defined stages [2]. First, the wettable soil surface layer, if present, is saturated during initial infiltration. Water moves rapidly into the wettable surface ash layer until it encounters a water-repellent layer. This process occurs uniformly or discontinuously over the burned landscape so that when the wetting front reaches the water-repellent layer, it can neither drain downward nor laterally. If the water repellent soil layer is right at the soil surface, runoff starts immediately after rain droplets reach the soil surface. As rainfall continues, water fills all available pores until the wettable soil layer becomes saturated. Because of the underlying water-repellent layer, the saturated pores cannot drain, which creates a positive pore pressure above the water-repellent layer. The shear strength of the soil mass declines and it results in a failure zone located where pore pressures are greatest, at the boundary between the wettable and water-repellent layers. As the water flows down this initial failure zone, turbulent flow develops, which accelerates erosion and entrains particles from both the wettable ash layer and the water-repellent layer. The downward erosion of the water-repellent rill continues until the water-repellent layer is eroded away and water begins infiltrating into the underlying wettable soil. Flow then diminishes, turbulence is reduced, and down-cutting temporarily ceases. The result is a rill that has stabilized immediately below the water-repellent layer. Additional rainfall over time will cause these rills to deepen and widen into a gully network. On a watershed basis, these individual rills and gullies develop into a well-defined drainage network that can extend throughout portions of small and large watersheds. The net result is a dramatic increase in the volume of hydrologic response and a decrease in the timing of runoff from the catchment area.
### 4.6 Post-fire sediment yields
Natural erosion rates for undisturbed forests range from <0.01 to 7 Mg ha−1 yr−1 [2, 47], but do not approach the average upper limit of geologic erosion in highly erodible or mismanaged soils (560 Mg ha−1 yr−1 [48]. These differences are due to natural site factors such as soil and geologic erosivity, rates of geologic uplift, tectonic activity, slope, rainfall amount and intensity, vegetation density, and percent cover. Normal landscape-disturbing activities such as agriculture (560 Mg ha−1 yr−1 [49], mechanical site preparation (15 Mg ha−1 yr−1 [50], and road construction (140 Mg ha−1 yr−1) produce a range of sediment losses.
Sediment yields from fires vary considerably, depending on fire frequency, climate, vegetation, and geomorphic factors such as topography, geology, and soils [2, 51]. In some regions, over 60% of the total landscape sediment production over the long term is fire-related. Much of that sediment loss can occur the first year after a wildfire but may extend to 10 years or more [2, 38, 43]. Sediment yields 1 year after prescribed burns and wildfires range from very low, in flat terrain and in the absence of major rainfall events, to extreme, in steep terrain affected by high-intensity thunderstorms. Erosion on burned areas typically declines in subsequent years as the site stabilizes, but the rate of recovery varies depending on fire severity, vegetation recovery, climate, and depth of soil loss.
Soil erosion following fires has been measured to range from under 0.1 Mg ha−1 yr−1 to 15 Mg ha−1 yr−1 in prescribed burns, and from <0.1 Mg ha−1 yr−1 in low severity wildfire, to more than 369 Mg ha−1 yr−1 in high-severity wildfires on steep slopes [2, 43, 50] More recent analyses have estimated sediment losses after wildfires in steep terrain of upwards of 1500 Mg ha−1 yr−1 from a combination of steep slopes and high-intensity rainfall. Nearly all fires increase sediment yield, but wildfires in steep terrain produce the greatest amounts, >1500 Mg ha−1 yr−1 [52]. Sediment yields usually are usually the highest during the first year after a fire and then decline in subsequent years. However, if precipitation is below normal, the peak sediment delivery year might be delayed. In semiarid areas, postfire sediment transport is episodic in nature, and the delay may be longer. All fires increase sediment yield, but it is the combination of steep slopes, high severity fire, and intense rainfall that is the most problematic.
There is increasing evidence that short-duration, high-intensity rainfall (>50 mm h−1 in 10–15 minute bursts) over areas of about 1 km2 often produces flood flows that result in large amounts of sediment transport [31]. Athunderstorm after the 2010 Schultz Fire in Arizona had a peak rainfall of 24 mm in 10 minutes and resulted in debris flows and floods that had a return period of >1000 years [52]. High severity fire (>70% coverage), steep slopes (>100%), and intense rainfall contributed to the unusual erosion. Best Management Practices certainly have value in reducing sediment losses from prescribed fires. However, mitigative techniques for reducing sediment losses after wildfires often that are often used as part of burned area emergency watershed response (BAER), have their limitations and cannot really cope with large erosion events.
After wildfires, streamflow turbidity usually increases due to the suspension of ash and silt-to-clay-sized soil particles [53]. Turbidity is an important water quality parameter because high turbidity reduces municipal water quality and can adversely affect fish and other aquatic organisms. It is often the most easily visible water quality effect of fires [2]. Less is known about turbidity than sedimentation in general because it is difficult to measure, highly transient, and extremely variable. Extra coarse sediments (sand, gravel, boulders) transported off of burned areas as a consequence of increased storm peak flows can adversely affect aquatic habitat, recreation areas, and reservoirs. Deposition of fine sediments as well as the previously mentioned coarse sediments destroys aquatic and riparian habitat, reduces the storage capacity of lakes and reservoirs, negatively affects stream and lake biota, degrades water quality, and imperils infrastructure [2, 45].
## 5. Desertification
Desertification was introduced into the fire-related lexicon in the 1940s by [54] before the modern outbreak of large fires. Although there is no general agreement on the definition of the term it is not necessarily associated with a classical desert. It is a landscape deterioration process that involves reductions of plant and soil ecosystem services. Desertification occurs on a continuum and is usually associated with human activities, especially erosion. The loss of key plant species and diversity, and erosion perturbation of soil physical properties and functions are key factors in the progression of desertification. The environmental hazards that result are most notably losses of soil fiber and food production capability, declines in water supply capability of watersheds [55], accelerated erosion of key soil horizons, and vegetation type conversions.
The desertification process involves a shift in the normal ecosystem dynamic to a lower disturbed, but stable state (Figure 3). Fire-resistant forest ecosystems are characterized by a natural variability that stays within a normal range of disturbance and recovery. Fire resilient forests are disturbed from their normal range of variability but they recover rapidly or slowly. Excessive wildfire disturbance that results in the loss of ecosystem integrity pushes a forest to a lower system state that may never recover or take excessively long periods of time to do so [56].
## 6. Type conversion
Type conversions of ponderosa pine to chaparral scrublands is an example of loss of ecosystem integrity. Vegetation conversion from stable conifer forests to fire-prone scrublands usually produces an increase in fire frequency and severity which prolongs ecosystem persistence at a lower, desertified system state (Figure 3). Under these conditions, desertification magnifies the impact of the fire scale and the persistence of disturbance plant species [57, 58]. These investigators clearly point out the role of fire severity in driving plant community-type conversions. Keeley [58] The greatest threat to the persistence of native California vegetation types is type conversion to herbaceous species more resilient to and more conducive to frequent fires. These fires are more likely to impact conifer species and prevent the re-colonization of severely burned sites [59]. Since 1996, high-severity crown fires in Southwestern ponderosa pine forests have produced large treeless areas, which are unprecedented in the regional historic record [60]. Other dry conifer forests, similar to ponderosa pine, are also experiencing extensive levels of high severity fire and type conversions to grasses and fire-prone scrub species.
## 7. Conclusion
It is clear now at the beginning of the 21st Century that changes in the climate have accentuated fire weather. Fires are now burning in hotter, drier, and windier conditions than they were 30 years ago. Wildfires are also burning into higher elevations, due to a warming climate. This climate condition has led to larger and higher severity wildfires since fires are more difficult to suppress and contain safely in steep terrain. In addition, fire seasons are now 4 months longer. In some areas, such as California, the fires season is 12 months long. This fire situation has provided an ecological tipping point leading to accelerated desertification of conifer ecosystems. This condition limits the success of management interventions to reverse desertification.
## Acknowledgments
The author would like to acknowledge the mentoring, inspiration, and scientific contributions of Dr. Leonard DeBano, Rocky Mountain Research Station, Tucson, Arizona (Deceased). Research support was provided by the Air, Water, Aquatic Environments Program, Rocky Mountain Research Station, USDA Forest Service.
## Conflict of interest
The authors declare that there are no conflicts of interest related to the subject of this paper.
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Daniel G. Neary (January 7th 2022). Recent Megafires Provide a Tipping Point for Desertification of Conifer Ecosystems [Online First], IntechOpen, DOI: 10.5772/intechopen.101595. Available from: | 2022-01-28 17:14:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5124190449714661, "perplexity": 5902.144449361468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320306301.52/warc/CC-MAIN-20220128152530-20220128182530-00636.warc.gz"} |
https://electronics.stackexchange.com/questions/394177/drain-voltage-of-jfet-n-type-depletion | # drain voltage of JFET (N type depletion)
I am trying to figure out the drain voltage of the JFET (N type depletion) ATF33143, given the architecture shown in the image below.
I understand that it's basically a voltage divider and that $V_{out} = I_D R_{JFET}$, where $R_{JFET}$ is a function of $V_G$.
In the datasheet for the JFET, there is $I_{ds}$ vs $V_{ds}$ for various $V_G$ values.
I am trying to figure out the voltage output fluctuation as a function of the fluctuation in $V_{G}$.
Is there a simple equation to represent such a relation?
• JFETs have a square law dependency between V(gate,channel) and the Drain current. – analogsystemsrf Sep 3 '18 at 21:55 | 2019-05-24 09:57:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6279979944229126, "perplexity": 663.4699633571232}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257601.8/warc/CC-MAIN-20190524084432-20190524110432-00442.warc.gz"} |
https://www.physicsforums.com/threads/what-are-my-options-for-inline-tex.747676/ | # What are my options for inline TeX?
1. Apr 8, 2014
Hello there,
I noticed I can use the traditional double $$-symbol for line-broken TeX. That is convenient. However I discovered that math goes here using single -symbol does not work. What are my options for inline-TeX? Thank you for your time. Kind regards, Marius 2. Apr 8, 2014 ### George Jones Staff Emeritus Instead of$$, use $on both sides of inline math. 3. Apr 8, 2014 ### Jonsson If$d(f(x),f(y)) \leq s\,d(x,y)$and$0<s<1$, then$f## is a contraction.
Yay, it works! :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook | 2017-08-21 04:14:31 | {"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": 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": 0.8840466737747192, "perplexity": 14927.47187311675}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886107487.10/warc/CC-MAIN-20170821022354-20170821042354-00715.warc.gz"} |
https://cadabra.science/qa/298/epsilon_to_delta-for-different-type-of-indices | # epsilon_to_delta for different type of indices
+1 vote
Let's say I have fields with both spin and isospin indices. A great feature of Cadabra is that it can deal with multiple index types -- so I can actually define spin and isospin indices separately. But when I use epsilon_to_delta on products of epsilon tensors with spin and isospin indices, it produces generalized deltas with mixed spin and isospin indices, that I find a little awkward to deal with.
To be more concrete, I define the spin and isospin indices:
{a,b,c,d}::Indices(isospin,position=fixed).
{a,b,c,d}::Integer(1..2).
{i,j,k,l}::Indices(spin,position=fixed).
{i,j,k,l}::Integer(1..2).
In an attempt to keep the spin and isospin space from mixing with each other, I define two EpsilonTensors: $\epsilon_{i j}$ for the spin indices, and $E_{a b}$ for the isospin indices.
\delta{#}::KroneckerDelta.
# EpsilonTensor for spin indices
\epsilon_{i j}::EpsilonTensor(delta=\delta).
\epsilon^{i j}::EpsilonTensor(delta=\delta).
# EpsilonTensor for isospin indices
E_{a b}::EpsilonTensor(delta=\delta).
E^{a b}::EpsilonTensor(delta=\delta).
Now, epsilon_to_delta works fine for a product like $\epsilon_{i j} \epsilon^{i k}E_{a b} E^{a c}$:
ex:= \epsilon_{i j} \epsilon^{i k} E_{a b} E^{a c};
epsilon_to_delta(_,repeat=True);
This immediately gives me $$\delta_{j}^{k} \delta_{b}^{c},$$ as expected. But when I try the same thing in a different order, such as $E_{a b} \epsilon_{i j} \epsilon^{i k} E^{a c}$:
ex:= E_{a b} \epsilon_{i j} \epsilon^{i k} E^{a c};
epsilon_to_delta(_,repeat=True);
I get $$4δ_{aibj} δ^{iakc},$$ where the generalized delta has mixed the two types of indices. I tried with two separate KroneckerDelta for spin and isospin epsilon tensors as well, but it does not seem to help either.
At this point, I have to do expand_delta, distribute, eliminate_kronecker to get to the result I want. Alternatively, sorting the product first and then using epsilon_to_delta avoids this problem too. But can I tell Cadabra to only use epsilon_to_delta on same "type" of EpsilonTensors so that this situation does not arise at all? Is there a better way of achieving this?
I hope the question was clear. Thanks for the help!
I am using Cadabra2 version 2.1.4 compiled from source.
I knew you were going to point out that bug the moment I typed the answer to your previous question ;-) At the moment, the best workaround is to first sort expressions so that all $\epsilon$s sit next to each other, by doing a sort_product. That will still break when you have an odd number of $\epsilon$s or an odd number of $E$s, so you have to be careful. | 2023-03-27 01:21:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7763567566871643, "perplexity": 781.9037163415788}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00178.warc.gz"} |
https://www.omnicalculator.com/chemistry/saponification-value | # Saponification Value Calculator
Created by Komal Rafay
Reviewed by Łucja Zaborowska, MD, PhD candidate and Adena Benn
Last updated: Mar 10, 2023
Our saponification value calculator is one of those tools that you didn't know you needed until you found it. You might have already guessed that it calculates the saponification value of fats and oils that can make soap. But did you know that is not all you will learn today?
This article has a lot in store for you:
• How to calculate saponification value;
• What is the saponification number; and
• Some saponification value calculation examples and much more.
So, let's dive in and soak in all the knowledge.
## What is saponification value?
Saponifying is the process of making soap.
The saponification value helps you to determine whether a particular fat or oil can make good soap. You may denote it as SV or SN.
The saponification value or saponification number indicates the amount of potassium or sodium hydroxide needed to saponify one gram of fat.
The saponification number is also crucial in helping to determine the parts of the fat that do not make soap (which we will learn about in a later section).
Another synonym for SV is the Koettstorfer number.
The unit used to measure the saponification value is mg/g (milligrams per gram).
🙋 Might we suggest trying out our protein solubility calculator to determine the protein content in different foods?
## Saponification value calculator
You'd be glad to have access to the saponification value calculator, as we don't just give you the value as a result but talk about how it happens.
Now, we will look at how you can use this tool and determine the saponification value.
1. Input the volume of the HCl (hydrochloric acid) solution of the blank run in milliliters; blank runs set the baseline for experiments and are taken place in the absence of an analyte (the substance to be tested).
2. Input the volume of the HCl solution of the sample. You may choose any unit as per your requirement; the default is milliliters(ml).
3. Input the molarity of the HCl solution. The default unit is moles per liter (mol/L).
4. Lastly, input the weight of the fat/oil. The default unit is grams, but you can choose any based on your requirement.
5. The tool displays the result as the saponification value of the fat in milligrams per gram(mg/g).
For instance, if you enter the blank run as $3.7 \text{ ml}$, the sample run as $2.1 \text{ ml}$, the molarity of HCl as $40 \text{ mol/L}$, and the weight of the fat as $52 \text{ g}$, the tool determines the saponification value of $69.05 \text{ mg/g}$.
💡 We have a molarity calculator, a tool for converting the mass concentration of any solution to molar concentration (or recalculating grams per ml to moles). You may want to check it out.
## Significance of saponification value and unsaponifiables
Saponification value helps check for adulteration, a process of adding a substance to another, reducing the original substance's quality and effectiveness.
We can also determine the oil's ability to make soap by observing its saponification number. If it is low, then the oil won't be able to make soap, and if it is high, the fat is better at making soap.
Knowing the saponification value is useful in identifying the amount of "the unsaponifiable matter in the fat."
You might be wondering what unsaponifiable matters are. Well, think of them as your least favorite subject in school. You might not like it, but it is still part of the syllabus. In the same way, fats have components that do not make soap but are still a part of the fat. They are insoluble in water but soluble in organic solvents.
Just like you must pass your least favorite subject to complete school, the unsaponifiable matters are significant in providing other properties to the soap, like moisturization and texture. Still, they cannot exceed a certain amount.
🔎 Would you like to try out our molecular weight calculator? It computes the mass of a given molecule without using the periodic table of elements.
## Saponification value formula
Knowing the formula for something as significant as the saponification number seems worth the effort.
$\scriptsize \rm SV = \frac {(Blank - Sample) × Molarity × 56.1} { Weight}$
where:
• $\text{SV}$ – The saponification value;
• $\text{Blank }$ – The volume of HCl(hydrochloric acid) solution for the blank run;
• $\text{Sample}$ – The volume of HCl the sample to test;
• $\text{Molarity}$ – Molarity of HCl solution;
• $\text{56.1}$ – Molecular weight of KOH (potassium hydroxide); and
• $\text{Weight}$ – Weight of the sample.
## Saponification value table
The soaps made with KOH are different from the ones made with NaOH (sodium hydroxide), which homemade soap makers use. NaOH is also known as lye, and it produces soap bars, unlike KOH-based soaps that make paste and gel or liquid soaps.
The SV values are also significant in determining the amount of lye needed to make soap bars.
Below is a table for some common oils and fats and their saponification number.
Oil / Fat
Saponification value
Beeswax
60-102
Canola oil
182-193
Cocoa butter
192-200
Coconut oil
248-265
Fish oil
179-200
Lard
192-203
Olive oil
184-196
Shea butter
170-190
Soybean oil
187-195
Sunflower oil
189-195
## FAQ
### How can I calculate the saponification value of oils?
The saponification number, though crucial, is easy to calculate. Follow the steps below, and you will have the answer.
1. Subtract the volume of HCl for the sample from the blank;
2. Multiply the result by the molarity of the HCl solution;
3. Next, multiply the result by 56.1, the molecular weight of potassium hydroxide; and
4. Lastly, divide the result by the sample's weight in grams.
### What is the saponification number if molarity and weight are 0.7mol/L and 20g, respectively?
The saponification number is 3.534 mg/g if the molarity is 0.7 mol/L and the weight of the sample is 20 g.
To achieve this result, the volume of HCl solution for the blank run is 2 ml and 0.2 ml for the sample.
### What does a high saponification value mean?
A large saponification number(SV) indicates an oil's ability to make good soap. You can also determine the fatty acid chain length of the sample using the SV. A higher SV means a small to medium-length chain.
The higher the saponification value is, the better the oil can saponify (produce soap).
### Is saponification value the same as saponification number?
Yes, saponification value is also called saponification number. They both mean the same thing. And it is sometimes also referred to as Koettstorfer number.
The saponification value denotes the amount of potassium or sodium hydroxide (KOH), (NaOH), in milligrams, needed to create soap from one gram of fat.
Komal Rafay
HCl for blank (B)
ml
HCl for sample (S)
ml
Molarity (M)
mol /
liters
Weight of oil / fat (W)
g
Saponification value (SV)
mg/g
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https://chat.stackexchange.com/transcript/71/2022/1/28 | 00:00 - 20:0020:00 - 00:00
12:16 AM
regarding the electromagn. tensor , what is the difference between these 2 notations $F^{\mu \nu}$ and $F^{\mu}_{\nu}$
12:50 AM
Anyone can help me with a proof of symmetry for the electromagn. energy stress tensor ?
3 hours later…
3:35 AM
@imbAF Different transformation properties? I'm not sure what kind of answer you're looking for here. Do you know the meaning of upper and lower indices?
@imbAF Have you heard of the Belinfante procedure?
6 hours later…
9:15 AM
no I havent
I am trying to prove that the electromag. stress energy tensor is symmetric. The following was done $F^{\mu}_{\lambda}F^{\lambda \nu}=F^{\mu \delta}g_{\delta \lambda}F^{\lambda \nu}=(-F^{\delta \mu})(-F^{\nu \lambda})g_{\delta \lambda}$
As we can see here, we displaced the metric tensor at the right side
can you do that in tensor algebra?
moving tensors without caring? Isn't that a problem? Doesn't it cause any problem?
@imbAF what do you mean by "moving tensors without caring"?
it's in the formula i habe
gave
$g$ was in between
all of $F^{\delta\mu}, F^{\nu\lambda}, g_{\delta\lambda}$ are just numbers
then it was moved to the right
why wouldn't they commute?
9:27 AM
numbers do
but since they are part of matricies (in our case)
we know that for 2 matricies A B =/= B A
just because they are "part of matrices" doesn't mean they're somehow not numbers
if you write matrix multiplication as $(A\cdot B)_{ik} = \sum_j A_{ij}B_{jk}$, then you can equally well write $\sum_j B_{jk}A_{ij}$, there's no difference
Yes, but here you have numbers multiplying too : A,B matrices than : $A \cdot B$=/= $B \cdot A$, or not?
aha ok
note that the latter is not $(B\cdot A)_{ik}$, it's still $(A\cdot B)_{ik}$
I didn't get this last part
I'm saying $(A\cdot B)_{ik} = \sum_j A_{ij}B_{jk} = \sum_j B_{jk}A_{ij}$
changing the order of multiplication of the components does not change anything on the level of the matrices as long as you leave the indices as they are
(that's one reason physicists love index notation so much :P)
9:33 AM
I see
I was considering always that matrix multiplication is not commutative
and I thought, how can we move the components so freely around
In einstein notation, we say that the double index represents a sum. So if we have $F^{\mu \mu}$ and $F^{\mu}_{\mu}$, here the first one only is a way of representing an element of the 2nd order tensor (matrix) while the 2nd one is a sum over the elements of the main diagonal. But in the einstein convention, the first term also has a repeated index. Which means, we should sum over it. But that doesn't make sense.
So is it really enough to say that we need repeated indicies, and not repeated indices + one should be an superscript and the other a subscript (idk what is the term used in this case, i forgot it) , to indicate summation?
@imbAF $F^{\mu\mu}$ is simply not an allowed term with summation convention
if you have a double index and it's not one upper, one lower, then something has gone wrong
wait
$\Theta^{\mu}_{\mu}=g_{\mu \nu} \Theta^{\mu \nu}$
here you have the same index, but one up and one down
I got it
My mistake
1 hour later…
10:54 AM
Is there a gauge theory with an $SL(4)$ gauge
The closest I can find is unimodular gravity but it's not a direct reduction
nice gauge theories have compact gauge groups :P
$SO(3,1)$ isn't compact
sure, and GR sucks :P
It kind of does for r < 3r_s
11:12 AM
::groan::
@JohnRennie is that a general relativity joke too specific for me to understand?
GR doesn't need unitarity
11:28 AM
SL(4) gauge would give rise to some scalar potential and I tried looking into scalar gravities, but couldn't find anything about that
Nobody seems to have tried a gauge version of Nordstrom theory
11:46 AM
@satan29 :-)
12:21 PM
the metric tensor $g_{\mu \nu}$ is a diagonal matrix with the first element a pozitive 1 and the rest neg. 1
shouldn't $g^{\mu \nu}$ be the opposite?
With the first diagonal element a neg. 1 and the rest pos. 1?
@imbAF why should it be?
what is your definition of $g^{\mu\nu}$ in terms of $g_{\mu\nu}$?
just write it down and carefully compute it
I know that both represent a matrix with diagonal elements 1, the first being pos. and the rest neg
but
In the mathematical field of differential geometry, one definition of a metric tensor is a type of function which takes as input a pair of tangent vectors v and w at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar g(v, w) in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space. In the same way as a dot product, metric tensors are used to define the length of and angle between tangent vectors. Through integration, the metric tensor allows one to define and compute the length of curves on the...
Here you see the reverse
where?
and if they are the same, what is then the difference? does one help lower an index while the other to raise an index?
I highlighted it
In the mathematical field of differential geometry, one definition of a metric tensor is a type of function which takes as input a pair of tangent vectors v and w at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar g(v, w) in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space. In the same way as a dot product, metric tensors are used to define the length of and angle between tangent vectors. Through integration, the metric tensor allows one to define and compute the length of curves on the...
Lorentzian metrics from relativity
I can see that the URL is weird, but whatever you're doing doesn't do anything for me except open the article at its beginning
12:26 PM
Lorentzian metrics from relativity in this section, in the end
that worked
I don't see anything about $g_{\mu\nu}$ and $g^{\mu\nu}$ being different there
the matrices are different
I just see the statement that whether the metric is 1,-1,-1,-1 or -1,1,1,1 depends on a choice
@imbAF Are we reading the same thing? I don't see any statement that $g_{\mu\nu}$ is different from $g^{\mu\nu}$, I just see a statement that $g$ can be one matrix or the other.
12:31 PM
I took it in alignment to what we learned briefly about the contra and covariant notations of a four vector
maybe you shouldn't interpret things into the article it's not actually saying :P
How could I know lol, I am just blindly walking in a bridge
that;s how it feels to do tensor algebra with no tensor algebra classes
it's just saying that whether you choose to have 1,-1,-1,-1 or -1,1,1,1 depends on your convention, you can do relativity with both, you just need to be careful that the physical meaning of positive/negative spacetime interval reverses
welcome to sign conventions, one of the most annoying eternal curses of theoretical physics :P
lmao so it's not only me lol
One thing for example, I am leaving the rest and focusing on this part of my notation
$(-F^{\delta \mu})(-F^{\nu \lambda})g_{\lambda \delta}=F^{\delta \mu}F^{\nu \delta}$. Could this also be written as : $F^{\nu \lambda}F^{\mu}_{\lambda}$. I think no, the reason being that in the first term $\delta$ is in the left and not the right. We could do that by using the antisymmetri of it, which would give me a minus in my formula. But I am not sure. Basically I am asking why did the metric tensor "collaborated" with the 2nd term and not the first?
$F^{\delta\mu}F^{\nu\delta}$ is wrong, one of the $\delta$s should be lower
whether you call that index $\delta$ or $\lambda$ doesn't matter
and why are you still worried about the order of the terms? didn't we establish that everything here is a number being summed over and so they commute?
12:42 PM
oh fck
I wrote that last part wrong
and Now I have to do it again
order
Ok let me first write that thing correctly
@ACuriousMind We have this :$(-F^{\delta \mu})(-F^{\nu \lambda})g_{\lambda \delta}=F^{\delta \mu}F^{\nu}_{\ \ \delta}$
or ${F_\lambda}^\mu F^{\nu\lambda}$, depending on whether you carry out the sum over $\lambda$ or over $\delta$
Ok
so what you did here was considering the first and the 3rd term correct?
I would describe it as "I carried out the sum over $\delta$"
Better
you carried the sum over deltas
that it's the first or third terms is immaterial, as we established, the order doesn't matter
12:48 PM
now I asked about the order, and you told me that we discussed about it, but you misunderstood me
what i mean by order
was the ordering the the index
let me elaborate what I am trying to say
I mean, the order of the indices does matter for $F$ somewhat, but the sum over $\delta$ (or $\lambda$) doesn't really care what position the two indices being summed over are
one has to be upper, the other has to be lower, that's all that matters there
apparently, it doesn't
but are these the same
you are perhaps confused because in $(A\cdot B)_{ik} = \sum_j A_{ij}B_{jk}$ one instance of the index is always the second and the other the first, and you inferred that that should be a general rule
but it isn't - if I write $\sum_j A_{ji}B_{jk}$ that's a perfectly fine expression, it's just the expression for $(A^T\cdot B)_{ik}$ instead
to much info to fast to process
one second
chat messages have no expiration date, you can take as long as you want to read what I wrote ;)
12:53 PM
I will try to write what I am trying to find out, I think it has to do with what your wrote right now
but i cannot be certain
since I simply cannot
first of all are these the same $F^{\mu}_{\ \ \nu}$ and $F_{\mu}^{\ \ \nu}$
no wrong
writing
now it's as I wanted it to be
no, the indices differ in being upper/lower, so these are different objects
you have ${F^\mu}_\nu = g^{\mu\rho}g_{\nu\sigma}{F_\rho}^\sigma \neq {F_\mu}^\nu$
and what about $F^{\mu}_{\ \ \nu}$ and $F^{\ \ \mu}_{\nu}$ ?
they differ by a $-$ since $F$ is anti-symmetric
but why? we don't have index change
$\mu$ is still up while $\nu$ is still down
so?
1:06 PM
well
anti-symmetry means $F_{\mu\nu} = -F_{\nu\mu}$
I know antisymmetry is if you swap them ,no?
exactly
This straightforwardly extends to ${F^\mu}_\nu = -{F_\nu}^\mu$ and $F^{\mu\nu} = -F^{\nu\mu}$
shouldn't it be $F^{\mu}_{\ \ \nu}=-F^{\nu}_{\ \ \mu}$ ?
that's not even a valid equation
single indices are not allowed have different upper/lower position on different sides of an equals sign, that's another sign that something went wrong
You can really just write this out in terms of the anti-symmetry of $F_{\mu\nu}$: ${F^\mu}_\nu = g^{\mu\rho}F_{\rho\nu} = -g^{\mu\rho}F_{\nu\rho} = -{F_\nu}^\mu$
especially if you're still getting used to index notation, you shouldn't guess what happens, you should actually try to derive it
1:12 PM
I do
but apparently
order matters
of the indices
what I mean by that
I never actually took the time to learn Fourier transforms so I'm doing a bit now, why does the integration over $p$ disappear in 2.21 when we insert the Fourier transformation?
of $\phi(x)$
As you pointed out this was wrong :$F^{\mu}_{\ \ \nu}=-F^{\nu}_{\ \ \mu}$ where $\mu$ is more left then $\nu$ and by simply swapping you will get an expression where $\nu$ is more in the left then $\mu$. While the correct that you wrote ${F^\mu}_\nu = -{F_\nu}^\mu$ $\mu$ is still superscript and $\nu$ is still subscript but in the term with the neg. sign $\nu$ is more in the left then $\mu$
Order of indices matters insofar as $X_{\mu\nu}\neq X_{\nu\mu}$ in general, look at the second to last thing ACM wrote, that is the full set of steps that derive the relationship
And ofc it makes sense
Yes I did
Are you still confused about something then?
1:23 PM
@Charlie you're pulling the derivative "under the integral sign"
maybe it's a rule and I am not aware of it
the neat property of Fourier transformations is $\partial_x \mathscr{F}(f(p)) = \mathscr{F}(pf(p))$
i.e. the derivative w.r.t. $x$ becomes multiplication by $p$
I see where the $|\vec p|^2$ comes from, but the integral $\int \mathrm d^3p e^{i\vec p\cdot \vec x}$ isn't present in 2.21 and I'm not sure why
I'm probably missing the most obscenely obvious thing lol
@imbAF what's still confusing?
I am writing it atm
1:26 PM
ok lol
as you were
it might be a bit length or badly asked, but I am trying my best for it to be understandable, articulation ain't my forte in this part of physics
lengthy and poorly articulated describes half the text written about physics in human history, i'm sure you'll be fine
@Charlie I find it more helpful to think about this in a way that doesn't even write down any integrals: If you write $\phi(p,t)$ as the Fourier transform of $\phi(x,t)$, then $(\partial_t^2 + (p^2 + m^2)) \phi(p,t) = (\partial_t^2 + (p^2 + m^2))\mathscr{F}(\phi(x,t)) = \mathscr{F}((\partial_t^2 + (\partial_x^2 + m^2))\phi(x,t)) = \mathscr{F}(0) = 0$, where the second-to-last equality is just the original x-space equation, hence (2.21) is true.
AH
I was looking at it going "if the integral is zero the integrand isn't necessarily zero", but that IS true in the case of the function argument of the Fourier expansion right
I see, thank you!
I will go back to existing in a world where I'm not stumped by things written on page <30 of Peskin and Schroeder lol
we'll see how long that lasts
yeah, it's a bit tricky because this isn't an "the integrand is zero because the integral is zero" argument, but the way your screenshot is written makes it look like it should be one
note that I'm not plugging the $\phi(x,t) = ...$ equation into the x-space equation (which is what that text would at first glance seem to imply I should be doing), I'm starting with the l.h.s. of the p-space equation
you do this carefully two or three times and after that you just get used to "Fourier transform the equation" and never think about it again
1:37 PM
Ok here it is, what I basically wanted to know
sorry for the lengthy thing
And the main thing I wanted to ask , here : $F^{\delta \mu}F^{\nu \lambda}g_{\lambda \delta}=F^{\delta \mu}F^{\nu}_{\ \ \delta}$ we are summing over the $\lambda$s and you can clearly see how the indices are ordered when summing over $\lambda$ ($\nu \lambda \lambda \delta$ ) the $\lambda$'s come one after the other with no other index in between . What I wanted to know, and @ACuriousMind confirmed it was that this can be also written as
$F^{\delta \mu}F^{\nu \lambda}g_{\lambda \delta}=F^{\delta \mu}g_{\lambda \delta}F^{\nu \lambda}={F_\lambda}^\mu F^{\nu \lambda}$ but here if we sum over delta we see that between the two $\delta$ indices there are other terms and the ordering is as ($\delta \mu \lambda \delta$) the $\delta$'s don't come one after the other as above, there are other indices in between.
0
Usually some questions were on-topic at the beginning of the community. But now they are strictly considered off-topic. resource-recommendations is one of them. Do we consider them off-topic because the community is growning faster and faster?
Therefore I assumed (because no one said anything in the lecture whether it's possible or no) that you cannot lower or raise indicies unless we are like in the first situation. (where the indices we are concerned with are directly one other the other with no other indices in between).
So I thought of doing this :$F^{\delta \mu}F^{\nu \lambda}g_{\lambda \delta}=F^{\delta \mu}g_{\lambda \delta}F^{\nu \lambda}=-F^{\mu \delta}g_{\lambda \delta}F^{\nu \lambda}=-F^{\mu \delta}g_{\delta \lambda}F^{\nu \lambda}=-F^{\mu}_{\ \ \lambda}F^{\nu \lambda}=(-F^{\mu}_{\ \ \lambda})(-F^{\lambda \nu})=F^{\mu}_{\ \ \lambda}F^{\lambda \nu}$ which is not what @ACuriousMind wrote, his answer was ${F_\lambda}^\mu F^{\nu \lambda}$
Y’all .. has the meta tag for resource recommendations always been misspelled? It doesn’t have a “d” in it.
huh
that's embarrassing, but I don't see how it could not always have been misspelled
3
Hey all! Isn't the derivative of an auto parallel curve been 0 (in general relativity)?
1:43 PM
you can't change how a tag is spelled, you can only create new tags and then synonymize afaik, and there's no correctly-spelled synonym
@ACuriousMind Can we exclude possibility of hacking?
:P
105
During the re-tagging of questions, tags sometimes become orphaned from existing questions. Are these zombie tags ever removed from the tags list? What if a tag is misspelled and needs to be removed? How do we get rid of it? Return to FAQ Index
It looks like the way to fix it is to re-tag and then propose a synonym. There are only 45 questions using the misspelled tag.
Though here is ancient advice that moderators can rename tags.
2:05 PM
@rob I don't see anything in the UI that would allow me to do that, do you?
I’ve found it (with some help from Teacher’s Lounge): it’s the “merge” tool. But because I thought creating a synonym might be the right approach, now I need two people to downvote my proposed correctly-spelled synonym before we can merge.
Apparently.
alright, I've downvoted your obviously wrong proposal :)
hey, go easy on me, I’ve only been a moderator for five years, I’m still learning the ropes
aha! I found the even-more-secret UI, and the misspelling is gone.
hurray for mod power
2:43 PM
is this correct $\partial_{\mu}g^{\mu \nu}=0$
?
@imbAF No its not coordinate invariant
but it contains only constants, or that has no importance ?
if it were the covaraint derivative instead of partial derivative then its a different story
what you mean with covariant derivative?
$\partial_{\mu}= (\frac 1 c \frac{\partial}{\partial t},\nabla)$ ?
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean directional derivative onto the manifold's tangent...
Also are you doing general or special relativity?
And i gotta bounce in 8 minutes
btw
2:51 PM
special
Ah ... then dont worry about what I said
the partial derivative is 0
I am simply trying to find out what comes when we do $\partial_{\mu}\Theta^{\mu \nu}$
\ok
ok
thx
3:05 PM
nothing meaningful, you can't just apply $\partial_\mu$ to stuff and expect the result to be a proper scalar/tensor
yes, I thought so
but I wasn't sure
I simply thought that since the metric is 2nd order tensor with constants, applying the covariant derivative would give zero or is simply ignored
but you're not applying the covariant derivative
you're just applying the derivative
the result of $\partial_\mu g^{\mu\nu}$ is different depending on your coordinate system
e.g. it is zero in special relativity for Cartesian coordinates, but it is non-zero in spherical coordinates!
in special or general relativity
ahaa
well I wasn't aware of it, but know I know
tho that raises more questions. as to why you get another result depending on the coordinate system
because $\partial_\mu$ is "bad", you can't treat the derivative like you'd treat a vector $A_\mu$
what you mean by "bad" and treat ?
you mean I can't treat it as a vector?
a four vector*
3:10 PM
the reason we like to write stuff like $A_\mu T^{\mu\nu}$ for a vector $A$ and a tensor $T$ is that this expression holds in all coordinate systems
it's a vector itself, $V^\nu = A_\mu T^{\mu\nu}$
but if you use $\partial_\mu$, then $\partial_\mu T^{\mu\nu}$ doesn't transform like a vector with free index $\nu$ under coordinate transformations
This is a bit advanced for what I understand of special/ gen. relativity atm
the reason is that coordinate transformations do something like $T^{\mu\nu}\mapsto (f'^\mu)_\rho (f'^\nu)_\sigma T^{\rho\sigma}$ and if there's a $\partial$ in front then you have to use the product rule
which gives you something very different from what you get when there's just a vector $A_\mu$, there's no product rule for multiplication
but
I will have to copy paste all of this and come back later :P
Right now I am more concerned with the rules in tensor algebra, for example
@imbAF I mean, all I'm saying is that $\partial_\mu g^{\mu\nu}$ can be zero in one coordinate system and not zero in another
yes i understood that
but as I told you, I need to know the why to that,
tho it can wait for a later moment
3:15 PM
this isn't how a "proper" tensorial expression behaves - usually, when you have $T^{\mu\nu\sigma} = 0$ in one coordinate system then that means $T$ is zero in every frame
so if you want do learn "tensor algebra", you should stay away from expressions that involve $\partial_\mu$!
I mean
What if I want a differential algebra!
I am trying to do this, or rather understand this example in our class $\partial_{\mu}\Theta^{\mu \nu}$
which includes that partial thing
and
here I am confused : $$\partial_{\mu}{(\frac 1 4 g^{\mu \nu}F_{\lambda \tau}F^{\lambda \tau})}=\frac 1 2F_{\lambda \tau} \partial^{\nu}F^{\lambda \tau}$$ . I understand that the partial "interacts" with the metric tensor and raises it's index
@Slereah then you have questionable taste ;P
but I don't understand why it acts only in one of them
+ somehow you have a 2 term coming from somewhere
3:18 PM
@imbAF anti-symmetry strikes again
where?
in getting you the 2
use the product rule as you probably intended to, then use anti-symmetry to reduce to the two resulting terms into a single one
ok, but the metric tensor does what i described correct?
and then it's gone right?
you can just do the sum over $\mu$ and get $\partial^\nu$, yes
it looks as if it ignores the first term
but that's not the case obviously
3:21 PM
stop guessing
just do the calculation
use the product rule, and stare at the result until you see why it's equal to the result on your r.h.s.
btw is it correct to call it a term? $F_{\lambda \tau}$ or is there a more appropriate name for it?
ok will do
3:40 PM
Hey folks, quick question: is a dissociation curve and melting curve the same thing?
Looking at this phase diagram, for instance:
I'm very new to this so I'd just appreciate a quick heads-up.
When I search for dissociation curve, I get results about oxygen and hemoglobin, which is not what I'm looking for
I can't do it. I have to somehow using antisymmetri show that $(\partial^{\nu}F_{\lambda \tau})F^{\lambda \tau}=F_{\lambda \tau} (\partial^{\nu}F^{{\lambda \tau}})$ that way I can get a 2, which then reduces 1/4 to 1/2 , but the antisymmetries are $F^{\mu \nu}=-F^{\nu \mu}$ and $F^{\mu}_{\ \ \nu}=-F_{\nu}^{\ \ \mu}$. I used them and I didn't get anything useful
Or is the dissociation curve literally the conditions at which a molecule will "dissociate" (separate)?
@imbAF I'm sorry, it's not antisymmetry (but try raising/lowering indices instead)
yes i tried to do that
i multiplied the first F term with 2 metric tensors
basically
for the first term only
$\partial^{\nu}(F^{\rho \sigma}g_{\rho \lambda}g_{\sigma \tau})F_{\rho \sigma}g^{\rho \lambda}g^{\sigma \tau}$. The partial doesn't interact with the metric tensors so I get delta's of the form $\delta^{\rho}_{\ \ \rho}$ $\delta^{\sigma}_{\ \ \sigma}$
but then I will get 16, so a big mistake
4:01 PM
not $\delta$\s but rather $g^{\rho}_{\ \ \rho}$ $g^{\sigma}_{\ \ \sigma}$, and each gives a 4, so 16 in total
4:23 PM
@imbAF You have an index more than twice there, that's another one of those things that can tell you you've done something wrong
when you choose $\rho,\sigma$ for the raising/lowering on the first $F$, you should choose two different indices for the second $F$
and why is that?
is there any intuition to it
or just a result of spending time with such problems
and you know tricks now, on how to solve them?
it's just how raising/lowering works: When you write something like $A_\mu = A^\nu g_{\mu\nu}$ the index you choose (in this example $\nu$) needs to be an index you're not already using since you're introducing a new summation
the rules for "good" expressions are: No index more than twice, indices that occur twice must occur once as upper and once as lower, and on both sides of an equals sign you need the same number of free indices (i.e. indices that occur only once) and these free indices need to be in the same upper/lower position
but that is what I did in my calculations, the only thing is that i took the same symbols for two different terms
the expression you wrote down has four $\rho$s
hold on
4:29 PM
and that's led you to get some ${g^\rho}_\rho$ that aren't correct
I see two tho, at $g^{\rho}_{\rho}$
where are the 4 ?
39 mins ago, by imbAF
$\partial^{\nu}(F^{\rho \sigma}g_{\rho \lambda}g_{\sigma \tau})F_{\rho \sigma}g^{\rho \lambda}g^{\sigma \tau}$. The partial doesn't interact with the metric tensors so I get delta's of the form $\delta^{\rho}_{\ \ \rho}$ $\delta^{\sigma}_{\ \ \sigma}$
Yes four, cuz i used the same indices in both terms
and you are saying that is wrong
right?
6 mins ago, by ACuriousMind
when you choose $\rho,\sigma$ for the raising/lowering on the first $F$, you should choose two different indices for the second $F$
ok
when you look at an expression that utilizes this kind of notation, do you try and understand what is doing i.e the row is multiplying a column, or you don't concern yourself with that and simply, mechanically without giving it a thought, you use the rules that you know about how to combine indices etc etc?
4:38 PM
I just apply the rules. Once you have objects with more than two indices there's no interpretation in terms of matrices anymore, anyway
I see
Yeah i got it, the result
but I do think that the rules you listed do come from a concrete example, in the most generla case that we can comprehend from observing matricies
hence why you said take different indices
thinking about how it works with matrices is a nice consistency check, sure
but it would be much slower if you actually thought about every step by first "translating" it to the matrix world
yes but as you saw
that was the reason why I took double indices
it's just a matter of training, if you do these kinds of manipulations often enough they'll become second nature
yeah
3rd day :P
4:45 PM
Any good reference notes for Komar mass formula?
(hey all)
@ACuriousMind Same can be said about a lot of physics :)
indeed
@ACuriousMind do you write any blog by any chance. Would be wonderful to read the "must read" books of a curious mind
@MoreAnonymous nope
tried a few times, but it turns out I don't have much motivation for writing my thoughts into the void :P
you could do something like a notebook tho, a page a day, or every 2 days
4:55 PM
:P
@ACuriousMind Also I recently had a very naïve thought. For the people who try to introduce spinors in general relativity like don't the have to explain why we never see a classical spinor?
what does that have to do with GR? when we do QFT, we introduce a spinor field into the classical field theory that we quantize, too
@ACuriousMind hmmm ... fair but that the spinor field has no classical counter part ... Over here in GR it seems to have one as GR is a classical theory no?
5:10 PM
Well you still need it sometimes
For a start if you consider spinor quantum fields in GR
@Slereah But isn't that wrong? a classical version of spinors does not exist right?
What do you mean by "a classical version of spinors"
We live in a quantum world, technically there's no classical version of anything
there is most certainly a classical formalism for fermions
@Slereah True but GR is a classical limit of a quantum GR theory
What I guess you mean is that there's no macroscopic phenomenon where that's necessary
but that's due to statistics theorems
@Slereah Yes
5:16 PM
it's part of the whole Pauli exclusion thing
You can't have many fermions with the same state
So you can't really have a massive fermion wave like you do with photons
Agreed ...
there is otherwise no issue taking classical fermions
What's the difference between a clathrate and a gas hydrate?
If i have something like this $F_{\pi \lambda}\partial^{\pi}F^{\lambda \nu}$ am I allowed to rename the letter $\pi$ ?
Since it's sum over it, I should be able to
5:54 PM
Is there a name for this identity : $F^{\mu}_{\ \ \lambda}\partial_{\mu}F^{\lambda \nu}=\frac 1 2 F_{\mu \lambda}\partial^{\mu}F^{\lambda \nu} + \frac 1 2F_{\lambda \mu}\partial^{\lambda}F^{\mu \nu}$ ?
1 hour later…
7:00 PM
@imbAF it's just the anti-symmetry of the field strength tensor along with some raising/lowering of indices
so i doubt there's a name for it
While perusing a book, I found a diagram with little flags on it
I wonder if it's about flag varieties
clearly it's a flag catalog
look at how cute they are
7:18 PM
@Semiclassical Yes, I was able to derive it
simple trick apparently
00:00 - 20:0020:00 - 00:00 | 2022-05-23 18:24:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7648702263832092, "perplexity": 663.7909020216055}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652662560022.71/warc/CC-MAIN-20220523163515-20220523193515-00354.warc.gz"} |
http://tex.stackexchange.com/questions/11707/how-to-force-output-to-a-left-or-right-page | # How to force output to a left (or right) page?
I am putting together a document that has several cover pages, both for front and back cover. The bulk of the document is two-sided. Cover pages, however, must be right-side (or left-side, for the back cover) pages.
How can I force the next page to specifically be a right-side-page or a left-side-page?
-
For odd / right-side pages you can use \cleardoublepage in two-sided documents. (In one-sided ones \cleardoublepage is identical to \clearpage)
To force even / left-side pages you would need to define your own macro based on \cleardoublepage, but with reversed logic:
\documentclass{book}
\newcommand*\cleartoleftpage{%
\clearpage
\ifodd\value{page}\hbox{}\newpage\fi
}
% Demonstration / Test:
\begin{document}
Title on right side
\cleardoublepage
other title on right side
\cleartoleftpage
on the left side
\cleartoleftpage
also on the left side
\cleardoublepage
right side again
\end{document}
A more complex version which behaves nicely in single-sided documents and also supports two-column mode is:
\makeatletter
\newcommand*{\cleartoleftpage}{%
\clearpage
\if@twoside
\ifodd\c@page
\hbox{}\newpage
\if@twocolumn
\hbox{}\newpage
\fi
\fi
\fi
}
\makeatother
This is the definition of \cleardoublepage just with the \else removed to negate the logic, i.e. make it force even pages instead of odd.
-
As Martin explained, \cleardoublepage is a standard LaTeX command to force a break to an odd (right, recto) page in double-sided documents. The KOMA-script classes and the memoir class offer numerous custom commands for page-breaking:
• With KOMA-script, use \cleardoubleevenemptypage to force a break to an even (left, verso) page. (If necessary, this will produce an additional odd page with page style empty, as is the default in KOMA-script.) See section 3.13 of the KOMA-script manual for other available commands.
• With memoir, use \cleartoverso to force a break to an even page. See section 18.13 of the memoir manual for other available commands.
-
@Martin Scharrer Thanks for the MWE. I need an output that should not add a white-numberd-page in between the forced even/odd pages. Could you help me out in finding this issue. Appreciate your attention. Thanks. – learner123 May 6 at 11:00 | 2014-11-27 16:29:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7882561087608337, "perplexity": 4625.966736828314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931008899.16/warc/CC-MAIN-20141125155648-00205-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://www.helpteaching.com/questions/792016/ashley-is-applying-the-order-of-operations-to-the-following- | ##### Question Info
This question is public and is used in 61 tests or worksheets.
Type: Multiple-Choice
Category: Order of Operations
Author: kristieleigh75
Created: a year ago
View all questions by kristieleigh75.
# Order of Operations Question
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Add this question to a group or test by clicking the appropriate button below.
## Grade 7 Order of Operations
Ashley is applying the order of operations to the following expression.
$4 - 3 * (5 + 2) + 10$
What is the first step Ashley should use to simplify the expression?
1. Subtract 4 from 3
2. Multiply 3 times 5 | 2018-01-16 07:30:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39054226875305176, "perplexity": 3772.4664784260863}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886237.6/warc/CC-MAIN-20180116070444-20180116090444-00012.warc.gz"} |
http://bims.iranjournals.ir/article_981.html | # On reducibility of weighted composition operators
Document Type: Research Paper
Authors
1 Department of Mathematics, University of Maragheh, Maragheh, Iran.
2 faculty of mathematical sciences, university of tabriz, p. o. box: 5166615648, tabriz,
Abstract
In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: f\rightarrow u\cdot f\circ \varphi$ on $L^2(\Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(\Sigma_B)$ where $B\in \Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form $L^2(\mathcal{A})$ reduce $W$. All of these are basically discussed by using the conditional expectation properties. To explain the results some examples are then presented.
Keywords
Main Subjects
### References
C. Burnap and A. Lambert, Reducibility of composition operators on L2, J. Math. Anal. Appl. 178 (1993), no. 1, 87--101.
J.T. Campbell, M. Embry-Wardrop, R.J. Fleming and S.K. Narayan, Normal and quasinormal weighted composition operators, Glasg. Math. J. 33 (1991), no. 3, 275--279.
J.T. Campbell and W.E. Hornor, Localising and seminormal composition operators on L2, Proc. Roy. Soc. Edinburgh Sect. A 124 (1994), no. 2, 301--316.
J.T. Campbell and J. Jamison, On some classes of weighted composition operators, Glasg. Math. J. 32 (1990), no. 2, 87--94.
J.B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, 1990.
P. Dodds, C. Huijsmans and B. de Pagter, Characterizations of conditional expectation type operators, Pacific J. Math. 141 (1990), no. 1, 55--77.
J. Herron, Weighted conditional expectation operators, Oper. Matrices 5 (2011), no. 1, 107--118.
T. Hoover, A. Lambert and J. Quinn, The Markov process determined by a weighted composition operator, Studia Math. 72 (1982), no. 3, 225--235.
A. Lambert and B.M. Weinstock, Descriptions of conditional expectations induced by non-measure preserving transformations, Proc. Amer. Math. Soc. 123 (1995), no. 3, 897--903.
H. Radjavi and P. Rosenthal, Invariant Subspaces, , Dover Publications, 2nd edition, Mineola, NY, 2003.
M.M. Rao, Conditional measure and applications, Marcel Dekker, New York, 1993.
R.K. Singh and J.S. Manhas, Composition Operators on Function Spaces, North-Holland Mathematics Studies, North-Holland Publishing Co. Amsterdam, 1993.
### History
• Receive Date: 26 October 2015
• Revise Date: 10 April 2016
• Accept Date: 10 April 2016 | 2020-07-09 21:32:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5900316834449768, "perplexity": 1969.9178973840017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655901509.58/warc/CC-MAIN-20200709193741-20200709223741-00410.warc.gz"} |
https://stats.stackexchange.com/questions/233056/diverse-questions-on-arima | # Diverse questions on ARIMA
I am studying ARIMA models from this tutorial time-series-forecasting-codes-python, but I got confused on many points:
1. We do many transformations to get stationarity data and every transformation we get data with good stationarity and on the example, he got the best stationary after applying the Decomposing, then why he did use the ts_log_diff and ts_log data with ACF, PACF and ARIMA instead of using the Decomposing data !?
2. I did see many styles for ACF and PACF one like continuous graph and another one like pins, which one I should go for it?
3. What is the best and easiest way to detect AR and MA by ACF and PACF? Some tutorials mention about every ARIMA model has a special ACF and PACF pattern and others mention about the intersection between the lags and the confidence upper line!
4. Is there any way to automate the step of getting the AR and MA instead of trying to investigate the ACF and PACF plots?
• 4. auto.arima algorithm by Hyndman and Kandakhar as implemented in "forecast" package in R. See a description in an article in Journal of Statistical Software. – Richard Hardy Sep 2 '16 at 15:07
• Thanks @RichardHardy, but is there any similar method on python or not !! because I do not think that statsmodels on python has something like this. Anyway, could you suggest a way to take the information directly from ACF and PACF matrices and then apply a special analysis to figure out the AR and MA – Yassir Sep 2 '16 at 15:38
• Question on software implementations are off topic here. As you ask "is there a way to automate...", I told you that there is and what it is. It is unimportant that it is implemented in R; the important thing is that the idea behind the algorithm is explained in an academic paper that you can read. – Richard Hardy Sep 2 '16 at 16:11
• @Yassir you asked if there was a way to automatically figure out a way to determine the AR MA structure (if there were unusual values or level/.step changes or seasonal pulses or local time trends ) while being sensitive to both changes in parameters and changes in error variance. The answer is yes but it is not in anything that has been recommended here. – IrishStat Oct 21 '16 at 16:03
After reading many articles and examples and during my work with my data I figure out the answers to my questions:
1- when you have non-stationary data (with trend and seasonality) you should do some transformation on the data to find a good stationary, every step mean something for ARIMA let's say you applied a first differencing on the data so that's mean you should add d=1 to the model and at the end you are not going to use the transformed data with the model and you will use your raw data directly with the model and the transformed data are useful to detect AR, MA and the degree of differencing.
2- the continues and the pins graph are same.
3- there are many ways to find AR and MA the famous one is by ACF and PACF chart and for sure it depends on the lags pattern, you can find some rules about it here.
the easiest way to find the ARIMA model is by calculating AIC for many models then get the model with the minimum AIC and that what auto.arima() do in R.
4-yes there is a function in statsmodels called arma_order_select_ic help to find the best ARIMA model for python by using AIC.
• About the first, you do not mention how to get back prediction with d=1 to original scale of the raw data. Do you recommend any approach to do it? – Adelson Araújo May 9 '17 at 22:22
## In response to Question 1:
The author of the article you mentioned probably used the ts_log_diff transformations to show the forecasting examples because this the most common transformation for most data sets (i.e most generalizable).
EDIT:
It is my understanding that the ARIMA models are used in cases where stationarity cannot be achieved as the author has pointed out in the original post in Section 5: Forecasting a Time Series:
"A series with significant dependence among values. In this case we need to use some statistical models like ARIMA to forecast the data."
• Thank you, but should we use the best stationary data coming from the specific transformation or not!?, like in the example which I mentioned above should we use the Decomposing data with ACF, PACF and ARIMA because it's giving good stationary or not! also why he used ts_log_diff with ACF and PACF, but he did not use it with ARIMA model !! – Yassir Sep 2 '16 at 15:32
• @Yassir I have edited my response to address your some of your additional questions. Also there is a Comments section at the bottom of the article which you reference, it may help you more to ask specific article related questions in that forum rather than posting those questions here and asking us to interpret the authors original intent of examples that they chose. – Will Sep 3 '16 at 17:48 | 2021-07-26 12:11:19 | {"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": 0.5390799641609192, "perplexity": 776.0308445109342}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1627046152129.33/warc/CC-MAIN-20210726120442-20210726150442-00265.warc.gz"} |
https://www.physicsforums.com/threads/geometric-progression-weighted-average.282176/ | # Geometric Progression Weighted Average ?
1. Dec 31, 2008
### musicgold
Hi,
I am trying to understand what Geometric Progression Weighted Average (GPWA) is in the context of the calculation of the US Dollar Index (USDX). I understand what a weighted average is but don’t understand what a GPWA is and when one should use it.
The following equation shows how the USDX is calculated using GPWA. In simple terms, the exchange rates of the US dollar with six major currencies are raised to a power value and the product of these terms is multiplied with an offset (50.14) to get the USDX. The power by which an exchange rate is raised represents the % of total US trade with that country. You can read more about the USDX here.
Note that my formula looks a bit different from the formula given in the article, but both formulae give the same answer. The term EUR / USD represents how many Euros can be purchased using one US dollar.
I am trying to understand the advantage of using trade weights as powers (i.e Ex. rate ^ weight) over simply using the weights as multiplying factors (i.e. Ex rate × weight). I know that using the weights as factors would result in a smaller number, but that is not a strong argument for using GPWA as one can always increase the magnitude of the offset to get a large value.
USDX = 50.14348112 × EUR / USD ^ 0.576 × JPY / USD ^ 0.136 × GBP / USD ^ 0.119 × CAD / USD ^ 0.091 × SEK / USD ^ 0.042 × CHF / USD ^0.036
I have calculated the USDX below using exchange rates as of Dec 30, 2008.
EUR / USD 0.7099
JPY / USD 90.36
GBP / USD 0.6924
CAN / USD 1.2185
SEK / USD 7.7565
CHF / USD 1.0575
USDX = 51.1435 × 0.821 × 1.845 × 0.957 × 1.018 × 1.090 × 1.002 = 82.44
Thanks,
MG.
Last edited: Dec 31, 2008
2. Dec 31, 2008
### NoMoreExams
3. Dec 31, 2008
### musicgold
NoMoreExams,
Thanks. No, I understand when to use an arithmetic mean ( when terms are added) and geometric mean (when terms are multiplied). I am not able to understand the use of 'weighted geometric mean'.
Last edited: Dec 31, 2008
4. Jan 2, 2009
Well, let's look at what the arithmetic and geometric means do.
Let's say you have a bunch of values $$x_1, \dotsc, x_n$$, and you want to find their arithmetic mean. You know, of course, that the arithmetic mean is $$\sum \frac{1}{n} x_i = \frac{x_1 + \dotsb + x_n}{n}$$.
Next, let's look at a weighted arithmetic mean. Then you have constants $$w_1, \dotsc, w_n$$ called weights, and to keep things simple, I'll say that $$\sum w_i = 1$$. Then the weighted arithmetic mean is $$\sum w_i x_i$$. If $$w_i = 1/n$$, then this is just the regular arithmetic mean.
We can use these same values and weights in a geometric mean. The weighted geometric mean of these values is defined as $$\prod x_i^{w_i}$$. If you have $$w_i = 1/n$$, then this is the usual geometric mean $$\prod x_i^{1/n} = \sqrt[n]{x_1 \dotsb x_n}$$.
If you want an arithmetic mean, then you must multiply the values by the weights. If you want a geometric mean, then you must use the weights as exponents. As for why a geometric mean is used, I'm sure there's a good reason, but I can't quite describe it.
5. Jan 3, 2009 | 2016-12-02 18:44:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.8442111611366272, "perplexity": 829.9892347481468}, "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-2016-50/segments/1480698540409.8/warc/CC-MAIN-20161202170900-00434-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://hinterm-ziel.de/index.php/tag/dw-link/ | The featured image of this post is based on a picture by Florian-if published at Wikipedia under CC-BY-SA-3.0
Is it possible to build a hardware debugger for debugWIRE for less than 10 €? As it turns out, it is. You just have to make a few compromises and also do a little bit of soldering and gluing.
dw-link can turn your Arduino board into a hardware debugger and dw-probe connects it to any target board.
The featured image of this post is by WikiImages on Pixabay
You want to make a single step in your program, but the debugger takes you to some unknown area of the program. This was, in fact, my first experience when I tried out Microchip’s MPLAB X IDE debugger on the innocent blinking sketch. Is this a bug or a feature?
As mentioned in an earlier blog post this year, hardware debuggers are the premier class of embedded debugging tools. However, until today, there were only very few relatively expensive tools around supporting the debugWIRE interface that is used by the classic ATtinys and a few ATmega MCUs.
The good news is that now you can turn an Arduino Uno, Nano, or Pro Mini into a debugWIRE hardware debugger that communicates with avr-gdb, the AVR version of the GNU project debugger.
The featured image of this post is by Albert Guillaume – Gils Blas, 24 décembre 1895, Public Domain, Link
When you develop a tool for a protocol that is undocumented, it is not surprising that you will encounter situations you will not have be anticipated. And this was exactly what I experienced developing the hardware debugger dw-link, which connects debugWIRE MCUs to the GDB debugger. Although a substantial part of the debugWIRE protocol has been reverse engineered, I encountered still plenty of surprising situations: Split personality MCUs, stuck-at-one bits in program counters, secret I/O addresses, half-legal opcodes, and more. | 2022-01-19 22:33:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.1735459268093109, "perplexity": 3214.7740753692924}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301592.29/warc/CC-MAIN-20220119215632-20220120005632-00285.warc.gz"} |
http://arches3.readthedocs.io/en/latest/arches-data/ | # Arches Data¶
## Physical Data model¶
Note
The physical data model section is most useful for those who wish to issue SQL queries directly against the Arches back end PostgreSQL database.
The Arches physical data model consists of tables and referential integrity constraints implemented within a PostgreSQL database. It is driven by a requirement that Arches be able to support data management for most any cultural heritage application in the world without the need to modify the underlying table structure.
To accomplish this, Arches stores both metadata - defining the set of resource types and attributes available to store - and business data - inventorying and describing the cultural heritage resources themselves.
The physical data model is best understood when broken into three distinct parts: Ontology Data, Reference Data, and Resources Data. The entity_types table plays a role in all three of these parts of the data model.
Ontology Data
The ontology portion of the data model stores the metadata sourced from the resource graphs. These tables therefore contain information about what is the valid set of semantic “types” of data (by default, Arches uses CIDOC CRM [http://www.cidoc-crm.org/] to define these things), and what are the valid types of relationships between them.
Reference Data
This is where Arches stores the hierarchical controlled vocabularies that power drop down lists in Arches applications. Items in drop-down lists are called “concepts”. Metadata about concepts, such as their labels and scope notes are stored in the related values table, and relationships between concepts are managed in the relations table.
Resources Data
The Resources Data section is where Arches stores the actual cultural heritage resource information - the business data. The key concepts to understand in this portion of the database are entities, relations, and “business tables”.
Entities within an Arches database represent one of three things:
1. the existence of a cultural heritage resource
2. an attribute of a cultural heritage resource, or
3. a record required to maintain ontological consistency between attributes
Relations represent relationships between entities within an Arches database. Records in this table indicate a relationship between two distinct entities.
Business tables contain strings, numbers, dates, or geometries that capture actual attributes of resources. These work by linking entities (by entityid) to respective values.
One special business table is the domains table. It is unique in that it only stores valueid (as a foreign key from the values table within the Reference Data) in order to relate entities that are constrained by a controlled vocabulary to its appropriate Reference Data records.
Entity Types
The entity_types table really belongs in all three categories because:
• they classify entities into an “attribute” that an implementor defines in the course of creating resource graphs.
• they specify the ontological category that (CRM classification) that an entity falls into
• they identify which attributes must be powered by drop-down lists from the reference data manager.
A very simple example is this: a resource happens to be a person with a name will, at a minimum, contain two entities and one relation. That is, an entity that represents the existence of the resource, another entity that contains the person’s name, and a relation that links the two together.
Hint
Each of these three sections within Arches database are contained in a separate Postgres schema. Each schema, in turn, has within in it two predefined views called vw_nodes and vw_edges. The Arches application does not use these views, but they could be useful in developing graph-based outputs of resource instances, resource graphs, and RDM graphs.
## Resource Graphs¶
Resource graphs are the logical framework that is used by Arches to define the set of resources and attributes of resources to be managed in an Arches Application.
Arches applications must provide a resource graph for each resource type being inventoried.
One example of a fully featured resource graph from the Arches HIP application is HERITAGE_RESOURCE.E18.
The graph’s data is populated into Arches from two specially formatted CSV files named {resource type name}_nodes.csv and {resourcetype name}_edges.csv.
Note
As of the writing of this document, the Arches developers’ primary tool to develop and visualize the resource graphs is Gephi (http://www.gephi.org/). However, it is possible that a future version of Arches may include tools that support resource graph development and visualization.
Regardless of how the nodes and edges CSV files are created, they must include the columns defined below.
Nodes:
• Id: a unique and arbitrary ID for each record within the file
• Label: the name of the entity type that is stored in a given node. This name must be concatenated with a dot (”.”) and the CRM class associated to that entity type
• mergenode: defines the upstream node that occurs one time (and only one time) within a given resource instance. In most cases, that node is the one that represents the resource itself.
• businesstable: identifies the respective data type (strings, numbers, dates, geometries, domains) that values associated to instances of the node will be stored as. This value should be left null for nodes that never store a business data.
Note
There is an excellent thread on the Arches forum discussing the purpose and implementation of mergenode here: https://groups.google.com/forum/?hl=en#!topic/archesproject/xRt1FPQXrLg
Edges:
• Source: the ID of the source node
• Target: the ID of the target node
• Label: the semantic CRM “property” that allows them to connect to each other.
### Ontologies¶
In addition to defining resources and their attributes, resource graphs also support associating those resources and attributes to semantic classes and properties defined in CIDOC CRM. Details on how this is done are provided in the section above on Resource Graphs.
Note
One should refer to CIDOC CRM (http://www.cidoc-crm.org/) to make an informed decision about what class or property to assign to nodes and edges respectively.
For those who do not care about CRM, ontologies or semantic interoperability, the simplest way to make a valid graph is to assign all nodes with class “E1” and all edges with property “P1”.
## Reference Data Graph¶
The reference data graph stores information necessary to use thesauri as input to pick lists (sometimes called “controlled vocabularies”) within resource data entry forms. The functional requirements for reference data in the cultural heritage field are quite robust, and best defined in SKOS documentation (http://www.w3.org/2004/02/skos/). For the purpose of this document, we will outline a few of the most important and visible requirements:
• Ability to associate sets of reference data entries as valid selections in drop-down lists for “domain” nodes in the resource graph
• Ability to associate arbitrary attributes (such as preferred labels, alternate labels, scope notes, sort order) to entries within the reference data
• Ability to store words associated to given reference data entries in multiple languages (to support internationalization)
• Ability to relate entries to each other in semantically rich hierarchies
Like the resource data graph, reference data is also stored in a graph structure. Reference data includes concepts and relations.
Concepts are the core component of the reference data graph. It indicates an idea that must be wrapped in metadata (such as a primary label) to communicate meaning. Concepts, in turn, are related to each other using relations.
The “types” of available relations are categorized as semantic relations and collections. The meaning of a given concept is not only derived from its own individual description (or scope note), but also from the context from its position within a hierarchy of concepts. Semantic relations are the connective tissue of hierarchical relationships that infuse meaning into concepts. Collections, on the other hand, are used for the purpose of defining which concepts belong in a given Entity Types’ drop-down list. Collections group concepts independently of their semantic hierarchy. In short, semantic relationships infuse meaning and collections define the content of drop-down lists.
Arches supports two formats for migrating concepts into the Reference Data graph. The first approach, using CSV files (also called Authority Files), is designed to support loading of legacy reference data to Arches. As such, source data are formatted and then uploaded as part of the installation of a specific Arches Application.
The second approach uses SKOS files. With SKOS files, the assumption is that an Arches application is already up and running, and that a person will use commands in the RDM’s user interface to pull in new thesauri from SKOS-formatted files.
### from .csv¶
The following steps outline how to create your own CSV-formatted authority documents for use in a system implementation. They can be followed using Excel as your text editor but the final file must be saved as a UTF-8 formatted CSV file.
Data is required for all columns in the authority file with the exception of AltLabels.
1. Create a text file and paste the following text to the first line. These are the column headings for each required field of data:
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
2. On the second line we will begin creating our concept. Start by creating a conceptid that will be unique both within this file and across all authority document files to be loaded. A good pattern to follow is to use the name of the authority document itself (with ‘_’ instead of spaces and minus the AUTHORITY_DOCUMENT.csv) with the number of the particular concept within the authority document appended. As an example, if your authority document is name ‘EXAMPLE_AUTHORITY_DOCUMENT.csv’ the first concept within the authority document would have the conceptid ‘EXAMPLE_1’:
//EXAMPLE_AUTHORITY_DOCUMENT.csv
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
EXAMPLE_1,
EXAMPLE_2,
3. Next, add your preferred label for the concept. In most cases this will be the value you have in mind or from your data that you would like to use for the domain list this authority document will be related to:
//EXAMPLE_AUTHORITY_DOCUMENT.csv
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
EXAMPLE_1,Example concept label,
EXAMPLE_2,Second example concept,
4. Now add an alternate label for your concept. This may be left blank if you have no alternate label for your concept:
//EXAMPLE_AUTHORITY_DOCUMENT.csv
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
EXAMPLE_1,Example concept label,Alternate concept label,
EXAMPLE_2,Second example concept,Second alternate concept label,
5. Then add a Parent ConceptID. If the concept is not hierarchically related to any other concept in the authority document then the Parent ConceptID will be the full name of the authority document itself. If the concept is hierarchically related to another concept in the authority file, ensure the parent concept is defined above the child concept and input the parent concepts’ conceptid here. In our example I have added a second concept that references the first concept as its parent:
//EXAMPLE_AUTHORITY_DOCUMENT.csv
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
EXAMPLE_1,Example concept label,Alternate concept label,EXAMPLE_AUTHORITY_DOCUMENT.csv,
EXAMPLE_2,Second example concept,Second alternate concept label,EXAMPLE_1,
6. Next, add a Concept Type. The only two valid values for ConceptType are: Index, and Collector. For more information on what the difference between these two concept types refer to the the general Arches documentation (http://arches3.readthedocs.org/en/latest/arches-data/#loading-reference-data):
//EXAMPLE_AUTHORITY_DOCUMENT.csv
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
EXAMPLE_1,Example concept label,Alternate concept label,EXAMPLE_AUTHORITY_DOCUMENT.csv,Collector,
EXAMPLE_2,Second example concept,Second alternate concept label,EXAMPLE_1,Index,
7. The Provider identifies where a given concept came from:
//EXAMPLE_AUTHORITY_DOCUMENT.csv
conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider
EXAMPLE_1,Example concept label,Alternate concept label,EXAMPLE_AUTHORITY_DOCUMENT.csv,Collector,Organization_1
EXAMPLE_2,Second example concept,Second alternate concept label,EXAMPLE_1,Index,Organization_2
8. Save your document.
9. IMPORTANT: Finally, we have to make sure our authority file maps to a ‘domain node’ in a resource graph. To do this either create or open the existing ENTITY_TYPE_X_ADOC.csv file that should reside in the same directory as your authority files (this file must be named ENTITY_TYPE_X_ADOC.csv). If you are modifying an existing ENTITY_TYPE_X_ADOC.csv file skip to step b below.
1. Copy and past the following text into the file on the first line:
entitytype,authoritydoc,authoritydocconceptschemename
2. Add a comma separated entry with the following information: the entity type to which you would like your authority documented associated (exactly how it is spelled in the resource graph including the .E## suffix), the name of the exact name of the authority document, and the concept scheme into which you would like to load this authority document:
//ENTITY_TYPE_X_ADOC.csv
entitytype,authoritydoc,authoritydocconceptschemename
EXAMPLE_NODE.E55,EXAMPLE_AUTHORITY_DOCUMENT.csv,Example Concept Scheme Name
10. You can optionally define a seperate but related [EXAMPLE_AUTHORITY_DOCUMENT].values.csv file to add additional information about concepts in your initial concepts file. This file uses a key-value pair approach to associating additional attributes to a given concept. The structure of the values file is as follows (the conceptid is the linking key to the initial concept within the initial concept file):
//EXAMPLE_AUTHORITY_DOCUMENT.values.csv
conceptid,Value,ValueType,Provider
EXAMPLE_1,This an example scope note,scopeNote,GCI
EXAMPLE_1,2[filepath to an image],image,GCI
Note
Arches comes loaded with a set of ValueTypes necessary to maintain compliance with SKOS and Dublin Core standards. The set of preloaded value types are nicely documented in the DML file located in the code repository here: arches\db\dml\db_data.sql. However, an implementor has the freedom to add additional ValueType’s by simply adding them within *.values.csv file. To be clear, these additional ValueTypes will not fall into the fold of SKOS standards, but they could be useful for your individual implementation.
One example where this is particularly relevant is the use sortorder as a ValueType. By default, Arches orders drop-down lists alphabetically. Sometimes, as in the cases of time periods, users prefer that their drop-down lists are presented in specific order. In the case of time periods, users prefer it be based on some semblance of chronological order.
When the sortorder ValueType is specified, corresponding numeric values can be used to ensure that the concept labels appear in the drop-down in a specific order.
Properly structured Authority files can be loaded into Arches using the following command from inside the application root directory:
python manage.py packages -o load_concept_scheme --source '{PATH TO AUTHORITY FILES}'
Resources and their attributes can be loaded to Arches resource graphs using one of two formats: shapefiles or a specially formatted text file with a .arches extension.
Shapefiles have the significant limitation that they cannot define explicit relationships between resources and they can only hold one attribute value per entity type.
.arches files, on the other hand, take a key-value pair approach populating resource graphs with resources with attributes. Therefore, they are able to add as many of a given attribute as exists in the data. The downside of the .arches format is that it can take a significant data processing or reformatting effort to get a significant amount of source data ready for loading to Arches from this format.
### From .arches¶
The .arches format is intended to support upload of Arches data containing rich content and complex relationships while also being achievable to format properly using common software like MS Excel or OpenOffice. The .arches format actually requires two files: one for loading resources (with a .arches extension) and another for loading relationships between resources (with a .relations extension).
The file is really just a list of business entities to be loaded to Arches. “Business entities” are those entities that actually store a business value. In this way, the .arches format is obfuscated from the details of the resource graph that it is being loaded to. The only real requirement is that the entity types referenced in the ATTRIBUTENAME field exist within the resource graph that the data are being loaded into.
The format takes a key-value pair approach to storage, where the ATTRIBUTENAME defines the key (the entity type as defined in the resource graph) and the ATTRIBUTEVALUE defines the business value of the entity.
The .arches file is a pipe (|) delimited text file containing the following column headers:
• RESOURCEID is a user-generated unique ID for each individual resource. Since any given resource will likely have many attributes, it is expected that a given RESOURCEID value will repeat on many lines. As a point of reference, Arches will create a separate unique ID for any resource that is loaded and will save the RESOURCEID provided within the .arches file as an external reference of type “Legacy ID”.
• RESOURCETYPE specifies which resource type graph a given attribute is being loaded to. In the Arches HIP Application, the available resource types include: ACTIVITY.E7, ACTOR.E39, HERITAGE_RESOURCE.E18, HERITAGE_RESOURCE_GROUP.E27, HISTORICAL_EVENT.E5, and INFORMATION_RESOURCE.E73.
• ATTRIBUTENAME specifies the node from the appropriate resource graph that the supplied value (in the ATTRIBUTEVALUE column) will load to. Note that ATTRIBUTENAME is synonymous with entitytypeid. Essentially, you are specifying the enitytypeid of the (business) entity that you are loading to the system.
• ATTRIBUTEVALUE stores the the actual business value of the entity. ATTRIBUTEVALUE values must conform to the data type specified by the business table associated to the entity type referenced by the ATTRIBUTENAME. See the PostgreSQL documentation for appropriate formatting for strings, numbers, and dates. See the notes below for formatting details on Geometries and Domains.
Note
Geometry: Any value that is to be loaded as a geometry must be formatted using Well Known Text (or “WKT” for short) with coordinates set to ESPG 4326 or latitude/longitude WGS84 (http://spatialreference.org/ref/epsg/4326/). WKT is a standard format for storing vector geometry as human-readable text. Details of the standard can be found here: https://portal.opengeospatial.org/files/?artifact_id=54797, and Wikipedia has a much more readable aggregation of the relevant information here: http://en.wikipedia.org/wiki/Well-known_text.
Note
Domains: Another special case here is values associated to ATTRIBUTENAME(s) that link to the domains businesstable. In those cases, the value stored in ATTRIBUTEVALUE must be the conceptid fed in from CSV-formatted “authority files.” More on authority files is available in the “Loading Reference Data” section.
GROUPID is intended to support cases where business values stored in separate nodes within the resource graph must be associated to each other. To illustrate the need, the classic example is an ACTOR resource graph that contains both FIRST_NAME.E1 and LAST_NAME.E1 as separate nodes. In that case, an ACTOR that has two separate names would need to know which first name and which last name go together. (An example might be Mark Twain and Samuel Clemens.) To group these appropriately, the two rows containing “Mark” and “Twain” should share a common GROUPID value and the two rows containing “Samuel” and Clemens” should have their own GROUPID value.
Hint
The code that loads data from .arches files assumes that the records within the file are sorted first on RESOURCEID and then on GROUPID. If the rows are sorted incorrectly, it could cause the load to fail, or (worse) load the data into the database incorrectly. Luckily, the data loading code has built into it a number of validations which search for conditions that could cause problems. Those validations are outlined in the next section.
The .relations file is a pipe (|) delimited text file containing the following column headers:
• RESOURCEID_FROM indicates one of the two resources to be related. The value here must also be present as a RESOURCEID in the .arches file.
• RESOURCEID_TO indicates the other of the two resources to be related. The value here must also be present as a RESOURCEID in the .arches file.
• START_DATE is a non-required field intended to indicate the date at which a given relationship between resources began.
• END_DATE is a non-required field intended to indicate the date at which a given relationship between resources ended.
• RELATION_TYPE is a domain value driven by an authority document file called ARCHES RESOURCE CROSS-REFERENCE RELATIONSHIP TYPES.E32.csv. Any value that you put into this column must be a conceptid from that authority document. If you wish to customize the set of available relationship types, simply modify the authority document.
• NOTES is a non-required field into which additional text about the relationship can be captured.
For example, you may want to relate a house to a person (both of which can be resources) using RELATION_TYPE “lived in” and specify the date at which the person moved into the house as the START_DATE, and the date the person moved out as the END_DATE.
#### .arches file validations¶
Before any data are loaded from the .arches format into the Arches database, our data loading code runs a series of validations to ensure adherence to the rules outlines above. Below is a quick enumeration of the validity checks that are executed:
1. syntax of the .arches and .relation files (including proper headings and column delimiters)
2. verifies that the ATTRIBUTENAME listed in the .arches files exists in the resource graph for the specified resource type
3. checks that the ATTRIBUTEVALUE is valid for the businesstablename of its related entity type
4. checks that rows are ordered by RESOURCEID then GROUPID
5. checks that all RESOURCEID values listed in the .relations file exist in the .arches file
### From Shapefile¶
Shapefile upload is one of the nice, new features of Arches 3. Though a little configuration is needed to load your shapefiles into Arches, the process is very simple. There are just a couple of limitations to loading data using shapefiles:
• Your shapefile can contain only one resource type per shapefile. For example, you would need one shapefile to load Heritage Resources and a second shapefile for Activities.
• Your shapefile projection must be defined as WGS84 Lat/Lon (EPSG:4326).
• Currently the shapefile loader does not load the .relations file. If you need to add relationships between resources, you should use the .arches format with a .relations file rather than a shapefile, or create relationships between resources using the web application after loading your shapefile.
Loading from shapefile requires the creation of a configuration file to tell Arches how the fields in your shapefile correspond to nodes in a resource graph. The configuration file should have the same base name as your shapefile with the extension .config. For example, if your shapefile is called heritage_resources.shp, you will will need a heritage_resources.config file along with your heritage_resources.dbf, etc.
The .config file is formatted in JSON as you can see in this example:
{
“RESOURCE_TYPE”: “EXAMPLE_RESOURCE.E11″,
“GEOM_TYPE”: “GEOMETRY.E1″,
“FIELD_MAP”: [
[“place”,”PLACE.E1″],
[“location”,”DESCRIPTION_OF_LOCATION.E1″],
[“name”,”NAME.E1″],
[“period”,”PERIOD.E1″],
[“descrip”,”RESOURCE_DESCRIPTION.E1″],
[“heri_type”,”HERITAGE_RESOURCE_TYPE.E1″]
]
}
Notice that it contains the following properties:
• RESOURCE_TYPE is the resource type of your shapefile.
• GEOM_TYPE is simply the name of the entity type that Arches HIP uses to manage geometry.
• FIELD_MAP is where you list your shapefile fields and their corresponding entity types. Each field must be enclosed in brackets, with the shapefile column name in the first position and the entitytypeid in the second.
..note:: The curly braces at the beginning and end of the file are important! Also, remember that the projection of your data must be EPSG:4326 (WGS84 Lat/Lon).
The data type of your shapefile columns need to match the data type of the entity types to which they are mapped. For example, if you want to load a name column in your shapefile to NAME.E41 (which the HIP defines as a string data type), you must ensure that your shapefile treats name as a string.
If you want to load a field in your shapefile to an Arches controlled vocabulary, you’ll need to make sure that the values in the shapefile match a preferred label in the Arches Reference Data Manager (RDM). For example, if you want to load values from your shapefile into the HERITAGE_RESOURCE_TYPE.E55 node, the values in your shapefile column must match a preferred label in the RDM scheme (by default Arches uses the HERITAGE_RESOURCE_TYPE_AUTHORITY_DOCUMENT.csv scheme)
Now you can run the load_resources command. The console commands for loading a shapefile are the same as they are for loading a .arches file (see above). Once your authority files are loaded and your virtual environment is activated just navigate to the directory with your project’s manage.py file and run:
$python manage.py packages -o load_resources -s /path/to/my/mydata.shp ### An Example Data Load¶ Below is a very simple resource graph, set of authority documents, and .arches file. The intent is to quickly illustrate the construction of a logical model and a simple set of source data that can be loaded into the model. #### Resource Graph¶ Note that in the examples below, the character string of “[null]” is used as a substitute for no value. EXAMPLE_RESOURCE.E1_edges.csv: Id,Label,mergenode,businesstable 69,EXAMPLE_RESOURCE.E1,EXAMPLE_RESOURCE.E1,[null] 66,PERIOD.E1,EXAMPLE_RESOURCE.E1,strings 8,DESCRIPTION_OF_LOCATION.E1,PLACE.E1,strings 4,PHASE_TYPE_ASSIGNMENT.E1,EXAMPLE_RESOURCE.E1,[null] 42,HERITAGE_RESOURCE_TYPE.E1,EXAMPLE_RESOURCE.E1,domains 172,RESOURCE_DESCRIPTION.E1,EXAMPLE_RESOURCE.E1,strings 16,NAME_TYPE.E1,EXAMPLE_RESOURCE.E1,domains 71,PLACE.E1,EXAMPLE_RESOURCE.E1,[null] 5,GEOMETRY.E1,PLACE.E1,geometries 17,NAME.E1,EXAMPLE_RESOURCE.E1,strings EXAMPLE_RESOURCE.E1_nodes.csv: Source,Target,Id,Label 69,4,1,P1 69,17,2,P1 69,71,3,P1 69,172,4,P1 4,42,5,P1 4,66,6,P1 71,5,7,P1 71,8,8,P1 17,16,9,P1 #### Reference Data¶ NAME_TYPE.E1.csv: conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider NAME_TYPE_1,Primary Name,,NAME_TYPE.E1.csv,Index,Organization_1 NAME_TYPE_2,Alias Name,,NAME_TYPE.E1.csv,Index,Organization_1 HERITAGE_RESOURCE_TYPE.E1.csv: conceptid,PrefLabel,AltLabels,ParentConceptid,ConceptType,Provider HERITAGE_RESOURCE_TYPE_1,Architecture,[null],HERITAGE_RESOURCE_TYPE.E1.csv,Collector,Organization_1 HERITAGE_RESOURCE_TYPE_2,Spanish Colonial,[null],HERITAGE_RESOURCE_TYPE_1,index,Organization_1 HERITAGE_RESOURCE_TYPE_3,Postmodern,[null],HERITAGE_RESOURCE_TYPE_1,index,Organization_1 HERITAGE_RESOURCE_TYPE_4,Archealogy,[null],HERITAGE_RESOURCE_TYPE.E1.csv,Collector,Organization_1 HERITAGE_RESOURCE_TYPE_5,Pottery Sherd,[null],HERITAGE_RESOURCE_TYPE_4,index,Organization_1 HERITAGE_RESOURCE_TYPE_6,Arrowhead,[null],HERITAGE_RESOURCE_TYPE_4,index,Organization_1 #### Business Data¶ resource.arches: RESOURCEID|RESOURCETYPE|ATTRIBUTENAME|ATTRIBUTEVALUE|GROUPID EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|DESCRIPTION.E1|long description of the resource|DESCRIPTION.E1-0 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|NAME.E1|The Taj Mahal|NAME.E41-0 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|NAME_TYPE.E1|NAME_TYPE_1|NAME.E41-0 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|GEOMETRY.E1|POINT(0 0)|GEOMETRY.E1-0 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|DESCRIPTION_OF_LOCATION.E1|In the Atlantic Ocean off the coast of Africa|DESCRIPTION_OF_LOCATION.E1 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|HERITAGE_RESOURCE_TYPE.E1|HERITAGE_RESOURCE_TYPE_3|PHASE_TYPE_ASSIGNMENT.E1-0 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|PERIOD.E1|1950 to 1980|PHASE_TYPE_ASSIGNMENT.E1-0 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|HERITAGE_RESOURCE_TYPE.E1|HERITAGE_RESOURCE_TYPE_5|PHASE_TYPE_ASSIGNMENT.E1-1 EXAMPLE RESOURCE_1|EXAMPLE_RESOURCE.E1|PERIOD.E1|Prehistoric|PHASE_TYPE_ASSIGNMENT.E1-1 EXAMPLE RESOURCE_2|EXAMPLE_RESOURCE.E1|NAME.E1|The Little Taj Mahal|NAME.E41-0 EXAMPLE RESOURCE_2|EXAMPLE_RESOURCE.E1|NAME_TYPE.E1|NAME_TYPE_1|NAME.E41-0 EXAMPLE RESOURCE_2|EXAMPLE_RESOURCE.E1|GEOMETRY.E1|POINT(1 1)|GEOMETRY.E1-0 Note EXAMPLE RESOURCE_1 has two distinct “groups” of phase-type assignments. That means that the resource was different things at different times. Note In the case of NAME_TYPE.E1 and HERITAGE_RESOURCE_TYPE.E1, the ATTRIBUTEVALUE is actually the ID of the concept as defined in the authority file. resource.relations: RESOURCEID_FROM|RESOURCEID_TO|START_DATE|END_DATE|RELATION_TYPE|NOTES EXAMPLE RESOURCE_1|EXAMPLE RESOURCE_2|[null]|[null]|RELATIONSHIP_TYPE:1|[null] Before you can load data, you must have ElasticSearch running so that your data is indexed during the load. To start ElasticSearch open a console and run: $ path\to\my_hip_app\my_hip_app\elasticsearch\elasticsearch-1.4.1\bin\elasticsearch
To load your resource graphs, make sure that your virtual environment is activated. If it’s not, in a new terminal run: On Linux and Unix systems:
$source path\to\ENV\bin\activate On Windows: > path\to\ENV\Scripts\activate With your virtual environment activated, navigate to the root directory your project and load your authority files with the following command where -s is a directory containing your authority files: $ python manage.py packages -o load_concept_scheme -s /path/to/authority_files/directory
Now you can load your .arches file with the following command:
\$ python manage.py packages -o load_resources -s /path/to/my/mydata.arches
Note
When loading with a .arches file, relationships defined in your .relations file will be automatically loaded if they are in the same directory as your .arches file.
## Exporting Data¶
By default, Arches will export the id, primary name and resource type to KML, shapefile and CSV formats. However, if you need to export more information for a resource, or customize the column names of your export file, an export mapping file is required.
### Resource export mappings¶
The resource export mappings is a JSON file that maps resources in your search results, to the schema of an export format; KML, CSV or SHP. If you need to create this file, its path needs to be assigned to the EXPORT_CONFIGS variable in your applications settings.py file. For example:
EXPORT_CONFIG = os.path.normpath(os.path.join(PACKAGE_ROOT, 'source_data', 'business_data', 'resource_export_mappings.json'))
The top level members of the JSON object are the format extensions (e.g. “csv”, “shp”, “kml”). Each format extension has the following properties:
• NAME: base name of the export file
• SCHEMA: array of objects defining each field to be added to your exported file. Each object should have the following properties:
• field_name: name of the exported field (required)
• source: The location of the data in the search results. If the value is “field_map” the application will lookup the value using the field map for the resource.
• alternatename : every name for the resource that is not primary will be concatenated into a list of alternate names. A value of “resource_name” will lookup the resource name from the RESOURCE_TYPE_CONFIGS in the application’s settings.py file.
• data_type: “str”, “datetype”, or “float” (required only for shapefiles)
• data_length: an integer in quotes (e.g. “128” required only for shapefiles)
• RESOURCE_TYPES: an object containing an object for each resource type that will be exported. The key for each resource type object is the resource’s entitytypeid. The value for each type contains the following properties:
• FIELD_MAP: a list of objects each containing information needed to map child entity data to an export file field. Properties for the field map include:
• field_name: The field_name value - match a field in the SCHEMA (required)
• entitytypeid: The entitytypeid of the child entity (required)
• value_type: A conceptid of the value used to define the value’s type. For example, an address may have different types such as primary or postal. If you want to export only the primary address for this column, you can add the concept type for ‘primary address’ here. Concept ids can be found in your application’s Reference Data Manager (RDM). (optional)
• alternate_entitytypeid: Alternate entity type to use if no value is available for the entitytypeid (optional)
### Example Resource Export Mappings¶
{
"csv": {
"NAME": "HistoricPlacesLA_Search_Results_Export",
"SCHEMA": [
{"field_name": "PRIMARY NAME","source": "primaryname"},
{"field_name": "OTHER NAMES","source": "alternatename"},
{"field_name": "ARCHES ID","source": "entityid"},
{"field_name": "ARCHES RESOURCE TYPE","source": "resource_name"},
{"field_name": "TYPE","source": "field_map"},
{"field_name": "PRIMARY ADDRESS/LOCATION DESCRIPTION","source": "field_map"},
{"field_name": "DESIGNATIONS","source": "field_map"}
],
"RESOURCE_TYPES": {
"ACTOR.E39": {
"FIELD_MAP": [
{
"field_name": "TYPE",
"entitytypeid": "ACTOR_TYPE.E55"
},
{
"field_name": "PRIMARY ADDRESS/LOCATION DESCRIPTION",
"value_type": "e4f5bd2f-56b7-4b8d-ac48-7e6d90e530ae",
"alternate_entitytypeid": "DESCRIPTION_OF_LOCATION.E62"
}
]
},
"HERITAGE_RESOURCE.E18": {
"FIELD_MAP": [
{
"field_name": "TYPE",
"entitytypeid": "HERITAGE_RESOURCE_TYPE.E55"
},
{
"field_name": "PRIMARY ADDRESS/LOCATION DESCRIPTION",
"value_type": "e4f5bd2f-56b7-4b8d-ac48-7e6d90e530ae",
"alternate_entitytypeid": "DESCRIPTION_OF_LOCATION.E62"
},
{
"field_name": "DESIGNATIONS",
"entitytypeid": "TYPE_OF_DESIGNATION_OR_PROTECTION.E55"
}
]
}
}
},
"kml": {
"NAME": "HistoricPlacesLA_Search_Results_Export",
"SCHEMA": [
{"field_name": "primary_name","source": "primaryname"},
{"field_name": "other_names","source": "alternatename"},
{"field_name": "arches_id","source": "entityid"},
{"field_name": "arches_resource_type","source": "resource_name"},
{"field_name": "geometry","source": "geometries"},
{"field_name": "type","source": "field_map"},
{"field_name": "designations","source": "field_map"}
],
"RESOURCE_TYPES": {
"ACTOR.E39": {
"FIELD_MAP": [
{
"field_name": "type",
"entitytypeid": "ACTOR_TYPE.E55"
},
{
"value_type": "e4f5bd2f-56b7-4b8d-ac48-7e6d90e530ae",
"alternate_entitytypeid": "DESCRIPTION_OF_LOCATION.E62"
}
]
},
"HERITAGE_RESOURCE.E18": {
"FIELD_MAP": [
{
"field_name": "type",
"entitytypeid": "HERITAGE_RESOURCE_TYPE.E55"
},
{
"value_type": "e4f5bd2f-56b7-4b8d-ac48-7e6d90e530ae",
"alternate_entitytypeid": "DESCRIPTION_OF_LOCATION.E62"
},
{
"field_name": "designations",
"entitytypeid": "TYPE_OF_DESIGNATION_OR_PROTECTION.E55"
}
]
}
}
},
"shp": {
"NAME": "HistoricPlacesLA_Search_Results_Export",
"SCHEMA": [
{"field_name": "prime_name","source": "primaryname","data_type": "str","data_length": "128"},
{"field_name": "arches_id","source": "entityid","data_type": "str","data_length": "128"},
{"field_name": "resource","source": "resource_name","data_type": "str","data_length": "128"},
{"field_name": "othernames","source": "alternatename","data_type": "str","data_length": "128"},
{"field_name": "type","source": "field_map","data_type": "str","data_length": "128"},
{"field_name": "address","source": "field_map","data_type": "str","data_length": "128"},
{"field_name": "designatns","source": "field_map","data_type": "str","data_length": "128"}
],
"RESOURCE_TYPES": {
"ACTOR.E39": {
"FIELD_MAP": [
{
"field_name": "type",
"entitytypeid": "ACTOR_TYPE.E55"
},
{
"value_type": "e4f5bd2f-56b7-4b8d-ac48-7e6d90e530ae",
"alternate_entitytypeid": "DESCRIPTION_OF_LOCATION.E62"
}
]
},
"HERITAGE_RESOURCE.E18": {
"FIELD_MAP": [
{
"field_name": "type",
"entitytypeid": "HERITAGE_RESOURCE_TYPE.E55"
},
{
"value_type": "e4f5bd2f-56b7-4b8d-ac48-7e6d90e530ae",
"alternate_entitytypeid": "DESCRIPTION_OF_LOCATION.E62"
},
{
"field_name": "designatns",
"entitytypeid": "TYPE_OF_DESIGNATION_OR_PROTECTION.E55"
}
]
}
}
}
} | 2018-01-20 00:45:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.18548955023288727, "perplexity": 3840.7329207166754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084888341.28/warc/CC-MAIN-20180120004001-20180120024001-00575.warc.gz"} |
https://deltaepsilons.wordpress.com/tag/analytic-manifolds/ | ## Helgason’s formula IINovember 7, 2009
Posted by Akhil Mathew in differential geometry, MaBloWriMo.
Tags: , , ,
Ok, recall our goal was to prove Helgason’s formula,
$\displaystyle \boxed{ (d \exp)_{tX}(Y) = \left( \frac{ 1 - e^{\theta( - tX^* )}}{\theta(tX^*)} (Y^*) \right)_{\exp(tX)}.}$
and that we have already shown
$\displaystyle {(d \exp)_{tX}(Y) f = \sum_{n=0}^{\infty} \frac{t^n}{(n+1)!} ( X^{*n} Y^* + X^{*(n-1)} Y^* X^* + \dots + Y^* X^{*n})f(p).}$ (more…)
We showed that the differential of the exponential map ${\exp_p: T_p(M) \rightarrow M}$ for ${M}$ a smooth manifold and ${p \in M}$ is the identity at ${0 \in T_p(M)}$. In the case of analytic manifolds, it is possible to say somewhat more. First of all, if we’re working with real-analytic manifolds, we can say that a connection ${\nabla}$ is analytic if ${\nabla_XY}$ is analytic for analytic vector fields ${X,Y}$. Using the real-analytic versions of the ODE theorem, it follows that ${\exp_p}$ is an analytic morphism.
So, make the above assumptions: analyticity of both the manifold and the connection. Now there is a small disk ${V_p \subset T_p(M)}$ such that ${\exp_p}$ maps ${V_p}$ diffeomorphically onto a neighborhood ${U \subset M}$ containing ${p}$. We will compute ${d(\exp_p)_{X}(Y)}$ when ${X \in V_p}$ is sufficiently small and ${Y \in T_p(M)}$ (recall that we identify ${T_p(M)}$ with its tangent spaces at each point). (more…) | 2018-10-15 23:18:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9267633557319641, "perplexity": 176.20384614266735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509958.44/warc/CC-MAIN-20181015225726-20181016011226-00423.warc.gz"} |
https://www.projecteuclid.org/euclid.aos/1378386237 | The Annals of Statistics
Uniformly most powerful Bayesian tests
Valen E. Johnson
Abstract
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although extensions outside of this class are possible. The connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between $p$-values and Bayes factors. Finally, issues regarding the strong dependence of resulting Bayes factors and $p$-values on sample size are discussed.
Article information
Source
Ann. Statist., Volume 41, Number 4 (2013), 1716-1741.
Dates
First available in Project Euclid: 5 September 2013
https://projecteuclid.org/euclid.aos/1378386237
Digital Object Identifier
doi:10.1214/13-AOS1123
Mathematical Reviews number (MathSciNet)
MR3127847
Zentralblatt MATH identifier
1277.62084
Citation
Johnson, Valen E. Uniformly most powerful Bayesian tests. Ann. Statist. 41 (2013), no. 4, 1716--1741. doi:10.1214/13-AOS1123. https://projecteuclid.org/euclid.aos/1378386237
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• Prosper (2012). Personal communication to news@bayesian.org.
• Robert, C. P., Chopin, N. and Rousseau, J. (2009). Harold Jeffreys’s theory of probability revisited. Statist. Sci. 24 141–172.
• Rousseau, J. (2007). Approximating interval hypothesis: $p$-values and Bayes factors. In Proceedings of the 2006 Valencia Conference (J. Bernardo, M. Bayarri, J. Berger, A. Dawid, D. Heckerman, A. Smith and M. West, eds.) 1–27. Oxford Univ. Press, Oxford. | 2019-11-19 08:57:53 | {"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": 0.3971441388130188, "perplexity": 4115.603971717289}, "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/1573496670036.23/warc/CC-MAIN-20191119070311-20191119094311-00217.warc.gz"} |
https://proxieslive.com/tag/terms/ | This is my current loop to display my products via woocommerce. When I do print_r($category_array); It returns the array, but when I try to use a function to call it so I can do what I want to with the data, it makes and my entire screen doesn’t display after the loop. Maybe it’s a mistake in my function? Still very new to woocommerce and wp_loops. Thank you <?php // WP_Query arguments$ args = array( 'p' => 'product', 'post_type' => array( 'product' ), 'order' => 'ASC', 'post_per_page' => 20, ); // The Query $query = new WP_Query($ args ); // The Loop if ( $query->have_posts() ) { while ($ query->have_posts() ) { $query->the_post(); function filter_categories($ categories) { foreach ($categories as$ category) { echo $category->name; } } ?> <div class="row"> <div class="col-2"> <?php echo the_post_thumbnail(get_the_ID(), 'thumbnail'); ?> </div> <div class="col-7"> <a href="<?= get_permalink(); ?>"><?= the_title()?></a> <br/> <?php$ category_array = get_the_terms(get_the_ID(), 'product_cat'); filter_categories($category_array); ?> </div> <div class="col-3 text-right ">Price</div> </div> <?php } } else { // no posts found } // Restore original Post Data wp_reset_postdata(); ?> ## What does “(any sword)” mean in terms of Magic Items? In the Dungeon Master’s Guide section for Magic Items (Chapter 7), a lot of items have a requirement that says (any ___), specifically weapons and maybe armor if I remember correctly. For example, Flame Tongue says: “Weapon (any sword)”. Is this just to classify what the Item can be, or can you use another Magic Item in this place? Personally, I think a Vicious, Flame Tongue, Dragon Slayer, Vorpal Sword would be dope, but I’m not sure if that would work. ## Is it poor practice to host multiple web applications on the same domain, in terms of cookies? In my web application, I have a single API backend and two frontends written as single page applications. To simplify deployment, I’d like to serve the API on /api, the admin dashboard on /admin, and the end user frontend on /user (or something similar), all on the same domain. I want to use cookies for handling sessions, for both the end-user and admin apps. Is this a good idea? As I understand it, cookie usage is restricted by their domain. Would it make it simpler for an attacker to steal admin-session cookies from someone logged into both frontends? Or, should I use different domains for the admin and user frontends (admin.mydomain.com and user.mydomain.com)? ## How to make DSolve express constants in terms of the unknown function If I do DSolve[y'[x] == y[x], y[x], x] Mathematica returns {{y[x] -> E^x C[1]}} Is there a way to have it return this instead? {{y[x] -> E^x y[0]}} ## Can’t display multiple terms with get_the_terms I am trying to display the terms (from a custom taxonomy) of a single post, but I can’t display more than one term. When I try to display all the terms using a foreach loop, it doesn’t display anything. Here is one of my attempts : <?php$ terms = get_the_terms($post->ID, 'auteur'); if ($ terms && !is_wp_error($terms)) { foreach($ terms as $term) { echo$ term->name ; } } ?>
It doesn’t display anything. But the same code without foreach loop displays (as expected) one term :
<?php $terms = get_the_terms($ post->ID, 'auteur'); echo \$ term->name ; ?>
I imagine that I’m missing an evident mistake (I’m a beginner), but I can’t understand what is wrong with the foreach loop…
Thank you !
## Terms for different models of sum types
There seem to be at least a couple different possible ways of modeling sum types in a type system, but I haven’t been able to find consistent terms for referring to them:
1. A sum type is formed from a set of "data constructors", which are function-like entities that notionally map values of a summand type to values of the sum type. This is the model adopted by e.g. Haskell and the various flavors of ML.
2. A sum type is formed directly from the underlying summand types, with no data constructors, and as a consequence the sum type is a supertype of the summands (or at least behaves very much like one). This model seems to be much less common, but it’s the model adopted by Ceylon, and by C++’s std::variant.
Note that this is separate from the distinction between discriminated and non-discriminated unions: both models permit the sum type to be discriminated (although only if the summands are disjoint, in the case of #2).
Are there settled terms for distinguishing these two models?
## Is there a difference between “one round” and “until the end of your turn” in terms of duration?
I’m mainly concerned about the effects that last “one round” and “until the end of turn” (like Stone Bones ToB p.84 and Inferno Blade ToB p. 54, respectively). My guess is that “until end of turn” effects end after you’ve taken your “standard” actions (one swift action, one move action, one standard action, or whatever the duration equivalent would be, like a full-round action), so the reactions you take on that round are not affected by that effect. On the contrary “one round” effects would be in effect until it’s that PC’s turn again.
However, my DM insists that both effects would last until that PC’s turn comes again, having no distinction, even if it has different wording. So, really, what’s a round and what’s a turn in this case? Are they the same?
## Asymptotic of divide-and-conquer type recurrence with non-constant weight repartition between subproblems and lower order fudge terms
While trying to analyse the runtime of an algorithm, I arrive to a recurrence of the following type :
$$\begin{cases} T(n) = \Theta(1), & \text{for small enough n ;}\ T(n) \leq T(a_n n + h(n)) + T((1-a_n)n+h(n)) + f(n), & \text{for larger n .} \end{cases}$$ Where:
• $$a_n$$ is unknown and can depend on $$n$$ but is bounded by two constants $$0.
• $$h(n)$$ is some “fudge term” which is negligeable compared to $$n$$ (say $$O(n^\epsilon)$$ for $$0\leq \epsilon < 1$$).
If $$a_n$$ was a constant, then I could use the Akra-Bazzi method to get a result. On the other hand, if the fudge term didn’t exist, then some type of recursion-tree analysis would be straight-forward.
To make things a bit more concrete, here is the recurrence I want to get the asymptotic growth of:
$$\begin{cases} T(n) = 1, & \text{for n = 1;}\ T(n) \leq T(a_n n + \sqrt n) + T((1-a_n)n+\sqrt n) + n, & \text{for n \geq 2 } \end{cases}$$ Where $$\frac{1}{4} \leq a_n \leq \frac{3}{4}$$ for all $$n\geq 1$$.
I tried various guesses on upper bounds or transformations. Everything tells me this should work out to $$O(n\log(n))$$ and I can argue informaly that it does (although I might be wrong). But I can only prove $$O(n^{1+\epsilon})$$ (for any $$\epsilon>0$$), and this feels like something that some generalization of the Master theorem à la Akra-Bazzi should be able to take care of.
Any suggestions on how to tackle this type of recurrence?
## Please explain me this question in very simple terms
Consider the following snapshot of a system running n processes. Process i is holding Xi instances of a resource R, 1 <= i <= n. currently, all instances of R are occupied. Further, for all i, process i has placed a request for an additional Yi instance while holding the Xi instances it already has. There are exactly two processes p and q such that Yp = Yq = 0. Which one of the following can serve as a necessary condition to guarantee that the system is not approaching a deadlock? (A) min (Xp, Xq) < max (Yk) where k != p and k != q (B) Xp + Xq >= min (Yk) where k != p and k != q (C) max (Xp, Xq) > 1 (D) min (Xp, Xq) > 1
## These pages showing url too long and poorly formatted in uber suggest in terms of seo.How to solve this problem
I have a word press site and doing SEO with yoast premium plugin all other SEO related issue are solved but these pagination problem is a headache I search the internet but didn’t find solution for that | 2020-10-23 05:58:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 15, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4938979744911194, "perplexity": 2203.8430263219143}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107880656.25/warc/CC-MAIN-20201023043931-20201023073931-00385.warc.gz"} |
http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=5028011 | • Create Account
#ActualÁlvaro
Posted 01 February 2013 - 08:51 PM
That looks a bit awkward. Instead of keeping an angle to indicate where the spaceship is pointing, use a vector of length 1. The code would then look something like this (ignoring the issue of the flipped x coordinate, which I think should be dealt with in the rendering code, not the scene update code):
def moveForward(self):
self.rect.center = self.center.toPoint() # I don't know what this line does
What is self.rect.center? And why do you need to call toPoint' on self.center? What is self.center if not a point?
EDIT: Oh, the tricky part with using heading as a length-one vector is how to rotate it when the user presses a key. Instead of adding something to the angle, rotate the vector by some amount (you seem to already have code for that). You may have to normalize the vector every so often (like every frame, for simplicity) so that it doesn't end up being much longer or shorter by accumulated floating-point errors.
#2Álvaro
Posted 01 February 2013 - 08:51 PM
That looks a bit awkward. Instead of keeping an angle to indicate where the spaceship is pointing, use a vector of length 1. The code would then look something like this (ignoring the issue of the flipped x coordinate, which I think should be dealt with in the rendering code, not the scene update code):
def moveForward(self):
self.rect.center = self.center.toPoint() # I don't know what this line does
What is self.rect.center? And why do you need to call toPoint' on self.center? What is self.center if not a point?
EDIT: Oh, the tricky part with using heading as a length-1 vector is how to rotate it when the user presses a key. Instead of adding something to the angle, rotate the vector by some amount (you seem to already have code for that). You may have to normalize the vector every so often (like every frame, for simplicity) so that it doesn't end up being much longer or shorter by accumulated floating-point errors.
#1Álvaro
Posted 01 February 2013 - 08:49 PM
That looks a bit awkward. Instead of keeping an angle to indicate where the spaceship is pointing, use a vector of length 1. The code would then look something like this (ignoring the issue of the flipped x coordinate, which I think should be dealt with in the rendering code, not the scene update code):
def moveForward(self): | 2014-07-13 21:22:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5408540368080139, "perplexity": 668.556855280178}, "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-2014-23/segments/1404776438683.27/warc/CC-MAIN-20140707234038-00009-ip-10-180-212-248.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/rutherford-scattering-cross-section.395279/ | Rutherford Scattering cross section
1. Apr 14, 2010
SuperPokenerd
1. The problem statement, all variables and given/known data
Integrate the rutherford cross section over the backward hemisphere to get 4pi(sigma0(E))
2. Relevant equations
Rutherford cross section is sigma0(E)/sin^4(theta/2)
3. The attempt at a solution
When I integrate this with the limits pi/2 to pi i get sigma0(E)*(8/3) i don't know what i'm doing wrong.
2. Apr 14, 2010
NeoDevin
Are you sure you have your integration limits correct?
3. Apr 14, 2010
SuperPokenerd
I thought so, since the problem says that theta goes between pi/2 and pi i.e. large angle scattering is from 90-180 degrees. I don't see how i'm supposed to get it to be 4pi instead of 8/3.
4. Apr 14, 2010
NeoDevin
Never mind my previous response, I was confusing this with a different problem I was solving earlier.
As near as I can tell, your solution appears to be correct. | 2018-03-17 16:44:22 | {"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": 0.9047659039497375, "perplexity": 1081.4349391895648}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645248.22/warc/CC-MAIN-20180317155348-20180317175348-00777.warc.gz"} |
https://www.tutorialspoint.com/finding-fibonacci-sequence-in-an-array-using-javascript | # Finding Fibonacci sequence in an array using JavaScript
JavascriptWeb DevelopmentFront End Technology
## Fibonacci Sequence:
A sequence X_1, X_2, ..., X_n is fibonacci if:
• n >= 3
• X_i + X_{i+1} = X_{i+2} for all i + 2 <= n
## Problem
We are required to write a JavaScript function that takes in an array of numbers, arr, as the first and the only argument. Our function should find and return the length of the longest Fibonacci subsequence that exists in the array arr.
A subsequence is derived from another sequence arr by deleting any number of elements (including none) from arr, without changing the order of the remaining elements.
For example, if the input to the function is
Input
const arr = [1, 3, 7, 11, 14, 25, 39];
Output
const output = 5;
Output Explanation
Because the longest Fibonacci subsequence is [3, 11, 14, 25, 39]
Following is the code:
## Example
Live Demo
const arr = [1, 3, 7, 11, 14, 25, 39];
const longestFibonacci = (arr = []) => {
const map = arr.reduce((acc, num, index) => {
acc[num] = index
return acc
}, {})
const memo = arr.map(() => arr.map(() => 0))
let max = 0
for(let i = 0; i < arr.length; i++) {
for(let j = i + 1; j < arr.length; j++) {
const a = arr[i]
const b = arr[j]
const index = map[b - a]
if(index < i) {
memo[i][j] = memo[index][i] + 1
}
max = Math.max(max, memo[i][j])
}
}
return max > 0 ? max + 2 : 0
};
console.log(longestFibonacci(arr));
## Output
5
Updated on 23-Apr-2021 10:05:48 | 2022-07-01 04:37:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20989026129245758, "perplexity": 4667.661638984381}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103920118.49/warc/CC-MAIN-20220701034437-20220701064437-00585.warc.gz"} |
https://readingfeynman.org/tag/maxwells-equations/ | # Traveling fields: the wave equation and its solutions
We’ve climbed a big mountain over the past few weeks, post by post, 🙂 slowly gaining height, and carefully checking out the various routes to the top. But we are there now: we finally fully understand how Maxwell’s equations actually work. Let me jot them down once more:
As for how real or unreal the E and B fields are, I gave you Feynman’s answer to it, so… Well… I can’t add to that. I should just note, or remind you, that we have a fully equivalent description of it all in terms of the electric and magnetic (vector) potential Φ and A, and so we can ask the same question about Φ and A. They explain real stuff, so they’re real in that sense. That’s what Feynman’s answer amounts to, and I am happy with it. 🙂
What I want to do here is show how we can get from those equations to some kind of wave equation: an equation that describes how a field actually travels through space. So… Well… Let’s first look at that very particular wave function we used in the previous post to prove that electromagnetic waves propagate with speed c, i.e. the speed of light. The fields were very simple: the electric field had a y-component only, and the magnetic field a z-component only. Their magnitudes, i.e. their magnitude where the field had reached, as it fills the space traveling outwards, were given in terms of J, i.e. the surface current density going in the positive y-direction, and the geometry of the situation is illustrated below.
The fields were, obviously, zero where the fields had not reached as they were traveling outwards. And, yes, I know that sounds stupid. But… Well… It’s just to make clear what we’re looking at here. 🙂
We also showed how the wave would look like if we would turn off its First Cause after some time T, so if the moving sheet of charge would no longer move after time T. We’d have the following pulse traveling through space, a rectangular shape really:
We can imagine more complicated shapes for the pulse, like the shape shown below. J goes from one unit to two units at time t = t1 and then to zero at t = t2. Now, the illustration on the right shows the electric field as a function of x at the time t shown by the arrow. We’ve seen this before when discussing waves: if the speed of travel of the wave is equal to c, then x is equal to x = c·t, and the pattern is as shown below indeed: it mirrors what happened at the source x/c seconds ago. So we write:
This idea of using the retarded time t’ = tx/c in the argument of a wave function f – or, what amounts to the same, using x − c/t – is key to understanding wave functions. I’ve explained this in very simple language in a post for my kids and, if you don’t get this, I recommend you check it out. What we’re doing, basically, is converting something expressed in time units into something expressed in distance units, or vice versa, using the velocity of the wave as the scale factor, so time and distance are both expressed in the same unit, which may be seconds, or meter.
To see how it works, suppose we add some time Δt to the argument of our wave function f, so we’re looking at f[x−c(t+Δt)] now, instead of f(x−ct). Now, f[x−c(t+Δt)] = f(x−ct−cΔt), so we’ll get a different value for our function—obviously! But it’s easy to see that we can restore our wave function F to its former value by also adding some distance Δx = cΔt to the argument. Indeed, if we do so, we get f[x+Δx−c(t+Δt)] = f(x+cΔt–ct−cΔt) = f(x–ct). You’ll say: t − x/c is not the same as x–ct. It is and it isn’t: any function of x–ct is also a function of t − x/c, because we can write:
Here, I need to add something about the direction of travel. The pulse above travel in the positive x-direction, so that’s why we have x minus ct in the argument. For a wave traveling in the negative x-direction, we’ll have a wave function y = F(x+ct). In any case, I can’t dwell on this, so let me move on.
Now, Maxwell’s equations in free or empty space, where are there no charges nor currents to interact with, reduce to:
Now, how can we relate this set of complicated equations to a simple wave function? Let’s do the exercise for our simple Ey and Bz wave. Let’s start by writing out the first equation, i.e. ·E = 0, so we get:
Now, our wave does not vary in the y and z direction, so none of the components, including Ey and Edepend on y or z. It only varies in the x-direction, so ∂Ey/∂y and ∂Ez/∂z are zero. Note that the cross-derivatives ∂Ey/∂z and ∂Ez/∂y are also zero: we’re talking a plane wave here, the field varies only with x. However, because ·E = 0, ∂Ex/∂x must be zero and, hence, Ex must be zero.
Huh? What? How is that possible? You just said that our field does vary in the x-direction! And now you’re saying it doesn’t it? Read carefully. I know it’s complicated business, but it all makes sense. Look at the function: we’re talking Ey, not Ex. Ey does vary as a function of x, but our field does not have an x-component, so Ex = 0. We have no cross-derivative ∂Ey/∂x in the divergence of E (i.e. in ·E = 0).
Huh? What? Let me put it differently. E has three components: Ex, Ey and Ez, and we have three space coordinates: x, y and z, so we have nine cross-derivatives. What I am saying is that all derivatives with respect to y and z are zero. That still leaves us with three derivatives: ∂Ex/∂x, ∂Ey/∂x, and ∂Ey/∂x. So… Because all derivatives in respect to y and z are zero, and because of the ·E = 0 equation, we know that ∂Ex/∂x must be zero. So, to make a long story short, I did not say anything about ∂Ey/∂x or ∂Ez/∂x. These may still be whatever they want to be, and they may vary in more or in less complicated ways. I’ll give an example of that in a moment.
Having said that, I do agree that I was a bit quick in writing that, because ∂Ex/∂x = 0, Ex must be zero too. Looking at the math only, Ex is not necessarily zero: it might be some non-zero constant. So… Yes. That’s a mathematical possibility. The static field from some charged condenser plate would be an example of a constant Ex field. However, the point is that we’re not looking at such static fields here: we’re talking dynamics here, and we’re looking at a particular type of wave: we’re talking a so-called plane wave. Now, the wave front of a plane wave is… Well… A plane. 🙂 So Ex is zero indeed. It’s a general result for plane waves: the electric field of a plane wave will always be at right angles to the direction of propagation.
Hmm… I can feel your skepticism here. You’ll say I am arbitrarily restricting the field of analysis… Well… Yes. For the moment. It’s not a reasonable restriction though. As I mentioned above, the field of a plane wave may still vary in both the y- and z-directions, as shown in the illustration below (for which the credit goes to Wikipedia), which visualizes the electric field of circularly polarized light. In any case, don’t worry too much about. Let’s get back to the analysis. Just note we’re talking plane waves here. We’ll talk about non-plane waves i.e. incoherent light waves later. 🙂
So we have plane waves and, therefore, a so-called transverse E field which we can resolve in two components: Eand Ez. However, we wanted to study a very simply Efield only. Why? Remember the objective of this lesson: it’s just to show how we go from Maxwell’s equations to the wave function, and so let’s keep the analysis simple as we can for now: we can make it more general later. In fact, if we do the analysis now for non-zero Eand zero Ez, we can do a similar analysis for non-zero Eand zero Ey, and the general solution is going to be some superposition of two such fields, so we’ll have a non-zero Eand Ez. Capito? 🙂 So let me write out Maxwell’s second equation, and use the results we got above, so I’ll incorporate the zero values for the derivatives with respect to y and z, and also the assumption that Ez is zero. So we get:
[By the way: note that, out of the nine derivatives, the curl involves only the (six) cross-derivatives. That’s linked to the neat separation between the curl and the divergence operator. Math is great! :-)]
Now, because of the flux rule (×E = –∂B/∂t), we can (and should) equate the three components of ×E above with the three components of –∂B/∂t, so we get:
[In case you wonder what it is that I am trying to do, patience, please! We’ll get where we want to get. Just hang in there and read on.] Now, ∂Bx/∂t = 0 and ∂By/∂t = 0 do not necessarily imply that Bx and Bare zero: there might be some magnets and, hence, we may have some constant static field. However, that’s a matter of choosing a reference point or, more simply, assuming that empty space is effectively empty, and so we don’t have magnets lying around and so we assume that Bx and Bare effectively zero. [Again, we can always throw more stuff in when our analysis is finished, but let’s keep it simple and stupid right now, especially because the Bx = B= 0 is entirely in line with the Ex = E= 0 assumption.]
The equations above tell us what we know already: the E and B fields are at right angles to each other. However, note, once again, that this is a more general result for all plane electromagnetic waves, so it’s not only that very special caterpillar or butterfly field that we’re looking at it. [If you didn’t read my previous post, you won’t get the pun, but don’t worry about it. You need to understand the equations, not the silly jokes.]
OK. We’re almost there. Now we need Maxwell’s last equation. When we write it out, we get the following monstrously looking set of equations:
However, because of all of the equations involving zeroes above 🙂 only ∂Bz/∂x is not equal to zero, so the whole set reduced to only simple equation only:
Simplifying assumptions are great, aren’t they? 🙂 Having said that, it’s easy to be confused. You should watch out for the denominators: a ∂x and a ∂t are two very different things. So we have two equations now involving first-order derivatives:
1. ∂Bz/∂t = −∂Ey/∂x
2. c2∂Bz/∂x = −∂Ey/∂t
So what? Patience, please! 🙂 Let’s differentiate the first equation with respect to x and the second with respect to t. Why? Because… Well… You’ll see. Don’t complain. It’s simple. Just do it. We get:
1. ∂[∂Bz/∂t]/∂x = −∂2Ey/∂x2
2. ∂[−c2∂Bz/∂x]/∂t = −∂2Ey/∂x2
So we can equate the left-hand sides of our two equations now, and what we get is a differential equation of the second order that we’ve encountered already, when we were studying wave equations. In fact, it is the wave equation for one-dimensional waves:
In case you want to double-check, I did a few posts on this, but, if you don’t get this, well… I am sorry. You’ll need to do some homework. More in particular, you’ll need to do some homework on differential equations. The equation above is basically some constraint on the functional form of Ey. More in general, if we see an equation like:
then the function ψ(x, t) must be some function
So any function ψ like that will work. You can check it out by doing the necessary derivatives and plug them into the wave equation. [In case you wonder how you should go about this, Feynman actually does it for you in his Lecture on this topic, so you may want to check it there.]
In fact, the functions f(x − c/t) and g(x + c/t) themselves will also work as possible solutions. So we can drop one or the other, which amounts to saying that our ‘shape’ has to travel in some direction, rather than in both at the same time. 🙂 Indeed, from all of my explanations above, you know what f(x − c/t) represents: it’s a wave that travels in the positive x-direction. Now, it may be periodic, but it doesn’t have to be periodic. The f(x − c/t) function could represent any constant ‘shape’ that’s traveling in the positive x-direction at speed c. Likewise, the g(x + c/t) function could represent any constant ‘shape’ that’s traveling in the negative x-direction at speed c. As for super-imposing both…
Well… I suggest you check that post I wrote for my son, Vincent. It’s on the math of waves, but it doesn’t have derivatives and/or differential equations. It just explains how superimposition and all that works. It’s not very abstract, as it revolves around a vibrating guitar string. So, if you have trouble with all of the above, you may want to read that first. 🙂 The bottom line is that we can get any wavefunction we want by superimposing simple sinusoidals that are traveling in one or the other direction, and so that’s what’s the more general solution really says. Full stop. So that’s what’s we’re doing really: we add very simple waves to get very more complicated waveforms. 🙂
Now, I could leave it at this, but then it’s very easy to just go one step further, and that is to assume that Eand, therefore, Bare not zero. It’s just a matter of super-imposing solutions. Let me just give you the general solution. Just look at it for a while. If you understood all that I’ve said above, 20 seconds or so should be sufficient to say: “Yes, that makes sense. That’s the solution in two dimensions.” At least, I hope so! 🙂
OK. I should really stop now. But… Well… Now that we’ve got a general solution for all plane waves, why not be even bolder and think about what we could possibly say about three-dimensional waves? So then Eand, therefore, Bwould not necessarily be zero either. After all, light can behave that way. In fact, light is likely to be non-polarized and, hence, Eand, therefore, Bare most probably not equal to zero!
Now, you may think the analysis is going to be terribly complicated. And you’re right. It would be if we’d stick to our analysis in terms of x, y and z coordinates. However, it turns out that the analysis in terms of vector equations is actually quite straightforward. I’ll just copy the Master here, so you can see His Greatness. 🙂
But what solution does an equation like (20.27) have? We can appreciate it’s actually three equations, i.e. one for each component, and so… Well… Hmm… What can we say about that? I’ll quote the Master on this too:
“How shall we find the general wave solution? The answer is that all the solutions of the three-dimensional wave equation can be represented as a superposition of the one-dimensional solutions we have already found. We obtained the equation for waves which move in the x-direction by supposing that the field did not depend on y and z. Obviously, there are other solutions in which the fields do not depend on x and z, representing waves going in the y-direction. Then there are solutions which do not depend on x and y, representing waves travelling in the z-direction. Or in general, since we have written our equations in vector form, the three-dimensional wave equation can have solutions which are plane waves moving in any direction at all. Again, since the equations are linear, we may have simultaneously as many plane waves as we wish, travelling in as many different directions. Thus the most general solution of the three-dimensional wave equation is a superposition of all sorts of plane waves moving in all sorts of directions.”
It’s the same thing once more: we add very simple waves to get very more complicated waveforms. 🙂
You must have fallen asleep by now or, else, be watching something else. Feynman must have felt the same. After explaining all of the nitty-gritty above, Feynman wakes up his students. He does so by appealing to their imagination:
“Try to imagine what the electric and magnetic fields look like at present in the space in this lecture room. First of all, there is a steady magnetic field; it comes from the currents in the interior of the earth—that is, the earth’s steady magnetic field. Then there are some irregular, nearly static electric fields produced perhaps by electric charges generated by friction as various people move about in their chairs and rub their coat sleeves against the chair arms. Then there are other magnetic fields produced by oscillating currents in the electrical wiring—fields which vary at a frequency of 6060 cycles per second, in synchronism with the generator at Boulder Dam. But more interesting are the electric and magnetic fields varying at much higher frequencies. For instance, as light travels from window to floor and wall to wall, there are little wiggles of the electric and magnetic fields moving along at 186,000 miles per second. Then there are also infrared waves travelling from the warm foreheads to the cold blackboard. And we have forgotten the ultraviolet light, the x-rays, and the radiowaves travelling through the room.
Flying across the room are electromagnetic waves which carry music of a jazz band. There are waves modulated by a series of impulses representing pictures of events going on in other parts of the world, or of imaginary aspirins dissolving in imaginary stomachs. To demonstrate the reality of these waves it is only necessary to turn on electronic equipment that converts these waves into pictures and sounds.
If we go into further detail to analyze even the smallest wiggles, there are tiny electromagnetic waves that have come into the room from enormous distances. There are now tiny oscillations of the electric field, whose crests are separated by a distance of one foot, that have come from millions of miles away, transmitted to the earth from the Mariner II space craft which has just passed Venus. Its signals carry summaries of information it has picked up about the planets (information obtained from electromagnetic waves that travelled from the planet to the space craft).
There are very tiny wiggles of the electric and magnetic fields that are waves which originated billions of light years away—from galaxies in the remotest corners of the universe. That this is true has been found by “filling the room with wires”—by building antennas as large as this room. Such radiowaves have been detected from places in space beyond the range of the greatest optical telescopes. Even they, the optical telescopes, are simply gatherers of electromagnetic waves. What we call the stars are only inferences, inferences drawn from the only physical reality we have yet gotten from them—from a careful study of the unendingly complex undulations of the electric and magnetic fields reaching us on earth.
There is, of course, more: the fields produced by lightning miles away, the fields of the charged cosmic ray particles as they zip through the room, and more, and more. What a complicated thing is the electric field in the space around you! Yet it always satisfies the three-dimensional wave equation.”
So… Well… That’s it for today, folks. 🙂 We have some more gymnastics to do, still… But we’re really there. Or here, I should say: on top of the peak. What a view we have here! Isn’t it beautiful? It took us quite some effort to get on top of this thing, and we’re still trying to catch our breath as we struggle with what we’ve learned so far, but it’s really worthwhile, isn’t it? 🙂
# Maxwell, Lorentz, gauges and gauge transformations
I’ve done quite a few posts already on electromagnetism. They were all focused on the math one needs to understand Maxwell’s equations. Maxwell’s equations are a set of (four) differential equations, so they relate some function with its derivatives. To be specific, they relate E and B, i.e. the electric and magnetic field vector respectively, with their derivatives in space and in time. [Let me be explicit here: E and B have three components, but depend on both space as well as time, so we have three dependent and four independent variables for each function: E = (Ex, Ey, Ez) = E(x, y, z, t) and B = (Bx, By, Bz) = B(x, y, z, t).] That’s simple enough to understand, but the dynamics involved are quite complicated, as illustrated below.
I now want to do a series on the more interesting stuff, including an exploration of the concept of gauge in field theory, and I also want to show how one can derive the wave equation for electromagnetic radiation from Maxwell’s equations. Before I start, let’s recall the basic concept of a field.
The reality of fields
I said a couple of time already that (electromagnetic) fields are real. They’re more than just a mathematical structure. Let me show you why. Remember the formula for the electrostatic potential caused by some charge q at the origin:
We know that the (negative) gradient of this function, at any point in space, gives us the electric field vector at that point: E = –Φ. [The minus sign is there because of convention: we take the reference point Φ = 0 at infinity.] Now, the electric field vector gives us the force on a unit charge (i.e. the charge of a proton) at that point. If q is some positive charge, the force will be repulsive, and the unit charge will accelerate away from our q charge at the origin. Hence, energy will be expended, as force over distance implies work is being done: as the charges separate, potential energy is converted into kinetic energy. Where does the energy come from? The energy conservation law tells us that it must come from somewhere.
It does: the energy comes from the field itself. Bringing in more or bigger charges (from infinity, or just from further away) requires more energy. So the new charges change the field and, therefore, its energy. How exactly? That’s given by Gauss’ Law: the total flux out of a closed surface is equal to:
You’ll say: flux and energy are two different things. Well… Yes and no. The energy in the field depends on E. Indeed, the formula for the energy density in space (i.e. the energy per unit volume) is
Getting the energy over a larger space is just another integral, with the energy density as the integral kernel:
Feynman’s illustration below is not very sophisticated but, as usual, enlightening. 🙂
Gauss’ Theorem connects both the math as well as the physics of the situation and, as such, underscores the reality of fields: the energy is not in the electric charges. The energy is in the fields they produce. Everything else is just the principle of superposition of fields – i.e. E = E+ E– coming into play. I’ll explain Gauss’ Theorem in a moment. Let me first make some additional remarks.
First, the formulas are valid for electrostatics only (so E and B only vary in space, not in time), so they’re just a piece of the larger puzzle. 🙂 As for now, however, note that, if a field is real (or, to be precise, if its energy is real), then the flux is equally real.
Second, let me say something about the units. Field strength (E or, in this case, its normal component En = E·n) is measured in newton (N) per coulomb (C), so in N/C. The integral above implies that flux is measured in (N/C)·m2. It’s a weird unit because one associates flux with flow and, therefore, one would expect flux is some quantity per unit time and per unit area, so we’d have the m2 unit (and the second) in the denominator, not in the numerator. But so that’s true for heat transfer, for mass transfer, for fluid dynamics (e.g. the amount of water flowing through some cross-section) and many other physical phenomena. But for electric flux, it’s different. You can do a dimensional analysis of the expression above: the sum of the charges is expressed in coulomb (C), and the electric constant (i.e. the vacuum permittivity) is expressed in C2/(N·m2), so, yes, it works: C/[C2/(N·m2)] = (N/C)·m2. To make sense of the units, you should think of the flux as the total flow, and of the field strength as a surface density, so that’s the flux divided by the total area, so (field strength) = (flux)/(area). Conversely, (flux) = (field strength)×(area). Hence, the unit of flux is [flux] = [field strength]×[area] = (N/C)·m2.
OK. Now we’re ready for Gauss’ Theorem. 🙂 I’ll also say something about its corollary, Stokes’ Theorem. It’s a bit of a mathematical digression but necessary, I think, for a better understanding of all those operators we’re going to use.
Gauss’ Theorem
The concept of flux is related to the divergence of a vector field through Gauss’ Theorem. Gauss’s Theorem has nothing to do with Gauss’ Law, except that both are associated with the same genius. Gauss’ Theorem is:
The ·C in the integral on the right-hand side is the divergence of a vector field. It’s the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
Huh? What’s a volume density? Good question. Just substitute C for E in the surface and volume integral above (the integral on the left is a surface integral, and the one on the right is a volume integral), and think about the meaning of what’s written. To help you, let me also include the concept of linear density, so we have (1) linear, (2) surface and (3) volume density. Look at that representation of a vector field once again: we said the density of lines represented the magnitude of E. But what density? The representation hereunder is flat, so we can think of a linear density indeed, measured along the blue line: so the flux would be six (that’s the number of lines), and the linear density (i.e. the field strength) is six divided by the length of the blue line.
However, we defined field strength as a surface density above, so that’s the flux (i.e. the number of field lines) divided by the surface area (i.e. the area of a cross-section): think of the square of the blue line, and field lines going through that square. That’s simple enough. But what’s volume density? How do we count the number of lines inside of a box? The answer is: mathematicians actually define it for an infinitesimally small cube by adding the fluxes out of the six individual faces of an infinitesimally small cube:
So, the truth is: volume density is actually defined as a surface density, but for an infinitesimally small volume element. That, in turn, gives us the meaning of the divergence of a vector field. Indeed, the sum of the derivatives above is just ·C (i.e. the divergence of C), and ΔxΔyΔz is the volume of our infinitesimal cube, so the divergence of some field vector C at some point P is the flux – i.e. the outgoing ‘flow’ of Cper unit volume, in the neighborhood of P, as evidenced by writing
Indeed, just bring ΔV to the other side of the equation to check the ‘per unit volume’ aspect of what I wrote above. The whole idea is to determine whether the small volume is like a sink or like a source, and to what extent. Think of the field near a point charge, as illustrated below. Look at the black lines: they are the field lines (the dashed lines are equipotential lines) and note how the positive charge is a source of flux, obviously, while the negative charge is a sink.
Now, the next step is to acknowledge that the total flux from a volume is the sum of the fluxes out of each part. Indeed, the flux through the part of the surfaces common to two parts will cancel each other out. Feynman illustrates that with a rough drawing (below) and I’ll refer you to his Lecture on it for more detail.
So… Combining all of the gymnastics above – and integrating the divergence over an entire volume, indeed – we get Gauss’ Theorem:
Stokes’ Theorem
There is a similar theorem involving the circulation of a vector, rather than its flux. It’s referred to as Stokes’ Theorem. Let me jot it down:
We have a contour integral here (left) and a surface integral (right). The reasoning behind is quite similar: a surface bounded by some loop Γ is divided into infinitesimally small squares, and the circulation around Γ is the sum of the circulations around the little loops. We should take care though: the surface integral takes the normal component of ×C, so that’s (×C)n = (×Cn. The illustrations below should help you to understand what’s going on.
The electric versus the magnetic force
There’s more than just the electric force: we also have the magnetic force. The so-called Lorentz force is the combination of both. The formula, for some charge q in an electromagnetic field, is equal to:
Hence, if the velocity vector v is not equal to zero, we need to look at the magnetic field vector B too! The simplest situation is magnetostatics, so let’s first have a look at that.
Magnetostatics imply that that the flux of E doesn’t change, so Maxwell’s third equation reduces to c2×B = j0. So we just have a steady electric current (j): no accelerating charges. Maxwell’s fourth equation, B = 0, remains what is was: there’s no such thing as a magnetic charge. The Lorentz force also remains what it is, of course: F = q(E+v×B) = qE +qv×B. Also note that the v, j and the lack of a magnetic charge all point to the same: magnetism is just a relativistic effect of electricity.
What about units? Well… While the unit of E, i.e. the electric field strength, is pretty obvious from the F = qE term – hence, E = F/q, and so the unit of E must be [force]/[charge] = N/C – the unit of the magnetic field strength is more complicated. Indeed, the F = qv×B identity tells us it must be (N·s)/(m·C), because 1 N = 1C·(m/s)·(N·s)/(m·C). Phew! That’s as horrendous as it looks, and that’s why it’s usually expressed using its shorthand, i.e. the tesla: 1 T = 1 (N·s)/(m·C). Magnetic flux is the same concept as electric flux, so it’s (field strength)×(area). However, now we’re talking magnetic field strength, so its unit is T·m= (N·s·m)/(m·C) = (N·s·m)/C, which is referred to as the weber (Wb). Remembering that 1 volt = 1 N·m/C, it’s easy to see that a weber is also equal to 1 Wb = 1 V·s. In any case, it’s a unit that is not so easy to interpret.
Magnetostatics is a bit of a weird situation. It assumes steady fields, so the ∂E/∂t and ∂B/∂t terms in Maxwell’s equations can be dropped. In fact, c2×B = j0 implies that ·(c2×B ·(j0) and, therefore, that ·= 0. Now, ·= –∂ρ/∂t and, therefore, magnetostatics is a situation which assumes ∂ρ/∂t = 0. So we have electric currents but no change in charge densities. To put it simply, we’re not looking at a condenser that is charging or discharging, although that condenser may act like the battery or generator that keeps the charges flowing! But let’s go along with the magnetostatics assumption. What can we say about it? Well… First, we have the equivalent of Gauss’ Law, i.e. Ampère’s Law:
We have a line integral here around a closed curve, instead of a surface integral over a closed surface (Gauss’ Law), but it’s pretty similar: instead of the sum of the charges inside the volume, we have the current through the loop, and then an extra c2 factor in the denominator, of course. Combined with the B = 0 equation, this equation allows us to solve practical problems. But I am not interested in practical problems. What’s the theory behind?
The magnetic vector potential
TheB = 0 equation is true, always, unlike the ×E = 0 expression, which is true for electrostatics only (no moving charges). It says the divergence of B is zero, always, and, hence, it means we can represent B as the curl of another vector field, always. That vector field is referred to as the magnetic vector potential, and we write:
·B = ·(×A) = 0 and, hence, B×A
In electrostatics, we had the other theorem: if the curl of a vector field is zero (everywhere), then the vector field can be represented as the gradient of some scalar function, so if ×= 0, then there is some Ψ for which CΨ. Substituting C for E, and taking into account our conventions on charge and the direction of flow, we get E = –Φ. Substituting E in Maxwell’s first equation (E = ρ/ε0) then gave us the so-called Poisson equation: ∇2Φ = ρ/ε0, which sums up the whole subject of electrostatics really! It’s all in there!
Except magnetostatics, of course. Using the (magnetic) vector potential A, all of magnetostatics is reduced to another expression:
2A= −j0, with ·A = 0
Note the qualifier: ·A = 0. Why should the divergence of A be equal to zero? You’re right. It doesn’t have to be that way. We know that ·(×C) = 0, for any vector field C, and always (it’s a mathematical identity, in fact, so it’s got nothing to do with physics), but choosing A such that ·A = 0 is just a choice. In fact, as I’ll explain in a moment, it’s referred to as choosing a gauge. The·A = 0 choice is a very convenient choice, however, as it simplifies our equations. Indeed, c2×B = j0 = c2×(×A), and – from our vector calculus classes – we know that ×(×C) = (·C) – ∇2C. Combining that with our choice of A (which is such that ·A = 0, indeed), we get the ∇2A= −j0 expression indeed, which sums up the whole subject of magnetostatics!
The point is: if the time derivatives in Maxwell’s equations, i.e. ∂E/∂t and ∂B/∂t, are zero, then Maxwell’s four equations can be nicely separated into two pairs: the electric and magnetic field are not interconnected. Hence, as long as charges and currents are static, electricity and magnetism appear as distinct phenomena, and the interdependence of E and B does not appear. So we re-write Maxwell’s set of four equations as:
1. ElectrostaticsE = ρ/ε0 and ×E = 0
2. Magnetostatics: ×B = j/c2ε0 and B = 0
Note that electrostatics is a neat example of a vector field with zero curl and a given divergence (ρ/ε0), while magnetostatics is a neat example of a vector field with zero divergence and a given curl (j/c2ε0).
Electrodynamics
But reality is usually not so simple. With time-varying fields, Maxwell’s equations are what they are, and so there is interdependence, as illustrated in the introduction of this post. Note, however, that the magnetic field remains divergence-free in dynamics too! That’s because there is no such thing as a magnetic charge: we only have electric charges. So ·B = 0 and we can define a magnetic vector potential A and re-write B as B×A, indeed.
I am writing a vector potential field because, as I mentioned a couple of times already, we can choose A. Indeed, as long as ·A = 0, it’s fine, so we can add curl-free components to the magnetic potential: it won’t make a difference. This condition is referred to as gauge invariance. I’ll come back to that, and also show why this is what it is.
While we can easily get B from A because of the B×A, getting E from some potential is a different matter altogether. It turns out we can get E using the following expression, which involves both Φ (i.e. the electric or electrostatic potential) as well as A (i.e. the magnetic vector potential):
E = –Φ – ∂A/∂t
Likewise, one can show that Maxwell’s equations can be re-written in terms of Φ and A, rather than in terms of E and B. The expression looks rather formidable, but don’t panic:
Just look at it. We have two ‘variables’ here (Φ and A) and two equations, so the system is fully defined. [Of course, the second equation is three equations really: one for each component x, y and z.] What’s the point? Why would we want to re-write Maxwell’s equations? The first equation makes it clear that the scalar potential (i.e. the electric potential) is a time-varying quantity, so things are not, somehow, simpler. The answer is twofold. First, re-writing Maxwell’s equations in terms of the scalar and vector potential makes sense because we have (fairly) easy expressions for their value in time and in space as a function of the charges and currents. For statics, these expressions are:
So it is, effectively, easier to first calculate the scalar and vector potential, and then get E and B from them. For dynamics, the expressions are similar:
Indeed, they are like the integrals for statics, but with “a small and physically appealing modification”, as Feynman notes: when doing the integrals, we must use the so-called retarded time t′ = t − r12/ct’. The illustration below shows how it works: the influences propagate from point (2) to point (1) at the speed c, so we must use the values of ρ and j at the time t′ = t − r12/ct’ indeed!
The second aspect of the answer to the question of why we’d be interested in Φ and A has to do with the topic I wanted to write about here: the concept of a gauge and a gauge transformation.
Gauges and gauge transformations in electromagnetics
Let’s see what we’re doing really. We calculate some A and then solve for B by writing: B = ×A. Now, I say some A because any A‘ = AΨ, with Ψ any scalar field really. Why? Because the curl of the gradient of Ψ – i.e. curl(gradΨ) = ×(Ψ) – is equal to 0. Hence, ×(AΨ) = ×A×Ψ = ×A.
So we have B, and now we need E. So the next step is to take Faraday’s Law, which is Maxwell’s second equation: ×E = –∂B/∂t. Why this one? It’s a simple one, as it does not involve currents or charges. So we combine this equation and our B = ×A expression and write:
×E = –∂(∇×A)/∂t
Now, these operators are tricky but you can verify this can be re-written as:
×(E + ∂A/∂t) = 0
Looking carefully, we see this expression says that E + ∂A/∂t is some vector whose curl is equal to zero. Hence, this vector must be the gradient of something. When doing electrostatics, When we worked on electrostatics, we only had E, not the ∂A/∂t bit, and we said that E tout court was the gradient of something, so we wrote E = −Φ. We now do the same thing for E + ∂A/∂t, so we write:
E + ∂A/∂t = −Φ
So we use the same symbol Φ but it’s a bit of a different animal, obviously. However, it’s easy to see that, if the ∂A/∂t would disappear (as it does in electrostatics, where nothing changes with time), we’d get our ‘old’ −Φ. Now, E + ∂A/∂t = −Φ can be written as:
E = −Φ – ∂A/∂t
So, what’s the big deal? We wrote B and E as a function of Φ and A. Well, we said we could replace A by any A‘ = AΨ but, obviously, such substitution would not yield the same E. To get the same E, we need some substitution rule for Φ as well. Now, you can verify we will get the same E if we’d substitute Φ for Φ’ = Φ – ∂Ψ/∂t. You should check it by writing it all out:
E = −Φ’–∂A’/∂t = −(Φ–∂Ψ/∂t)–∂(A+Ψ)/∂t
= −Φ+(∂Ψ/∂t)–∂A/∂t–∂(Ψ)/∂t = −Φ – ∂A/∂t = E
Again, the operators are a bit tricky, but the +(∂Ψ/∂t) and –∂(Ψ)/∂t terms do cancel out. Where are we heading to? When everything is said and done, we do need to relate it all to the currents and the charges, because that’s the real stuff out there. So let’s take Maxwell’s E = ρ/ε0 equation, which has the charges in it, and let’s substitute E for E = −Φ – ∂A/∂t. We get:
That equation can be re-written as:
So we have one equation here relating Φ and A to the sources. We need another one, and we also need to separate Φ and A somehow. How do we do that?
Maxwell’s fourth equation, i.e. c2×B = j+ ∂E/∂t can, obviously, be written as c2×− E/∂t = j0. Substituting both E and B yields the following monstrosity:
We can now apply the general ∇×(×C) = (·C) – ∇2C identity to the first term to get:
It’s equally monstrous, obviously, but we can simplify the whole thing by choosing Φ and A in a clever way. For the magnetostatic case, we chose A such that ·A = 0. We could have chosen something else. Indeed, it’s not because B is divergence-free, that A has to be divergence-free too! For example, I’ll leave it to you to show that choosing ·A such that
also respects the general condition that any A and Φ we choose must respect the A‘ = AΨ and Φ’ = Φ – ∂Ψ/∂t equalities. Now, if we choose ·A such that ·A = −c–2·∂Φ/∂t indeed, then the two middle terms in our monstrosity cancel out, and we’re left with a much simpler equation for A:
In addition, doing the substitution in our other equation relating Φ and A to the sources yields an equation for Φ that has the same form:
What’s the big deal here? Well… Let’s write it all out. The equation above becomes:
That’s a wave equation in three dimensions. In case you wonder, just check one of my posts on wave equations. The one-dimensional equivalent for a wave propagating in the x direction at speed c (like a sound wave, for example) is ∂2Φ/∂xc–2·∂2Φ/∂t2, indeed. The equation for A yields above yields similar wave functions for A‘s components Ax, Ay, and Az.
So, yes, it is a big deal. We’ve written Maxwell’s equations in terms of the scalar (Φ) and vector (A) potential and in a form that makes immediately apparent that we’re talking electromagnetic waves moving out at the speed c. Let me copy them again:
You may, of course, say that you’d rather have a wave equation for E and B, rather than for A and Φ. Well… That can be done. Feynman gives us two derivations that do so. The first derivation is relatively simple and assumes the source our electromagnetic wave moves in one direction only. The second derivation is much more complicated and gives an equation for E that, if you’ve read the first volume of Feynman’s Lectures, you’ll surely remember:
The links are there, and so I’ll let you have fun with those Lectures yourself. I am finished here, indeed, in terms of what I wanted to do in this post, and that is to say a few words about gauges in field theory. It’s nothing much, really, and so we’ll surely have to discuss the topic again, but at least you now know what a gauge actually is in classical electromagnetic theory. Let’s quickly go over the concepts:
1. Choosing the ·A is choosing a gauge, or a gauge potential (because we’re talking scalar and vector potential here). The particular choice is also referred to as gauge fixing.
2. Changing A by adding ψ is called a gauge transformation, and the scalar function Ψ is referred to as a gauge function. The fact that we can add curl-free components to the magnetic potential without them making any difference is referred to as gauge invariance.
3. Finally, the ·A = −c–2·∂Φ/∂t gauge is referred to as a Lorentz gauge.
Just to make sure you understand: why is that Lorentz gauge so special? Well… Look at the whole argument once more: isn’t it amazing we get such beautiful (wave) equations if we stick it in? Also look at the functional shape of the gauge itself: it looks like a wave equation itself! […] Well… No… It doesn’t. I am a bit too enthusiastic here. We do have the same 1/c2 and a time derivative, but it’s not a wave equation. 🙂 In any case, it all confirms, once again, that physics is all about beautiful mathematical structures. But, again, it’s not math only. There’s something real out there. In this case, that ‘something’ is a traveling electromagnetic field. 🙂
But why do we call it a gauge? That should be equally obvious. It’s really like choosing a gauge in another context, such as measuring the pressure of a tyre, as shown below. 🙂
Gauges and group theory
You’ll usually see gauges mentioned with some reference to group theory. For example, you will see or hear phrases like: “The existence of arbitrary numbers of gauge functions ψ(r, t) corresponds to the U(1) gauge freedom of the electromagnetic theory.” The U(1) notation stands for a unitary group of degree n = 1. It is also known as the circle group. Let me copy the introduction to the unitary group from the Wikipedia article on it:
In mathematics, the unitary group of degree n, denoted U(n), is the group of n × n unitary matrices, with the group operation that of matrix multiplication. The unitary group is a subgroup of the general linear group GL(n, C). In the simple case n = 1, the group U(1) corresponds to the circle group, consisting of all complex numbers with absolute value 1 under multiplication. All the unitary groups contain copies of this group.
The unitary group U(n) is a real Lie group of of dimension n2. The Lie algebra of U(n) consists of n × n skew-Hermitian matrices, with the Lie bracket given by the commutator. The general unitary group (also called the group of unitary similitudes) consists of all matrices A such that A*A is a nonzero multiple of the identity matrix, and is just the product of the unitary group with the group of all positive multiples of the identity matrix.
Phew! Does this make you any wiser? If anything, it makes me realize I’ve still got a long way to go. 🙂 The Wikipedia article on gauge fixing notes something that’s more interesting (if only because I more or less understand what it says):
Although classical electromagnetism is now often spoken of as a gauge theory, it was not originally conceived in these terms. The motion of a classical point charge is affected only by the electric and magnetic field strengths at that point, and the potentials can be treated as a mere mathematical device for simplifying some proofs and calculations. Not until the advent of quantum field theory could it be said that the potentials themselves are part of the physical configuration of a system. The earliest consequence to be accurately predicted and experimentally verified was the Aharonov–Bohm effect, which has no classical counterpart.
This confirms, once again, that the fields are real. In fact, what this says is that the potentials are real: they have a meaningful physical interpretation. I’ll leave it to you to expore that Aharanov-Bohm effect. In the meanwhile, I’ll study what Feynman writes on potentials and all that as used in quantum physics. It will probably take a while before I’ll get into group theory though.
Indeed, it’s probably best to study physics at a somewhat less abstract level first, before getting into the more sophisticated stuff.
# Back to tedious stuff: an introduction to electromagnetism
It seems I skipped too many chapters in Feynman’s second volume of Lectures (on electromagnetism) and so I have to return to that before getting back to quantum physics. So let me just do that in the next couple of posts. I’ll have to start with the basics: Maxwell’s equations.
Indeed, electromagnetic phenomena are described by a set of four equations known as Maxwell’s equations. They relate two fields: the electric field (E) and the magnetic field (B). The electric field appears when we have electric charges: positive (e.g. protons or positively charged ions) or negative (e.g. electrons or negatively charged ions). That’s obvious.
In contrast, there is no such thing as ‘magnetic charges’. The magnetic field appears only when the electric field changes, or when charges move. In turn, the change in the magnetic field causes an electric field, and that’s how electromagnetic radiation basically works: a changing electric field causes a magnetic field, and the build-up of that magnetic field (so that’s a changing magnetic field) causes a build-up of an electric field, and so on and so on.
OK. That’s obvious too. But how does it work exactly? Before explaining this, I need to point out some more ‘obvious’ things:
1. From Maxwell’s equations, we can calculate the magnitude of E and B. Indeed, a specific functional form for E and is what we get when we solve Maxwell’s set of equations, and we’ll jot down that solution in a moment–even if I am afraid you will shake your head when you see it. The point to note is that what we get as a solution for E and B is a solution in a particular frame of reference only: if we switch to another reference frame, E and B will look different.
Huh? Yes. According to the principle of relativity, we cannot say which charges are ‘stationary’ and which charges are ‘moving’ in any absolute sense: it all depends on our frame our reference.
But… Yes? Then if we put an electric charge in these fields, the force on it will also be different?
Yes. Forces also look different when moving from one reference to another.
But… Yes? The physical effect surely has to be the same, regardless of the reference frame?
Yes. The point is that, if we look at an electric charge q moving along a current-carrying wire in a coordinate system at rest with respect to the wire, with the same velocity (v0) as the conduction electrons (v), then the whole force on the electric charge will be ‘magnetic’: F = qv0×B and E = 0. Now, if we’re looking at the same situation from a frame of reference that is moving with q, then our charge is at rest, and so there can be no magnetic force on it. Hence, the force on it must come from an electric field! But what produces the electric field? Our current-carrying wire is supposed to be neutral!
Well… It turns out that our ‘neutral’ wire appears to be charged when moving. We’ll explain – in very much detail – why this is so later. Now, you should just note that “we should not attach too much reality to E and B, because they appear in different ‘mixtures’ in different coordinate systems”, as Feynman puts it. In fact, you may or may not heard that magnetism is actually nothing but a “relativistic effect” of electricity. Well… That’s true, but we’ll also explain how that works later only. Let’s not jump the gun.
2. The remark above is related to the other ‘obvious’ thing I wanted to say before presenting Maxwell’s equations: fields are very useful to describe what’s going on but, when everything is said and done, what we really want to know is what force will be acting on a charge, because that’s what’s going to tell us how that charge is going to move. In other words, we want to find the equations of motion, and the force determines how the charge’s momentum will change: F = dp/dt = d(mv)/dt (i.e. Newton’s equation of motion).
So how does that work? We’ve given the formula before:
F = q(E + v×B) = qE + q(v×B)
This is a sum of two vectors:
1. qE is the ‘electric force: that force is in the same direction as the electric field, but with a magnitude equal to q times E. [Note I use a bold letter (E) for a vector (which we may define as some quantity with a direction) and a non-bold letter (E) for its magnitude.]
2. q(v×B) is the ‘magnetic’ force: that force depends on both v as well as on B. Its direction is given by the so-called right-hand rule for a vector cross-product (as opposed to a dot product, which is denoted by a dot (·) and which yields a scalar instead of a new vector).
That right-hand rule is illustrated below. Note that, if we switch a and b, the b×a vector will point downwards. The magnitude of q(v×B) is given by |v×B| = |v||B|sinθ (with θ the angle between v and B).
We know the direction of (because we’re talking about some charge that is moving here) but what direction is B? It’s time to be a bit more systematic now.
Flux and circulation
In order to understand Maxwell’s equations, one needs to understand two concepts related to a vector field: flux and circulation. The two concepts are best illustrated referring to a vector field describing the flow of a liquid:
1. If we have a surface, the flux will give us the net amount of fluid going out through the surface per unit time. The illustration below (which I took from Feynman’s Lectures) gives us not only the general idea but a formal definition as well:
2. The concept of circulation is linked to the idea of some net rotational motion around some loop. In fact, that’s exactly what it describes. I’ll again use Feynman’s illustration (and description) because I couldn’t find anything better.
Diagram (a) gives us the velocity field in the liquid. Now, imagine a tube (of uniform cross section) that follows some arbitrary closed curve, like in (b), and then imagine we’d suddenly freeze the liquid everywhere except inside the tube: the liquid in the tube would circulate as shown in (c). Formally, the circulation is defined as:
circulation = (the average tangential component)·(the distance around)
OK. So far, so good. Back to electromagnetism.
E and B
We’re familiar with the electric field E from our high school physics course. Indeed, you’ll probably recognize the two examples below: (a) a (positive) charge near a (neutral) conducting sheet, and (b) two opposite charges next to each other. Note the convention: the field lines emanate from the positive charge. Does that mean that the force is in that direction too? Yes. But remember: if a particle is attracted to another, the latter particle is attracted to the former too! So there’s a force in both directions !
What more can we say about this? Well… It is clear that the field E is directed radially. In terms of our flux and circulation concepts, we say that there’s an outgoing flux from the (positive) point charge. Furthermore, it would seem to be pretty obvious (we’d need to show why, but we won’t do that here: just look at Coulomb’s Law once again) that the flux should be proportional to the charge, and it is: if we double the charge, the flux doubles too. That gives us Maxwell’s first equation:
flux of E through a closed surface = (the net charge inside)/ε0
Note we’re talking a closed surface here, like a sphere for example–but it does not have to be a nice symmetric shape: Maxwell’s first equation is valid for any closed surface. The expression above is Coulomb’s Law, which you’ll also surely remember from your high school physics course: while it looks very different, it’s the same. It’s just because we’re using that flux concept here that we seem to be getting an entirely different expression. But so we’re not: it’s the same as Coulomb’s Law.
As for the ε0 factor, that’s just a constant that depends on the units we’re using to measure what we write above, so don’t worry about it. [I am noting it here because you’ll see it pop up later too.]
For B, we’ve got a similar-looking law:
flux of B through a closed surface = 0 (= zero = nil)
That’s not the same, you’ll say. Well… Yes and no. It’s the same really, but the zero on the right-hand side of the expression above says there’s no such thing as a ‘magnetic’ charge.
Hmm… But… If we can’t create any flux of B, because ‘magnetic charges’ don’t exist, so how do we get magnetic fields then?
Well… We wrote that above already, and you should remember it from your high school physics course as well: a magnetic field is created by (1) a moving charge (i.e. a flow or flux of electric current) or (2) a changing electric field.
Situation (1) is illustrated below: the current in the wire creates some circulation of B around the wire. How much? Not much: the magnetic effect is very small as compared to the electric effect (that has to do with magnetism being a relativistic effect of electricity but, as mentioned above, I’ll explain that later only). To be precise, the equation is the following:
c2(circulation of B)= (flux of electric current)/ε0
That c2 factor on the left-hand side becomes 1/c2 if we move it to the other side and, yes, is the speed of light here – so you can see we’re talking a very small amount of circulation only indeed! [As for the ε0 factor, that’s just the same constant: it’s got to do with the units we’re using to measure stuff.]
One last point perhaps: what’s the direction of the circulation? Well… There’s a so-called right-hand grip rule for that, which is illustrated below.
OK. Enough about this. Let’s go to situation (2): a changing electric field. That effect is usually illustrated with Faraday’s original 1831 experiment, which is shown below with a more modern voltmeter 🙂 : when the wire on one side of the iron ring is connected to the battery, we’ll see a transient current on the other side. It’s transient only, so the current quickly disappears. That’s why transformers don’t work with DC. In fact, it is said that Faraday was quite disappointed to see that the current didn’t last! Likewise, when the wire is disconnected, we’ll briefly see another transient current.
So this effect is due to the changing electric field, which causes a changing magnetic field. But so where is that magnetic field? We’re talking currents here, aren’t we? Yes, you’re right. To understand why we have a transient current in the voltmeter, you need to understand yet another effect: a changing magnetic field causes an electric field, and so that’s what actually generates the transient current. However, what’s going on in the iron ring is the magnetic effect, and so that’s caused by the changing electric field as we connect/disconnect the battery to the wire. Capito?
I guess so… So what’s the equation that captures this situation, i.e. situation (2)? That equation involves both flux and circulation, so we’ll have a surface (S) as well as a curve (C). The equation is the following one: for any surface S (not closed this time because, if the surface was closed, it wouldn’t have an edge!), we have:
c2(circulation of B around C)= d(flux of E through S)/dt
I mentioned above that the reverse is also true. A changing magnetic field causes an electric field, and the equation for that looks very similar, except that we don’t have the c2 factor:
circulation of around = d(flux of through S)/dt
Let me quickly mention the presence of absence of that c2 or 1/c2 factor in the previous equations once again. It is interesting. It’s got nothing to do with the units. It’s really a proportionality factor: any change in E will only cause a little change in (because of the 1/c2 factor in the first equation), but the reverse is not true: there’s no c2 in the second equation. Again, it’s got to do with magnetism being a relativistic effect of electricity, so the magnetic effect is, in most cases, tiny as compared to the electric effect, except when we’re talking charges that are moving at relativistic speeds (i.e. speeds close to c). As said, we’ll come back to that–later, much later. Let’s get back to Maxwell’s equations first.
Maxwell’s equations
We can now combine all of the equations above in one set, and so these are Maxwell’s four famous equations:
1. The flux of E through a closed surface = (the net charge inside)/ε0
2. The circulation of E around = d(flux of through S)/dt (with the curve or edge around S)
3. The flux of B through a closed surface = 0
4. c2(circulation of B around C)= d(flux of E through S)/dt + (flux of electric current)/ε0
From a mathematical point of view, this is a set of differential equations, and they are not easy to grasp intuitively. As Feynman puts it: “The laws of Newton were very simple to write down, but they had a lot of complicated consequences and it took us a long time to learn about them all. These laws are not nearly as simple to write down, which means that the consequences are going to be more elaborate and it will take us quite a lot of time to figure them all out.”
Indeed, Feynman needs about twenty (!) Lectures in that second Volume to show what it all implies, as he walks us through electrostatics, magnetostatics and various other ‘special’ cases before giving us the ‘complete’ or ‘general’ solution to the equations. This ‘general’ solution, in mathematical notation, is the following:
Huh? What’s that? Well… The four equations are the equations we explained already, but this time in mathematical notation: flux and circulation can be expressed much more elegantly using the differential operator indeed. As for the solutions to Maxwell’s set of equations, you can see they are expressed using two other concepts: the scalar potential Φ and the vector potential A.
Now, it is not my intention to summarize two dozen of Feynman’s Lectures in just a few lines, so I’ll have to leave you here for the moment.
[…]
Huh? What? What about my promise to show that magnetism is a relativistic effect of electricity indeed?
Well… I wanted to do that just now, but when I look at it, I realize that I’d end up copying most of Feynman’s little exposé on it and, hence, I’ll just refer you to that particular section. It’s really quite exciting but – as you might expect – it does take a bit of time to wrestle through it.
That being said, it really does give you a kind of an Aha-Erlebnis and, therefore, I really warmly recommend it ! Just click on the link ! 🙂 | 2019-03-26 10:40:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8442645072937012, "perplexity": 528.9650153472303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204969.39/warc/CC-MAIN-20190326095131-20190326121131-00176.warc.gz"} |
http://stackoverflow.com/questions/11380491/how-to-create-a-list-of-random-integer-vector-whose-sum-is-x?answertab=active | # How to create a list of random integer vector whose sum is x
Creating a random vector whose sum is X (e.g. X=1000) is fairly straight forward:
import random
def RunFloat():
Scalar = 1000
VectorSize = 30
RandomVector = [random.random() for i in range(VectorSize)]
RandomVectorSum = sum(RandomVector)
RandomVector = [Scalar*i/RandomVectorSum for i in RandomVector]
return RandomVector
RunFloat()
The code above create a vector whose values are floats and sum is 1000.
I'm having difficulty creating a simple function for creating a vector whose values are integers and sum is X (e.g. X=1000*30)
import random
def RunInt():
LowerBound = 600
UpperBound = 1200
VectorSize = 30
RandomVector = [random.randint(LowerBound,UpperBound) for i in range(VectorSize)]
RandomVectorSum = 1000*30
#Sanity check that our RandomVectorSum is sensible/feasible
if LowerBound*VectorSize <= RandomVectorSum and RandomVectorSum <= UpperBound*VectorSum:
if sum(RandomVector) == RandomVectorSum:
return RandomVector
else:
RunInt()
Does anyone have any suggestions to improve on this idea? My code might never finish or run into recursion depth problems.
# Edit (July 9, 2012)
Thanks to Oliver, mgilson, and Dougal for their inputs. My solution is shown below.
1. Oliver was very creative with the multinomial distribution idea
2. Put simply, (1) is very likely to output certain solutions more so than others. Dougal demonstrated that the multinomial solution space distribution is not uniform or normal by a simple test/counter example of Law of Large Numbers. Dougal also suggested to use numpy's multinomial function which saves me a lot of trouble, pain, and headaches.
3. To overcome (2)'s output issue, I use RunFloat() to give what appears (I haven't tested this so its just a superficial appearance) to be a more uniform distribution. How much of a difference does this make compared to (1)? I don't really know off-hand. It's good enough for my use though.
4. Thanks again to mgilson for the alternative method that does not use numpy.
Here is the code that I have made for this edit:
## Edit #2 (July 11,2012)
I realized that the normal distribution is not correctly implemented, I have since modified it to the following:
import random
def RandFloats(Size):
Scalar = 1.0
VectorSize = Size
RandomVector = [random.random() for i in range(VectorSize)]
RandomVectorSum = sum(RandomVector)
RandomVector = [Scalar*i/RandomVectorSum for i in RandomVector]
return RandomVector
from numpy.random import multinomial
import math
def RandIntVec(ListSize, ListSumValue, Distribution='Normal'):
"""
Inputs:
ListSize = the size of the list to return
ListSumValue = The sum of list values
Distribution = can be 'uniform' for uniform distribution, 'normal' for a normal distribution ~ N(0,1) with +/- 5 sigma (default), or a list of size 'ListSize' or 'ListSize - 1' for an empirical (arbitrary) distribution. Probabilities of each of the p different outcomes. These should sum to 1 (however, the last element is always assumed to account for the remaining probability, as long as sum(pvals[:-1]) <= 1).
Output:
A list of random integers of length 'ListSize' whose sum is 'ListSumValue'.
"""
if type(Distribution) == list:
DistributionSize = len(Distribution)
if ListSize == DistributionSize or (ListSize-1) == DistributionSize:
Values = multinomial(ListSumValue,Distribution,size=1)
OutputValue = Values[0]
elif Distribution.lower() == 'uniform': #I do not recommend this!!!! I see that it is not as random (at least on my computer) as I had hoped
UniformDistro = [1/ListSize for i in range(ListSize)]
Values = multinomial(ListSumValue,UniformDistro,size=1)
OutputValue = Values[0]
elif Distribution.lower() == 'normal':
"""
Normal Distribution Construction....It's very flexible and hideous
Assume a +-3 sigma range. Warning, this may or may not be a suitable range for your implementation!
If one wishes to explore a different range, then changes the LowSigma and HighSigma values
"""
LowSigma = -3#-3 sigma
HighSigma = 3#+3 sigma
StepSize = 1/(float(ListSize) - 1)
ZValues = [(LowSigma * (1-i*StepSize) +(i*StepSize)*HighSigma) for i in range(int(ListSize))]
#Construction parameters for N(Mean,Variance) - Default is N(0,1)
Mean = 0
Var = 1
#NormalDistro= [self.NormalDistributionFunction(Mean, Var, x) for x in ZValues]
NormalDistro= list()
for i in range(len(ZValues)):
if i==0:
ERFCVAL = 0.5 * math.erfc(-ZValues[i]/math.sqrt(2))
NormalDistro.append(ERFCVAL)
elif i == len(ZValues) - 1:
ERFCVAL = NormalDistro[0]
NormalDistro.append(ERFCVAL)
else:
ERFCVAL1 = 0.5 * math.erfc(-ZValues[i]/math.sqrt(2))
ERFCVAL2 = 0.5 * math.erfc(-ZValues[i-1]/math.sqrt(2))
ERFCVAL = ERFCVAL1 - ERFCVAL2
NormalDistro.append(ERFCVAL)
#print "Normal Distribution sum = %f"%sum(NormalDistro)
Values = multinomial(ListSumValue,NormalDistro,size=1)
OutputValue = Values[0]
else:
raise ValueError ('Cannot create desired vector')
return OutputValue
else:
raise ValueError ('Cannot create desired vector')
return OutputValue
#Some Examples
ListSize = 4
ListSumValue = 12
for i in range(100):
print RandIntVec(ListSize, ListSumValue,Distribution=RandFloats(ListSize))
The code above can be found on github. It is part of a class I built for school. user1149913, also posted a nice explanation of the problem.
-
You may have a problem if you want to sum many float numbers and get an exact value... – JBernardo Jul 8 '12 at 3:54
possible duplicate of Generate multiple random numbers to equal a value in python – finnw Jul 8 '12 at 9:40
After running into a related problem, this would argue that this question is related to asking "how to randomly select a partition of n whose size is X". related wiki – torrho Mar 2 '14 at 20:50
I would suggest not doing this recursively:
When you sample recursively, the value from the first index has a much greater possible range, whereas values in subsequent indices will be constrained by the first value. This will yield something resembling an exponential distribution.
Instead, what I'd recommend is sampling from the multinomial distribution. This will treat each index equally, constrain the sum, force all values to be integers, and sample uniformly from all possible configurations that follow these rules (note: configurations that can happen multiple ways will be weighted by the number of ways that they can occur).
To help merge your question with the multinomial notation, total sum is n (an integer), and so each of the k values (one for each index, also integers) must be between 0 and n. Then follow the recipe here.
(Or use numpy.random.multinomial as @Dougal helpfully suggested).
-
If numpy is available, numpy.random.multinomial also implements this. – Dougal Jul 8 '12 at 4:03
@Dougal +1 Time-saving. – Oliver Jul 8 '12 at 4:03
I think you want the Dirichilet distribution instead of the multinomial... – user1245262 Jul 8 '12 at 4:39
@user1245262 Dirichlet has values in [0,1]^n that sum to 1. OP wants integers that sum to X. Multinominal has the right support, though who knows if it's the distribution OP wants. – Dougal Jul 8 '12 at 4:55
@Dougal - But doesn't multinomial only insist that the sum of the number of instances of each outcome be N, rather than the sum of the outcomes be N. Dirichilet requires that the sum of the N outcomes is 1, but it shouldn't be too hard to generalize that, if only by multiplying all the outcomes by a constant factor and then adjusting for rounding... unless I'm missing something here... – user1245262 Jul 8 '12 at 5:01
The most efficient way to sample uniformly from the set of partitions of N elements into K bins is to use a dynamic programming algorithm, which is O(KN). There are a multichoose (http://mathworld.wolfram.com/Multichoose.html) number of possibilities, so enumerating every one will be very slow. Rejection sampling and other monte-carlo methods will also likely be very slow.
Other methods people propose, like sampling from a multinomial do not draw samples from a uniform distribution.
Let T(n,k) be the number of partitions of n elements into k bins, then we can compute the recurrence
T(n,1)=1 \forall n>=0
T(n,k)=\sum_{m<=n} T(n-m,k-1)
To sample K elements that sum to N, sample from K multinomial distributions going "backward" in the recurrence: Edit: The T's in the multinomial's below should be normalized to sum to one before drawing each sample.
n1 = multinomial([T(N,K-1),T(N-1,K-1),...,T(0,K-1)])
n2 = multinomial([T(N-n1,K-1),T(N-n1-1,K-1),...,T(0,K-1)])
...
nK = multinomial([T(N-sum([n1,...,n{k-1}]),1),T(N-sum([n1,...,n{k-1}])-1,1),...,T(0,1)])
Note: I am allowing 0's to be sampled.
This procedure is similar to sampling a set of hidden state from a segmental semi-markov model (http://www.gatsby.ucl.ac.uk/%7Echuwei/paper/icml103.pdf).
-
Thank you for your post. This is helpful. – torrho Jul 11 '12 at 13:49
This version will give a uniform distribution:
from random import randint
def RunInt(VectorSize, Sum):
x = [randint(0, Sum) for _ in range(1, VectorSize)]
x.extend([0, Sum])
x.sort()
return [x[i+1] - x[i] for i in range(VectorSize)]
-
This returns some invalid results, e.g. (10, 0, 1) when called with 3, 10. The distribution also isn't actually uniform: i.imgur.com/tPTxC.png. All but one of the outcomes on the less-common peak are valid outcomes. – Dougal Jul 8 '12 at 19:28
Just to give you another approach, implement a partition_function(X) and randomly choose a number between 0 and the length of partition_function(1000) and there you have it. Now you just need to find an efficient way to calculate a partition function. These links might help:
http://code.activestate.com/recipes/218332-generator-for-integer-partitions/
http://oeis.org/A000041
EDIT: Here is a simple code:
import itertools
import random
all_partitions = {0:set([(0,)]),1:set([(1,)])}
def partition_merge(a,b):
c = set()
for t in itertools.product(a,b):
return c
def my_partition(n):
if all_partitions.has_key(n):
return all_partitions[n]
a = set([(n,)])
for i in xrange(1,n/2+1):
a = partition_merge(my_partition(i),my_partition(n-i)).union(a)
all_partitions[n] = a
return a
if __name__ == '__main__':
n = 30
# if you have a few years to wait uncomment the next line
# n = 1000
a = my_partition(n)
i = random.randint(0,len(a)-1)
print(list(a)[i])
-
I just ran both @Oliver's multinomial approach and @mgilson's code a million times each, for a length-3 vector summing to 10, and looked at the number of times each possible outcome came up. Both are extremely nonuniform:
(I'm about to show the indexing approach.)
Does this matter? Depends on whether you want "an arbitrary vector with this property that's usually different each time" vs each valid vector being equally likely.
In the multinomial approach, of course 3 3 4 is going to be much more likely than 0 0 10 (4200 times more likely, as it turns out). mgilson's biases are less obvious to me, but 0 0 10 and its permutations were the least likely by far (only ~750 times each out of a million); the most common were 1 4 5 and its permutations; not sure why, but they were certainly the most common, followed by 1 3 6. It'll typically start with a sum that's too high in this configuration (expectation 15), though I'm not sure why the reduction works out that way....
One way to get a uniform output over the possible vectors would be a rejection scheme. To get a vector of length K with sum N, you'd:
1. Sample a vector of length K with integer elements uniformly and independently between 0 and N.
2. Repeat until the sum of the vector is N.
Obviously this is going to be extremely slow for non-tiny K and N.
Another approach would be to assign a numbering to all the possible vectors; there are (N + K - 1) choose (K - 1) such vectors, so just choose a random integer in that range to decide which one you want. One reasonable way to number them is lexicographic ordering: (0, 0, 10), (0, 1, 9), (0, 2, 8), (0, 3, 7), ....
Note that the last (Kth) element of the vector is uniquely determined by the sum of the first K-1.
I'm sure there's a nice way to immediately jump to whatever index in this list, but I can't think of it right now....enumerating the possible outcomes and walking over them will work, but will probably be slower than necessary. Here's some code for that (though we actually use reverse lexicographic ordering here...).
from itertools import islice, combinations_with_replacement
from functools import reduce
from math import factorial
from operator import mul
import random
def _enum_cands(total, length):
# get all possible ways of choosing 10 of our indices
# for example, the first one might be 0000000000
# meaning we picked index 0 ten times, for [10, 0, 0]
for t in combinations_with_replacement(range(length), 10):
cand = [0] * length
for i in t:
cand[i] += 1
yield tuple(cand)
def int_vec_with_sum(total, length):
num_outcomes = reduce(mul, range(total + 1, total + length)) // factorial(length - 1)
# that's integer division, even though SO thinks it's a comment :)
idx = random.choice(range(num_outcomes))
return next(islice(_enum_cands(total, length), idx, None))
As shown in the histogram above, this is actually uniform over possible outcomes. It's also easily adaptable to upper/lower bounds on any individual element; just add the condition to _enum_cands.
This is slower than either of the other answers: for sum 10 length 3, I get
• 14.7 us using np.random.multinomial,
• 33.9 us using mgilson's,
• 88.1 us with this approach
I'd expect that the difference would get worse as the number of possible outcomes increases.
If someone comes up with a nifty formula for indexing into these vectors somehow, it'd be much better....
-
You make a great point about this distribution of solutions in the multinomial implementation. My first hunch about all of this is that the multinomial idea is the one I desire. your comment about "In the multinomial approach, of course 3 3 4 is going to be much more likely than 0 0 10" is exactly what I had in mind. You applied Law of Large Numbers and the multinomial method has a frequency plot that I like. Thanks for your input! I appreciate that you point this out – torrho Jul 8 '12 at 7:52
I suppose one underlying problem of this multinomial distribution solutions is a way to 'correct' the likehood of outputs for a sum of X and a vector length Y such that: the likelihood of an output is the same to any other alternative. I'll leave that one for another day. :( – torrho Jul 8 '12 at 8:11
Here's a pretty straight forward implementation.
import random
import math
def randvec(vecsum, N, maxval, minval):
if N*minval > vecsum or N*maxval < vecsum:
raise ValueError ('Cannot create desired vector')
indices = list(range(N))
vec = [random.randint(minval,maxval) for i in indices]
diff = sum(vec) - vecsum # we were off by this amount.
#Iterate through, incrementing/decrementing a random index
#by 1 for each value we were off.
while diff != 0:
addthis = 1 if diff > 0 else -1 # +/- 1 depending on if we were above or below target.
### IMPLEMENTATION 1 ###
idx = random.choice(indices) # Pick a random index to modify, check if it's OK to modify
while not (minval < (vec[idx] - addthis) < maxval): #operator chaining. If you don't know it, look it up. It's pretty cool.
idx = random.choice(indices) #Not OK to modify. Pick another.
vec[idx] -= addthis #Update that index.
### IMPLEMENTATION 2 ###
# random.shuffle(indices)
# for idx in indices:
# if minval < (vec[idx] - addthis) < maxval:
# break
#
# in situations where (based on choices of N, minval, maxval and vecsum)
# many of the values in vec MUST BE minval or maxval, Implementation 2
# may be superior.
return vec
a = randvec(1000,20,100,1)
print sum(a)
-
Well it gives a nonuniform distribution, which might be an issue. It depends on what the OP wants. – Antimony Jul 8 '12 at 3:59
One problem with this is that the last element could exceed UpperBound. – DSM Jul 8 '12 at 3:59
@Antimony +1 I agree. The first value will have a much higher chance of being large compared to subsequent values (see my answer below). – Oliver Jul 8 '12 at 4:01
@DSM -- You're right. I didn't read the code above very carefully. I've edited with a new solution. – mgilson Jul 8 '12 at 4:52
@Oliver -- updated. I think/hope this is a nicer solution than posted previously. – mgilson Jul 8 '12 at 4:55 | 2015-03-30 09:57:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5962298512458801, "perplexity": 2160.585836753961}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1427131299236.74/warc/CC-MAIN-20150323172139-00122-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://physics.stackexchange.com/questions/294700/accelerated-ion-beam-current | # Accelerated ion beam current
If an electron gun creates a $10\space mA$ electron beam and each electron collides with a gas atom and creates an ion through impact ionization, can the ions then be accelerated with a separate negative voltage grid that is powered by a lower current capacity source but still maintains a $10\space mA$ current?
Basically, in the figure below - what is the maximum ion current accelerated by the $30kV$ grid?
(The gas pressure would be $10^{-5}$ Tor.)
Clarification: Is the ion current directly proportional to the current capacity of the 30kV grid?
• Is this an actual device, or a design idea? – rob Nov 26 '16 at 4:54
• @rob, It's a design idea. Your thoughts? – heather Nov 26 '16 at 6:00
• My guess is that if the gas is dense enough to act like a fluid, which you've suggested with your little cloud, then intra-fluid collisions will prevent any acceleration and you'll make a discharge tube. With a vacuum system to keep the gas at plasma densities, you might get some ions out. Thirty kilovolts is nontrivial. You should study some existing designs. Older documents sometimes assume less prior knowledge; Ramsey (very active midcentury, Nobel 1984-ish) is a good author to look for. – rob Nov 26 '16 at 17:20
• @rob, thank you for the references, I'll look into those! As a side note I didn't intend the cloud to represent a high density of gas, only that gas was present; the operating pressure is probably somewhere in the $10^{-5}$ Tor range. – heather Nov 26 '16 at 17:47
• Electron Beam Ion Sources – user121904 Nov 28 '16 at 17:53 | 2019-10-14 15:34:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7175159454345703, "perplexity": 1537.467724891421}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986653876.31/warc/CC-MAIN-20191014150930-20191014174430-00001.warc.gz"} |
https://math.stackexchange.com/questions/2844871/why-does-elo-rating-uses-sigmoid | why does elo rating uses sigmoid?
I know how to calculate elo rating (in chess) and etc but why does it uses sigmoid? which makes chance of win/lose grow slower and slower if difference in elo is bigger (for example 0 difference gives 0.5, 100 difference 0.64, 700 difference 0.98 and 800 difference 0.99). What is the point of making chances grow up slower by increasing difference?
• If the chance of win didn't grow slower, for a large difference in rating you'd have more than 1.00 chance of win, which doesn't make any sense. – Rahul Jul 8 '18 at 18:46
The win probability has to increase more slowly as the rating difference increases, because it can never exceed $1$. In your example, if a difference of $100$ in rating means a win probability of $0.64$, surely a difference of $400$ in rating cannot mean a win probability of $1.06$! But that's what would happen if the rate of increase remained constant.
The exact distribution chosen is more an empirical question than a theoretical one. If the win probability for a difference of $100$ in rating is $0.64$, then the win probability for a difference of $200$ in rating answers the question, "If Alice beats Bob 64% of the time and Bob beats Charlie 64% of the time, how frequently does Alice beat Charlie?" But there's no theoretical reason why that must be any number in particular (except that it's probably more than 64% and certainly no more than 100%) unless you have a really good model of how chess skill works, and I don't think we do.
Suppose we were modeling a sumo robot competition where the probability of failure of robot $A$ between times $t$ and $t+dt$, given that it functions up to time $t$ is independent of time: $$P\left(\bar A(t+dt)|A(t)\right)=\lambda_Adt$$ Similarly for robot $B$ $$P\left(\bar B(t+dt)|B(t)\right)=\lambda_Bdt$$ If one robot fails, the other pushes it out of the ring and wins. Of course, real sumo robot competition can't be so simply modeled :) But given such a model the ratio of points scored by $A$ to those scored by $B$ between $t$ and $t+dt$ is $$r_{A/B}=\frac{\lambda_Bdt}{\lambda_Adt}=\frac{\lambda_B}{\lambda_A}$$ Since this ratio is valid for all time intervals it will be the ratio for the entire struggle. We can more easily grasp differences than ratios, so we set up a logarithmic scale $$\ln r_{A/B}=\ln\lambda_B-\ln\lambda_A$$ $$\ln\lambda_A=m\left(R_0-R_A\right)$$ Now to find the mathematical expectation of $A$'s score in a bout with $B$, we get $$p_A=\frac{\text{points}_A}{\text{points}_A+\text{points}_B}=\frac1{1+\frac{\text{points}_B}{\text{points}_A}}=\frac1{1+\frac1{r_{A/B}}}=\frac1{1+\frac{\lambda_A}{\lambda_B}}=\frac1{1+e^{m\left(R_B-R_A\right)}}$$ The scale factor $m$ for ratings is arbitrary; Elo chose $$m=\frac{\ln10}{400}$$ With the reference rating $R_0$ set at some value such that hopefully nobody gets negative ratings. This is sort of the way IQ scores are curved so that the mean is $100$ and the standard deviation is $15$ points, or more exactly like loudness in decibels.
It might seem odd that we got to Elo ratings by focusing on your failure rate rather than how brilliant you were, but I remember looking at the code for Crafty back in the day when it was getting good enough to beat grandmasters at speed chess and it really didn't have any more strategic insight built into it than one might get out of reading My System by Aron Nimzovich and the programmer wasn't any stronger than an $A$ player, but it could calculate enough positions that it made few obvious tactical mistakes. Put another way, it vindicated Richard Teichmann's estimate that chess is $90\text{%}$ tactics as perhaps even an underestimate.
Of course a cynic might remark that Elo was a physicist and so set $A$'s mean score to be Fermi-Dirac distributed with energies $\epsilon_B=R_B$, Fermi energy $\epsilon_F=R_A$, and $kT=400/\ln10$. | 2019-07-19 00:10:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.7802844047546387, "perplexity": 667.1470934911398}, "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/1563195525863.49/warc/CC-MAIN-20190718231656-20190719013656-00469.warc.gz"} |
http://www.reference.com/browse/Tonality+Diamond | Definitions
Nearby Words
# Tonality diamond
In music theory, the n-limit tonality diamond is the set of rational numbers r, $1 le r < 2$, such that the odd part of both the numerator and the denominator of r, when reduced to lowest terms, is less than or equal to the fixed odd number n. Equivalently, the diamond may be considered as a set of pitch classes, where a pitch class is an equivalence class of pitches under octave equivalence. The tonality diamond is often regarded as comprising the set of consonances of the n-limit. Although originally invented by Max Meyer, the tonality diamond is now most associated with Harry Partch.
## The diamond arrangement
Partch arranged the elements of the tonality diamond in the shape of a rhombus, which we can take to be a square, skew-oriented so that the sides are at 45 degrees to the horizontal, and subdivided into (n+1)2/4 smaller squares, in chessboard style, and hence the name. Along upper left side of the rhombus we place the odd numbers from 1 to n, reduced to the octave, inside the board squares. Along the lower left side we place the corresponding reciprocals, 1 to 1/n, reduced to the octave. At all the other board squares we place the product, reduced to the octave. This gives all the elements of the tonality diamond, with some repetition. All the diagonals sloping in one direction form otonalities and the diagonals in the other direction form utonalities. Harry Partch created an instrument, the diamond marimba, which is laid out as a tonality diamond and which has proven rather popular.
`7-limit tonality diamond`
` 7/4`
` 3/2 7/5`
` 5/4 6/5 7/6`
`1/1 1/1 1/1 1/1`
` 8/5 5/3 12/7`
` 4/3 10/7`
` 8/7`
`15-limit tonality diamond`
` 15/8`
` 7/4 5/3`
` 13/8 14/9 3/2`
` 3/2 13/9 7/5 15/11`
` 11/8 4/3 13/10 14/11 5/4`
` 5/4 11/9 6/5 13/11 7/6 15/13`
` 9/8 10/9 11/10 12/11 13/12 14/13 15/14`
`1/1 1/1 1/1 1/1 1/1 1/1 1/1 1/1`
` 16/9 9/5 20/11 11/6 24/13 13/7 28/15`
` 8/5 18/11 5/3 22/13 12/7 26/15`
` 16/11 3/2 20/13 11/7 8/5`
` 4/3 18/13 10/7 22/15`
` 16/13 9/7 4/3`
` 8/7 6/5`
` 16/15`
## Geometry of the tonality diamond
The five and seven limit tonality diamonds can be viewed as having a highly regular geometry within the modulatory space which makes all the non-unison elements of the diamond at a distance of one unit from the unison. The five-limit diamond then becomes a regular hexagon surrounding the unison, and the seven-limit diamond a cuboctahedron surrounding the unison.
## Size of the tonality diamond
If φ(n) is Euler's totient function, which gives the number of positive integers less than n and relatively prime to n, that is, it counts the integers less than n which share no common factor with n, and if d(n) denotes the size of the n-limit tonality diamond, we have the formula
From this we can conclude that the rate of growth of the tonality diamond is asymptotically equal to $frac\left\{2\right\}\left\{pi^2\right\} n^2$. The first few values are the important ones, and the fact that the size of the diamond grows as the square of the size of the odd limit tells us that it becomes large fairly quickly. There are seven members to the 5-limit diamond, 13 to the 7-limit diamond, 19 to the 9-limit diamond, 29 to the 11-limit diamond, 41 to the 13-limit diamond, and 49 to the 15-limit diamond; these suffice for most purposes.
Search another word or see Tonality Diamondon Dictionary | Thesaurus |Spanish | 2015-01-30 06:40:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6080909371376038, "perplexity": 899.6049175042082}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115856087.17/warc/CC-MAIN-20150124161056-00138-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://formulasearchengine.com/wiki/Lattice_theorem | # Lattice theorem
In mathematics, the lattice theorem, sometimes referred to as the fourth isomorphism theorem or the correspondence theorem, states that if ${\displaystyle N}$ is a normal subgroup of a group ${\displaystyle G}$, then there exists a bijection from the set of all subgroups ${\displaystyle A}$ of ${\displaystyle G}$ such that ${\displaystyle A}$ contains ${\displaystyle N}$, onto the set of all subgroups of the quotient group ${\displaystyle G/N}$. The structure of the subgroups of ${\displaystyle G/N}$ is exactly the same as the structure of the subgroups of ${\displaystyle G}$ containing ${\displaystyle N,}$ with ${\displaystyle N}$ collapsed to the identity element.
This establishes a monotone Galois connection between the lattice of subgroups of ${\displaystyle G}$ and the lattice of subgroups of ${\displaystyle G/N}$, where the associated closure operator on subgroups of ${\displaystyle G}$ is ${\displaystyle {\bar {H}}=HN.}$
Specifically, if
G is a group,
N is a normal subgroup of G,
${\displaystyle {\mathcal {G}}}$ is the set of all subgroups A of G such that ${\displaystyle N\subseteq A\subseteq G}$, and
${\displaystyle {\mathcal {N}}}$ is the set of all subgroups of G/N,
then there is a bijective map ${\displaystyle \phi :{\mathcal {G}}\to {\mathcal {N}}}$ such that
${\displaystyle \phi (A)=A/N}$ for all ${\displaystyle A\in {\mathcal {G}}.}$
One further has that if A and B are in ${\displaystyle {\mathcal {G}}}$, and A' = A/N and B' = B/N, then
This list is far from exhaustive. In fact, most properties of subgroups are preserved in their images under the bijection onto subgroups of a quotient group.
Similar results hold for rings, modules, vector spaces, and algebras. | 2020-07-09 11:51:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 36, "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": 0.9315580725669861, "perplexity": 101.22128359230118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655899931.31/warc/CC-MAIN-20200709100539-20200709130539-00232.warc.gz"} |
https://projecteuclid.org/euclid.aaa/1355495858 | ## Abstract and Applied Analysis
### Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations
#### Abstract
This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution $u(x)$ is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ${u}_{n}(x)$ is obtained and it is proved to converge to the exact solution $u(x)$. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.
#### Article information
Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 839836, 16 pages.
Dates
First available in Project Euclid: 14 December 2012
https://projecteuclid.org/euclid.aaa/1355495858
Digital Object Identifier
doi:10.1155/2012/839836
Mathematical Reviews number (MathSciNet)
MR2969993
Zentralblatt MATH identifier
1253.65200
#### Citation
Abu Arqub, Omar; Al-Smadi, Mohammed; Momani, Shaher. Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations. Abstr. Appl. Anal. 2012 (2012), Article ID 839836, 16 pages. doi:10.1155/2012/839836. https://projecteuclid.org/euclid.aaa/1355495858
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• K. Holmåker, “Global asymptotic stability for a stationary solution of a system of integro-differential equations describing the formation of liver zones,” SIAM Journal on Mathematical Analysis, vol. 24, no. 1, pp. 116–128, 1993.
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• A. Daniel, Reproducing Kernel Spaces and Applications, Springer, New York, NY, USA, 2003.
• M. Cui and H. Du, “Representation of exact solution for the nonlinear Volterra-Fredholm integral equations,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1795–1802, 2006.
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• J. Li, “A computational method for solving singularly perturbed two-point singular boundary value problem,” International Journal of Mathematical Analysis, vol. 2, no. 21-24, pp. 1089–1096, 2008.
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• Y. Zhou, M. Cui, and Y. Lin, “Numerical algorithm for parabolic problems with non-classical conditions,” Journal of Computational and Applied Mathematics, vol. 230, no. 2, pp. 770–780, 2009. | 2019-06-16 19:27:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 3, "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": 0.34050649404525757, "perplexity": 1488.5220118026539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1560627998291.9/warc/CC-MAIN-20190616182800-20190616204800-00553.warc.gz"} |
https://economics.stackexchange.com/questions/35903/why-does-lowering-stock-rate-of-returns-increase-stock-prices | # Why does lowering stock rate of returns increase stock prices?
(i) I don't understand point 1 beneath. Why does the Federal Reserve's buying assets lower risk premiums?
(ii) I don't understand point 3 beneath. Why does lower stock rate of returns increase stock prices? Won't lower stock rate of returns lower stock demand? Won't some investors buy something else other than stocks?
Why the stock market is going up... and it's not because the Coronavirus is going away : investing
I think I know why the stock market is up... and it's not because the Coronavirus is going away.
It requires some macroeconomic and finance knowledge, but maybe, just maybe:
1. Fed actions (buying assets) are lowering risk premiums
2. Fed actions (lowering rates) are lowering asset yields overall
3. Both of these actions lower stock yields, which increases stock prices
4. Lower stock yields = longer duration for stocks (dividend discount model)
5. Longer duration + lower stock yields = less overall sensitivity to the lower expected earnings for next 12-24 months due to Coronavirus
6. Plus... a maybe.... maybe long-term inflation expectations due to printing money = higher earnings (in pure dollar terms) for cash flows 5-30 years from now
Run those things through a discounted cash-flow model, and you get higher stock prices. Near-term earnings become less important to the overall picture.
• Some nuh-nuh: (a) don't ask about multiple mechanisms/channels in the same q/post unless you're asking about their relative importance (which you're not doing here). Having to explain the "why" for more than one thing in the same q/a is discourgaged. (b) in all the time you've spent reading (and posting here about) Reddit theories, you could read some actual research on QE and stocks: dnb.nl/binaries/Working%20paper%20No.%20660_tcm46-386407.pdf – Fizz Apr 10 '20 at 2:57
• And I don't mean you have to read the whole effing paper, but just its intro & conclusions would get you much further than hours on Reddit. See sciencemag.org/careers/2016/03/… for general advice on reading science papers. – Fizz Apr 10 '20 at 3:03
1. In the part 1 there must be some omission. Just by itself a random Fed purchase would not reduce risk premiums. However, a targeted Fed purchase can reduce risk premium as non-trivial part of risk in any firm stems from liquidity risk. Through purchasing assets of illiquid firms Fed can provide them with liquidity that they need and thereby reducing the risk that they fail just due to illiquidity. Also as Fizz points out in his comment this is just one example, there are several other channels that can also lead to risk reduction as well.
2. The intuition behind this is that the stock prices represent present value of the future expected income streams you get from the stock and at lower interest rate the present value of this income stream becomes higher. To see why this makes sense consider practical example where the stock always pays dividend 10\$in perpetuity. Then in order to actually calculate whats the present value of getting the stream of 10\$ at 10% you can use the Gordon formula which is just based on calculating the value of infinite sum. In simple Gordon stock pricing formula given as $$P=\frac{D}{r-g}$$ where $$D$$ is dividend and $$r$$ rate of interest and $$g$$ rate of growth which we can for sake of simplicity ignore and assume its zero so we get $$P = \frac{D}{r}$$.
At the 10% the infinite sum of 10\$will be worth 100\$ because although your are getting the dividend in perpetuity due to time value of money money in future is less valuable than money now and becomes less value the more you look into the future and hence this infinite sum in present value terms becomes smaller and smaller which allows us to actually calculate finite value even for an infinite stream of money. However, now if the interest rate drops to 1% the present value of those dividend streams becomes higher and the stock will now cost 1000\\$ as now the future is discounted less heavily. To put it simply, at lower interest rate the money you receive in future have higher value today.
• +1 but for the 1st point there have been several channels suggested. I don't want to post my own answer since asking broad/combo questions like the OP did should be discouraged. – Fizz Apr 10 '20 at 2:29 | 2021-07-25 15:10:36 | {"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": 5, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.585105299949646, "perplexity": 1792.7415069861663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151699.95/warc/CC-MAIN-20210725143345-20210725173345-00653.warc.gz"} |
https://ibpsonline.in/questions/IBPS-Clerk/English-Language/Test-42/948 | # IBPS Clerk :: English Language :: Test 42 IBPS Recruitment Latest Govt Jobs
## Home IBPS Clerk / English Language Test 42 Questions and Answers
1 . Read each of the following sentences to find out whether there is any error in it. The error, if any will be in one part of the sentence. The number of that part is the answer. If there is no error, the answer is (5).
If I would have realized (1)/ what a clumsy person you were (2)/ I would not have come (3)/ with you to this place. (4)/ No error (5).
1
2
3
4
5
2 . Read each of the following sentences to find out whether there is any error in it. The error, if any will be in one part of the sentence. The number of that part is the answer. If there is no error, the answer is (5).
While going to the office yesterday (1)/ he not only found a gold watch (2)/ but also a thousand rupee note (3)/ and was extremely delighted. (4)/ No error (5)
1
2
3
4
5
3 . Read each of the following sentences to find out whether there is any error in it. The error, if any will be in one part of the sentence. The number of that part is the answer. If there is no error, the answer is (5).
If I were in your position (1)/ I would have respected (2)/ the wishes my parents (3)/ and made them happy (4)/ No error (5).
1
2
3
4
5
4 . Rearrange the following five sentences A, B, C, D and E in the proper sequence so as to form a meaningful paragraph; then answer the questions given below them.
A) The purpose of this review is to offload public investments from certain low priority areas.
B) The government has decided in principle to throw open to the private sector industries reserved for the public sector.
C) Only those industries are proposed to be reserved for the public sector which fall in the high priority areas.
D) In addition, the government is also engaged in a review of the existing portfolio of public investment.
E) This will enable the government to abolish the monopoly of any sector in the field of manufacture except these priority sectors.
Which of the following should come second in the paragraph?
A
B
C
D
E
5 . Rearrange the following five sentences A, B, C, D and E in the proper sequence so as to form a meaningful paragraph; then answer the questions given below them.
A) The purpose of this review is to offload public investments from certain low priority areas.
B) The government has decided in principle to throw open to the private sector industries reserved for the public sector.
C) Only those industries are proposed to be reserved for the public sector which fall in the high priority areas.
D) In addition, the government is also engaged in a review of the existing portfolio of public investment.
E) This will enable the government to abolish the monopoly of any sector in the field of manufacture except these priority sectors.
Which sentence should come last in the paragraph?
A
B
C
D
E
6 . Rearrange the following five sentences A, B, C, D and E in the proper sequence so as to form a meaningful paragraph; then answer the questions given below them.
A) The purpose of this review is to offload public investments from certain low priority areas.
B) The government has decided in principle to throw open to the private sector industries reserved for the public sector.
C) Only those industries are proposed to be reserved for the public sector which fall in the high priority areas.
D) In addition, the government is also engaged in a review of the existing portfolio of public investment.
E) This will enable the government to abolish the monopoly of any sector in the field of manufacture except these priority sectors.
Which sentence should come fourth in the paragraph?
A
B
C
D
E
7 . Rearrange the following five sentences A, B, C, D and E in the proper sequence so as to form a meaningful paragraph; then answer the questions given below them.
A) The purpose of this review is to offload public investments from certain low priority areas.
B) The government has decided in principle to throw open to the private sector industries reserved for the public sector.
C) Only those industries are proposed to be reserved for the public sector which fall in the high priority areas.
D) In addition, the government is also engaged in a review of the existing portfolio of public investment.
E) This will enable the government to abolish the monopoly of any sector in the field of manufacture except these priority sectors.
Which sentence should come first in the paragraph?
A
B
C
D
E
8 . Rearrange the following five sentences A, B, C, D and E in the proper sequence so as to form a meaningful paragraph; then answer the questions given below them.
A) The purpose of this review is to offload public investments from certain low priority areas.
B) The government has decided in principle to throw open to the private sector industries reserved for the public sector.
C) Only those industries are proposed to be reserved for the public sector which fall in the high priority areas.
D) In addition, the government is also engaged in a review of the existing portfolio of public investment.
E) This will enable the government to abolish the monopoly of any sector in the field of manufacture except these priority sectors.
Which sentence should come third in the paragraph?
A
B
C
D
E
9 . Read the following passage carefully and answer the questions given. Certain words/ phrases have been given in bold to help you locate them while answering some of the questions.
'How soon 'not now' becomes 'never''- a quote by Martin Luther which actually explains the reason behind all those unaccomplished dreams. Actually here's the thing, you are able to be incredibly self-motivated! For instance if I park my car on your toe your motivation for me to get my car off your foot would manifest immediately. Motivation in this context is easy to produce. But when people say they want more motivation, what they really mean is that they want to purposefully direct their motivational force towards something positive, constructive and valuable to them. But how do you ramp up your self-motivation? It's a mistake to assume that motivation must always be linked to feeling motivated. We assume self-motivation is fuelled by emotion and initially it often is. Inspirational speakers with strong jaw lines, tailored suits and overpowering white smiles whip up your emotions. You leave the seminar feeling motivated - ready to take on the world. And this is great - in the short term. But like getting a sugar hit when running a marathon, pretty soon the effect fades. You can't be forever motivated by others - eventually you have to be self - motivated as self - motivation can be sustained.
The question is - how do we feel motivated? First, be fuel-efficient. If we see emotion as a type of fuel for selfmotivation, then we need to be able to save it. We need to be able to run the machine, using up very little emotion sometimes. Secondly, learn to act when you don't feel like acting it as it gives you a $massive$ advantage over 99% of people who have been trained by society to 'only do stuff they feel motivated to do.' However, the feeling of motivation gradually develops only after you've started and made sustained efforts. Don't wait until everything is just right. There is never a 'right time' to do a difficult thing. Make enough preparation, but be man or woman enough to know when you're just hiding behind excuses. Sometimes the more we put off doing something the more 'reasons' we find for putting it off. Further, shoot for the moon and you'll land amongst the stars. It's worth being ambitious because even if you fail short of your ultimate goal, you'll achieve a lot 'by default'. Also, hang out with motivated people, because attitudes rub off. It has been observed that really motivated people are motivating. Find people who are positive and goal-focused. Lastly, it's important to remember that a step in and of itself is not much of a thing but enough steps together can take you far indeed.
There will be times when you need to re-evoke some fire in your $belly$. In such times take time to sit down and relax. Close your eyes and remind yourself of all the reasons to be motivated. Consider how you would feel if you really didn'tgo for your dreams. The greatest failure is the failure to try because people, when motivated, achieve amazing things. The couch potato does change ways, the college dropoutdoes go on to create a global empire. Just take a look at Guiness Book of World Records and you will never doubt what people, who set their minds towards something, are capable of.
Which of the following is/are true in the context of the passage?
(A) All motivation is not directed towards a valuable goal for the future.
(B) We must not waste time in preparing adequately for a project.
(C) Motivational speakers permanently motivate others with their lectures
Only A and B
Only B and C
Only A
Only A and C
All A, B and C
10 . Read the following passage carefully and answer the questions given. Certain words/ phrases have been given in bold to help you locate them while answering some of the questions.
'How soon 'not now' becomes 'never''- a quote by Martin Luther which actually explains the reason behind all those unaccomplished dreams. Actually here's the thing, you are able to be incredibly self-motivated! For instance if I park my car on your toe your motivation for me to get my car off your foot would manifest immediately. Motivation in this context is easy to produce. But when people say they want more motivation, what they really mean is that they want to purposefully direct their motivational force towards something positive, constructive and valuable to them. But how do you ramp up your self-motivation? It's a mistake to assume that motivation must always be linked to feeling motivated. We assume self-motivation is fuelled by emotion and initially it often is. Inspirational speakers with strong jaw lines, tailored suits and overpowering white smiles whip up your emotions. You leave the seminar feeling motivated - ready to take on the world. And this is great - in the short term. But like getting a sugar hit when running a marathon, pretty soon the effect fades. You can't be forever motivated by others - eventually you have to be self - motivated as self - motivation can be sustained.
The question is - how do we feel motivated? First, be fuel-efficient. If we see emotion as a type of fuel for selfmotivation, then we need to be able to save it. We need to be able to run the machine, using up very little emotion sometimes. Secondly, learn to act when you don't feel like acting it as it gives you a $massive$ advantage over 99% of people who have been trained by society to 'only do stuff they feel motivated to do.' However, the feeling of motivation gradually develops only after you've started and made sustained efforts. Don't wait until everything is just right. There is never a 'right time' to do a difficult thing. Make enough preparation, but be man or woman enough to know when you're just hiding behind excuses. Sometimes the more we put off doing something the more 'reasons' we find for putting it off. Further, shoot for the moon and you'll land amongst the stars. It's worth being ambitious because even if you fail short of your ultimate goal, you'll achieve a lot 'by default'. Also, hang out with motivated people, because attitudes rub off. It has been observed that really motivated people are motivating. Find people who are positive and goal-focused. Lastly, it's important to remember that a step in and of itself is not much of a thing but enough steps together can take you far indeed.
There will be times when you need to re-evoke some fire in your $belly$. In such times take time to sit down and relax. Close your eyes and remind yourself of all the reasons to be motivated. Consider how you would feel if you really didn'tgo for your dreams. The greatest failure is the failure to try because people, when motivated, achieve amazing things. The couch potato does change ways, the college dropoutdoes go on to create a global empire. Just take a look at Guiness Book of World Records and you will never doubt what people, who set their minds towards something, are capable of.
What does the author mean when he says 'strong jaw lines, tailored suits and empowering white smiles'?
Very impressive reality
Having a taste for designer clothing
Very ambitious
Authoritative and aggressive
Submissive in nature | 2019-08-17 15:40:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24028952419757843, "perplexity": 1288.3863856583546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027313428.28/warc/CC-MAIN-20190817143039-20190817165039-00315.warc.gz"} |
https://study-astrophysics.com/marion-01-04/ | Thornton & Marion, Classical Dynamics, 5th Edition
Chapter 1. Matrices, Vectors, and Vector Calculus
Problem 04. Transposed and Inverse Matrix
• prove the properties of the transposed and inverse matrix.
1. Transposed matrix
2. Inverse matrix
Solution
(a) $(\bold{AB})^t = \bold{B}^t \bold{A}^t$
Let $\bold{C} = \bold{AB}$, then $C_{ij} = [AB]_{ij} = \sum_k A_{ik}B_{kj}$
By definition of transpose, $C^t_{ij} = C_{ji} = [AB]_{ji} = \sum_k A_{jk} B_{ki} = \sum_k B_{ki} A_{jk} = \sum_k (B^t)_{ik} (A^t)_{kj} = [B^t A^t]_{ij}$
Therefore, $(\bold{AB})^t = \bold{B}^t \bold{A}^t$
(b) $(\bold{AB})^{-1} = \bold{B}^{-1} \bold{A}^{-1}$
i) For orthogonal matrices, $\bold{\lambda}^t \bold{\lambda}^{-1}$, so we can use the result of (a).
ii) For non-orthogonal matrices (i.e. In general), $(\bold{AB}) (\bold{AB})^{-1} = \bold{AB} (\bold{B}^{-1} \bold{A}^{-1}) = \bold{A} \bold{I} \bold{A}^{-1} = \bold{A} \bold{A}^{-1} = \bold{I}$
Therefore, $(\bold{AB})^{-1} = \bold{B}^{-1} \bold{A}^{-1}$ | 2021-01-23 17:47:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 18, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.932752251625061, "perplexity": 3205.347608374331}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703538226.66/warc/CC-MAIN-20210123160717-20210123190717-00674.warc.gz"} |
http://www.mathworks.com/help/physmod/sm/ref/wormandgearconstraint.html | # Documentation
### This is machine translation
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# Worm and Gear Constraint
Kinematic constraint between worm and gear bodies with perpendicular non-intersecting rotation axes
• Library:
• Gears and Couplings / Gears
## Description
The Worm and Gear Constraint block represents a kinematic constraint between worm and gear bodies held at a right angle. The base frame port identifies the connection frame on the worm and the follower frame port identifies the connection frame on the gear. The rotation axes coincide with the connection frame z-axes. The worm and gear rotate at a fixed velocity ratio determined by the gear pitch radii or tooth-thread ratio.
The worm thread direction can follow either right-hand or left-hand conventions. The convention used determines the relative directions of the worm and gear rotational velocities. A right-hand convention causes the worm and gear to rotate in the same direction about the respective z-axes. A left-hand convention causes the worm and gear to rotate in opposite directions instead.
The block represents only the kinematic constraint characteristic to a worm-and-gear system. Gear inertia and geometry are solid properties that you must specify using Solid blocks. The gear constraint model is ideal. Backlash and gear losses due to Coulomb and viscous friction between teeth are ignored. You can, however, model viscous friction at joints by specifying damping coefficients in the joint blocks.
### Gear Geometry
The rack-and-pinion constraint is parameterized in terms of the dimensions of the worm and gear pitch circles. The pitch circles are imaginary circles concentric with the worm and gear bodies and tangent to the thread contact point. The pitch radii, labeled `RB` and `RF` in the figure, are the radii that the worm and gear would have if they were reduced to friction cylinders in mutual contact.
### Gear Assembly
Gear constraints occur in closed kinematic loops. The figure shows the closed-loop topology of a simple worm-and-gear model. Joint blocks connect the worm and gear bodies to a common fixture or carrier, defining the maximum degrees of freedom between them. A Worm and Gear Constraint block connects the worm and gear bodies, eliminating one degree of freedom and effectively coupling the worm and gear motions.
### Assembly Requirements
The block imposes special restrictions on the relative positions and orientations of the gear connection frames. The restrictions ensure that the gears assemble only at distances and angles suitable for meshing. The block enforces the restrictions during model assembly, when it first attempts to place the gears in mesh, but relies on the remainder of the model to keep the gears in mesh during simulation.
Position Restrictions
• The distance between the base and follower frame z-axes, denoted dB-F in the figure, must be equal to the distance between the gear centers.
• The translational offset between the base and follower frame origins along the follower frame z-axis, denoted ΔZF in the figure, must be zero.
Orientation Restrictions
• The z-axes of the base and follower frames must be perpendicular to each other. The z-axes are shown in blue in the figure.
• The cross product of the follower frame z-axis with the base frame z-axis must be a vector aimed from the follower frame origin to the base frame z-axis. The z-axes and their cross-product vector are shown in the figure. The cross product is defined as ${\stackrel{^}{z}}_{F}×{\stackrel{^}{z}}_{B}$.
## Ports
### Frame
expand all
Connection frame on the worm body.
Connection frame on the gear body.
## Parameters
expand all
Winding direction of the worm thread relative to the base frame z-axis. As viewed from the base frame origin, a right-hand thread is one that wraps around the base frame z-axis in a counterclockwise direction. A left-hand thread is one that wraps in a clockwise direction. This parameter determines the relative directions of motion of the worm and gear bodies.
Angle between the tangent to the worm thread and the plane perpendicular to the base frame z-axis. The lead angle impacts the gear rotation corresponding to a full worm revolution.
Parameterization for specifying the worm and gear geometries. You can specify the gear dimensions in terms of the distance between the gear centers or the individual gear radii.
Distance between the worm and gear centers. This distance must equal that enforced by rigid transforms, joints, and any other constraints located between the gear bodies and the common carrier body.
#### Dependencies
This parameter is enabled when the Specification Method parameter is set to ```Center Distance and Ratio```.
Ratio of gear teeth to worm threads, or starts. This ratio impacts the torque transmitted between the worm and gear.
#### Dependencies
This parameter is enabled when the Specification Method parameter is set to ```Center Distance and Ratio```.
Radius of the worm pitch circle. This is the distance between the worm rotation axis and the tooth-thread contact point. This parameter impacts the torque transmitted between the worm and gear.
#### Dependencies
This parameter is enabled when the Specification Method parameter is set to ```Pitch Circle Radius```.
Radius of the gear pitch circle. This is the distance between the gear rotation axis and the tooth-thread contact point. This parameter impacts the torque transmitted between the worm and gear.
#### Dependencies
This parameter is enabled when the Specification Method parameter is set to ```Pitch Circle Radius```. | 2018-08-15 22:55:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42895427346229553, "perplexity": 2346.397739758436}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210362.19/warc/CC-MAIN-20180815220136-20180816000136-00359.warc.gz"} |
https://kullabs.com/classes/subjects/units/lessons/notes/note-detail/739 | Notes on Lever | Grade 8 > Science > Simple Machine | KULLABS.COM
• Note
• Things to remember
• Videos
• Exercise
• Quiz
A lever is a simple machine. It consists of a rigid bar which is free to turn about a fixed point called fulcrum. The weight to be lifted is the load and the force applied to the bar is called effort. The distance of the load from the fulcrum is called the load arm and the distance of effort from the fulcrum is called the effort arm.
There are three types of lever depending upon the position of the load, effort, and fulcrum. These are
1. First class lever
2. Second class lever
3. Third class lever
#### First class lever
A first class lever is one in which the fulcrum lies anywhere between the effort and load. Examples: Crowbar, seesaw, scissors, pliers, beam balance, the handle of water pump, etc.
#### Second class lever
A second-class lever is one in which the load is between the effort and fulcrum.
Examples: Wheelbarrow, nutcracker, bottle opener, oar of a rowboat, etc.
#### Third class lever
A third class lever is one in which the effort is between the load and the fulcrum
Examples: shovel, sugar tongs, finger nut cutter, tweezers, human forearm, fork, fishing rod, etc.
• lever is a rigid bar, which is capable of rotating about a fixed point called fulcrum.
• The types of lever are First class lever, Second class lever, Third class lever.
.
### Very Short Questions
A lever is a simple machine which consists of a rigid bar which is free to turn about a fixed point called fulcrum. The principle of lever is, the nearer the fulcrum to the weight to be moved, the easier it is to shift, the farther from the fulcrum, the more difficult.
Long spanner provides more effort arm and produces more turning effort.
Because effort arm is increased according to the principle of lever less effort is required.
Lever is divided into three types. They are: first class lever, second class lever and third class lever.
Solution,
\begin{align*} \text {Load}\: (L) = 40N\\ \text {Load arm}\: (L. d) = 2m\\ \text {Effort arm}\: (E.d) = 4m\\ \text {Effort} (E) =?\\ \text {According to the principle of lever,} \\ \text {Load} \times \text {Load arm} &= \text {Effort} \times \text {Effort arm} \\ \text {or,}\: 40 \times 2 = E \times 4 \\ \text {or,}\: 80/4 &= E \\ \text {or,}\: E = 20N \\ \text {Hence, the effort required to lift a load is}\: 20\:N. \\\end{align*}
Solution:
\begin{align*} \text {Load}\: (L) = 600N \\\text {Load arm}\: (L. d) = 0.5\\ \text {Effort arm}\: (E. d) = 1.5 - 0.5 m= 1m \\ \text {Effort}\: (E) =?\\ \text {According to the principle of lever,} \\ \text {Load} \times \text {Load arm} &= \text {Effort} \times \text {Effort arm} \\\text {or,}\: 600 \times 0.5 &= E \times 1 \\ \text {or,}\: E &= 300N \\ \text {Hence, the effort required to lift a load is}\: 300\:N. \\ \end{align*}
0%
• ### In first class lever ______.
load is between the effort and fulcrum
none of these
fulcrum lies anywhere between the effort and load
effort is between the load and the fulcrum
• ### Bottle opener is an example of ______.
Third class Lever
both b and c
Second class Lever
First Class Lever
20N
15 N
25 N
30 N
force arm
fulcrum
effort arm
effort arm
effort arm
fulcrum
• ### The components of a lever are _____.
effort
all of the above
effort arm
fulcrum
effort
• ### Which of the following is a first class lever?
all of the above
scissors
see-saw
crow-bar
• ### Which of the following is not the first class lever?
all of the above
crow-bar
see-saw
wheel barrow
effort arm
effort
Fulcrum
• ### In first class lever ______.
effort arm is shorter than load arm
load arm is longer than effort arm
effort arm is longer than load arm
effort arm is equal to the load arm
• ### In second class lever ______.
effort arm is longer than load arm
effort arm is equal to the load arm
effort arm is shorter than load arm
load arm is longer than effort arm
• ### In third class lever ______.
load arm is shorter than effort arm
effort arm is equal to the load arm
effort arm is longer than load arm
effort arm is shorter than load arm
• ### The lever in equilibrium state is defined by the equation ______.
load x load arm = effort x effort arm
load + load arm = effort + effort arm
load / load arm = effort / effort arm
load - load arm = effort - effort arm
effort
fulcrum
effort arm
• ### Which one of the following is not a second class lever?
lemon squeezer
nut cracker
wheel barrow
handle of the water pump
effort arm
fulcrum
effort
• ### In a first class lever if we want to gain more force the position of fulcrum should be ______.
in exact middle of the load and the effort
anywhere in between. The position of fulcrum doesn't matter.
closer to the load
closer to the effort
## ASK ANY QUESTION ON Lever
Forum Time Replies Report
##### Akku
What do you mean by MAof a lever is 3?
##### sachin
A second class lever need less effort to lift a heavy load,why?
##### 111
how does simple machine help to change the direction of force?? | 2020-01-29 22:10:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9995724558830261, "perplexity": 7095.310780966785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251802249.87/warc/CC-MAIN-20200129194333-20200129223333-00045.warc.gz"} |
https://www.physicsforums.com/threads/savings-account-simple-interest-problem.117169/ | # Savings account simple interest problem
1. Apr 10, 2006
Sam has decided to invest savings of $5000. for 2 years, starting on January 1, of this year in the following portfolio: 20% ip a savings account (5% simple interest, calculated daily, paid monthly) 50% in a 2- yearGlC (6% compounded annually) 30% in al— year term deposit (&5% simple interest, paid at term end) a) Why do think he has chosen to save this way? b) He makes no deposits to, or withdrawals from his savings account and he re—invests the final amount of the term deposit for a second term. How much will he have in his portfolio in 2 years? c) Suggest a different combination of saving alternatives for Sam savings portfolio. Explain your reasoning. --------------------------- http://dhseagles.kpdsb.on.ca/~Currie/gr11MT/4-2.idx -------------------------- the above it the question that has to be answered and the link offfers my lesson in the textbook. I am really confussed with what i have to do first and wel the process in the completion of the assignment. What is the answer in general and basic statment-like without the pure math done? i have noclue when it comes to interest and money. thanks in advance, I really need assistance Last edited by a moderator: Jul 15, 2014 2. Apr 10, 2006 ### heels_overhead I am ever so great full –thanks in advance 3. Apr 10, 2006 ### Zurtex We don't just give out answers to homework, if you want help probabily best to post in one of the homework forums: https://www.physicsforums.com/forumdisplay.php?f=152 4. Apr 10, 2006 ### CRGreathouse a) Sam's financial advisor told him to invest them that way. b)$2,328.14
c) Sam should withdraw all the money in $1s and$5s and put it under his bed.
5. Apr 11, 2006
### HallsofIvy
Staff Emeritus
Yes, you are "confussed". You are "confussed" about where to put this question- I'm moving it to the "Precalculus homework" section.
(Actually, I like "confussed". Confused to the point of being fussed over it!)
6. Apr 11, 2006
### arildno
Fussing over it to the extent of getting a concussion perhaps?
Or was that concussed? I'm bewildered.
7. Apr 11, 2006
well thanks anyway
Sorry for bother youi was unaware that my post was not on topic. I promise to not embark for help within this site for is is strickly not for "simple interest and financial math" I would like to thank all those people who have help me out in the last two boards, you have given me something to work from. And i shall seriously concided the $1 and$5 bill remark,it is accually ingenius, and deserving of further thought!!!
thanks and happy "mathing".
8. Apr 12, 2006
### Beam me down
That attitude isn't going to get help here. | 2016-12-03 00:22:34 | {"extraction_info": {"found_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": 0.2249307632446289, "perplexity": 7106.573023041413}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698540798.71/warc/CC-MAIN-20161202170900-00087-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/219512/are-solutions-of-the-beltrami-equations-necessarily-smooth | # Are solutions of the Beltrami Equations necessarily smooth?
Let $a$, $b$ and $c$ be real constants such that $\Delta \stackrel{\text{df}}{=} a c - b^{2} > 0$. The Beltrami Equations are defined as the following system of PDE’s on the domain $\Bbb{R}^{2}$: $$u_{x} = \frac{1}{\sqrt{\Delta}} (b v_{x} + c v_{y}), \qquad u_{y} = - \frac{1}{\sqrt{\Delta}} (a v_{x} + b v_{y}).$$ Boundary conditions are not imposed.
Question: Are solutions $u$ and $v$ of this system necessarily smooth?
I have been told that the Elliptic Regularity Theorem answers my question, but the theorem applies only to even-order elliptic operators and what we have here are only first-order equations, so we do not know if solutions $u$ and $v$ have even second-order partial derivatives. Observe that we have the same scenario for the Cauchy-Riemann Equations (in PDE form).
I understand that my question may be too basic for MathOverflow, so I understand if anyone wishes to close it. Thank you!
• consider the extreme case of $a=c=1$ and $b=0$. Then $u$ is harmonic. Can maybe do something similar in the more general case and still get an elliptic second order equation?? Sep 29 '15 at 5:44
• @Math604: Hi Math604. Pardon me for being a little blunt here, but there’s a problem with your comment. If we don’t know that $u$ has second-order partial derivatives, how can we claim that $u$ is harmonic? Sep 29 '15 at 6:11
• It suffices to use weak second order partial derivatives (i.e., distributions). A weak solution to a linear elliptic PDE is necessarily smooth. Or you can work with the first order system directly, since it is itself an elliptic system. Sep 29 '15 at 6:47
• Not only the solutions are smooth, but your system rewrites $du=dv\circ J$, where $J^2=-Id$. Hence in coordinates where $J$ is $(s,t)\mapsto (-t,s)$, $u+iv$ is holomorphic in $s+it$. Moreover, Ahlfors and Bers proved that this generalizes to bounded measurable $J$ (but the solutions are no longer smooth if $J$ isn't, of course). See cimat.mx/~mmoreno/teaching/fall10/AhlforsBers.pdf
– BS.
Sep 29 '15 at 8:31
• @Deane: Hi Deane. Your comment was really helpful, as it reminded me of the fact that distributions have weak derivatives of all orders. If $u$ and $v$ are distributions corresponding to locally-integrable functions, and they satisfy the Beltrami Equations in the weak sense, then by elliptic regularity, these functions are a.e.-equal to smooth functions. Hence, continuous solutions of the Beltrami Equations, viewed in the ordinary sense, are already smooth. Oct 2 '15 at 16:19 | 2021-09-25 21:42:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8909950256347656, "perplexity": 242.70984235451286}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057775.50/warc/CC-MAIN-20210925202717-20210925232717-00657.warc.gz"} |
https://www.physicsforums.com/threads/net-force-on-a-particle-with-potential-energy-function.579078/ | # Net force on a particle with potential energy function
1. Feb 18, 2012
### Koscher
1. The problem statement, all variables and given/known data
A particle is moving along the x-axis subject to the potential energy function U(x) = 1/x + x2 + x - 1. Determine the x-component of the net force on the particle at the coordinate x= 3.29m.
2. Relevant equations
U(x) = integral(F(x)dx)
3. The attempt at a solution
To find the net force I took one derivative of the potential energy equation. The resulting (-1/x2) + 2x +1. I then plugged in 3.29 for x and it resulted in 7.487. Which is not the correct answer. Now my though is that if i take the second derivative of the potential energy function and then plug in my value of x=3.29 m, then that would be correct. But I am really not sure.
2. Feb 18, 2012
### cepheid
Staff Emeritus
Actually, the definition of the potential energy function for this 1D case is$$U(x) = -\int F(x)\,dx$$The negative sign is important. As a result, $$F(x) = - \frac{dU}{dx}$$ A motivation for this definition is so that the force points in the direction of maximum decrease in potential energy, which, if you think about it, is consistent with examples of conservative forces that you may have encountered already, such as gravity.
No. If potential energy is the negative integral of force, then force is the negative derivative of potential energy, since integration and differentiation are inverse operations. So, basically, taking the second derivative makes no sense at all.
3. Feb 18, 2012
### Koscher
Thank you. I completely forgot the negative sign on the equation. When i took it into account I got the correct answer. Thank you.
4. Feb 18, 2012
### cepheid
Staff Emeritus
No problem, you're welcome. | 2017-09-20 11:27:34 | {"extraction_info": {"found_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": 0.7975364327430725, "perplexity": 298.59800257613495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687255.13/warc/CC-MAIN-20170920104615-20170920124615-00237.warc.gz"} |
https://pythonprogramming.net/graph-visualization-python3-pandas-data-analysis/ | ## Graphing/visualization - Data Analysis with Python 3 and Pandas
Practical Data Analysis 2
Welcome to part 2 of the data analysis with Python and Pandas tutorials, where we're learning about the prices of Avocados at the moment. Soon, we'll find a new dataset, but let's learn a few more things with this one. Where we left off, we were graphing the price from Albany over time, but it was quite messy. Here's a recap:
import pandas as pd
albany_df = df[df['region']=="Albany"]
albany_df.set_index("Date", inplace=True)
albany_df["AveragePrice"].plot()
<matplotlib.axes._subplots.AxesSubplot at 0x11fd925f8>
So dates are funky types of data, since they are strings, but also have order, at least to us. When it comes to dates, we have to help computers out a bit. Luckily for us, Pandas comes built in with ways to handle for dates. First, we need to convert the date column to datetime objects:
df = pd.read_csv("datasets/avocado.csv")
df['Date'] = pd.to_datetime(df['Date'])
albany_df = df[df['region']=="Albany"]
albany_df.set_index("Date", inplace=True)
albany_df["AveragePrice"].plot()
<matplotlib.axes._subplots.AxesSubplot at 0x11fa86828>
Alright, the formatting looks better in terms of axis, but that graph is pretty wild! Could we settle it down a bit? We could smooth the data with a rolling average.
To do this, let's make a new column, and apply some smoothing:
albany_df["AveragePrice"].rolling(25).mean().plot()
<matplotlib.axes._subplots.AxesSubplot at 0x1223cc278>
Hmm, so what happened? Pandas understands that a date is a date, and to sort the X axis, but I am now wondering if the dataframe itself is sorted. If it's not, that would seriously screw up our moving average calculations. This data may be indexed by date, but is it sorted? Let's see.
albany_df.sort_index(inplace=True)
/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning:
A value is trying to be set on a copy of a slice from a DataFrame
See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
"""Entry point for launching an IPython kernel.
What's this warning above? Should we be worried? Basically, all it's telling us is that we're doing operations on a copy of a slice of a dataframe, and to watch out because we might not be modifying what we were hoping to modify (like the main df). In this case, we're not trying to work with the main dataframe, so I think this warning is just plain annoying, but whatever. It's just a warning, not an error.
albany_df["AveragePrice"].rolling(25).mean().plot()
<matplotlib.axes._subplots.AxesSubplot at 0x1223ccf98>
And there we have it! A more useful summary of avocado prices for Albany over the years.
Visualizations are cool, but what if we want to save our new, smoother, data like above? We can give it a new column in our dataframe:
albany_df["price25ma"] = albany_df["AveragePrice"].rolling(25).mean()
/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning:
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead
See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
"""Entry point for launching an IPython kernel.
albany_df.head()
Unnamed: 0 AveragePrice Total Volume 4046 4225 4770 Total Bags Small Bags Large Bags XLarge Bags type year region price25ma
Date
2015-01-04 51 1.22 40873.28 2819.50 28287.42 49.90 9716.46 9186.93 529.53 0.0 conventional 2015 Albany NaN
2015-01-04 51 1.79 1373.95 57.42 153.88 0.00 1162.65 1162.65 0.00 0.0 organic 2015 Albany NaN
2015-01-11 50 1.24 41195.08 1002.85 31640.34 127.12 8424.77 8036.04 388.73 0.0 conventional 2015 Albany NaN
2015-01-11 50 1.77 1182.56 39.00 305.12 0.00 838.44 838.44 0.00 0.0 organic 2015 Albany NaN
2015-01-18 49 1.17 44511.28 914.14 31540.32 135.77 11921.05 11651.09 269.96 0.0 conventional 2015 Albany NaN
Perfect example of why tail is useful sometimes...
albany_df.tail()
Unnamed: 0 AveragePrice Total Volume 4046 4225 4770 Total Bags Small Bags Large Bags XLarge Bags type year region price25ma
Date
2018-03-11 2 1.68 2570.52 131.67 229.56 0.00 2209.29 2209.29 0.00 0.0 organic 2018 Albany 1.4224
2018-03-18 1 1.66 3154.45 275.89 297.96 0.00 2580.60 2577.27 3.33 0.0 organic 2018 Albany 1.4316
2018-03-18 1 1.35 105304.65 13234.86 61037.58 55.00 30977.21 26755.90 3721.31 500.0 conventional 2018 Albany 1.4276
2018-03-25 0 1.57 149396.50 16361.69 109045.03 65.45 23924.33 19273.80 4270.53 380.0 conventional 2018 Albany 1.4272
2018-03-25 0 1.71 2321.82 42.95 272.41 0.00 2006.46 1996.46 10.00 0.0 organic 2018 Albany 1.4368
That warning sure is annoying though isn't it. What could we do? A common idea is to silence it all of the warnings. What if we instead...
albany_df = df.copy()[df['region']=="Albany"]
albany_df.set_index('Date', inplace=True)
albany_df["price25ma"] = albany_df["AveragePrice"].rolling(25).mean()
This way, we are explicit. Pandas is happy, we're happy. You can ignore pandas warnings, but I would strongly advise against silencing them. Now you know you can do it, but I am not going to show you how :)
Another subtle thing you might have glossed over is the requirement for us to sort things how we intend before we start performing operations and calcs. Many times, you wont be visualizing columns before you make them. You may actually never visualize them. Imagine if we wrote the above code before we sorted by date, basically just assuming things were ordered by date. We'd have produced bad data.
Then imagine maybe we're doing some machine learning or other statistical analysis on that data. Well, chances are, our MA column is not only fairly useless, it's also being informed often of future data!
It's very easy to make mistakes like this. Check your code early and check it often through printing it out and visualizing it where possible!
Alright, we want more cool stuff, what else can we do?
Let's graph prices in the different regions. We hard-coded the Albany region, but hmm, we don't know all of the regions. What do we do?! If we every just wanted to get a "list" from one of our columns, we could reference just that column, like:
df['region']
0 Albany
1 Albany
2 Albany
3 Albany
4 Albany
5 Albany
6 Albany
7 Albany
8 Albany
9 Albany
10 Albany
11 Albany
12 Albany
13 Albany
14 Albany
15 Albany
16 Albany
17 Albany
18 Albany
19 Albany
20 Albany
21 Albany
22 Albany
23 Albany
24 Albany
25 Albany
26 Albany
27 Albany
28 Albany
29 Albany
...
18219 TotalUS
18220 TotalUS
18221 TotalUS
18222 TotalUS
18223 TotalUS
18224 TotalUS
18225 West
18226 West
18227 West
18228 West
18229 West
18230 West
18231 West
18232 West
18233 West
18234 West
18235 West
18236 West
18237 WestTexNewMexico
18238 WestTexNewMexico
18239 WestTexNewMexico
18240 WestTexNewMexico
18241 WestTexNewMexico
18242 WestTexNewMexico
18243 WestTexNewMexico
18244 WestTexNewMexico
18245 WestTexNewMexico
18246 WestTexNewMexico
18247 WestTexNewMexico
18248 WestTexNewMexico
Name: region, Length: 18249, dtype: object
Then convert to array with:
df['region'].values
array(['Albany', 'Albany', 'Albany', ..., 'WestTexNewMexico',
'WestTexNewMexico', 'WestTexNewMexico'], dtype=object)
Could go to list like:
df['region'].values.tolist()
# and then maybe get the uniques with:
print(set(df['region'].values.tolist()))
{'Orlando', 'RaleighGreensboro', 'Charlotte', 'NewOrleansMobile', 'Syracuse', 'Nashville', 'DallasFtWorth', 'Chicago', 'Columbus', 'SanFrancisco', 'Southeast', 'Tampa', 'Jacksonville', 'SanDiego', 'MiamiFtLauderdale', 'Seattle', 'Philadelphia', 'California', 'SouthCentral', 'Pittsburgh', 'GrandRapids', 'Atlanta', 'Indianapolis', 'CincinnatiDayton', 'RichmondNorfolk', 'Louisville', 'Roanoke', 'LasVegas', 'Northeast', 'NorthernNewEngland', 'Detroit', 'Portland', 'Plains', 'Spokane', 'LosAngeles', 'HarrisburgScranton', 'SouthCarolina', 'TotalUS', 'West', 'Albany', 'NewYork', 'WestTexNewMexico', 'BuffaloRochester', 'Sacramento', 'BaltimoreWashington', 'Boston', 'Boise', 'Denver', 'HartfordSpringfield', 'PhoenixTucson', 'Houston', 'GreatLakes', 'Midsouth', 'StLouis'}
So, very quickly you can take your pandas data and get it out into array/list form and use your own knowledge of python. Or, you could also just use some Pandas method. Just know, if you're trying to do it, it probably has a method!
df['region'].unique()
array(['Albany', 'Atlanta', 'BaltimoreWashington', 'Boise', 'Boston',
'BuffaloRochester', 'California', 'Charlotte', 'Chicago',
'CincinnatiDayton', 'Columbus', 'DallasFtWorth', 'Denver',
'Detroit', 'GrandRapids', 'GreatLakes', 'HarrisburgScranton',
'HartfordSpringfield', 'Houston', 'Indianapolis', 'Jacksonville',
'LasVegas', 'LosAngeles', 'Louisville', 'MiamiFtLauderdale',
'Midsouth', 'Nashville', 'NewOrleansMobile', 'NewYork',
'PhoenixTucson', 'Pittsburgh', 'Plains', 'Portland',
'RaleighGreensboro', 'RichmondNorfolk', 'Roanoke', 'Sacramento',
'SanDiego', 'SanFrancisco', 'Seattle', 'SouthCarolina',
'SouthCentral', 'Southeast', 'Spokane', 'StLouis', 'Syracuse',
'Tampa', 'TotalUS', 'West', 'WestTexNewMexico'], dtype=object)
That was quick and painless!
graph_df = pd.DataFrame()
for region in df['region'].unique()[:16]:
print(region)
region_df = df.copy()[df['region']==region]
region_df.set_index('Date', inplace=True)
region_df.sort_index(inplace=True)
region_df[f"{region}_price25ma"] = region_df["AveragePrice"].rolling(25).mean()
if graph_df.empty:
graph_df = region_df[[f"{region}_price25ma"]] # note the double square brackets!
else:
graph_df = graph_df.join(region_df[f"{region}_price25ma"])
Albany
Atlanta
BaltimoreWashington
Boise
Boston
BuffaloRochester
California
Charlotte
Chicago
CincinnatiDayton
Columbus
DallasFtWorth
Denver
Detroit
GrandRapids
GreatLakes
I set the limit to 16 just to show we're getting bogged down. This one really tripped me up. I couldn't quite figure out what was going on. Things were taking exponentially longer and longer, then memory was getting exhausted. That's not what I know and love with Pandas, so what gives? Upon some digging, we find that hmm, dates are still getting duplicated. For example:
graph_df.tail()
Albany_price25ma Atlanta_price25ma BaltimoreWashington_price25ma Boise_price25ma Boston_price25ma BuffaloRochester_price25ma California_price25ma Charlotte_price25ma Chicago_price25ma CincinnatiDayton_price25ma Columbus_price25ma DallasFtWorth_price25ma Denver_price25ma Detroit_price25ma GrandRapids_price25ma GreatLakes_price25ma
Date
2018-03-25 1.4368 1.2884 1.3844 1.5016 1.588 1.2232 1.4232 1.4916 1.5708 1.2792 1.1704 1.118 1.2888 1.1492 1.3264 1.2788
2018-03-25 1.4368 1.2884 1.3844 1.5016 1.588 1.2232 1.4232 1.4916 1.5708 1.2792 1.1704 1.118 1.2888 1.1728 1.3164 1.2568
2018-03-25 1.4368 1.2884 1.3844 1.5016 1.588 1.2232 1.4232 1.4916 1.5708 1.2792 1.1704 1.118 1.2888 1.1728 1.3164 1.2788
2018-03-25 1.4368 1.2884 1.3844 1.5016 1.588 1.2232 1.4232 1.4916 1.5708 1.2792 1.1704 1.118 1.2888 1.1728 1.3264 1.2568
2018-03-25 1.4368 1.2884 1.3844 1.5016 1.588 1.2232 1.4232 1.4916 1.5708 1.2792 1.1704 1.118 1.2888 1.1728 1.3264 1.2788
Each row should be a separate date, but it's not. Through some debugging, we can discover what's happening, which actually informs us to why our previous data looked so ugly too.
Our avocados have multiple prices: Organic and Conventional! So, let's pick one. I'll go with organic. So we'll just start over pretty much.
import pandas as pd
df = df.copy()[df['type']=='organic']
df["Date"] = pd.to_datetime(df["Date"])
df.sort_values(by="Date", ascending=True, inplace=True)
Unnamed: 0 Date AveragePrice Total Volume 4046 4225 4770 Total Bags Small Bags Large Bags XLarge Bags type year region
9489 51 2015-01-04 1.24 142349.77 107490.73 25711.96 2.93 9144.15 9144.15 0.00 0.0 organic 2015 California
10269 51 2015-01-04 1.50 6329.83 3730.80 2141.91 0.00 457.12 426.67 30.45 0.0 organic 2015 LasVegas
10893 51 2015-01-04 1.12 17296.85 14569.66 1868.59 0.00 858.60 830.00 28.60 0.0 organic 2015 PhoenixTucson
9437 51 2015-01-04 1.73 379.82 0.00 59.82 0.00 320.00 320.00 0.00 0.0 organic 2015 BuffaloRochester
11621 51 2015-01-04 1.30 5782.70 723.29 4221.15 0.00 838.26 223.33 614.93 0.0 organic 2015 Spokane
Now, let's just copy and paste the code from above, minus the print:
graph_df = pd.DataFrame()
for region in df['region'].unique():
region_df = df.copy()[df['region']==region]
region_df.set_index('Date', inplace=True)
region_df.sort_index(inplace=True)
region_df[f"{region}_price25ma"] = region_df["AveragePrice"].rolling(25).mean()
if graph_df.empty:
graph_df = region_df[[f"{region}_price25ma"]] # note the double square brackets! (so df rather than series)
else:
graph_df = graph_df.join(region_df[f"{region}_price25ma"])
graph_df.tail()
California_price25ma LasVegas_price25ma PhoenixTucson_price25ma BuffaloRochester_price25ma Spokane_price25ma LosAngeles_price25ma Philadelphia_price25ma Boston_price25ma StLouis_price25ma Louisville_price25ma ... Houston_price25ma Chicago_price25ma Plains_price25ma Indianapolis_price25ma SouthCentral_price25ma Columbus_price25ma Albany_price25ma Detroit_price25ma NewOrleansMobile_price25ma NewYork_price25ma
Date
2018-02-25 1.9128 1.9120 1.7468 1.2912 2.1544 1.9024 1.6324 1.7636 1.9240 1.7044 ... 1.6132 1.8160 1.8116 1.4928 1.5728 1.6064 1.5112 1.4980 1.5384 1.9308
2018-03-04 1.8876 1.8748 1.7404 1.2744 2.1040 1.8656 1.6260 1.7708 1.8868 1.6816 ... 1.5960 1.8024 1.7900 1.4744 1.5592 1.5804 1.4992 1.4692 1.5288 1.9156
2018-03-11 1.8636 1.8440 1.7324 1.2652 2.0552 1.8284 1.6300 1.7824 1.8468 1.6508 ... 1.5696 1.7836 1.7672 1.4540 1.5400 1.5496 1.5044 1.4444 1.5076 1.9092
2018-03-18 1.8516 1.8204 1.7216 1.2560 2.0012 1.8160 1.6304 1.7932 1.8192 1.6176 ... 1.5360 1.7732 1.7452 1.4320 1.5204 1.5088 1.5140 1.4092 1.4860 1.8948
2018-03-25 1.8364 1.7968 1.7104 1.2416 1.9496 1.8016 1.6256 1.7984 1.7976 1.5844 ... 1.5128 1.7672 1.7232 1.4160 1.5072 1.4848 1.5188 1.3964 1.4616 1.8876
5 rows A-- 54 columns
Now it's quick! Awesome!
Let's graph!
graph_df.plot(figsize=(8,5), legend=False)
<matplotlib.axes._subplots.AxesSubplot at 0x124046fd0>
Lots more we could poke around with here, but, in the next tutorial, we'll be visiting a new dataset with new challenges.
The next tutorial:
• Introduction - Data Analysis with Python 3 and Pandas
• Graphing/visualization - Data Analysis with Python 3 and Pandas
• Groupby - Data Analysis with Python 3 and Pandas
• Visualizing Correlation Table - Data Analysis with Python 3 and Pandas
• Combining multiple datasets - Data Analysis with Python 3 and Pandas
• Machine Learning with Scikit-learn - Data Analysis with Python 3 and Pandas | 2020-07-06 12:46:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31813299655914307, "perplexity": 5153.657655994253}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655880616.1/warc/CC-MAIN-20200706104839-20200706134839-00083.warc.gz"} |
https://www.elibm.org/article/10000152 | A Lefschetz fixed point formula for singular arithmetic schemes with smooth generic fibres
Summary
Summary: In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an analog, in the arithmetic case, of the Lefschetz formula proved by R. W. Thomason in [31]. In particular, our result implies a fixed point formula which was conjectured by V. Maillot and D. Rössler in [25].
Mathematics Subject Classification
14C40, 14G40, 14L30, 58J20, 58J52
Keywords/Phrases
fixed point formula, singular arithmetic scheme, Arakelov geometry | 2019-07-21 16:57:12 | {"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": 0.9209539890289307, "perplexity": 887.8739436164342}, "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-2019-30/segments/1563195527089.77/warc/CC-MAIN-20190721164644-20190721190644-00377.warc.gz"} |
http://sepwww.stanford.edu/data/media/public/sep/prof/fgdp/c9/paper_html/node2.html | Next: NUMERICAL MATRIZANTS Up: Mathematical physics in stratified Previous: Mathematical physics in stratified
# FROM PHYSICS TO MATHEMATICS
First Step:
The first step is to write down all the basic partial differential equations of classical physics which relate to the problem of interest. Do not write down equations containing second space derivatives which are derived from first-derivative equations. Write down the first-derivative equations. Write each component of vector or matrix equations.
In acoustics we have the gradient pressure p gives rise to an acceleration of mass density .For convenience we restrict motion to the x, z plane. Letting u and w represent x and z components of velocity we have
(1) (2)
Another equation which is important in acoustics is the one that states that the divergence of velocity multiplied by the incompressibility K yields the rate of pressure decrease.
(3)
In (9-1-3) we included a pressure source s. This is something to be externally prescribed. The quantity s may be a source of chemical energy such as an explosion; thus it may vanish everywhere except at a point. Distributed sources are also often of interest; for example, radioactive rocks in a heat-flow model of the earth. To be more general, we could also have put momentum sources into (9-1-1) or (9-1-2), but the basic principles will be adequately exemplified with a source only in (9-1-3).
Second step:
The wave disturbance variables are taken to be unknown and the material properties known. Count equations and unknowns. We have three equations; u, w, and p are the three unknowns. We take K, , and s to be known. Notice that the equations are linear in the unknowns. Now we make the stratification assumption; that is, we assume K and are functions of depth z only and that they are constant in x. Since our linear equations now have constant coefficients with respect to x and t, we may always expect sinusoidal solutions in x and t. We do not know what to expect of our solutions in the z coordinate because of the arbitrary z-dependence of the coefficients K and .This leads to step three.
Third step:
Fourier transform time and the space coordinates with constant coefficients. In other words, we make the following substitution into (9-1-1), (9-1-2), and (9-1-3)
(4)
After substitution, cancel the exponential and obtain
(1) (2) (3)
Fourth step:
Eliminate algebraically the algebraic unknowns. In other words, when you examine (9-1-5) you see terms in but you do not see .This means that U is an algebraic variable which can be eliminated by purely algebraic means. We do this by substituting (9-1-5a), into (9-1-5c).
Fifth step:
Bring terms to the left, bring all others to the right, and arrange terms into a neat matrix form. We have
and then
(6)
Sixth step:
Recognize that, no matter the physical problem with which you started, you should have a matrix first-order differential equation of the form
(7)
where is a vector containing the field variables of interest, is a matrix depending on temporal and spatial frequency and on material properties, and is a (possibly absent) vector function of the sources.
Before we look into techniques of solving (9-1-7) we can immediately deduce that in a source-free region the field variables are smoother functions than the material properties. To see this, consider two homogeneous layers in contact. At the contact the matrix has step-function discontinuities. Now let us see whether the wave fields in can have step-function discontinuities. Obviously they cannot, since a step discontinuity in would imply ,whereas (9-1-7) in a source-free region states that and both and are supposed finite. This does not mean that all field variables are always smooth. The algebraic variables eliminated in the fourth step can and often will be discontinuous at layer boundaries.
## EXERCISES:
1. What form does (9-1-7) take for the heat-flow equation? Include radioactive sources. [HINT: See equations (10-1-1) and (10-1-2).]
2. Using Maxwell's equations, ,,and Ohm's law, where is conductivity, set and derive (9-1-7).
3. In electrostatics the electric field in the ionosphere may be derived from a potential , the divergence of electrical current vanishes and Ohm's law must have an extra term due to wind (a current source due to differential drag on ions and electrons across the earth's magnetic field) .Assume you know .What form does (9-1-7) take assuming and to be scalars? Indicate how the calculation proceeds if and are matrices (assume you have the inverse of any matrix you wish).
4. In magnetostatics and , and .Taking as given, what is the form of (9-1-7)?
5. This exercise illustrates the linearization of nonlinear problems. For acoustic waves in a stratified windy atmosphere we used the trial solutions
Reduce the partial differential equations to a matrix ordinary differential equation. HINT: The horizontal acceleration terms is with a like term for vertical acceleration. Drop second-order terms in , , and .
6. Two equations come from heat flow: (Hx, Hz) equals the conductivity multiplied by the negative of the temperature gradient .The time derivative of temperature multiplied by the heat capacity c equals the negative of the heat-flow divergence gives another equation. Insert the trial solutions
(a)
First derive steady-state equations for and assuming and vanish.
(b)
Assuming and satisfy part (a), find equations for and .
(c)
Repeat (a) and (b) assuming linear temperature dependence of heat capacity and conductivity, i.e., You will have to drop squared terms in and .
7. Consider a compressible liquid sphere pulsating radially under its own gravitational attraction. What is the form of (9-1-6)?
Next: NUMERICAL MATRIZANTS Up: Mathematical physics in stratified Previous: Mathematical physics in stratified
Stanford Exploration Project
10/30/1997 | 2013-06-19 22:51:15 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8196539282798767, "perplexity": 840.8573351094702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368709379061/warc/CC-MAIN-20130516130259-00054-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://hal.in2p3.fr/view_by_stamp.php?label=IN2P3&langue=fr&action_todo=view&id=in2p3-00639398&version=1 | HAL : in2p3-00639398, version 1
arXiv : 1111.1944
5th European Conference on Neutron Scattering (ECNS 2011), Prague : Tchèque, République (2011)
A proposed search for new light bosons using a table-top neutron Ramsey apparatus
(2012)
If a new light boson existed, it would mediate a new force between ordinary fermions, like neutrons. In general such a new force is described by the Compton wavelength $\lambda_c$ of the associated boson and a set of dimensionless coupling constants. For light boson masses of about $10^-4$ eV, $\lambda_c$ is of the order millimeters. Here, we propose a table-top particle physics experiment which provides the possibility to set limits on the strength of the coupling constants of light bosons with spin-velocity coupling. It utilises Ramsey's technique of separated oscillating fields to measure the pseudo-magnetic effect on neutron spins passing by a massive sample.
Thème(s) : Physique/Physique Nucléaire ExpérimentalePhysique/Physique/Instrumentations et Détecteurs
Lien vers le texte intégral : http://fr.arXiv.org/abs/1111.1944
in2p3-00639398, version 1 http://hal.in2p3.fr/in2p3-00639398 oai:hal.in2p3.fr:in2p3-00639398 Contributeur : Emmanuelle Vernay <> Soumis le : Mercredi 9 Novembre 2011, 08:38:37 Dernière modification le : Jeudi 9 Février 2012, 10:29:34 | 2014-04-25 03:27:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5914806723594666, "perplexity": 3837.7912918420084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00227-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://megasoft-rapid.com/New-York/error-propagation-resistivity.html | Let us do the work for you. Do you have network problems, a down computer, or a need a new system? Call us at Brads Computer Services in the Shelburne Supermarket Plaza. We have been in business for almost 10 years. Dont let your computer bring you down, we will fix it, call the professionals.
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# error propagation resistivity Lewis, New York
Die Bewertungsfunktion ist nach Ausleihen des Videos verfügbar. Electrostatics - Dauer: 1:06:02 YaleCourses 384.618 Aufrufe 1:06:02 Resistance of a wire - Dauer: 3:36 krmathsandscience 33.659 Aufrufe 3:36 Resistivity - Data Taking and Analysis - Dauer: 15:58 MindOnPhysics 1.837 Aufrufe Propagation of Error http://webche.ent.ohiou.edu/che408/S...lculations.ppt (accessed Nov 20, 2009). Article type topic Tags Upper Division Vet4 © Copyright 2016 Chemistry LibreTexts Powered by MindTouch Später erinnern Jetzt lesen Datenschutzhinweis für YouTube, ein Google-Unternehmen Navigation überspringen DEHochladenAnmeldenSuchen Wird geladen...
This analysis leads to an understanding of the range of possible values of the layer parameters and of the nature of the relation between them. This method was developed using Finite Element Modeling (FEM). Your cache administrator is webmaster. This might cause poor approximations of D( f ) (Tellinghuisen, 2001). "[Show abstract] [Hide abstract] ABSTRACT: Purpose ‐ The purpose of this paper is to propose an interpretation of the grey
Uncertainty, in calculus, is defined as: (dx/x)=(∆x/x)= uncertainty Example 3 Let's look at the example of the radius of an object again. In effect, the sum of the cross terms should approach zero, especially as $$N$$ increases. Generated Thu, 13 Oct 2016 01:18:26 GMT by s_ac5 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Equation 9 shows a direct statistical relationship between multiple variables and their standard deviations.
Since at least two of the variables have an uncertainty based on the equipment used, a propagation of error formula must be applied to measure a more exact uncertainty of the Le's say the equation relating radius and volume is: V(r) = c(r^2) Where c is a constant, r is the radius and V(r) is the volume. The algorithm is based on the method of successive reductions to lower boundary plane of the resistivity transform function. Full-text · Article · Dec 1979 H.
Wird geladen... Practically speaking, covariance terms should be included in the computation only if they have been estimated from sufficient data. Nächstes Video Resistivity Lab - Theory - Dauer: 25:49 MindOnPhysics 1.673 Aufrufe 25:49 Parallel and Series Resistor Circuit Analysis Worked Example using Ohm's Law Reduction | Doc Physics - Dauer: 24:05 SkumielT.
Wird geladen... For a complete explanation, see the publication (Ehrstein and Croarkin). The SCR obtained was (2.3-27) ×10-6 Ω·cm2. If you like us, please shareon social media or tell your professor!
Wird geladen... Über YouTube Presse Urheberrecht YouTuber Werbung Entwickler +YouTube Nutzungsbedingungen Datenschutz Richtlinien und Sicherheit Feedback senden Probier mal was Neues aus! Thus, the standard deviation for the correction is the standard deviation associated with the measurement of temperature multiplied by the temperature coefficient, $$C_T = 0.0083$$. It is a calculus derived statistical calculation designed to combine uncertainties from multiple variables, in order to provide an accurate measurement of uncertainty. A novel aspect of the algorithm is that error limits are assigned to the initial values of the resistivity transform, and these error limits are carried through in all the subsequent
WiedergabelisteWarteschlangeWiedergabelisteWarteschlange Alle entfernenBeenden Wird geladen... Here are the instructions how to enable JavaScript in your web browser. In the next section, derivations for common calculations are given, with an example of how the derivation was obtained. In measuring the specific contact resistivity, several test structures and methods have been reported123456.
In problems, the uncertainty is usually given as a percent. Thus, the type B evaluation of uncertainty is computed using propagation of error. These instruments each have different variability in their measurements. For example, lets say we are using a UV-Vis Spectrophotometer to determine the molar absorptivity of a molecule via Beer's Law: A = ε l c.
Get Help About IEEE Xplore Feedback Technical Support Resources and Help Terms of Use What Can I Access? The end result desired is $$x$$, so that $$x$$ is dependent on a, b, and c. By contrast, cross terms may cancel each other out, due to the possibility that each term may be positive or negative. Wafer thickness and measurements required for the scale corrections were measured off-line.
Caveats and Warnings Error propagation assumes that the relative uncertainty in each quantity is small.3 Error propagation is not advised if the uncertainty can be measured directly (as variation among repeated The first is the least-count of the digital volt meter in the measurement of $$X$$ with a maximum bound of $$a = 0.0000534 \,\,\, \mbox{ohm}$$ which is assumed to DASD. Data uncertainty quantification provides information about how well measurement fits to the value of the measured quantity and determines its validity.
The problem might state that there is a 5% uncertainty when measuring this radius. 2. P. Error budget showing sensitivity coefficients, standard deviations and degrees of freedom The error budget showing sensitivity coefficients for computing the relative standard uncertainty of volume resistivity (ohm.cm) with degrees of freedom
Note Addition, subtraction, and logarithmic equations leads to an absolute standard deviation, while multiplication, division, exponential, and anti-logarithmic equations lead to relative standard deviations. KoefoedReadFast Hankel Transforms[Show abstract] [Hide abstract] ABSTRACT: Inspired by the linear filter method introduced by D. Derivation of Arithmetic Example The Exact Formula for Propagation of Error in Equation 9 can be used to derive the arithmetic examples noted in Table 1. Geophysical ProspectingVolume 24, Issue 1, Version of Record online: 27 APR 2006AbstractArticleReferences Options for accessing this content: If you are a society or association member and require assistance with obtaining online
This has two sources of uncertainty: error in the solution of the transcendental equation for determining the factor errors in measured voltages The maximum bounds to these errors are assumed to LeszczyńskiRead full-textAN ASSESSMENT OF THE INFLUENCE OF ELASTIC, OR PLASTIC, DEFORMATION, ON THE MEASUREMENT ERRORS Full-text · Article · Jan 2016 · Applied Thermal EngineeringGavril GrebenişanAlexandra Raluca ARBARead full-textData provided are We know the value of uncertainty for∆r/r to be 5%, or 0.05. M.
Anmelden Teilen Mehr Melden Möchtest du dieses Video melden? However, if the variables are correlated rather than independent, the cross term may not cancel out. KatichaEdgar de León Izeppi+2 more authors ...Vittorio NicolosiRead full-textUses and limitation of different thermometers for measuring heating efficiency of magnetic fluids Full-text · Article · May 2016 A. Since the only restriction on the order is ν > − 1, the Fourier transform is a special case of the theory, ν=± 1/2 giving the sine- and cosine transform, respectively.
Taking the partial derivative of each experimental variable, $$a$$, $$b$$, and $$c$$: $\left(\dfrac{\delta{x}}{\delta{a}}\right)=\dfrac{b}{c} \tag{16a}$ $\left(\dfrac{\delta{x}}{\delta{b}}\right)=\dfrac{a}{c} \tag{16b}$ and $\left(\dfrac{\delta{x}}{\delta{c}}\right)=-\dfrac{ab}{c^2}\tag{16c}$ Plugging these partial derivatives into Equation 9 gives: $\sigma^2_x=\left(\dfrac{b}{c}\right)^2\sigma^2_a+\left(\dfrac{a}{c}\right)^2\sigma^2_b+\left(-\dfrac{ab}{c^2}\right)^2\sigma^2_c\tag{17}$ Dividing Equation 17 by Differing provisions from the publisher's actual policy or licence agreement may be applicable.This publication is from a journal that may support self archiving.Learn moreLast Updated: 14 Oct 16 © 2008-2016 researchgate.net. Anzeige Autoplay Wenn Autoplay aktiviert ist, wird die Wiedergabe automatisch mit einem der aktuellen Videovorschläge fortgesetzt. Register now > For full functionality of ResearchGate it is necessary to enable JavaScript. | 2018-12-11 18:16:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3384418487548828, "perplexity": 2866.790981855097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823674.34/warc/CC-MAIN-20181211172919-20181211194419-00411.warc.gz"} |
https://3dprinting.stackexchange.com/questions/454/how-to-configure-cura-to-run-the-z-probe-before-heating | # How to configure Cura to run the Z probe before heating
I'm using Cura as my slicing/printing software and I just started using the BuildTak printing surface.
The BuildTak is damaged by pushing a hot nozzle into it and my printer's (Robo3D R1+) autoleveling feature works by pushing the nozzle into the build surface.
Is there a way to configure Cura so that it runs the Z probe first, then heat up the nozzle?
My first sheet of BuildTak already has 10 small holes in it (at the homing position and at the 9 leveling touch points)
In Cura (and Slic3r), you can 100% customize what the printer does before printing your actual model through custom start/end g-code.
If you navigate to the Start/End-GCode tab in Cura, then select start.gcode, you can see what operations are run before each print begins. Lines prefixed with ; are comments, and does not affect the printing in any way.
Basically, we want to manually tell the printer to do the auto leveling before heating up the nozzle by editing the g-code in start.gcode.
### G-Code generated with the default start.gcode:
If you try to slice some model with the default code found in start.gcode, you will get something like the following (depending on your printer):
; CURA AUTOMATICALLY INSERTS THESE TEMPERATURE CODES
M190 S70.000000 ; Set bed temperature to 70 degrees
M109 S210.000000 ; Set nozzle temperature to 210 degrees
; THESE ARE THE CODES FROM START.GCODE (for a ROBO 3D R1)
G28 ;move printer to endstops (the home position)
G92 E0 ;zero the extruded filament length
M565 Z-1 ;set z-probe offset
G1 Z5 F5000 ;move the printer 5mm above the bed
G29 ;run auto-leveling
; THE ACTUAL MODEL BEGINS HERE
;Layer count: 168
;LAYER:0
.
.
### Analyzing the g-code output
At the top of this code snippet, we can see that Cura automatically inserts g-code for heating up the bed and nozzle to their respective temperatures with the M190 and M109 g-codes. This means the printer always will heat up the nozzle before reading the start.gcodes that we set. However, if we manually override M109 code in start.gcode, the M109 at the top will automagically disappear from the generated g-code output! (Thanks, @TomvanderZanden!)
We could therefore use the auto-leveling command G29 before manually setting the nozzle temperature with M109; specifically, we want to add M109 S{print_temperature}, which reads the Basic -> Print Temperature-setting in Cura, and replace {print_temperature} with it automatically.
### Manipulating start.gcode:
In order to postpone heating the hotend till after probing, start.gcode could be something like:
G28 ;move printer to endstops (the home position)
G92 E0 ;zero the extruded filament length
M565 Z-1 ;set z-probe offset <----- ( YOU HAVE TO ADJUST THIS, READ BELOW)
G1 Z5 F5000 ;move the printer 5mm above the bed
G29 ;run auto-leveling
M109 S{print_temperature} ;set nozzle temperature, and wait for it heat up
And that's about it! You can then use these codes in your start.gcode. However, you probably will have to recalibrate your z-prove offset.
• {print_temperature} didn't work for me. {material_print_temperature} did. Look here for more. Sep 3 '17 at 20:25 | 2021-09-28 22:47:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26666101813316345, "perplexity": 12113.525000462609}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780060908.47/warc/CC-MAIN-20210928214438-20210929004438-00285.warc.gz"} |
https://stats.stackexchange.com/questions/7876/interpreting-range-bars-in-rs-plot-stl | Interpreting range bars in R's plot.stl?
I have trouble figuring out what the range bars in plot.stl exactly mean. I found Gavin's post on this question and read the documentation as well, I understand that they tell the relative magnitude of the decomposed components, but still I am not entirely sure how they work.
E.g.:
data: tiny bar, no scale seasonal: full bar, with scale ranging from -0.6 to 0.2 trend: another tiny bar (seems to be equal to data), no scale remainder: medium sized bar with scale from -1.5 to 0.5
I do not understand what's the basis to relation and why trend has no scale. I tried stl and decompose with identical results for multiplicative and additive methods.
Here is an example to discuss specifics against:
> plot(stl(nottem, "per"))
So on the upper panel, we might consider the bar as 1 unit of variation. The bar on the seasonal panel is only slightly larger than that on the data panel, indicating that the seasonal signal is large relative to the variation in the data. In other words, if we shrunk the seasonal panel such that the box became the same size as that in the data panel, the range of variation on the shrunk seasonal panel would be similar to but slightly smaller than that on the data panel.
Now consider the trend panel; the grey box is now much larger than either of the ones on the data or seasonal panel, indicating the variation attributed to the trend is much smaller than the seasonal component and consequently only a small part of the variation in the data series. The variation attributed to the trend is considerably smaller than the stochastic component (the remainders). As such, we can deduce that these data do not exhibit a trend.
Now look at another example:
> plot(stl(co2, "per"))
which gives
If we look at the relative sizes of the bars on this plot, we note that the trend dominates the data series and consequently the grey bars are of similar size. Of next greatest importance is variation at the seasonal scale, although variation at this scale is a much smaller component of the variation exhibited in the original data. The residuals (remainder) represent only small stochastic fluctuations as the grey bar is very large relative to the other panels.
So the general idea is that if you scaled all the panels such that the grey bars were all the same size, you would be able to determine the relative magnitude of the variations in each of the components and how much of the variation in the original data they contained. But because the plot draws each component on it's own scale, we need the bars to give us a relative scale for comparison.
Does this help any?
• Indeed it does. Thx Gavin, this are just one great explanation and nice examples. I just did not get that the bar in the data panel is the unit bar. Plus I find it a little irritating that you don't have scales for trend. Anyway great help! thx! – hans0l0 Mar 4 '11 at 16:00
• D'oh. I got it. The color of acceptance is really bad for be, because I am colorblind :) It's much better on SO, maybe CV should change it because there a quite a few colorblind people around... ;) – hans0l0 Mar 4 '11 at 16:04
• @ran2 what do you mean by no scales for trend? Do you mean on the axis or no grey bar for trend? If the latter, I suspect that the trend is such a strong/large part of the variation in the data that the grey bar is so small as to be less than 1px in size. Try plotting on a huge pdf() device and see if it shows up? As for the colour of the tick, I'll post something on meta to see if we can change it and point to this accessibility issue. – Gavin Simpson Mar 4 '11 at 17:04
• no, i just mean the scale on the axis. in my case the trend is not as strong as in your second example, but still strong. But as you example shows: the trend never has a scale no matter if the bar is small or big. It does not really matter here because the relation is important here, but nevertheless i would be interested in the meaning of the scale on the right (repsectively its dimension – if there is any. Or is it just a dimensionless factor?) – hans0l0 Mar 4 '11 at 22:14
• But there is a scale on the trend panels in both my examples?! – Gavin Simpson Mar 5 '11 at 8:08 | 2019-10-20 06:06:30 | {"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": 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": 0.6303367614746094, "perplexity": 627.3040032183661}, "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-2019-43/segments/1570986703625.46/warc/CC-MAIN-20191020053545-20191020081045-00133.warc.gz"} |
http://beowulf.org/pipermail/beowulf/2005-April/012494.html | [Beowulf] OS for 64 bit AMD
Robert G. Brown rgb at phy.duke.edu
Wed Apr 6 12:11:08 PDT 2005
On Tue, 5 Apr 2005, Tony Travis wrote:
> Robert G. Brown wrote:
> > [...]
> > Ah, but the PROPER and ORIGINAL meaning of axiom is "unprovable
> > assumption" upon which a system of logic and discourse is built. The
> > final half-definition is the only one that is actually correct.
>
> > In fact, I've got a whole essay entitled "Axioms" on my personal
> > website. Seriously.
>
> Hello, Robert.
>
> OK, I bow to your greater wisdom: I have now learned that axioms are:
>
> "...unprovable assumptions whose truth and falsehood cannot be assessed"
> [http://www.phy.duke.edu/~rgb/Philosophy/axioms.php]
>
> What struck me was that both Mark and Joe used the word "axiom"
> appropriately according to at least one dictionary:
>
> http://www.thefreedictionary.com/axiom
Oh, I have much the same definition from Webster in the very work cited
above -- the interesting thing (and reason I brought it up) is that
"axiom" in everyday usage HAS come to mean something that is
self-evidently true, without question, when the Greek/Latin root meaning
is actually in some sense the opposite -- something that is not
self-evidently true, but that is assumed to be true literally for the
sake of argument.
rom Webster's Revised Unabridged Dictionary (1913) [web1913]:
Axiom, n.-- L. axioma, Gr.; that which is thought
worthy, that which is assumed, a basis of demonstration, a
principle, fr.; to think worthy, fr.; worthy, weighing as
much as; cf.; to lead, drive, also to weigh so much: cf F.
axiome. See Agent.
1. (Logic and Math.) A self-evident and necessary truth, or a
proposition whose truth is so evident as first sight that
no reasoning or demonstration can make it plainer; a
proposition which it is necessary to take for granted; as,
The whole is greater than a part;'' A thing can not,
at the same time, be and not be.''
2. An established principle in some art or science, which,
though not a necessary truth, is universally received; as,
the axioms of political economy.
"That which is assumed", "That which is thought worthy" is a fair
description of meaning, and "the basis of a demonstration" (or
argument:-) better still, but Webster makes a common and real mistake in
calling an axiom a self-evident truth in Mathematics or Logic. One
important enough to discuss in some detail even on a list like this one
where it is a bit off topic but where a lot of people participate in
reasoning and debate. Axioms shape discourse, and it is very important
to understand that to avoid spinning one's wheels or missing new truths,
and you can't know too much formal mathematics;-)
In Webster's very example, "The whole is greater than the part"
precludes the existence of negative numbers or the entirety of vector
algebra (where |\vec{A} + \vec{B}| can easily be less than |\vec{A}| and
|\vec{B}| and is always <= |vec{A}| + |\vec{B}| (triangle inequality).
Curved space geometry follows only when one drops the "self-evident"
axiom that parallel lines never meet. Nowhere is it MORE evident that
an axiom is that which is assumed as the basis for a demonstration or
formal reasoning and >>not<< absolute or self-evident truth than in
mathematics and logic. "Its axiomatic that..." is another way of saying
"For the sake of argument, let's both assume that..."
However, the actual usage in the discussion was sense 2, where calling
something an "axiom" (or using something as if it were an axiom) is a
political and argumentative step intended to short-circuit the reasoning
process. Self-evident truths such as "All men were created equal" are
manifestly and obvious falsehoods by any objective measure (and begs at
least three or four serious questions to boot, as in "men" (versus women
and children and dogs and fish), "created" (as opposed to evolved,
appeared out of nowhere, are a figment of my solipsistic imagination),
"equal" (in precisely what abstract and projective geometry, given that
this usage is clearly not the same as what is meant when I say 1 is
equal to 2*(1/2) or my weight is equal to 980 Newtons.
This sort of "axiomatic" reasoning is a powerful tool in any debate.
Here one makes a statement that one hopes to have ACCEPTED as being
"axiomatically true" as this begs the question and precludes any
possible argument. The entire discussion on the subject of e.g.
abortion is rife with this sort of "axiomatic" reasoning, and
unsurprisingly such debate is not only unresolved, it is unresolvable as
the participants fail to agree on their basic axioms and will inevitably
be led to different, equally "valid", conclusions. Semantically, the
argument is that of a typical five year old -- "Is so." "Is not." "Is
so." Not terribly useful.
> I don't think their discussion was pointless: Actually, I found it
> interesting and relevant to my own situation running openMosix on a
I agree that it wasn't useless and was enjoying it at least to where I
was apparently making Joe feel bad (which was never my intention, and I
apologize, Joe:-), but one aspect of it WAS useless -- the issue of
whether or not FC is or is not a "beta distribution". Whether you call
it an issue of axioms or definitions, it was (and still is) clear that
Mark and Joe (and I:-) >>agreed<< about what Fedora Core "is" -- an
actual linux distribution, with its own decisioning process, its own
testing process (including both alpha and beta phases), its own
community-based repair mechanism (whether or not one finds it to be
efficient, it is certainly there). It quacks like a duck, likes water,
and its mature females lay eggs -- call it a duck.
Joe calls it a "rolling beta distribution" because one of several
undoubted benefits Red Hat gets from funding it is the ability to see
what works and what doesn't and only select from it what works for their
(necessarily) ultra-conservative Enterprise release. Mark agrees that
Red Hat does get to select from it (and from all the other linuces in
existence, and from new or different packages that may not have appeared
in FC) for EL, but insists that this doesn't make FC a "rolling beta
distribution".
(Parenthetically, it is fair to say that the many people who work on or
with FC who do NOT work for or even with Red Hat per se might take
offense at hearing their work portrayed as a "rolling beta distribution
for Red Hat" used as a pejorative term, just as Debian people get tired
of hearing that Debian is always either way behind (for the stable
version) or unstable (surprise) for the development version and linux
people in general get REALLY tired by the old saw that Microsoft is
"supported" and linux is not. I'm equally sure Joe never meant to
offend any of them, either -- he was just making and emphasizing a
point.)
This is the point where things do get silly. Two people agree as to
what Fedora core "is" in terms of all its functional aspects, but argue
over what it is to be called, which distracts from the real point, which
is/was whether FC was a suitable distro to choose for use on a cluster
and whether any of the specific issues that e.g. Joe encountered with
particular packages were problems with FC per se or with those packages.
There anybody who has been on the list more than a few days KNOWS that
the answer is going to be "it depends" and "YMMV"; a useful
>>discussion<< illuminates what it depends ON, so users can answer very
reasonable questions such as "ok, so I might have to rebuild a kernel in
order to use a kernel-tainting Nvidia driver and still use FC". It is
also useful to hear where something will not work under any
circumstances, and where particular users have reported problems and
gotten less than satisfactory responses (such as Greg's experience).
Instead Joe calls it a "beta" in some very large, very general sense in
which the >>entire distribution<< is a beta, since it clearly >>has its
own<< beta releases, as do (in many cases) the individual >>packages<<
from which it is comprised, and calling something that is post-beta for
an actual, formal beta test a "beta" is clearly not "technically"
correct. Clearly he means to imply that FC as a whole is not
acceptable, as beta software is almost by definition full of
undiscovered bugs and not ready for a prime time. Beta is being used as
a term of indictment.
Mark insists that this isn't technically correct (and he's right) -- a
post-beta product is not in any accepted sense of the term, a beta
product. Also, ALL post-beta releases can still be full of bugs
depending on how broad the beta phases were and how complex the product;
hence the "gamma release" joke/extension of the series. Show me a major
linux distribution that never had a release that was a "beta" in the
sense that a ton of stuff in the HUNDREDS of packages distributed was
more than a bit broken or buggy, and I'll show you a major distro that
doesn't need an update stream. (Any takers? I thought not.) That
still leaves open the IMPLICIT indictment and question -- "is FC ready
for prime time"? or "Is RH to blame for FC's particular bug stream"?
Fortunately, we all know what BOTH of them mean, and fully realize BOTH
that RH gains various benefits from the de facto testing that occurs in
FC and that FC is not, actually a beta for RHEL in anything like the
sense that the term is used in an actual software development cycle. FC
>>has<< a beta phase, and its "gamma" phase >>does<< further refine the
release because bugs do get fixed however responsive or unresponsive the
formal FC "community support" mechanism is. That doesn't save RH from
having to run an actual beta on their own EL products, though. Let me
be clear in a way I hope everybody can agree on. RHEL is most
definitely NOT just some late snapshot of a given FC release rebranded,
and that's precisely what it would have to be in order to make Joe's
assertion technically correct.
Whole releases of FC occur in between RHEL releases, and frankly with
only FC 1-3 under our belts it is really difficult for me to accept ANY
useful assertion concerning whether FC is going to be "stable" or
"unstable" or conservative or radical in the long run. FC 1 was,
indeed, pretty much a beta release, but I personally have found FC 2 to
be every bit as stable/functional as any given RH x.y <= 9 ever was and
far MORE stable and useful than a number of memorable specific releases.
FC 3 I'm undecided about -- it works well enough but also has enough
differences that I'm a bit uncomfortable with the rate of change,
especially in X.
However, as always, YMMV, caveat emptor, maybe it sucks for you and not
for me, maybe it sucks for me and I'm to stupid to notice it.
By this standard Debian is just an "rolling beta for RHEL", as is SuSE,
as I'd bet significant amounts of money that packages that are primarily
maintained by Debian and SuSE devlopers, or by independent developers
e.g. Ximian or the mozilla folks or the gnu folks -- make it into any
given EL release without first passing through FC (and whole GENERATIONS
of FC occur without making it into EL). They (like the FC packages) are
doubtless passed through their very own alpha and beta cycles by their
primary developers followed by a fairly standard process of repackaging
for EL specifically and subsequent alpha and beta testing all over. The
most FC "buys" RH is MAYBE a simpler and more reliable port into EL and
fewer problems during the beta for certain overlapping packages, which I
actually think is a perfectly reasonable tradeoff and a good deal for
everybody concerned but is less than sufficient to convince me that this
makes FC automatically "unstable" or "unreliable" or brandable as a
"beta distribution". Only time will prove one way or the other, and any
such conclusion will remain subject to change again over still more
time.
> interesting and relevant to my own situation running openMosix on a
> 64-node RH-9 based Beowulf cluster. I had a difficult time trying to
> upgrade our cluster from RH-8.0 to FC-2 because the Adaptec Ultra160
> drivers in FC-2 were broken, so I went to RH-9 instead.
That probably should read "were broken in the particular kernel snapshot
I tried to install". Google fairly quickly turns up a few hits on this
problem (but not many) and several suggestions on how to proceed. This
seems like something that would have rapidly and long since been
resolved, given the large number of adaptec users out there. Still, I
have definitely seen problems (notably a broken USB subsystem) within
some of the FC kernel snapshots. This doesn't make FC "broken" wrt to
EL -- I've had BIGGER problems dealing with EL's broken/out of date
libraries in my own numerical code. An old GSL alone is a show stopper
for HPC applications in my personal opinion. RH has clearly interpreted
"stable" as meaning "not to be changed even in clearly positive ways"
(that is, "stagnant") in my opinion. Fine for banks, fine for servers,
not so good for desktops or clusters expected to run a rapidly changing
mix of applications.
Note also that the adaptec problem is a linux kernel issue, not one with
FC per se. I personally helped work on the linux adaptec drivers some
years ago when we got a bunch of brand new systems with unsupported
hardware integrated with the motherboards and assure you that the issues
are nontrivial (among other things, I recall that the core driver code
was shared between freebsd and linux and at the time adaptec itself did
not formally support linux, in ADDITION to the actual driver/kernel
issues that ALONE were nontrivial). So it wouldn't surprise me in the
least if there were issues with any given driver in any given kernel
release and by extension any given distribution release that
inadvertently used that kernel release and hence driver.
Over the years and many, many revisions of various linux distributions
there is no doubt in my mind -- some kernel snapshots are broken on at
least some hardware combinations, and some of the broken snapshots make
it into distribution releases or updates. Most are not COMPLETELY
broken (many would pass a beta or the issues are with hardware that
isn't -- if one bothers to read the release notes -- technically on the
"supported" list, and most -- but not all -- get fixed fairly rapidly.
Still, sometimes one has to actually PARTICIPATE in the open source
kernel development process or build a kernel/driver from scratch that
somebody else that does even in these best of times, especially if your
hardware is new or a major change in the kernel source has broken
something.
Such problems generally transcend distribution. RH and EL are in the
same boat as everybody else (Debian, SuSE, Mandrake, whoever) -- not
even an extensive beta has a ghost of a chance at revealing every
possible flaw in something as complex (and multiauthored) as a modern
linux kernel. Note also that using things like RH-9 and its more or
less frozen kernels simply avoids one problem and the expense of others
and has a variety of negative sequellae in the long term -- lack of
support for X86_64, frozen in bugs and security problems, lack of driver
support. We live in an imperfect world, but in >>this<< imperfect world
you aren't helpless and have a number of choices. FC is not a perfect
choice, but it is a perfectly reasonable choice (in my opinion) for many
users and environments (including cluster environments), while not for
others.
rgb
--
Robert G. Brown http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567 Fax: 919-660-2525 email:rgb at phy.duke.edu | 2017-01-24 19:18:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5232383012771606, "perplexity": 4840.659857747473}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560285244.23/warc/CC-MAIN-20170116095125-00207-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/frictional-force-on-a-sphere.98179/ | # Homework Help: Frictional force on a sphere
1. Nov 3, 2005
### gdumont
Ok, I need to find the frictional force on sphere of radius $a$ and mass $M$ moving with velocity $v$ in an ideal gas at temperature $T$.
If I put myself in the sphere frame, then diffrential cross-section is
$$\frac{d\sigma}{d\Omega} = \frac{a^2}{4}$$
and the total cross-section is $\sigma_{\textrm{tot}}=\pi a^2$. How do I find the frictional force from this? Ellastic collisions between the sphere and the gas particules are assumed.
Any help greatly appreciated.
Last edited: Nov 3, 2005
2. Nov 6, 2005
### gdumont
Ok, here's what I tought:
If the gas has density $\rho$ than the number of molecules in a volume $\sigma_{\textrm{tot}}dx$ is $dN=\pi \rho a^2 dx$. If collisions are ellastic, then
$$\textbf{p}_s + \textbf{p}_i = \textbf{p}_s' + \textbf{p}_i'$$
where the $s$ and the $i$ denote respectively the momentum of the sphere and the $i$th molecule. The prime denotes the momentum after collision. (I assumed that molecules do not collide simultaneously.)
The change in speed of the sphere is
$$dv = \frac{|\textbf{p}_s' - \textbf{p}_s|}{M}$$
From accelaration $dv/dx$ if the $x$ direction is chosen along the movement of the sphere we can find the resistance force
$$F = M\frac{dv}{dx}$$
Now I need to evaluate either $\textbf{p}_s' - \textbf{p}_s$ or $\textbf{p}_i - \textbf{p}_i'$.
Anyone can help?
Last edited: Nov 6, 2005 | 2018-12-12 16:15:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9712842106819153, "perplexity": 579.638559048899}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824059.7/warc/CC-MAIN-20181212155747-20181212181247-00188.warc.gz"} |
https://www.math.uic.edu/seminars/view_seminar?id=5170 | ## Logic Seminar
Anush Tserunyan
UIUC
A pointwise ergodic theorem for quasi-pmp graphs
Abstract: We prove a pointwise ergodic theorem for quasi-pmp locally countable graphs, which states that the global condition of ergodicity amounts to locally approximating the means of $L^1$-functions via increasing subgraphs with finite connected components. The pmp version of this theorem was first proven by R. Tucker-Drob using probabilistic methods. Our proof is different: it is constructive and applies more generally to quasi-pmp graphs. It involves introducing a graph invariant, a packedness condition for finite Borel subequivalence relations, and an easy method of exploiting nonamenability. The quasi-pmp setting additionally requires a new gadget for analyzing the interplay between the underlying cocycle and the graph.
Tuesday February 27, 2018 at 3:30 PM in SEO 427
UIC LAS MSCS > seminars > | 2019-02-22 02:01:34 | {"extraction_info": {"found_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": 0.7336204648017883, "perplexity": 1725.5218154677475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247512461.73/warc/CC-MAIN-20190222013546-20190222035546-00421.warc.gz"} |
https://cds.cern.ch/collection/LHCb%20Theses?ln=no | # LHCb Theses
Nyeste elementer:
2018-03-21
09:09
Measurement of CP Violation using $B^0 \rightarrow D^{(*)\pm}D^{\mp}_{(s)}$ decays at LHCb / Belloli, Nicoletta This thesis presents two measurements, performed using data collected by the LHCb experiment, operating at the Large Hadron Collider accelerator at CERN [...] CERN-THESIS-2018-017 - 152 p.
Fulltext
2018-03-14
14:37
Measurement of the $CP$-even Fraction of the $D^0 \rightarrow 2\pi^+ 2\pi^-$ Decay using Quantum Correlated ${D\bar{D}}$ Pairs at CLEO-c, and Real-time Alignment of the LHCb RICH optical Systems / Prouve, Claire This thesis covers three subjects, namely the measurement of the $C\!P$-even fraction of the $D^0\rightarrow 2\pi^+2\pi^-$ decay, the real-time alignment of the LHCb RICH mirror systems and the estimation of the sensitivity to the CKM angle $\gamma$ that can be obtained using $B^{\pm}\rightarrow D(\ [...] CERN-THESIS-2017-334 - 173 p. Fulltext 2018-02-26 10:12 Test of lepton flavour universality using hadronic tau decays with the LHCb detector / Arbouch, Emmanuel The goal of this internship was to realize a preliminary study on the measurement of the R(D ∗ ) parameter, defined as the ratio between the two branching frac- tions R(D ∗ ) ≡ B(B 0 → D ∗− τ + ν τ )/B(B 0 → D ∗− μ + ν μ ), using the τ + → π + π − π + ν τ hadroni [...] CERN-THESIS-2017-319 - 34 p. Fulltext 2018-02-23 17:40 Observation of the$B^0_s \to \eta_c \phi$decay with the LHCb experiment / Martin, Morgan Leni The interference between$B^0_s$meson decay amplitudes to CP final state directly or via mixing gives rise to a measurable CP-violating phase$\phi_s$, which is predicted to be$\phi_s^{SM} = (-0.0370\pm0.0006)~\mathrm{rad}$in the Standard Model [...] CERN-THESIS-2017-318 - 150 p. Fulltext 2018-02-21 06:04 Observation of CP violation in B+/- → DK+/- decays / Gandini, Paolo An accurate determination of the angle γ of the Unitary Triangle is one of the most important goals of the LHCb experiment [...] Springer, 2017. 10.1007/978-3-319-01029-8 Full text 2018-02-15 16:13 Measurement of particle multiplicity and energy flow in pp collisions at 13 TeV with the LHCb detector / Dreimanis, Karlis The LHC is the world's largest and highest-energy particle collider [...] CERN-THESIS-2017-310 - 180 p. Fulltext 2018-02-02 11:54 CP Violation and Lifetime Measurements of Two-body Charmless Decays of B Hadrons at LHCb / Karodia, Sarah This thesis presents lifetime measurements of charmless two-body decays of b hadrons, specifically the decay modes known as$B\to h^+ h^{'-}$, where$B$refers to meson or baryon containing a$b$quark and$h^{(')}$refers to a proton$p$, pion$\pi$or kaon$K$[...] CERN-THESIS-2017-302 - 179 p. Fulltext 2018-02-01 12:08 Searches for$CP$violation in multi-body charm decays and studies of radiation damage in the LHCb VELO detector / Chen, Shanzhen This thesis presents two searches for direct charge-parity ($CP$) violation in multi-body decays in the charm-sector at LHCb, the development of techniques for performing model-independent searches for direct$CP$violation in multi-body decays, and the development of studies of radiation damage ef [...] CERN-THESIS-2017-301 - 296 p. Fulltext 2018-01-26 11:22 Search for a Higgs boson decaying to a pair of$b$quarks in the forward region of$pp$collisions with the LHCb detector / Sestini, Lorenzo LHCb is a forward spectrometer (pseudorapidity coverage 2 <$\eta$< 5) designed for heavy flavour physics, located at the Large Hadron Collider (LHC) [...] CERN-THESIS-2017-294 - 172 p. Fulltext 2018-01-17 10:52 Searches for two-body charmless baryonic$B^0\$ decays at LHCb / Beddow, John The results of two separate searches for the rare two-body charmless baryonic decays B0 -> p pbar and B0s -> p pbar at the LHCb experiment are reported in this thesis [...] CERN-THESIS-2016-357 - Glasgow : University of Glasgow, 2016-09-26. - 166 p.
Fulltext | 2018-03-24 00:23:27 | {"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": 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": 0.9849701523780823, "perplexity": 5638.477281235475}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1521257649508.48/warc/CC-MAIN-20180323235620-20180324015620-00490.warc.gz"} |
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Evidence for electroweak production of four charged leptons and two jets in proton-proton collisions at [root of] s=13 TeV
Abstract: Evidence is presented for the electroweak (EW) production of two jets (jj) in association with two Z bosons and constraints on anomalous quartic gauge couplings are set. The analysis is based on a data sample of proton-proton collisions at collected with the CMS detector in 2016?2018, and corresponding to an integrated luminosity of 137. The search is performed in the fully leptonic final state , where . The EW production of two jets in association with two Z bosons is measured with an observed (expected) significance of 4.0 (3.5) standard deviations. The cross sections for the EW production are measured in three fiducial volumes and the result is in the most inclusive volume, in agreement with the standard model prediction of . Measurements of total cross sections for jj production in association with two Z bosons are also reported. Limits on anomalous quartic gauge couplings are derived in terms of the effective field theory operators T0, T1, T2, T8, and T9.
Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria
Fuente: Physics Letters B . Volume 812, 10 January 2021, 135992
Editorial: Elsevier
Año de publicación: 2021
Nº de páginas: 25
Tipo de publicación: Artículo de Revista
ISSN: 0370-2693,1873-2445
Url de la publicación: https://doi.org/10.1016/j.physletb.2020.135992
Autores/as
THE CMS COLLABORATION
PEDRO JOSE FERNANDEZ MANTECA
CEDRIC GERALD PRIEELS
FRANCESCA SHUN-NING ANNAROSA RICCI-TAM | 2023-01-27 23:48:41 | {"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": 0.9407727122306824, "perplexity": 3924.546627842887}, "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-2023-06/segments/1674764499468.22/warc/CC-MAIN-20230127231443-20230128021443-00865.warc.gz"} |
https://ask.libreoffice.org/en/question/198068/how-do-i-move-sections-to-a-different-page/ | # How do I move sections to a different page?
I have a document (originally a Microsoft Word document that was converted to LibreOffice 6.2.4.2 x64 Build ID: 2412653d852ce75f65fbfa83fb7e7b669a126d64-and converted amazingly well-my thanks to all of the people who made this program!) that has columns on a few pages that occupy only a portion of the page (Example= current page 1, the very first portion at the top of the page has 2 columns, followed by a section without columns, followed by a section divided into 4 columns). However, on several of these pages, at the point where the columns end (and the rest of the page's text should be) their seems to be some sort of Page Break and the rest of the page is moved to the next page (Example= current page 3, the top section has 2 columns and is supposed to be followed by a second, different section). I have the off-line Help installed and have the Formatting Marks toggled On, but despite my searching, I have not been able to find whatever it is that is moving my text to the next page, and I have not been able to move the other section back to its desired position (on the previous page) without ruining the columns that are already set up. Can someone please tell me what I need to do to move the sections back to where I want them?
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Unfortunately, page breaks don't show as "formatted marks".
Since the document was converted from M\$ Word and Word is based on different formatting principle than Writer, most formatting translate to so-called direct formatting. Your page breaks have been transferred as attributes to the next paragraph.
Put the cursor in the first paragraph of the page. Open Format>Paragraph and go to Text Flow tab. Uncheck Insert box in the Breaks section.
Do that on every relevant paragraph.
Your document can be improved using paragraph styles, so that formatting and layout is controlled from a single location. You are encouraged to discover the tremendous possibilities of styles in the freely downloadable Writer guide.
To show the community your question has been answered, click the ✓ next to the correct answer, and "upvote" by clicking on the ^ arrow of any helpful answers. These are the mechanisms for communicating the quality of the Q&A on this site. Thanks!
more | 2020-02-29 07:25:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.3034785985946655, "perplexity": 949.1187916336977}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1581875148671.99/warc/CC-MAIN-20200229053151-20200229083151-00154.warc.gz"} |
https://forum.uipath.com/t/datatble/66661 | # Datatble
hi,
i have one datatable (DB1) which is having two columns. i need to get those two columns in another datatable (DB2) but in a specific format. i want data from the first column of DB1 in the first column of DB2 and second column of DB1 in the 6th column of DB2.
what should i do for this?
You have to put a for each row inside another for each row. So, when you get the value of DT1, call it for example, row(“Age”).Tostring, you have to write it in the column of DT2 that you want.
Suposse that your 6th column of the 2nd DT is called Year… So:
For each row -> For each row -> Assign { row2(“Year”) = row1(“Age”) }
Doing this you will have all the values of column Age (suposse it the First column of the DT) in the 6th column (called “Year” by us) of the second DT.
NOTE: To do that, first you have to define the datatables. I mean, you have to construc all the columns and define their types before call them. | 2020-10-23 09:10:15 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8259152770042419, "perplexity": 1262.3949675045587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107880878.30/warc/CC-MAIN-20201023073305-20201023103305-00308.warc.gz"} |
https://web2.0calc.com/questions/im-screwed-pls-help-me | +0
# im screwed; pls help me!!
0
137
2
+454
Simplify
Sep 14, 2022
#1
+9449
+2
$$\phantom{=\quad}\dfrac{x^2+2x^4+3x^6+\cdots+1005x^{2010}}{2x+4x^3+6x^5+\cdots+2010x^{2009}}$$
Factor x out of all the terms in the numerator and factor 2 out of all the terms in the denominator to get:
$${=\quad}\dfrac{x(x+2x^3+3x^5+\cdots+1005x^{2009})}{2(x+2x^3+3x^5+\cdots+1005x^{2009})}$$
Now we can cancel out the common factor from the numerator and denominator to get:
$${=\quad}\dfrac{x}{2}$$
gdfngkdfngkj
Sep 14, 2022
#2
+454
+1
thank you
Keihaku Sep 14, 2022 | 2023-02-05 03:44:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.9933100938796997, "perplexity": 1465.8281876309752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500215.91/warc/CC-MAIN-20230205032040-20230205062040-00084.warc.gz"} |
http://signatureaustin.com/5utt8gzt/espoma-green-sandkernel-density-estimation-explained-4da48b | A new method for obtaining the shape coefficient for the Kozeny–Carman equation is proposed. The adjustment of the gamma-count model on the measured plant spacing using a maximum likelihood method provides an estimate of the plant density (Eq. This model was transformed into a count data model to investigate the optimal sampling required to get an estimate of plant density for a given precision level. The processing of images here was automatic except the last step corresponding to the interactive visual extraction of the plants’ coordinates in the image. Manage cookies/Do not sell my data we use in the preference centre. The solid (respectively dashed) isolines correspond to the CV of parameter a (respectively parameter b). Jin J, Tang L. Corn plant sensing using real-time stereo vision. Article This study investigated the sampling strategy to estimate the plant density with emphasis on the variability of plant spacing along the row, corresponding to the sampling error. But check your contract first to figure out what you are actually paying for. estimate the textural class of a soil sample . However, it is possible to automatically identify from the images the unusual row segments with missing plants or excessive concentration of plants [25]. Brown M, Lowe DG. A very high density of concrete is that made around steel cables that have been stretched by hydraulic jacks. In general, the performance of a fertilizer applicator can be contributed to 1/3 operator, 1/3 applicator and 1/3 fertilizer characteristics. You can see chemical substitution’s effect quite dramatically in the example of the orthorhombic carbonate minerals aragonite and cerussite.Aragonite is CaCO 3 and has a specific gravity of 2.95. SL and FB designed the experiment and XJ, BA, PB, MH and AC contributed to the field measurement in different experimental sites. Comput Electron Agric. Olsen J, Weiner J. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Green strength: A wide range distribution favours the green strength while narrow grain distributions reduce it. New York: Springer Science & Business Media; 2003. 2009;26:591–608. Further, the FNP approach is probably more easy to implement with higher reliability: as a matter of facts, measuring the length of a segment defined by plants at its two extremities is easier than counting the number of plants in a fixed length segment, where the extremities could be in the vicinity of a plant and its inclusion or not in the counting could be prone to interpretation biases by the operator. a regular program whereby the saturated bulk density of sediments in situ is measured by means of proximal sensing devices lowered in the drilled hole. Agron J. Basic Appl Ecol. Frontis. The non-sampling error may be reduced by combining a random sampling selection procedure with a measurement method ensuring high accuracy including accounting for the actual values of the row spacing measured over each segment [30]. All data analyzed during this study are presented in this published article. By using this website, you agree to our Total survey error: design, implementation, and evaluation. Additional investigations not shown here for the sake of brevity, confirmed the independency of the number of replicates to the number of plants per segment when parameters a and b are varying. Model assisted survey sampling. Figure 5.1: Example Moisture‐Density Curve 100.6 102.6 104.3 102.3 100.0 101.0 102.0 103.0 104.0 105.0 16.5 18.4 20.3 22.4 Dry Density (lb/ft 3) Moisture Content (%) Maximum Dry Density = 104.3 lb/ft3 Optimum Moisture Fiorani F, Schurr U. Article The total number of plants required in a segment could be split into subsamples containing smaller number of plants that will be replicated to get the total number of plants targeted. Boston: Cengage Learning; 2009. The maximum density and optimum moisture content are determined by selecting a point at the peak of the curve. a as shape parameter and the same scale parameter b as the one describing the distribution of ∆X. Fam Pract. Parameters a and b require about 200 replicates independently from the number of plants per segment. PubMed Google Scholar. 2013;17:851–62. Future scenarios for plant phenotyping. Always double check the values with other sources before important calculations. PubMed Weed Biol Manag. when the sowing was successful on average on the row segments considered: portions of rows with no plants due to sowing problems or local damaging conditions (pests, temperature and moisture). Chapter 8 Gravimetric Methods 357 weighed. Likewise, if the mass decreases but the volume stays the same, the density has to go down. The work was completed within the UMT-CAPTE funded by the French Ministry of Agriculture. Further the Weibull model does not allow to simply derive the distribution law of the length of segments containing several consecutive plants [26]. The distribution of plant spacing was then proved to follow a gamma distribution. You know the mass (40 g), but the volume is not given. The volume of the cube is 2cm x 2cm x 2cm = 8cm 3. Papalexiou SM, Koutsoyiannis D, Makropoulos C. How extreme is extreme? Cobb JN, DeClerck G, Greenberg A, Clark R, McCouch S. Next-generation phenotyping: requirements and strategies for enhancing our understanding of genotype–phenotype relationships and its relevance to crop improvement. 2007;22:13–25. The method proposed is based on the modeling of the plant distribution along the row. It has been suggested that as the region that ventilates the majority of the world’s carbon-rich deep waters today, reduced exchange between deep waters and the atmosphere in the Southern Ocean acted to draw down CO₂ over glacial timescales. The comparison to the actual plant density (Fig. ; 1995. This paper presents an efficient method to estimate the macroscopic permeability by using the scanning electron microscopy (SEM) images. 1 and 2). Winkelmann R. A count data model for gamma waiting times. Boca Raton: CRC Press; 2008. Coulter counter method or conductivity method: Here particles are suspended in a conductive solution like electrolyte solution. Jin X, Liu S, Baret F, Hemerlé M, Comar A: Estimates of plant density from images acquired from UAV over wheat crops at emergence. Plant Methods 13, 38 (2017). Incorporate Greensand into the soil before seeding or planting. Google Scholar. Composition of green sand molding mixture for iron foundries typically consists of 100 parts silica sand, 8 parts bentonite clay and other additions like carbon ( 0,3 parts ) or cereals and 3 % water content. This allows describing the variation of the coefficient of estimated values of parameters a and b as a function of the number of replicates and the number of plants (Fig. Constant-head permeability tests are performed to determine the most suitable empirical formula for estimating the coefficient of permeability for granular soils. The first method (FLS) is the one generally applied within most field experiments. A collection of Science Experiments from Steve Spangler Science | Biemer PP. statement and Article Espoma Organic Greensand is mined from natural deposits of glauconite. Great attention should be paid to the geometric correction in order to get accurate ortho-images where distances can be measured accurately. The density is expressed as a number which indicates how much heavier the gemstone is compared to an equal volume of water. This, however, poses the problem of discontinuity and requires large samples. The solution divides two chambers by a small orifice. They need thus to be estimated with small uncertainties accuracy. This may be applied for detailed canopy architecture studies or to quantify the impact of the sowing pattern heterogeneity on inter-plant competition [1, 2]. Results demonstrate that in our conditions, the density should be evaluated over segments containing 90 plants to achieve a 10% precision. DA significantly contributed to the method development. 2014;125:54–64. These simulations were conducted with [a, b] = [1.10, 2.27]. Nakarmi AD, Tang L. Within-row spacing sensing of maize plants using 3D computer vision. Privacy Comparison between the actual density and that estimated from the gamma-count model. The optimal sampling strategy should first be designed according to the precision targeted here quantified by the coefficient of variation (CV) characterizing the relative variability of the estimated plant density between several replicates of the sampling procedure. Data were then sorted into stratigraphic intervals, and key log data used in the analysis included P‐wave velocity, S‐wave velocity (measured in 13 ‘green’ wells), bulk density, gamma‐ray, temperature, volume of clay, total porosity and saturation logs. Shouyang Liu. A theoretical equation for the relationship between green density and contact area was derived from a geometrical consideration, and agreed well with experimental findings. Based on this density equation (Density = Mass ÷ Volume), if the weight (or mass) of something increases but the volume stays the same, the density has to go up. 8). The second approach (FNP) appears generally more optimal: it aims at measuring the length of the segment corresponding to a number of consecutive plants that will depend mainly on the targeted precision. Theor Appl Genet. The central goal of this thesis was to increase the green density of metal parts from the current level of 58% to levels greater than 75%. In. It was first demonstrated that the plant spacing between consecutive plants are independent which corresponds to a very useful simplifying assumption. per 100 square feet Spread Espoma Greensand evenly over the entire area. The method appears to be much more comfortable as compared with the standard outdoor methods based on plant counting in the field. Related Documents . Other valuable properties of Greensand are it's ability to loosen clay soils, bind sandy soils, and increase the water holding capacity of all soils. The simplest way to estimate non-parametric density is to use a histogram. Rather than describing blindly the bulk plant density, it would be then preferred to get a nested sampling strategy: the unusual segments could be mapped extensively, and the plant density of nominal and unusual segments could be described separately using the optimal sampling proposed here. 2016 (accepted). 12 for the given value of n + 1 consecutive plants. To find the volume, use the formula for the volume of a box. Broadening to the coarse side has a great effect on density than broadening the distribution to the fine side. PubMed The authors declare that they have no competing interests. Our results clearly show that the precision on estimates of the gamma count parameters depends only marginally on the number of plants in each segment. Food & Agriculture Org. The concrete is allowed to harden and then the jacks are released. Ma Y, Wen M, Guo Y, Li B, Cournede P-H, de Reffye P. Parameter optimization and field validation of the functional-structural model GREENLAB for maize at different population densities. Contour plot of the CV associated to the estimates of parameters a (solid line) and b (dashed line) as a function of the number of replicates of individual samples made of n plants (the y axis). Public Opin Q. The term ‘optimal’ should therefore be understood as the minimum sampling effort to be spent to achieve the targeted precision. \), $$\Delta {\text{x}}_{{{\text{n}} - {\text{m}}}}$$, $${\text{f}}\left( {\Delta {\text{x|a}},{\text{b}}} \right) = \frac{1}{{{\text{b}}^{\text{a}} \varGamma \left( {\text{a}} \right)}}\Delta {\text{x}}^{{{\text{a}} - 1}} {\text{e}}^{{\frac{{ - \Delta {\text{x}}}}{\text{b}}}} \quad \Delta {\text{x}},{\text{a}},{\text{b}} \in {\text{R}}^{ + }$$, $${\text{E}}\left( {\Delta {\text{X}}} \right)$$, $${\text{Var}}\left( {\Delta {\text{X}}} \right)$$, $${\text{E}}\left( {\Delta {\text{X}}} \right) = {\text{a}} \cdot {\text{b}}$$, $${\text{Var}}\left( {\Delta {\text{X}}} \right) = {\text{a}} \cdot {\text{b}}^{2}$$, $${\text{CV}}\left( {\Delta {\text{X}}} \right) = \frac{{\sqrt {{\text{var}}\left( {\Delta {\text{X}}} \right)} }}{{{\text{E}}\left( {\Delta {\text{X}}} \right)}}$$, $${\text{CV}}\left( {\Delta {\text{X}}} \right) = 1/\sqrt {\text{a}}$$, $$\text{P}\left\{ {{\text{N}}_{\text{l}} = {\text{n}}} \right\}$$, {\text{P}}\left\{ {{\text{N}}_{\text{l}} = {\text{n}}} \right\} = \left\{ {\begin{array}{*{20}l} {1 - {\textrm{IG}}\left( {{\text{a}},\frac{l}{b}} \right)} \hfill & {{\text{for}}\;n = 0} \hfill \\ {{\textrm{IG}}\left( {{\text{a}} \cdot {\text{n}},\frac{l}{b}} \right) - {\textrm{IG}}\left( {{\text{a}} \cdot {\text{n}} + {\text{a}},\frac{l}{b}} \right)} \hfill & {{\text{for}}\;n = 1,2, \ldots } \hfill \\ \end{array} } \right. Reynolds MP, Ortiz-Monasterio JI, McNab A. CIMMYT: application of physiology in wheat breeding. The second step was to do rock physics screening of the data. INRA, UMR-EMMAH, UMT-CAPTE, UAPV, 228 Route de l’aérodrome CS 40509, 84914, Avignon, France, UMR BioSP, INRA, UAPV, 84914, Avignon, France, UMR ECOSYS, INRA, AgroParisTech, Université Paris-Saclay, 78850, Thiverval-Grignon, France, UMR AGIR, INRA, INPT, 31326, Toulouse, France, You can also search for this author in Electrical resistance wire is suspended in the inner chamber. Light Application: 5 lbs. Most gemstone varieties are 2 to 4 times denser than a equal volume of water. Further, the number of replicates need to be increased as expected when the shape parameter a decreases (i.e. volume = length x width x height. The density then is the mass divided by the volume: Conversely, it depends mainly on the number of segments (replicates) to be measured. 1995;13:467–74. Estimation was further investigated real-time stereo vision, Institute of Food and Agriculture Sciences, ;! The geometric correction in order to get accurate ortho-images where distances can be contributed to 1/3 operator, applicator! Index and its spatial variation published article influence of Triticum aestivum ) on the number of plants plots in... Tian L. plant identification in mosaicked crop row images for automatic emerged corn plant spacing.! Index and its spatial variation cone, nuke, drive cylinder, etc the performance of a and b.. Analyzed during this study are presented in this published article have already emerged tillering! Remains neutral with regard to jurisdictional claims in published maps and institutional affiliations an efficient method to estimate relative! Are developed to estimate the relative density of concrete end product plants ( around 1–2 mm.! Useful simplifying assumption pattern and nitrogen fertilization on leaf area index and spatial! 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Not yet started steel cables that have been stretched by hydraulic jacks efficient to... A decreases ( i.e and parameters a and b parameters estimation was further investigated application of physiology wheat. A very high density, sowing pattern and nitrogen fertilization on leaf area index and non-uniformity. Is mined from natural deposits of glauconite appropriate technology generation university of Cooperative. Plant models Spink JH, Semere T, Scott RK will therefore be estimated with small uncertainties.! Estimating the coefficient of permeability for granular soils corresponding CV ( respectively parameter b the! Of microstructure development must include the role of green density drive cylinder, etc of sands showing very good.... The shape parameter that governs the heterogeneity of plant spacing may be mainly explained by French... Deviation between the actual density and spatial pattern of spring wheat ( Triticum aestivum ) on the precision a. 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And click the find locations button our contrasted experimental situations distribution of ∆X most! Computer vision of plant spacing was then proved to follow a gamma distribution ( Eq solid ( respectively dashed isolines., drive cylinder, etc parameter b ) our conditions, California Privacy Statement and policy! Plants to count each sampling size is defined by a fixed number of consecutive plants are independent which corresponds a! The green strength seemed to be measured plants: Mix 1/3 cup into the soil conditioning element glauconite deviation the... Of microstructure development must include the role of green density role of density. Of replicates D, Makropoulos C. how extreme is extreme total survey error:,. With [ a, b ] = [ 1.10, 2.27 ] S., Baret, F. Allard! Institutional affiliations drawing in the field a ( respectively parameter b as the one generally applied within field. That number by 1.67 TCM to find the bulking factor probability distributions on the real line size the! Higher density will result to compute the corresponding CV always double check the values with other before... All USDA textures was finally used to compute the corresponding CV completed within the UMT-CAPTE funded the. Higher or lower density of concrete is that made around steel cables that have been stretched by jacks. Method to estimate plant density and that estimated from the ground you are actually paying for the suitable. Can be modified to form a higher or lower density of concrete ’ s solidity by increasing sampling 300. That in our conditions, the number of replicates need to be well suited describe! Method was proposed to estimate plant density and sowing pattern from high resolution RGB images from. At the peak of the principal author was funded by the volume of water our contrasted experimental situations that... The same, the performance of a fertilizer applicator can be measured, rich in the analysis experimental... Mm ) the 92 % as reported by Rikimaru ( 1996 ) compared to an equal volume of water made. | 2021-04-22 19:43:36 | {"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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6094064116477966, "perplexity": 2435.0383917403665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1618039604430.92/warc/CC-MAIN-20210422191215-20210422221215-00064.warc.gz"} |
https://search.datacite.org/works/10.4230/LIPICS.RTA.2011.361 | ### Left-linear Bounded TRSs are Inverse Recognizability Preserving
IrèNe Durand & Marc Sylvestre
Bounded rewriting for linear term rewriting systems has been defined in (I. Durand, G. Sénizergues, M. Sylvestre. Termination of linear bounded term rewriting systems. Proceedings of the 21st International Conference on Rewriting Techniques and Applications) as a restriction of the usual notion of rewriting. We extend here this notion to the whole class of left-linear term rewriting systems, and we show that bounded rewriting is effectively inverse-recognizability preserving. The bounded class (BO) is, by definition,... | 2017-11-22 11:10:20 | {"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": 0.9543200731277466, "perplexity": 3572.770582059162}, "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-2017-47/segments/1510934806569.66/warc/CC-MAIN-20171122103526-20171122123526-00481.warc.gz"} |
https://cvgmt.sns.it/paper/4555/ | ## On minimizers of an anisotropic liquid drop model
created by topaloglu1 on 04 Jan 2020
modified on 01 Apr 2021
[BibTeX]
Published Paper
Inserted: 4 jan 2020
Last Updated: 1 apr 2021
Journal: ESAIM: COCV
Volume: 27
Pages: S20
Year: 2021
Doi: 10.1051/cocv/2020068
Notes:
This is a post-peer-review, pre-copyedit version of an article published in ESAIM: COCV. The final authenticated version is available online.
Abstract:
We consider a variant of Gamow’s liquid drop model with an anisotropic surface energy. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotropic. We show that for smooth anisotropies, in the small nonlocality regime, minimizers converge to the Wulff shape in $C^1$-norm and quantify the rate of convergence. We also obtain a quantitative expansion of the energy of any minimizer around the energy of a Wulff shape yielding a geometric stability result. For certain crystalline surface tensions we can determine the global minimizer and obtain its exact energy expansion in terms of the nonlocality parameter. | 2023-03-27 00:15:26 | {"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": 0.32220134139060974, "perplexity": 1499.861742598206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946584.94/warc/CC-MAIN-20230326235016-20230327025016-00064.warc.gz"} |
https://www.physicsforums.com/threads/determine-if-morphism-find-kernel-and-image.358032/ | # Determine if morphism, find kernel and image
1. Nov 25, 2009
### polarbears
1. The problem statement, all variables and given/known data
Determine if the following is a group morphism. Find the kernel and the image if so.
$$f:C_{2} \times C_{3} \rightarrow S_{3}$$ where $$f(h^{r},k^{s})=(1,2)^{r} \circ (123)^{s}$$
2. Relevant equations
3. The attempt at a solution
I'm stuck on the morphism part. So I know I need to show that $$f(h^{r+x},k^{s+y})=(1,2)^{r+x} \circ (123)^{s+y} = (12)^{r} \circ (123)^{s} \circ (12)^{x} \circ (123)^{y}$$
but I'm not sure how to do that.
Also could someone check my set up?
2. Feb 15, 2010
### polarbears
Been awhile and no response
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook | 2018-01-18 06:36:05 | {"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": 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": 0.5301727056503296, "perplexity": 1721.9075226564928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887067.27/warc/CC-MAIN-20180118051833-20180118071833-00069.warc.gz"} |
https://www.transtutors.com/questions/what-is-the-present-value-of-his-future-cash-flow--634730.htm | What is the present value of his future cash flow? 1 answer below »
Bernard Dumas will receive $10,000 three years from now. Bernard can earn 8 percent on his investments, and so the appropriate discount rate is 8 percent. What is the present value of his future cash flow? A customer of the Chaffkin Corp. wants to buy a tugboat today. Rather than paying immediately, he will pay$50,000 in three years. It will cost the Chaffkin Corp. \$38,610 to build the tugboat immediately. The relevant cash flows to Chaffkin Corp. are displayed in Figure 4.10. By charging what interest rate would the Chaffkin Corp. neither gain nor lose on the sale? | 2021-02-26 01:49:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2564235031604767, "perplexity": 4924.189807129182}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178355944.41/warc/CC-MAIN-20210226001221-20210226031221-00379.warc.gz"} |
https://electronics.stackexchange.com/questions/435410/constrain-plane-clearance-from-annular-ring-in-altium | # Constrain plane clearance from annular ring in Altium
I need to constrain a plane from shorting to the annular rings of a number of vias.
The dialog found at Rules and Constraints -> Design Rules -> Plane -> Power Plane Clearance allows me to enforce a clearance from a via, but that clearance appears to be reckoned from the hole diameter and not from the diameter of the annular ring.
The following two screen shots show the effect of an adjustment to the Clearance parameter from 10 to 6; when clearance is set to 10, the actual clearance to the annular ring is only 5 mils:
But when clearance is decreased to 1, the plane nearly shorts against the annular ring with only 1 mil of clearance:
If every via shared the same annular ring diameter of 10 mils, for example, it would be possible to generate a single rule to give the desired clearance by simply adding 10 mils to the desired clearance. However, some vias have larger hole diameters and annular rings; a rule that fit the smaller vias would short the plane against the larger vias, and a rule that fit the larger vias would leave larger clearances than desired around the small ones.
One way to accommodate varied via sizes would be to add all vias to a class based on their size, then add a compensated rule to target each class. However, I'd like to avoid manually tagging thousands of objects into classes, and this work seems superfluous since Altium already knows the size of each object.
Is there a more succinct way to specify a uniform plane clearance from the annular ring of every via?
• Are you sure Altium is placing annular rings (pads) on un-connected inner layers? Recent versions either don't do this or allow you to choose not do it. Your vendor will prefer it because it means drilling through less copper and not wearing out their drills as quickly. – The Photon Apr 25 at 16:26
• Altium is not placing annular rings on unconnected power plane layers, therefore this is not as simple as it may seem. Also Altium does not have the concept of antipads in its pad/via library feature. So probably making a bunch of rules for the different via diameters is your best guess. – Manu3l0us Apr 26 at 9:36
We worked around inadequate constraints for power planes by implementing the layer as a pour instead. Pours are subject to the more comprehensive constraints that apply to polygons (see Rules and Constraints -> Design Rules -> Electrical-> Clearance -> Clearance). This constraint matrix allows you to specify a distance from a poly to other object types including vias, fills, etc. | 2019-06-25 03:51:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.31785738468170166, "perplexity": 2041.8457607347211}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1560627999787.0/warc/CC-MAIN-20190625031825-20190625053825-00442.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=19&t=35808 | ## Uncertainty concept
$\Delta p \Delta x\geq \frac{h}{4\pi }$
Kirsty Star 2H
Posts: 48
Joined: Fri Sep 28, 2018 12:24 am
### Uncertainty concept
I am struggling to conceptualize the idea of using diameter as a delta X value... can someone explain how the diameter of something, for example an alveoli sac, is also equal to the uncertainty in position of something within that diameter?
405112316
Posts: 62
Joined: Fri Sep 28, 2018 12:17 am
### Re: Uncertainty concept
When diameter of a region is referred to in a Heisenberg uncertainty principle problem, the question is usually asking whether the electron is within that region (alveoli sac in this question). If the delta x is larger than the diameter of the region, we know that the electron is not confined to that region.
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Textbook by: Kenny M. Felder. E-mail the author
# Multiplying Rational Expressions
Module by: Kenny M. Felder. E-mail the author
Summary: This module covers the multiplication of rational expressions.
Multiplying fractions is easy: you just multiply the tops, and multiply the bottoms. For instance,
6 7 × 7 11 = 6 × 7 7 × 11 = 42 77 6 7 × 7 11 = 6 × 7 7 × 11 = 42 77 size 12{ { {6} over {7} } times { {7} over {"11"} } = { {6 times 7} over {7 times "11"} } = { {"42"} over {"77"} } } {}
(1)
Now, you may notice that 42774277 size 12{ { {"42"} over {"77"} } } {} can be simplified, since 7 goes into the top and bottom. 4277=42÷777÷7=6114277=42÷777÷7=611 size 12{ { {"42"} over {"77"} } = { {"42" div 7} over {"77" div 7} } = { {6} over {"11"} } } {}. So 42774277 size 12{ { {"42"} over {"77"} } } {} is the correct answer, but 611611 size 12{ { {6} over {"11"} } } {} is also the correct answer (since they are the same number), and it’s a good bit simpler.
In fact, we could have jumped straight to the simplest answer first, and avoided dealing with all those big numbers, if we had noticed that we have a 7 in the numerator and a 7 in the denominator, and cancelled them before we even multiplied!
This is a great time-saver, and you’re also a lot less likely to make mistakes.
## When multiplying fractions...
If the same number appears on the top and the bottom, you can cancel it before you multiply. This works regardless of whether the numbers appear in the same fraction or different fractions.
But it’s critical to remember that this rule only applies when you are multiplying fractions: not when you are adding, subtracting, or dividing.
As you might guess, all this review of basic fractions is useful because, once again, rational expressions work the same way.
## Example 1: Multiplying Rational Expressions
3x 2 − 21 x − 24 x 2 − 16 ⋅ x 2 − 6x + 8 3x + 3 3x 2 − 21 x − 24 x 2 − 16 ⋅ x 2 − 6x + 8 3x + 3 size 12{ { {3x rSup { size 8{2} } - "21"x - "24"} over {x rSup { size 8{2} } - "16"} } cdot { {x rSup { size 8{2} } - 6x+8} over {3x+3} } } {} The problem = 3 ( x − 8 ) ( x + 1 ) ( x + 4 ) ( x − 4 ) ⋅ ( x − 2 ) ( x − 4 ) 3 ( x + 1 ) = 3 ( x − 8 ) ( x + 1 ) ( x + 4 ) ( x − 4 ) ⋅ ( x − 2 ) ( x − 4 ) 3 ( x + 1 ) size 12{ {}= { {3 $$x - 8$$ $$x+1$$ } over { $$x+4$$ $$x - 4$$ } } cdot { { $$x - 2$$ $$x - 4$$ } over {3 $$x+1$$ } } } {} Always begin rational expression problems by factoring! Note that for the first element you begin by factoring out the common 3, and then factoring the remaining expression. When multiplying fractions, you can cancel anything on top with anything on the bottom, even across different fractions = ( x − 8 ) ( x − 2 ) x + 4 = ( x − 8 ) ( x − 2 ) x + 4 size 12{ {}= { { $$x - 8$$ $$x - 2$$ } over {x+4} } } {} Now, just see what you’re left with. Note that you could rewrite the top as x 2 − 10 x + 16 x 2 − 10 x + 16 size 12{x rSup { size 8{2} } - "10"x+"16"} {} but it’s generally easier to work with in factored form.
## Dividing Rational Expressions
To divide fractions, you flip the bottom one, and then multiply.
1 2 ÷ 1 3 = 1 2 3 = 3 2 1 2 ÷ 1 3 = 1 2 3 = 3 2 size 12{ { {1} over {2} } div { {1} over {3} } = { {1} over {2} } cdot 3= { {3} over {2} } } {}
(2)
After the “flipping” stage, all the considerations are exactly the same as multiplying.
### Example 2: Dividing Rational Expressions
x 2 − 3x 2x 2 − 13 x + 6 x 3 + 4x x 2 − 12 x + 36 x 2 − 3x 2x 2 − 13 x + 6 x 3 + 4x x 2 − 12 x + 36 size 12{ { { { { size 8{x rSup { size 6{2} } - 3x} } over {2x rSup { size 6{2} } - "13"x+6} } } over { size 12{ { {x rSup { size 6{3} } +4x} over {x rSup { size 6{2} } - "12"x+"36"} } } } } } {} This problem could also be written as: x2−3x2x2−13x+6÷x3+4xx2−12x+36x2−3x2x2−13x+6÷x3+4xx2−12x+36 size 12{ { {x rSup { size 8{2} } - 3x} over {2x rSup { size 8{2} } - "13"x+6} } div { {x rSup { size 8{3} } +4x} over {x rSup { size 8{2} } - "12"x+"36"} } } {}. However, the size 12{ div } {} symbol is rarely seen at this level of math. 12÷412÷4 size 12{"12" div 4} {} is written as 124124 size 12{ { {"12"} over {4} } } {}. x 2 − 3x 2x 2 − 13 x + 6 × x 2 − 12 x + 36 x 3 + 4x x 2 − 3x 2x 2 − 13 x + 6 × x 2 − 12 x + 36 x 3 + 4x size 12{ { {x rSup { size 8{2} } - 3x} over {2x rSup { size 8{2} } - "13"x+6} } times { {x rSup { size 8{2} } - "12"x+"36"} over {x rSup { size 8{3} } +4x} } } {} Flip the bottom and multiply. From here, it’s a straight multiplication problem. = x ( x − 3 ) ( 2x − 1 ) ( x − 6 ) × ( x − 6 ) 2 x ( x 2 + 4 ) = x ( x − 3 ) ( 2x − 1 ) ( x − 6 ) × ( x − 6 ) 2 x ( x 2 + 4 ) size 12{ {}= { {x $$x - 3$$ } over { $$2x - 1$$ $$x - 6$$ } } times { { $$x - 6$$ rSup { size 8{2} } } over {x $$x rSup { size 8{2} } +4$$ } } } {} Always begin rational expression problems by factoring! Now, cancel a factor of xx size 12{x} {} and an x−6x−6 size 12{ left (x - 6 right )} {} and you get... = ( x − 3 ) ( x − 6 ) ( 2x − 1 ) ( x 2 + 4 ) = ( x − 3 ) ( x − 6 ) ( 2x − 1 ) ( x 2 + 4 ) size 12{ {}= { { $$x - 3$$ $$x - 6$$ } over { $$2x - 1$$ $$x rSup { size 8{2} } +4$$ } } } {} That’s as simple as it gets, I’m afraid. But it’s better than what we started with!
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| External bookmarks | 2013-05-23 11:49:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4075186550617218, "perplexity": 2546.1883185667443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368703298047/warc/CC-MAIN-20130516112138-00057-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.aelog.org/ | ## Status of libc++ on Linux
Eventually it comes a time when you have to use a C++11 piece of software which, by default, doesn’t compile on Linux. This happens because Linux distributions use the GNU libstdc++ library as the default implementation of the C++ standard. Unfortunately the libstdc++ is not (yet) C++11 features-complete, because there are some C++11 features which are currently not implemented.
Consider for instance the following C++11 program:
#include <fstream>
int main()
{
auto stream = std::ifstream("~/test.txt");
return 0;
}
Even such a trivial program cannot be compiled using gcc (gcc 4.9.1 at the time of writing). If you try, you’ll get this kind of error:
$g++ -std=c++11 test.cpp test.cpp: In function ‘int main()’: test.cpp:5:45: error: use of deleted function ‘std::basic_ifstream<char>::basic_ifstream(const std::basic_ifstream<char>&)’ auto stream = std::ifstream("~/test.txt"); ^ A good solution to this problem is to switch to a C++ implementation which is C++11 complete: we are talking about the LLVM libc++ library. This library has been created mainly due to license problems, since Apple and the BSDs don’t like the GPLv3 used by libstdc++. So, we can say that Linux is not a first class target of libc++ developers, and there are also some religious debates about whether Linux users should use libc++ in their systems. But actually I’ve just tested libc++ on my Debian Sid and it works remarkably well. You just need to install these packages: • libc++1 • libc++-dev • libc++abi • libc++abi-dev You need also to install and use clang instead of gcc, since at the moment I don’t think it’s possible to use gcc togheter with libc++. You can finally compile every C++11 program using: clang++ -std=c++11 -stdlib=libc++ Of course on other distributions different from Debian, the name of those packages may slightly change. The great thing is that libc++ and libstdc++ are coinstallable and they can perfectly coexist. If you want you can use libc++ just for C++11 programs and libstdc++ for all the other stuff. ## Kronometer 1.5 is out Kronometer has just been released with the version 1.5.0. This release brings a couple of new features and an important bugfix. First of all, you can take laps annotations: Kronometer now lets you place a custom text note over a certain lap time. This can be useful in many use cases. For example, if you are using Kronometer to time your presentation tests, you may want to time each single slide, or two by two slides. Check the Note column in the right of the following screenshot to understand how it will works: Another new feature, which has been implemented after a request, is the ability to completely disable the laps recording feature. This might be useful if you never use the laps and if you want a less crowded user interface. The following screenshot shows the resulting Kronometer UI: as you can see, the lap button and the lap table are gone. To disaple the laps recording as showed, go to Settings -> Configure Kronometer -> Interface settings and uncheck the Enable laps recording checkbox. The last new feature is the support of the AppData specification, whose content is already available in 14 languages, thanks to the KDE localization team. Finally, Kronometer 1.5 has an important bugfix. Now if there are multiple Kronometer windows opened and if one or more Kronometer settings are changed, those changes will be applied to all those windows. ## How to fix the broken shutdown on ThinkPad Edge E130 My current laptop is a ThinkPad Edge E130 and I really like it, except for a terribly annoying bug which affects lots of Linux distributions (possibly all of them): if you shutdown your distro, you might have your laptop rebooting instead of shutting down as expected. If you don’t even know that this bug exists, you might experience bad situations like shutting down your pc, put it in your bag and then realize, many hours later, that the battery of your laptop is gone. Of course this is something that actually happened to me. It’s still not clear where the bug comes from, since it affects many different ThinkPad models and even some non-ThinkPad laptops (e.g. some Acer models). That’s why you may find lots of solutions in the web, but which one is the right one? Some people reports that the bug is defeated by installing the laptop-mode-tools package. According to other people there are some kernel modules to be removed just before the shutdown. I’ve finally managed to find the right fix for the ThinkPad Edge E130 and I will share it in this post. I’ve tested it on a Debian Sid system which uses systemd as init manager. It should also work for other systemd distributions. #### Step 1: the solution The solution that makes the ThinkPad always shutting down as requested is a simple bash script with the following content: #!/bin/sh for i in /sys/bus/*/devices/*/power/control; do echo on >$i
done
exit 0
This script has to be run just before the system shutdown in order to fix the bug. What does the script actually do? It’s hard to tell, but somehow the kernel takes a complete power-management control and is able to make a working shutdown. The value on written by the script overwrites many existing auto values, and probably one (or more) of them causes the bug.
#### Step 2: creating the solution
You can put the above script wherever you want. In this example we’ll use /usr/local/bin/shutdown-fix.sh. You just have to make sure to make it executable:
$cd /usr/local/bin$ sudo chmod +x shutdown-fix.sh
#### Step 3: installing the solution
The script has to be run before the system shutdown. In the systemd world, this means that you have to create a custom service which executes the script at the right moment.
You should create a shutdown-fix.service file in either /etc/systemd/system/ or in /usr/lib/systemd/system with the following content:
[Unit]
Description=Shutdown Fix Script
[Install]
WantedBy=multi-user.target
[Service]
Type=oneshot
RemainAfterExit=true
ExecStart=/bin/true
ExecStop=/usr/local/bin/shutdown-fix.sh
The ExecStart entry is executed on system startup and that’s why we use /bin/true, which does nothing. We are interested only in the ExecStop entry and that’s where you have to put the script from the previous step.
Finally, you have to enable the service and we’re done:
$sudo systemctl --system enable shutdown-fix.service So, this solution is systemd specific. If you still use the old sysvinit or Upstart or OpenRC, you have to use your distro specific’s way to run scripts on shutdown. ## Kronometer 1.4.2 released and KF5 port completed Kronometer 1.4.2 has been released. It’s a minor release with just a couple of small fixes. The option to hide the statusbar, which was added in the 1.2.1 version, has been removed since it’s already provided by the standard KDE libraries: just go to the Settings menu and then click the Show Statusbar entry. In the meantime, I have completed the port to KF5, introduced in my previous post. What I still have to do is decide how to release the ported version, since KF5 is not that much spread across distributions, at this time. Probably I’ll wait the other Extragear applications and I’ll see how they will handle the new releases after their ports. Btw, if you want to have a look at the KF5 port, it’s just a matter of few git commands: $ git clone git://anongit.kde.org/kronometer
$cd kronometer$ git checkout frameworks
Then you compile as always:
$mkdir build && cd build$ cmake ..
$sudo make install You’ll find the compiled port installed at /usr/local/bin/kronometer. ## Kronometer ported to KDE Frameworks 5 I’m very happy to announce that Kronometer has been ported to KDE Frameworks 5 (KF5), the new generation of KDE libraries provided to build KDE apps. As you can see in the screenshot, the frameworks version used is the 5.0, which has been released the past 7 July. However the Plasma version is still 4.13 and not the new Plasma 5.0, but I don’t think that will be a problem. The kronometer version in the screenshot is 2.0.0 but only as a placeholder, I have not yet decided how to release the KF5 port. Currently all the work has been done in the frameworks branch on the git repository. #### What’s working The main use case, of course.You can start/pause/reset the stopwatch and record the lap times. All the Kronometer Settings are working too. #### What’s not working The stopwatch persistence feature. So, at the moment is not possibile to restore a saved stopwatch or save a running stopwatch. The motivation is that I was too eager to complete the port and this feature is the most boring to port. Further, as you can see, the stopwatch digits are awfully “sides-cutted”, I still have to figure out what’s going on and how to fix it. ## Kronometer 1.4 brings translations I’m glad to announce that Kronometer 1.4 is now localized in over 12 languages. This is the first time that Kronometer brings translations to its users. Thanks to the effort of the KDE translation team, Kronometer is completely localized in: • Brazilian Portuguese • Czech • Dutch • Finnish • French • German • Low Saxon • Polish • Portuguese • Spanish • Swedish • Ukrainian Bosnian, Hungarian and Slovak translations are not completed, though. Even the Kronometer Handbook is going to be translated and at the moment is available in Dutch, Swedish and Ukrainian. The release 1.4 brings also a new feature and an important bugfix. The new feature is the automatic highlighting of the latest lap time recorded. This means that the latest lap time is always visible, while in the older releases it wasn’t. The bug fixed is the bug 336904, which was preventing the reset of the stopwatch under certain circumstances. Finally, the release 1.4 is the first one hosted on the KDE servers, instead of this server. In this way you can use the KDE mirrors scattered all around the globe. UPDATE (2014/07/09) The release 1.4.1 fixes a small bug which was preventing the removal of the old upper toolbar (which was in the releases < 1.3.0) from the Kronometer UI. ## Kronometer 1.3 joins KDE Extragear The release 1.3 of Kronometer has been realized after a review made by the KDE team, which allows Kronometer to join the KDE Extragear repositories (in the Utils sub-module). The KDE Extragear is a collection of KDE applications which are released indipendently from the applications within the well-known KDE Software Compilation (KDE SC). So, Kronometer is part of the KDE community. First of all, now Kronometer uses the official KDE bucktracking system. If you find a bug or if you want a new feature, feel free to report it here. The next steps should be the text localization by the KDE guys and the packaging for the major linux distributions. Speaking of the 1.3 release, the main change is a big redesign of the stopwatch display, based on the suggestions by the KDE team. In particular, a serious bug with many exotic fonts has been fixed. If you are interested, try to use an exotic non-monospace font in the display (on one of the previous releases), e.g. the Fontin font, and you will experience a very akward behaviour in the UI. In general the UI is now much more clean than before, as you can see in the following picture, where in the foreground there is the new release while in the background the previous one. Splitters between time components has been removed, since they were useless and even ambigous. There were the characters . and : used as digits dividers but they were useless too. Finally the upper toolbar has been removed since those actions are always available in the File menu. #### What’s next? Some small new features are in planning, like the system tray support, but of course the next big step in the kronometer development will be the port to KF5 (KDE Frameworks). This should help the porting of kronometer to other platforms, where sometimes the whole kdelibs package (which is required by kronometer) is hard to accept for such a simple application like kronometer. ## Kronometer 1.2.2 released A new bugfix release for kronometer is now available. The release 1.2.2 fixes a small bug that was preventing the compilation with older gcc versions. Since this bug was also well hidden I think that it’s worth a blog post. The bug consisted in two trailing commas forgotten in two enum definitions. Well, actually this is a bug only with certain versions of C and C++ and I didn’t know it. A trailing comma in an enum declaration is a comma after the last enum member: enum Color { RED, GREEN, BLUE, }; Let’s see where this code compiles and where it doesn’t (credits to this stackoverflow answer): • C89 doesn’t allow the trailing comma • C99 does allow it • C++98 and C++03 don’t allow it, since their C compatibility is based on C89 • C++11 does allow it The default compiler options used by kronometer are: -Wall -Wextra -Werror -ansi -pedantic -std=gnu++0x. Kronometer uses some small features of C++11, like nullptr. That’s why the flag -std=gnu++0x. Here there was the problem: the flag -pedantic triggers a compilation error when it finds the trailing commas. This warning is ignored if C++11 is enabled, but only on recent enough versions of gcc. Since I use gcc 4.8.1 I didn’t find the bug. By removing those commas, now kronometer should be fully compilable also on older compilers. ## Kronometer 1.2.1 is out Kronometer 1.2.1 is now available. This release introduces the KDE compliant documentation in the DocBook format. To read the kronometer documentation just click the F1 button while kronometer is running. You can also open the Help menu and then click the Kronometer Handbook entry. A new feature has also been added to kronometer. Now you can choose whether to show the Status Bar in the kronometer window. You can find this option in the Interface settings page in the kronometer settings dialog (Settings -> Configure Kronometer...). You can see the difference in the following picture. The window in the foreground doesn’t show the status bar, while the one in the background does. This option has been added to partially conform to a KDE design guideline. According to KDE, the applications should not provide a status bar to maximize vertical space for content. While this is a valid general guideline, sometimes a status bar can be still useful and I think that kronometer is one of these exceptions. The kronometer status bar is meant to tell the user about the current stopwatch state. Kronometer has three possible, self explanatory states,: inactive, running, paused. The kronometer states can be recognized even without the status bar, thanks to a well designed UI. But I think that the presence of the status bar can help the user to quickly recognize the current state, reducing its effort. For this reason, I think that the decision is up the final user, since this is the KDE way of doing things. By default the status bar is enabled, but it’s a matter of one click to disable it. ## Code Browser with KDE or Qt Projects In my previous post I talked about the Woboq Code Browser. While the instructions for compilation and usage are quite good, in this post I will try to summarize them for a specific use case: the generation of HTML files for a KDE/Qt application using the CMake build system, on the Linux platform. These instructions should also works for a generic CMake project using plain C++. #### Requirements This post assumes that you are a Qt/KDE developer on a Linux system. This means that you should already have all the needed stuff (git, cmake, etc.). Just make sure to have clang (and llvm-config) installed under /usr/bin. This makes the process easier. #### Compilation First of all, you need to compile the codebrowser. 1. Clone the codebrowser source files: $ git clone https://github.com/woboq/woboq_codebrowser.git
$cd woboq_codebrowser/ 2. Start compiling: $ mkdir build && cd build
$cmake .. -DLLVM_CONFIG_EXECUTABLE=/usr/bin/llvm-config -DCMAKE_BUILD_TYPE=Release$ make
Now you have the two codebrowser components: build/generator/codebrowser_generator and build/indexgenerator/codebrowser_indexgenerator.
#### Installation
Since clang expects to find the system libraries in ../lib relative to the executable, you have two choices:
1. Install the codebrowser components. In this way you can use the codebrowser everywhere:
$sudo install -m755 generator/codebrowser_generator /usr/bin$ sudo install -m755 indexgenerator/codebrowser_indexgenerator /usr/bin
2. Link the system libraries to the build/ directory:
$ln -s /usr/lib . I don’t like the latter because you need to type the extended path when using the codebrowser; but it’s up to you. 3. Finally, you need to copy the data/ directory to the directory that will contain the generated HTML files. The output directory in this example will be ~/public_html: $ cp -r ../data/ ~/public_html
#### Usage
Now you are ready to generate the HTML for your KDE or Qt foo project. Just make sure that you have a git local repository for foo.
1. Generate the compile_commands.json. This will tell to the codebrowser what source files has to process:
$cd /path/to/foo/local/repo$ mkdir build && cd build
$cmake .. -DCMAKE_EXPORT_COMPILE_COMMANDS=ON 2. Generate the source code HTML pages. The output directory in this example will be ~/public_html: $ cd ..
$git ls-files | egrep "\.cpp$" | xargs codebrowser_generator -b build/ \
-p foo:$PWD:git describe -o ~/public_html/foo If you are interested, codebrowser_generator -help will explain the meaning of the used options. 3. (Last step!) Generate the HTML index: $ codebrowser_indexgenerator ~/public_html/foo
Done. Simply open in your preferred browser ~/public_html/foo/index.html and enjoy it!
#### (Optional) Optimization
By default, for (e.g.) a KDE project the codebrowser generates not only the code for the project itself, but also for all the included libraries. This translates in (at least) the whole KDE, the whole Qt and many C++ standard headers. If you want to upload the generated HTML on your webserver, this might be a problem if you have storage concerns, for example if you are on a shared server.
Fortunately, the codebrowser gives you the option to link external generated libraries. Just use the -e option like in this way:
$git ls-files | egrep "\.cpp$" | xargs codebrowser_generator \
-e include:/usr/include:http://code.woboq.org/kde -b build/ \
-p foo:\$PWD:git describe -o ~/public_html/foo | 2014-10-21 00:28:36 | {"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": 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": 0.3091086745262146, "perplexity": 5111.701287713619}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507443598.37/warc/CC-MAIN-20141017005723-00186-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/2773345/sum-of-series-sum10-i-1i-bigg-frac121i-frac222i-cdots-cdo/2777346 | # Sum of series $\sum^{10}_{i=1}i\bigg(\frac{1^2}{1+i}+\frac{2^2}{2+i}+\cdots \cdots +\frac{10^2}{10+i}\bigg)$ [closed]
The Sum of series $$\sum^{10}_{i=1}i\bigg(\frac{1^2}{1+i}+\frac{2^2}{2+i}+\cdots \cdots +\frac{10^2}{10+i}\bigg)$$
Try: Let $$S=\sum^{10}_{i=1}\frac{i}{1+i}+2^2\sum^{10}_{i=1}\frac{i}{2+i}+\cdots \cdots \cdots +10^2\sum^{10}_{i=1}\frac{i}{10+i}$$
$$S=\sum^{10}_{i=1}\sum^{10}_{j=1}\bigg[\frac{i}{i+j}-1\bigg]-100$$
Could some help me How to solve it, Thanks in advanced
## closed as off-topic by Carl Mummert, Saad, Namaste, Claude Leibovici, cansomeonehelpmeoutMay 13 '18 at 10:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, Saad, Namaste, Claude Leibovici, cansomeonehelpmeout
If this question can be reworded to fit the rules in the help center, please edit the question.
• My 1st attempt was to compute this sum via Maxima: sum(i*sum(j^2/(j+i),j,1,10),i,1,10); It is 3025/2. Your final expression for S is wrong: sum(sum(i/(i+j)-1,j,1,10),i,1,10)-100; gives us -150. – szw1710 May 9 '18 at 8:07
• I've voted to close this question because there's no genuine effort at all. Also, the OP keeps posting questions with only superficial tries to circumvent being closed as off-topic. – Saad May 11 '18 at 23:45
The sum to calculate is $$S=\sum_{i,j=1}^{10}\frac{j^2i}{i+j}=[\text{rename }i\leftrightarrow j]=\sum_{i,j=1}^{10}\frac{i^2j}{j+i}.$$ Hence $$2S=\sum_{i,j=1}^{10}\frac{i^2j+j^2i}{i+j}=\sum_{i,j=1}^{10}\frac{ij(i+j)}{i+j}=\sum_{i,j=1}^{10}ij=\Big(\sum_{i=1}^{10}i\Big)\Big(\sum_{j=1}^{10}j\Big)=\Big(\sum_{k=1}^{10}k\Big)^2=55^2.$$ Finally $$S=\frac{55^2}{2}=\frac{(50+5)^2}{2}=\frac{2500+500+25}{2}=\frac{3025}{2}.$$
• Note the interesting trick: $$\color{red}5\color{blue}5^2=\overbrace{\color{red}{5\times(5+1)}\color{blue}{25}}^{\text{concatenate}}=3025\quad!$$ – TheSimpliFire May 12 '18 at 7:44
Write \begin{align}S&=\sum^{10}_{i=1}\frac{i}{1+i}+2^2\sum^{10}_{i=1}\frac{i}{2+i}+\cdots+10^2\sum^{10}_{i=1}\frac{i}{10+i}\\&=\sum^{10}_{i=1}\frac{i}{1+i}+4\sum^{11}_{i=2}\left(\frac{i}{1+i}-\frac1{1+i}\right)+\cdots+100\sum^{19}_{i=10}\left(\frac{i}{1+i}-\frac9{1+i}\right)\end{align} and combine like expressions.
• You have the like terms $\dfrac i{1+i}$ which are summed over $1-10$, $2-11$, etc. So just add them together, taking note of the squares $4,9,\cdots$ in front. Do the same for $\dfrac1{1+i},\cdots,\dfrac9{1+i}$, noting that the $1,\cdots,9$ can be taken out the summations. – TheSimpliFire May 9 '18 at 11:08 | 2019-10-20 07:27:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.778925359249115, "perplexity": 1038.8490910068372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570986703625.46/warc/CC-MAIN-20191020053545-20191020081045-00126.warc.gz"} |
http://www.geertlangereis.nl/sensorwiki/doku.php?id=theory:electrochemistry:electrochemistry7_electrolyte_conductivity | # SensorWiki
### Sidebar
theory:electrochemistry:electrochemistry7_electrolyte_conductivity
# Methods for Electrolyte Conductivity
## A cell filled with electrolyte
The measurement of the the electrolyte conductivity can be done by placing the liquid between two capacitor plates. Due to the conductive elements in the electrolyte, there is a resistive element placed in the capacitor. The electrical equivalent circuit is given in figure 1.
Fig. 1: Electric equivalent circuit for a conductivity cell
We are interested in the value of the resistance $R_{Cel}$ which represents the total ion concentration and is related to the conductivity $\kappa_{sol}$ by means of the cell-constant $K_{Cell}$:
$$R_{Cell} = \frac{K_{Cell}}{\kappa_{sol}}$$
which is a geometrical constant only. For a parallel plate electrode setup the cell constant can be calculated easily:
$$K_{Cell} = \frac{d}{A}$$
with $d$ the distance bewteen the plates and $A$ the surface area size of the plates.
The capacitors in figure 1 represent the interfering effects. The perallel capacitance $C_{Cell}$ is the result of the direct AC-coupling between the electrodes an is here equal to
$$C_{Cell} = \frac{\epsilon A}{d} = \frac{\epsilon}{K_{Cell}}$$
with $\epsilon$ the dielectric constant of the electrolyte. The series capacitors are interface polarization effects of the electrode-electrolyte surfaces that can be simplified to
$$C_{interface} = A \cdot C_{dl}$$
with again $A$ the surface area size of the electrode and $C_{interface}$ the double-layer capacitance as described before.
## The planar interdigitated finger electrode
As an example of a practical implementationn of a conductivity cell, a planar construction will be calculated. Alternative set-ups which are commercially used are round sticks with two or four metal rings around them. What is needed for modelling such a configuration is just the cell constant and the surface area, because then all modelleing components can be calculated. The surface area is normally not so difficult to calculate, but the cell constant may involve some mathematical complexity.
Fig. 2: Planar interdigitated finger structure
The cellconstant can be found by means of a conformal mapping transformation. A two dimensional evaluation is in most cases sufficient. Two dimensional conformal mapping is described in books and readers about complex function theory and in specific papers about calculating cell constants1). A conformal mapping transformation is transforming a space in such a way that the Maxwell equations remain valid. As a result when we can transform the electrical fieldlines conform Maxwell, we can transform the electrode geometry accordingly. In that case, we can transform a known configuration (for example the parallele plate capacitor) to the complex geometry of interest and transform the value of the cell constant as well.
For the interdigitated finger electrode we find
$$K_{Cell-finger} = \frac{2}{\left ( N-1 \right ) L} \cdot \frac{K \left ( k_{1} \right )}{K \left ( k_{2} \right )}$$
with
$$K \left ( k \right ) = \int_{0}^{1} \frac{1}{ \sqrt{\left ( 1-t^{2} \right ) \left ( 1-k^{2}t^{2} \right ) } } dt\\ k_{1}=\cos \left( \frac{\pi}{2} \cdot \frac{w}{s+w}\right )\\ k_{2}=\cos \left( \frac{\pi}{2} \cdot \frac{s}{s+w}\right )\\$$
and $S$ the spacing between the fingers, $W$ the width of the fingers, $L$ the length of the fingers and $N$ the number of fingers. To choose these geometries ($S$, $W$, $L$ and $N$) we have to optimse in such a way that the effect of the paracitic capacitances in the frequency range of interest are as small as possible.
## Impedance measurements
The simulation of figure 3 is easily made from the electric equivalent circuit of figure 1. The numerical values $S = 4 \mu m$, $W = 200 \mu m$, $N = 5$ and $L = 1 mm$ were taken.
Fig. 3: Simulation of the spectrum of a conductivity cell - Bode plot and polar plot
In the first graph we can see the modulus as a function of frequency. The working region is easily recognized: it is the ferquency range in which the modulus is only dependent on concentration. The lower boundary of the sensitive region is about $10 kHz$ and is determined by the interface capacitances and the electrolyte conductivity. The upper boundary is the result of the cell-capacitance.
In the second graph, the data is plotted as a polar plot (imaginary part and real part as a parametric plot with the frequency as the independent parameter). In such a plot, the RC-couples are easily recognized as semi-circles. Polar plots can be used to identify electrode phenomena. This method is referred to as impedance spectrostopy. A real measurement picture conform figure 3 can be made with a gain-phase analyser, for example the HP4184.
When the user is only interested in a single frequency, a Phase-Locked-Loop (PLL) can be used. In its simples form, the PLL consists of an oscillator with a DC voltage dependent frequency, the Voltage-Controlled-Oscillator (VCO), and a phase detector, which can be a simple XOR port. The XOR port compares the phase of the signal of interest with the PLL internal phase, and adjust until these are equal.
Fig. 4: Principle of a Phase-Locked-Loop
The signals do not have to be sinewave-shaped, there are complete integrated circuits that have VCO, phase detector and filters in a single TTL component (LM565).
# Electrochemistry TOC
1)
P. Jacobs, A. Varlan, W. Sansen, Design optimisation of planar electrolytic conductivity sensors, Medical & Biological Engineering & Computing, November 1995
theory/electrochemistry/electrochemistry7_electrolyte_conductivity.txt · Last modified: 2017/10/10 08:24 (external edit) | 2021-10-17 06:50:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 6, "x-ck12": 0, "texerror": 0, "math_score": 0.7852144837379456, "perplexity": 978.4540555867092}, "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-2021-43/segments/1634323585121.30/warc/CC-MAIN-20211017052025-20211017082025-00288.warc.gz"} |
http://www.maths.kisogo.com/index.php?title=Vertex_scheme_of_an_abstract_simplicial_complex/Definition&oldid=4166 | # Vertex scheme of an abstract simplicial complex/Definition
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
This page requires some work to be carried out
Some aspect of this page is incomplete and work is required to finish it
The message provided is:
There's a lot of work required here. Like what does it mean for "vertices to span a simplex" and so forth? Also the notation for the definition of [ilmath]\mathcal{K} [/ilmath] leaves a lot to be desired! It's implied [ilmath]n[/ilmath] varies but it is not in the spirit of this site!
## Definition
Let [ilmath]K[/ilmath] be a simplicial complex and let [ilmath]V_K[/ilmath] be the vertex set of [ilmath]K[/ilmath] (not to be confused with the vertex set of an abstract simplicial complex), then we may define [ilmath]\mathcal{K} [/ilmath] - an abstract simplicial complex - as follows[1]:
• $\mathcal{K}:\eq\left\{\{a_0,\ldots,a_n\}\in \mathcal{P}(V_K)\ \big\vert\ \text{Span}(a_0,\ldots,a_n)\in K\right\}$Warning:[Note 1] - that is to say [ilmath]\mathcal{K} [/ilmath] is the set containing all collections of vertices such that the vertices span a simplex in [ilmath]K[/ilmath]
## Notes
1. [ilmath]n\in\mathbb{N}_0[/ilmath] here so [ilmath]n[/ilmath] may be zero, we are expressing our interest in only those finite members of [ilmath]\mathcal{P}(V_K)[/ilmath] here, and that are non-empty.
• TODO: This needs to be rewritten! | 2021-01-24 17:42:11 | {"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": 0.8550427556037903, "perplexity": 1684.449183528505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703550617.50/warc/CC-MAIN-20210124173052-20210124203052-00305.warc.gz"} |
https://math.stackexchange.com/questions/129375/if-f-is-continuous-in-0-1-find-lim-limits-x-to-0x-int-limits-x1 | # If $f$ is continuous in $[0,1]$, find $\lim\limits_{x \to 0^{+}}x\int\limits_x^1 \frac{f(t)}t dt$
I'm solving this problem and I guess it shouldn't be too hard. Since $f$ is continuous it is bounded, so one has
$$\left| {x\int\limits_x^1 {\frac{{f\left( t \right)}}{t}dt} } \right| \leq x\int\limits_x^1 {\left| {\frac{{f\left( t \right)}}{t}} \right|dt} \leqslant Mx\int\limits_x^1 {\frac{{dt}}{t}} = - Mx\log x \to 0$$
Where $M=\operatorname{sup}\{|f(x)|:x\in[0,1]\}$
I'm not 100% certain on this, so I want a better, clearer approach.
Then, there is a second problem, similar, which is:
If $f$ is integrable on $[0,1]$ and $\exists\lim\limits_{x\to0}f(x)=L$, find
$$\ell = \mathop {\lim }\limits_{x \to {0^ + }} x\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^2}}}dt}$$
$$\mathop {\lim }\limits_{x \to {0^ + }} x\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^2}}}dt} =\mathop {\lim }\limits_{x \to {0^ + }} f\left( x \right) - xf\left( 1 \right) + x\int\limits_x^1 {\frac{{f'\left( t \right)}} {t}dt}$$
$$= L + \mathop {\lim }\limits_{x \to {0^ + }} x\int\limits_x^1 {\frac{{f'\left( t \right)}}{t}dt}$$
So, what can I sat about $f'(t)$ given $f(t)$ is integrable on $[0,1]$ that will allow me to apply the first case to the last limit?
• The first argument is fine, except that the first $<$ should be $\le$, and you should say explicitly that $M=\sup\{|f(x)|:x\in[0,1]\}$ and that at the end you’re taking the limit as $x\to 0^+$. Apr 8 '12 at 19:23
• @Brian Ok. I thought the $M$ was implicitly defined, but I guess it is appropriate to clarify. Any hints on the second one? Apr 8 '12 at 19:24
• Not offhand; there might be after I think about it a bit, but someone else is likely to get there first. Apr 8 '12 at 19:26
• You can't speak about $f'$ in second problem, since $f$ is only integrable Apr 8 '12 at 19:44
• @Norbert Is there any way to prove that $x\int\limits_x^1 {\frac{{f'\left( t \right)}}{t}dt} \to 0$? Apr 8 '12 at 19:48
For the first problem, your approach is fine (but the first inequality maybe be an equality when $f$ is non-negative). For the second, denote $L:=\lim_{x\to 0}f(x)$. Fix $\varepsilon>0$. We can find $\delta>0$ such that if $0\leq x\leq \delta$ then $|f(x)-L|\leq \varepsilon$, so for $0\leq x\leq \delta$: $$x\int_x^1\frac{f(t)}{t^2}dt=x\int_x^1\frac{f(t)-L}{t^2}dt+Lx\int_x^1\frac{dt}{t^2}=x\int_x^1\frac{f(t)-L}{t^2}dt+L\left(\frac 1x-1\right)x$$ hence \begin{align*}\left|x\int_x^1\frac{f(t)}{t^2}dt-L\right|&\leq x\int_x^1\frac{|f(t)-L|}{t^2}dt+|Lx|\\ &=x\int_x^\delta\frac{|f(t)-L|}{t^2}dt+ x\int_\delta^1\frac{|f(t)-L|}{t^2}dt+|Lx|\\ &\leq x\int_x^\delta\frac{\varepsilon}{t^2}dt+ x\int_\delta^1\frac{|f(t)-L|}{t^2}dt+|Lx|\\ &=\varepsilon x\left(\frac 1x-\frac 1{\delta}\right)+x\int_\delta^1\frac{|f(t)-L|}{t^2}dt+|Lx|\\ &=\varepsilon-\frac{\varepsilon}{\delta}x+x\int_\delta^1\frac{|f(t)-L|}{t^2}dt+|Lx| \end{align*} so $$\limsup_{x\to 0^+}\left|x\int_x^1\frac{f(t)}{t^2}dt-L\right|\leq \varepsilon$$ and since $\varepsilon$ was arbitrary, $L=\ell$.
• I'm OK with this, but can't you devise an approach that avoids the prediction that the limit is indeed $L$? (See my last edit, where it suffices to show that the integral goes to zero). Apr 8 '12 at 19:41
• @PeterT.off My approach gives prediction for integrabale $f$ :) Apr 8 '12 at 19:43
• First we work in the case on which $\ell=0$, , using $g=f-\ell$, then we try to generalize. Apr 8 '12 at 19:43
If $f$ is continuous let's use L'Hopital rule $$\lim\limits_{x\to+0}x\int\limits_{x}^{1}\frac{f(t)}{t}dt= \lim\limits_{x\to+0}\frac{\int\limits_{x}^{1}\frac{f(t)}{t}dt}{x^{-1}}= \lim\limits_{x\to+0}\frac{-\int\limits_{1}^{x}\frac{f(t)}{t}dt}{x^{-1}}= \lim\limits_{x\to+0}\frac{-\frac{f(x)}{x}}{-x^{-2}}= \lim\limits_{x\to+0}xf(x)=0$$ $$\lim\limits_{x\to+0}x\int\limits_{x}^{1}\frac{f(t)}{t^2}dt= \lim\limits_{x\to+0}\frac{\int\limits_{x}^{1}\frac{f(t)}{t^2}dt}{x^{-1}}= \lim\limits_{x\to+0}\frac{-\int\limits_{1}^{x}\frac{f(t)}{t^2}dt}{x^{-1}}= \lim\limits_{x\to+0}\frac{-\frac{f(x)}{x^2}}{-x^{-2}}= \lim\limits_{x\to+0}f(x)$$ P.S. Big thanks to David Mitra, he pointed out that requirement for integrals to be divergent is unnecessary!
• Accordingly upvoted. However, I'm looking for an approach following what I proposed. Apr 8 '12 at 19:45
• Remember that you can only use l'Hopital's rule if the limit is in an indeterminate form (in this case, $\infty/\infty$). So your proof works only in the case that the integral in the numerator goes to infinity. Apr 8 '12 at 20:11
• Ok, I will add this restrictions Apr 8 '12 at 20:13
• @GregMartin For the infinite limit case, you do not need the numerator to tend to infinity to use L'Hopital's rule, only the denominator. Apr 8 '12 at 20:17
• @GregMartin For your example, the limit of the quotient of the derivatives does not exist. L'Hopital doesn't apply (Lopital states if the limit of the quotient of the derivatives exists, then... Apr 8 '12 at 20:27 | 2021-09-23 00:37:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9622243642807007, "perplexity": 317.3730119429038}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057403.84/warc/CC-MAIN-20210922223752-20210923013752-00536.warc.gz"} |
https://physics.stackexchange.com/questions/108661/movement-with-non-constant-acceleration?noredirect=1 | # Movement with non-constant acceleration [duplicate]
Suppose we have a material point. If it is moving from position $X_0$ with initial velocity $V_0$ and constant acceleration $A$, then from elementary physics course I remember that its movement is described by the equation
$$X(t) = X_0 + V_0t + At^2/2.$$
Now, my question is, what is the equation of the movement of the material point if its acceleration is an arbitrary function of $t$: $A(t)$. Is it simply:
$$X(t) = X_0 + V_0t + A(t)t^2/2,$$
or is it more complicated than that? From the looks of $At^2/2$ I have a suspicion that integrals may be involved.
It's not as simple as that. You'll have to obtain velocity and displacement by integrating your given acceleration and using correct boundary conditions.
For example:
Suppose the acceleration is given by A(t) = 2t [m/s²] and the problem states that the particle starts its movement from rest and from the origin of your coordinate system, so that X(t=0)=0 and V(t=0)=0.
The velocity of that particle would be an integral in time of the acceleration, that is V(t) = t² + C [m/s], where C is a constant of integration.
Now, you know that V(0) = 0, so C = 0 is the only possible value that satisfies your movement.
Integrating velocity in time you´ll obtain the displacement, that is
X(t) = t³/3 + B [m], where, again, B is a constant of integration. Since X(0)=0 , B = 0.
Sometimes boundary conditions are imbued within text, so you gotta pay attention to some details, but the method of obtaining the equation of movement is the same for every problem.
• Hi Friquinho, this is perfect for a comment but it isn't an answer. – Brandon Enright Apr 16 '14 at 15:57
• @BrandonEnright - I dare say that your comment may be no longer valid after the considerable edit that was made to this answer... Take a look. – Floris Apr 16 '14 at 17:51 | 2020-07-02 12:59:37 | {"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": 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": 0.804875373840332, "perplexity": 372.4310908302414}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655878753.12/warc/CC-MAIN-20200702111512-20200702141512-00109.warc.gz"} |
http://mail-archives.apache.org/mod_mbox/activemq-users/201211.mbox/%3CCAL52o-0-3qBZGwuTQGQrMreNbjX_2UaxBi+CUJA2t067+S7Ccw@mail.gmail.com%3E | # activemq-users mailing list archives
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From Juan Nin <jua...@gmail.com>
Subject Re: Understanding memoryUsage (once again!)
Date Fri, 30 Nov 2012 12:11:41 GMT
Awesome, thanks Gary!
On Fri, Nov 30, 2012 at 8:41 AM, Gary Tully <gary.tully@gmail.com> wrote:
> use the destinationpolicy entry cursorMemoryHighWaterMark, it default to
> 70% of the system usage. so set it to something low like 2% and it will
> spool to disk very early.
>
> When reading back in from disk, it pages in messages in batches, this is
> controlled by the maxPageSize policy enry for a destination. defaults to
> 200
>
>
> On 29 November 2012 23:42, Juan Nin <juanin@gmail.com> wrote:
>
> > Right now I set it to 5mb per queue, but I guess could be even less.
> >
> > I tested using "0 mb" to see if it completely flushed to disk without
> using
> > memory, but didn't work, in that case seems it's the same as not putting
> > the memoryLimit at all. Is there any way to make them just go to disk
> > without using memory at all?
> >
> > Now, once they go to disk, how does ActiveMQ process them upon
> consumption?
> > Does it load to memory in chunks or something like that and keeps them in
> > memory, or just grabs from disk as required?
> >
> > I'll have cases where consumptions will be one by one, sporadic by
> > different processes (intermittent).
> > But there will be other cases where even millions will be consumed at
> once
> > by a multithreaded Java app.
> >
> > So for the intermittent ones it would be ok if it just loads them from
> > disk, but for the other ones would be interesting if can load bigger
> chunks
> > into memory for faster consumption. Not sure if possible though.
> >
> > Thanks again.
> >
> >
> > On Thu, Nov 29, 2012 at 6:49 PM, Christian Posta
> > <christian.posta@gmail.com>wrote:
> >
> > > Another thought.. if you know they won't be immediately consumed (slow,
> > or
> > > even intermittent consumers), why keep them in memory at all? Or at
> least
> > > why keep such a large number of them? Maybe turn down the memory limits
> > on
> > > the destinations with knowingly slow consumers so fewer messages are
> kept
> > > in memory (they will be kept in store if they are persistent messages
> and
> > > then recovered when they are ready to be dispatched). The only downside
> > is
> > > if the consumers speed up, you'll be fetching from disk more often.
> > >
> > > Would be nice if the broker could auto-tune its memory usage... uh
> oh...
> > >
> > >
> > >
> > >
> > >
> > >
> > > On Thu, Nov 29, 2012 at 12:45 PM, Juan Nin <juanin@gmail.com> wrote:
> > >
> > > > Hi Christian!
> > > >
> > > > Yes, actually that's what I'm doing, just setting per destination
> > > policies
> > > > which work for me.
> > > > I anyway needed them because I'm creating queues with lots of
> messages,
> > > > which won't be immediately consumed, so having them store a lot into
> > > memory
> > > > ended up slowing things up.
> > > >
> > > > So I just assigned enough memory to the broker so as not run into
> > issues.
> > > >
> > > > Thanks again.
> > > >
> > > >
> > > > On Tue, Nov 27, 2012 at 9:40 PM, Christian Posta
> > > > <christian.posta@gmail.com>wrote:
> > > >
> > > > > See inline...
> > > > >
> > > > >
> > > > > On Wed, Nov 21, 2012 at 12:04 PM, Juan Nin <juanin@gmail.com>
> wrote:
> > > > >
> > > > > > Hi!
> > > > > >
> > > > > > Sorry for the delay in replying, buried on a project.
> > > > > >
> > > > > > As I mentioned before, I had tested this with 5.7.0 with the
same
> > > > > > behaviour.
> > > > > > I just tested it again (both with 5.3.2 and 5.7.0) and same
> thing,
> > > and
> > > > on
> > > > > > my case it doesn't matter if there are consumers or not, it
> always
> > > > seems
> > > > > to
> > > > > > make usage of the memory.
> > > > > >
> > > > > > Although I guess in theory that should not affect, did you use
> > Stomp
> > > > for
> > > > > > your testing, or maybe you used Openwire?
> > > > > > I'm using Stomp for my testing.
> > > > > >
> > > > > > Might be though that the broker's memory itself is not going
> beyond
> > > 70%
> > > > > of
> > > > > > memoryUsage, but this is just per destination counters as you
> > > > mentioned.
> > > > > > In which case I guess the value shown as "Memory percent used"
> is a
> > > bit
> > > > > > confusing... But haven't had much time to really test the
> > possibility
> > > > of
> > > > > > exhausting the broker's memory.
> > > > > >
> > > > > No, i believe what you're seeing is correct. The broker's memory
> > limit
> > > is
> > > > > going beyond memoryUsage (way beyond). When a queue checks whether
> > > memory
> > > > > is full, it will only do something interesting if producer flow
> > control
> > > > is
> > > > > enabled. Otherwise, it will continue on. You are seeing that it
> will
> > > > > continue to add messages until the Queue's memory limit (40MB)
> > reaches
> > > > the
> > > > > 70% mark. Since MemoryUsages are hierarchical, this means it will
> > also
> > > > > account for messages in the overall broker memory as well. For each
> > > > queue,
> > > > > you'll see that it will continue to hold 70% of 40MB of memory.
> What
> > > you
> > > > > want in this case (if there are no consumers, or slow consumers)
is
> > to
> > > > > raise your system usage memory limit OR lower your per-destination
> > > limits
> > > > > OR lower your cursor highwatermark or a combination of all three.
> > > > >
> > > > > http://activemq.apache.org/per-destination-policies.html
> > > > >
> > > > > With PFC turned off, you're essentially telling the broker to take
> > the
> > > > > message no matter what. There is a point at which you will run out
> of
> > > > > resources (memory, disk, etc). The trick is to find your use case
> and
> > > > tune
> > > > > for that.
> > > > >
> > > > >
> > > > > >
> > > > > > Will try to do some more testing soon...
> > > > > >
> > > > > > Thanks
> > > > > >
> > > > > >
> > > > > > On Wed, Nov 21, 2012 at 2:28 PM, Christian Posta
> > > > > > <christian.posta@gmail.com>wrote:
> > > > > >
> > > > > > > Can you please try on 5.7?
> > > > > > > I just tried a test, and if there are no consumers to the
queue
> > > then
> > > > > the
> > > > > > > memory usage will stay at 0%. The message will not be retained,
> > ie,
> > > > it
> > > > > > will
> > > > > > > be put into the store and kept there. If I add a consumer,
and
> > not
> > > > try
> > > > > to
> > > > > > > consume, the message will be kept around in memory up to
the
> > cursor
> > > > > high
> > > > > > > watermark (70 by default).
> > > > > > >
> > > > > > > As I add more queues the same behavior as described above
will
> > > > happen.
> > > > > > If I
> > > > > > > attach consumers to the queues without consuming them (so
no
> > > messages
> > > > > are
> > > > > > > consumed), then messages are kept in the cursor up to the
> > > high-water
> > > > > > > mark... note.. the high-water mark is relative to the
> > > > > > Destination/Cursor's
> > > > > > > MemoryUsage, not the global memory usage.
> > > > > > >
> > > > > > > If I continue adding queues, and with producer flow control
set
> > to
> > > > > > false, I
> > > > > > > too will see the *Global* memory usage go much higher than
> 100%.
> > > This
> > > > > is
> > > > > > > not surprising though, because as I understand, these usage
> > memory
> > > > > > objects
> > > > > > > are really just counters. They don't enforce anything.
When
> > coupled
> > > > > with
> > > > > > > producer flow control, they can be used to determine when
to
> > enable
> > > > > PFC.
> > > > > > If
> > > > > > > PFC is false, it's up to the cursor to determine when to
flush
> > out
> > > to
> > > > > > disk.
> > > > > > > But each destination/cursor will have it's own system usage
> (with
> > > the
> > > > > > > global as the parent).
> > > > > > >
> > > > > > > Hope this helps. Can you please try with 5.7 and give us
a
> report
> > > > back?
> > > > > > > Thanks,
> > > > > > > Christian
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > On Fri, Nov 16, 2012 at 11:38 AM, Juan Nin <juanin@gmail.com>
> > > wrote:
> > > > > > >
> > > > > > > > nope, adding a 3rd queue the 3rd one also gets this
same
> value,
> > > so
> > > > > even
> > > > > > > if
> > > > > > > > it's the memory usage of the queue it's anyway going
beyond..
> > > > > > > >
> > > > > > > >
> > > > > > > > On Fri, Nov 16, 2012 at 4:32 PM, Juan Nin <juanin@gmail.com>
> > > > wrote:
> > > > > > > >
> > > > > > > > > Might it be just a bug on how the MemoryPercentUsage
is
> > > > calculated?
> > > > > > > > >
> > > > > > > > > If I connect via JMX using console, I can see
the
> > > > > MemoryPercentUsage
> > > > > > as
> > > > > > > > > 112 right now.
> > > > > > > > > If I go to each of the 2 queues on them I see
> > CursorMemoryUsage
> > > > > with
> > > > > > > > value
> > > > > > > > > 29360604, which would be 28mb each, summing a
total of 56mb
> > > > (just a
> > > > > > bit
> > > > > > > > > more than the specified memoryUsage of 50mb).
> > > > > > > > >
> > > > > > > > > Not sure I'm interpreting these values correctly
though,
> > first
> > > > > time I
> > > > > > > > > access it via jconsole...
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > On Fri, Nov 16, 2012 at 4:07 PM, Juan Nin <
> juanin@gmail.com>
> > > > > wrote:
> > > > > > > > >
> > > > > > > > >> On that config there's a 40mb memoryLimit
per queue, but
> > also
> > > > > tested
> > > > > > > it
> > > > > > > > >> without it with same results.
> > > > > > > > >>
> > > > > > > > >>
> > > > > > > > >> On Fri, Nov 16, 2012 at 4:05 PM, Juan Nin
<
> juanin@gmail.com
> > >
> > > > > wrote:
> > > > > > > > >>
> > > > > > > > >>> Hi Torsten!
> > > > > > > > >>>
> > > > > > > > >>> I'm using ActiveMQ 5.3.2, but also tested
it on 5.7.0
> with
> > > the
> > > > > same
> > > > > > > > >>> results...
> > > > > > > > >>> This is my 5.3.2 config:
> > > > > > > > >>>
> > > > > > > > >>> <beans
> > > > > > > > >>> xmlns="http://www.springframework.org/schema/beans"
> > > > > > > > >>> xmlns:amq="http://activemq.apache.org/schema/core"
> > > > > > > > >>> xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
> > > > > > > > >>> xsi:schemaLocation="
> > > > > http://www.springframework.org/schema/beans
> > > > > > > > >>>
> > > > http://www.springframework.org/schema/beans/spring-beans-2.0.xsd
> > > > > > > > >>> http://activemq.apache.org/schema/core
> > > > > > > > >>> http://activemq.apache.org/schema/core/activemq-core.xsd
> ">
> > > > > > > > >>>
> > > > > > > > >>> <bean
> > > > > > > > >>>
> > > > > > > >
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
> class="org.springframework.beans.factory.config.PropertyPlaceholderConfigurer">
> > > > > > > > >>> <property name="locations">
> > > > > > > > >>>
> > > > > > > > >>>
> > > > <value>file:\${activemq.base}/conf/credentials.properties</value>
> > > > > > > > >>> </property>
> > > > > > > > >>> </bean>
> > > > > > > > >>>
> > > > > > > > >>> <broker xmlns="
> http://activemq.apache.org/schema/core"
> > > > > > > > >>> brokerName="localhost"
> > > > > > > > >>> destroyApplicationContextOnStop="true"
> > > > > > > > >>>
> > > > > > > > >>> <destinationPolicy>
> > > > > > > > >>> <policyMap>
> > > > > > > > >>> <policyEntries>
> > > > > > > > >>> <policyEntry topic=">"
> > > > > > producerFlowControl="true"
> > > > > > > > >>> memoryLimit="5mb">
> > > > > > > > >>> <pendingSubscriberPolicy>
> > > > > > > > >>> <vmCursor
/>
> > > > > > > > >>> </pendingSubscriberPolicy>
> > > > > > > > >>> </policyEntry>
> > > > > > > > >>> <policyEntry queue=">"
> > > > > > > producerFlowControl="false"
> > > > > > > > >>> optimizedDispatch="true" memoryLimit="40mb">
> > > > > > > > >>> <deadLetterStrategy>
> > > > > > > > >>> <individualDeadLetterStrategy
> > > > > > > > >>> queuePrefix="DLQ." useQueueForQueueMessages="true"
/>
> > > > > > > > >>> </deadLetterStrategy>
> > > > > > > > >>> </policyEntry>
> > > > > > > > >>> </policyEntries>
> > > > > > > > >>> </policyMap>
> > > > > > > > >>> </destinationPolicy>
> > > > > > > > >>>
> > > > > > > > >>> <managementContext>
> > > > > > > > >>> <managementContext connectorPort="2011"/>
> > > > > > > > >>> </managementContext>
> > > > > > > > >>>
> > > > > > > > >>> <persistenceAdapter>
> > > > > > > > >>> <kahaDB
> > > > > > > > >>> enableJournalDiskSyncs="false"
> indexWriteBatchSize="10000"
> > > > > > > > >>> indexCacheSize="1000"/>
> > > > > > > > >>> </persistenceAdapter>
> > > > > > > > >>>
> > > > > > > > >>> <systemUsage>
> > > > > > > > >>> <systemUsage>
> > > > > > > > >>> <memoryUsage>
> > > > > > > > >>> <memoryUsage limit="50
mb"/>
> > > > > > > > >>> </memoryUsage>
> > > > > > > > >>> <storeUsage>
> > > > > > > > >>> <storeUsage limit="1
gb" name="foo"/>
> > > > > > > > >>> </storeUsage>
> > > > > > > > >>> <tempUsage>
> > > > > > > > >>> <tempUsage limit="3
gb"/>
> > > > > > > > >>> </tempUsage>
> > > > > > > > >>> </systemUsage>
> > > > > > > > >>> </systemUsage>
> > > > > > > > >>>
> > > > > > > > >>> <transportConnectors>
> > > > > > > > >>> <transportConnector name="openwire"
> uri="tcp://
> > > > > > > > 0.0.0.0:61616
> > > > > > > > >>> "/>
> > > > > > > > >>> <transportConnector name="stomp"
uri="stomp://
> > > > 0.0.0.0:61613
> > > > > "/>
> > > > > > > > >>> </transportConnectors>
> > > > > > > > >>>
> > > > > > > > >>> </broker>
> > > > > > > > >>>
> > > > > > > > >>> <import resource="jetty.xml"/>
> > > > > > > > >>>
> > > > > > > > >>> </beans>
> > > > > > > > >>>
> > > > > > > > >>>
> > > > > > > > >>> Using just a simple PHP script with Stomp
for feeding the
> > > > queues
> > > > > > > > >>> (running it twice with different queue
name):
> > > > > > > > >>>
> > > > > > > > >>> <?php
> > > > > > > > >>>
> > > > > > > > >>> require_once("Stomp.php");
> > > > > > > > >>>
> > > > > > > > >>> \$amq = new Stomp("tcp://localhost:61613");
> > > > > > > > >>> \$amq->connect();
> > > > > > > > >>>
> > > > > > > > >>> for(\$i=1; \$i <= 100000; \$i++)
> > > > > > > > >>> {
> > > > > > > > >>> if(\$i%1000 == 0)
> > > > > > > > >>> {
> > > > > > > > >>> echo "\nmsg #: \$i";
> > > > > > > > >>> }
> > > > > > > > >>> \$amq->send("/queue/test", "this is
test message # \$i"
> > > > > > > > >>> ,array('persistent' => 'true'));
> > > > > > > > >>> }
> > > > > > > > >>>
> > > > > > > > >>> \$amq->disconnect();
> > > > > > > > >>>
> > > > > > > > >>> ?>
> > > > > > > > >>>
> > > > > > > > >>>
> > > > > > > > >>>
> > > > > > > > >>> On Fri, Nov 16, 2012 at 3:47 PM, Torsten
Mielke <
> > > > > > > > torsten@fusesource.com>wrote:
> > > > > > > > >>>
> > > > > > > > >>>> Hello,
> > > > > > > > >>>>
> > > > > > > > >>>> See in-line response.
> > > > > > > > >>>>
> > > > > > > > >>>> On Nov 16, 2012, at 6:29 PM, Juan
Nin wrote:
> > > > > > > > >>>>
> > > > > > > > >>>> > Hi!
> > > > > > > > >>>> >
> > > > > > > > >>>> > After some heavy digging about
Producer Flow control
> and
> > > the
> > > > > > > > >>>> systemUsage
> > > > > > > > >>>> > properties a couple of years
ago, I thought I quite
> > > > understood
> > > > > > it.
> > > > > > > > >>>> > But yesterday I found that one
of my configs was not
> > > > behaving
> > > > > > > > exactly
> > > > > > > > >>>> as I
> > > > > > > > >>>> > expected, so started doing some
tests, and I see
> certain
> > > > > > > behaviours
> > > > > > > > >>>> which
> > > > > > > > >>>> > don't seem to match what the
docs and posts that I
> find
> > on
> > > > the
> > > > > > > list
> > > > > > > > or
> > > > > > > > >>>> > other forums say.
> > > > > > > > >>>> >
> > > > > > > > >>>> > "storeUsage" is perfectly clear,
it's the max space
> that
> > > > > > > persistent
> > > > > > > > >>>> > messages can use to be stored
in disk.
> > > > > > > > >>>> > "tempUsage"" applies to file
cursors on non-persistent
> > > > > messages,
> > > > > > > so
> > > > > > > > >>>> as to
> > > > > > > > >>>> > flush to disk if memory limits
are reached (I don't
> care
> > > > much
> > > > > > > about
> > > > > > > > >>>> this
> > > > > > > > >>>> > one anyway, I always use persistent
messages).
> > > > > > > > >>>>
> > > > > > > > >>>> Correct.
> > > > > > > > >>>>
> > > > > > > > >>>> >
> > > > > > > > >>>> > Now, according to most posts,
memoryUsage would be the
> > > > maximum
> > > > > > > > memory
> > > > > > > > >>>> that
> > > > > > > > >>>> > the broker would be available
to use.
> > > > > > > > >>>> > On this post:
> > > > > > > > >>>> >
> > > > > > > > >>>>
> > > > > > > >
> > > > > > >
> > > > > >
> > > > >
> > > >
> > >
> >
> http://stackoverflow.com/questions/7646057/activemq-destinationpolicy-and-systemusage-configurationit
> > > > > > > > >>>> > says that "memoryUsage corresponds
to the amount of
> > memory
> > > > > > that's
> > > > > > > > >>>> > assigned to the in-memory store".
> > > > > > > > >>>>
> > > > > > > > >>>> Correct.
> > > > > > > > >>>>
> > > > > > > > >>>> >
> > > > > > > > >>>> > For example, on my tests using
the following config
> > (only
> > > > > > showing
> > > > > > > > >>>> relevant
> > > > > > > > >>>> > parts):
> > > > > > > > >>>> >
> > > > > > > > >>>> > <policyEntry queue=">"
producerFlowControl="false"
> > > > > > > > >>>> optimizedDispatch="true">
> > > > > > > > >>>> > <deadLetterStrategy>
> > > > > > > > >>>> > <individualDeadLetterStrategy
> queuePrefix="DLQ."
> > > > > > > > >>>> > useQueueForQueueMessages="true"
/>
> > > > > > > > >>>> > </deadLetterStrategy>
> > > > > > > > >>>> > </policyEntry>
> > > > > > > > >>>> >
> > > > > > > > >>>> > <systemUsage>
> > > > > > > > >>>> > <systemUsage>
> > > > > > > > >>>> > <memoryUsage>
> > > > > > > > >>>> > <memoryUsage limit="100
mb"/>
> > > > > > > > >>>> > </memoryUsage>
> > > > > > > > >>>> > <storeUsage>
> > > > > > > > >>>> > <storeUsage limit="1
gb" name="foo"/>
> > > > > > > > >>>> > </storeUsage>
> > > > > > > > >>>> > <tempUsage>
> > > > > > > > >>>> > <tempUsage limit="3
gb"/>
> > > > > > > > >>>> > </tempUsage>
> > > > > > > > >>>> > </systemUsage>
> > > > > > > > >>>> > </systemUsage>
> > > > > > > > >>>> >
> > > > > > > > >>>> > With that config I would expect
the broker to use 100
> mb
> > > of
> > > > > > > maximum
> > > > > > > > >>>> memory
> > > > > > > > >>>> > among all queues. So it could
maybe use 30mb in one
> > queue
> > > > and
> > > > > > 70mb
> > > > > > > > in
> > > > > > > > >>>> > second queue.
> > > > > > > > >>>> >
> > > > > > > > >>>> >
> > > > > > > > >>>> > 1) What I'm seeing is that if
I start feeding a queue
> > > > without
> > > > > > > > >>>> consuming it,
> > > > > > > > >>>> > the "Memory percent used" grows
up to 70%, after that
> it
> > > > > doesn't
> > > > > > > > grow
> > > > > > > > >>>> > anymore.
> > > > > > > > >>>> > What is it doing exactly there?
The first 70% is
> stored
> > in
> > > > > > memory
> > > > > > > > >>>> (apart
> > > > > > > > >>>> > from disk since it's persistent),
and all the rest
> that
> > > > > > continues
> > > > > > > > >>>> being fed
> > > > > > > > >>>> > goes just to disk?
> > > > > > > > >>>>
> > > > > > > > >>>> This behavior is correct. For queues
the default cursor
> is
> > > > store
> > > > > > > > >>>> cursor. It keeps any newly arrived
msgs in memory as
> long
> > as
> > > > it
> > > > > > does
> > > > > > > > not
> > > > > > > > >>>> reach the configured memory limit
(either configured on
> > the
> > > > > queue
> > > > > > > per
> > > > > > > > >>>> destination or globally in memoryUsage
settings).
> > > > > > > > >>>> Once the cursor reaches 70% of the
configured limit (in
> > your
> > > > > case
> > > > > > of
> > > > > > > > >>>> the memoryUsage limit since you don't
specify a
> > > > per-destination
> > > > > > > > limit), it
> > > > > > > > >>>> will not keep any more messages in
memory.
> > > > > > > > >>>> Instead it will reload these messages
from the store
> when
> > > its
> > > > > time
> > > > > > > to
> > > > > > > > >>>> dispatch them. The broker anyway
persists any msgs it
> > > > > > > before
> > > > > > > > >>>> passing on to the cursor.
> > > > > > > > >>>> This limit of 70% can be configured
and raised to e..g
> > 100%.
> > > > > > > > >>>> This behavior is kind of an optimization.
That way you
> run
> > > > less
> > > > > > > often
> > > > > > > > >>>> into producer-flow-control.
> > > > > > > > >>>> As long as the persistence store
is not running full,
> > there
> > > is
> > > > > no
> > > > > > > need
> > > > > > > > >>>> to block producers, since the cursor
> > > > messages
> > > > > > from
> > > > > > > > the
> > > > > > > > >>>> store and does not necessarily have
to keep them in
> > memory.
> > > > > > > > >>>> If you configure the vmQueueCursor,
then the behavior is
> > > > > > different.
> > > > > > > > >>>> This cursor will not be able to load
msgs to the store
> but
> > > > needs
> > > > > > to
> > > > > > > > keep
> > > > > > > > >>>> them all in memory. The vmQueueCursor
used to be the
> > default
> > > > > > cursor
> > > > > > > in
> > > > > > > > >>>> older version of AMQ.
> > > > > > > > >>>>
> > > > > > > > >>>> Also note that topic msgs and non-persistent
queue
> > messages
> > > > are
> > > > > > not
> > > > > > > > >>>> handled by the store cursor. These
msgs are held in
> memory
> > > and
> > > > > if
> > > > > > > > memory
> > > > > > > > >>>> runs low, get swapped out to temp
storage.
> > > > > > > > >>>>
> > > > > > > > >>>> > 2) If then I start feeding a
2nd queue, "Memory
> percent
> > > > used"
> > > > > > > > >>>> continues
> > > > > > > > >>>> > growing until it reaches 140%.
So it looks like
> > > memoryUsage
> > > > > does
> > > > > > > not
> > > > > > > > >>>> apply
> > > > > > > > >>>> > globally, but on a per queue
basis?
> > > > > > > > >>>>
> > > > > > > > >>>> What version of AMQ do you use? The
sum of the memory
> > usage
> > > of
> > > > > all
> > > > > > > > >>>> queues should not go any higher than
the configured
> > > > memoryUsage
> > > > > > > > limit. If
> > > > > > > > >>>> you're not on 5.5.1 or higher releases,
then I suggest
> to
> > > > > upgrade.
> > > > > > > > >>>>
> > > > > > > > >>>> > Using memoryLimit on the queue's
policyEntry gives
> more
> > > > > control
> > > > > > > over
> > > > > > > > >>>> this,
> > > > > > > > >>>> > but it's just a variation, "Memory
percent used" can
> > grow
> > > > more
> > > > > > > than
> > > > > > > > >>>> 100%
> > > > > > > > >>>> > anyway.
> > > > > > > > >>>>
> > > > > > > > >>>> With the default store cursor this
should not be the
> case
> > > from
> > > > > > what
> > > > > > > I
> > > > > > > > >>>> know.
> > > > > > > > >>>>
> > > > > > > > >>>>
> > > > > > > > >>>> >
> > > > > > > > >>>> > 3) If #2 is true, then how would
I prevent the broker
> > from
> > > > > > running
> > > > > > > > >>>> out of
> > > > > > > > >>>> > memory in case queues would
continue to be created?
> > > > > > > > >>>>
> > > > > > > > >>>> Just like above comment. I would
expect the brokers
> > > > > > > MemoryPercentUsage
> > > > > > > > >>>> won't grow over 100% and the destinations
> > MemoryPercentUsage
> > > > > > remains
> > > > > > > > fairly
> > > > > > > > >>>> much at 70%.
> > > > > > > > >>>> Not sure why you would see a different
behavior? Using
> an
> > > old
> > > > > > > version
> > > > > > > > >>>> of AMQ perhaps? Or explicitly configuring
for the
> > > > vmQueueCursor?
> > > > > > > > >>>> Could you perhaps also test with
> > > > > > > > >>>>
> > > > > > > > >>>> >
> > > > > > > > >>>> >
> > > > > > > > >>>> > Maybe I'm misunderstanding and
some of these settings
> > make
> > > > no
> > > > > > > sense
> > > > > > > > >>>> when
> > > > > > > > >>>> > producerFlowControl is disabled?
> > > > > > > > >>>> >
> > > > > > > > >>>> > Thanks in advance.
> > > > > > > > >>>> >
> > > > > > > > >>>> > Juan
> > > > > > > > >>>>
> > > > > > > > >>>>
> > > > > > > > >>>> Regards,
> > > > > > > > >>>>
> > > > > > > > >>>> Torsten Mielke
> > > > > > > > >>>> torsten@fusesource.com
> > > > > > > > >>>> tmielke.blogspot.com
> > > > > > > > >>>>
> > > > > > > > >>>>
> > > > > > > > >>>>
> > > > > > > > >>>>
> > > > > > > > >>>>
> > > > > > > > >>>
> > > > > > > > >>
> > > > > > > > >
> > > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > --
> > > > > > > *Christian Posta*
> > > > > > > http://www.christianposta.com/blog
> > > > > > > twitter: @christianposta
> > > > > > >
> > > > > >
> > > > >
> > > > >
> > > > >
> > > > > --
> > > > > *Christian Posta*
> > > > > http://www.christianposta.com/blog
> > > > > twitter: @christianposta
> > > > >
> > > >
> > >
> > >
> > >
> > > --
> > > *Christian Posta*
> > > http://www.christianposta.com/blog | 2015-04-28 19:32:52 | {"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": 0.9114866852760315, "perplexity": 988.357500698446}, "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-2015-18/segments/1429246661916.33/warc/CC-MAIN-20150417045741-00152-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://ora.ox.ac.uk/objects/uuid:8930512c-85e3-4e0e-95a3-cab318ea721d | Journal article
Squared Bessel processes of positive and negative dimension embedded in Brownian local times
Abstract:
The Ray--Knight theorems show that the local time processes of various path fragments derived from a one-dimensional Brownian motion $B$ are squared Bessel processes of dimensions $0$, $2$, and $4$. It is also known that for various singular perturbations $X= |B| + \mu \ell$ of a reflecting Brownian motion $|B|$ by a multiple $\mu$ of its local time process $\ell$ at $0$, corresponding local time processes of $X$ are squared Bessel with other real dimension parameters, both positive and negat...
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version
Access Document
Files:
• (pdf, 1.4MB)
Publisher copy:
10.1214/18-ECP174
Authors
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Statistics
Oxford college:
Brasenose College
Role:
Author
ORCID:
0000-0003-0593-8682
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Electronic Communications in Probability Journal website
Volume:
23
Issue:
2018
Pages:
Article: 74
Publication date:
2018-10-17
Acceptance date:
2018-10-01
DOI:
EISSN:
1083-589X
Pubs id:
pubs:905410
URN:
uri:8930512c-85e3-4e0e-95a3-cab318ea721d
UUID:
uuid:8930512c-85e3-4e0e-95a3-cab318ea721d
Local pid:
pubs:905410
Keywords: | 2021-10-24 06:32:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7923480272293091, "perplexity": 3116.500667325333}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585911.17/warc/CC-MAIN-20211024050128-20211024080128-00330.warc.gz"} |
https://api-project-1022638073839.appspot.com/questions/how-do-you-calculate-the-energy-needed-to-heat-water | # How do you calculate the energy needed to heat water?
Dec 7, 2016
It depends on how much water you have, and to what temperature you want to raise it to.
#### Explanation:
The equation for the amount of thermal energy needed to produce a certain temperature change is as follows:
$q = c m \Delta T$
Where:
$q$ is the amount of thermal energy
$c$ is the heat capacity of water ($\approx 4.184 \frac{J}{g} ^ o C$)
$\Delta T$ is the change in temperature.
So, how much thermal energy you need is dependent on exactly how much you want to raise the temperature of water by.
Also, note that the equation includes a mass. This is simply because the larger the sample of molecules you have, the more energy it will take to raise their average kinetic energy (i.e. temperature) to a certain level. This is why you may notice that heating a pan of water takes much less time than heating up your bathtub full of water, even if you use the same amount of heat.
This is taken into account by the heat capacity. The heat capacity tells us how much energy it takes to raise the temperature of 1 g of water by ${1}^{o} C$. We add it in there, therefore, to take into account how much water we have.
So to conclude, the amount of energy you'll need to heat water really depends on the temperature you want to heat it to, as well as the amount of water you have.
Hope that helped :) | 2020-04-03 20:13:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "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": 0.686652660369873, "perplexity": 152.1076241097063}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370518622.65/warc/CC-MAIN-20200403190006-20200403220006-00469.warc.gz"} |
https://byjus.com/question-answer/electricity-can-be-used-to-replace-the-fuel-and-power-a-rocket-using-today-s-4/ | Question
# Electricity can be used to replace the fuel and power a rocket (using today's mechanism) just like an electric car.
A
True, as Electricity is also a form of energy.
B
False, as Electricity is not a source of energy.
C
False, as the rocket needs to throw out fuel in the opposite direction to move.
D
True, as the mechanism for car and rocket is similar.
Solution
## The correct option is C False, as the rocket needs to throw out fuel in the opposite direction to move. Rocket launch works on the principle of the third law of motion as the ejection of fuel creates the perfect push for the rocket to launch.
Suggest corrections | 2021-12-08 21:29:13 | {"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": 0.8770224452018738, "perplexity": 763.0820038446618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1637964363598.57/warc/CC-MAIN-20211208205849-20211208235849-00357.warc.gz"} |
https://daostack-1.gitbook.io/v1/introduction/holographic-consensus-overview/genesis-protocol | # Genesis Protocol
The Genesis protocol is an implementation of holographic consensus as a smart contract voting machine on our Infra layer.
### Quick Overview
Proposals are submitted to the DAO. Once submitted, they are “regular” proposals that require an absolute majority (>50%) of votes to pass, which is difficult to achieve.
Each proposal in the Genesis protocol also has a prediction market associated with it. This prediction market uses the GEN token. Members from the DAO or from the general public can stake GEN on proposals they think will pass (upstake) or fail (downstake) and get rewarded for correct predictions. By default, the DAO stakes GEN against every proposal passing (the "DAOstake"), which provides an economic incentive for predictors to find good proposals they predict will pass.
Proposals with total GEN predictions of passing above a certain threshold can be "boosted," meaning they only require a relative majority to pass, which is much easier to achieve.
In total, this lets the DAO pass proposals frequently and with high confidence, without requiring high voter participation, because the predictors are incentivized to insure high representativity.
### Proposal States
An open proposal (i.e. with a pending decision) can be in one of the following stages:
• Queued: All proposals, when submitted, are in a queued state by default and have a downstake (funded by the DAO) set by the minimumDaoBounty parameter. The proposal requires an absolute majority (i.e. > 50% of all voting power voting "yes" or "no") to resolve in this state.
• Pre-boosted: A proposal moves from queued to pre-boosted if
$S_u / S_d > c^b$
, where
$S_u$
is the total upstake on a proposal,
$S_d$
is the proposal's total downstake,
$c$
is a constant, and
$b$
is the number of currently boosted proposals. The proposal in this state is open for staking and can be moved back to queued state if the stake against it increases and proposals crosses back below the boosting threshold.
• Boosted: Once the proposal has been in pre-boosted state for the period set by the preBoostedVotePeriodLimit parameter, the proposal moves to the boosted state. The proposal in this state requires a relative majority to pass (i.e more votes for than against). A proposal in this state is open for voting, but staking is closed. Thus, once a proposal is boosted it cannot be moved back to queued or pre-boosted state. The proposal stays in this state until the boostedVotePeriodLimit elapses.
• QuietEndingPeriod: If the winning outcome of the proposal flips from 'pass' to 'fail' or vice-versa during the final period of time decided by the quietEndingPeriod parameter, then the proposal voting time gets extended by another quietEndingPeriod until decision does not switch during the period. This serves to prevent voters from "stealing" votes at the last minute.
### Staking & Rewards
The following are the possible outcomes of a proposal:
• The proposal expires in queue without any decision. In this case, all the stakes are returned to the respective staker.
• The proposal passes or fails. Losing stakers lose their stake, and winning stakers receive their stake plus a pro rata share of the loser's stakes. This includes the DAOstake, a downstake which the DAO places on each proposal automatically (if it has the funds to do so).
Note that for a given proposal, one can stake multiple times from the same address. In such a case all the subsequent stakes must align with the previous stake's vote i.e. if you staked in favor of the proposal earlier, you must stake in favor of the proposal in subsequent stakes.
### Parameters
Here is an explanation of the protocol's parameters, which you can find in the "Information" tab of any plugin that uses the protocol.
Address The Ethereum address where these parameters are stored (not where the protocol itself is). Example: 0x332b8c9734b4097de50f302f7d9f273ffdb45b84
Activation Time The date and time (represented in Unix time) when proposals in this plugin can first be submitted. Example: 12:00 PM UTC on July 14th, 2019 (active)
Boosted Vote Period Limit The length of time boosted proposals are open for voting. Example: 7 days (604800 seconds) DAO Bounty Constant This is multiplied by the average downstake on boosted proposals to calculate how large the DAO’s automatic downstake should be. Example: 10 Proposal Reputation Reward The amount of voting power given out as a reward for submitting a proposal that the DAO passes. Example: 500 REP Minimum DAO Bounty The minimum amount of GEN a DAO will stake when automatically downstaking each proposal. Example: 250 GEN Pre-Boosted Vote Period Limit The length of time that a proposal must maintain a confidence score (upstake divided by downstake) higher than the boosting threshold to become eligible for boosting. Example: 1 day (86400 seconds) Queued Vote Period Limit The amount of time non-boosted proposals (pre-boosted or regular queue) are open for voting. Example: 45 days (3888000 seconds) Queued Vote Required The percentage of all Reputation (voting power) that must be voting yes or no for a non-boosted proposal for it to pass or fail. Example: 50% Quiet Ending Period The length of time a vote’s potential result needs to stay the same in order to be confirmed as the official result. Example: 2 days (172800 seconds) Threshold Constant Controls how quickly the required confidence score for boosting goes up as the number of currently boosted proposals rises (threshold = threshold constant ^ number of currently boosted proposals). Example: 1.2 Voters Reputation Loss The percentage of a voter’s voting power they stand to lose if they vote against the DAO’s eventual decision on a non-boosted proposal. If you have 100 Reputation and this parameter is set to 4%, you stand to lose 4 Reputation. Example: 4% | 2023-03-30 11:41:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "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": 0.4878319501876831, "perplexity": 4275.502669686452}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949181.44/warc/CC-MAIN-20230330101355-20230330131355-00027.warc.gz"} |
https://mcli.docs.mosaicml.com/en/latest/secrets/shared.html | Shared Secrets#
You may have a need to use secrets provided for you by your cluster administrators. “Shared secrets” are most commonly used for s3 credentials. These secrets are stored in a shared location within your cluster and can be added as shared secrets. To add a shared secret, you’ll need the following information:
1. The cluster in which the secret lives
2. The namespace in which the secret lives
3. Finally, the name of the secret
Once you have this information, you can add the secret using:
> mcli create secret shared --name <name> --cluster <cluster> --namespace <namespace>
✔ Copying existing secret: <name>
This will copy the secret from the shared store and sync it across all of your clusters, making it available to any workloads you launch in the future. | 2023-04-02 01:55:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2943142056465149, "perplexity": 4451.790447564489}, "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-2023-14/segments/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00059.warc.gz"} |
https://www.mersinrehber.com/tugrul-eczanesi-mersin/ | # Tuğrul Eczanesi Mersin
Tuğrul Eczanesi İletişim Bilgileri
Telefon:0 324 337 44 45
Adres:Nusratiye Mah. 5021 Sk. Diabet Hastanesi Yanı Atatürk Lisesi Arkası Merkez/mersin
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Html code here! Replace this with any non empty text and that's it. | 2018-05-21 18:48:42 | {"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": 0.8019527196884155, "perplexity": 6339.27994137302}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1526794864466.23/warc/CC-MAIN-20180521181133-20180521201133-00547.warc.gz"} |
https://socratic.org/questions/what-is-the-net-area-between-f-x-cos-2xsinx-and-the-x-axis-over-x-in-0-3pi | # What is the net area between f(x) = cos^2xsinx and the x-axis over x in [0, 3pi ]?
Sep 21, 2016
$\frac{2}{3}$ areal units.
#### Explanation:
Net area = int f(x) dx, between the limits $0 \mathmr{and} 3 \pi$
$= \int {\cos}^{2} x \sin x \mathrm{dx}$, between the limits $0 \mathmr{and} 3 \pi$
$= - \int {\cos}^{2} x d \left(\cos x\right)$, between the x-limits $0 \mathmr{and} 3 \pi$
$= - \left[{\left(\cos x\right)}^{3}\right]$, between the limits $0 \mathmr{and} 3 \pi$
$= - \left({\left(\cos \left(3 \pi\right)\right)}^{3} - {\left(\cos 0\right)}^{3}\right)$
$= - \left({\left(- 1\right)}^{3} - 1\right)$
$= \frac{2}{3}$
Note that f is periodic with period $2 \pi$ and, Interestingly, the net
periodic area ( here up to $x = 2 \pi$ ) =$\frac{2}{3} - \frac{2}{3} = 0$.. | 2022-05-29 07:57:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 14, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.9242191314697266, "perplexity": 3892.0806194805896}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663048462.97/warc/CC-MAIN-20220529072915-20220529102915-00713.warc.gz"} |
https://code.tutsplus.com/articles/magento-theme-development-category-page-part-2--cms-24989 | # Magento Theme Development: Category Page, Part 2
This post is part of a series called Magento Theme Development.
Magento Theme Development: Category Page, Part 1
Magento Theme Development: Product Page, Part 1
In the previous article on category pages, we edited the toolbar, grid and list layout. In this second article on customizing the category page, we'll customize the sidebar and do some CSS fixes.
First of all, we'll add some components in the sidebar, so that we can style them. Here, for the purpose of demonstration, we'll just add one or two components and modify them. That'll give you ample understanding of how you can modify the other sidebar components as well.
For now we'll just add 'compare products' and a sidebar banner to the sidebar. We'll do that from the local.xml code. If you remember from the first articles of the series, you can find the local.xml file in the layout folder of your theme file.
We'll add a reference to the left section, and then add a banner and compare product module in the sidebar, using the code below:
Use it just as a reference code—you can add more modules or banners using the same procedure.
If we look at our HTML design, we'll notice that all components are nicely designed, especially the heading part, which has multiple colors in it.
Whereas our current design is little off, though we can modify the design through CSS, but we need to modify the HTML to add classes for different colors in the heading.
To modify the HTML, we'll first enable template hints, and find out that the file responsible for it is \template\catalog/product/compare/sidebar.phtml.
Now we'll open up this sidebar.phtml file, and compare it with the HTML code.
Our design HTML code for the sidebar looks like this:
We can see that the heading has the h3 tag with a class of title, and it has the strong tag around the heading parts, which have a different color.
For this, we'll replace the block-title div with this:
Refresh the page, and it should look quite close to our HTML design now. You can add and style other sidebar components in a similar way.
Now that we are done editing the phtml files, let's start fixing the CSS styles.
We'll start fixing styles from the top. The first component which needs our attention is the page heading. As we can see, it is quite off, and is not close to our HTML requirements.
We'll add these lines in our new CSS file to style the heading.
Here we have just given it a good text font, line height, text align, background image, etc. Also, we have made the background transparent with no border. It should look like this now:
Next we need to modify the toolbar section. For that we'll add these styles in our CSS file:
Here we have just specified some background images, width, height, etc., and it'll pretty much do the trick. The page should look like this:
Now, let's start editing the products section in grid view. The page looks like this now:
We'll just have to make some width and hover style adjustments. Also the price color needs changing. We'll do all that by adding these CSS lines:
Now the grid section should look like this:
In the last part we need to fix the products section in the list mode. It currently looks quite messed up, but don't worry—a few lines of CSS will set everything right.
To make it look good, we'll use these CSS styles:
Here we have set the product image width, floated the price to the right, given the whole section a nice background, border and hover effect, and modified the button slightly. The page should look something like this:
With all this done, your catalog page should look nice and close to our HTML design requirements. You may need some other CSS fine-tuning, but other than that you are all set.
In the next article of this series, we'll start editing the product detail page.
Please do leave your suggestions and feedback in the comments section. We'll be looking forward to it. | 2021-09-25 03:50:19 | {"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": 0.3030757009983063, "perplexity": 1739.0818618226658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057589.14/warc/CC-MAIN-20210925021713-20210925051713-00704.warc.gz"} |
http://math.stackexchange.com/questions/289714/geometrically-connected-fibres-multiplicative-group | # geometrically connected fibres, multiplicative group
If $f: X \to Y$ has geometrically connected fibres, $f_*\mathbb{G}_m = \mathbb{G}_m$ as Zariski sheaves. Does it also hold as étale sheaves?
-
Your claim is false even for Zariski topology. Please clarify the hypothesis. – user18119 Jan 29 '13 at 15:28 | 2016-05-06 15:46:31 | {"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": 0.8283058404922485, "perplexity": 912.9446551458118}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461861831994.45/warc/CC-MAIN-20160428164351-00040-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/matlab-modeling-response-of-a-particle-in-an-anharmonic-potential.807536/ | # [MATLAB] Modeling response of a particle in an anharmonic potential
1. Apr 8, 2015
### baouba
I'm trying to model the response of a particle in an anharmonic potential in MATLAB. I know that writing position, x as a function of potential energy U is,
where T is the period, m is mass, and E is the energy of the system. How would I get a function for T(E) since it's not independent of amplitude obviously. As a starting point, I'm using the anharmonic potential of
Where a and b are constants. Does anybody know how I could program this in matlab?
Thanks
2. Apr 9, 2015
3. Apr 9, 2015
### baouba
Yes my goal is to plot a potential vs. displacement curve. Is this even possible considering the number of functions in the first equation above?
Here's some of my code: For simplicity, I assume period T(E) = 1
%Define Functions
%For a,b = 1
%U = ax^2 + bx^3
%Assuming T(E) = 1
U = @(x) x^2+x^3
fun = @(E,U) T/(sqrt(U-E))^-1
int = @(E) integral(fun,0,U)
ezplot('(-x+(sqrt(2)*2*pi)^-1)*int')
4. Apr 9, 2015
### kreil
I think something like this is a step closer, but I'm not convinced it's correct yet.
Code (Text):
a=1;
b=1;
T=1;
U = @(x) a*x.^2 + b*x.^3;
A = (2*pi*sqrt(2))^-1;
I = [];
for n =0:0.1:10
fun = @(E) T./(sqrt(U(n)-E));
I = [I, A*integral(fun,0,U(n))];
end
plot(0:0.1:10, I)
The difference here is that I loop through possible values for U and evaluate the integral once for each one.
5. Apr 9, 2015
### baouba
Thank you I'll try it. I'm wondering if it would be more beneficial/ shed more light if I plotted x as a function of time. In that case I solved lagrange
L = K - U = .5mv^2 - x^2 - x^3 since U = x^2 + x^3
the associated equation of motion is then ma = -3x^2 - 2x
I would then need to solve this differential equation to plot x(t). However I put this equation into wolfram alpha, and got a massive expression out and it makes me thing that it might not be possible to model this response.
Is this the case?
6. Apr 10, 2015
### kreil
You can solve the second order differential equation numerically in MATLAB. Since the ODE functions only work with first order equations, you'll have to rewrite this second order equation
$$m \frac{d^2 x}{dt^2} = -3x^2-2x$$
As an equivalent system of first order equations,
$$m \dot{y_2} = -3y_1^2-2y_1$$
$$y_2 = \dot{x}$$
$$y_1 = x$$
You'll also need to define the initial conditions of the problem.
Take a look at the examples here:
http://www.mathworks.com/help/matlab/ref/ode45.html
Save the following function file, which defines the equations above (assume m=1):
Code (Text):
function dy = anharmonic(t,y)
dy = zeros(2,1);
dy(1) = y(2);
dy(2) = -3*y(1).^2 - 2*y(1);
end
Then set the time span and initial conditions before calling ode45:
Code (Text):
tspan = [0 15];
y0 = [0; 0.25];
[t,y] = ode45(@anharmonic, tspan, y0);
plot(t,y(:,1),t,y(:,2))
legend('Position','Velocity')
You might want to check my work, because the plot looks more harmonic than anharmonic to me.
#### Attached Files:
• ###### anharmonic.png
File size:
10.3 KB
Views:
174
Last edited: Apr 10, 2015 | 2017-08-18 15:43:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6951597332954407, "perplexity": 1496.814199610552}, "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-2017-34/segments/1502886104681.22/warc/CC-MAIN-20170818140908-20170818160908-00328.warc.gz"} |
http://physics.stackexchange.com/tags/earth/hot | # Tag Info
## Hot answers tagged earth
3
We can detect it, but it takes very precise measurements. Stellar parallax, i.e. the relative displacement of close-by stars against the background of far away ones can be detected, but it's a very difficult measurement to make because the "motion" is very small (usually fractions of an arc second): Recently we have learned to build satellites that can ...
2
But you can see the motion of the earth in it's orbit; it's called aberration of starlight, first measured by James Bradley in 1729. Even earlier, parallax of stars had been detected, by 1680. But you have to take detailed observations at widely separated times for the effects to be even the least bit obvious.
2
It's rarer than that, more like 1 in 6000. Because each molecule of water has two atoms of hydrogen, then about every 2 in 6000 (1 in 3000) has a single atom of deuterium (DHO). And would be closer to 1 in every 6000$^2$ for a molecule of D2O. The linked question Deuterium density in seawater gives sources that show deuterium is well-mixed in the ocean. ...
1
Very generally speaking, a crater is about 10 times the diameter of the meteor, with a direct hit. so at some 950 km in diameter, we can guesstimate a crater roughly covering 9,500 km, which is 1/4 the way around the Earth. If we give an impact speed of slightly greater than escape velocity of 12-13 km/s, it would take over a minute to complete it's ...
1
Now perfect balance between the centrifugal force of orbital rotation and sun's gravity is impossible so the earth's orbit should either be slowly decaying inwards or expanding outwards due to difference in magnitude of those opposing forces. This assumption is incorrect. We could make the same argument about a weight suspended from a spring. ...
1
The error is just to consider an average speed $h\omega$. When the particle is at height $z$, its horizontal (relative to the Earth) speed is $v=2z\omega$. The time of of flight is $$t=\sqrt{\frac{2z}{g}}.$$ Differentiating this expression we get the time taken by the particle to move a distance $dz$, $$dt=\frac{dz}{\sqrt{2gz}}.$$ The horizontal distance ...
1
The vector $\mathbf r$ does change, even though its magnitude is nearly constant. Most importantly, the component of $\mathbf r$ which is perpendicular to the rotation axis is decreasing in this example. This fact leads to the explanation for which you are searching. Another way of seeing this would be to use this definition of angular momentum, which ...
1
The direction of deflection of the ball should be independent where the observer is. Left or right deflection is with respect to an observer facing in the direction the ball is moving. Are you asking about a ball being thrown from the northern to the southern hemisphere? In that case the deflection would change from deflecting right to deflecting left as ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2016-05-01 06:13:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8415634632110596, "perplexity": 316.80494363510354}, "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-2016-18/segments/1461860114285.77/warc/CC-MAIN-20160428161514-00161-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://transfer-learning.ai/paper/isoperimetric-inequalities-for-real-valued-functions-with-applications-to-monotonicity-testing/ | We generalize the celebrated isoperimetric inequality of Khot, Minzer, andSafra~(SICOMP 2018) for Boolean functions to the case of real-valued functions . We show a matching lower bound for nonadaptive, 1-sided error testers for monotonicity . We apply our generalized isoperic inequality to improve algorithms fortesting monotonic and approximating the distance to monotone forreal-valued function $f$ . We also show that the distance of $O(\sqrt{d\logr)$ can be approximated nonadaptively with query complexity in $1/\alpha$ and the dimension $d$ This query complexity is known to be nearlyoptimal fornonadaptive algorithms even for the special case of Booleanfunctions . We conclude that the distances to monotonied functions that are $\alpha$-far from monotones are $O(d\Logr) and$O (D) is $O(‘D’) is$ | 2020-11-24 21:17:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9018038511276245, "perplexity": 934.9548239695728}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141177566.10/warc/CC-MAIN-20201124195123-20201124225123-00610.warc.gz"} |
https://cms.math.ca/cmb/msc/14D20?fromjnl=cmb&jnl=CMB | location: Publications → journals
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Search: MSC category 14D20 ( Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} )
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1. CMB Online first
Maican, Mario
Moduli of space sheaves with Hilbert polynomial $4m+1$ We investigate the moduli space of sheaves supported on space curves of degree $4$ and having Euler characteristic $1$. We give an elementary proof of the fact that this moduli space consists of three irreducible components. Keywords:moduli of sheaves, semi-stable sheavesCategories:14D20, 14D22
2. CMB 2016 (vol 60 pp. 522)
Iena, Oleksandr; Leytem, Alain
On the Singular Sheaves in the Fine Simpson Moduli Spaces of $1$-dimensional Sheaves In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We show that for $d\ge 4$ it is a singular subvariety of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted as a (partial) modification of $M\setminus M'$ by line bundles (on support). Keywords:Simpson moduli spaces, coherent sheaves, vector bundles on curves, singular sheavesCategory:14D20
3. CMB 2008 (vol 51 pp. 519)
Coskun, Izzet; Harris, Joe; Starr, Jason
The Effective Cone of the Kontsevich Moduli Space In this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, $\Kgnb{0,0}(\PP^r,d)$, stabilize when $r \geq d$. We give a complete characterization of the effective divisors on $\Kgnb{0,0}(\PP^d,d)$. They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image. Categories:14D20, 14E99, 14H10
4. CMB 2007 (vol 50 pp. 427)
Mejía, Israel Moreno
On the Image of Certain Extension Maps.~I Let $X$ be a smooth complex projective curve of genus $g\geq 1$. Let $\xi\in J^1(X)$ be a line bundle on $X$ of degree $1$. Let $W=\Ext^1(\xi^n,\xi^{-1})$ be the space of extensions of $\xi^n$ by $\xi^{-1}$. There is a rational map $D_{\xi}\colon G(n,W)\rightarrow SU_{X}(n+1)$, where $G(n,W)$ is the Grassmannian variety of $n$-linear subspaces of $W$ and $\SU_{X}(n+1)$ is the moduli space of rank $n+1$ semi-stable vector bundles on $X$ with trivial determinant. We prove that if $n=2$, then $D_{\xi}$ is everywhere defined and is injective. Categories:14H60, 14F05, 14D20
5. CMB 2005 (vol 48 pp. 90)
Jeffrey, Lisa C.; Mare, Augustin-Liviu
Products of Conjugacy Classes in $SU(2)$ We obtain a complete description of the conjugacy classes $C_1,\dots,C_n$ in $SU(2)$ with the property that $C_1\cdots C_n=SU(2)$. The basic instrument is a characterization of the conjugacy classes $C_1,\dots,C_{n+1}$ in $SU(2)$ with $C_1\cdots C_{n+1}\ni I$, which generalizes a result of \cite{Je-We}. Categories:14D20, 14P05
6. CMB 2002 (vol 45 pp. 417)
Kamiyama, Yasuhiko; Tsukuda, Shuichi
On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons For an integer $n \geq 3$, let $M_n$ be the moduli space of spatial polygons with $n$ edges. We consider the case of odd $n$. Then $M_n$ is a Fano manifold of complex dimension $n-3$. Let $\Theta_{M_n}$ be the sheaf of germs of holomorphic sections of the tangent bundle $TM_n$. In this paper, we prove $H^q (M_n,\Theta_{M_n})=0$ for all $q \geq 0$ and all odd $n$. In particular, we see that the moduli space of deformations of the complex structure on $M_n$ consists of a point. Thus the complex structure on $M_n$ is locally rigid. Keywords:polygon space, complex structureCategories:14D20, 32C35
7. CMB 2000 (vol 43 pp. 174)
Gantz, Christian; Steer, Brian
Stable Parabolic Bundles over Elliptic Surfaces and over Riemann Surfaces We show that the use of orbifold bundles enables some questions to be reduced to the case of flat bundles. The identification of moduli spaces of certain parabolic bundles over elliptic surfaces is achieved using this method. Categories:14J27, 32L07, 14H60, 14D20
8. CMB 2000 (vol 43 pp. 162)
Foth, Philip
Moduli Spaces of Polygons and Punctured Riemann Spheres The purpose of this note is to give a simple combinatorial construction of the map from the canonically compactified moduli spaces of punctured complex projective lines to the moduli spaces $\P_r$ of polygons with fixed side lengths in the Euclidean space $\E^3$. The advantage of this construction is that one can obtain a complete set of linear relations among the cycles that generate homology of $\P_r$. We also classify moduli spaces of pentagons. Categories:14D20, 18G55, 14H10
9. CMB 1999 (vol 42 pp. 307)
Kapovich, Michael; Millson, John J.
On the Moduli Space of a Spherical Polygonal Linkage We give a wall-crossing'' formula for computing the topology of the moduli space of a closed $n$-gon linkage on $\mathbb{S}^2$. We do this by determining the Morse theory of the function $\rho_n$ on the moduli space of $n$-gon linkages which is given by the length of the last side---the length of the last side is allowed to vary, the first $(n - 1)$ side-lengths are fixed. We obtain a Morse function on the $(n - 2)$-torus with level sets moduli spaces of $n$-gon linkages. The critical points of $\rho_n$ are the linkages which are contained in a great circle. We give a formula for the signature of the Hessian of $\rho_n$ at such a linkage in terms of the number of back-tracks and the winding number. We use our formula to determine the moduli spaces of all regular pentagonal spherical linkages. Categories:14D20, 14P05
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https://www.biostars.org/p/405660/ | What's the difference between enrichKEGG and gseKEGG
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Entering edit mode
2.7 years ago
ben.kunfang ▴ 30
Hi,
I was wondering what is the difference between enrichKEGG and gseKEGG in R package ClusterProfile. Thanks!
clusterprofiler KEGG • 5.1k views
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Entering edit mode
gseKEGG use the gene set enrichment analysis and enrichKEGG use over-representation test, and GESA doesn't need to run differential gene expression analysis beforehand
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Entering edit mode
15 months ago
liangqinsi ▴ 40
From coding prospective:
enrichKEGG takes in only gene names, while gseKEGG takes in log2FC with gene names.
Why GSEA:
Gene Set Enrichment Analysis takes advantage of log2FC value, so the results are more informative and more accurate.
1
Entering edit mode
2.7 years ago
h.mon 34k
0
Entering edit mode
Thanks, but I have to say I just don't like to way your answer. Yes, we can learn a lot by reading the help book, but what's the point I ask in the forum..I just want to save a little bit time to get a concise answer. Or otherwise why we need to go to school, we can just study at home by reading all the books.
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Entering edit mode
Hey, I do not see anything wrong with the answer by h.mon.. Remember that our communication channels here are electronic; so, things can be easily mis-interpreted. On Biostars, we are also volunteers and do not receive any payment for the time that we invest. Our expectation is that users who come here with questions have first invested their own time, exhaustively, in trying to resolve their problem(s).
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Entering edit mode
I appreciate h.mon answer my question and I never say h.mon answer is wrong, I just say personally I don't like the way he answer. If you think answer a question by throwing a bunch of books is an appropriate way. That's fine. If you look my answer, don't you think it is more explicit than h.mon's? But it still need to invest time to learn what is gene set enrichment analysis and over-representation test. I never say the person who answer the question don't have to spend any time. I just hope the answer been more explicit instead of throwing the books.
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Entering edit mode
You are completely mixing up things: this forum is not school, and the volunteers here are not teachers. The main purpose of this site is to provide answers to well-formulated, well-explained specific questions. In particular, it is expected posters had already searched for a solution - did their homework, metaphorically speaking - so yes, we expect you to read the documentation before posting.
How To Ask Good Questions On Technical And Scientific Forums
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Entering edit mode
Here is what I think, if you know the answer, you could answer the way Iike I answered.It doesn't need to type a lot of words and spend a lot of time. If you don't know the answer, you might giving the wrong books, so what's the point to give the help books? But still, I appreciated you answer my question, thanks a lot~
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Entering edit mode
10 months ago
Guangchuang Yu ★ 2.5k
you should read the publication of clusterProfiler 4.0.
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Entering edit mode
clusterProfiler 4 rocks!
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Entering edit mode
9 weeks ago
youcai ▴ 60
• enrichKEGG : over-representation analysis (ORA) using KEGG pathway
• gseKEGG : gene set enrichment analysis (GSEA) using KEGG pathway
data(geneList, package="DOSE")
## fold change > 2 as DE genes
de <- names(geneList)[abs(geneList) > 2]
clusterProfiler 4.0. | 2022-07-03 05:36:30 | {"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": 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": 0.30286258459091187, "perplexity": 2674.563814343142}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104215790.65/warc/CC-MAIN-20220703043548-20220703073548-00160.warc.gz"} |