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https://www.physicsforums.com/threads/word-problem-question.135843/ | # Homework Help: Word Problem Question
1. Oct 11, 2006
### DethRose
Ive got an assignment of word problems and cant seem to figure this one out:
A 6 Litre car radiator is 2 thirds full of water. How much of a 90% antifreeze solution (90% is alcohol by volume) must be added to it to make a 10% antifreeze solution in the radiator?
I came up with the equation: 0.9x=(0.1)(6)
but that didnt work so any help about what the way to set up the problem would be great.
2. Oct 11, 2006
### Office_Shredder
Staff Emeritus
How much water is in the radiator?
3. Oct 11, 2006
### DethRose
4L of water
4. Oct 11, 2006
### DethRose
i tried to do it a new way which was :
4+0.9x=(0.1)(6)
but i got a negative number from that attempt so that cant be the answer
5. Oct 11, 2006
### HallsofIvy
You are assuming that the total liquid volume in the radiator is 6 litres. If that were the case, that would mean that you were adding 2 litres of antifreeze solution. But then you would be adding .9(2)= 1.8 litres of pure antifreeze which would give a concentration of 1.8/6.0= 0.3 or 30%. That's too high so you must not be filling the radiator.
Let x be the number of litres of 90% solution you are adding. Then the total liquid volume in the radiator is 4+ x litres. The amount of pure anti-freeze you are adding is (as you say) .9x. The concentration of pure anti-freeze in the radiator is $\frac{.9x}{4+ x}= .1$. Solve that for x. | 2018-10-18 12:05:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5486413836479187, "perplexity": 1295.8109992540442}, "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-2018-43/segments/1539583511806.8/warc/CC-MAIN-20181018105742-20181018131242-00292.warc.gz"} |
https://www.physicsforums.com/threads/query-on-indexing-to-determine-coefficients.631615/ | # Query on indexing to determine coefficients
## Main Question or Discussion Point
Folks,
I am interested to know what the author is doing in the following
$\displaystyle B_{ij}=EL ij (L)^{(i+j-1)} \left[ \frac{(i-1)(j-1)}{i+j-3} -\frac{2(ij-1)}{i+j-2}+\frac{(i+1)(j+1)}{i+j-1}\right]$
he states that this expression is not valid for $B_{ij}$ when $i=1$ and $j=1,2,...N$
......yet he goes on to actually calculate
$B_{11}=4EIL$, $B_{1j}=B_{j1}=2EIL^j$, $(j>1)$
I understand the the numerator in the first 2 terms inside the big brakets are both 0 when i=j=1 but we still yield a value from the third term...
Any insight will be appreciated
Regards
PS:I notice there is some editing problem with the 3 terms inside the big brackets. There should be a minus and plus separating the terms.
Mark44
Mentor
Folks,
I am interested to know what the author is doing in the following
$\displaystyle B_{ij}=EL ij (L)^{(i+j-1)} \left[ \frac{(i-1)(j-1)}{i+j-3} -\frac{2(ij-1)}{i+j-2}+\frac{(i+1)(j+1)}{i+j-1}\right]$
he states that this expression is not valid for $B_{ij}$ when $i=1$ and $j=1,2,...N$
That's not at all obvious. The only restrictions I see are that
1. i + j ≠ 3 (would make the first denominator vanish)
2. i + j ≠ 2 (would make the second denominator vanish)
3. i + j ≠ 1 (would make the third denominator vanish)
......yet he goes on to actually calculate
$B_{11}=4EIL$, $B_{1j}=B_{j1}=2EIL^j$, $(j>1)$
I don't see how. With i = 1, j = 1, the second term in the brackets is 0/0.
I understand the the numerator in the first 2 terms inside the big brakets are both 0 when i=j=1 but we still yield a value from the third term...
Any insight will be appreciated
Regards
PS:I notice there is some editing problem with the 3 terms inside the big brackets. There should be a minus and plus separating the terms.
Could you give a link to where you found this question?
I don't see how. With i = 1, j = 1, the second term in the brackets is 0/0.
Are you saying because one of the terms is indeterminate then the whole equation is invalid and thus cannot be usedt o calcualte $B_{ij}$ for i=j=1?
Could you give a link to where you found this question?
See attached jpeg of question. The answer involves converting the DE into a weak form using a weight function w and splitting the differentiation between the weight function and the dependent variable u.
Would the choice of the approximation functions affect the outcome?
regards
#### Attachments
• 28.6 KB Views: 214 | 2020-02-21 11:14:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.79814213514328, "perplexity": 482.1532537364562}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1581875145529.37/warc/CC-MAIN-20200221111140-20200221141140-00433.warc.gz"} |
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# If p and q are two distinct numbers chosen from the set ..............
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If p and q are two distinct numbers chosen from the set .............. [#permalink]
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30 Jan 2019, 01:43
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If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.
A. $$\frac{1}{30}$$
B. $$\frac{1}{15}$$
C. $$\frac{1}{9}$$
D. $$\frac{2}{15}$$
E. $$\frac{2}{9}$$
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Re: If p and q are two distinct numbers chosen from the set .............. [#permalink]
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30 Jan 2019, 02:07
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prime factors in the set: -3, -2, 2, 3, 5
Each product with 1 or -1 is also prime.
5*2/10C2=10/45=2/9→(E)
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If p and q are two distinct numbers chosen from the set .............. [#permalink]
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Updated on: 01 Feb 2019, 09:21
prime no are +ve integer value (2,3,5)
2,3,5 can be formed ( -3,-1) ,( -2,-1), ( 1,2), ( 1,3),(1,5) ; total 5 pairs p*q can be 2 ways; 5*2 = 10
total pairs = 5 and p*q = 10c2
5/10c2 ; 5/45
=1/9
IMOC
EgmatQuantExpert wrote:
If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.
A. $$\frac{1}{30}$$
B. $$\frac{1}{15}$$
C. $$\frac{1}{9}$$
D. $$\frac{2}{15}$$
E. $$\frac{2}{9}$$
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Originally posted by Archit3110 on 30 Jan 2019, 07:04.
Last edited by Archit3110 on 01 Feb 2019, 09:21, edited 1 time in total.
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Joined: 04 Jan 2015
Posts: 3074
Re: If p and q are two distinct numbers chosen from the set .............. [#permalink]
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01 Feb 2019, 01:57
1
1
Solution
Given:
• A set of 10 integers, {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
• p and q are two distinct integers chosen from the given set
To find:
• The probability that p * q is a prime number
Approach and Working:
The total number of ways of choosing two distinct integers from a set of 10 elements = $$^{10}C_2 = 45$$
Now, for p * q to be prime, one of them must be ±1 and the other must be = ± a prime number.
• Thus, the possible cases are {-1, -2}, {-1, -3}, {1, 2}, {1, 3}, {1, 5}
Therefore, probability = $$\frac{5}{45} = \frac{1}{9}$$
Hence the correct answer is Option C.
_________________
Re: If p and q are two distinct numbers chosen from the set .............. [#permalink] 01 Feb 2019, 01:57
Display posts from previous: Sort by | 2019-10-15 01:33:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.8617401123046875, "perplexity": 2089.044556549482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570986655735.13/warc/CC-MAIN-20191015005905-20191015033405-00166.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/136938-laplace-transform-weibull-pdf.html | # Math Help - laplace transform of a weibull pdf
1. ## laplace transform of a weibull pdf
Can someone help me in finding out the laplace transform or laplace steiltjes transform of a weibull pdf or cdf ?
Thanks
2. Originally Posted by ranaanil13
Can someone help me in finding out the laplace transform or laplace steiltjes transform of a weibull pdf or cdf ?
Thanks
See what the Wikipedia article has to say about the mgf
CB | 2014-03-16 00:06:53 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9387724995613098, "perplexity": 933.0255776860063}, "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-2014-10/segments/1394678700701/warc/CC-MAIN-20140313024500-00071-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/permutations-abstract-algebra.297275/ | # Permutations abstract algebra
#### kathrynag
1. The problem statement, all variables and given/known data
Compute the expression shown for the permutations
1.$$\left|<\phi>\right|$$
2..$$\left|<\tau^2>\right|$$
3.$$\phi^{100}$$
where:
$$\phi$$= top row:1, 2 , 3 ,4 , 5 ,6
bottom row: 3,1, 4,5,6,2
$$\tau$$ = top row: 1,2,3,4,5,6
bottom row: 2,4,1,3,6,5
2. Relevant equations
3. The attempt at a solution
Ok, my main problem is that I don't even know what they're asking. I understand how to do permutation multiplication and composition, but not this.
I do know from the back of the book that #2 is 2, but I want to know why this is true.
#### kathrynag
Does it just mean finding the identity?
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• Solo and co-op problem solving | 2019-03-27 02:50:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.5279316902160645, "perplexity": 3764.7866118775005}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1552912207618.95/warc/CC-MAIN-20190327020750-20190327042750-00190.warc.gz"} |
https://ask.sagemath.org/question/52555/pre-set-memory-limit-reached-gaperror/ | # Pre-set memory limit reached - Gaperror
Hello everyone, I am using a Sage code to compute galois group of a polynomial of degree 24. It is a symbolic polynomial so this code gives possible galois groups. When I run it for lower degrees it gives output but when the polynomial has degree 24 it doesn't compute. Because it computes subgroups of a group of order over 264 million. I know it is very hard to find these groups but i need it. I tried so hard for 3 weeks or more. I use sagemathcell, cocalc and Oracle Virtual Box. I tried so many things but they didn't work. It gives GAPerror: reached pre-set memory limit OR runtime error Gap produced error output, error, variable \$sage37 must have a value. I guess the problem is computing conjugacy classes of subgroups. How can I eliminate this Gap error?
P.S1: I am very beginner at Sage. My knowledge about coding, programming etc. is very small. P.S2: I cannot write the code here because it doesn't belong to me. I found it on internet. But if you want to see I can send you the link.
edit retag close merge delete
1
Can you post the polynomial?
For example: https ://example .com. | 2020-10-27 04:28:29 | {"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": 0.2429567277431488, "perplexity": 725.8558260982469}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1603107893011.54/warc/CC-MAIN-20201027023251-20201027053251-00537.warc.gz"} |
http://math.tutorcircle.com/geometry/can-a-triangle-be-acute-and-scalene.html | Sales Toll Free No: 1-800-481-2338
# Can a Triangle be Acute and Scalene?
TopThe angles of Acute Triangle lie between 0 and 90 degrees and the angles which are less than 90 degree are known as acute angles.
Now we will discuss can a triangle be acute and scalene?
No, it is not possible for all Triangles because a Scalene Triangle has all its angles of different degrees. When we assume a triangle which has all the angles of 60 degrees then this triangle is not scalene triangle. So we cannot say that all the triangles are acute and scalene. Those triangles which have different angles are acute as well as scalene triangle.
A scalene triangle is a type of an acute triangle because an Acute Angle has all angles less than 90 degrees. It satisfies all properties of a scalene triangle.
If all sides and angles of a triangle are different then the triangle is known as a scalene triangle. A scalene triangle can also have one Right Angle.
In this given diagram all the angles are different. So this is a scalene triangle.
Now we have another triangle which is not a scalene triangle.
In this triangle all the angles are equal so it is not a scalene triangle.
Some Properties of scalene triangle are:
A scalene triangle has interior angles, area, and perimeter. In a scalene triangle all the interior angles are different; it means all the angles are of different degrees. If the triangle has two of its angles of same degree then the triangle is said to be an Isosceles Triangle. If the triangle has all its angles of same degrees then the triangle is known as an Equilateral Triangle. Then the area of scalene triangle is given by-
Area = √s(s – u) (s – v) (s – w),
Where, the value of‘s’ is the half of the perimeter, and the 's' of a scalene triangle is: s = $\frac{u+v+w}{2}$
These all are the properties of a scalene triangle. | 2015-01-27 16:51:47 | {"extraction_info": {"found_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": 0.5417583584785461, "perplexity": 320.52495421995013}, "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-2015-06/segments/1422115860277.59/warc/CC-MAIN-20150124161100-00166-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://nbviewer.jupyter.org/github/BMClab/bmc/blob/master/notebooks/Three-dimensional%20rigid%20body%20Kinetics.ipynb | # Three-dimensional rigid body kinetics¶
Renato Naville Watanabe
## The Newton-Euler laws¶
The Newton-Euler laws remain valid in the three-dimensional motion of a rigid body (for revision on Newton-Euler laws, see this notebook about these laws).
$$\vec{\bf{F}} = m\vec{\bf{a_{cm}}}$$$$\vec{\bf{M_O}} = \frac{d\vec{\bf{H_O}}}{dt}$$
## Resultant force and moments¶
The resultant force and the resultant moment around a point O are computed in the same way of the two-dimensional case.
$$\vec{\bf{F}} = \sum\limits_{i=1}^n \vec{\bf{F_n}}$$$$\vec{\bf{M_O}} = \sum\limits_{i=1}^n \vec{\bf{r_{i/O}}} \times \vec{\bf{F_i}}$$
## Deduction of the angular momentum in three-dimensional movement¶
The major difference that appears when we are dealing with three-dimensional motions is to compute the derivative of the angular momentum. For the sake of simplicity, the analysis will only consider the point O as the center of mass of the body.
We begin computing the angular momentum of a rigid body around its center of mass.
$$\vec{\boldsymbol{H_{cm}}} = \int_B \vec{\boldsymbol{r_{/cm}}} \times \vec{\boldsymbol{v}}\,dm = \int \vec{\boldsymbol{r_{/cm}}} \times (\vec{\boldsymbol{\omega}}\times\vec{\boldsymbol{r_{/cm}}})\,dm$$
where $\vec{\boldsymbol{r_{/cm}}}$ is the vector from the point O to the position of the infinitesimal mass considered in the integral. For simplicity of the notation, we will use $\vec{\boldsymbol{r}} = \vec{\boldsymbol{r_{/cm}}}$.
So, the angular momentum is:
$$\vec{\boldsymbol{H_{cm}}} = \int \vec{\boldsymbol{r}} \times (\vec{\boldsymbol{\omega}}\times\vec{\boldsymbol{r}})\,dm = \int (r_x\hat{\boldsymbol{i}} + r_y\hat{\boldsymbol{j}}+r_z\hat{\boldsymbol{k}}) \times \left[(\omega_x\hat{\boldsymbol{i}} + \omega_y\hat{\boldsymbol{j}}+\omega_z\hat{\boldsymbol{k}})\times(r_x\hat{\boldsymbol{i}} + r_y\hat{\boldsymbol{j}}+r_z\hat{\boldsymbol{k}})\right]\,dm$$
$$\vec{\boldsymbol{H_{cm}}}= \int (r_x\hat{\boldsymbol{i}} + r_y\hat{\boldsymbol{j}}+r_z\hat{\boldsymbol{k}}) \times \left[(\omega_x r_y\hat{\boldsymbol{k}} - \omega_xr_z\hat{\boldsymbol{j}} - \omega_yr_x\hat{\boldsymbol{k}} + \omega_yr_z\hat{\boldsymbol{i}}+ \omega_zr_x\hat{\boldsymbol{j}}- \omega_zr_y\hat{\boldsymbol{i}}\right]\,dm$$
$$\vec{\boldsymbol{H_{cm}}}= \int-\omega_x r_xr_y\hat{\boldsymbol{j}} -\omega_x r_xr_z\hat{\boldsymbol{k}} +\omega_y r_x^2\hat{\boldsymbol{j}} + \omega_zr_x^2\hat{\boldsymbol{k}}+ \omega_xr_y^2\hat{\boldsymbol{i}} -\omega_yr_xr_y\hat{\boldsymbol{i}}-\omega_yr_yr_z\hat{\boldsymbol{k}}+\omega_zr_y^2\hat{\boldsymbol{k}}+\omega_x r_z^2\hat{\boldsymbol{i}} +\omega_y r_z^2\hat{\boldsymbol{j}} -\omega_z r_xr_z\hat{\boldsymbol{i}} - \omega_zr_yr_z\hat{\boldsymbol{j}}\,dm$$
$$\vec{\boldsymbol{H_{cm}}}=\left(\int \omega_xr_y^2 -\omega_yr_xr_y+\omega_x r_z^2-\omega_z r_xr_z\,dm\right)\;\hat{\boldsymbol{i}}+\left(\int-\omega_x r_xr_y +\omega_y r_x^2 +\omega_y r_z^2 - \omega_zr_yr_z\,dm\right)\hat{\boldsymbol{j}}+\left(\int-\omega_x r_xr_z + \omega_zr_x^2-\omega_yr_yr_z+\omega_zr_y^2 \,dm\right)\hat{\boldsymbol{k}}$$
$$\vec{\boldsymbol{H_{cm}}}=\left(\int \omega_x(r_y^2+r_z^2)\,dm+ \int-\omega_yr_xr_y\,dm + \int-\omega_z r_xr_z\,dm\right)\;\hat{\boldsymbol{i}} + \left(\int-\omega_x r_xr_y\,dm +\int\omega_y (r_x^2 +r_z^2)\,dm + \int- \omega_zr_yr_z\,dm\right)\hat{\boldsymbol{j}} + \left(\int-\omega_x r_xr_z\,dm + \int-\omega_yr_yr_z\,dm + \int \omega_z(r_x^2+r_y^2) \,dm\right)\hat{\boldsymbol{k}}$$
$$\vec{\boldsymbol{H_{cm}}}=\bigg(\omega_x\int (r_y^2+r_z^2)\,dm+ \omega_y\int-r_xr_y\,dm + \omega_z\int- r_xr_z\,dm\bigg)\;\hat{\boldsymbol{i}}+\bigg(\omega_x\int- r_xr_y\,dm +\omega_y\int (r_x^2 +r_z^2)\,dm + \omega_z\int-r_yr_z\,dm\bigg)\hat{\boldsymbol{j}} + \bigg(\omega_x\int- r_xr_z\,dm + \omega_y\int-r_yr_z\,dm + \omega_z\int (r_x^2+r_y^2) \,dm\bigg)\hat{\boldsymbol{k}}$$
$$\vec{\boldsymbol{H_{cm}}}=\left(\omega_xI_{xx}^{cm}+ \omega_yI_{xy}^{cm} + \omega_zI_{xz}^{cm}\right)\;\hat{\boldsymbol{i}} + \left(\omega_xI_{xy}^{cm} +\omega_yI_{yy}^{cm} + \omega_zI_{yz}^{cm}\right)\hat{\boldsymbol{j}}+\left(\omega_xI_{yz}^{cm} + \omega_yI_{yz}^{cm} + \omega_zI_{zz}^{cm}\right)\hat{\boldsymbol{k}}$$
## Angular momentum in three-dimensional movement¶
\begin{align} \begin{split} \vec{\boldsymbol{H_{cm}}}=\left[\begin{array}{ccc}I_{xx}^{cm}&I_{xy}^{cm}&I_{xz}^{cm}\\ I_{xy}^{cm}&I_{yy}^{cm}&I_{yz}^{cm}\\ I_{xz}^{cm}&I_{yz}^{cm}&I_{zz}^{cm}\end{array}\right]\cdot \left[\begin{array}{c}\omega_x\\\omega_y\\\omega_z \end{array}\right] = I\vec{\boldsymbol{\omega}} \end{split} \label{eq:angmom} \end{align}
where this matrix is the Matrix of Inertia (or more rigorously, Tensor of Inertia) as defined previously in this notebook about moment of inertia.
## The matrix of inertia is different depending on the body orientation¶
So, to compute the angular momentum of a body we have to multiply the matrix of inertia $I$ of the body by its angular velocity $\vec{\boldsymbol{\omega}}$. The problem on this approach is that the moments and products of inertia depends on the orientation of the body relative to the frame of reference. As they depend on the the distances of each point of the body to the axes, if the body is rotating, the matrix of inertia $I$ will be different at each instant.
## The solution is to attach a frame reference to the body¶
The solution to this problem is to attach a frame of reference to the body. We will denote this frame of reference as $\hat{\boldsymbol{e_1}}$, $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$, with origin in the center of mass of the body. As can be noted from the figure below, the frame of reference moves along the body. Now the matrix of inertia $I$ will be constant relative to this new basis $\hat{\boldsymbol{e_1}}$, $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$.
## The angular velocity in the fixed frame¶
So, we can write the angular momentum vector relative to this new basis. To do this, we must write the angular velocity in this new basis:
$$\vec{\boldsymbol{\omega}} = \omega_1\hat{\boldsymbol{e_1}} + \omega_2\hat{\boldsymbol{e_2}} + \omega_3\hat{\boldsymbol{e_3}}$$
Note that this angular velocity is the same vector that we used previously in Eq. \eqref{eq:angmom}. We are just describing it in a basis attached to the body (local basis).
## The fixed frame is chosen in a way that the matrix of inertia is a diagonal matrix¶
As we can choose the basis versors as we want, we can choose them so as to the products of inertia be equal to zero. This can always be done. If the body has axes of symmetry, we can choose these axes (principal axes) as the direction of the basis to the products of inertia be equal to zero. Having the basis $\hat{\boldsymbol{e_1}}$, $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$, the matrix of inertia will be a diagonal matrix:
$$I = \left[\begin{array}{ccc}I_1&0&0\\ 0&I_2&0\\ 0&0&I_3\end{array}\right]$$
## The angular momentum in the fixed frame¶
So, using the basis in the direction of the principal axes of the body the angular momentum simplifies to:
$$\vec{\boldsymbol{H_{cm}}} = I\vec{\boldsymbol{\omega}} = I_1\omega_1 \hat{\boldsymbol{e_1}} + I_2\omega_2 \hat{\boldsymbol{e_2}} +I_3\omega_3 \hat{\boldsymbol{e_3}} \label{eq:angmomprinc}$$
## Derivative of the angular momentum¶
For the second Newton-Euler law, we must compute the derivative of the angular momentum. So, we derive the angular momentum in Eq. \eqref{eq:angmomprinc}. As the versors $\hat{\boldsymbol{e_1}}$, $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$ are varying in time, we must consider their derivatives.
$$\frac{d\vec{\boldsymbol{H_{cm}}}}{dt} = I_1\dot{\omega_1}\hat{\boldsymbol{e_1}} + I_2\dot{\omega_2}\hat{\boldsymbol{e_2}}+I_3\dot{\omega_3}\hat{\boldsymbol{e_3}} + I_1\omega_1\frac{d\hat{\boldsymbol{e_1}}}{dt} + I_2\omega_2\frac{d\hat{\boldsymbol{e_2}}}{dt}+I_3\omega_3\frac{d\hat{\boldsymbol{e_3}}}{dt} \label{eq:derivangmom}$$
Now it only remains to find an expression for the derivative of the versors $\frac{d\hat{\boldsymbol{e_1}}}{dt}$, $\frac{d\hat{\boldsymbol{e_2}}}{dt}$ and $\frac{d\hat{\boldsymbol{e_3}}}{dt}$.
## Angular velocity (from Kane and Levinson (1985))¶
It would be interesting to find some relation between these derivatives and the angular velocity of the body.
First we will express the angular velocity $\vec{\boldsymbol{\omega}}$ in terms of these derivatives.
Remember that the angular velocity is described as a vector in the orthogonal plane of the rotation. ($\vec{\boldsymbol{\omega_1}} = \frac{d\theta_1}{dt}\hat{\boldsymbol{e_1}}$, $\vec{\boldsymbol{\omega_2}} = \frac{d\theta_2}{dt}\hat{\boldsymbol{e_2}}$ and $\vec{\boldsymbol{\omega_3}} = \frac{d\theta_3}{dt}\hat{\boldsymbol{e_3}}$).
Note also that the derivative of the angle $\theta_1$ can be described as the projection of the vector $\frac{d\hat{\boldsymbol{e_2}}}{dt}$ on the vector $\hat{\boldsymbol{e_3}}$.
This can be written by using the scalar product between these vectors: $\frac{d\theta_1}{dt} = \frac{d\hat{\boldsymbol{e_2}}}{dt}\cdot \hat{\boldsymbol{e_3}}$. Similarly, the same is valid for the angles in the other two directions: $\frac{d\theta_2}{dt} = \frac{d\hat{\boldsymbol{e_3}}}{dt}\cdot \hat{\boldsymbol{e_1}}$ and $\frac{d\theta_3}{dt} = \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_2}}$.
## The derivative of the versors¶
Now, we must isolate the derivative of the versors to substitute them in the Eq. \eqref{eq:derivangmom}. To isolate the derivative of the versor $\hat{\boldsymbol{e_1}}$, first we cross multiply both sides of the equation above by $\hat{\boldsymbol{e_1}}$:
$$\vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_1}} = - \left(\frac{d\hat{\boldsymbol{e_3}}}{dt}\cdot \hat{\boldsymbol{e_1}}\right) \hat{\boldsymbol{e_3}} + \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_2}}\right) \hat{\boldsymbol{e_2}}$$
If we note that the term multipliying $\hat{\boldsymbol{e_3}}$ in the right side of the identity can be obtained by $\frac{d\hat{\boldsymbol{e_1}}\cdot\hat{\boldsymbol{e_3}} }{dt} = \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_3}} + \frac{d\hat{\boldsymbol{e_3}}}{dt}\cdot\hat{\boldsymbol{e_1}} \rightarrow 0 = \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_3}} + \frac{d\hat{\boldsymbol{e_3}}}{dt}\cdot\hat{\boldsymbol{e_1}} \rightarrow \frac{d\hat{\boldsymbol{e_3}}}{dt}\cdot\hat{\boldsymbol{e_1}} = - \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_3}}$ (the scalar product $\hat{\boldsymbol{e_1}}\cdot\hat{\boldsymbol{e_3}}$ is zero because these vectors are orthogonal ), we can write the equation above becomes:
$$\vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_1}} = \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_3}}\right) \hat{\boldsymbol{e_3}} + \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_2}}\right) \hat{\boldsymbol{e_2}}$$
Finally, we can note that $\frac{d\hat{\boldsymbol{e_1}}\cdot\hat{\boldsymbol{e_1}} }{dt} = \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_1}} + \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_1}} \rightarrow \frac{d(1)}{dt} = 2\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_1}} \rightarrow \frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_1}} = 0$. As this term is equal to zero, we can add it to the expression above:
$$\vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_1}} = \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot\hat{\boldsymbol{e_1}}\right)\hat{\boldsymbol{e_1}} + \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_3}}\right) \hat{\boldsymbol{e_3}} + \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_2}}\right) \hat{\boldsymbol{e_2}}$$
Note that the expression above is just another manner to write the vector $\frac{d\hat{\boldsymbol{e_1}}}{dt}$, as any vector can be described by the sum of the projections on each of the versors forming a basis.
So, the derivative of the versor $\hat{\boldsymbol{e_1}}$ can be written as:
$$\frac{d\hat{\boldsymbol{e_1}}}{dt} = \vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_1}}$$
Similarly, the derivatives of the versors $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$ can be written as:
$$\frac{d\hat{\boldsymbol{e_2}}}{dt} = \vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_2}} ~~~~~~~~\text{and} ~~~~~~ \frac{d\hat{\boldsymbol{e_3}}}{dt} = \vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_3}}$$
## The derivative of the angular momentum¶
Now we can get back to the equation describing the derivative of the angular momentum (Eq.\eqref{eq:derivangmom}):
\begin{align} \begin{split} \frac{d\vec{\boldsymbol{H_{cm}}}}{dt} =&I_1\dot{\omega_1}\hat{\boldsymbol{e_1}} + I_2\dot{\omega_2}\hat{\boldsymbol{e_2}}+I_3\dot{\omega_3}\hat{\boldsymbol{e_3}} + I_1\omega_1\frac{d\hat{\boldsymbol{e_1}}}{dt} + I_2\omega_2\frac{d\hat{\boldsymbol{e_2}}}{dt}+I_3\omega_3\frac{d\hat{\boldsymbol{e_3}}}{dt}=\\ =& I_1\dot{\omega_1}\hat{\boldsymbol{e_1}} + I_2\dot{\omega_2}\hat{\boldsymbol{e_2}}+I_3\dot{\omega_3}\hat{\boldsymbol{e_3}} + I_1\omega_1(\vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_1}}) + I_2\omega_2(\vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_2}})+I_3\omega_3(\vec{\boldsymbol{\omega}} \times \hat{\boldsymbol{e_3}}) = \\ =& I_1\dot{\omega_1}\hat{\boldsymbol{e_1}} + I_2\dot{\omega_2}\hat{\boldsymbol{e_2}}+I_3\dot{\omega_3}\hat{\boldsymbol{e_3}} + \vec{\boldsymbol{\omega}} \times I_1\omega_1\hat{\boldsymbol{e_1}} + \vec{\boldsymbol{\omega}} \times I_2\omega_2\hat{\boldsymbol{e_2}}+\vec{\boldsymbol{\omega}} \times I_3\omega_3\hat{\boldsymbol{e_3}} = \\ =& I_1\dot{\omega_1}\hat{\boldsymbol{e_1}} + I_2\dot{\omega_2}\hat{\boldsymbol{e_2}}+I_3\dot{\omega_3}\hat{\boldsymbol{e_3}} + \vec{\boldsymbol{\omega}} \times (I_1\omega_1\hat{\boldsymbol{e_1}} + I_2\omega_2\hat{\boldsymbol{e_2}} + I_3\omega_3\hat{\boldsymbol{e_3}})=\\ =&I\vec{\dot{\boldsymbol{\omega}}} + \vec{\boldsymbol{\omega}} \times (I\vec{\boldsymbol{\omega}}) \end{split} \label{eq:derivangmomVec} \end{align}
Performing the cross products, we can get the expressions for each of the coordinates attached to the body:
\begin{align} \begin{split} \frac{d\vec{\boldsymbol{H_{cm}}}}{dt} =\left[\begin{array}{c}I_1\dot{\omega_1}\\I_2\dot{\omega_2}\\I_3\dot{\omega_3}\end{array}\right] + \left[\begin{array}{c}\omega_1\\\omega_2\\\omega_3\end{array}\right] \times \left[\begin{array}{c}I_1\omega_1\\I_2\omega_2\\I_3\omega_3\end{array}\right] = \left[\begin{array}{c}I_1\dot{\omega_1} + \omega_2\omega_3(I_3-I_2)\\I_2\dot{\omega_2}+\omega_1\omega_3(I_1-I_3)\\I_3\dot{\omega_3}+\omega_1\omega_2(I_2-I_1)\end{array}\right] \end{split} \end{align}
## Newton-Euler laws¶
Having computed the derivative of the angular momentum, we have the final forms of the Newton-Euler laws:
$$F_x = ma_{cm_x}$$$$F_y = ma_{cm_y}$$$$F_z = ma_{cm_z}$$$$M_{cm_1} = I_1\dot{\omega_1} + \omega_2\omega_3(I_3-I_2) \label{eq:M1}$$$$M_{cm_2} = I_2\dot{\omega_2}+\omega_1\omega_3(I_1-I_3) \label{eq:M2}$$$$M_{cm_3} = I_3\dot{\omega_3}+\omega_1\omega_2(I_2-I_1) \label{eq:M3}$$
Note that the equations of the forces are written in the global frame of reference and the equations of the moments are described in the frame of reference of the body. So, before using Eq.~\eqref{eq:derivangmomVec} or the equations Eq.\eqref{eq:M1},\eqref{eq:M2} and \eqref{eq:M3} you must transform all the forces and moment-arms to the frame of reference of the body by using rotation matrices.
Below are shown some examples with three-dimensional kinematic data to find the forces and moments acting on the body.
## Examples¶
### 1 ) 3D pendulum bar¶
At the file '../data/3Dpendulum.txt' there are 3 seconds of data of 3 points of the three-dimensional cylindrical pendulum, very similar to the pendulum shown in the notebook about free-body diagrams, except that it can move in every direction. Also it has a motor at the upper part of the cylindrical bar producing torques to move the bar. It has mass $m=1$ kg, length $l=1$ m and radius $r=0.1$ m.
The point m1 is at the upper part of the cylinder and is the origin of the system.
The point m2 is at the center of mass of the cylinder.
The point m3 is a point at the surface of the cylinder.
The free-body diagram of the 3d pendulum is depicted below. There is the gravitational force acting at the center of mass of gravity of the body and the torque $M_1$ due to the motor acting on the pendulum and the force $F_1$ due to the restraint at the upper part of the cylinder. Together with the forces, the local basis $\hat{\boldsymbol{e_1}}$, $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$ in the direction of the principal axes an origin at the center of mass of the body is also shown.
The resultant forces acting on the cylinder is:
$$\vec{\boldsymbol{F}} = \vec{\boldsymbol{F_O}} - mg\hat{\boldsymbol{k}}$$
So, the first Newton-Euler law, at each component of the global basis, is written as:
\begin{align} \begin{split} F_{O_x} &= ma_{cm_x} &\rightarrow F_{O_x} &= ma_{cm_x} \\ F_{O_y} &= ma_{cm_y} &\rightarrow F_{O_y} &= ma_{cm_y}\\ F_{O_z} - mg &= ma_{cm_z} &\rightarrow F_{O_z} &= ma_{cm_z} + mg \end{split} \label{eq:fnependulum} \end{align}
Now, the resultant moment applied to the body, computed relative to the center of mass, is:
$$\vec{\boldsymbol{M}} = \vec{\boldsymbol{M_O}} + \vec{\boldsymbol{r_{O/cm}}} \times \vec{\boldsymbol{F_O}}$$
So, the second Newton-Euler law, at each of the components at the local basis of the body, is written as:
\begin{align} \begin{split} M_{O_1} + MFocm_1 &= I_1\dot{\omega_1} + \omega_2\omega_3(I_3-I_2) \rightarrow M_{O_1} &= I_1\dot{\omega_1} + \omega_2\omega_3(I_3-I_2) - MFocm_1\\ M_{O_2} + MFocm_2 &= I_2\dot{\omega_2} + \omega_1\omega_3(I_1-I_3) \rightarrow M_{O_2} &= I_2\dot{\omega_2} + \omega_1\omega_3(I_1-I_3) - MFocm_2\\ M_{O_3} + MFocm_3 &= I_3\dot{\omega_3} + \omega_1\omega_2(I_2-I_1) \rightarrow M_{O_3} &= I_3\dot{\omega_3} + \omega_1\omega_2(I_2-I_1) - MFocm_3 \end{split} \end{align}
where $\vec{\boldsymbol{MFocm}} = \vec{\boldsymbol{r_{O/cm}}} \times \vec{\boldsymbol{F_O}}$.
The moments of inertia at the directions of $\hat{\boldsymbol{e_1}}$, $\hat{\boldsymbol{e_2}}$ and $\hat{\boldsymbol{e_3}}$ are, $I_1 = \frac{mR^2}{12}$ and $I_2=I_3=\frac{m(3R^2+l^2)}{12}$. Now, to compute the moment $\vec{\boldsymbol{M_O}}$ and the force $\vec{\boldsymbol{F_O}}$, we will need to find the acceleration of the center of mass $\vec{\boldsymbol{a_{cm}}}$, the angular velocity $\vec{\boldsymbol{\omega}}$, the time-derivatives of each component of the angular velocity, and the moment-arm $\vec{\boldsymbol{r_{O/cm}}}$ to compute the torque due to the force $\vec{\boldsymbol{F_O}}$. These signals will come from the kinematic data file.
First, we need to open the file with the data:
In [1]:
import numpy as np
import matplotlib.pyplot as plt
%matplotlib notebook
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
data = np.loadtxt('../data/3dPendulum.txt', skiprows=1, delimiter = ',')
m = 1
g= 9.81
l = 1
r = 0.1
I1 = m*r**2/12
I2 = m*(3*r**2+l**2)/12
I3 = I2
Now, we assign the proper columns to variables:
In [2]:
t = data[:,0]
m1 = data[:,1:4]
m2 = data[:,4:7]
m3 = data[:,7:]
As the center of mass is the data contained in m2, we can find the acceleration of the center of mass $\vec{\boldsymbol{a_{cm}}}$. This will be performed by deriving numerically the position of the center of mass twice. The numerical derivative of a function $f(t)$ with the samples $f(i)$ can be performed by taking the forward difference of the values $f(i)$:
$$\frac{df}{dt}(i) = \frac{f(i+1)-f(i)}{\Delta t}$$
The numerical derivative could be obtained by taking the backward differences as well:
$$\frac{df}{dt}(i) = \frac{f(i)-f(i-1)}{\Delta t}$$
A better estimation of the derivative of the time derivative of the function $f(t)$ would be obtained by the average value between the estimations using the backward and forward differences (this subject is treated in this notebook about data filtering):
$$\frac{df}{dt}(i) = \frac{\frac{f(i+1)-f(i)}{\Delta t} + \frac{f(i)-f(i-1)}{\Delta t}}{2} = \frac{f(i+1)-f(i-1)}{2\Delta t} \label{eq:centralderiv}$$
So, the acceleration of the center of mass, is:
In [3]:
dt = t[1]-t[0]
rcm = m2
vcm = (rcm[2:,:]-rcm[0:-2,:])/(2*dt)
acm = (vcm[2:,:]-vcm[0:-2,:])/(2*dt)
Now we can find the force $\vec{\boldsymbol{F_O}}$ using the Eq. \eqref{eq:fnependulum}.
In [4]:
Fox = m*acm[:,0]
Foy = m*acm[:,1]
Foz = m*acm[:,2] + m*g
Fo=np.hstack((Fox.reshape(-1,1),Foy.reshape(-1,1),Foz.reshape(-1,1)))
plt.figure()
plt.plot(t[0:acm.shape[0]], Fox)
plt.plot(t[0:acm.shape[0]], Foy,'--')
plt.plot(t[0:acm.shape[0]], Foz)
plt.legend(('x','y','z'))
plt.title('Force (N)')
plt.show()
Now, to find the moment being applied to the body, we need to compute a basis attached to the body
In [5]:
e1 = m2 - m1
e1 = e1/np.linalg.norm(e1,axis=1,keepdims=True)
e2 = m3-m2
e2 = e2/np.linalg.norm(e2,axis=1,keepdims=True)
e3 = np.cross(e1,e2,axis=1)
e3 = e3/np.linalg.norm(e3,axis=1,keepdims=True)
e2 = np.cross(e3,e1, axis=1)
e2 = e2/np.linalg.norm(e2,axis=1,keepdims=True)
To compute the moment applied to the body, we need the angular velocity described in the basis attached to the body. The easiest way to find this angular velocity is to use Eq. \eqref{eq:angvel}, repeated here.
$$\vec{\boldsymbol{\omega}} = \left(\frac{d\hat{\boldsymbol{e_2}}}{dt}\cdot \hat{\boldsymbol{e_3}}\right) \hat{\boldsymbol{e_1}} + \left(\frac{d\hat{\boldsymbol{e_3}}}{dt}\cdot \hat{\boldsymbol{e_1}}\right) \hat{\boldsymbol{e_2}} + \left(\frac{d\hat{\boldsymbol{e_1}}}{dt}\cdot \hat{\boldsymbol{e_2}}\right) \hat{\boldsymbol{e_3}}$$
To do this we need the derivatives of the basis versors. This will also be performed with Eq. \eqref{eq:centralderiv}.
To perform the computation of the angular velocity remember that the scalar product between two vectors is given by:
$$\vec{\bf{v}}\cdot\vec{\bf{w}} = \left[\begin{array}{c}v_x\\v_y\\v_z \end{array}\right]\cdot \left[\begin{array}{c}w_x\\w_y\\w_z \end{array}\right] = v_x.w_x+v_yw_y+v_zw_z$$
In [6]:
de1dt = (e1[2:,:]-e1[0:-2,:])/(2*dt)
de2dt = (e2[2:,:]-e2[0:-2,:])/(2*dt)
de3dt = (e3[2:,:]-e3[0:-2,:])/(2*dt)
omega = np.hstack((np.sum(de2dt*e3[1:-1,:], axis = 1).reshape(-1,1),
np.sum(de3dt*e1[1:-1,:], axis = 1).reshape(-1,1),
np.sum(de1dt*e2[1:-1,:], axis = 1).reshape(-1,1)))
From the angular velocity vector we can obtain the derivatives of each component of it, also needed to compute the moment applied to the body. To do this we will use Eq. \eqref{eq:centralderiv}:
In [7]:
alpha = (omega[2:,:]-omega[0:-2,:])/(2*dt)
It remains to find the moment caused by the force $\vec{\boldsymbol{F_O}}$, $\vec{\boldsymbol{MFocm}} = \vec{\boldsymbol{r_{O/cm}}} \times \vec{\boldsymbol{F_O}}$. The moment-arm $\vec{\boldsymbol{r_{O/cm}}} =-\vec{\boldsymbol{r_{cm}}}$.
In [8]:
MFocm = np.cross(-rcm[2:-2], Fo, axis = 1)
The problem is that this moment is in the global basis. We need to transform it to the local basis. This will be performed using the rotation matrix of the bar. Each row of this matrix is one of the basis versors. Note that at each instant the matrix of rotation $R$ will be different. After the matrix is formed, we can find the components of the moment $\vec{\boldsymbol{MFocm}}$ in the local basis by multiplying the matrix of rotation $R$ by the vector $\vec{\boldsymbol{MFocm}}$.
In [9]:
MFocmRotated = np.zeros_like(MFocm)
for i in range(MFocm.shape[0]):
R = np.vstack((e1[i,:],e2[i,:],e3[i,:]))
MFocmRotated[i,:]=R@MFocm[i,:]
In [10]:
Mo1 = I1*alpha[:,0] + omega[0:alpha.shape[0],1]*omega[0:alpha.shape[0],2]*(I3-I2) - MFocmRotated[:,0]
Mo2 = I2*alpha[:,1] + omega[0:alpha.shape[0],0]*omega[0:alpha.shape[0],2]*(I1-I3) - MFocmRotated[:,1]
Mo3 = I3*alpha[:,2] + omega[0:alpha.shape[0],0]*omega[0:alpha.shape[0],1]*(I2-I1) - MFocmRotated[:,2]
plt.figure()
plt.plot(t[2:-2], Mo1)
plt.plot(t[2:-2], Mo2)
plt.plot(t[2:-2], Mo3)
plt.legend(('$e_1$','$e_2$','$e_3$'))
plt.show()
We could also have used the vectorial form of the derivative of the angular momentum (Eq. \eqref{eq:derivangmomVec}) and instead of writing three lines of code, write only one. The result is the same.
In [11]:
I = np.array([[I1,0,0],[0,I2,0],[0,0,I3]])
Mo = (I@alpha.T).T + np.cross(omega[0:alpha.shape[0],:], (I@omega[0:alpha.shape[0],:].T).T,axis=1) - MFocmRotated
plt.figure()
plt.plot(t[2:-2], Mo)
plt.legend(('$e_1$','$e_2$','$e_3$'))
plt.show()
## 2 ) Data from postural control¶
This example will use real data from a subject during quiet standing during 60 seconds. This data is from the database freely available at https://github.com/demotu/datasets/tree/master/PDS. The data of this subject is in the file '../data/postureData.txt'.
The mass of the subject was $m = 53$ kg and her height was $h= 1.65$ m.
The free-body diagram is very similar to the free-body diagram shown in the notebook about free-body diagram, except that the force $\vec{\boldsymbol{F_A}}$ and the moment $\vec{\boldsymbol{M_A}}$ have components at all 3 directions.
So, the first Newton-Euler law, at each component of the global basis, is written as (note that in these data, the vertical direction is the y coordinate):
\begin{align} \begin{split} F_{A_x} &= ma_{cm_x} &\rightarrow F_{O_x} &= ma_{cm_x} \\ F_{A_y} - mg &= ma_{cm_y} &\rightarrow F_{O_y} &= ma_{cm_y} + mg\\ F_{A_z} &= ma_{cm_z} &\rightarrow F_{O_z} &= ma_{cm_z} \end{split} \label{eq:fnequiet} \end{align}
Now, the resultant moment applied to the body, computed relative to the center of mass, is:
$$\vec{\boldsymbol{M}} = \vec{\boldsymbol{M_A}} + \vec{\boldsymbol{r_{A/cm}}} \times \vec{\boldsymbol{F_A}}$$
So, the second Newton-Euler law, at each of the components at the local basis of the body, is written as:
\begin{align} \begin{split} \vec{\boldsymbol{M_A}} + \vec{\boldsymbol{MFacm}} &= I\left[\begin{array}{c}\dot{\omega_1}\\\dot{\omega_2}\\\dot{\omega_3}\end{array}\right] + \vec{\boldsymbol{\omega}}\times I\vec{\boldsymbol{\omega}} \rightarrow \vec{\boldsymbol{M_A}} = I\left[\begin{array}{c}\dot{\omega_1}\\\dot{\omega_2}\\\dot{\omega_3}\end{array}\right] + \vec{\boldsymbol{\omega}} \times I\vec{\boldsymbol{\omega}}- \vec{\boldsymbol{MFacm}} \end{split} \end{align}
where $\vec{\boldsymbol{MFAcm}} = \vec{\boldsymbol{r_{A/cm}}} \times \vec{\boldsymbol{F_A}}$.
Now we open the data and assign the coordinates of each marker to a variable.
In [12]:
data = np.loadtxt('../data/postureData.txt', skiprows=1, delimiter = ',')
t = data[:,0]
dt = t[1]-t[2]
rcm = data[:,1:4] #center of mass
rrA = data[:,4:7] # Right lateral malleolus
rlA = data[:,7:] # Left lateral maleolus
The body will be approximated by a cylinder with the height of the subject and radius equal to half of the mean distances between the right and left medial malleoli.
In [13]:
m = 53
h = 1.65
r = np.mean(np.linalg.norm(rrA-rlA, axis = 1))/2
I1 = m*r**2/12 # longitudnal
I2 = m*(3*r**2+h**2)/12 # sagittal
I3 = I2 # transversal
In [14]:
# acceleration of the center of mass by deriving the center of mass twice
vcm = (rcm[2:,:]-rcm[0:-2,:])/(2*dt)
acm = (vcm[2:,:]-vcm[0:-2,:])/(2*dt)
FAx = m*acm[:,0]
FAy = m*acm[:,1] + m*g
FAz = m*acm[:,2]
FA=np.hstack((FAx.reshape(-1,1),FAy.reshape(-1,1),FAz.reshape(-1,1)))
Now we form the basis attached to the body. The first versor $\hat{\boldsymbol{e_1}}$ will be a versor from the midpoint between the medial malleoli and the center of mass of the body. The second versor $\hat{\boldsymbol{e_2}}$ will be a versor from the right to the left malleolus. The third versor $\hat{\boldsymbol{e_3}}$ will be a cross product between $\hat{\boldsymbol{e_1}}$ and $\hat{\boldsymbol{e_2}}$.
In [15]:
e1 = rcm - (rlA+rrA)/2
e1 = e1/np.linalg.norm(e1,axis=1,keepdims=True)
e2 = rlA-rrA
e2 = e2/np.linalg.norm(e2,axis=1,keepdims=True)
e3 = np.cross(e1,e2,axis=1)
e3 = e3/np.linalg.norm(e3,axis=1,keepdims=True)
e2 = np.cross(e3,e1, axis=1)
e2 = e2/np.linalg.norm(e2,axis=1,keepdims=True)
Now we can find the angular velocity $\vec{\boldsymbol{\omega}}$ at the basis attached to the body using Eq.\eqref{eq:angvel} and the time derivatives of its components.
In [16]:
de1dt = (e1[2:,:]-e1[0:-2,:])/(2*dt)
de2dt = (e2[2:,:]-e2[0:-2,:])/(2*dt)
de3dt = (e3[2:,:]-e3[0:-2,:])/(2*dt)
omega = np.hstack((np.sum(de2dt*e3[1:-1,:], axis = 1).reshape(-1,1),
np.sum(de3dt*e1[1:-1,:], axis = 1).reshape(-1,1),
np.sum(de1dt*e2[1:-1,:], axis = 1).reshape(-1,1)))
alpha = (omega[2:,:]-omega[0:-2,:])/(2*dt)
Now we need to find the moment caused by the force at the ankles $\vec{\boldsymbol{F_A}}$, $\vec{\boldsymbol{MFAcm}} = \vec{\boldsymbol{r_{A/cm}}} \times \vec{\boldsymbol{F_A}}$. The moment-arm $\vec{\boldsymbol{r_{A/cm}}}$ is the vector from the center of mass to the midpoint of the lateral malleoli.
Besides the description of the moment due to the force $\vec{\boldsymbol{F_A}}$ in the basis attached to the body, we will also describe the force $\vec{\boldsymbol{F_A}}$ at the local basis. This is useful because it has an anatomical meaning. After this we can use the equations of Newton-Euler to obtain the moment at the ankle.
After having all signals described in the basis of the body, the moment being applied by the muscles of the ankle is computed using Eq. \eqref{eq:derivangmomVec}.
In [17]:
#computing the moment due to the ankle force
racm = (rlA+rrA)/2-rcm
MFAcm = np.cross(racm[0:FA.shape[0],:], FA, axis =1)
MFAcmRotated = np.zeros_like(MFAcm)
FARotated = np.zeros_like(MFAcm)
# rotation matrix and description of the ankle force and moment due to the ankle force
for i in range(MFAcm.shape[0]):
R = np.vstack((e1[i,:],e2[i,:],e3[i,:]))
MFAcmRotated[i,:]=R@MFAcm[i,:]
FARotated[i,:]=R@FA[i,:]
# Second Newton-Euler law to obtain the ankle moment
I = np.array([[I1,0,0],[0,I2,0],[0,0,I3]])
MA = (I@alpha.T).T + np.cross(omega[0:alpha.shape[0],:], (I@omega[0:alpha.shape[0],:].T).T,axis=1) - MFAcmRotated
plt.figure()
plt.plot(t[2:-2], MA)
plt.legend(('longitudinal','sagittal','mediolateral'))
plt.title('Ankle Torque')
plt.xlabel('t (s)')
plt.ylabel('M (N.m)')
plt.show()
plt.figure()
plt.plot(t[2:-2], FARotated[:,0])
plt.plot(t[2:-2], FARotated[:,1])
plt.plot(t[2:-2], FARotated[:,2])
plt.title('Ankle Force')
plt.legend(('longitudinal','sagittal','mediolateral'))
plt.xlabel('t (s)')
plt.ylabel('F (N)')
plt.show()
## Problems¶
Compute the derivative of the angular momentum of the foot and the leg using one of the following data acquired during the gait of a subject: '../data/BiomecII2018_gait_d.txt' or '../data/BiomecII2018_gait_n.txt'.
## References¶
• Beer, F P; Johnston, E R; Cornwell, P. J.(2010) Vector Mechanics for Enginners: Dynamics.
• Kane T, Levinson D (1985) Dynamics: Theory and Applications. McGraw-Hill, Inc
• Hibbeler, R. C. (2005) Engineering Mechanics: Dynamics.
• Taylor, J, R (2005) Classical Mechanics
• Winter D. A., (2009) Biomechanics and motor control of human movement. John Wiley and Sons.
• Santos DA, Fukuchi CA, Fukuchi RK, Duarte M. (2017) A data set with kinematic and ground reaction forces of human balance. PeerJ Preprints.
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http://www.computer.org/csdl/mags/cs/2005/04/c4067.html | The Community for Technology Leaders
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Issue No.04 - July/August (2005 vol.7)
pp: 67
Published by the IEEE Computer Society
ABSTRACT
The SIAM 100-Digit Challenge is an entertaining and valuable book that belongs on the shelf of everyone who takes numerical computation seriously. Even the story of how the book came to be is interesting.
Is that Your Final Answer?
The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing, by Folkmar Bornemann et al., SIAM, 2004, ISBN 089871561X, US$57. The SIAM 100-Digit Challenge is an entertaining and valuable book that belongs on the shelf of everyone who takes numerical computation seriously. Even the story of how the book came to be is interesting. In January 2002, Nick Trefethen published an article in SIAM News in which he posed 10 computational problems, each having a single real number as its answer. He challenged readers to solve these problems, and offered a prize of one dollar per correct digit, up to 10 for each problem, and hence up to a total of$100 for all 10 solved with 10 correct digits each. But Trefethen made one mistake: he assumed that there would probably be, at most, one perfect score and went so far as to say, "If anyone gets 50 digits in total, I will be impressed."
Naturally, the computational science community, sensing that its honor was at stake, responded to the challenge with a great big, "Oh yeah?" In all, there were 20 perfect scores and many more with at least 50 correct digits. Trefethen apparently spent $100 of his own funds, plus another$200 from Oxford Scientific Consulting, to give three of the winners the promised prize. The SIAM 100-Digit Challenge consists of descriptions of how the problems were solved, written by some of the winners. David Bailey provides an interesting foreword.
The problems involved many subjects in computational science, ranging from evaluation of a very difficult integral through topics in linear algebra, approximation methods, function minimization, partial differential equations, and the theory of random walk. The 20 winners employed an impressive variety of mathematical techniques to obtain the solutions, including conformal mapping, interval arithmetic, p-adic arithmetic, approximation via complex functions, probability theory, and more. Reading about the various mathematical strategies and software tools used is fascinating: the authors knew how and when to work backward, when to use purely analytic methods, exactly how far Matlab alone could get them, and much, much more. Anyone who thinks that the main topic of numerical analysis is how to reduce round-off will come away from this book with a different opinion.
No mere mortal working in the computational science business can write a review of this book without at least one suggestion of how a problem could have been done even better, or at least differently. My favorite is Problem 7, "Too Large to Be Easy, Too Small to Be Hard." We're given a 20,000 × 20,000 matrix A whose entries are all zero except for the primes 2, 3, 5, 7, ..., 224,737 along the main diagonal and the number 1 in all positions a ij, such that | i - j| is a power of two; we're to compute the (1, 1) element of A-1. The problem's author mentions that because the entries of A are integers, it's possible to do the problem exactly by doing many instances modulo a set of prime numbers. My approach would have been to use the Bareiss algorithm as I described in a previous issue ("Determining the Determinant," Computing in Science & Eng., vol. 2, no. 5, 2000, pp. 63–66). Its advantage is that all intermediate results are integers, but its drawback is that unlike Wiedemann's algorithm, it doesn't make use of A's sparsity.
One topic that Trefethen's problem set didn't touch is computational issues at the interface between combinatorics and statistical physics, especially those problems that are known to be "hard" in the sense of complexity theory. For example, it's well known that random instances of 3-SAT undergo a phase transition between satisfiability and unsatisfiability when the ratio c of clauses to variables passes a critical value. The value of c is approximately 4.25, but as far as I know, the value of c is not known to 10 digits. Another example is the hard-square entropy constant in three dimensions, which requires accurate counting of independent sets of certain grid graphs. We could easily list 10 or more such problems, but it would probably be wise to accumulate a stack of \$100 bills before doing so.
Francis Sullivan is the director of the IDA Center for Computing Sciences in Bowie, Maryland. From 2000 through 2004, he served as CiSE magazine's editor in chief. Contact him at fran@super.org.
FULL ARTICLE
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https://jen20.dev/post/configuring-aws-autoscaling-event-notifications-in-slack/ | # Configuring AWS AutoScaling Event Notifications in Slack
One of the easiest ways of building resilience into a system running in AWS is to use an autoscaling group. Generally speaking, I use one for any service which is required to self-heal - even when aiming to maintain a steady number of instances, as is desirable when running servers for Consul and Nomad, as well as a whole host of other clustered systems. Unhealthy instances can simply be replaced, usually without operator intervention, and launch configurations can be used to simplify upgrading clustered software one instance at a time.
However, it is often useful to be able to easily track activity within the chat system of your choice. In this post, we'll look at how to use Terraform to deploy an AWS Lambda function which posts a message in Slack whenever a scaling operation happens - regardless of whether it was caused by an operator in the AWS console, API-driven changes, or automatic scaling for health.
One of the features of AWS Autoscaling is the ability to deliver notifications to an SNS topic whenever a scaling event happens. We can configure notifications for the following types of events:
• successful launch of a new instance
• failed launch of a new instance
• successful termination of a running instance
• failed termination of a running instance
• test notifications (more on these later)
In Terraform, a resource named aws_autoscaling_notification is used to configure notification delivery. We need to specify the notification event types we are interested in, the names of the autoscaling groups whose events we want, and the ARN of the SNS topic the notifications should be delivered to.
First though, we'll use the aws_sns_topic resource to configure the SNS topic for notifications to be delivered to:
resource "aws_sns_topic" "asg_slack_notify" {
name = "SlackNotify-ASG"
display_name = "Autoscaling Notifications to Slack"
}
Then we can configure notifications to be delievered to the topic we created:
resource "aws_autoscaling_notification" "slack_notify" {
group_names = ["${var.asg_names}"] notifications = [ "autoscaling:EC2_INSTANCE_LAUNCH", "autoscaling:EC2_INSTANCE_TERMINATE", "autoscaling:EC2_INSTANCE_LAUNCH_ERROR", "autoscaling:EC2_INSTANCE_TERMINATE_ERROR", "autoscaling:TEST_NOTIFICATION" ] topic_arn = "${aws_sns_topic.asg_slack_notify.arn}"
}
For now, we're setting the autoscaling group names to the value of a variable named asg_names - we'll look more at how that gets populated later, when we talk about the overall structure of this module.
### Lambda Function
Now we have notifications being delivered, we can write a Lambda function to extract the important information and use the Slack Webhooks API to send messages into the channel of our choice. I'm using JavaScript for this, but in principle you could use any of the supported Lambda platforms.
var https = require('https');
var util = require('util');
exports.handler = function(event, context) {
try {
var message = JSON.parse(event.Records[0].Sns.Message);
var channel = process.env.SLACK_CHANNEL
var webhookId = process.env.SLACK_WEBHOOK
var eventType = message.Event;
var autoScaleGroupName = message.AutoScalingGroupName;
var description = message.Description;
var cause = message.Cause;
var slackMessage = [
"*Event*: " + eventType,
"*Description*: " + description,
"*Cause*: " + cause,
].join("\n");
var postData = {
channel: channel,
text: "*" + autoScaleGroupName + "*",
attachments: [{ text: slackMessage, mrkdwn_in: ["text"] }]
};
var options = {
method: 'POST',
hostname: 'hooks.slack.com',
port: 443,
path: '/services/' + webhookId
};
var req = https.request(options, function(res) {
res.setEncoding('utf8');
res.on('data', function (chunk) {
context.done(null);
});
});
req.on('error', function(e) {
context.fail(e);
console.log('request error: ' + e.message);
});
req.write(util.format("%j", postData));
req.end();
} catch (e) {
context.fail(e)
}
};
This is fairly self-explanatory code - the important things to note are the variables which must be set in the function's environment - SLACK_CHANNEL, SLACK_USERNAME and SLACK_WEBHOOK_ID.
### Packaging
Lambda requires the code that makes up a function to be packaged as a zip archive before it can be deployed. We can use of Terraform's archive_file resource to do this:
data "archive_file" "notify_js" {
type = "zip"
}
In this case we're not using any third party NPM modules, so simply archiving the JavaScript file itself is sufficient.
### Creating the Lambda Function
Next, we can use the aws_lambda_function resource to create the lambda function itself, using the archive:
resource "aws_lambda_function" "slack_notify" {
depends_on = ["data.archive_file.notify_js"]
description = "Send notifications to Slack when Autoscaling events occur"
runtime = "nodejs4.3"
role = "${aws_iam_role.slack_notify.arn}" filename = "${data.archive_file.notify_js.output_path}"
source_code_hash = "${base64sha256(file(data.archive_file.notify_js.output_path))}" environment { variables { SLACK_CHANNEL = "${var.channel}"
SLACK_USERNAME = "${var.username}" SLACK_WEBHOOK = "${var.asg_hook_id}"
}
}
}
• The depends_on specification ensures that the archive file has finished being to processing this resource - it consists of the Terraform type and the specified name of the resource.
• Assigning a hash of the source code archive ensures that we will appropriately update the lambda function if the code package changes.
• The environment variables we called out in the code above are set in the environment block. A future improvement is to encrypt the ID of the webhook using KMS, and use the AWS kms:Decrypt operation in the lambda function in order to obtain the value so it is not availabe in plain text to an operator looking at the console.
• The handler must match the module name and function name in the source file, or invocations of the function will fail.
• We assign an IAM role to the function by ARN. We'll look at the content of this next.
### Creating an IAM Role
In order to create the role associated with the Lambda function, we need a couple of resources and data sources:
Using the aws_iam_policy_document data source in Terraform allows us to author policies using HCL rather than templating. Whether you choose to use this is something of a matter of preference, but we tend to find it substantially better than writing or templating JSON.
First, we'll look at the data source for the policy for who can assume the role:
data "aws_iam_policy_document" "assume_role" {
statement {
effect = "Allow"
actions = [
"sts:AssumeRole",
]
principals {
type = "Service"
identifiers = ["lambda.amazonaws.com"]
}
}
}
When reified at plan time, this will produce the following JSON policy text as the json attribute:
{
"Version": "2012-10-17",
"Statement": [
{
"Sid": "",
"Effect": "Allow",
"Action": "sts:AssumeRole",
"Principal": {
"Service": "lambda.amazonaws.com"
}
}
]
}
We can use the rendered JSON to create our role:
resource "aws_iam_role" "slack_notify" {
assume_role_policy = "${data.aws_iam_policy_document.assume_role.json}" } Next, we can write the text of the policy, which allows writing logs to CloudWatch. data "aws_iam_policy_document" "slack_notify" { statement { sid = "CloudwatchLogs" effect = "Allow" actions = [ "logs:CreateLogGroup", "logs:CreateLogStream", "logs:GetLogEvents", "logs:PutLogEvents" ] resources = ["arn:aws:logs:*:*:*"] } } Finally, we create an inline policy on the role, using the reified policy text: resource "aws_iam_role_policy" "slack_notify" { name = "SlackNotifications" role = "${aws_iam_role.slack_notify.id}"
policy = "${data.aws_iam_policy_document.slack_notify.json}" } ### Subscribing to the SNS topic Before we can subscribe a Lambda function to an SNS topic, we must first add a permission to the function to allow the lambda:InvokeFunction permission to the SNS topic. We can use the aws_lambda_permission resource to do so: resource "aws_lambda_permission" "with_sns" { statement_id = "AllowExecutionFromSNS" action = "lambda:InvokeFunction" function_name = "${aws_lambda_function.slack_notify.arn}"
principal = "sns.amazonaws.com"
source_arn = "${aws_sns_topic.asg_slack_notify.arn}" } Finally, we can create a subscription with a aws_sns_topic_subscription resource: resource "aws_sns_topic_subscription" "lambda" { depends_on = ["aws_lambda_permission.with_sns"] topic_arn = "${aws_sns_topic.asg_slack_notify.arn}"
protocol = "lambda"
endpoint = "${aws_lambda_function.slack_notify.arn}" } This is the final piece of the configuration puzzle needed to provision all our cloud resources. Before we can plan or apply it though, we need to talk a bit about module arrangement and instantiation. ## The Composition Root Pattern Many of the Terraform best practices discussed on the web today revolve around the idea of building an entire infrastructure with one command. I prefer a world of small, cohesive modules instead - where infrastructure is made up of many states representing individual components. I'll go into the rationale for this shortly, but first let's look at the layout of a component: $ tree
.
└── terraform
├── environments
│ ├── production
│ │ └── main.tf
│ └── staging
│ └── main.tf
├── lambda
└── modules
├── iam.tf
├── interface.tf
├── lambda.tf
In this repository layout, we separate individual functional units into modules, and then use a composition root per individual environment - in this case staging and production.
We consider there to be a number of benefits to this approach versus the commonly seen terraform.tfvars-per-environment approach. They will be covered in a lot more depth in future posts, but the big reason for now is that composition roots which are Terraform configuration files rather than variables files can use data sources to obtain values to plug in to the modules, and additional modules can be composed on a per-environment basis as necessary.
Composition roots tend to have a pattern which includes the following elements:
• Provider instantiation
• Data sources to query module values
• Module instantiation
• Outputs to provide for use in other composition roots
### Staging Environment
The composition root for our staging environment looks like this:
provider "aws" {
region = "us-west-2"
}
data "aws_autoscaling_groups" "all" {}
asg_names = "${data.aws_autoscaling_groups.all.names}" asg_hook_id = "<redacted>" channel = "#ops-staging" username = "aws" } Notice the hard-coded environment specific variables such as the channel name, which would normally live within a .tfvars file. In this case we do not need to provide any outputs. In the case of needing to replicate this in another environment, a separate composition root in a different subdirectory of environments would be used - for example environments/production/main.tf. ### Planning and Applying Now the module and composition root for our target environment root are ready, we can run a plan and ensure all is as we expect. To do this, we use the terraform plan command, with the -out flag to ensure the plan is saved. $ export AWS_ACCESS_KEY_ID=<redacted>
$export AWS_SECRET_ACCESS_KEY=<redacted>$ cd staging
\$ terraform plan -out 001.plan
# Plan output removed for brevity
Plan: 10 to add, 0 to change, 0 to destroy.
Finally, we can apply the plan using terraform apply 001.plan to create the resources and start receiving notifications!
## Summary
In this post we've seen a few things which will feature more heavily in future in my posts on this blog:
• Managing SNS topics and subscriptions, Lambda functions and permissions
• Using aws_iam_policy_document to write IAM policies in HCL rather than JSON
If you want to run this for yourself, you'll need Terraform version 0.8.5 (for the aws_autoscaling_groups data source). If you're running in Terraform Enterprise and using the composition root pattern, be sure to set the TF_ATLAS_DIR environment variable to the root of the environment you are provisioning for. | 2020-01-20 09:16:37 | {"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": 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": 0.19471774995326996, "perplexity": 5829.211568848598}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1579250598217.23/warc/CC-MAIN-20200120081337-20200120105337-00360.warc.gz"} |
https://math.stackexchange.com/questions/2191651/triangles-formed-by-the-points-of-contact-of-the-sides-with-the-excircles-and-by | # Triangles formed by the points of contact of the sides with the excircles and by that of the sides of the triangle with the inscribed circle.
Prove that the triangle formed by the points of contact of the sides of a given triangle with the excircles corresponding to these sides is equivalent to the triangle formed by the points of contact of the sides of the triangle with the inscribed circle.
Can it be approached using Ceva's, Menalaus' or Stewart's theorems?
• Hmm. Is this true? (I'm thinking of a skinny isosceles triangle). What do you mean by "equivalent" here? – Joffan Mar 18 '17 at 1:20
• Probably, it means having same area according to the same question on Google search. – Dayal Kumar Mar 18 '17 at 1:23
• I have a GeoGebra sketch that seems to confirm that "equivalent" means "having equal area" in this context. – Blue Mar 18 '17 at 2:26
• Please give solution? – Dayal Kumar Mar 18 '17 at 10:50
I don't see a clever way to invoke Ceva, Menelaus, or Stewart here. Nevertheless, there's a general principle at work. Consider $\triangle ABC$ with points $D$, $E$, $F$ on appropriate sides at shown ...
... where we define $$p := \frac{|\overline{BD}|}{|\overline{BC}|} \qquad q := \frac{|\overline{CE}|}{|\overline{CA}|} \qquad r := \frac{|\overline{AF}|}{|\overline{AB}|} \tag{1}$$
(These are not Ceva-Menelaus ratios.) Then, for instance, since $\triangle AEF$ shares an angle with $\triangle ABC$, but the corresponding sides enclosing that angle are scaled by $(1-q)$ and $r$, we can write $$|\triangle AEF| = (1-q) r\;|\triangle ABC| \tag{2}$$ Likewise, $$|\triangle BFD| = (1-r)p\;|\triangle ABC| \qquad\qquad |\triangle CDE| = (1-p)q\;|\triangle ABC| \tag{3}$$ so that \begin{align} |\triangle DEF| &= |\triangle ABC| - |\triangle AEF| - |\triangle BFD| - |\triangle CDE| \\[4pt] &=|\triangle ABC|\;\left(1-(1-q)r-(1-r)p-(1-p)q\right) \\[4pt] &=|\triangle ABC|\;\left( 1 - p - q - r + p q + p r + q r \right) \\[4pt] &=|\triangle ABC|\;\left(\; (1-p)(1-q)(1-r) + p q r \;\right) \tag{4} \end{align}
Observe that $(4)$ is obviously unchanged under the substitutions $$p \leftrightarrow 1-p \qquad q \leftrightarrow 1-q \qquad r \leftrightarrow 1-r$$
This implies that,
If $D$, $E$, $F$, $D^\prime$, $E^\prime$, $F^\prime$ are such that $$\overline{BD} \cong \overline{D^\prime C} \qquad \overline{CE} \cong \overline{E^\prime A} \qquad \overline{AF} \cong \overline{F^\prime B} \tag{\star}$$ then $$|\triangle DEF| = |\triangle D^\prime E^\prime F^\prime| \tag{\star\star}$$
(Note: To avoid marking overlapping segments, the diagram depicts $$\overline{BD^\prime} \cong \overline{DC} \qquad \overline{CE^\prime} \cong \overline{EA} \qquad \overline{AF} \cong \overline{F^\prime B}$$ but clearly these conditions are equivalent to $(\star)$.)
For the problem at hand, one needs only show that the points of contact of $\triangle ABC$'s edges with its incircles and excircles make a collection of points $D$, $E$, $F$, $D^\prime$, $E^\prime$, $F^\prime$ satisfying $(\star)$. Well, this certainly looks true:
Proof is not too difficult. See, for instance, the first part of this answer. $\square$ | 2020-02-20 22:00:05 | {"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": 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": 0.9534779191017151, "perplexity": 341.6708828804068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1581875145282.57/warc/CC-MAIN-20200220193228-20200220223228-00154.warc.gz"} |
https://www.ssccglapex.com/hi/a-shopkeeper-sells-sugar-in-such-a-way-that-the-selling-price-of-950g-of-sugar-is-the-same-s-the-cost-price-of-1-kg-of-sugar-what-is-his-gain-percent/ | ### A shopkeeper sells sugar in such a way that the selling price of 950g of sugar is the same s the cost price of 1 kg of sugar. What is his gain percent?
A. $5 \frac{5}{19} \%$ B. $5 \frac{1}{5} \%$ C. 5% D. $4 \frac{1}{19} \%$ Answer: Option A
$\begin{array}{l}\text{Sell sugar }\\ \text{= 950 g instead of 1000 g}\\ \text{Profit in sugar}\\ \text{= 1000-950 = 50 g}\\ \text{Now, % profit}\\ =\frac{50\times100}{950}=5\frac{5}{19}\%\\ \end{array}$ Short-cut $\begin{array}{l}\%\text{ profit }\\ =\frac{\text{ Goods left }}{\text{ Goods sold }}\times100\\ =\frac{50}{950}\times100\\ =5\frac{5}{19}\%\end{array}$ | 2022-09-28 12:08:03 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5143102407455444, "perplexity": 851.8989391850026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1664030335254.72/warc/CC-MAIN-20220928113848-20220928143848-00049.warc.gz"} |
https://wikimili.com/en/Optical_fiber | # Optical fiber
Last updated
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. [1] Optical fibers are used most often as a means to transmit light [lower-alpha 1] between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss; in addition, fibers are immune to electromagnetic interference, a problem from which metal wires suffer. [2] Fibers are also used for illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. [3] Specially designed fibers are also used for a variety of other applications, some of them being fiber optic sensors and fiber lasers. [4]
## Contents
Optical fibers typically include a core surrounded by a transparent cladding material with a lower index of refraction. Light is kept in the core by the phenomenon of total internal reflection which causes the fiber to act as a waveguide. [5] Fibers that support many propagation paths or transverse modes are called multi-mode fibers, while those that support a single mode are called single-mode fibers (SMF). [6] Multi-mode fibers generally have a wider core diameter [7] and are used for short-distance communication links and for applications where high power must be transmitted. [8] Single-mode fibers are used for most communication links longer than 1,000 meters (3,300 ft).[ citation needed ]
Being able to join optical fibers with low loss is important in fiber optic communication. [9] This is more complex than joining electrical wire or cable and involves careful cleaving of the fibers, precise alignment of the fiber cores, and the coupling of these aligned cores. For applications that demand a permanent connection a fusion splice is common. In this technique, an electric arc is used to melt the ends of the fibers together. Another common technique is a mechanical splice, where the ends of the fibers are held in contact by mechanical force. Temporary or semi-permanent connections are made by means of specialized optical fiber connectors. [10]
The field of applied science and engineering concerned with the design and application of optical fibers is known as fiber optics. The term was coined by Indian-American physicist Narinder Singh Kapany. [11]
## History
Daniel Colladon and Jacques Babinet first demonstrated the guiding of light by refraction, the principle that makes fiber optics possible, in Paris in the early 1840s. John Tyndall included a demonstration of it in his public lectures in London, 12 years later. [12] Tyndall also wrote about the property of total internal reflection in an introductory book about the nature of light in 1870: [13] [14]
When the light passes from air into water, the refracted ray is bent towards the perpendicular... When the ray passes from water to air it is bent from the perpendicular... If the angle which the ray in water encloses with the perpendicular to the surface be greater than 48 degrees, the ray will not quit the water at all: it will be totally reflected at the surface... The angle which marks the limit where total reflection begins is called the limiting angle of the medium. For water this angle is 48°27′, for flint glass it is 38°41′, while for a diamond it is 23°42′.
In the late 19th century, a team of Viennese doctors guided light through bent glass rods to illuminate body cavities. [15] Practical applications such as close internal illumination during dentistry followed, early in the twentieth century. Image transmission through tubes was demonstrated independently by the radio experimenter Clarence Hansell and the television pioneer John Logie Baird in the 1920s. In the 1930s, Heinrich Lamm showed that one could transmit images through a bundle of unclad optical fibers and used it for internal medical examinations, but his work was largely forgotten. [12] [16]
In 1953, Dutch scientist Bram van Heel [ nl ] first demonstrated image transmission through bundles of optical fibers with a transparent cladding. [16] That same year, Harold Hopkins and Narinder Singh Kapany at Imperial College in London succeeded in making image-transmitting bundles with over 10,000 fibers, and subsequently achieved image transmission through a 75 cm long bundle which combined several thousand fibers. [16] [17] [18] The first practical fiber optic semi-flexible gastroscope was patented by Basil Hirschowitz, C. Wilbur Peters, and Lawrence E. Curtiss, researchers at the University of Michigan, in 1956. In the process of developing the gastroscope, Curtiss produced the first glass-clad fibers; previous optical fibers had relied on air or impractical oils and waxes as the low-index cladding material. [16]
Kapany coined the term fiber optics after writing a 1960 article in Scientific American that introduced the topic to a wide audience. He subsequently wrote the first book about the new field. [16] [19]
The first working fiber-optic data transmission system was demonstrated by German physicist Manfred Börner at Telefunken Research Labs in Ulm in 1965, followed by the first patent application for this technology in 1966. [20] [21] In 1968, NASA used fiber optics in the television cameras that were sent to the moon. At the time, the use in the cameras was classified confidential, and employees handling the cameras had to be supervised by someone with an appropriate security clearance. [22]
Charles K. Kao and George A. Hockham of the British company Standard Telephones and Cables (STC) were the first to promote the idea that the attenuation in optical fibers could be reduced below 20 decibels per kilometer (dB/km), making fibers a practical communication medium, in 1965. [23] They proposed that the attenuation in fibers available at the time was caused by impurities that could be removed, rather than by fundamental physical effects such as scattering. They correctly and systematically theorized the light-loss properties for optical fiber and pointed out the right material to use for such fibers—silica glass with high purity. This discovery earned Kao the Nobel Prize in Physics in 2009. [24] The crucial attenuation limit of 20 dB/km was first achieved in 1970 by researchers Robert D. Maurer, Donald Keck, Peter C. Schultz, and Frank Zimar working for American glass maker Corning Glass Works. [25] They demonstrated a fiber with 17 dB/km attenuation by doping silica glass with titanium. A few years later they produced a fiber with only 4 dB/km attenuation using germanium dioxide as the core dopant. In 1981, General Electric produced fused quartz ingots that could be drawn into strands 25 miles (40 km) long. [26]
Initially, high-quality optical fibers could only be manufactured at 2 meters per second. Chemical engineer Thomas Mensah joined Corning in 1983 and increased the speed of manufacture to over 50 meters per second, making optical fiber cables cheaper than traditional copper ones. [27] [ self-published source ] These innovations ushered in the era of optical fiber telecommunication.
The Italian research center CSELT worked with Corning to develop practical optical fiber cables, resulting in the first metropolitan fiber optic cable being deployed in Turin in 1977. [28] [29] CSELT also developed an early technique for splicing optical fibers, called Springroove. [30]
Attenuation in modern optical cables is far less than in electrical copper cables, leading to long-haul fiber connections with repeater distances of 70–150 kilometers (43–93 mi). Two teams, led by David N. Payne of the University of Southampton and Emmanuel Desurvire at Bell Labs, developed the erbium-doped fiber amplifier, which reduced the cost of long-distance fiber systems by reducing or eliminating optical-electrical-optical repeaters, in 1986 and 1987 respectively. [31] [32] [33]
The emerging field of photonic crystals led to the development in 1991 of photonic-crystal fiber, [34] which guides light by diffraction from a periodic structure, rather than by total internal reflection. The first photonic crystal fibers became commercially available in 2000. [35] Photonic crystal fibers can carry higher power than conventional fibers and their wavelength-dependent properties can be manipulated to improve performance.
## Uses
### Communication
Optical fiber is used as a medium for telecommunication and computer networking because it is flexible and can be bundled as cables. It is especially advantageous for long-distance communications, because infrared light propagates through the fiber with much lower attenuation compared to electricity in electrical cables. This allows long distances to be spanned with few repeaters.
10 or 40 Gbit/s is typical in deployed systems. [36] [37]
Through the use of wavelength-division multiplexing (WDM), each fiber can carry many independent channels, each using a different wavelength of light. The net data rate (data rate without overhead bytes) per fiber is the per-channel data rate reduced by the forward error correction (FEC) overhead, multiplied by the number of channels (usually up to 80 in commercial dense WDM systems as of 2008).
Transmission speed milestones
DateMilestone
2006111 Gbit/s by NTT. [38] [39]
2009100 Pbit/s·km (15.5 Tbit/s over a single 7000 km fiber) by Bell Labs. [40]
2011101 Tbit/s (370 channels at 273 Gbit/s each) on a single core. [41]
January 20131.05 Pbit/s transmission through a multi-core (lightpath) fiber cable. [42]
June 2013400 Gbit/s over a single channel using 4-mode orbital angular momentum multiplexing. [43]
October 20221.84 Pbit/sec using a photonic chip [44]
For short-distance applications, such as a network in an office building (see fiber to the office), fiber-optic cabling can save space in cable ducts. This is because a single fiber can carry much more data than electrical cables such as standard category 5 cable, which typically runs at 100 Mbit/s or 1 Gbit/s speeds.
Fibers are often also used for short-distance connections between devices. For example, most high-definition televisions offer a digital audio optical connection. This allows the streaming of audio over light, using the S/PDIF protocol over an optical TOSLINK connection.
### Sensors
Fibers have many uses in remote sensing. In some applications, the fiber itself is the sensor (the fibers channel optical light to a processing device that analyzes changes in the light's characteristics). In other cases, fiber is used to connect a sensor to a measurement system.
Optical fibers can be used as sensors to measure strain, temperature, pressure, and other quantities by modifying a fiber so that the property being measured modulates the intensity, phase, polarization, wavelength, or transit time of light in the fiber. Sensors that vary the intensity of light are the simplest since only a simple source and detector are required. A particularly useful feature of such fiber optic sensors is that they can, if required, provide distributed sensing over distances of up to one meter. Distributed acoustic sensing is one example of this.
In contrast, highly localized measurements can be provided by integrating miniaturized sensing elements with the tip of the fiber. [45] These can be implemented by various micro- and nanofabrication technologies, such that they do not exceed the microscopic boundary of the fiber tip, allowing for such applications as insertion into blood vessels via hypodermic needle.
Extrinsic fiber optic sensors use an optical fiber cable, normally a multi-mode one, to transmit modulated light from either a non-fiber optical sensor—or an electronic sensor connected to an optical transmitter. A major benefit of extrinsic sensors is their ability to reach otherwise inaccessible places. An example is the measurement of temperature inside jet engines by using a fiber to transmit radiation into a pyrometer outside the engine. Extrinsic sensors can be used in the same way to measure the internal temperature of electrical transformers, where the extreme electromagnetic fields present make other measurement techniques impossible. Extrinsic sensors measure vibration, rotation, displacement, velocity, acceleration, torque, and torsion. A solid-state version of the gyroscope, using the interference of light, has been developed. The fiber optic gyroscope (FOG) has no moving parts and exploits the Sagnac effect to detect mechanical rotation.
Common uses for fiber optic sensors include advanced intrusion detection security systems. The light is transmitted along a fiber optic sensor cable placed on a fence, pipeline, or communication cabling, and the returned signal is monitored and analyzed for disturbances. This return signal is digitally processed to detect disturbances and trip an alarm if an intrusion has occurred.
Optical fibers are widely used as components of optical chemical sensors and optical biosensors. [46]
### Power transmission
Optical fiber can be used to transmit power using a photovoltaic cell to convert the light into electricity. [47] While this method of power transmission is not as efficient as conventional ones, it is especially useful in situations where it is desirable not to have a metallic conductor as in the case of use near MRI machines, which produce strong magnetic fields. [48] Other examples are for powering electronics in high-powered antenna elements and measurement devices used in high-voltage transmission equipment.
### Other uses
Optical fibers are used as light guides in medical and other applications where bright light needs to be shone on a target without a clear line-of-sight path. Many microscopes use fiber-optic light sources to provide intense illumination of samples being studied.
Optical fiber is also used in imaging optics. A coherent bundle of fibers is used, sometimes along with lenses, for a long, thin imaging device called an endoscope, which is used to view objects through a small hole. Medical endoscopes are used for minimally invasive exploratory or surgical procedures. Industrial endoscopes (see fiberscope or borescope) are used for inspecting anything hard to reach, such as jet engine interiors.
In some buildings, optical fibers route sunlight from the roof to other parts of the building (see nonimaging optics). Optical-fiber lamps are used for illumination in decorative applications, including signs, art, toys and artificial Christmas trees. Optical fiber is an intrinsic part of the light-transmitting concrete building product LiTraCon.
Optical fiber can also be used in structural health monitoring. This type of sensor can detect stresses that may have a lasting impact on structures. It is based on the principle of measuring analog attenuation.
In spectroscopy, optical fiber bundles transmit light from a spectrometer to a substance that cannot be placed inside the spectrometer itself, in order to analyze its composition. A spectrometer analyzes substances by bouncing light off and through them. By using fibers, a spectrometer can be used to study objects remotely. [49] [50] [51]
An optical fiber doped with certain rare-earth elements such as erbium can be used as the gain medium of a fiber laser or optical amplifier. Rare-earth-doped optical fibers can be used to provide signal amplification by splicing a short section of doped fiber into a regular (undoped) optical fiber line. The doped fiber is optically pumped with a second laser wavelength that is coupled into the line in addition to the signal wave. Both wavelengths of light are transmitted through the doped fiber, which transfers energy from the second pump wavelength to the signal wave. The process that causes the amplification is stimulated emission.
Optical fiber is also widely exploited as a nonlinear medium. The glass medium supports a host of nonlinear optical interactions, and the long interaction lengths possible in fiber facilitate a variety of phenomena, which are harnessed for applications and fundamental investigation. [52] Conversely, fiber nonlinearity can have deleterious effects on optical signals, and measures are often required to minimize such unwanted effects.
Optical fibers doped with a wavelength shifter collect scintillation light in physics experiments.
Fiber-optic sights for handguns, rifles, and shotguns use pieces of optical fiber to improve the visibility of markings on the sight.
## Principle of operation
An optical fiber is a cylindrical dielectric waveguide (nonconducting waveguide) that transmits light along its axis through the process of total internal reflection. The fiber consists of a core surrounded by a cladding layer, both of which are made of dielectric materials. [53] To confine the optical signal in the core, the refractive index of the core must be greater than that of the cladding. The boundary between the core and cladding may either be abrupt, in step-index fiber , or gradual, in graded-index fiber . Light can be fed into optical fibers using lasers or LEDs.
Fiber is immune to electrical interference; there is no cross-talk between signals in different cables and no pickup of environmental noise. Information traveling inside the optical fiber is even immune to electromagnetic pulses generated by nuclear devices. [lower-alpha 2] [ citation needed ]
Fiber cables do not conduct electricity, which makes fiber useful for protecting communications equipment in high voltage environments such as power generation facilities or applications prone to lightning strikes. The electrical isolation also prevents problems with ground loops. Because there is no electricity in optical cables that could potentially generate sparks, they can be used in environments where explosive fumes are present. Wiretapping (in this case, fiber tapping) is more difficult compared to electrical connections.
Fiber cables are not targeted for metal theft. In contrast, copper cable systems use large amounts of copper and have been targeted since the 2000s commodities boom.
### Refractive index
The refractive index is a way of measuring the speed of light in a material. Light travels fastest in a vacuum, such as in outer space. The speed of light in a vacuum is about 300,000 kilometers (186,000 miles) per second. The refractive index of a medium is calculated by dividing the speed of light in a vacuum by the speed of light in that medium. The refractive index of a vacuum is therefore 1, by definition. A typical single-mode fiber used for telecommunications has a cladding made of pure silica, with an index of 1.444 at 1500 nm, and a core of doped silica with an index around 1.4475. [53] The larger the index of refraction, the slower light travels in that medium. From this information, a simple rule of thumb is that a signal using optical fiber for communication will travel at around 200,000 kilometers per second. Thus a phone call carried by fiber between Sydney and New York, a 16,000-kilometer distance, means that there is a minimum delay of 80 milliseconds (about ${\displaystyle {\tfrac {1}{12}}}$ of a second) between when one caller speaks and the other hears. [lower-alpha 3]
### Total internal reflection
When light traveling in an optically dense medium hits a boundary at a steep angle (larger than the critical angle for the boundary), the light is completely reflected. This is called total internal reflection. This effect is used in optical fibers to confine light in the core. Most modern optical fiber is weakly guiding, meaning that the difference in refractive index between the core and the cladding is very small (typically less than 1%). [54] Light travels through the fiber core, bouncing back and forth off the boundary between the core and cladding.
Because the light must strike the boundary with an angle greater than the critical angle, only light that enters the fiber within a certain range of angles can travel down the fiber without leaking out. This range of angles is called the acceptance cone of the fiber. There is a maximum angle from the fiber axis at which light may enter the fiber so that it will propagate, or travel, in the core of the fiber. The sine of this maximum angle is the numerical aperture (NA) of the fiber. Fiber with a larger NA requires less precision to splice and work with than fiber with a smaller NA. The size of this acceptance cone is a function of the refractive index difference between the fiber's core and cladding. Single-mode fiber has a small NA.
### Multi-mode fiber
Fiber with large core diameter (greater than 10 micrometers) may be analyzed by geometrical optics. Such fiber is called multi-mode fiber, from the electromagnetic analysis (see below). In a step-index multi-mode fiber, rays of light are guided along the fiber core by total internal reflection. Rays that meet the core-cladding boundary at an angle (measured relative to a line normal to the boundary) greater than the critical angle for this boundary, are completely reflected. The critical angle is determined by the difference in the index of refraction between the core and cladding materials. Rays that meet the boundary at a low angle are refracted from the core into the cladding where they terminate. The critical angle determines the acceptance angle of the fiber, often reported as a numerical aperture. A high numerical aperture allows light to propagate down the fiber in rays both close to the axis and at various angles, allowing efficient coupling of light into the fiber. However, this high numerical aperture increases the amount of dispersion as rays at different angles have different path lengths and therefore take different amounts of time to traverse the fiber.
In graded-index fiber, the index of refraction in the core decreases continuously between the axis and the cladding. This causes light rays to bend smoothly as they approach the cladding, rather than reflecting abruptly from the core-cladding boundary. The resulting curved paths reduce multi-path dispersion because high-angle rays pass more through the lower-index periphery of the core, rather than the high-index center. The index profile is chosen to minimize the difference in axial propagation speeds of the various rays in the fiber. This ideal index profile is very close to a parabolic relationship between the index and the distance from the axis.[ citation needed ]
### Single-mode fiber
Fiber with a core diameter less than about ten times the wavelength of the propagating light cannot be modeled using geometric optics. Instead, it must be analyzed as an electromagnetic waveguide structure, according to Maxwell's equations as reduced to the electromagnetic wave equation. [lower-alpha 4] As an optical waveguide, the fiber supports one or more confined transverse modes by which light can propagate along the fiber. Fiber supporting only one mode is called single-mode. [lower-alpha 5] The waveguide analysis shows that the light energy in the fiber is not completely confined in the core. Instead, especially in single-mode fibers, a significant fraction of the energy in the bound mode travels in the cladding as an evanescent wave. The most common type of single-mode fiber has a core diameter of 8–10 micrometers and is designed for use in the near infrared. Multi-mode fiber, by comparison, is manufactured with core diameters as small as 50 micrometers and as large as hundreds of micrometers.
### Special-purpose fiber
Some special-purpose optical fiber is constructed with a non-cylindrical core or cladding layer, usually with an elliptical or rectangular cross-section. These include polarization-maintaining fiber used in fiber optic sensors and fiber designed to suppress whispering gallery mode propagation.
Photonic-crystal fiber is made with a regular pattern of index variation (often in the form of cylindrical holes that run along the length of the fiber). Such fiber uses diffraction effects instead of or in addition to total internal reflection, to confine light to the fiber's core. The properties of the fiber can be tailored to a wide variety of applications.
## Mechanisms of attenuation
Attenuation in fiber optics, also known as transmission loss, is the reduction in the intensity of the light signal as it travels through the transmission medium. Attenuation coefficients in fiber optics are usually expressed in units of dB/km. The medium is usually a fiber of silica glass [lower-alpha 6] that confines the incident light beam within. Attenuation is an important factor limiting the transmission of a digital signal across large distances. Thus, much research has gone into both limiting the attenuation and maximizing the amplification of the optical signal. The four orders of magnitude reduction in the attenuation of silica optical fibers over four decades was the result of constant improvement of manufacturing processes, raw material purity, preform, and fiber designs, which allowed for these fibers to approach the theoretical lower limit of attenuation. [55]
Single-mode optical fibers can be made with extremely low loss. Corning's SMF-28 fiber, a standard single-mode fiber for telecommunications wavelengths, has a loss of 0.17 dB/km at 1550 nm. [56] For example, an 8 km length of SMF-28 transmits nearly 75% of light at 1,550 nm. It has been noted that if ocean water was as clear as fiber, one could see all the way to the bottom even of the Mariana Trench in the Pacific Ocean, a depth of 11,000 metres (36,000 ft). [57]
Empirical research has shown that attenuation in optical fiber is caused primarily by both scattering and absorption.
### Light scattering
The propagation of light through the core of an optical fiber is based on the total internal reflection of the lightwave. Rough and irregular surfaces, even at the molecular level, can cause light rays to be reflected in random directions. This is called diffuse reflection or scattering, and it is typically characterized by a wide variety of reflection angles.
Scattering depends on the wavelength of the light being scattered. Thus, limits to spatial scales of visibility arise, depending on the frequency of the incident light wave and the physical dimension (or spatial scale) of the scattering center, which is typically in the form of some specific micro-structural feature. Since visible light has a wavelength of the order of one micrometer (one-millionth of a meter) scattering centers will have dimensions on a similar spatial scale.
Thus, attenuation results from the incoherent scattering of light at internal surfaces and interfaces. In (poly)crystalline materials such as metals and ceramics, in addition to pores, most of the internal surfaces or interfaces are in the form of grain boundaries that separate tiny regions of crystalline order. It has been shown that when the size of the scattering center (or grain boundary) is reduced below the size of the wavelength of the light being scattered, the scattering no longer occurs to any significant extent.[ citation needed ] This phenomenon has given rise to the production of transparent ceramic materials.
Similarly, the scattering of light in optical quality glass fiber is caused by molecular level irregularities (compositional fluctuations) in the glass structure. Indeed, one emerging school of thought is that glass is simply the limiting case of a polycrystalline solid. Within this framework, domains exhibiting various degrees of short-range order become the building blocks of metals as well as glasses and ceramics. Distributed both between and within these domains are micro-structural defects that provide the most ideal locations for light scattering. This same phenomenon is seen as one of the limiting factors in the transparency of IR missile domes. [58]
At high optical powers, scattering can also be caused by nonlinear optical processes in the fiber. [59] [60]
### UV-Vis-IR absorption
In addition to light scattering, attenuation or signal loss can also occur due to selective absorption of specific wavelengths. Primary material considerations include both electrons and molecules as follows:
• At the electronic level, it depends on whether the electron orbitals are spaced (or "quantized") such that they can absorb a quantum of light (or photon) of a specific wavelength or frequency in the ultraviolet (UV) or visible ranges. This is what gives rise to color.
• At the atomic or molecular level, it depends on the frequencies of atomic or molecular vibrations or chemical bonds, how closely packed its atoms or molecules are, and whether or not the atoms or molecules exhibit long-range order. These factors will determine the capacity of the material to transmit longer wavelengths in the infrared (IR), far IR, radio, and microwave ranges.
The design of any optically transparent device requires the selection of materials based upon knowledge of its properties and limitations. The crystal structure absorption characteristics observed at the lower frequency regions (mid- to far-IR wavelength range) define the long-wavelength transparency limit of the material. They are the result of the interactive coupling between the motions of thermally induced vibrations of the constituent atoms and molecules of the solid lattice and the incident light wave radiation. Hence, all materials are bounded by limiting regions of absorption caused by atomic and molecular vibrations (bond-stretching) in the far-infrared (>10 µm).
In other words, the selective absorption of IR light by a particular material occurs because the selected frequency of the light wave matches the frequency (or an integer multiple of the frequency, i.e. harmonic) at which the particles of that material vibrate. Since different atoms and molecules have different natural frequencies of vibration, they will selectively absorb different frequencies (or portions of the spectrum) of IR light.
Reflection and transmission of light waves occur because the frequencies of the light waves do not match the natural resonant frequencies of vibration of the objects. When IR light of these frequencies strikes an object, the energy is either reflected or transmitted.
### Loss budget
Attenuation over a cable run is significantly increased by the inclusion of connectors and splices. When computing the acceptable attenuation (loss budget) between a transmitter and a receiver one includes:
• dB loss due to the type and length of fiber optic cable,
• dB loss introduced by connectors, and
• dB loss introduced by splices.
Connectors typically introduce 0.3 dB per connector on well-polished connectors. Splices typically introduce less than 0.2 dB per splice.[ citation needed ]
The total loss can be calculated by:
Loss = dB loss per connector × number of connectors + dB loss per splice × number of splices + dB loss per kilometer × kilometers of fiber,
where the dB loss per kilometer is a function of the type of fiber and can be found in the manufacturer's specifications. For example, a typical 1550 nm single-mode fiber has a loss of 0.3 dB per kilometer.[ citation needed ]
The calculated loss budget is used when testing to confirm that the measured loss is within the normal operating parameters.
## Manufacturing
### Materials
Glass optical fibers are almost always made from silica, but some other materials, such as fluorozirconate, fluoroaluminate, and chalcogenide glasses as well as crystalline materials like sapphire, are used for longer-wavelength infrared or other specialized applications. Silica and fluoride glasses usually have refractive indices of about 1.5, but some materials such as the chalcogenides can have indices as high as 3. Typically the index difference between core and cladding is less than one percent.
Plastic optical fibers (POF) are commonly step-index multi-mode fibers with a core diameter of 0.5 millimeters or larger. POF typically have higher attenuation coefficients than glass fibers, 1 dB/m or higher, and this high attenuation limits the range of POF-based systems.
#### Silica
Silica exhibits fairly good optical transmission over a wide range of wavelengths. In the near-infrared (near IR) portion of the spectrum, particularly around 1.5 μm, silica can have extremely low absorption and scattering losses of the order of 0.2 dB/km. Such low losses depend on using ultra-pure silica. A high transparency in the 1.4-μm region is achieved by maintaining a low concentration of hydroxyl groups (OH). Alternatively, a high OH concentration is better for transmission in the ultraviolet (UV) region. [61]
Silica can be drawn into fibers at reasonably high temperatures and has a fairly broad glass transformation range. One other advantage is that fusion splicing and cleaving of silica fibers is relatively effective. Silica fiber also has high mechanical strength against both pulling and even bending, provided that the fiber is not too thick and that the surfaces have been well prepared during processing. Even simple cleaving of the ends of the fiber can provide nicely flat surfaces with acceptable optical quality. Silica is also relatively chemically inert. In particular, it is not hygroscopic (does not absorb water).
Silica glass can be doped with various materials. One purpose of doping is to raise the refractive index (e.g. with germanium dioxide (GeO2) or aluminium oxide (Al2O3)) or to lower it (e.g. with fluorine or boron trioxide (B2O3)). Doping is also possible with laser-active ions (for example, rare-earth-doped fibers) in order to obtain active fibers to be used, for example, in fiber amplifiers or laser applications. Both the fiber core and cladding are typically doped, so that the entire assembly (core and cladding) is effectively the same compound (e.g. an aluminosilicate, germanosilicate, phosphosilicate or borosilicate glass).
Particularly for active fibers, pure silica is usually not a very suitable host glass, because it exhibits a low solubility for rare-earth ions. This can lead to quenching effects due to the clustering of dopant ions. Aluminosilicates are much more effective in this respect.
Silica fiber also exhibits a high threshold for optical damage. This property ensures a low tendency for laser-induced breakdown. This is important for fiber amplifiers when utilized for the amplification of short pulses.
Because of these properties, silica fibers are the material of choice in many optical applications, such as communications (except for very short distances with plastic optical fiber), fiber lasers, fiber amplifiers, and fiber-optic sensors. Large efforts put forth in the development of various types of silica fibers have further increased the performance of such fibers over other materials. [62] [63] [64] [65] [66] [67] [68] [69]
#### Fluoride glass
Fluoride glass is a class of non-oxide optical quality glasses composed of fluorides of various metals. Because of the low viscosity of these glasses, it is very difficult to completely avoid crystallization while processing it through the glass transition (or drawing the fiber from the melt). Thus, although heavy metal fluoride glasses (HMFG) exhibit very low optical attenuation, they are not only difficult to manufacture, but are quite fragile, and have poor resistance to moisture and other environmental attacks. Their best attribute is that they lack the absorption band associated with the hydroxyl (OH) group (3,200–3,600 cm−1; i.e., 2,777–3,125 nm or 2.78–3.13 μm), which is present in nearly all oxide-based glasses. Such low losses were never realized in practice, and the fragility and high cost of fluoride fibers made them less than ideal as primary candidates.
Fluoride fibers are used in mid-IR spectroscopy, fiber optic sensors, thermometry, and imaging. Fluoride fibers can be used for guided lightwave transmission in media such as YAG (yttrium aluminium garnet) lasers at 2.9 μm, as required for medical applications (e.g. ophthalmology and dentistry). [70] [71]
An example of a heavy metal fluoride glass is the ZBLAN glass group, composed of zirconium, barium, lanthanum, aluminium, and sodium fluorides. Their main technological application is as optical waveguides in both planar and fiber forms. They are advantageous especially in the mid-infrared (2,000–5,000 nm) range.
#### Phosphate glass
Phosphate glass is a class of optical glasses composed of metaphosphates of various metals. Instead of the SiO4 tetrahedra observed in silicate glasses, the building block for this glass phosphorus pentoxide (P2O5), which crystallizes in at least four different forms. The most familiar polymorph is the cagelike structure of P4O10.
Phosphate glasses can be advantageous over silica glasses for optical fibers with a high concentration of doping rare-earth ions. A mix of fluoride glass and phosphate glass is fluorophosphate glass. [72] [73]
#### Chalcogenide glass
The chalcogens—the elements in group 16 of the periodic table—particularly sulfur (S), selenium (Se) and tellurium (Te)—react with more electropositive elements, such as silver, to form chalcogenides. These are extremely versatile compounds, in that they can be crystalline or amorphous, metallic or semiconducting, and conductors of ions or electrons. Glass containing chalcogenides can be used to make fibers for far infrared transmission.[ citation needed ]
### Process
#### Preform
Standard optical fibers are made by first constructing a large-diameter "preform" with a carefully controlled refractive index profile, and then "pulling" the preform to form the long, thin optical fiber. The preform is commonly made by three chemical vapor deposition methods: inside vapor deposition, outside vapor deposition, and vapor axial deposition. [74]
With inside vapor deposition, the preform starts as a hollow glass tube approximately 40 centimeters (16 in) long, which is placed horizontally and rotated slowly on a lathe. Gases such as silicon tetrachloride (SiCl4) or germanium tetrachloride (GeCl4) are injected with oxygen in the end of the tube. The gases are then heated by means of an external hydrogen burner, bringing the temperature of the gas up to 1,900 K (1,600 °C, 3,000 °F), where the tetrachlorides react with oxygen to produce silica or germania (germanium dioxide) particles. When the reaction conditions are chosen to allow this reaction to occur in the gas phase throughout the tube volume, in contrast to earlier techniques where the reaction occurred only on the glass surface, this technique is called modified chemical vapor deposition (MCVD).
The oxide particles then agglomerate to form large particle chains, which subsequently deposit on the walls of the tube as soot. The deposition is due to the large difference in temperature between the gas core and the wall causing the gas to push the particles outward (this is known as thermophoresis). The torch is then traversed up and down the length of the tube to deposit the material evenly. After the torch has reached the end of the tube, it is then brought back to the beginning of the tube and the deposited particles are then melted to form a solid layer. This process is repeated until a sufficient amount of material has been deposited. For each layer the composition can be modified by varying the gas composition, resulting in precise control of the finished fiber's optical properties.
In outside vapor deposition or vapor axial deposition, the glass is formed by flame hydrolysis, a reaction in which silicon tetrachloride and germanium tetrachloride are oxidized by reaction with water (H2O) in an oxyhydrogen flame. In outside vapor deposition, the glass is deposited onto a solid rod, which is removed before further processing. In vapor axial deposition, a short seed rod is used, and a porous preform, whose length is not limited by the size of the source rod, is built up on its end. The porous preform is consolidated into a transparent, solid preform by heating to about 1,800 K (1,500 °C, 2,800 °F).
Typical communications fiber uses a circular preform. For some applications such as double-clad fibers another form is preferred. [75] In fiber lasers based on double-clad fiber, an asymmetric shape improves the filling factor for laser pumping.
Because of the surface tension, the shape is smoothed during the drawing process, and the shape of the resulting fiber does not reproduce the sharp edges of the preform. Nevertheless, careful polishing of the preform is important, since any defects of the preform surface affect the optical and mechanical properties of the resulting fiber. In particular, the preform for the test fiber shown in the figure was not polished well, and cracks are seen with the confocal optical microscope.
#### Drawing
The preform, regardless of construction, is placed in a device known as a drawing tower, where the preform tip is heated and the optical fiber is pulled out as a string. By measuring the resultant fiber width, the tension on the fiber can be controlled to maintain the fiber thickness.
### Coatings
The light is guided down the core of the fiber by an optical cladding with a lower refractive index that traps light in the core through total internal reflection.
The cladding is coated by a buffer that protects it from moisture and physical damage. [63] The buffer coating is what gets stripped off the fiber for termination or splicing. These coatings are UV-cured urethane acrylate composite or polyimide materials applied to the outside of the fiber during the drawing process. The coatings protect the very delicate strands of glass fiber—about the size of a human hair—and allow it to survive the rigors of manufacturing, proof testing, cabling, and installation.
Today’s glass optical fiber draw processes employ a dual-layer coating approach. An inner primary coating is designed to act as a shock absorber to minimize attenuation caused by microbending. An outer secondary coating protects the primary coating against mechanical damage and acts as a barrier to lateral forces, and may be colored to differentiate strands in bundled cable constructions.
These fiber optic coating layers are applied during the fiber draw, at speeds approaching 100 kilometers per hour (60 mph). Fiber optic coatings are applied using one of two methods: wet-on-dry and wet-on-wet. In wet-on-dry, the fiber passes through a primary coating application, which is then UV cured—then through the secondary coating application, which is subsequently cured. In wet-on-wet, the fiber passes through both the primary and secondary coating applications, then goes to UV curing.
Fiber optic coatings are applied in concentric layers to prevent damage to the fiber during the drawing application and to maximize fiber strength and microbend resistance. Unevenly coated fiber will experience non-uniform forces when the coating expands or contracts and is susceptible to greater signal attenuation. Under proper drawing and coating processes, the coatings are concentric around the fiber, continuous over the length of the application, and have a constant thickness.
The thickness of the coating is taken into account when calculating the stress that the fiber experiences under different bend configurations. [76] When a coated fiber is wrapped around a mandrel, the stress experienced by the fiber is given by
${\displaystyle \sigma =E{d_{f} \over d_{m}+d_{c}}}$,
where E is the fiber’s Young’s modulus, dm is the diameter of the mandrel, df is the diameter of the cladding and dc is the diameter of the coating.
In a two-point bend configuration, a coated fiber is bent in a U-shape and placed between the grooves of two faceplates, which are brought together until the fiber breaks. The stress in the fiber in this configuration is given by
${\displaystyle \sigma =1.198E{d_{f} \over d-d_{c}}}$,
where d is the distance between the faceplates. The coefficient 1.198 is a geometric constant associated with this configuration.
Fiber optic coatings protect the glass fibers from scratches that could lead to strength degradation. The combination of moisture and scratches accelerates the aging and deterioration of fiber strength. When fiber is subjected to low stresses over a long period, fiber fatigue can occur. Over time or in extreme conditions, these factors combine to cause microscopic flaws in the glass fiber to propagate, which can ultimately result in fiber failure.
Three key characteristics of fiber optic waveguides can be affected by environmental conditions: strength, attenuation, and resistance to losses caused by microbending. External optical fiber cable jackets and buffer tubes protect glass optical fiber from environmental conditions that can affect the fiber’s performance and long-term durability. On the inside, coatings ensure the reliability of the signal being carried and help minimize attenuation due to microbending.
### Cable construction
In practical fibers, the cladding is usually coated with a tough resin coating and an additional buffer layer, which may be further surrounded by a jacket layer, usually plastic. These layers add strength to the fiber but do not contribute to its optical wave guide properties. Rigid fiber assemblies sometimes put light-absorbing ("dark") glass between the fibers, to prevent light that leaks out of one fiber from entering another. This reduces crosstalk between the fibers, or reduces flare in fiber bundle imaging applications. [77] [78]
Modern cables come in a wide variety of sheathings and armor, designed for applications such as direct burial in trenches, high voltage isolation, dual use as power lines, [79] [ failed verification ] installation in conduit, lashing to aerial telephone poles, submarine installation, and insertion in paved streets. Multi-fiber cable usually uses colored coatings and/or buffers to identify each strand. The cost of small fiber-count pole-mounted cables has greatly decreased due to the high demand for fiber to the home (FTTH) installations in Japan and South Korea.
Some fiber optic cable versions are reinforced with aramid yarns or glass yarns as an intermediary strength member. In commercial terms, usage of the glass yarns are more cost-effective while no loss in mechanical durability of the cable. Glass yarns also protect the cable core against rodents and termites.
## Practical issues
### Installation
Fiber cable can be very flexible, but traditional fiber's loss increases greatly if the fiber is bent with a radius smaller than around 30 mm. This creates a problem when the cable is bent around corners or wound around a spool, making FTTX installations more complicated. "Bendable fibers", targeted toward easier installation in home environments, have been standardized as ITU-T G.657. This type of fiber can be bent with a radius as low as 7.5 mm without adverse impact. Even more bendable fibers have been developed. [80] Bendable fiber may also be resistant to fiber hacking, in which the signal in a fiber is surreptitiously monitored by bending the fiber and detecting the leakage. [81]
Another important feature of cable is cable's ability to withstand horizontally applied force. It is technically called max tensile strength defining how much force can be applied to the cable during the installation period.
### Termination and splicing
Optical fibers are connected to terminal equipment by optical fiber connectors. These connectors are usually of a standard type such as FC, SC, ST, LC, MTRJ, MPO or SMA. Optical fibers may be connected by connectors, or permanently by splicing, that is, joining two fibers together to form a continuous optical waveguide. The generally accepted splicing method is arc fusion splicing, which melts the fiber ends together with an electric arc. For quicker fastening jobs, a “mechanical splice” is used.
Fusion splicing is done with a specialized instrument. The fiber ends are first stripped of their protective polymer coating (as well as the more sturdy outer jacket, if present). The ends are cleaved (cut) with a precision cleaver to make them perpendicular, and are placed into special holders in the fusion splicer. The splice is usually inspected via a magnified viewing screen to check the cleaves before and after the splice. The splicer uses small motors to align the end faces together, and emits a small spark between electrodes at the gap to burn off dust and moisture. Then the splicer generates a larger spark that raises the temperature above the melting point of the glass, fusing the ends permanently. The location and energy of the spark is carefully controlled so that the molten core and cladding do not mix, and this minimizes optical loss. A splice loss estimate is measured by the splicer, by directing light through the cladding on one side and measuring the light leaking from the cladding on the other side. A splice loss under 0.1 dB is typical. The complexity of this process makes fiber splicing much more difficult than splicing copper wire.
Mechanical fiber splices are designed to be quicker and easier to install, but there is still the need for stripping, careful cleaning, and precision cleaving. The fiber ends are aligned and held together by a precision-made sleeve, often using a clear index-matching gel that enhances the transmission of light across the joint. Such joints typically have a higher optical loss and are less robust than fusion splices, especially if the gel is used. All splicing techniques involve installing an enclosure that protects the splice.
Fibers are terminated in connectors that hold the fiber end precisely and securely. A fiber-optic connector is a rigid cylindrical barrel surrounded by a sleeve that holds the barrel in its mating socket. The mating mechanism can be push and click, turn and latch ( bayonet mount ), or screw-in (threaded). The barrel is typically free to move within the sleeve and may have a key that prevents the barrel and fiber from rotating as the connectors are mated.
A typical connector is installed by preparing the fiber end and inserting it into the rear of the connector body. Quick-set adhesive is usually used to hold the fiber securely, and a strain relief is secured to the rear. Once the adhesive sets, the fiber's end is polished to a mirror finish. Various polish profiles are used, depending on the type of fiber and the application. For single-mode fiber, fiber ends are typically polished with a slight curvature that makes the mated connectors touch only at their cores. This is called a physical contact (PC) polish. The curved surface may be polished at an angle, to make an angled physical contact (APC) connection. Such connections have higher loss than PC connections but greatly reduced back reflection, because light that reflects from the angled surface leaks out of the fiber core. The resulting signal strength loss is called gap loss . APC fiber ends have low back reflection even when disconnected.
In the 1990s, terminating fiber optic cables was labor-intensive. The number of parts per connector, polishing of the fibers, and the need to oven-bake the epoxy in each connector made terminating fiber optic cables difficult. Today, many connector types are on the market that offer easier, less labor-intensive ways of terminating cables. Some of the most popular connectors are pre-polished at the factory and include a gel inside the connector. Those two steps help save money on labor, especially on large projects. A cleave is made at a required length, to get as close to the polished piece already inside the connector. The gel surrounds the point where the two pieces meet inside the connector for very little light loss.[ citation needed ] Long-term performance of the gel is a design consideration, so for the most demanding installations, factory pre-polished pigtails of sufficient length to reach the first fusion splice enclosure is normally the safest approach that minimizes on-site labor.
### Free-space coupling
It is often necessary to align an optical fiber with another optical fiber or with an optoelectronic device such as a light-emitting diode, a laser diode, or a modulator. This can involve either carefully aligning the fiber and placing it in contact with the device, or can use a lens to allow coupling over an air gap. Typically the size of the fiber mode is much larger than the size of the mode in a laser diode or a silicon optical chip. In this case, a tapered or lensed fiber is used to match the fiber mode field distribution to that of the other element. The lens on the end of the fiber can be formed using polishing, laser cutting [82] or fusion splicing.
In a laboratory environment, a bare fiber end is coupled using a fiber launch system, which uses a microscope objective lens to focus the light down to a fine point. A precision translation stage (micro-positioning table) is used to move the lens, fiber, or device to allow the coupling efficiency to be optimized. Fibers with a connector on the end make this process much simpler: the connector is simply plugged into a pre-aligned fiber-optic collimator, which contains a lens that is either accurately positioned to the fiber or is adjustable. To achieve the best injection efficiency into a single-mode fiber, the direction, position, size, and divergence of the beam must all be optimized. With good beams, 70 to 90% coupling efficiency can be achieved.
With properly polished single-mode fibers, the emitted beam has an almost perfect Gaussian shape—even in the far field—if a good lens is used. The lens needs to be large enough to support the full numerical aperture of the fiber, and must not introduce aberrations in the beam. Aspheric lenses are typically used.
### Fiber fuse
At high optical intensities, above 2 megawatts per square centimeter, when a fiber is subjected to a shock or is otherwise suddenly damaged, a fiber fuse can occur. The reflection from the damage vaporizes the fiber immediately before the break, and this new defect remains reflective so that the damage propagates back toward the transmitter at 1–3 meters per second (4–11 km/h, 2–8 mph). [83] [84] The open fiber control system, which ensures laser eye safety in the event of a broken fiber, can also effectively halt propagation of the fiber fuse. [85] In situations, such as undersea cables, where high power levels might be used without the need for open fiber control, a "fiber fuse" protection device at the transmitter can break the circuit to keep damage to a minimum.
### Chromatic dispersion
The refractive index of fibers varies slightly with the frequency of light, and light sources are not perfectly monochromatic. Modulation of the light source to transmit a signal also slightly widens the frequency band of the transmitted light. This has the effect that, over long distances and at high modulation speeds, the different frequencies of light can take different times to arrive at the receiver, ultimately making the signal impossible to discern, and requiring extra repeaters. [86] This problem can be overcome in several ways, including the use of a relatively short length of fiber that has the opposite refractive index gradient.
## Notes
1. Infrared light is used in optical-fiber communication due to its lower attenuation
2. This feature is offset by the fiber's susceptibility to the gamma radiation from the weapon. The gamma radiation causes the optical attenuation to increase considerably during the gamma-ray burst due to the darkening of the material, followed by the fiber itself emitting a bright light flash as it anneals. How long the annealing takes and the level of the residual attenuation depends on the fiber material and its temperature.
3. The fiber, in this case, will probably travel a longer route, and there will be additional delays due to communication equipment switching and the process of encoding and decoding the voice onto the fiber.
4. The electromagnetic analysis may also be required to understand behaviors such as speckle that occur when coherent light propagates in multi-mode fiber.
5. The behavior of larger-core multi-mode fiber can also be modeled using the wave equation, which shows that such fiber supports more than one mode of propagation (hence the name). The results of such modeling of multi-mode fiber approximately agree with the predictions of geometric optics, if the fiber core is large enough to support more than a few modes.
6. For applications requiring spectral wavelengths, especially in the mid-infrared wavelengths (~2–7 μm), a better alternative is represented by fluoride glasses such as ZBLAN and InF3.
## Related Research Articles
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Multi-mode optical fiber is a type of optical fiber mostly used for communication over short distances, such as within a building or on a campus. Multi-mode links can be used for data rates up to 100 Gbit/s. Multi-mode fiber has a fairly large core diameter that enables multiple light modes to be propagated and limits the maximum length of a transmission link because of modal dispersion. The standard G.651.1 defines the most widely used forms of multi-mode optical fiber.
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An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light guides, and liquid waveguides.
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Silicon photonics is the study and application of photonic systems which use silicon as an optical medium. The silicon is usually patterned with sub-micrometre precision, into microphotonic components. These operate in the infrared, most commonly at the 1.55 micrometre wavelength used by most fiber optic telecommunication systems. The silicon typically lies on top of a layer of silica in what is known as silicon on insulator (SOI).
Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of infrared light through an optical fiber. The light is a form of carrier wave that is modulated to carry information. Fiber is preferred over electrical cabling when high bandwidth, long distance, or immunity to electromagnetic interference is required. This type of communication can transmit voice, video, and telemetry through local area networks or across long distances.
A fiber-optic cable, also known as an optical-fiber cable, is an assembly similar to an electrical cable but containing one or more optical fibers that are used to carry light. The optical fiber elements are typically individually coated with plastic layers and contained in a protective tube suitable for the environment where the cable is used. Different types of cable are used for different applications, for example, long-distance telecommunication or providing a high-speed data connection between different parts of a building.
Cladding in optical fibers is one or more layers of materials of lower refractive index, in intimate contact with a core material of higher refractive index. The cladding causes light to be confined to the core of the fiber by total internal reflection at the boundary between the two. Light propagation within the cladding is typically suppressed for most fibers. However, some fibers can support cladding modes in which light propagates through the cladding as well as the core. Depending upon the quantity of modes that are supported, they are referred to as multi-mode fibers and single-mode fibers. Improving transmission through fibers by applying a cladding was discovered in 1953 by Dutch scientist Bram van Heel.
Microstructured optical fibers (MOF) are optical fiber waveguides where guiding is obtained through manipulation of waveguide structure rather than its index of refraction.
Glass poling is the physical process through which the distribution of the electrical charges is changed. In principle, the charges are randomly distributed and no permanent electric field exists inside the glass.
An erbium-doped waveguide amplifier is a type of an optical amplifier enhanced with erbium. It is a close relative of an EDFA, erbium-doped fiber amplifier, and in fact EDWA's basic operating principles are identical to those of the EDFA. Both of them can be used to amplify infrared light at wavelengths in optical communication bands between 1500 and 1600 nm. However, whereas an EDFA is made using a free-standing fiber, an EDWA is typically produced on a planar substrate, sometimes in ways that are very similar to the methods used in electronic integrated circuit manufacturing. Therefore, the main advantage of EDWAs over EDFAs lies in their potential to be intimately integrated with other optical components on the same planar substrate and thus making EDFAs unnecessary.
## References
1. "Optical Fiber". www.thefoa.org. The Fiber Optic Association . Retrieved 17 April 2015.
2. Senior, John M.; Jamro, M. Yousif (2009). Optical fiber communications: principles and practice. Pearson Education. pp. 7–9. ISBN 978-0130326812.
3. "Birth of Fiberscopes". www.olympus-global.com. Olympus Corporation. Retrieved 17 April 2015.
4. Lee, Byoungho (2003). "Review of the present status of optical fiber sensors". Optical Fiber Technology. 9 (2): 57–79. Bibcode:2003OptFT...9...57L. doi:10.1016/s1068-5200(02)00527-8.
5. Senior, pp. 12–14
6. Pearsall, Thomas (2010). Photonics Essentials, 2nd edition. McGraw-Hill. ISBN 978-0-07-162935-5. Archived from the original on 2021-08-17. Retrieved 2021-02-24.
7. The Optical Industry & Systems Purchasing Directory. Optical Publishing Company. 1984.
8. Hunsperger (2017-10-19). Photonic Devices and Systems. Routledge. ISBN 9781351424844.
9. Senior, p. 218
10. Senior, pp. 234–235
11. "Narinder Singh Kapany Chair in Opto-electronics". ucsc.edu. Archived from the original on 2017-05-21. Retrieved 2016-11-01.
12. Bates, Regis J (2001). Optical Switching and Networking Handbook. New York: McGraw-Hill. p. 10. ISBN 978-0-07-137356-2.
13. Tyndall, John (1870). "Total Reflexion". Notes about Light.
14. Tyndall, John (1873). Six Lectures on Light. New York : D. Appleton.
15. Mary Bellis. "How Fiber Optics Was Invented" . Retrieved 2020-01-20.
16. Hecht, Jeff (2004). City of Light: The Story of Fiber Optics (revised ed.). Oxford University. pp. 55–70. ISBN 9780195162554.
17. Hopkins, H. H. & Kapany, N. S. (1954). "A flexible fibrescope, using static scanning". Nature. 173 (4392): 39–41. Bibcode:1954Natur.173...39H. doi:10.1038/173039b0. S2CID 4275331.
18. Two Revolutionary Optical Technologies. Scientific Background on the Nobel Prize in Physics 2009. Nobelprize.org. 6 October 2009
19. How India missed another Nobel Prize – Rediff.com India News. News.rediff.com (2009-10-12). Retrieved on 2017-02-08.
20. DEpatent 1254513,Börner, Manfred,"Mehrstufiges Übertragungssystem für Pulscodemodulation dargestellte Nachrichten.",issued 1967-11-16, assigned to Telefunken Patentverwertungsgesellschaft m.b.H.
21. USpatent 3845293,Börner, Manfred,"Electro-optical transmission system utilizing lasers"
22. Lunar Television Camera. Pre-installation Acceptance Test Plan. NASA. 12 March 1968
23. Hecht, Jeff (1999). City of Light, The Story of Fiber Optics. New York: Oxford University Press. p. 114. ISBN 978-0-19-510818-7.
24. "Press Release — Nobel Prize in Physics 2009". The Nobel Foundation. Retrieved 2009-10-07.
25. Hecht, Jeff (1999). City of Light, The Story of Fiber Optics. New York: Oxford University Press. p. 271. ISBN 978-0-19-510818-7.
26. "1971–1985 Continuing the Tradition". GE Innovation Timeline. General Electric Company. Retrieved 2012-09-28.
27. "About the Author – Thomas Mensah". The Right Stuff Comes in Black. Archived from the original on 2 January 2015. Retrieved 29 March 2015.
28. Catania, B.; Michetti, L.; Tosco, F.; Occhini, E.; Silvestri, L. (September 1976). "First Italian Experiment with a Buried Optical Cable" (PDF). Proceedings of 2nd European Conference on Optical Communication (II ECOC). pp. 315–322. Retrieved 2022-08-18.
29. "15 settembre 1977, Torino, prima stesura al mondo di una fibra ottica in esercizio". Archivio storico Telecom Italia. Archived from the original on 2017-09-17. Retrieved 2017-02-15.
30. "Springroove, il giunto per fibre ottiche brevettato nel 1977". Archivio storico Telecom Italia. Archived from the original on 2016-08-16. Retrieved 2017-02-08.
31. Mears, R.J.; Reekie, L.; Poole, S.B.; Payne, D.N. (30 January 1986). "Low-threshold tunable CW and Q-switched fibre laser operating at 1.55 µm" (PDF). Electronics Letters . 22 (3): 159–160. Bibcode:1986ElL....22..159M. doi:10.1049/el:19860111.
32. Mears, R.J.; Reekie, L.; Jauncey, I.M.; Payne, D.N. (10 September 1987). "Low-noise erbium-doped fibre amplifier operating at 1.54µm" (PDF). Electronics Letters . 23 (19): 1026–1028. Bibcode:1987ElL....23.1026M. doi:10.1049/el:19870719.
33. Desurvire, E.; Simpson, J.; Becker, P.C. (1987). "High-gain erbium-doped traveling-wave fiber amplifier". Optics Letters . 12 (11): 888–890. Bibcode:1987OptL...12..888D. doi:10.1364/OL.12.000888. PMID 19741905.
34. Russell, Philip (2003). "Photonic Crystal Fibers". Science. 299 (5605): 358–62. Bibcode:2003Sci...299..358R. doi:10.1126/science.1079280. PMID 12532007. S2CID 136470113.
35. "The History of Crystal fiber A/S". Crystal Fiber A/S. Retrieved 2008-10-22.
36. Yao, S. (2003). "Polarization in Fiber Systems: Squeezing Out More Bandwidth" (PDF). The Photonics Handbook. Laurin Publishing. p. 1. Archived from the original (PDF) on July 11, 2011.
37. "JANET Delivers Europe's First 40 Gbps Wavelength Service". Ciena (Press release). 2007-07-09. Archived from the original on 2010-01-14. Retrieved 29 October 2009.
38. NTT (September 29, 2006). "14 Tbps over a Single Optical Fiber: Successful Demonstration of World's Largest Capacity" (Press release). Nippon Telegraph and Telephone. Archived from the original on 2017-09-21. Retrieved 2017-02-08.
39. Alfiad, M. S.; et al. (2008). "111 Gb/s POLMUX-RZ-DQPSK Transmission over 1140 km of SSMF with 10.7 Gb/s NRZ-OOK Neighbours" (PDF). Proceedings ECOC 2008. pp. Mo.4.E.2. Archived from the original (PDF) on 2013-12-04. Retrieved 2013-09-17.
40. Alcatel-Lucent (September 29, 2009). "Bell Labs breaks optical transmission record, 100 Petabit per second kilometer barrier". Phys.org (Press release). Archived from the original on October 9, 2009.
41. Hecht, Jeff (2011-04-29). "Ultrafast fibre optics set new speed record". New Scientist. 210 (2809): 24. Bibcode:2011NewSc.210R..24H. doi:10.1016/S0262-4079(11)60912-3 . Retrieved 2012-02-26.
42. "NEC and Corning achieve petabit optical transmission". Optics.org. 2013-01-22. Retrieved 2013-01-23.
43. Bozinovic, N.; Yue, Y.; Ren, Y.; Tur, M.; Kristensen, P.; Huang, H.; Willner, A. E.; Ramachandran, S. (2013). "Terabit-Scale Orbital Angular Momentum Mode Division Multiplexing in Fibers" (PDF). Science. 340 (6140): 1545–1548. Bibcode:2013Sci...340.1545B. doi:10.1126/science.1237861. PMID 23812709. S2CID 206548907. Archived from the original (PDF) on 2019-02-20.
44. Kostovski, G; Stoddart, P. R.; Mitchell, A (2014). "The optical fiber tip: An inherently light-coupled microscopic platform for micro- and nanotechnologies". Advanced Materials. 26 (23): 3798–820. Bibcode:2014AdM....26.3798K. doi:10.1002/adma.201304605. PMID 24599822. S2CID 32093488.
45. Bănică, Florinel-Gabriel (2012). Chemical Sensors and Biosensors: Fundamentals and Applications. Chichester: John Wiley and Sons. Ch. 18–20. ISBN 978-0-470-71066-1.
46. Anna Basanskaya (1 October 2005). "Electricity Over Glass". IEEE Spectrum.
47. "Photovoltaic feat advances power over optical fiber - Electronic Products". ElectronicProducts.com. 2006-06-01. Archived from the original on 2011-07-18. Retrieved 2020-09-26.
48. Al Mosheky, Zaid; Melling, Peter J.; Thomson, Mary A. (June 2001). "In situ real-time monitoring of a fermentation reaction using a fiber-optic FT-IR probe" (PDF). Spectroscopy. 16 (6): 15.
49. Melling, Peter; Thomson, Mary (October 2002). "Reaction monitoring in small reactors and tight spaces" (PDF). American Laboratory News.
50. Melling, Peter J.; Thomson, Mary (2002). "Fiber-optic probes for mid-infrared spectrometry" (PDF). In Chalmers, John M.; Griffiths, Peter R. (eds.). Handbook of Vibrational Spectroscopy. Wiley.
51. Govind, Agrawal (10 October 2012). Nonlinear Fiber Optics, Fifth Edition. ISBN 978-0-12-397023-7.
52. Paschotta, Rüdiger. "Fibers". Encyclopedia of Laser Physics and Technology . RP Photonics. Retrieved Feb 22, 2015.
53. Gloge, D. (1 October 1971). "Weakly Guiding Fibers". Applied Optics. 10 (10): 2252–8. Bibcode:1971ApOpt..10.2252G. doi:10.1364/AO.10.002252. PMID 20111311 . Retrieved 31 January 2015.
54. Cozmuta, Ioana; Cozic, Solenn; Poulain, Marcel; Poulain, Samuel; Martini, Jose R. L. (2020). Breaking the Silica Ceiling: ZBLAN based opportunities for photonics applications. Optical Components and Materials XVII. Vol. 11276. SPIE. p. 25. Bibcode:2020SPIE11276E..0RC. doi:10.1117/12.2542350. ISBN 9781510633155. S2CID 215789966.
55. "Corning SMF-28 ULL optical fiber". Archived from the original on February 26, 2015. Retrieved April 9, 2014.
56. Jachetta, Jim (2007). "6.10 – Fiber–Optic Transmission Systems". In Williams, E. A. (ed.). National Association of Broadcasters Engineering Handbook (10th ed.). Taylor & Francis. pp. 1667–1685. ISBN 978-0-240-80751-5.
57. Archibald, P.S. & Bennett, H.E. (1978). "Scattering from infrared missile domes". Opt. Eng. 17 (6): 647. Bibcode:1978OptEn..17..647A. doi:10.1117/12.7972298.
58. Smith, R. G. (1972). "Optical Power Handling Capacity of Low Loss Optical Fibers as Determined by Stimulated Raman and Brillouin Scattering". Applied Optics. 11 (11): 2489–94. Bibcode:1972ApOpt..11.2489S. doi:10.1364/AO.11.002489. PMID 20119362.
59. Paschotta, Rüdiger. "Brillouin Scattering". Encyclopedia of Laser Physics and Technology. RP Photonics.
60. Skuja, L.; Hirano, M.; Hosono, H.; Kajihara, K. (2005). "Defects in oxide glasses". Physica Status Solidi C. 2 (1): 15–24. Bibcode:2005PSSCR...2...15S. doi:10.1002/pssc.200460102.
61. Glaesemann, G. S. (1999). "Advancements in Mechanical Strength and Reliability of Optical Fibers". Proc. SPIE. CR73: 1. Bibcode:1999SPIE.CR73....3G.
62. Kurkjian, Charles R.; Simpkins, Peter G.; Inniss, Daryl (1993). "Strength, Degradation, and Coating of Silica Lightguides". Journal of the American Ceramic Society. 76 (5): 1106–1112. doi:10.1111/j.1151-2916.1993.tb03727.x.
63. Kurkjian, C (1988). "Mechanical stability of oxide glasses". Journal of Non-Crystalline Solids. 102 (1–3): 71–81. Bibcode:1988JNCS..102...71K. doi:10.1016/0022-3093(88)90114-7.
64. Kurkjian, C. R.; Krause, J. T.; Matthewson, M. J. (1989). "Strength and fatigue of silica optical fibers". Journal of Lightwave Technology. 7 (9): 1360–1370. Bibcode:1989JLwT....7.1360K. doi:10.1109/50.50715.
65. Kurkjian, Charles R.; Gebizlioglu, Osman S.; Camlibel, Irfan (1999). "Strength variations in silica fibers". In Matthewson, M. John (ed.). Optical Fiber Reliability and Testing. Photonics '99. Proceedings of SPIE. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series. Vol. 3848. p. 77. Bibcode:1999SPIE.3848...77K. doi:10.1117/12.372757. S2CID 119534094.
66. Skontorp, Arne (2000). Gobin, Pierre F; Friend, Clifford M (eds.). Nonlinear mechanical properties of silica-based optical fibers. Fifth European Conference on Smart Structures and Materials. Proceedings of SPIE. Vol. 4073. p. 278. Bibcode:2000SPIE.4073..278S. doi:10.1117/12.396408. S2CID 135912790.
67. Proctor, B. A.; Whitney, I.; Johnson, J. W. (1967). "The Strength of Fused Silica". Proceedings of the Royal Society A . 297 (1451): 534–557. Bibcode:1967RSPSA.297..534P. doi:10.1098/rspa.1967.0085. S2CID 137896322.
68. Bartenev, G (1968). "The structure and strength of glass fibers". Journal of Non-Crystalline Solids. 1 (1): 69–90. Bibcode:1968JNCS....1...69B. doi:10.1016/0022-3093(68)90007-0.
69. Tran, D.; Sigel, G.; Bendow, B. (1984). "Heavy metal fluoride glasses and fibers: A review". Journal of Lightwave Technology. 2 (5): 566–586. Bibcode:1984JLwT....2..566T. doi:10.1109/JLT.1984.1073661.
70. Nee, Soe-Mie F.; Johnson, Linda F.; Moran, Mark B.; Pentony, Joni M.; Daigneault, Steven M.; Tran, Danh C.; Billman, Kenneth W.; Siahatgar, Sadegh (2000). "Optical and surface properties of oxyfluoride glass". Inorganic Optical Materials II. International Symposium on Optical Science and Technology. Proceedings of SPIE. Vol. 4102. p. 122. Bibcode:2000SPIE.4102..122N. doi:10.1117/12.405276. S2CID 137381989.
71. Karabulut, M.; Melnik, E.; Stefan, R; Marasinghe, G. K.; Ray, C. S.; Kurkjian, C. R.; Day, D. E. (2001). "Mechanical and structural properties of phosphate glasses". Journal of Non-Crystalline Solids. 288 (1–3): 8–17. Bibcode:2001JNCS..288....8K. doi:10.1016/S0022-3093(01)00615-9.
72. Kurkjian, C. (2000). "Mechanical properties of phosphate glasses". Journal of Non-Crystalline Solids. 263–264 (1–2): 207–212. Bibcode:2000JNCS..263..207K. doi:10.1016/S0022-3093(99)00637-7.
73. Gowar, John (1993). Optical communication systems (2d ed.). Hempstead, UK: Prentice-Hall. p. 209. ISBN 978-0-13-638727-5.
74. Kouznetsov, D.; Moloney, J.V. (2003). "Highly efficient, high-gain, short-length, and power-scalable incoherent diode slab-pumped fiber amplifier/laser". IEEE Journal of Quantum Electronics . 39 (11): 1452–1461. Bibcode:2003IJQE...39.1452K. CiteSeerX . doi:10.1109/JQE.2003.818311.
75. Matthewson, M. (1994). "Optical Fiber Mechanical Testing Techniques" (PDF). Critical Reviews of Optical Science and Technology. Fiber Optics Reliability and Testing: A Critical Review. Fiber Optics Reliability and Testing, September 8-9, 1993. CR50: 32–57. Bibcode:1993SPIE10272E..05M. doi:10.1117/12.181373. S2CID 136377895. Archived from the original (PDF) on 2019-05-02. Retrieved 2019-05-02 via Society of Photo-Optical Instrumentation Engineers.{{cite journal}}: CS1 maint: location (link)
76. "Light collection and propagation". National Instruments' Developer Zone. National Instruments Corporation. Archived from the original on January 25, 2007. Retrieved 2007-03-19.
77. Hecht, Jeff (2002). Understanding Fiber Optics (4th ed.). Prentice Hall. ISBN 978-0-13-027828-9.
78. "Screening report for Alaska rural energy plan" (PDF). Alaska Division of Community and Regional Affairs. Archived from the original (PDF) on May 8, 2006. Retrieved April 11, 2006.
79. "Corning announces breakthrough optical fiber technology" (Press release). Corning Incorporated. 2007-07-23. Archived from the original on June 13, 2011. Retrieved 2013-09-09.
80. Olzak, Tom (2007-05-03). "Protect your network against fiber hacks". Techrepublic. CNET. Archived from the original on 2010-02-17. Retrieved 2007-12-10.
81. "Laser Lensing". OpTek Systems Inc. Archived from the original on 2012-01-27. Retrieved 2012-07-17.
82. Atkins, R. M.; Simpkins, P. G.; Yablon, A. D. (2003). "Track of a fiber fuse: a Rayleigh instability in optical waveguides". Optics Letters. 28 (12): 974–976. Bibcode:2003OptL...28..974A. doi:10.1364/OL.28.000974. PMID 12836750.
83. Hitz, Breck (August 2003). "Origin of 'fiber fuse' is revealed". Photonics Spectra. Archived from the original on 2012-05-10. Retrieved 2011-01-23.
84. Seo, Koji; et al. (October 2003). "Evaluation of high-power endurance in optical fiber links" (PDF). Furukawa Review (24): 17–22. ISSN 1348-1797 . Retrieved 2008-07-05.
85. G. P. Agrawal, Fiber Optic Communication Systems, Wiley-Interscience, 1997. | 2023-03-24 12:09:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "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": 0.5705046057701111, "perplexity": 2804.0024185619386}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00706.warc.gz"} |
https://plainmath.net/94039/how-is-simple-harmonic-motion-related-to | # How is simple harmonic motion related to Hooke law?
How is simple harmonic motion related to Hooke law?
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A particle is said to be in simple harmonic motion if it satisfies the following differential equation:
$\stackrel{¨}{x}+{\omega }^{2}x=0$.
where x is the position of the particle, $\stackrel{¨}{x}$ is it's second derivative with respect to time (the acceleration) and $\omega$ is a constant that gives us the angular frequency of the oscillation.
Hooke's law is a model for the behavior of ellastic materials, such as a spring (and is only valid if the material does not suffer strong deformations). It states that the magnitude of the force F is proportional to a certain displacement x (with respect to an equilibrium position), with the proportinality given by a constant factor k. Additionaly, the force is a restoring force, that is, it's direction is opposite to the direction of the displacement vector:
F=-kx
Newton's second law states that the force F acting over a particle is equal to the product of it's mass m and it's acceleration $\stackrel{¨}{x}$, or:
$F=m\stackrel{¨}{x}$
This two equations give us the relation
$m\stackrel{¨}{x}=-kx$
Rearranging, we get:
$m\stackrel{¨}{x}+kx=0$
Divind by the mass m, we have:
$\stackrel{¨}{x}+\frac{k}{m}x=0$
Associating the ${\omega }^{2}=\frac{k}{k}m$ (which gives us the expression $\omega =\sqrt{\frac{k}{m}}$ for the angular frequency) gives us the equation for simple harmonic motion.
Therefore, any system that satisfies Hooke's law and isn't acted upon by any other forces is in simple harmonic motion. | 2022-12-07 06:11:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "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": 0.8423029184341431, "perplexity": 323.3686889558096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711150.61/warc/CC-MAIN-20221207053157-20221207083157-00459.warc.gz"} |
http://openstudy.com/updates/51106f59e4b0d9aa3c481ab1 | Here's the question you clicked on:
## dietrich_harmon Group Title Find the surface area of the cone to the nearest tenth. A. 203 cm2 B. 1341.5 cm2 C. 747.7 cm2 D. 213.5 cm2 one year ago one year ago
• This Question is Closed
1. dietrich_harmon Group Title
2. dietrich_harmon Group Title
@Hero
3. Hero Group Title
Use the surface area of a cone formula: $SA = \pi r^2 + \pi r s$
4. dietrich_harmon Group Title
c | 2014-08-01 08:10:12 | {"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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8142709136009216, "perplexity": 13318.629675700915}, "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-2014-23/segments/1406510274866.27/warc/CC-MAIN-20140728011754-00392-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://researchpad.co/article/doi/10.1111/cjag.12240 | John Wiley and Sons Inc.
Economic thoughts on the potential implications of COVID‐19 on the Canadian dairy and poultry sectors
Doi: 10.1111/cjag.12240
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### Notes
Abstract
The dumping of milk, the offering of hospitality size goods in grocery stores, and the closure of processing facilities are examples of the disruptions caused by the pandemic to the dairy, poultry, and egg sectors. These supply management sectors, however, are more resilient to the impacts of COVID‐19 than other sectors as producers are generally more financially stable, losses are pooled, and production/marketing efforts are coordinated.
Weersink, von Massow, and McDougall: Economic thoughts on the potential implications of COVID‐19 on the Canadian dairy and poultry sectors
## 1 1. INTRODUCTION
COVID‐19 has shaken the world. The death toll continues to increase, as does the unemployment level as non‐essential businesses are forced to shut down in an effort to slow the transmission of the disease. Excluded from the mandatory closures are those industries involved in the production and distribution of food, including dairy and poultry. While the food supply chains continue to operate, the shocks imposed on the economy by the pandemic have impacted all components of the agrifood sector.
In this paper, we discuss the repercussions of COVID‐19 on the supply chain for dairy and poultry in Canada. Although there are significant short‐term disruptions as highlighted by the dumping of milk and the temporary closure of poultry processing facilities, the focus on a domestic market by these sectors along with the stability and coordination of its supply management marketing systems has mitigated, to an extent, the economic implications of COVID‐19. The discussion highlights the importance of distinguishing between the farm output (i.e., milk, chicken, and eggs) and the products stemming from that output, the difference in the demand for those products for home consumption versus dining out, and the difference in the distribution systems for grocery retailers and the hospitality industry.
## 2 2. FOOD DISTRIBUTION CHAINS AND COVID‐19 SHOCKS
Governments in Canada have imposed strict measures to reduce the spread of COVID‐19. Movement has been severely curtailed as the population has been told to stay home except for trips to grocery stores or pharmacies, which are the only retail outlets operating at close to normal. The restrictions have significantly limited the ability to purchase food away from home, and, even if the hospitality sector was open for business, the economic fallout from the pandemic has lowered the discretionary spending of many Canadians. The consumption patterns for dairy and poultry products have been altered as a result, with implications for the whole value chain. These impacts are discussed below, along with the adjustments required for each part of the distribution system to deal with COVID‐19 directly or indirectly through actions to lower its transmission rate.
### 2.1 2.1. Retail
The first change stemming from COVID‐19 is the reduction in the demand by the hospitality sector and a corresponding increase at the food retail sector. Canning, Weersink, and Kelly (2016) and Kelly, Canning, and Weersink (2015) calculated the overall farmer share of the food dollar spent at home versus away from home for Canada (17%) and the United States (14%). The farm share of expenditures on food for home consumption is approximately 22% across both countries, but it is 4% in the United States and 7% in Canada for meals consumed away from home. Using these values, it is estimated that Canadians spend approximately one‐third of their food budget at restaurants and bars, Americans spend approximately 40%. The percentage is higher if beverages are included in the calculations.
The one‐third reduction in total consumer food dollar from food services would be expected to shift to food retail. The extent of the change in sales in grocery stores for the week ending March 14 in 2020 compared to 2019 is illustrated in Figure 1. Overall sales were 46% higher in grocery stores—significantly higher than the 33% suggested if expenditures were simply shifted from hospitality to grocery. As discussed elsewhere in this issue , panic and hoarding behavior without limits on number of items purchased led to sales 16% higher than that for the typical busiest week of the year in early December (Statistics Canada, 2020). Recent reports suggest that the extent of the increase in sales at grocery stores has fallen after consumers loaded up in mid‐March, but the volume is still higher than previous years.
FIGURE 1
Fresh and frozen foods, percent change in sales for the week ending March 14 in 2020 compared to 2019Source : Statistics Canada (2020)
The resulting higher demand at grocery stores requires greater staff to meet the higher total volume and the higher percentage of online sales with pickup as consumers want to avoid physically entering the store. Food retail stores have also limited shopping hours to allow more time to restock shelves and deal with the increase in nightly shipments to deal with the larger volume.
Milk sales in grocery stores increased by 31% from the same week a year earlier, while butter increased by 76%, reflecting an increase in baking at home and hoarding of more storable products. It is expected that fluid milk sales will continue at this rate as the higher milk consumption by individuals at home offsets a decline in food service demand (i.e., school lunch programs). In general, the use of creams and cheeses by the hospitality sector is greater than the corresponding at‐home demand, so the initial 44% increase in sales of cheese in the middle of March 2020 compared to 2019 is not expected to continue.
The volume of fresh chicken sold in grocery stores increased by 50% in mid‐March 2020 compared to the same week a year earlier (Statistics Canada, 2020). Weekly retail chicken sales figures through Nielsens from the Chicken Farmers of Canada (CFC) are lower than those reported by Statistics Canada, but the CFC has more recent data. Of particular note is the further increase in chicken sales at grocery stores for the week ending March 21 but then a reduction the following week. Discussions with industry personnel suggest that, eventually, total chicken sales will fall compared to pre‐COVID‐19 as the increase in sales at grocery stores will not offset the loss from food services.
In addition to a change in the volume of chicken sold, there has been a change in the demand for chicken products associated with the shift away from hospitality services to grocery stores. Prices for various chicken parts in the northeast United States over the last 4 months are illustrated in Figure 2, with the black vertical line indicating the date when New York declared a state of emergency (March 12). The relative price movements of alternative chicken parts for the northeast United States are consistent with changes noted through discussions with industry personnel in Canada. Wing consumption primarily occurs outside the home, and the sharp drop in wholesale wing prices corresponds to the reduction in food service demand. The price for chicken breasts has also fallen due to lower relative use of chicken at home versus dining out and the smaller desired size of chicken breasts at the grocery store versus restaurants. Chickens (and parts) sold to the retail chain are generally smaller than those sold into food service.
FIGURE 2
Daily Northeast U.S. chicken part prices, December 2, 2019, to April 6, 2020
The consumption pattern for eggs has also changed as a result of the spread of COVID‐19. Precrisis, 70% of egg consumption was in shelled eggs and the remainder was through breaker eggs, which are eggs in liquid form (not in shell) used in baking, food manufacturing, and the hospitality sector. Liquid eggs are usually broken from shells that are still intact but that have a visible flaw. In times of normal demand, unflawed eggs are sometimes also broken to serve this market. If breaker demand decreases below a threshold, there will be blemished eggs for which there is no demand.
Given the closure of most hotels, restaurants, and convention centers, breaker egg demand fell between 40% and 60% in the 3 weeks leading up to April 7 (Bill Mitchell, personal discussions, April 2020). This loss of demand has not been compensated by increases in demand from the shell market, which increased by 67% in grocery stores for the week ending March 14 compared to the previous year (Statistics Canada, 2020). While prices for chicken parts have fallen (Figure 2), the wholesale prices for eggs in the United States have tripled from mid‐March to early‐April (Urner‐Barry, 2020). Lusk (2020) offers several potential reasons for the price increase, ranging from hoarding behavior, the approaching of Easter, the difficulty of switching the distribution chain from hospitality to grocery, and industry concentration. Grocery store shelves should replenish as limits are imposed on the number of eggs that can be purchased and supply chains adjust, with part of the adjustment involving the size of the egg cartons offered for sale.
### 2.2 2.2. Distribution
The shift from food service to food retail and its impact on the type and amount of product required alters the whole supply chain, which cannot adjust instantaneously as the system tends to be operating near capacity with minimal inventory carryover. It also requires an adaptation or re‐allocation in the food distribution system that tends to focus on either food retail or food service sectors. The major grocery chains rely on their own distribution systems. Processors, including dairy and poultry, tend to ship their products in bulk to distribution centers for the chain, and the needs of individual stores within that chain are gathered and shipped from these warehouses.
In contrast, the distribution system for the hospitality sector is not vertically integrated, and the companies that focus on away‐from‐home outlets are distinct from the system serving grocery stores. The two large players in food service distribution, Sysco and Gordon Food Services controls more than two thirds of the market share, with the remainder covered by regional companies. The shutdown of restaurants and conference centers has forced these companies to shift focus. However, it takes time to establish new relationships with agents at the food retail level and to change their operations to meet requirements of new customers at a different part of the value chain (Blaze Baum, Silcoff, & Krahshinsky Robertson, 2020). It is not expected that these distributors will make significant inroads into the retail market as the established and vertically integrated distribution for food retail adjusts.
### 2.3 2.3. Processor
The impact of the changing volume and mix of their offering by individual processors will differ depending upon their portfolio of customers. Even when product changes are not required, alterations to packaging may be necessary. For example, a dairy processing plant sells cream to coffee shops in large bags that fit in dispensers, while sales to grocery stores are for households wanting small amounts in a carton that fits in a fridge. In some cases, both processors and retailers are adjusting in the short run. Sobeys is now selling flats of 30 eggs in addition to the typical dozen eggs offered in their stores. The flats from Burnbrae Farms, which is an egg producer and processor supplying to both food service and grocery stores, were originally intended for the hospitality sector (Blaze Baum et al., 2020). Another example are the boxes of 40 frozen chicken breasts now offered for sale in grocery stores that were originally slated for the food service sector. Chicken processing companies, according to industry personnel, are also simplifying their product offerings to increase operating capacity as they adjust to the higher volume from grocery stores.
In addition to the impacts of COVID‐19 brought about by the changes in consumer demand discussed above, the processing sector is particularly vulnerable to disruptions caused directly by the virus. The processing sector has significantly less opportunity to physically distance its employees than other parts of the value chain. In addition, there is a relatively high degree of concentration, which means that product flows through a smaller number of players on the way to the consumer. If one of those processing plants were to close or be restricted, then there could be a disruption, with the extent of the impact being largest on perishable goods such as milk and smaller on chicken, which can be frozen and stored. The degree to which the flow would be altered by the closure of a processing plant also depends on the ease of finding other processors, which is influenced by the degree of specialization and concentration.
It is not expected that COVID‐19 would cause long‐term plant closures given businesses in food production are designated as essential. Sanderson Farms, which is located in Mississippi, was the first dairy or poultry processing company to experience a case of COVID‐19. Management sent the employee home, along with others working in close proximity, but the plant remained open. More recently, an employee at a Tyson poultry processing plant in Georgia died from the virus, highlighting the difficulty of containing its spread in a meat processing plant (Jordan & Dickerson, 2020). The first Canadian poultry or dairy processing facility to be affected by staff contracting COVID‐19 was a Maple Leaf plant in Brampton. Maple Leaf suspended operations on April 8 and will not open until an investigation and deep cleaning of the plant is completed (Maple Leaf, 2020). If the number of closures remains small, it is expected that animals or inputs can be rerouted to other facilities, which increases costs but maintains output. Further closures of other, larger processing facilities could significantly disrupt the food distribution chains, leaving producers and their marketing boards searching for other outlets for their commodities.
It is more likely that there could be capacity constraints as plants adapt to provide protection and physical distancing between workers. There have been some reports of this in the dairy industry in Ireland, for example. Another issue could be employees refusing to come in to work because of the risk. Food processors often struggle to find sufficient labor under normal circumstances, and it would be difficult to replace skilled workers even in a period of high unemployment with COVID‐19‐related layoffs. As individual plants have different portfolios of products, individual plant closures or slowdowns could have an impact on the availability of specific dairy or poultry products.
### 2.4 2.4. Farm
Dairy and poultry farms are operating as they were several months ago, aside from the social distancing occurring between visitors to the farm and the farm workforce. Input deliveries and output pickups can be done without direct contact among those involved. As discussed in Brewin (2020), the seeds, fertilizers, fuel, and pesticides are all in place for planting this spring. Similarly, the supply of feed and other inputs for livestock production have not been affected in the short run.
The most direct impact from COVID‐19 on livestock feed thus far has not been on the supply of feed in aggregate but rather on the availability and, subsequently, the cost of certain ingredients, such as dried distillers grain (DDGs). The nearby futures price of crude oil fell from above $60 (USD) per barrel at the beginning of the year to just above$20 (USD) per barrel on March 23. Oil and ethanol prices are correlated, and the low returns have reduced production of ethanol at plants continuing to operate and led to the closure of others. On March 27, ethanol production plummeted to its lowest levels since June 2010. The fall in ethanol output means a corresponding fall in the supply of its by‐products such as DDGs. The subsequent increase in DDG price alters the least‐cost ration and feed costs for livestock farmers (Skinner, Weersink, & deLange, 2012). Prices for another common feed ingredient, wheat shorts, have also increased due to an increase in demand for flour with more in‐home baking.
While production systems have not been altered in the short term by the pandemic, the level of output has been affected for both dairy and poultry. In the middle of March, it appeared that quota‐free days (producers are allowed to ship milk in excess of their quota without penalty) might become available to dairy producers in some parts of the country as a means to create incentives to meet reduced overall supply of milk combined with a run on dairy products resulting from panic buying in the immediate onset of COVID‐19. A few weeks later, dairy farmers were forced to dispose of certain milk shipments (DFO, 2020). We may see a return to quota‐free days depending on total demand once the adaptation has taken place. Similarly, chicken farmers are being forced to shorten the production cycle with their current allotment of birds and will likely face smaller production quota levels along with raising smaller birds in the future (CFO, 2020).
The unfortunate situation of dumping raw milk is occurring as the supply chain adjusts to disruptions caused by COVID‐19. Some dairy processors require less milk because hospitality customers are demanding less volume of specific goods (i.e., cream) and milk needs to be redirected to products and processors for whom demand is higher. In some cases, the same product is required but the packaging is different (single‐serving wraps of butter or large tubs for hospitality to 454 g of butter for grocery stores). This production shift takes planning and time. There will also be logistical issues in redirecting supply to different processors. The process of cutting production for food service is quicker than that of ramping up production for retail.
While dairy processors can typically adapt to small increases or decreases, the enhanced demand on retail lines combined with the shutting down of food service lines takes time. During the adjustment, cows continue to be milked and milk is stored by farmers in tanks large enough to hold a maximum of 72 hours of production. The raw, unpasteurized milk is brought by transporters to processors, who now do not have sufficient storage to keep excess milk as they shift their operational focus. Typically, fluid milk goes from a farm bulk tank to a retail fridge in a matter of days, but there is no buffer capacity to hold milk that is not immediately processed. Since milk is produced on the farm daily, milk needs to be dumped to make room for new production.
The phenomenon of dumping milk is not unique to Canada as up to 7% of all milk produced in the United States was dumped in first week of April (Newman & Bunge, 2020). The problem will be particularly acute in markets like Wisconsin with a high proportion of processors focused on products (i.e., cheese) particularly affected by the reduction in demand by the hospitality sector. If the need for milk by these processors is lowered and fluid milk processing happens in other states, those dairy farmers will struggle to quickly find alternative markets. Milk dumping is likely to continue, and dairy farm returns will subsequently fall. In contrast, the Canadian single‐desk selling system for dairy, poultry, and egg farmers works in conjunction with processors to coordinate production and marketing, as evident by the joint statement on the milk supply situation issued by the Dairy Farmers of Canada and Dairy Processors of Canada (DPAC, 2020). The Canadian system, with central selling and transportation coordination, as well as more localized provincial production, may facilitate quicker adaptation and reallocation than in the United States.
Producers in supply managed industries are paid based on a cost of production formula and, as such, are less susceptible to the cyclicality of commodity prices. There continues to be an ongoing debate as to the value of supply management. In this circumstance, however, the stability provided by the system insulates producers against the potential disruption. The milk that is dumped at the farm level will be paid for. Returns are pooled across all processors and classes of milk. Milk is priced to processors based on end‐use, with fluid milk products being the highest class. Milk is allocated on demand to the highest classes, and then allocated based on historical shares in the lower classes. Producers are paid a pooled price based on all the milk sold, so it doesn't matter where an individual producer's milk is shipped and which producers were required to dump milk. In the United States, on the other hand, the loss is incurred by the dairy farmer and/or the cooperative in the region in which processor demand is significantly reduced. This would be similar in Canada for products that do not have central desk selling.
## 3 3. CONCLUSIONS
There have been some clear and significant disruptions to dairy and poultry supply chains that can be directly attributed to challenges arising from COVID‐19. The structure of supply management in dairy, poultry, and eggs may allow the industries to recover more quickly from the disruptions caused by the pandemic. Producers in the supply managed sectors are generally more financially stable, which should allow them to weather any decreases in returns more easily than producers in other sectors. Losses are shared across individual producers and marketing/transport is coordinated, providing resilience within the system. The supply chain has adapted relatively quickly in the short term to both shortages and surpluses, resulting in the changes in volume and nature of products offered through the shift from hospitality to grocery.
There are several longer‐term implications on the dairy and supply managed sectors arising from the pandemic. One relates to what will be the new “normal” once businesses, including restaurants, return. By then, the volume and nature of demand for dairy and poultry products may be altered permanently, or at least become slow to adjust due to income effects associated with the job losses suffered by a large number of Canadians. The resulting adaptation over the longer term will be easier to manage based on both experience and rate of change. Second, the process of automation will accelerate at all levels of the supply chain. The movement to labor‐saving technology will be spurred by the increase in wages paid to workers during the crisis and an increased reliance on machines not vulnerable to disease. The third implication is the enhanced desire for local production as opposed to dependence on global distribution chains to supply goods, from food to safety masks. Since the supply managed sectors already have a focus on domestic production, the impact of such a shift in preferences will not significantly impact its supply chain but could have implications for other sectors.
## REFERENCES
1
Blaze Baum, K., Silcoff, S., & Krahshinsky Robertson, S. (2020). . As restaurants close and demand for groceries surges, food distributors shift their focus to retailers. Globe and Mail Retrieved from https://www.theglobeandmail.com/business/article-as-restaurants-close-and-demand-for-groceries-surges-food/
2
Brewin, D. (2020). . The impact of COVID‐19 on the grains and oilseeds sector. Canadian Journal of Agricultural Economics. (this issue).
3
Canning, P., Weersink, A., & Kelly, J. (2016). . Farm share of the food dollar: An IO approach for the United States and Canada. Agricultural Economics, 47(5), , pp.505–512.
4
Chicken Farmers of Ontario . (2020). . Production planning during COVID‐19. COVID‐19 Information Retrieved from https://www.ontariochicken.ca/Farmer-Member-Resources/COVID-19-Information/Production-Planning-During-COVID-19
5
Dairy Farmers of Ontario . (2020, March 31). . Letter to producers, from Murray Sherk, Chair, Dairy Farmers of Ontario. Retrieved from https://files.constantcontact.com/577a9199701/f220719d-14f6-4619-aef8-67215e9c615d.pdf
6
Dairy Processors Association of Canada . (2020, 2). . Joint DPAC‐DFC statement on milk supply situation. Retrieved from http://www.dpac-atlc.ca/media/joint-dpac-dfc-statement-milk-supply-situation/
7
Jordan, M., & Dickerson, C. (2020). . Poultry worker death highlights the spread of coronavirus in meat plants, New York Times. Retrieved from https://www.nytimes.com/2020/04/09/us/coronavirus-chicken-meat-processing-plants-immigrants.html?referringSource=articleShare
8
Kelly, J., Canning, P., & Weersink, A. (2015). . Decomposing the farmer's share of the food dollar. Applied Economic Perspectives and Policy, 37(2), , pp.311–331.
9
Lusk, J. (2020). . Meat and egg prices following the COVID‐19 outbreak. Blogpost Retrieved from http://jaysonlusk.com/blog/2020/4/5/food-sales-and-prices-following-covid-19-outbreak
10
Maple Leaf Foods . (2020, 8). . Doing our Part During the COVID‐19 Pandemic. Around the Table‐Blog Retrieved from https://www.mapleleaffoods.com/stories/our-operational-status-during-covid-19-pandemic/
11
Newman, J., & Bunge, J. (2020). . Farmers dump milk, break eggs as coronavirus restaurant closings destroy demand. Wall Street Journal Retrieved from https://www.wsj.com/articles/farmers-deal-with-glut-of-food-as-coronavirus-closes-restaurants-11586439722
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https://mathhelpboards.com/threads/floquet.1873/ | # [SOLVED]Floquet
#### dwsmith
##### Well-known member
For the scalar linear ODE with periodic coefficients,
$$x' = a(t)x,\quad\quad a(t + T) = a(t),$$
show that the solution is of the form
$$x(t) = x_0e^{\mu t}p(t),$$
where $\mu$ and $x_0$ are constants, and $p(t)$ is a $T$-periodic function.
How can I show the solution is of the form mentioned? Can I just say by Floquet Theory, the solution is of the form $X(t) = \sum\limits_{n=1}^{n}c_nx_n(t)$ where $x_n(t) = e^{\mu_nt}p_n(t)$ but then how do I get the $x_0$ for $c_1$?
By Floquet Theory, we can define $X_k = X(t)v_k$.Suppose $Bv_k = \lambda_kv_k$.
$$X_k(t + T) = X(t + T)v_k = X(t)Bv_k = X(t)\lambda_kv_k = \lambda_kX(t)v_k = \lambda_kX_k(t)$$
Let $\underbrace{\lambda_k}_{\text{characteristic multipliers}} = \text{exp}\left[\overbrace{\rho_k}^{\text{characteristic exponents}}T\right]$.
Define $p_k(t) = \frac{X_k(t)}{e^{\rho_k t}}$.
Then
\begin{alignat*}{3}
p_k(t + T) & = & \frac{X_k(t + T)}{\text{exp}\left[\rho_k(t + T)\right]}\\
& = & \frac{\lambda_kX_k(t)}{\text{exp}\left[\rho_k(t + T)\right]}\\
& = & \frac{\lambda_kX_k(t)}{\lambda_k\text{exp}\left[\rho_kt\right]}\\
& = & \frac{X_k(t)}{\text{exp}\left[\rho_kt\right]}\\
& = & p_k(t)
\end{alignat*}
Thus $p(t)$ is T periodic.
Since $x_0 = x(0)$ is an initial condition, can I just say that is why it is constant. What about $\mu$?
Last edited:
#### Alan
##### Member
If x is one dimensional then by separation of variables you get:
$$x(t)=x_0 e^{\int a(t) dt}$$
Now if you can expand a(t) to power series around 0 (which is not given in your premise), then
a(t) = a(0)+ a'(0)t + a''(0)t^2/2!+...
a(T)=a(0)=\mu
you'll get one part of exp(\mu t) and the other part is
$$p(t)=e^{a'(0)t^2/2+a''(0)t^3/6+...}$$
$$p'(t)=p(t) (a(t)-a(0))=p(t)(a(t)-a(T))$$
plug t-> t+T to get:
$$p'(t+T)=0$$
i.e $$p(t+T)=const$$
And this I believe finishes the proof, but it's not general without assuming something on our 'a'.
#### dwsmith
##### Well-known member
If x is one dimensional then by separation of variables you get:
$$x(t)=x_0 e^{\int a(t) dt}$$
Now if you can expand a(t) to power series around 0 (which is not given in your premise), then
a(t) = a(0)+ a'(0)t + a''(0)t^2/2!+...
a(T)=a(0)=\mu
you'll get one part of exp(\mu t) and the other part is
$$p(t)=e^{a'(0)t^2/2+a''(0)t^3/6+...}$$
$$p'(t)=p(t) (a(t)-a(0))=p(t)(a(t)-a(T))$$
plug t-> t+T to get:
$$p'(t+T)=0$$
i.e $$p(t+T)=const$$
And this I believe finishes the proof, but it's not general without assuming something on our 'a'.
By separation of variables, we have that $\int\frac{\dot{x}}{x}dx = \int a(t)dt$.
$$x = C\exp\left[\int a(t)dt\right].$$
Let's expand the the Taylor series of $a(t)$ about 0.
$$a(0) = a(0) + a'(0)t + \frac{a''(0)t^2}{2} + \cdots$$
Since $a(t)$ is periodic with period $T$, we have $a(T) = a(0) = \mu$.
By substitution, we have
\begin{alignat*}{3}
x(0) & = & C\exp\left[\int \mu dt\right]\\
& = & Ce^{\mu t}
& = & C = x_0
\end{alignat*}
Therefore, we have $x(t) = x_0e^{\mu t}$
But why is p(t) multiplied by x? How do we go from the x above to saying it is $x(t) = x_0e^{\mu t}p(t)$
#### Alan
##### Member
The solution is
$$x(t)=x_0 e^{a(T)t} e^{a'(0)t^2/2+a''(0)t^3/6+...}$$
Denote by p(t) the third factor, you can see that it satisfies:
$$p'(t)=p(t)(a(t)-a(0))$$
So you get that p'(T)=0, and this is true for any m integer that p'(mT)=0, thus p(t+T)=p(t).
#### dwsmith
##### Well-known member
The solution is
$$x(t)=x_0 e^{a(T)t} e^{a'(0)t^2/2+a''(0)t^3/6+...}$$
Denote by p(t) the third factor, you can see that it satisfies:
$$p'(t)=p(t)(a(t)-a(0))$$
So you get that p'(T)=0, and this is true for any m integer that p'(mT)=0, thus p(t+T)=p(t).
How do you go from
$$\exp\left[a(t + T)\right]$$
to
$$e^{a(T)t} e^{a'(0)t^2/2+a''(0)t^3/6+...}$$
#### Alan
##### Member
You have $$x(t)=x_0 e^{\int a(t)dt}$$
I assumed that I can expand a(t) by a power series (I don't see how to show this otherwise), so a(t)=a(0)+a'(0)t+a''(0)t^2/2!+... and a(0)=a(T) from T-periodicity of a(t), plug back to the integral to get what I wrote.
If I can't expand a(t) with a powers series then I am not sure how to solve this.
#### dwsmith
##### Well-known member
You have $$x(t)=x_0 e^{\int a(t)dt}$$
I assumed that I can expand a(t) by a power series (I don't see how to show this otherwise), so a(t)=a(0)+a'(0)t+a''(0)t^2/2!+... and a(0)=a(T) from T-periodicity of a(t), plug back to the integral to get what I wrote.
If I can't expand a(t) with a powers series then I am not sure how to solve this.
So $p(t) = \exp\left[\int\left(a'(0)t + \frac{a''(0)t^2}{2} + \cdots\right)dt\right]$ is defined this way?
#### dwsmith
##### Well-known member
$$p'(t)=p(t)(a(t)-a(0))$$
So you get that p'(T)=0, and this is true for any m integer that p'(mT)=0, thus p(t+T)=p(t).
Ok so I understand p(t) now. Why are you taking the derivative of p(t) to show it is T-periodic?
#### dwsmith
##### Well-known member
$$p'(t)=p(t) (a(t)-a(0))=p(t)(a(t)-a(T))$$
plug t-> t+T to get:
$$p'(t+T)=0$$
i.e $$p(t+T)=const$$
I don't get this part.
#### dwsmith
##### Well-known member
This is all wrong. Is there another way to do this?
What I wrote original comes from Floquet. Is it enough to just say what I was doing in post 1?
#### Raluca
##### New member
Hello, I am a phd student in Romania and I have to study Floquet Theory. I need some help with documentation and research. Do you have any? Appreciate your help
#### Raluca
##### New member
do you think i could apply this floquet theory in economics?
#### dwsmith
##### Well-known member
do you think i could apply this floquet theory in economics?
This is just the mathematics about it so you should be able to since the ecnomic version is probably built off of the math. | 2021-07-27 10:45:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8934228420257568, "perplexity": 1321.1084997051366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1627046153391.5/warc/CC-MAIN-20210727103626-20210727133626-00398.warc.gz"} |
https://www.semanticscholar.org/paper/Study-of-charmless-hadronic-B-decays-into-the-final-collaboration/0bd00e589f935f36c33e5ca7995e3b1d2901292b | Corpus ID: 119419309
# Study of charmless hadronic B decays into the final states $K\pi, \pi\pi$, and KK, with the first observation of $B \to \pi^+ \pi^-$ and $B\to K^0\pi^0$
@inproceedings{collaboration1999StudyOC,
title={Study of charmless hadronic B decays into the final states \$K\pi, \pi\pi\$, and KK, with the first observation of \$B \to \pi^+ \pi^-\$ and \$B\to K^0\pi^0\$},
author={C. collaboration},
year={1999}
}
• C. collaboration
• Published 1999
• Physics
• We have studied charmless hadronic decays of B mesons into two-body final states with kaons and pions. We present preliminary results based on 9.66 million $B\bar{B}$ pairs collected with the CLEO detector. We have made the first observation of the decay $B \to \pi^+\pi^-$, with the branching fraction of $Br(B \to \pi^+ \pi^-) = (4.7^{+1.8}_{-1.5} \pm 0.6) \times 10^{-6}$. We have also observed for the first time the decay $B \to K^0\pi^0$ with the branching fraction of \$Br(B \to K^0 \pi^0… CONTINUE READING | 2021-03-01 14:05:03 | {"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": 0.9693835973739624, "perplexity": 4262.559067216967}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362513.50/warc/CC-MAIN-20210301121225-20210301151225-00138.warc.gz"} |
http://math.stackexchange.com/tags/banach-spaces/hot | # Tag Info
3
Yes, it's complete. First, observe that your norm is comparable to the simpler norm $$\|f\| = \sup_{n\in\mathbb{Z}} \int_n^{n+1}|f(y)|\,dy \tag{1}$$ Indeed, $\|f\|\le |f|\le 2\|f\|$ because every interval of length $1$ is contained in some interval of the form $[n,n+2]$. The space with $(1)$ is just the direct sum $\bigoplus_\infty X_n$ of Banach spaces ...
3
It is well-known (and easy to see) that $c/Y$ is isomorphic to $c_0$. So we just need to renorm $c_0$ so that the natural map between them is an isometry. In fact, the norm $|||\cdot|||$ will do, where \begin{equation*}|||(x_n)|||=\frac{1}{2}\sup_{m,n}|x_n-x_m|.\end{equation*} Notice that for any $(x_n)\in c_0$ we have ...
2
For completeness, I post the proof here. The first two facts are valid for all metric spaces. If a Cauchy sequence has a convergent subsequence, it converges. Every Cauchy sequence contains a subsequence (denoted $\{x_n\}$ here) such that $$d(x_n,x_{n+1})\le 2^{-n},\quad n\in\mathbb{N} \tag{1}$$ (Note that $(1)$ implies being Cauchy.) So, it suffices ...
1
The following claim is not true in general. Let $X$ and $Y$ be Banach spaces and $X_1 \subset X$ a subspace. If $T: X_1 \to Y$ is a continuous bounded operator, then there exists a continuous linear extension to the whole space $X$, i.e. there exists a bounded linear operator $\hat T: X \to Y$ such that $\hat{T}\restriction_{X_1} = T$. Take for ...
1
First of all: since all norms on a finite-dimensional space are comparable, the condition could be simpler stated as $$C_1\|x-y\| \leq d(x,y) \leq C_2\|x-y\|$$ where $\|\cdot \|$ is a norm of our choice, e.g., Euclidean. Second: the answer is negative, for example $$d(x,y) = |x-y|+\min(|x-y|,1)$$ is a translation-invariant metric on $\mathbb{R}$ that ...
1
Recall that an operator is closed if a sequence $(x_{n})\subset D(T)$ converges to some $x\in X$ and $Tx_{n}$ converges to $y\in Y$ implies $x\in D(T)$. Equivalently, the graph of $T$ is closed in the direct sum $X\oplus Y$. Proof of i). Since $T$ is injective, we can define a linear operator $T^{-1}$ on the range of $T$, denoted $R(T)$, by $T^{-1}y=x$, ...
1
Let $S$ be the subspace of $c$ of convergent sequences $x = (x_1,x_2,\dotsc)$ satisfying $\sup x + \inf x = 0$. Let $y_\alpha$ denote the constant sequence $\alpha, \alpha, \dotsc$. Let $h(x)$ denote the number $\sup(x) + \inf(x) \over 2$ Then the map $c/Y \rightarrow S$ given by $[x] \mapsto x - y_{h(x)}$ is an isometry onto $S$.
1
In your situation, you have $x_n \to x$. This can be proved by contradiction. Suppose $(x_n)$ does not converge to $x$. Then, there is $\varepsilon > 0$ and a subsequence $(x_{n_k})$ with $\|x_{n_k} - x\| \ge \varepsilon$ for all $k$. But this subsequence converges weakly to $x$ and, hence, is bounded. By compacity of $K$, a subsequence converges ...
1
The space $\ell_2$ is the space of infinity sequences square additive. You can map a vector in $\ell_2$, for example $(\xi_1, \xi_2 ,\cdots, \xi_k \, \cdots)$ to a power series $\xi_1 + \xi_2 z + \cdots, \xi_k z^k + ...$. This is known as the Z transform. think about $z=\exp(i \omega \Delta t)$ where $\omega = 2 \pi f$, and $f=1/\Delta t$ is the frequency. ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2015-05-22 13:16:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9882976412773132, "perplexity": 78.36071525807264}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207925201.39/warc/CC-MAIN-20150521113205-00073-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://chemistry.stackexchange.com/questions/144842/how-does-one-prove-avogadros-law-from-gay-lussacs | # How does one prove Avogadro's law from Gay-Lussac's?
To understand Gay-Lussac's law, Amedeo Avogadro said
In equal volumes of air under constant temperature and pressure, there are equal number of atoms (or molecules).
Let's take a hydrogen and an oxygen molecule. As the latter is larger in size, when stored in two separate equally-volumed containers, doesn't oxygen increase the pressure inside that container, if the same number of molecules occupied each container? (Does this make Avogadro's statement of constant pressure go wrong?) Again,
$$2mvN\cos\theta = F,$$
where $$F$$ is the force acting on the walls of the container, $$N$$ is the number of collisions of the molecules with the walls, $$2mv$$ is the change of momentum of the molecules, and $$\theta$$ is the angle of collision of the molecules on the walls.
Therefore, if Avogadro was correct, could anyone give me any reason why $$N_\ce{H2} > N_\ce{O2}$$ or $$v_\ce{H2} > v_\ce{O2}?$$
If Avogadro was correct, the above conditions must hold, as $$m_\ce{H2} < m_\ce{O2},$$ right?
Could you please prove the above phenomena happen when Avogadro's statement above holds?
• The kinetic theory of the collisions has no connection with Avogadro's law. – Maurice Jan 10 at 20:05
• @Maurice why do you say they have no connection? – donthababakka Jan 12 at 11:23
• Avogadro's law describes the state of a system, and not a change. Gay-Lussac's law describes what happens when a change happens, when the system temperature is modified – Maurice Jan 12 at 12:01
• @Maurice yes but, 2mvNcosθ=F is not Gay-Lussac's theory, right? and what I'm asking is how to describe Avogadro's law when above mentioned conditions (in the question) satisfy? – donthababakka Jan 12 at 17:02
equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.
More exactly, it also includes single atoms, e.g. for a case of noble gases, due the way how IUPAC defines a molecule.
But remember the Avogadro law implies ideal gases, similarly as the Gay-Lussac's law,Boyle's law and Charles' law. For ideal gases, sizes of molecules play no role. Both the size and volume of ideal gas molecules are considered negligible.
Real gases have deviations from this ideal behavior. See van der Waals equation as the most used real gas state equation.
$$\left(p+a \frac{n^2}{V^2}\right)(V-n b)=nRT$$ $$\left(p+ \frac{a}{V_\mathrm{m}^2}\right)(V_\mathrm{m} - b)=RT$$
where parameters $$a$$ (addressing cohesive forces ) and $$b$$ (addresing non zero molecular volume) are specific for the particular gas.
Then the molar amount of a real gas for given $$V$$, $$p$$ and $$T$$ is the solution of the cubic equation for variable $$n$$ :
$$pV - n ( pb + RT ) + a \frac{n^2}{V} - ab \frac{n^3}{V^2} = 0$$
It clearly shows that the same volumes of different real gases, at the same temperature and pressure, contain ( usually slightly ) different counts of molecules/atoms. | 2021-04-15 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": 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": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7434459924697876, "perplexity": 840.6965134802747}, "config": {"markdown_headings": true, "markdown_code": false, "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-2021-17/segments/1618038082988.39/warc/CC-MAIN-20210415005811-20210415035811-00027.warc.gz"} |
https://zbmath.org/?q=an:1333.47021 | ## Topological properties of path connected components in spaces of weighted composition operators into $$L^{1}$$.(English)Zbl 1333.47021
The paper studies weighted composition operators from $$L^\infty,H^\infty$$, and the disk algebra into $$L^\infty$$. It is shown that the topological structures for the connected components of such operators are all the same in the three cases.
Reviewer: Kehe Zhu (Albany)
### MSC:
47B33 Linear composition operators 47B38 Linear operators on function spaces (general) 30H10 Hardy spaces
Full Text:
### References:
[1] R. Aron, P. Galindo and M. Lindström, Connected components in the space of composition operators in $$H^{\infty}$$ functions of many variables , Int. Equat. Oper. Th. 45 (2003), 1-14. · Zbl 1029.46053 [2] E. Berkson, Composition operators isolated in the uniform operator topology , Proc. Amer. Math. Soc. 81 (1981), 230-232. · Zbl 0464.30027 [3] J. Bonet, M. Lindström and E. Wolf, Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order , Int. Equat. Oper. Th. 65 (2009), 195-210. · Zbl 1193.47030 [4] P.S. Bourdon, Components of linear-fractional composition operators , J. Math. Anal. Appl. 279 (2003), 228-245. · Zbl 1043.47021 [5] J.S. Choa, K.J. Izuchi and S. Ohno, Composition operators on the space of bounded harmonic functions , Int. Equat. Oper. Th. 61 (2008), 167-186. · Zbl 1155.47027 [6] C.C. Cowen and B.D. MacCluer, Composition operators on spaces of analytic functions , CRC Press, Boca Raton, 1995. · Zbl 0873.47017 [7] E.A. Gallardo-Gutiérrez, M.J. González, P J. Nieminen and E. Saksman, On the connected component of compact composition operators on the Hardy space , Adv. Math. 219 (2008), 986-1001. · Zbl 1187.47021 [8] T.W. Gamelin, Uniform algebras , Prentice Hall, New Jersey, 1969. · Zbl 0213.40401 [9] K. Hoffman, Banach spaces of analytic functions , Prentice Hall, New Jersey, 1962. · Zbl 0117.34001 [10] T. Hosokawa, K.J. Izuchi and S. Ohno, Topological structure of the space of weighted composition operators on $$H^{\infty}$$ , Int. Equat. Oper. Th. 53 (2005), 509-526. · Zbl 1098.47025 [11] T. Hosokawa, K.J. Izuchi and D. Zheng, Isolated points and essential components of composition operators on $$H^{\infty}$$ , Proc. Amer. Math. Soc. 130 (2002), 1765-1773. · Zbl 1008.47031 [12] K.J. Izuchi, Y. Izuchi and S. Ohno, Weighted composition operators on the space of bounded harmonic functions , Int. Equat. Oper. Th. 71 (2011), 91-111. · Zbl 1241.47023 [13] —-, Path connected components in weighted composition operators on $$h^\infty$$ and $$H^\infty$$ with the operator norm , Trans. Amer. Math. Soc. 365 (2013), 3593-3612. · Zbl 1282.47048 [14] —-, Path connected components in weighted composition operators on $$h^\infty$$ and $$H^\infty$$ with the essential operator norm , Houston J. Math. 40 (2014), 161-187. · Zbl 1303.47045 [15] —-, Boundary vs. interior conditions associated with weighted composition operators , Cent. Eur. J. Math. 12 (2014), 761-777. · Zbl 1307.47033 [16] B.D. MacCluer, Components in the space of composition operators , Int. Equat. Oper. Th. 12 (1989), 725-738. · Zbl 0685.47027 [17] B. MacCluer, S. Ohno and R. Zhao, Topological structure of the space of composition operators on $$H^{\infty}$$ , Int. Equat. Oper. Th. 40 (2001), 481-494. · Zbl 1062.47511 [18] J.S. Manhas, Topological structures of the spaces of composition operators on spaces of analytic functions , Contemp. Math. 435 (2007), 283-299. · Zbl 1144.47020 [19] J. Moorhouse and C. Toews, Differences of composition operators , Contemp. Math. 321 (2003), 207-213. · Zbl 1052.47018 [20] P.J. Nieminen and E. Saksman, On compactness of the difference of composition operators , J. Math. Anal. Appl. 298 (2004), 501-522. · Zbl 1072.47021 [21] J. Ryff, Subordinate $$H^p$$ functions , Duke Math. J. 33 (1966), 347-354. · Zbl 0148.30205 [22] D. Sarason, Composition operators as integral operators , Analysis and partial differential equations , Lect. Notes Pure Appl. Math. 122 , Marcel Dekker, New York, 1990. · Zbl 0712.47026 [23] J.H. Shapiro, Composition operators and classical function theory , Springer-Verlag, New York, 1993. · Zbl 0791.30033 [24] J.H. Shapiro and C. Sundberg, Isolation amongst the composition operators , Pac. J. Math. 145 (1990), 117-152. · Zbl 0732.30027 [25] —-, Compact composition operators on $$L^1$$ , Proc. Amer. Math. Soc. 108 (1990), 443-449. · Zbl 0704.47018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-05-28 18:02:35 | {"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": 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": 0.8509663939476013, "perplexity": 1243.8582515780997}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652663016949.77/warc/CC-MAIN-20220528154416-20220528184416-00411.warc.gz"} |
https://zbmath.org/?q=an:0614.35021 | # zbMATH — the first resource for mathematics
The method of approximate spectral projection. (English. Russian original) Zbl 0614.35021
Math. USSR, Izv. 27, 451-502 (1986); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 49, No. 6, 1177-1228 (1985).
The method of approximate spectral projection [see V. N. Tulovskij and M. A. Šubin, Mat. Sb., Nov. Ser. 92(134), 571-588 (1973; Zbl 0286.35059)] is further developed. The improvement includes a better estimation of the remainder in the problem of the type $$Au=tBu$$ (A is a pseudodifferential operator of elliptic type in the sense of Douglis- Nirenberg, B is a subordered operator and one of the operators A, B is positive definite). The pseudodifferential operators are calculated similarly as by Weyl-Hörmander [see L. Hörmander, Commun. Pure Appl. Math. 32, 359-443 (1979; Zbl 0388.47032)] only in this article the operator order is determined by two operator-functions and not by one scalar function. Essential theorems are proved in the first part. In the second part these theorems are used under conditions of the Dirichlet type to study following problems: spectral problems of the shell theory, problems of the $$Au=tBu$$ type, spectral asymptotics of pseudodifferential operators, asymptotics of the discrete spectrum becoming dense at the lower boundary of real, scalar and matrix Schrödinger operators perturbed by differential operators of the first order.
Reviewer: V.Burjan
##### MSC:
35J10 Schrödinger operator, Schrödinger equation 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35S15 Boundary value problems for PDEs with pseudodifferential operators 47A10 Spectrum, resolvent 74K25 Shells 74H45 Vibrations in dynamical problems in solid mechanics
Full Text: | 2021-01-28 09:46:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.439394474029541, "perplexity": 1062.1101272061503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610704839214.97/warc/CC-MAIN-20210128071759-20210128101759-00579.warc.gz"} |
https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.opt.qpconvex2_sparse_option_double_set.html | # naginterfaces.library.opt.qpconvex2_sparse_option_double_set¶
naginterfaces.library.opt.qpconvex2_sparse_option_double_set(string, rvalue, comm, io_manager=None)[source]
qpconvex2_sparse_option_double_set may be used to supply individual float options to qpconvex2_sparse_solve(). The initialization function qpconvex2_sparse_init() must have been called before calling qpconvex2_sparse_option_double_set.
For full information please refer to the NAG Library document for e04nu
https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/e04/e04nuf.html
Parameters
stringstr
A single valid keyword of a float option (as described in Other Parameters for qpconvex2_sparse_solve).
rvaluefloat
The value associated with the keyword in .
commdict, communication object, modified in place
Communication structure.
This argument must have been initialized by a prior call to qpconvex2_sparse_init().
io_managerFileObjManager, optional
Manager for I/O in this routine.
Raises
NagValueError
(errno )
The initialization function qpconvex2_sparse_init() has not been called.
(errno )
The supplied option is invalid. Check that the keywords are neither ambiguous nor misspelt. The option string is and .
Notes
qpconvex2_sparse_option_double_set may be used to supply values for float options to qpconvex2_sparse_solve(). It is only necessary to call qpconvex2_sparse_option_double_set for those arguments whose values are to be different from their default values. One call to qpconvex2_sparse_option_double_set sets one argument value.
Each float option is defined by a single character string in and the corresponding value in .
Option settings are preserved following a call to qpconvex2_sparse_solve() and so the keyword ‘Defaults’ is provided to allow you to reset all the options to their default values before a subsequent call to qpconvex2_sparse_solve().
A complete list of options, their abbreviations, synonyms and default values is given in Other Parameters for qpconvex2_sparse_solve. | 2022-08-19 10:48:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2343398630619049, "perplexity": 3655.3643221136276}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573667.83/warc/CC-MAIN-20220819100644-20220819130644-00087.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/consider-system-two-2-d-point-vortices-defined-hamiltonian-x1-y1-x2-y2-positions-first-sec-q1309356 | Proper way to write Hamiltonian for 3 vertices?
Only need part c
Image text transcribed for accessibility: Consider a system of two 2-D point vortices, defined by a Hamiltonian where (x1, y1) and (x2, y2) are the positions of the first and second vortex, respectively. In every pair, the two coordinates are canonically conjugate variables (in other words, the rate of change of one variable from a pair is given by the partial derivative of the Hamiltonian with respect of the other). Derive the equations of motion. Derive the invariants (conserved quantities). You may want to use results from part (b). Sketch and / or plot (using Mat lab) the trajectories for several pairs of initial conditions. If there are not two. but three vertices, what is the proper way to write the Hamiltonian? What are the invariants for three-vortices system? | 2014-10-24 23:19:10 | {"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": 0.911457359790802, "perplexity": 326.8259080599417}, "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-2014-42/segments/1414119646484.16/warc/CC-MAIN-20141024030046-00205-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://psha.org.ru/irc/%23emc/2007-07-27.html | # #emc | Logs for 2007-07-27
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[00:00:15] <ds2> you are refering to the area near PCC?
[00:00:30] <cradek> R0BH: ask either way - sometimes someone else can jump in and help
[00:00:30] <Jymmm> yes
[00:00:37] <R0BH> iv set g53, its in center spindle now, and g28 54mm to get to home on edge of x travel where i like it to be, but if i g28 home, and turn off, when turn back on it says machine is in middle of x when it is not
[00:01:15] <R0BH> so in effect its 54mm out of postion each time
[00:01:32] <Jymmm> I also miss hitting in-person auctions.... that is really a lot of fun.
[00:01:32] <cradek> yes you have to home every time
[00:01:43] <R0BH> on 53
[00:01:45] <cradek> can you add a home switch at least on X?
[00:02:29] <R0BH> there is a limit switch on x as it is, which is triggered on ether over travel
[00:02:35] <ds2> eh? onlything on there that is really surplus is C&H and they are worse then Halted here
[00:02:38] <cradek> home on that sucker
[00:03:21] <ds2> hmm they claim to be open sat...
[00:03:53] <R0BH> ok, ill have to wire him up then
[00:14:32] <ds2> for a small desktop machine with a 1hp spindle, is 300W a good ballpark power budget for the steppers, drivers, and control?
[00:14:43] <ds2> or would that be overkill?
[00:20:28] <SWPadnos> does "control" include the PC?
[00:20:53] <ds2> yes, PC + a small (<9inch) LCD + any LEDs, buttons, etc
[00:22:33] <ds2> nope, it will probally be something like an 800MHz VIA C3 unless RT/EMC fails on it...
[00:22:45] <SWPadnos> ok, that'll be a low power unit then
[00:24:12] <ds2> didn't think the choice of MB's would be that significant for a ball park estimate...esp. since anything more modern then a PIII is not even considered
[00:44:47] <R0BH> think i have found a bug in css
[00:47:40] <R0BH> when contoring in css it seems to rapid on the G02 and G03 moves willing to send program to someone to test out
[00:48:47] <cradek> is it CSS or FPR that causes it? are you using both?
[00:49:06] <R0BH> let me show u the program
[00:49:43] <R0BH> http://innovative-rc.co.uk/EMC/TEST1-5CUT-R.ngc
[00:49:47] <cradek> my lathe is not set up right now so the more precisely you can describe the problem you see, the better
[00:51:49] <R0BH> where it would retract on the arc on ruthing it will rapid out along it not fpr
[00:52:08] <jmkasunich> so you are using FPR
[00:52:10] <R0BH> same on finish finish, on g02 and g03 lines it will rapid around the moves and go back into fpr on g01
[00:52:18] <jmkasunich> (you said "bug in css")
[00:53:02] <R0BH> sorry getting late here :s
[00:53:19] <cradek> oh! I see it here too
[00:54:03] <cradek> I think I see the bug - testing a fix
[00:55:18] <R0BH> no problem
[00:55:25] <SWPadnos> come on - this is taking too long!
[00:55:36] <R0BH> lol
[00:56:16] <R0BH> nearly 2am here
[00:56:33] <CIA-8> 03cradek 07TRUNK * 10emc2/src/emc/kinematics/tp.c: fix FPR arcs
[00:56:35] <R0BH> can u do us some autocorner radius and chamfering please ;)
[00:57:13] <R0BH> many thanks will update and retest
[01:00:20] <cradek> R0BH: you should get your cam to put a G21 at the beginning of your program - when I loaded it here it was a BIG part!
[01:03:08] <cradek> (adding G21 was the only change I had to make to run it on my inch configuration)
[01:03:58] <R0BH> aah yea, here we are allways in metric and all our full size CNCs are pre G21 anyway
[01:04:09] <R0BH> it does put it in but we normlay take it out to save on NC code space
[01:04:21] <cradek> ahh, not an issue with emc!
[01:04:24] <R0BH> as 17k on CNC does not go too fair these days
[01:04:49] <R0BH> yes we have a leadwell CNC we would like to EMC onto when we have time
[01:05:09] <cradek> wow 17k doesn't seem like much - how old is that control?
[01:06:12] <R0BH> one we want to convert has a mitsubishi control, where bigger one we have has fanuc
[01:06:55] <R0BH> it has resolvers not encoders so we have got to buy converters or new encoders for it also to convert it
[01:07:15] <R0BH> control is about 1980 something i belive
[01:07:58] <R0BH> cvs updated and is fully working
[01:08:07] <cradek> cool thanks for testing so fast
[01:08:57] <R0BH> so didt u want to make a chess set for your garden with out G21 ;)
[01:09:27] <R0BH> but thank you for fixing the problem so fast to
[01:09:29] <cradek> I think it would be about as tall as me!
[01:09:42] <cradek> you're welcome, I knew right were to find this one.
[01:09:51] <R0BH> ye about 30inch high lol
[01:09:55] <Jymmm> 1/3 human height chess pieces are huge.
[01:10:24] <Jymmm> It looks funny when they're moving them too
[01:10:37] <R0BH> ye even hubals mirrors where wrong when they could not get conversion right metric to imperial
[01:11:23] <R0BH> do you guys have any plans for diamiter programming soon?
[01:11:41] <Jymmm> Plan, what plan?
[01:12:06] <cradek> in diameter mode, arcs aren't round anymore - it's a big can of worms
[01:12:25] <ds2> when is G71 ready for testing? ;)
[01:12:45] <Jymmm> ds2: It's in the plan
[01:12:59] <Jymmm> ds2: didn't you get the memo?
[01:13:13] <R0BH> best one we have used here is one written by philips for there control
[01:13:40] <ds2> the one written in hyroglphics carved on the stone tablet? no... it cracked in transit
[01:14:01] <cradek> hmm, time for dinner II - hungry again
[01:14:02] <Jymmm> ds2: well, glue the pieces back together
[01:14:19] <R0BH> good night
[01:14:23] <R0BH> speak again soon
[01:14:42] <ds2> Jymmmm: I sent the messenger back to get a new one
[01:17:01] <R0BH> going to land of nod now, cya all soon
[01:17:14] <R0BH> does g83 work on lathe
[04:07:21] <GuySoft> hello all, i want to build a controllable camera mount (2 axis) for this i need a 2 stepper motor controller, did any of you get something like this working under linux?: http://tinyurl.com/3b8qmw .
[04:08:28] <GuySoft> anyone alive today?]
[04:08:30] <SWPadnos> I don't know of anyone doing that
[04:08:37] <SWPadnos> err - using that
[04:09:38] <GuySoft> dont you work with CNC devices? its the same principle.. i need 2 stepper motors controllable in linux..
[04:09:44] <GuySoft> who are the geckodrive?
[04:10:01] <SWPadnos> nevermind - someone recently asked a similar question on a mailing list
[04:10:30] <SWPadnos> yes, I work with CNC devices, but I don't know of anyone using that device with Linux
[04:12:16] <SWPadnos> they don't appear to publish the command set for their controller, so it's unlikely to be usable under Linux
[04:13:31] <GuySoft> SWPadnos, id be glad if you recommend a simular device.. that was more or less my budget..
[04:14:08] <GuySoft> LPT... thats what i have on this laptop
[04:14:24] <SWPadnos> err - so USB yea but LPT no?
[04:15:33] <GuySoft> SWPadnos, i would like this to be as flexible as possible.. however if LPT is much simpler, ill go for it.. the best i am familiar with LPT, is turning LEDs on and off it
[04:15:58] <SWPadnos> driving small steppers basically only requires beefier transistors
[04:16:16] <SWPadnos> but it needs to be a real parport, not something connected via USB
[04:16:33] <Jymmm> SWPadnos: I was gonna ask you a question since yesterday, but I forgot! LOL
[04:16:59] <SWPadnos> the other option, if you're comfortable writing some microcontroller code, would be to get an inexpensive microcontroller development kit and write the stepper code yourself. it's not too hard
[04:17:28] <GuySoft> SWPadnos, well, i want it to interface with INDI : http://indi.sourceforge.net/index.php/Main_Page
[04:17:27] <SWPadnos> Jymmm, good. I'm in the middle of some work right now, but decided to help out a newcomer :)
[04:18:07] <GuySoft> SWPadnos, can you direct me to such a kit, or something.. i am just new and looking for where to start
[04:18:53] <ds2> SWPadnos: did you comment any more about my power q during the netsplit?
[04:19:04] <SWPadnos> ds2, I don't think so
[04:19:06] <GuySoft> also, if anyone can give me hands-on experience advice.. this is what i am looking for.. i am new to this and trying to figure out what to use for what..
[04:19:21] <ds2> okie
[04:19:29] <GuySoft> SWPadnos, well i took the motors of a 5.4 harddrive.. thats a start..
[04:19:44] <ds2> i'll go with the 1KW figure and verify later
[04:19:53] <SWPadnos> hmmm. how many wires do they have?
[04:20:02] <GuySoft> i found something that does more than what i want here: http://fred.unis.no/StampII3Mx/Default.htm
[04:20:10] <GuySoft> 5 pins
[04:20:41] <GuySoft> here is a diagram of it: http://de.wikipedia.org/wiki/Bild:Schrittmotor.PNG .. i was lucky to find this.. only exists on the german wiki! (and i dont know german)
[04:22:01] <GuySoft> so there you have it, the plan is to connect these two on one side.. and kstars on the other :)
[04:22:01] <SWPadnos> ok - that's just a standard unipolar 4-phase stepper diagram
[04:23:02] <GuySoft> SWPadnos, if its simple to you, then you are wiser than me.. i figured out how they worked with zaping the pins around with 3 watss battary
[04:23:23] <GuySoft> still, i need to figure out what controller i am using on the electric side
[04:23:34] <SWPadnos> well, I'm an electrical engineer, and I've been involved with EMC for several years (and motor control starting about 20 years ago :) )
[04:23:48] <SWPadnos> hmmm. maybe only 18 years ago
[04:23:53] <GuySoft> i started last winter..
[04:24:25] <GuySoft> and it wasnt really motors for most of the time.. i never even soldered before then.. now i have a desk for it here..
[04:24:31] <SWPadnos> anyway, that step driver you saw - they're just using the ULN5803 driver chip to get high current output, and they use a microcontroller to control that
[04:24:40] <SWPadnos> well, you're doing fine so far, it seems
[04:24:58] <SWPadnos> sorry - ULN2803 - typo
[04:25:08] <GuySoft> 2003 it says there
[04:25:20] <ds2> or a UN2003 + 8bit latch on a USB printer cable?
[04:25:31] <SWPadnos> you can make a PC board with a 2803 that plugs into the parallel port, and drive it directly with EMC
[04:26:03] <SWPadnos> or at least HAL - you probably don't need all the G-code wizardry - just the step generator and a means of feeding it positions
[04:26:13] <GuySoft> carnt i even use for that ua741s? i have 2 of them here...
[04:26:42] <ds2> 741 as in the opamp?
[04:26:55] <SWPadnos> so no, you can't use those
[04:27:04] <GuySoft> SWPadnos, i lost you now.. whats an 8bit latch?
[04:27:22] <SWPadnos> ds2 was mentioning another possibility for that board, or for you to use
[04:27:31] <SWPadnos> I'd say, don't bother with that :)
[04:27:35] <GuySoft> SWPadnos, ok.. about the 741 it was just an idea because i mucked about with them last week
[04:27:45] <SWPadnos> USB takes the "real" out of "real-time"
[04:27:58] <ds2> but it isn't like the camera will "crash"
[04:28:12] <SWPadnos> but you'll only get one step every 2 ms
[04:28:19] <GuySoft> ah, the 8-bit latch question was directed at ds2 ..
[04:28:25] <ds2> only reason I even mention it is to have a quick and dirt way of driving a camera
[04:28:33] <SWPadnos> and the torque on those motors means there'll probably need to be gearing
[04:28:55] <SWPadnos> sure, but a parport should be easier, no?
[04:29:07] <ds2> if you can find the paraport on a modern computer :(
[04:29:09] <SWPadnos> 8 data lines - connect one to each input of the driver ...
[04:29:13] <GuySoft> SWPadnos, well i am using this for digital astro-photography, 2ms is more than what i need.
[04:29:15] <SWPadnos> I'm pretty sure GuySoft said he has one
[04:29:26] <ds2> GuySoft: something like a 74LS373
[04:29:40] <GuySoft> SWPadnos, yes i have one.. r52 IBM laptops come with an LPT port :)
[04:29:54] <SWPadnos> 2 ms per step, and you'll want very very precise angular positioning, I suspect
[04:29:57] <ds2> Oh if you have a real parallel port, go with that
[04:30:16] <GuySoft> i also rather use USB through because i am scared to fry it.. dont have money for a new one
[04:30:56] <GuySoft> USB have in their standard things to cope with overloads.. lpt dont..
[04:31:20] <SWPadnos> LPT has no 5V supply
[04:31:32] <ds2> not really
[04:31:33] <SWPadnos> which can be a pain in many cases, but may be a benefit here
[04:32:04] <ds2> you send 10KV down the USB line, it'll release smoke just as well as anything else
[04:32:31] <ds2> main thing USB has is current limit on the power lines if the followedthe spec
[04:32:42] <GuySoft> ds2, i can also send a hammer to it.. still, the safer the better...
[04:33:09] <ds2> GuySoft: eh? driving a motor can generate 10KV back EMF during the switching!
[04:33:30] <SWPadnos> ideally the 2803 would catch that
[04:33:31] <GuySoft> anyway. if it will work with LPT, then LPT it is.. now how do i find a controller for that.. and also drivers would be handy.. coding it from scratch would be really long and painful
[04:33:49] <GuySoft> EMF/
[04:33:51] <SWPadnos> there's a mode in the EMC2 step generator that will generate 4-phase waveforms
[04:33:50] <GuySoft> ?
[04:33:51] <ds2> "ideally" heheh
[04:34:09] <SWPadnos> EMF=ElectroMotive Force = voltage
[04:34:09] <jmkasunich> GuySoft: have you seen the Mel Bartels software for driving Dobsonian telescopes with steppers?
[04:34:30] <GuySoft> jmkasunich, i dont think so.. do you have a url?
[04:35:08] <jmkasunich> http://www.bbastrodesigns.com/BBAstroDesigns.html
[04:35:11] <jmkasunich> heh
[04:35:25] <jmkasunich> yep, I didn't know the URL either, but google found it
[04:35:28] <GuySoft> oh, and mine is a reflector.. however i might use this first on a camera mount.. lets energy needed
[04:35:33] <GuySoft> googling now..
[04:35:53] <GuySoft> ah, nm just saw you posted it, thanks :)
[04:36:35] <jmkasunich> because scopes need low speeds, a simple 4 transistor unipolar drive works fine
[04:36:45] <jmkasunich> two axes = 8 bits = easy to do on a printer port
[04:37:02] <jmkasunich> he uses PWM to microstep the motors for smoothness
[04:39:13] <GuySoft> PWM?
[04:39:27] <jmkasunich> pulse width modulation
[04:39:35] <GuySoft> also, i think i saw this before.. its just i am more in to the basics now of this
[04:39:58] <SWPadnos> gotta run, good luck.
[04:40:37] <GuySoft> thanks, SWPadnos i think i might be back here.. get other peoples ideas..
[04:41:28] <GuySoft> jmkasunich, i think splitting that acronym didn't do me any good at :-S ..
[04:41:49] <GuySoft> jmkasunich, i am trying to find stuff that would be more easy to make thaugh..
[04:42:23] <jmkasunich> PWM means instead of just turning a bit on continuously, or off continuously, you turn it rapidly on and off, to get an average value somewhere between 0 and 1
[04:42:43] <jmkasunich> GuySoft: I don't think you can get much easier than the BBastro stuff
[04:43:46] <jmkasunich> you have a choice between totally free (schematic and bill of materials are published, build it yourself), totally turnkey (assembled board ready to use) for 145, or multiple steps in between [04:43:59] <jmkasunich> the software is free in both price and freedom (GPL'ed) [04:44:07] <GuySoft> jmkasunich, maybe, just keep in mind that the part lists a hard for me to understand, also the circuit diagrams.. usualy i need someone that knows electronics to explain lines to me [04:44:43] <GuySoft> jmkasunich, i am looking at it.. i am just not sure how the hardware even works yet. let alone if i can build it [04:44:55] <GuySoft> jmkasunich, i am looking at it as we are talking :) [04:45:10] <jmkasunich> if you can't build that stuff (which is in kit form) you won't be able to design and build something from scratch [04:45:36] <jmkasunich> that software has been evolving for about 10 years [04:46:14] <jmkasunich> I used to be interested in telescopes, before I got into machine tools instead... Bartels has a very good reputation as one of the leaders in computer controlled scopes for hobbiests [04:47:11] <GuySoft> jmkasunich, of course i wont.. but if you saw what i posted before, you could see what i was looking at.. i thought of appending different devices to something working [04:47:45] <jmkasunich> running some motors with EMC/HAL isn't hard [04:47:48] <jmkasunich> but thats just the start [04:48:20] <GuySoft> jmkasunich, i am scheming along that data on this page.. there is a lot to take in. should i look at semething spesific? i want to figure out what chips ill need for this.. i dont know if i could get them around here [04:48:32] <GuySoft> jmkasunich, why is it the start? [04:48:41] <jmkasunich> the bartels stuff does polar alignment, lets you go to specific stars, etc - lots of astronomy specific features that you won't get from EMC [04:49:04] <GuySoft> when i interface with indi i am done... it will get the commands directly from kstars [04:49:55] <jmkasunich> I don't know what indi is [04:50:11] <jmkasunich> I didn't read the entire conversation (and I'm not going to, its almost 1am here) [04:50:38] <jmkasunich> I just wanted to let you know that somebody has already invented what you are looking for, and has been refining it for about 10 years [04:50:47] <jmkasunich> and its available under the GPL [04:50:50] <GuySoft> http://indi.sourceforge.net/index.php/Main_Page here it is , they say its a: INDI is a distributed control protocol designed to operate astronomical instrumentation. INDI is small, flexible, easy to parse, and scalable. It supports common DCS functions such as remote control, data acquisition, monitoring, and a lot more. [04:51:23] <jmkasunich> * jmkasunich looks [04:51:24] <GuySoft> jmkasunich, i know its invented. its the implementation thats the hard part now [04:51:58] <jmkasunich> ? [04:52:03] <jmkasunich> the bartels stuff is already implemented [04:52:41] <GuySoft> jmkasunich, yes, but i need to repeat the implantation ;-) [04:52:49] <jmkasunich> why? [04:52:57] <SWPadnos> building another unit [04:53:11] <jmkasunich> "unit" = what? [04:53:13] <jmkasunich> a scope mount? [04:53:16] <SWPadnos> assembly [04:53:21] <SWPadnos> not implementation, assembly [04:53:33] <jmkasunich> please clarify [04:53:36] <SWPadnos> GuySoft, you're in Italy? [04:54:07] <SWPadnos> jmkasunich, all the parts are designed, but the assembly for him isn't yet [04:54:08] <GuySoft> no, israel.. [04:54:14] <jmkasunich> parts for what? [04:54:19] <GuySoft> why, you saw il ? [04:54:22] <jmkasunich> are we talking about a scope mount? [04:54:35] <GuySoft> SWPadnos, yes sorry, the word slipped from my mind [04:54:34] <SWPadnos> building up kits (low budget), figuring out all the rest of it [04:54:37] <SWPadnos> yes [04:55:14] <jmkasunich> so GuySoft wants to build and sell scope mounts, not just build one for his own use? [04:55:18] <SWPadnos> no [04:55:23] <GuySoft> jmkasunich, a scope mount/camera mount.. the motors i have dont have sufficient power at the moment.. but i should be able to solve that [04:55:25] <SWPadnos> well, I don't know :) [04:55:58] <GuySoft> what was the question just now about me? [04:55:58] <jmkasunich> indi is NOT a scope mount controller, it is a high level interface to a controller [04:56:19] <jmkasunich> you have to provide the controller, and if there isn't an indi driver for it, you have to provide the driver [04:56:28] <jmkasunich> the bartels stuff IS a scope mount controller [04:56:47] <GuySoft> jmkasunich, i know.. its a long way up from the physical level [04:57:30] <SWPadnos> the idea is to make the mount controllable from some other Linux software, like the indi thing or kstars [04:57:48] <jmkasunich> http://indi.sourceforge.net/index.php/Devices [04:58:16] <jmkasunich> I notice the bartels controller is one of the target devices for indi, although there is no page behind that link (which makes me think there is no support yet) [04:58:50] <GuySoft> jmkasunich, they also have a manual for writing new drivers.. it shouldn't be hard to write if i have the right existing functions already on a driver [04:58:50] <SWPadnos> right [04:59:03] <jmkasunich> GuySoft: if you want/need to build a controller, I can't think of any better source of info than bbastro and the links from that page [04:59:31] <GuySoft> jmkasunich, right, i just noticed you said they are using it in the indi project [04:59:33] <jmkasunich> the amateur telescope making list (bartels is an active member) has been refining the design for years, you can learn lots there [04:59:56] <jmkasunich> theres also a scope-drive group at yahoo-groups [05:00:00] <jmkasunich> (link on the bartels page) [05:00:03] <GuySoft> jmkasunich, i am sure they are, much better than me [05:00:38] <jmkasunich> most of that work is completley public - reading those pages will teach you what you need to know far better than we can [05:01:08] <GuySoft> jmkasunich, where do you see that they are working on bbastro integration? [05:01:22] <jmkasunich> I didn't say they were working on it [05:01:38] <GuySoft> jmkasunich, well you are more understandable than the pages :) [05:01:51] <jmkasunich> under "Telescopes" on the indi Devices page there is a link for Mel Bartels Controllers [05:02:10] <jmkasunich> GuySoft: the problem is that I cannot spend weeks interpreting that info for you [05:02:32] <GuySoft> jmkasunich, ah yes i see. hang on, it might be supported already.. let me check kstars [05:02:36] <jmkasunich> that page and the pages linked to it are as close as you will get to an encyclopedia of amateur scope drive design [05:02:41] <jmkasunich> you can educate yourself there [05:02:56] <GuySoft> jmkasunich, thanks for all the help [05:03:13] <jmkasunich> are you subscribed to the indi mailing list? ask there.... [05:03:23] <GuySoft> just can we go back to the first problem? [05:03:40] <jmkasunich> I have to go to bed [05:03:58] <GuySoft> jmkasunich, i will. they just came back online.. a few hours ago they were down for maintenance [05:04:21] <GuySoft> jmkasunich, me 2, its 8am here.. i slept only 3 hours.. and i did that because there was a power cut here.. [05:04:35] <jmkasunich> you must be young [05:04:57] <jmkasunich> I have to get up for work in the morning [05:05:06] <GuySoft> YAY, mel bartels is allready integrated to kstars.. if i use that, it will save me alot of work [05:05:23] <jmkasunich> ;-) [05:06:19] <GuySoft> jmkasunich, i am, however i am on vacation from the army, this is the time i can muck about with hardware.. and not be surrounded by semi-evolved simians [05:06:52] <jmkasunich> heh [05:07:49] <GuySoft> its mandatory service here.. i am counting the days down.. i hope by the time i get out ill have better home-built astronomical equipment .. [05:08:05] <GuySoft> well, i wont keep you, sleep well, thank you for the link.. i have alot to read now [05:08:18] <jmkasunich> you should really subscribe to the scope-drives yahoo list, and/or the amateur telescope makers mailing list [05:08:32] <jmkasunich> great groups of people on both lists, very helpfull [05:10:08] <jmkasunich> goodnight [05:13:33] <GuySoft> i find IRC more responsive. goodnight [06:07:33] <fenn> grumph [06:44:23] <Jymmm> grumf? [10:18:45] <Jymmm> alex_joni: you got ballscrews? [10:43:43] <Jymmm> Well, I inspected each of the 68 balls in the ballnut.. nice and round (no ovals) and all the same size. [10:45:55] <Jymmm> Inside the ballnut itself, I did see a shiny track along the ball thread groove, looks like wear. Checked out the return tube too, seems look... balls travel thru it unobstructed. [10:46:27] <lerneaen_hydra> Jymmm: how did you inspect hte balls? [10:46:32] <lerneaen_hydra> just look at them? [10:46:38] <lerneaen_hydra> or something more advanced? [10:47:00] <Jymmm> Not sure what to do at this point. Before I took it apart, I turned the leadscrew vertical, and I'd notice when I let the nut free-spin, it would drag about every 1.5" [10:47:34] <Jymmm> when going from A to B, the other way B to A, no drag. [10:47:49] <Jymmm> Under a magnifying glass [10:48:46] <Jymmm> lerneaen_hydra: Under a magnifying glass [10:50:22] <lerneaen_hydra> oh ok [10:51:29] <Jymmm> No micrometers, so I used my dial calipers to measure each ball, move it around, measure it again. All were consistant size. [10:52:03] <Jymmm> and I didn't drop one =) [10:52:44] <toast> measuring balls? [10:53:10] <Jymmm> (03:43:41) Jymmm: Well, I inspected each of the 68 balls in the ballnut.. nice and round (no ovals) and all the same size. [10:53:10] <Jymmm> (03:45:54) Jymmm: Inside the ballnut itself, I did see a shiny track along the ball thread groove, looks like wear. Checked out the return tube too, seems look... balls travel thru it unobstructed. [10:53:10] <Jymmm> (03:46:27) lerneaen_hydra: Jymmm: how did you inspect hte balls? [10:53:10] <Jymmm> (03:46:30) lerneaen_hydra: just look at them? [10:53:11] <Jymmm> (03:46:36) lerneaen_hydra: or something more advanced? [10:53:15] <Jymmm> (03:47:00) Jymmm: Not sure what to do at this point. Before I took it apart, I turned the leadscrew vertical, and I'd notice when I let the nut free-spin, it would drag about every 1.5" [10:53:16] <Jymmm> (03:47:33) Jymmm: when going from A to B, the other way B to A, no drag. [10:53:18] <Jymmm> (03:47:47) Jymmm: Under a magnifying glass [10:53:20] <Jymmm> toast: ^^^ [10:53:38] <toast> ty sir! [10:53:46] <Jymmm> np [10:53:54] <toast> also there's no way to measure bearings with a micrometer [10:53:58] <toast> they're too accurate [10:54:36] <toast> verrry tiny doodads in the surface geometry will cause problems [10:54:48] <Jymmm> I wonder if I should NOT be using grease to lube them [10:55:01] <toast> dunno, i see grease on a lot of ballscrews, and not on others [10:55:22] <toast> i think some manufactuers reccomend grease, some tell you to hit it with waylube [10:55:47] <Jymmm> It seems to place drag on them, and lot build up inside the ballnut even after I cleaned it up. [10:56:50] <Jymmm> I have to use a grease gun for my rails, lithium grease is available easily, so I've been using that on the ballscrews as well. [10:56:57] <toast> oooh. [10:57:21] <toast> yeah, grease is only a good idea if there's a grease joint thingy [10:57:31] <toast> otherwise, it is a bad idea [10:57:38] <Jymmm> zirk fitting on the rail trucks [10:57:46] <toast> oh, neat [10:58:28] <toast> i'd probably use waylube over grease on screws [10:58:38] <Jymmm> maybe not a good thing for the ballsscrews though, maybe I'll call thompson tomorrow when wake up. [10:58:42] <toast> you might want to ask the manufacturer [10:58:42] <Jymmm> what's waylube? [10:58:42] <toast> yar [10:58:55] <toast> waylube is a specific kind of oil meant for machine ways [10:59:15] <toast> big machines are really particular about what kind of oil your hit the ways with [10:59:59] <Jymmm> it's an oil? [11:00:03] <toast> yeah [11:00:07] <toast> almost like syrup or honey [11:00:08] <Jymmm> not grease? [11:00:11] <toast> yes [11:00:17] <Jymmm> spray can? [11:00:20] <toast> loool [11:00:25] <toast> you aren't gonna get waylube to spray [11:00:30] <toast> you might be able to brush it on [11:00:30] <Jymmm> k [11:00:41] <toast> it's for automatic oilers [11:00:45] <Jymmm> I have an oil can here [11:00:47] <toast> both single shot and full auto [11:00:52] <toast> yeah, that will work [11:01:06] <toast> one of the real popular ones is Mobil Vatra 2 [11:01:10] <Jymmm> just not easy since I have to apply it upside down [11:01:24] <toast> also you have to be careful with waylube [11:01:35] <toast> is your ballscrew shielded? [11:01:47] <toast> because waylube will turn into jeweler's rouge very fast if it gets dirty [11:01:50] <Jymmm> like wipers? [11:01:57] <Jymmm> no wipers [11:02:01] <toast> wipers or a sheath [11:02:07] <Jymmm> nothing [11:02:07] <toast> or just generally out of the way of chips [11:02:14] <toast> hmm [11:02:23] <toast> you might want to come up with some sort of like, cloth sheath for it [11:02:39] <toast> i'd sew an accordian thing for it [11:02:53] <toast> run some strings on self winding crap [11:02:59] <toast> so that the sheild bellows are held off the screw [11:03:09] <Jymmm> sawdust [11:03:13] <toast> ooooooh [11:03:15] <Jymmm> and plastic partical [11:03:24] <toast> do not put waylube on your ballscrews [11:03:24] <Jymmm> goes everywhere [11:03:26] <toast> until you shiled your screws [11:03:32] <toast> which i suggest you do anyway [11:04:30] <toast> if you have access to a sewing machine, protecive bellows are just doughnuts or squares [11:04:36] <toast> of material [11:04:36] <Jymmm> theres no direct drop on the screws, just flying dust, so cover wont do much good [11:04:47] <toast> i'm saying a full 360 degree cover [11:05:14] <lerneaen_hydra> toast: how do you seal the seams? tight stitches and PCV "cloth"? [11:05:32] <toast> kind of, yeah [11:05:38] <toast> you can glue the seams after sewing [11:05:41] <lerneaen_hydra> tight enough? [11:05:46] <toast> most of the time the seam is good enough [11:05:50] <toast> by itself [11:05:55] <lerneaen_hydra> oh ok [11:06:08] <toast> any heavy cloth will work [11:06:12] <lerneaen_hydra> so no need to seal it with heat/adhesive [11:06:14] <toast> right [11:06:19] <Jymmm> I'm outta here.... Zzzzzzzzzzz [11:06:21] <toast> you're not like, making it water/airtight [11:06:26] <toast> just trying to keep crap off it [11:07:09] <lerneaen_hydra> yeah [11:07:44] <toast> it increases the life of the machine by a very good factor [11:07:57] <toast> and allows you to run better lubricants on the ways and screws [11:08:09] <toast> i.e. waylube, which almost eliminates stick/slip [11:08:25] <lerneaen_hydra> oh, nice [11:08:39] <lerneaen_hydra> how are those felt scrapers compared to bellows? [11:08:46] <toast> big machines use both [11:08:51] <lerneaen_hydra> oh ok [11:08:54] <toast> felt scrapers are like, necessary [11:09:10] <lerneaen_hydra> bellows to get rid of most of the crap and scrapers to clean the stuff that gets through? [11:09:16] <toast> indeed [11:09:28] <toast> and also wipes the old oil off the way [11:09:57] <toast> the stuff that's turned into lapping compound =) [11:10:14] <lerneaen_hydra> heh yeah [11:10:30] <toast> a big problem on smaller machines is the use of compressed air [11:10:41] <toast> especially bridgeport sized machines [11:10:51] <toast> because nothing is protected and compressed air will blow chips right under the wipers [11:11:04] <toast> into the soft, unhardened bearing surface [11:11:13] <toast> and also onto the screws [11:11:32] <lerneaen_hydra> yeah [11:11:52] <lerneaen_hydra> therefore people using air on machines should be executed [11:11:53] <toast> but a well-designed bellow will allow a person to use air [11:12:05] <toast> people using air on machines that are not designed to handle compressed air [11:12:07] <toast> should be executed [11:12:13] <toast> and air should just be minimized [11:12:17] <lerneaen_hydra> yes, naturally [11:54:25] <fenn> i like les' way of shielding the ways, he has this roll-up window blind thing [11:54:30] <fenn> and its under constant tension [11:55:30] <fenn> http://www.lmwatts.com/cnc.html [13:04:42] <maddash> hm [13:05:01] <maddash> someone wanted to know about lostirc? [13:09:39] <fenn> lost on irc island... [13:11:29] <toast> i've always wondered if you could make a tv show [13:11:38] <toast> that is just essentially irc [13:12:05] <fenn> its called 'talk radio' [13:12:19] <fenn> picture rush limbaugh with some headphones and a mic [13:12:26] <toast> except this would be irc people talking about wangs [13:12:30] <toast> instead of like, stuff nobody cares about [13:12:35] <fenn> um, right [13:12:55] <fenn> 1) talk about wangs 2) ??? 3) profit! [13:13:28] <toast> that is essentially how irc works right now [13:13:34] <toast> "hey guys, wangs" [13:13:37] <toast> "holy shit three hundred dollars" [13:13:41] <lerneaen_hydra> utter boredom with the occasional, rare moment of utter terror [13:17:50] <archivist> trawl the logs for a good strory line [13:18:44] <toast> yeah man [13:18:46] <toast> and just play it back [13:18:50] <toast> according to the timestamps [13:19:28] <archivist> but there have been some choice statements worth saving for posterity (I save some in the #mysql bot) [13:20:52] <lerneaen_hydra> or better yet, print qdb.us [13:20:52] <toast> ? [13:21:04] <toast> re: mysql bot [13:21:07] <lerneaen_hydra> you've never been to qdb.us? [13:21:26] <lerneaen_hydra> http://www.qdb.us/top [13:21:30] <lerneaen_hydra> worlds best IRC quotes [13:21:38] <lerneaen_hydra> what bash.org was [13:21:46] <toast> i know the guy who runs qdb [13:21:53] <lerneaen_hydra> oh cool [13:22:00] <toast> well, know/sit in the same chatroom [13:22:02] <toast> digdug [13:22:08] <lerneaen_hydra> ah ok [13:22:20] <toast> never met the guy irl [13:22:24] <toast> HOTHACON never happened [13:22:34] <toast> so sad [13:32:47] <skunkworks> <TeamsterX> man watching 6 MSCE's around a sun box, looks alot like the opening scene's of 2001:space odyssey and the monkey's with the monolith [13:33:31] <cradek> TeamsterX: But, maybe they know not to form plurals with an apostrophe. [13:33:59] <jepler> zing! [13:34:14] <skunkworks> :) [13:34:35] <fenn> and rely on capitalization alone? sounds dangeroso [13:34:39] <skunkworks> atleast he is consitant [13:35:22] <skunkworks> consistent [13:35:43] <fenn> Did you know, Alt+Z makes your text go backwards in most IRC clients? [13:35:54] <skunkworks> ;) [13:36:36] <skunkworks> * skunkworks was going to exit for the fun of it.. ;) [13:41:33] <cradek> did you know you can cause someone else to exit irc by typing /quit and then their name? [13:42:33] <skunkworks> * skunkworks has quit ("leaving") [13:43:58] <cradek> is alt-Z something special in winders? [13:44:56] <jepler> if it said ctrl-z you might have gotten me :-P [13:57:33] <maddash> sheesh [13:58:23] <lerneaen_hydra> O_o [13:59:02] <lerneaen_hydra> * lerneaen_hydra see's a +o cradek, a maddash: oh shit, and a maddash was kicked ("better luck next time") [14:00:43] <maddash> sees*? [14:01:03] <lerneaen_hydra> oh kill me now [14:01:21] <lerneaen_hydra> I need to move to an english speaking country and fix my broken linguistics [14:01:45] <lerneaen_hydra> who the hell makes mistakes like that? 6th graders? [14:01:52] <lerneaen_hydra> bleh... [14:02:59] <jepler> lerneaen_hydra: almost any american might type "see's" [14:03:46] <cradek> * cradek shivers [14:04:34] <skunkworks> * skunkworks whistles to himself.. [14:04:38] <maddash> jepler: ahem. [14:07:19] <tomp> Cutting a Dash: a BBC radio series on how punctuation is murdered, this episode is about the (mis) use of the apostrophe try this cmd "mplayer rtsp://rmv8.bbc.net.uk/bbc7/1345_mon_thu.ra" [14:09:06] <skunkworks> npr has a show called 'a way with words.' I try to catch evey weekend. Doesn't seem to help much ;) [14:09:33] <lerneaen_hydra> jepler: still, it's very ugly IMO [14:09:47] <lerneaen_hydra> lack of common grammar skills [14:10:40] <cradek> nobody learning english should aspire to the average american's skills [14:11:40] <lerneaen_hydra> cradek: nobody learning anything should aspire to the average american's skills [14:11:47] <lerneaen_hydra> ;) [14:12:13] <maddash> what's with this growing trend of bashing Americans? [14:12:43] <jepler> maddash: r u kiddin'g? [14:13:24] <cradek> the average american has poor language skills: not bashing, just a simple statement of fact [14:17:13] <lerneaen_hydra> http://www.wellingtongrey.net/miscellanea/archive/2007-03-18--of-angels-monkeys-and-fat-men.html [14:17:53] <jepler> ba ha ha haha [14:27:19] <jepler> welcome, cnc_engineer, barum, and Vq^ [14:28:23] <cnc_engineer> i am unable to get lenearity in PWM output please help to solve the problem [14:30:11] <jepler> cnc_engineer: last time we talked about this, I suggested you use a component to map from requested RPM to PWM duty cycle: http://emergent.unpy.net/files/sandbox/linear8.comp [14:30:14] <jepler> cnc_engineer: did you ever try this approach? [14:30:50] <jepler> 17:38:57 <jepler> cnc_engineer123_: the is component, which I've just written, might be helpful. It performs linear interpolation with up to 8 data points: http://emergent.unpy.net/files/sandbox/linear8.comp [14:30:54] <jepler> 17:43:24 <jepler> you would find several pairs of (pwmgen input):(measured spindle speed); use (pwmgen input) as the yi values and (measured spindle speed) as the xi values [14:30:57] <jepler> 17:46:24 <jepler> if you use less than 8 value pairs, then set the 'n' parameter to the number of pairs you chose to use [14:32:06] <jepler> (from IRC log http://www.linuxcnc.org/irc/irc.freenode.net:6667/emc/2007-06-28.txt) [14:35:25] <cnc_engineer> Jepler: i could not try this approach, i think its first time we are discussing this matter [14:37:13] <maddash> rofl [14:38:51] <cnc_engineer> JeplerL: i need to convert Pwm to Analouge voltage command to control my servo moters but when i need to open 50% duty cycle actual thers 75% and when there should be 60% actual duty cycle goes 100% [14:40:30] <cradek> are you using pwmgen on the parallel port to control full size servos? [14:41:05] <jepler> cnc_engineer: when you say there is a difference between the 50% duty cycle (desired?) and 75% (measured?), how are you making the measurement? [14:44:09] <cnc_engineer> i am using osciloscope to check the duty cycle and i give position commands whithout powerup the motor [14:49:11] <SWPadnos> cnc_engineer, test the output pin by hooking a charge_pump component to it [14:49:27] <SWPadnos> the output you're using for PWM may have asymmetric drive strength [14:50:11] <SWPadnos> hmmm. nevermind. the jitter in interrupt timing will be far worse than any pin drive differences [14:50:36] <x3rox> I have a question on the L297+L298 IC's. Is it better to set the "control" input high or low? High=Chopper acts on phase lines ABCD, Low=Chopper acts on INH1+2. Currently I use "Low". What is better to lower heating of the L298? [14:52:01] <jepler> in halscope I can see that the pwmgen output is exactly what I would expect [14:53:09] <SWPadnos> halscope follows the software jitter [14:53:13] <jepler> indeed [14:53:27] <SWPadnos> you should get a real scope :) [14:53:31] <jepler> it's hard to see how jitter could systematically lengthen all duty cycles [14:54:04] <SWPadnos> that's true [14:54:33] <SWPadnos> there is probably some systematic issue from drive strength, but it should be some fraction of a percent [14:55:05] <SWPadnos> though if it's using the PDM mode (or other highest-frequency method), it could be more significant [14:59:01] <jepler> x3rox: the l297 datasheet says the effect of setting control high is to reduce power dissipation on the sense resistor .. I don't know that either setting affects the heating of the L298 itself [15:01:26] <x3rox> Ah, yes. I totally overread that. I always had in mind that this belongs to the drivers in the L298. So, actually, it doesn't matter as long as the resistors are cold enough... - Thanks. [15:02:29] <x3rox> jepler: Do you think that a PII-266 is fast enough for my mill? I want to mill with tools of 0.5 ... 2.0 mm ø, so I must move slow... [15:04:02] <x3rox> jepler: (This is an old industrial PC in 19" enclosure. Would be great to have a usage for it. [15:04:04] <jepler> x3rox: you can only find out by trying it.. [15:04:13] <x3rox> What happens in worst case? [15:04:18] <skunkworks> The slowest computer I have runn is a 400mhz. It ran fine. [15:04:51] <jepler> x3rox: worst case you can't get acceptable response time from the GUIs while running a BASE_PERIOD fast enough to get the step rate you want [15:04:57] <skunkworks> pentium II [15:04:57] <lerneaen_hydra> x3rox: you'll have to run slowly with a large base period [15:05:17] <lerneaen_hydra> you may have to have a remote graphical control [15:05:42] <fenn> reducing current thru the sense resistor would reduce power dissipation everywhere else too [15:05:48] <x3rox> Oh - So it is actually no real fun to work with? [15:06:07] <lerneaen_hydra> btw, if you SSH into a box, and start X over SSH, is there a lot of graphical load on the host machine or is most of it on the client that displays the graphics? [15:06:49] <x3rox> I assume that in addition the LAN will be a bottle neck... [15:07:28] <lerneaen_hydra> surely a 10 mb/s connection is fast enough? [15:07:46] <fenn> its prolly 100Mbit anyway [15:07:54] <x3rox> I will try to take a faster CPU and run everything on one PC. surely better. ;-D [15:07:58] <lerneaen_hydra> 200mhz, was 100base common then? [15:08:13] <fenn> eth cards werent common at all [15:08:20] <lerneaen_hydra> oh, right [15:08:33] <lerneaen_hydra> they weren't even integrated in the motherboard then [15:08:40] <x3rox> I think so. 100 MBit is not such new... [15:08:59] <x3rox> It's a Slot1 board :D [15:09:38] <x3rox> With some ISA slots! So I could add my old ISA LPT cards, if I need... :D [15:09:51] <fenn> cool beans [15:10:02] <x3rox> :D [15:10:45] <x3rox> As my father sais: Don't throw old things away, you never know if they will be useful sometimes... [15:11:21] <fenn> exercise moderation in all endeavors [15:12:10] <skunkworks> I come from a long line of horders.. [15:13:41] <skunkworks> hoarders? [15:14:03] <fenn> horde = yurt on wheels [15:15:00] <x3rox> How should I start testing the stepper hardware? Currently I fed a square-wave signal in, generated by an oscillator, but this is no real test. The stepper turns and I can change the direction, but I don't see if steps get lost. Would like to run a loop which moves some thousand times left/right a longer distance and then should stop exactly at the staring point again. How can I tell this EMC? Can it run loops? [15:15:21] <fenn> put a flag on the stepper so you can watch its rotational position [15:15:26] <fenn> line up the lines [15:16:07] <fenn> emc does loops with the O routines but i'm lazy so you'll have to look it up yourself [15:16:30] <fenn> note that it can lose steps in both directions and end up at the same place [15:16:51] <fenn> so a better test would be with gage blocks and a dial indicator or something [15:16:56] <skunkworks> now that is just crazy talk.. ;) [15:16:58] <fenn> ya [15:17:18] <fenn> easier to look at where the flag is pointing and calculate the "nominal" position [15:18:17] <x3rox> That's clear. Does EMC start immediately with full speed defined with F command, or does it use an acceleration ramp? [15:18:23] <fenn> btw skunkworks you can lose steps in both directions if your direction pulse isnt held long enough before the step pulse [15:18:36] <fenn> so you lose the first step in a new direction [15:18:53] <skunkworks> I can see that.. I hate those kind of problems. [15:18:57] <x3rox> And does EMC control the lines correctly? [15:19:16] <x3rox> (including the timing)? [15:19:22] <skunkworks> emc does everthing ;) - it accelerates and controls the lines the way you set it up.. [15:19:24] <fenn> x3rox: g0 does full speed, g1 goes F, always with acceleration ramp [15:19:45] <fenn> you define the accel per axis and also overall [15:20:44] <x3rox> Can I configure EMC to know up to which speed it can immediately start with 1 step, and from which speed on it must use acceleration? [15:21:37] <fenn> no [15:22:04] <skunkworks> it starte the accelleration from 0. [15:22:23] <fenn> you cant step less than a pulse anyway [15:23:24] <maddash> fenn: g0 obeys the acceleration limits, too [15:23:38] <fenn> that's what i meant if it wasnt clear [15:23:49] <x3rox> Don't understand. So if I mill a polygon, EMC accelerates from 0 to F, mills the vector, then breakes down to 0, then does the same with next vector? [15:24:08] <maddash> x3rox: only if you disable blending [15:25:12] <x3rox> Ok. "blending" remembers current speed in every axis and accelerates only to a new speed? [15:25:17] <fenn> x3rox: if you want to mill an exact polygon you must stop at the corners, otherwise you will have infinite acceleration at the corner [15:25:48] <fenn> in practice it's not a big deal unless you're doing high speed machining [15:26:22] <x3rox> You are right. With a tool-diameter below 1mm I will not have much speed at all. :-D [15:26:50] <fenn> actually blending is still important at that scale [15:27:07] <x3rox> What does blending in detail? [15:27:15] <fenn> say that again [15:27:32] <x3rox> ? [15:27:41] <fenn> do you mean what part of the code calculates blending? [15:27:54] <skunkworks> x3rox: http://wiki.linuxcnc.org/cgi-bin/emcinfo.pl?TrajectoryControl [15:28:17] <x3rox> No. I mean: What is the result of blending=enabled. [15:28:31] <fenn> the yellow curves on the first pic on that page [15:29:06] <x3rox> Huh... [15:29:11] <maddash> damn, I hope my brother doesn't eat all the spaghetti [15:29:28] <x3rox> Grab some before he can... ;-) [15:30:50] <x3rox> Ok - I browsed over the text in the link. Seems to be better to disable blending at all. [15:31:31] <fenn> try it out both ways and see what you like [15:31:41] <fenn> 99% of the time a rounded corner doesnt matter [15:32:00] <fenn> and you can program a stop in regular g-code easily enough [15:32:05] <fenn> for just one corner [15:32:24] <x3rox> Are the differences noticable, or are we talking about such minor differences that one has to search them? [15:32:46] <x3rox> (Is this G61, G64, ...) [15:32:47] <fenn> it would be hard to tell the difference in the final part, but the machine will go a lot smoother and faster with blending on [15:32:52] <lerneaen_hydra> usually your acceleration is so high and speed so low that's it's irrelevant [15:33:02] <lerneaen_hydra> (the rounded corners) [15:33:41] <x3rox> I see. So we are actually talking about 0.0x millimeters of a radius? [15:33:58] <x3rox> Or is it more? [15:34:02] <maddash> x3rox: depends. are you making nun-chucks? [15:34:15] <x3rox> What is a nun-chuck? [15:34:20] <fenn> ya .05mm sounds about right [15:34:47] <x3rox> So it is really no problem. [15:35:12] <maddash> not if you want to break skin [15:35:27] <fenn> hey arent nun-chucks usually round? [15:35:35] <archivist> where do you get hex nuns from [15:35:38] <SWPadnos> x3rox, it'blending is a physics problem. it's physically impossible to get a non-rounded corner unless you (a) use exact stop mode or (b) put big loops in the G-code that overshoot the endpoint and then come back on the new tangent [15:36:31] <maddash> fenn: concave polygons work quite well, actually [15:36:58] <SWPadnos> the path blending is controllable using G61 and G64. I think G64Pxx gives a tolerance of xx units before it slows the feed rate [15:37:10] <SWPadnos> but I could be wrong there - the docs are your friend :) [15:37:35] <x3rox> Yes, because if I want to mill a 90° corner, the second axis would need an infinite accel in such cases. I thought that blending sees such things and deccelerates before the endpoint to a level that the other axis stays inside its limits. [15:38:23] <SWPadnos> it does, and the Pxx tolerance option allows it to go a bit faster, as long as the resulting path is "close enough" [15:39:00] <maddash> omg the rs274ngc code thinks in metric [15:39:04] <maddash> atrocity! [15:39:05] <SWPadnos> hmmm. I may have mis-spoken there. I'm not sure that the normal blending mode will slow down to take corners [15:39:18] <SWPadnos> I know the tolerance mode does [15:39:18] <fenn> geez maddash what would you prefer, furlongs? [15:40:07] <x3rox> I see, the fine-tuning will somewhat difficile... [15:40:08] <fenn> SWPadnos: afaik the Pxx just lets you specify the tolerance, rather than the hard-coded 0.0001 or whatever [15:40:28] <SWPadnos> fenn, that could be [15:40:47] <fenn> and its not uniform, like, the tolerance is .0001 inches but its .001 mm [15:41:06] <fenn> unless you use g64 P.. [15:41:07] <lerneaen_hydra> what's the current default? [15:41:09] <lerneaen_hydra> keep speed constant, no limit on blending? [15:41:29] <fenn> default is g64 p.0001 inches or .001 mm [15:42:20] <fenn> i love this picture http://wiki.linuxcnc.org/uploads/planner-test.jpg [15:42:48] <x3rox> It is really impressive (and amazing) what EMC can do. I am only afraid that all this withh need a lot of time to get configured correctly. Or is a good average config for a 3-axes-mill with steppers included, which only must be fine-tuned? [15:43:13] <fenn> yep [15:43:20] <jepler> x3rox: start with sample-configs/stepper/stepper_inch.ini [15:43:29] <maddash> x3rox: stepper/stepper_*.ini [15:43:34] <maddash> oh, heh. [15:43:54] <x3rox> fenn: This is really a nice picture. ... so - abstract...? [15:43:59] <lerneaen_hydra> maddash: and having rs274 in metric is bad because...? [15:44:23] <jepler> x3rox: select your pinout ("standard" or "xylotex", or make your own by modifying the .hal file), and enter stuff like the steps per inch, max speed in inches per second, max accel in inches per second squared, etc [15:44:56] <jepler> x3rox: planner-test.jpg was a randomly generated program that included linear and circular moves in 4 axes (XYZA) [15:45:26] <jepler> x3rox: it was run with a special setup that checked 1000 times per second that the commanded acceleration and velocity were within the limits specified in the .ini file [15:45:57] <jepler> x3rox: also it could be visually inspected (actual path vs preview plot) to see if there were any gross errors in blending [15:46:09] <jepler> a few bugs of both kinds were found, but then we (cradek) fixed them [15:46:08] <x3rox> jepler: This is exactly what my mill will be able to do in final state. I can mount a turning axis on the machine desk. [15:46:24] <maddash> lerneaen_hydra: because i'm orthodox english and i lose accuracy from the conversion [15:47:04] <fenn> maddash: i believe it also uses floating point math, horror of horrors [15:47:24] <fenn> how will you ever get your 1/3 inch widget exactly perfect? [15:47:24] <lerneaen_hydra> yes you might loose 1e-23 somewhere there! [15:47:56] <x3rox> Because I am from Austria (and we use here the metric system), I would prefer to calibrate the mill in millimeters. Is this a problem? [15:48:19] <lerneaen_hydra> x3rox: no, it can be configured either way [15:48:41] <x3rox> And what's that mentioned above? [15:49:16] <jepler> x3rox: if you want millimeters, then start with stepper_mm.ini [15:49:35] <lerneaen_hydra> you loose an infitesemal amount of accuracy when running in inch mode becuase the conversion can't be completely accurate, due to the length of one inch [15:49:47] <maddash> x3rox: it would seem that you're better off with metric [15:49:49] <fenn> actually an inch is 25.4mm [15:49:51] <lerneaen_hydra> 1/25.4 is an irrational number [15:49:52] <maddash> lose* [15:49:54] <jepler> then you enter steps per mm, max speed in mm per second, max accel in mm per second squared. in gcode files, specify g21 so that coordinates are also in millimeters [15:49:57] <fenn> no it isnt [15:50:01] <lerneaen_hydra> isn't it? [15:50:12] <lerneaen_hydra> I always thought it was [15:50:12] <maddash> lerneaen_hydra: no, rational. [15:50:12] <fenn> .0393700787401574803149606299212598425196850393700787401574803149606\ [15:50:25] <cradek> irrational means it can't be expressed as a ratio [15:50:26] <jepler> lerneaen_hydra: the ratio of two integers is always rational [15:50:31] <maddash> lerneaen_hydra: 1/25.4 = 10/254 = a/b [15:50:40] <fenn> see the repeating er.. mantissa/ [15:50:43] <lerneaen_hydra> oh, right, transcendantal? [15:50:47] <maddash> cradek: irrational means that it's crazy. [15:50:49] <lerneaen_hydra> or whatever it was called [15:51:01] <fenn> 039370078740157480314960629921259842519685 repeats [15:52:06] <x3rox> Ok. Thanks. -- How do I find out the right calibration of my mill? It's a shame, but I don't know the pitch of the leading spindles, I only know that the steppers are 200 steps/turn (1.8°). [15:52:24] <cradek> you have to measure it then [15:52:31] <x3rox> I think that counting 10 turns and measuring is in best case an estimation? [15:52:33] <fenn> 42 digits [15:52:35] <cradek> first try using a thread gauge [15:52:48] <cradek> or measure the axis travel with something [15:52:48] <jepler> For all multiples of .0001 inch from -10.0000 to 9.9999, the maximum error introduced by converting from inches to mm to inches is 1.7763568394e-15. test program: http://pastebin.ca/636041 [15:52:54] <lerneaen_hydra> fenn: so the sequence repeats ad infinitum? [15:52:59] <fenn> ya [15:53:03] <jepler> that value is so much smaller than the accuracy of physical positioning that it can be ignored [15:53:14] <lerneaen_hydra> jepler: hence that the error is nearly infinitessimal [15:53:25] <fenn> lerneaen_hydra: check this out: 123456789/999999999 [15:54:27] <fenn> oh i guess i should mention you can get an arbitrary number of decimal points if you type 'bc' and then 'scale=999' [15:54:41] <lerneaen_hydra> fenn: type where? [15:54:48] <fenn> in the bc shell [15:54:48] <maddash> jepler: clever. [15:54:50] <jepler> interestingly, the maximum error in representation of a multiple of .0001 inch is larger: 1.45e-11, since .0001 is not exactly representable [15:54:59] <lerneaen_hydra> oh, right [15:55:17] <maddash> fenn: it only seems that way because your denominator is so close to 1000000000 [15:55:47] <fenn> i'm pretty sure there's a proof it goes on forever, but i'm no mathematician [15:55:51] <lerneaen_hydra> fenn: neat [15:55:53] <maddash> fenn: it doesn't. [15:56:10] <fenn> * fenn shrugs [15:56:14] <fenn> it's a religious thing [15:56:42] <x3rox> cradek: It's an acme thread, ø12.67mm. [15:56:56] <maddash> fenn: it does, then 1123456789/(10^9*(10^9-1)) [15:57:03] <maddash> fenn: if it does, then 123456789/(10^9*(10^9-1)) [15:57:09] <maddash> =0 [15:57:13] <lerneaen_hydra> x3rox: that's 1/2 inch diameter [15:57:38] <lerneaen_hydra> might be inch-based pitch [15:57:39] <maddash> ^^ equals zero, not some stupid emoticon [15:57:50] <fenn> uh, no [15:57:50] <lerneaen_hydra> * lerneaen_hydra pouts [15:58:26] <fenn> that thread is probably an inch thread [15:58:32] <cradek> x3rox: it's probably 1/2 inch then, it'll be an integer number of turns per inch [15:58:35] <fenn> and 1/0 is infinity and that's final [15:58:44] <x3rox> cradek: So I can be nearely sure that the thread will also have an "inch-pitch"? [15:58:55] <lerneaen_hydra> fenn: *coughnot*really*cough* [15:59:06] <cradek> x3rox: yes [15:59:30] <fenn> * fenn guesses 10 threads per inch [15:59:43] <jepler> if you had an algebra textbook, you could find the page where they prove that 1/3 = \sum_{i=1}^\inf 3/(10^i) [16:00:02] <maddash> jepler: but this isn't an infinite sum [16:00:15] <maddash> fenn: 1/0 is undefined [16:00:18] <jepler> the same property of sums of geometric sequences will show that the pattern in 123456789/999999999 repeats indefinitely [16:00:44] <cradek> fenn is right - it'll probably be 10tpi [16:00:53] <maddash> jepler: if it does, then 999999... = 99999...+1 [16:01:02] <maddash> jepler: if it does, then 999999...9 = 99999...9+1 [16:01:10] <fenn> you mean infinity = infinity+1? [16:01:23] <maddash> fenn: the second one, not the first one. [16:02:02] <fenn> infinity isnt in the set of addable numbers [16:02:25] <fenn> that's god giving you a type error [16:02:30] <maddash> infinity isn't even a number [16:02:33] <x3rox> This will become funny to convert/calibrate. Which pitch will usually be if the pitch I measure is ~3.12mm? (I pressed a sheet of paper on the oily thread and measured 6 turns) [16:02:48] <maddash> rofl novel [16:03:08] <jepler> x3rox: 1/8 inch is 3.175mm [16:03:12] <cradek> x3rox: if it's 10tpi, your pitch in mm is .3937 [16:03:20] <cradek> true it might be 8tpi [16:03:44] <cradek> if you have an inch scale you will be able to see easily which one it is [16:03:54] <fenn> oo there's that number again [16:04:06] <fenn> 3149606299 [16:05:31] <x3rox> yes, 8tpi looks good. Accidently I have exactly 8 stamps on the sheet of paper and they are 1 inch. So I hane 1/8 inc per turn.? [16:05:41] <cradek> yes [16:06:07] <x3rox> Will get a strange correction numer... [16:06:20] <jepler> You have: (1|8 in / rev) / (200 steps / rev) [16:06:18] <jepler> You want: steps / mm [16:06:18] <jepler> reciprocal conversion [16:06:18] <jepler> * 62.992126 [16:06:20] <cradek> so you could either configure the machine in inches, or use .31496 [16:06:21] <maddash> in class EMC-TRAJ-CIRCULAR-MOVE, how is the 'turn' member used? [16:06:49] <jepler> (or use 400 if half-stepping) [16:07:13] <x3rox> I'll use half-steps because this can L297+L298 do. [16:08:09] <maddash> no, that came out wrong. my problem is with the line of code in emccanon.cc: "circularMoveMsg.turn = rotation - 1;" So if I want the usual arc (eg, from 45 deg to 47 deg), then would 'turn' = 0? [16:08:09] <x3rox> So I will have to set (.31496 * 2) as correction value? [16:08:27] <cradek> maddash: http://www.isd.mel.nist.gov/personnel/kramer/pubs/RS274NGC_3.web/RS274NGC_34a.html#1000406 [16:08:28] <x3rox> (For metric setup) [16:09:04] <SWPadnos> x3rox, do you have any belt reduction? [16:09:20] <x3rox> No. [16:09:25] <SWPadnos> ok [16:09:27] <jepler> x3rox: [AXIS_0]INPUT_SCALE gives the number of steps to take to move one machine unit. I get 125.98425 steps per mm based on what you describe [16:09:52] <maddash> cradek: whoa, cool [16:10:15] <cradek> maddash: now there is also UVW but otherwise I think that documentation is still right [16:10:35] <x3rox> Thanks. I will try that out soon. (First I must finish the stepper drives.) Thanks a lot for your help! [16:10:45] <SWPadnos> those functions are actually in the user manual PDF, near the end [16:10:53] <cradek> maddash: for arbitrary arcs I think you want a new canon call ARBITRARY_ARC_FEED (or some such name) [16:11:17] <cradek> I wouldn't change this part of the API (I guess you could make it call ARBITRARY_ARC_FEED) [16:11:33] <x3rox> I'll re-read this part. Now I know (thanks to your help) which thread I have, so it is easier now. [16:11:40] <x3rox> Have a nice weekend! [16:11:56] <SWPadnos> have fun x3rox [16:12:01] <x3rox> Bye! [16:12:44] <maddash> cradek: i'm only adding to the api, and taking nothing away. [16:13:54] <cradek> * cradek cringes at the "mapping of rotation to turns" comment [16:14:41] <maddash> what the hell does it mean? [16:14:52] <maddash> "1 0 2 1 -1 -1 -2 -2" [16:14:56] <cradek> at least it seems to match the code [16:15:35] <maddash> the code's pretty screwed up, actually [16:15:41] <cradek> maddash: you're working in cvs trunk aren't you? don't tell me you're not [16:15:48] <cradek> maddash: I fixed that comment in trunk [16:15:57] <maddash> cradek: er...2.1.6? [16:15:59] <maddash> * maddash runs [16:16:11] <cradek> maddash: making substantial improvements to a release version means you will have to rewrite them for trunk if you want them incorporated [16:16:48] <SWPadnos> is it just me, or does that description leave out what a, b, and c are? [16:17:01] <SWPadnos> nevermind [16:17:12] <SWPadnos> * SWPadnos goes to make a pot of coffee [16:17:48] <cradek> SWPadnos: I agree, but it's "obviously" the endpoints [16:19:24] <maddash> cradek: 'center,' 'end,' and 'normal' aren't necessary [16:22:23] <maddash> s/it's/they're/ [16:22:27] <maddash> :P [16:25:10] <SWPadnos> I got that they're the endpoints, though it's interesting that the function doesn't take a pointer to the current position, which raises the "global variables are bad" issue [16:25:22] <SWPadnos> I'm sure that's all over the place though, so no biggie [16:25:36] <cradek> all of the canon calls specify the "new" position only [16:25:55] <SWPadnos> right - the globals are part of the spec, so it shouldn't be an issue [16:26:19] <SWPadnos> "but what if we want one canon to plan for 2 machines?" :) [16:26:31] <cradek> meh [16:26:36] <SWPadnos> heh [16:26:49] <maddash> in an XY arc, why is only the x tool offset accounted? [16:27:14] <maddash> 'case CANON_PLANE_XY:' [16:27:24] <SWPadnos> it's assumed that the tool is spinning, and therefore round (I think) [16:27:35] <cradek> there are only two tool offsets, X and Z [16:28:26] <maddash> why would you only account for the X and not the Y? it's an XY arc, so Y offset matters as well [16:28:45] <cradek> there is no Y tool offset [16:28:51] <maddash> oh shit, these are *tool* offsets, not work offsets [16:28:56] <cradek> right [16:28:56] <SWPadnos> the Y offset is the same as X, since the tool is round -you only need one number to offset the radius [16:29:03] <cradek> SWPadnos: nope [16:29:12] <SWPadnos> really? [16:29:16] <maddash> lathe. and mill. [16:29:27] <SWPadnos> sure, for a lathe it's totally different :) [16:29:41] <cradek> canon knows nothing about the tool shape, these calls move "the controlled point" only [16:29:54] <maddash> and why are the additions done in sequence and not all at once? some arcane optimization procedure? [16:30:30] <SWPadnos> ah, so the compensated arc is passed to canon [16:30:44] <jepler> most likely it's just a matter of programming style [16:30:45] <cradek> yes radius/shape compensation is an interpreter function [16:31:17] <SWPadnos> ah yes - I think there was some discussion about putting compensation into canon [16:31:23] <SWPadnos> I like it where it is, personally [16:31:49] <barum> Where to find smaller emc2 Live image than 660MB. Found old Puppy iso (51MB), but if it exist with newer version that whill be better. [16:32:17] <cradek> barum: I think those are your two choices fora Live CD [16:32:29] <maddash> third choice: make your own. [16:32:29] <barum> Thanks [16:32:45] <cradek> barum: I think the Puppy version is very old [16:33:19] <fenn> that xemet ever write up how he did it? [16:33:27] <fenn> s/that/did/ [16:33:31] <cradek> fenn: there's some stuff in the wiki I think [16:36:02] <fenn> all i see is emc-puppy [16:37:23] <jepler> I thought xemet's was also based around the emc2/ubuntu live CD [16:38:30] <fenn> yeah [16:38:48] <fenn> presumably once you get it on a usb stick you can start deleting stuff like mad [16:38:59] <fenn> i forget if i ever got emc to run on DSL [16:45:20] <maddash> feck [16:45:48] <maddash> can anyone else confirm that pmCirclePoint in _posemath.c handles arbitrary helices as well? [16:46:51] <cradek> looks like it to me [16:46:53] <maddash> or can I just forget about helices for now? [16:47:01] <maddash> ah, ok. [16:47:09] <cradek> (and it looks pretty well documented) [16:48:30] <maddash> hm, we need to discuss the syntax of G02.4 [16:48:45] <cradek> did you find docs saying how another system does it? [16:48:56] <maddash> yes, I'm mimicing fanuc as closely as I can [16:49:07] <cradek> are those docs on the web? [16:49:44] <maddash> (googling) [16:50:36] <maddash> www.compumachine.com/Support/Downloads/Fadal/GE%20Fanuc/0010__GE_FANUC_User_Manual.pdf [16:50:56] <maddash> search terms: "G02.4" [16:51:28] <maddash> fanuc actually implements a g03.4, but it's redundant [16:51:48] <maddash> page 719 of 1257 in that doc [16:53:09] <maddash> anyway, we've no support for X_1/2 Y_1/2, etc, so the next best thing I could come up with was using I,J,K [16:53:59] <maddash> right now, the syntax I have in mind is " G02.4 X- Y- Z- I- J- K- ," where xyz is the endpt and ijk is the midpt [16:54:36] <cradek> you could do this two block thing, I think [16:54:43] <cradek> but I don't think it supports helixes [16:55:01] <cradek> (I don't follow the alpha/beta stuff yet either) [16:55:24] <maddash> the problem arises when you want an arbitrary helix [16:55:40] <cradek> yes [16:56:17] <maddash> * maddash should stop staring at the keyboard when typing [16:56:19] <cradek> oh alpha/beta means you can specify more axes there (like our abcuvw) [16:56:27] <jepler> cradek: I think that it means you could command a move on up to two other axes (ABCUVW in the case of an adaptation to emc) [16:56:35] <jepler> right [16:56:39] <cradek> must be right if we both think that [16:56:41] <maddash> * maddash is contagious [16:57:01] <jepler> ("only two additional axes" seems like a stupid limitation..) [16:56:59] <cradek> up to two is a strange limitation [16:57:04] <cradek> hahaha [16:57:16] <cradek> one of us is redundant here [16:57:20] <jepler> so leave [16:57:26] <cradek> wanna go to lunch? [16:57:28] <maddash> the fanuc standard was designed specially for the fanuc machine, which only has 5-axes [16:57:58] <maddash> five axes* [16:59:21] <maddash> at any rate, i'm bringing up the syntax because of the helix issue. frankly, it would seem simpler to leave out helices entirely (because I'm a lazy-ass). [17:05:18] <lerneaen_hydra> one thing that IMO warrants thinking about: when would you need to code a helix manually? is there ever a case where you need a helix *and* need to code by hand? [17:05:43] <lerneaen_hydra> 3d arcs I can understand, smaller programs, faster loading [17:06:07] <lerneaen_hydra> helices can be appoximated with a couple 3d arcs [17:07:39] <SWPadnos> a helix is a good pattern for milling circular holes, and that can't be done with arcs if they're constrained to a plane [17:07:53] <SWPadnos> err - I should go drink some of that coffee [17:08:44] <maddash> a helix is also needed for threading [17:08:48] <maddash> useful* [17:11:26] <fenn> you cant thread without helices [17:11:30] <archivist> clockmakers need a special helix [17:12:04] <SWPadnos> you only need helixes for threadmilling, no? [17:12:09] <SWPadnos> (relative to threading) [17:12:51] <archivist> Im thinking of the Fusee [17:13:38] <SWPadnos> sure - you need a decreasing arc helix for that (or increasing) [17:15:43] <archivist> often a turned item on a fusee lathe, or could be milled with a rotary axis on a vertical mill [17:20:27] <maddash> hm, can I default circularmovemsg.turn to 0, since helices are left out? [17:20:52] <maddash> why am I even asking? [17:22:50] <lerneaen_hydra> what I meant is when you do stuff like that you're not going to code by hand, you'll use a cam app [17:23:27] <lerneaen_hydra> and with with the exception of threading that can be done with multiple G1 movements [17:23:43] <lerneaen_hydra> as I take it the threading needs spindle syns [17:23:59] <lerneaen_hydra> *sync [17:24:10] <lerneaen_hydra> though that depends on the type of cutter of course [18:05:30] <Roguish> hey all, what's the 'best' cad program for linux open source? [18:06:00] <Roguish> something just to sketch with.... [18:06:08] <jepler> Roguish: I don't know of any really good ones. I have put together a few drawings for emc2 documentation with qcad, however [18:06:56] <Roguish> how 'bout : http://brlcad.org/ [18:06:59] <jepler> http://linuxcnc.org/docs/devel/html/hal/drivers/img4.png and http://linuxcnc.org/docs/devel/html/hal/drivers/img6.png are two of them -- however they've suffered in quality by the conversion from dxf -> eps -> png [18:07:03] <jepler> I haven't used brlcad [18:08:08] <SWPadnos> if you can get your head around it, brlcad can do everything. getting past the UI isn't easy - I haven't managed it yet [18:08:20] <SWPadnos> you can join #brlcad if you have questions [18:09:15] <archivist> the UI sucks absolutely [18:09:41] <jepler> "varkon - A CAD-system with parametric modelling [18:09:42] <jepler> " [18:09:53] <jepler> has anyone use this? I see it in 'apt-cache search' but I have never heard of it [18:10:01] <archivist> nor me [18:10:50] <SWPadnos> I did install it on a machine, but I'm not sure I was able to do anything with it [18:11:06] <SWPadnos> I don't remember any results :) [18:12:04] <jepler> must be pretty old -- http://www.tech.oru.se/cad/varkon/scrdmp4.htm -- looks like fvwm + tk or motif [18:12:22] <archivist> tis old 85-86 [18:12:48] <archivist> see cant do at bottom http://www.tech.oru.se/cad/varkon/whatis.htm [18:13:07] <anonimasu> heh..i [18:13:09] <anonimasu> it's horrid [18:14:16] <archivist> about the same cant do as brlcad [18:15:49] <fenn> varkon isnt exactly a cad program [18:16:08] <fenn> its more of a software library [18:17:03] <archivist> as brlcad is [18:17:12] <fenn> fair enough :) [18:17:48] <archivist> although brlcad is more of a solid modeller [18:18:02] <fenn> brlcad is more of a solid modeller than most anything out there [18:18:31] <fenn> parallelepiped [18:18:52] <fenn> i cant remember the wacky geometries you'll never use [18:18:55] <archivist> I lurk in there hoping for some sense in the UI and real world dimensioning being added [18:21:09] <archivist> a solidworks UI on top of brlcad would be heaven probably [18:22:34] <archivist> but as a solidworks user I just cant go back to the Ark [18:30:17] <Roguish> how about qcad? [18:31:43] <fenn> qcad is good for simple drafting [18:32:10] <Roguish> that's all i am looking for. got Proe for design. [18:33:58] <fenn> skencil might be worth playing with too [18:36:02] <Roguish> just put in qcad. looks good. thanks. [18:37:25] <fenn> wow skencil is really similar to inkscape [18:38:02] <bill2or3> * bill2or3 googles [18:38:56] <fenn> it has this 'blend' function which is really neat though [18:39:40] <Jymmm> Does EPS, but no mention of PS [18:41:00] <fenn> meh, they're similar enough [18:41:20] <Jymmm> close, but no cigar [18:41:38] <fenn> skencil outputs .ps not .eps, but ps2eps works [18:41:52] <Jymmm> it says EPS, not PS [18:42:22] <fenn> well i just saved a .ps file so i dont care what it says [18:42:34] <Jymmm> Exports Encapsulated PostScript [18:42:48] <Jymmm> look at the file in a text editor [18:43:12] <Jymmm> then pastebin it [18:43:15] <fenn> %!PS-Adobe-3.0 EPSF-3.0 [18:43:24] <jepler> eps is postscript with additional restrictions [18:44:13] <jepler> "encapsulated" means there are special comments that can be read by compatible software, and restrictions on the operations that can be done inside so that a program can embed it in a larger document without worrying about the details [18:44:43] <fenn> apparently ps is a rather powerful language [18:44:53] <Jymmm> fenn: yep [18:45:11] <Jymmm> fenn: actually, very cool lang [18:47:30] <Jymmm> fenn: This was created using PS lang with randomly generated patterns... http://farm1.static.flickr.com/43/105089849_07aeb24900.jpg [18:49:26] <Jymmm> And yes, there is a solution. It's not just a optical illusion [18:50:24] <fenn> reminds me of mac-plus days [18:51:20] <Jymmm> fenn: you should see the EXTREME puzzles I've created... [18:51:37] <fenn> you gonna cut that maze on your router? [18:52:41] <Jymmm> I haven't figured out how to cut the labyrinths, as they're layers. But I have of the mazes. [18:56:02] <fenn> http://www.dollins.org/mazes/rt-25-25-4-closeup2.png [18:56:38] <Jymmm> yep, like that [19:00:30] <fenn> he's got some nice celtic knots too [19:00:48] <fenn> or, something like that [19:04:00] <fenn> http://davidbau.com/downloads/pymaze.py [20:24:07] <David36_LA> Hi, does the TRAJ_PERIOD variable affect how many GCODE blocks per second EMC can process ? [20:25:44] <awallin> I think so [20:25:48] <cradek> are you having trouble? [20:26:08] <cradek> (a lot of things can affect that) [20:26:36] <David36_LA> No, no problem. Bu assuming all others factors are not an issue (machine speed, etc) [20:27:06] <David36_LA> I was curious if the EMC code that reads the gcode file deals with only one block per traj_period [20:27:24] <cradek> if the userland code (interpreter etc) can keep it fed, the realtime motion controller can use up to one motion per traj/servo cycle [20:27:31] <cradek> often that's 1000/sec [20:27:54] <cradek> whether the interpreter can keep it fed is a matter of your machine speed and how busy it is doing "other" things like running the GUI [20:28:10] <David36_LA> In most configs file I saw servo is often 1ms but traj is more like 10ms [20:28:34] <jepler> however, the realtime motion controller begins to give poor performance (lower velocity than requested) when an individual segment is not long enough for the accel/decel phase, which is almost always well before 1 segment per ms [20:28:46] <cradek> I don't actually think the traj cycle is used, the planner runs every servo cycle [20:29:15] <cradek> yes jepler is right, that's why I asked if you were having a problem - to figure out exactly what question you were asking [20:30:21] <David36_LA> ok, a customer doesn lots of 3D with short segments [20:30:44] <David36_LA> he is asking me if EMC2 is good at fast 3D work in wax and such [20:30:45] <cradek> with tiny segments, be sure to use tolerance mode (G64 Px.xx) [20:30:53] <David36_LA> on a mill [20:31:05] <cradek> with P = an appropriate machining tolerance [20:32:39] <awallin> cradek: sounds interesting if traj_cycle is never actually used !? shouldn't that be documented and traj_cycle removed from the ini? [20:32:41] <David36_LA> For example, If I run sprial.ngc from EMC2 files [20:33:30] <cradek> whether it's "good" at "fast" is hard to answer without details about what "good" and "fast" mean [20:33:37] <David36_LA> and set feed rate to 115 ipm (my mill can take it and I am not actualy cutting material), the curves seemed to move well bellow 115ipm [20:33:57] <David36_LA> it seems to slow down alot towards the center of the spiral [20:34:14] <cradek> do you have the machine's acceleration set as high as possible? [20:34:26] <cradek> making any curvy path requires acceleration, so that may be limiting the motion [20:34:34] <cradek> also, try G64 Px.xx (tolerance) like I suggested [20:34:58] <David36_LA> ok [20:35:00] <David36_LA> will try [20:35:15] <jepler> tolerance mode probably won't make much difference on the spiral until near the end [20:35:22] <cradek> right, the acceleration setting is the most important for making small moves and direction changes [20:36:54] <David36_LA> thanks [20:36:57] <jepler> For the emc2 realtime trajectory planner to contour well, each segment should be long enough to have a "cruise phase": assume the mill is stopped when you begin the segment, accelerates to the requested speed, "cruises" for a time at the top speed, then decelerates to stop exactly at the end -- trapezoidal velocity profile [20:37:18] <jepler> if the segment becomes short enough relative to the acceleration and velocity, the profile becomes triangular and there is no "cruise phase" [20:39:25] <awallin> jepler: but in G64 mode you start out with some velocity, and can end the segment also at non-zero velocity, so the full acc-ramps at the beginning and end should in principle not be required ? [20:40:02] <cradek> awallin: yes but that's how the algorithm works [20:40:15] <davidf> hi.. [20:40:20] <cradek> hi davidf [20:40:22] <jepler> awallin: it's true that a different method altogether would not necessarily have this particular limitation [20:40:26] <jepler> but the one that is currently in emc does [20:40:41] <davidf> cradek, Hey :) [20:41:41] <davidf> Just wanted to stop in and pass this on. Probably not anything new to you guys but just in case: [20:42:23] <davidf> I was using windows for ACE converter dxf to g-code, then putting on floppy. [20:42:51] <davidf> Then I tried installing wine, and ace on ubuntu. Works! :) [20:43:09] <cradek> nice, no windows license required! [20:43:29] <awallin> jepler, cradek: ok, I understand. coming up with an alternative algorithm is not trivial... but that's still something I'd like to learn about when I have time. The problem when I read about this last time is how you react to changes in feed-override. It seems that for better lookahead you have to sacrifice a bit of response-time to feed-override... [20:43:56] <davidf> But you just have to use todos to convert the resulting g-code file for linux linefeed style. [20:45:21] <cradek> actually I think EMC2 will load CRLF gcode without complaining [20:45:23] <davidf> Oops. That's not right. I meant to say you need to convert your linux style dxf file with todos so ace can read it properly. [20:45:34] <cradek> oh ok! that's different [20:45:47] <davidf> Yes. very. sorry. [20:46:17] <cradek> certainly no apology necessary [20:46:33] <davidf> Anyway, I am finding that on ubuntu, with QCad for making dxf and ace. there is really great possibility. [20:46:38] <cradek> I'm going to suggest wine/ace to a friend who is wanting to work with dxfs, thanks for letting us know [20:46:51] <cradek> right, that's exactly what he might want to do [20:47:06] <cradek> a gcode export in qcad would be better ... all free/open source software then [20:47:12] <cradek> but maybe this is a good stopgap [20:47:14] <davidf> Can't tell you what a relief it is not to have to work on two boxes anymore. [20:49:49] <davidf> On my emc machine, I'm still running ubuntu 5.1 or something like that. Can I install eme 2.1.6 without a linux upgrade to 6.06? [20:50:03] <davidf> emc 2.2.6 [20:50:07] <cradek> yes you can update just emc2 to 2.1.6 [20:50:28] <davidf> Great. There is a ubuntu binary, right? [20:50:31] <cradek> ubuntu have stopped supporting version 5.10 - you should consider updating soon [20:50:35] <cradek> yes [20:50:48] <ds2> if someone got the time, the ACE source code is available [20:51:36] <davidf> Yeah, but I have a real tiny 4 gig HD on that machine, and it is kinda slow too, so I thought I'd probably wait to upgrade the whole thing soon. [20:51:42] <cradek> ah [20:51:57] <cradek> (I think 4G is still enough for ubuntu 6.06) [20:52:17] <davidf> Yes, the ace download has all the source code as well as the windows exe. [20:52:31] <cradek> oh, interesting - is it a free license? [20:52:34] <davidf> cradek, Oh that's great. [20:52:44] <davidf> Yup! [20:52:59] <davidf> GPL I think. [20:53:07] <cradek> very interesting [20:53:10] <davidf> I'll check... [20:53:16] <cradek> should be pretty easy to build a native unix binary then [20:53:18] <ds2> it is not a straight forward compile on LInux, unfortunately [20:53:23] <cradek> er, possible, maybe not easy [20:54:18] <davidf> Yes, it is GPL. [20:55:30] <davidf> I had a look at the source yesterday. Looks doable, but ace as is works great anyway. Does prioritized layers, arcs, optimization, etc. [20:56:50] <archivist> hmm looks interesting [20:56:58] <davidf> I was thinking of just trying to use the source as a guide to rewrite it for linux, then thought, duh. What if it will work with wine? Glad I tried it! [20:58:55] <davidf> cradek, You remember that old bug that gives an axis following errer sometimes, and you have to restart emc or wait a while? Is that problem totally fixed now? [21:01:40] <davidf> Also, I'm using emc to cut flutes on the reamer bits I make. Sometimes I'll be too deep by a couple thou, out of the blue. I think I saw a ref to some kind of 'overshoot' bug in older versions. Could that be it? Haven't been able to identify what does it. It is intermittent. [21:02:14] <cradek> davidf: I'm not familiar with either of these bugs... I suspect you have some kind of misconfiguration if you are having random problems [21:02:49] <cradek> if you are using servos, you may not have them tuned very well [21:03:31] <cradek> I have to run ... be back later [21:03:59] <davidf> Well, I remember bringing it up many moons ago, and either you or jepler I think, said 'someone was supposed to have fixed that, but then you realized he hadn't. I think swapdnos was in that chat as well. It had something to do with accel I think. [21:04:05] <davidf> OK. Bye. [21:04:37] <davidf> I'm suing steppers btw. [21:04:55] <davidf> ha. using steppers, not suing. [21:05:42] <davidf> Anyway, Thanks for the info. hope the ace thing helps some folks. I really like it. Bye... [21:09:33] <ds2> wow suing... hehe [21:33:48] <Roguish> hey, what's the latest status on M5i20 fpga code? 2.2.0? [22:08:01] <edmoore> hi chaps [22:08:22] <edmoore> completely newb question that would be better served be reading the website most probably, but, can emc do 5 axis cnc work? [22:08:29] <SWPadnos> yes [22:09:23] <SWPadnos> you'll need an appropriate CAM program to generate 5-axis G-code that will work with your machine [22:10:14] <edmoore> yes sure [22:10:29] <edmoore> i appreciate that's probably more likely to be the week link for the hobbyist [22:10:38] <edmoore> weak* [22:11:17] <anonimasu> SWPadnos: does that mean 5 axis interpolated work? [22:13:01] <floppy1234> hello [22:17:32] <SWPadnos> anonimasu, XYZABC (and now +UVW) interpolation is pretty well described in the manual [22:17:58] <SWPadnos> you can't do tooltip velocity with ABC included, or if you use any of XYZ along with any of UVW [22:18:15] <anonimasu> SWPadnos: I havent looked for quite some time.. I dont care as I dont have a 6 axis mill.. [22:18:43] <anonimasu> im not even sure about uvw [22:19:26] <floppy1234> i want to control a pneumatic system with emc. i've seen "etch-servo" which configures a closed loop system. how fast is this way to control the servopneumatic linear axies? [22:19:45] <anonimasu> floppy1234: are you building a new machine? [22:19:52] <SWPadnos> I think UVW are treated the same as ABC if there is any XYZ motion (ie, the UVW move completes in the time taken for XYZ) [22:19:57] <floppy1234> anonimasu yes [22:20:03] <anonimasu> floppy1234: dont go there please.. [22:20:08] <SWPadnos> and if there's no XYZ, then UVW are trerated as the cartesian group for tooltip velocity [22:20:10] <anonimasu> r:) [22:20:10] <floppy1234> anonimasu why? [22:20:15] <SWPadnos> treated [22:20:34] <anonimasu> floppy1234: because pneumatics arent too great at positioning [22:20:52] <floppy1234> anonimasu i have the axies [22:21:15] <floppy1234> anonimasu and they should cut with a hot wire [22:21:34] <floppy1234> do you know "styropor"? [22:21:49] <floppy1234> it is a light wight foam [22:22:27] <anonimasu> well, pneumatics have stiction and friction that makes them bad for positioning [22:23:07] <floppy1234> i drive with controled exit air [22:23:16] <floppy1234> so it works.. [22:23:28] <floppy1234> i mean, it is not the best way to positioning [22:23:51] <anonimasu> it's probably one of the worst ones.. [22:23:56] <anonimasu> but sure you could use emc to drive it.. [22:24:01] <floppy1234> but conside: the axies are a gift ;) [22:24:24] <floppy1234> and we want to drive 1mm or so [22:24:49] <anonimasu> that small? [22:24:51] <floppy1234> the incremental encoder's resolution is 5µm [22:25:16] <floppy1234> i mean we need a accuracy about 1mm [22:25:26] <anonimasu> I think that's hard to acheive.. [22:25:29] <floppy1234> our driveway is about 1200mm [22:26:25] <floppy1234> well, i think, if we can drive with a accuracy about 5mm it is also okay [22:27:08] <floppy1234> but i know the axies can be controlled more exacting [22:29:09] <floppy1234> hm... if the pneumatic control doesnt work, i changeover to spindles, but i first try with the existing systenm [22:29:12] <floppy1234> system [22:29:28] <skunkworks> what are you using for a valve? [22:29:34] <anonimasu> you probably need some hardware for controlling your valves.. [22:29:46] <floppy1234> hmmm [22:29:54] <floppy1234> the valves are from bosch rexroth [22:30:20] <floppy1234> they can be controlled between 0 to 100mA and let flow 0 to 6 bar [22:30:29] <skunkworks> I think it would be a cool experiment. :) [22:30:58] <floppy1234> so i made a operationamplifier circuit which control with 0 to 5V the current from 0 to 100mA [22:31:36] <floppy1234> this ciruit works... i have a adjustable power suply and can control very good [22:31:47] <floppy1234> wanna see some pictures? [22:32:20] <skunkworks> sure. what are your plans to interface emc to your control? [22:32:30] <floppy1234> http://www.rsp-design.de/plotter/Foto113.jpg [22:32:58] <floppy1234> skunkworks first i want to drive with PWM like the EMC's demofile "etch-servo" [22:33:07] <skunkworks> ah - cool [22:33:31] <floppy1234> if this is to slow, i wanna change to a microcontroller for each axis [22:33:39] <floppy1234> skunkworks what is cool? ;) [22:35:26] <skunkworks> using pwm out of the printer port - and the slides. you said the encoders res is .000005M? or or .005mm? [22:35:44] <floppy1234> the res is 5µm [22:35:57] <floppy1234> also 0.005mm [22:36:22] <skunkworks> that may be pretty hard to count with the printer port.. speed wise [22:36:39] <floppy1234> i think it will go very sloooooow [22:36:48] <floppy1234> but it must drive ;) [22:38:30] <skunkworks> The pluto would be a cool/cheap 4 axis servo controler you might want to look at. 4pwm out 4 encoder in and some i/o [22:38:50] <floppy1234> hmmm [22:39:06] <floppy1234> exists there a open source device? [22:39:09] <skunkworks> yes [22:39:39] <floppy1234> is this the controller called "pluto"? [22:40:17] <skunkworks> http://emergent.unpy.net/01166412010 [22:40:39] <skunkworks> if you want more power - the mesa card is open source also. [22:41:09] <skunkworks> the pluto is printer port - the mesa is pci [22:42:02] <floppy1234> well... 60 for the plutoboard isnt expensive
[22:42:15] <floppy1234> i think for this price i dont build a board
[22:44:41] <floppy1234> i cant find something about the mesa card
[22:44:53] <anonimasu> did anyone ever try making anything with fluid/pneumatic bearings+
[22:44:56] <anonimasu> ?
[22:45:37] <floppy1234> no
[22:45:41] <anonimasu> probably not..
[22:45:49] <anonimasu> :)
[22:45:50] <floppy1234> it is my first project ;)
[22:46:44] <anonimasu> I need a grinding attachment for my lathe
[22:47:31] <floppy1234> uuuuh
[22:47:39] <ds2> isn't a foredome handle in a boring bar holder equivalent?
[22:47:57] <anonimasu> ds2: to a grinder?
[22:47:58] <anonimasu> heh
[22:47:58] <skunkworks> http://www.mesanet.com/motioncardinfo.html
[22:47:59] <floppy1234> whar is a foredom?
[22:48:05] <anonimasu> or what do you mean
[22:48:10] <skunkworks> 5I20
[22:48:15] <ds2> yes, to a grinding attachment
[22:48:27] <anonimasu> I dont know what a "foredom"
[22:48:28] <anonimasu> is
[22:48:41] <ds2> think big dremel on flex shaft
[22:48:49] <anonimasu> hm, _flex_ shaft.. no
[22:48:50] <anonimasu> not really
[22:49:15] <anonimasu> http://www.golmatic.de/GOLmatic_EN/zubehoer_en/supportschleifer_en.htm
[22:49:41] <floppy1234> anonimasu are u german?
[22:49:43] <anonimasu> no
[22:49:51] <floppy1234> okay ;)
[22:50:08] <floppy1234> is there a german emc chat?
[22:50:17] <floppy1234> cause my english is very bad :p0
[22:50:18] <floppy1234> :p
[22:50:24] <ds2> http://www.fandfwoodcarving.com/images/TX&HP.jpg
[22:50:26] <ds2> much better picture
[22:50:39] <floppy1234> i tortue "dict.leo.org" all the time :p
[22:50:44] <anonimasu> _woodcarving_
[22:50:58] <anonimasu> ds2: I want to grind steel stuff.
[22:51:02] <ds2> yes, but you can put a mini grinding stone on it
[22:51:38] <floppy1234> hmmm
[22:51:56] <floppy1234> ive yet another question
[22:52:06] <archivist> anonimasu, thats lathe abuse, but Ive done it with a dremel as well
[22:52:12] <ds2> like this guy -
[22:52:13] <ds2> http://www.5bears.com/tshaft_1.htm
[22:52:17] <ds2> see bottom of the page
[22:52:40] <anonimasu> he crude homemade toolpost grinder shown in Part 1 was a failure. The bearings in the Foredom handle were simply not precise enough, and the finish was poor. So I scrapped the grinder concept and went forward with the traditional home-shop method of producing the shaft.
[22:52:51] <floppy1234> what is this like? can i display a 4 axis hot wire cut machine?
[22:53:07] <ds2> DOH
[22:55:48] <anonimasu> ds2: I want a spindle that'll go to 10krpm..
[22:55:50] <anonimasu> ;)
[22:55:58] <anonimasu> ds2: hence fluid bearings and stuff..
[22:56:44] <ds2> just did :/
[22:56:48] <floppy1234> so... i open a german beer ;)
[22:57:09] <floppy1234> are you all amarican?
[22:57:16] <anonimasu> no
[22:57:18] <anonimasu> im swedish
[22:57:35] <floppy1234> archivist is german?
[22:57:41] <archivist> no
[22:58:32] <floppy1234> hmm i think so cause you are in mysql.de
[22:59:28] <archivist> no I run the bot for mysql mysqlde and mysqles and thats why im there
[23:00:00] <floppy1234> mmm kay :)
[23:00:02] <anonimasu> http://pergatory.mit.edu/rcortesi/portf/spindle/mighty_spindlel_files/frame.htm
[23:00:07] <archivist> Im english
[23:00:25] <floppy1234> pity...
[23:00:56] <floppy1234> so i must break down in english :p
[23:02:50] <ds2> * ds2 refrains from complaining about machines using a mix of whitworth and metric screws
[23:03:15] <anonimasu> :p
[23:03:27] <archivist> its worse here, we still use BA as well
[23:03:35] <floppy1234> ds2 i think everytime so, when i must repair my car
[23:03:53] <ds2> serious? thought you guys outlawed anything nonmetric
[23:05:07] <anonimasu> ds2: http://pergatory.mit.edu/perg/awards/TURBOTOO.html
[23:05:10] <anonimasu> why does that make me drool :p
[23:05:48] <ds2> looks expensive to make ;)
[23:05:52] <floppy1234> yeah
[23:06:19] <floppy1234> ds2 looks depressing when it breaks ;)
[23:06:31] <anonimasu> :)
[23:06:44] <ds2> should ask for quotes at the local shops to scare them ;)
[23:06:51] <anonimasu> haha
[23:06:53] <archivist> ds2 actually BA is a british standard that used metric dimensions
[23:06:56] <floppy1234> hehe
[23:06:57] <anonimasu> 200 000rpm..
[23:07:07] <floppy1234> anonimasu so slow? *G*
[23:07:16] <anonimasu> or 100 000 rpm and 100kw
[23:07:17] <anonimasu> :p
[23:07:34] <anonimasu> have you ever seen a 100kw cut being made?
[23:07:40] <ds2> archivist: Hmmmm I am looking at a machine from the 80's and the plans call out something like 1/4-20BA so...
[23:07:49] <floppy1234> uuh.. there is my grandma faster with a gimlet
[23:07:50] <floppy1234> *GGG*
[23:07:57] <anonimasu> I'd love to see that :p
[23:08:27] <ds2> it doesn't look that horrible now that i study it a bit
[23:08:43] <anonimasu> :)
[23:08:45] <floppy1234> anonimasu i belive ;)
[23:08:47] <ds2> 4 axis mill can do most of it
[23:08:53] <anonimasu> yep
[23:09:02] <anonimasu> you need to grind the outer surface..
[23:09:08] <anonimasu> that's the complex part..
[23:09:11] <anonimasu> and the housing..
[23:09:11] <ds2> Oh
[23:09:13] <anonimasu> I guess..
[23:09:20] <anonimasu> hone it or something
[23:09:34] <anonimasu> and ofcourse it needs to be balanced..
[23:09:35] <floppy1234> hm mm
[23:09:52] <ds2> wonder if you put a die grinder stone in a collet and have the same CNC machine grind it
[23:09:59] <ds2> (assuming you have a 10K+ spindle)
[23:10:07] <anonimasu> no
[23:10:14] <anonimasu> I dont think you do :)
[23:10:25] <anonimasu> or do you mean to sharpen the flutes?
[23:10:29] <floppy1234> well my question again: can i show the 4 axis erode machine on my screen?
[23:10:41] <anonimasu> yes
[23:10:42] <ds2> 10K CNC spindles are an option on the Haas
[23:11:26] <anonimasu> dosent haas have everything as option?
[23:11:33] <ds2> heh
[23:11:39] <anonimasu> though they are cheap..
[23:11:41] <ds2> I know the tiny taig has a 10K spindle default
[23:11:49] <anonimasu> matsuura has 40krpm standard..
[23:11:53] <anonimasu> and 60k as option
[23:12:07] <anonimasu> or well 8-15krpm for other machines :)
[23:12:19] <ds2> nice, and how thick is the shelding plastic/glass? =)
[23:12:19] <floppy1234> anonimasu you mean yes to my question?
[23:12:28] <anonimasu> floppy1234: Yes
[23:12:36] <floppy1234> anonimasu how can i do?
[23:12:37] <ds2> a 1/8" bit breaking on a 60K spindle can hurt!
[23:12:42] <anonimasu> floppy1234: you do know you only seewhere the machines are going..
[23:12:47] <anonimasu> and not the actual machine
[23:12:49] <anonimasu> just the toolpath..
[23:12:57] <floppy1234> yes i konw
[23:13:01] <floppy1234> know
[23:13:02] <floppy1234> thats i wantr
[23:13:04] <floppy1234> want
[23:13:12] <anonimasu> how does that differ from a 3 axis mill?
[23:13:20] <anonimasu> :)
[23:13:38] <floppy1234> hmmm
[23:13:41] <anonimasu> except one axis less :)
[23:13:49] <anonimasu> ds2: yep
[23:13:53] <floppy1234> ok...
[23:14:03] <floppy1234> i think about when the machine run
[23:15:11] <anonimasu> ds2: I'd love to try that kind of setup
[23:15:25] <ds2> anonimasu: engraving or grinding?
[23:15:30] <anonimasu> making a tool like that
[23:15:33] <floppy1234> i wanna se the machine run ;)
[23:15:55] <floppy1234> how fast is the parallelport?
[23:15:57] <anonimasu> floppy1234: I dont get it.. you can see how it moves in realtime..
[23:16:02] <anonimasu> with axis :)
[23:21:30] <anonimasu> ds2: milling
[23:22:35] <floppy1234> kk
[23:24:09] <anonimasu> ds2: tell me 100krpm isnt a cool thing ;)
[23:27:15] <archivist> pcb drilling machines work at insane speeds
[23:27:44] <anonimasu> archivist: they dont cut aluminium..
[23:27:49] <anonimasu> :)
[23:27:51] <floppy1234> hmmm
[23:27:51] <archivist> I know
[23:28:53] <floppy1234> which expirience do you have with threaded bars from the do-it-yourself store to position a machine?
[23:29:43] <archivist> they are rolled threads to a price dont expect accuracy
[23:30:54] <floppy1234> hmmmm
[23:31:11] <floppy1234> you mean, i should not take them?
[23:31:22] <floppy1234> i will build a seccond machine
[23:31:39] <floppy1234> to drill pcbs and mill little things
[23:31:46] <anonimasu> they work.
[23:31:53] <floppy1234> okay
[23:32:19] <anonimasu> the bottom line is how mich are you willing to pay for accuracy
[23:33:49] <floppy1234> well... i think special spindles give not more accuracy but hey durable
[23:33:53] <floppy1234> or not?
[23:34:07] <archivist> has EMC got leadscrew compensation
[23:34:08] <anonimasu> floppy1234: 01:31 < floppy1234> which expirience do you have with threaded bars from the do-it-yourself store to position a machine?
[23:34:11] <anonimasu> 01:32 < archivist> they are rolled threads to a price dont expect accuracy
[23:34:50] <floppy1234> oh... i dont understand right, sorry
[23:36:38] <floppy1234> hmmm you mean, i cant await accuracy when i dont buy recirculating ballscrew?
[23:37:43] <anonimasu> floppy1234: yes.
[23:38:00] <floppy1234> okay
[23:38:02] <anonimasu> floppy1234: "How much should accuracy cost?" do you get that?
[23:38:48] <archivist> accuracy depends on quality, or it can be calibrated or movement can be measured so it does not matter so much
[23:38:55] <floppy1234> but is the gain of accuracy drastic for a homemade lowcost pcb mill?
[23:39:04] <archivist> no
[23:39:05] <anonimasu> no
[23:39:06] <floppy1234> okay
[23:39:10] <floppy1234> thank you
[23:39:15] <floppy1234> thats all i wanna kow
[23:39:21] <floppy1234> but stop....
[23:39:24] <floppy1234> not all :p
[23:39:45] <floppy1234> how is it about the galling?
[23:40:12] <anonimasu> the more stuff I do with cnc's the more I realize that what I want is a machine I can depend on to work, and not break..
[23:40:50] <archivist> yes, the toy here is not reliable
[23:41:14] <anonimasu> I hate fscking around when I need to facemill something
[23:41:34] <floppy1234> well
[23:41:36] <floppy1234> i go to bed
[23:41:47] <floppy1234> when i have a problem tomorrow, ill come back...
[23:42:06] <floppy1234> otherwise ill come also back
[23:42:28] <toast> fff
[23:42:29] <archivist> face milling here is on a turn of the century machine 1899-1900
[23:44:43] <anonimasu> :)
[23:46:40] <floppy1234> good night
[23:47:44] <archivist> www.archivist.info/skeleton
[23:48:34] <archivist> down in the basement
[23:53:18] <Ziegler> is that machine belt driven?
[23:53:29] <Ziegler> the spindle?
[23:53:29] <archivist> yes
[23:53:32] <Ziegler> cool
[23:53:48] <archivist> we think pre ww1
[23:53:57] <Ziegler> bet that has been fun to play with
[23:54:21] <archivist> and googling just now confirms that sort of date for the company
[23:54:31] <Ziegler> what company?
[23:54:37] <archivist> its a bit odd to use
[23:54:54] <archivist> Garvin machine co new york
[23:55:10] <Ziegler> ah... are the ways in good shape? | 2017-04-30 20:37:45 | {"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": 0.5971564054489136, "perplexity": 14518.885238003939}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125849.25/warc/CC-MAIN-20170423031205-00482-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.gamedev.net/forums/topic/696886-architecture-advice-ecs-without-events/ | # Custom Architecture Advice - ECS without events?
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Hi there.
I'm looking for some quick opinions, advice or other comments on my custom engine architecture.
For better or for worse, I have ended up with an ECS engine. I didn't intend to go this way, but countless searched through Google and the forum seem to confirm that this is the case. I have entities (mere Ids), components (pure data) and systems (holding raw resources and functionality) to operate on them. To be honest, I'm fairly happy with it.
However, I have yet to implement any actual logic into my 'game', and have been looking around for details on the various ways of handling interactivity, specifically, interactively between entities and components.
A topic that comes up a lot is events and event queues. I have not liked these. I don't want to add functionality to entities or components, and I don't like the idea of callbacks or event calling firing all over the place. So, I have been puzzling over this for the last two or so days. Eventually, I gave up on the musing and came to accept that some kind of event system is going to be needed. So, I had another look at the bitSquid blog (recommended on this forum), and something occurred to me. Isn't an event really just another form of entity? If it isn't, why isn't it?
I also realised that I already have something pretty similar running in my engine now. Specifically, my (admitted quite naive) implementation works more or less like this. The scene hands a list of physicalComponents and their corresponding placementComponents, and the collisionDetection sub-system iterates through them, looking for collisions. If it finds one, it creates a collision, adds it to the list, and moves on to the next one. Once it is finished, the collisionResolution sub-system goes through the list, and handles the collisions - again, currently very naively, by bouncing the objects off of one another.
So, I am wondering if I can just use this same approach to handle logical interactions. Entities with logical requirements have a collection of components related to interactivity (the range, the effect, and so on), and the various sub-systems iterate through potential candidates. If it notices an interaction, it creates an interactionEntity (with the necessary data) and the interactions are processed by the next sub-system.
I guess I'm looking for some feedback on this idea before I start implementing it. The hope i for more granularity in the components, and the ability to add a logical scripting system which combines various components into potential interactions, and omits the need for any kind of event system. Or am I just repeating the general idea of events and event queues in a slightly more complicated way?
Additionally, any comments or commentary on this approach (ECS, and so on), would be very gratefully received. I've pretty much run out of resources at this point.
Regards,
Simon
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I create interactions between components/entities by writing the main loop that controls the system in a procedural style, in a similar way to what you would write if you only had a single component of each type in the whole game.
e.g. If you had one homing missile made up of a laser targeting component, a rocket engine, and a proximity bomb, you might traditionally have some OO logic that makes them work together like:
Point target = entity->laserGuidance->GetTarget(); // find out where the laser wants us to go
entity->rocketEngine->SteerTowards( target, delta_time ); // steer towards it
entity->explosive->ExplodeIfWithinDistanceThreshold( target ); // blow up once we're close
To make that work for systems of components, my main loop would look like:
ArrayView<Pair<Entity,Point>> targets = laserGuidances->GetTarget( scratch ); // find out where the laser wants us to go
rocketEngines->SteerTowards( targets, delta_time ); // steer towards it
explosives->ExplodeIfWithinDistanceThreshold( targets ); // blow up once we're close
1 hour ago, SomeoneRichards said:
Isn't an event really just another form of entity? If it isn't, why isn't it?
An event is a deferred function call. What makes it an entity?
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Thank you for reading and responding to my post.
I think I might be referring to a specific application of the term event, and that that might lead to some confusion (on my part).
But, in response:
Interaction between components is not a problem. In fact, it seems unlikely that someone would add a component without counterpart components and systems to act upon them. That laser targeting/guiding component, for instance, is pointless without something(s) to guide. I can get entities into my game, and I can get them to work with the current systems and tick along as they are supposed to, using the game loop to ensure that systems operate when they're intended to, and so on.
The difficult part is having entities interact with one another. What if I wanted to have nearby guards (say up to 100ft) respond to the sound of the explosion? I suppose I could have another system that goes through all of the entities to see if they heard anything, but that seems like it could get pretty messy pretty quickly. If the were many various entities with different sound emitting components, then I'd have to poll the entities with sound-aware components every time something emitted a sound that they could be interested. Alternatively, I suppose I could shuffle the order that systems operate in, but that seems equally hard work.
The common response I have seen - and I could easily be misunderstanding here - is to use some kind of an event system to notify registered entities (or components thereof) that something they are interested in has occurred. So I have looked at various implementations of event/messaging queues/buses, and attempted to adapt my own. What I have noticed is, in my planning an implementation, is that I don't need an event/message, as such, since the behaviour more or less mimics that of my other components. But I could be wrong about events here. In other implementations events I suppose an event could be a deferred function - in that it has the capacity to lead to a function call - but with an event queue that processes over the events, they seem to function the same way as any other component. In my own planned implementation, the 'interaction' is really just data, and the logic system iterates over them, in the same way that any other system does.
But I might just be confusing things (and myself) here.
In the above example, how would you implement an interaction between entities? In the case of guards hearing the explosion?
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I have had some prototype in the past made with Unity that targets exact these scenario
We have had a NoiseTracker component added to our guards that was bound to an event system. This event system has had a noice channel that fires each frame when the player does an action that may lead to noise, its strength and position. The NoiseTracker registered to this specific event channel and then decided depending on it's character component's data (Position,AttentionLevel ..) if it should ship the event call to it's character.
This was C# and now comes C++; To implement a generic event handling system into my engine I took a look at what an event system needs to do and come to the conclusion that it is simply a static sync or async processed list of data that is dropped to certain audience. So what my event system does is exactly that, recording some kind of data that depends to the channel it is put to in a list and at some point, iterate through that list to execute all registered function delegates by passing each single data entry. To have the possibility to support several channels and also channels of the same data, I made a template for it that is of signature
template<int ChannelId, returnType (Parameter, Parameter ...)> struct Dispatcher
This way, we can not only define the signature of the function call that is an allowed recipient but also the structure of the data that can be passed to it. The ChannelId parameter lets one specify also different channels of the same data as described above.
I've used it in a long-term test with different things but mostly Input handling with very good results
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21 hours ago, SomeoneRichards said:
If it notices an interaction, it creates an interactionEntity (with the necessary data) and the interactions are processed by the next sub-system.
While you can implement this an entity, why create an entity when you can also just add it as a component? I've seen approaches before where people add the events that occurred as a component to the entities involved. The problem with creating a new entity is that it somehow needs to reference the old entity. That's of course not impossible, but you could have just as well attached it to the entity right away.
Regardless, the problem with having it either as an entity or component is that you need to keep track of whether it was processed. If you have two systems that are interested in knowing whether a collision has occurred, it becomes difficult to remove this Collision component/entity afterwards. None of the systems interested can assume another system that will process that entity afterwards is no longer interested in that Collision component/entity, so they cannot delete it. That means the system that added the Collision component/entity is also responsible for deleting it, otherwise the other systems may process it multiple times!
Again that's something that might seem easy to fix, until you want to have your physics system update at a different rate than the other systems. Now, let's say your physics system processes collisions at 20hz and the other systems run at 60hz. Obviously, that creates a problem; now your collision components/entities persist for too long and might get processed multiple times. You can bring solutions, but in the end whatever created these event entities/components are now likely to rely upon the rate of which the systems process it.
Your approach is more of a Model View Controller approach where the view (system) checks the model (the (presence of a) entity/component). It's not event based; you are likely to be creating scenarios where the events are not received. With this Model View Controller approach you are checking a state. The event of a collision having occurred should likely not be considered a state, but as it suggests, an event, i.e., a callback.
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Thanks again for responses. Again, I am probably confusing myself, but:
23 minutes ago, AthosVG said:
While you can implement this an entity, why create an entity when you can also just add it as a component? I've seen approaches before where people add the events that occurred as a component to the entities involved. The problem with creating a new entity is that it somehow needs to reference the old entity. That's of course not impossible, but you could have just as well attached it to the entity right away.
Doesn't that remove a lot of the decoupling between systems? If my physical collisions require a particle effect (some sparks) and a sound effect (like a clang) and audio responders (like guards), doesn't my physics system need to be about to create and add those components, or call into a higher level system to do so?
25 minutes ago, AthosVG said:
Your approach is more of a Model View Controller approach where the view (system) checks the model (the (presence of a) entity/component). It's not event based; you are likely to be creating scenarios where the events are not received. With this Model View Controller approach you are checking a state. The event of a collision having occurred should likely not be considered a state, but as it suggests, an event, i.e., a callback.
It's why it should be an event that confuses me. If I had 35 homing missiles, wouldn't I have the following:
Calculate the target for 35 missile. // Good
Move 35 missiles. //Good
Work out if 35 missile explodes //Looks good, however, on each missile exploding, I now have to fire off a load of events which take me out of the iteration to process for each individual system.
Obviously I am going to have to do this for explosions, but can't I save my structure by doing:
Calculate the target for 35 missile. // Good
Move 35 missiles. //Good
Work out if 35 missile explode. If they do, create an interaction to add to a higher level list // Good
Work out the effects of each explosion according to the higher level system. Remove each interaction as it occurs. If the interaction results in another interaction, add it to the end of the list so it gets resolved in due time. Still requires mixing systems and potentially updating components all over the place, but its now being handled by a higher level system designed to do this.
1 hour ago, Shaarigan said:
This way, we can not only define the signature of the function call that is an allowed recipient but also the structure of the data that can be passed to it. The ChannelId parameter lets one specify also different channels of the same data as described above.
I've used it in a long-term test with different things but mostly Input handling with very good results
I think this is pretty much what I am suggesting. I'm probably just quibbling over terminology.
But rather than having an event/message template, Im'm just talking about using the same entity system, and make the various data fields components. This way I can make different kinds of events/interaction through scripting. However, here I think I am just generalising and complicating the system completely needlessly...
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28 minutes ago, SomeoneRichards said:
Doesn't that remove a lot of the decoupling between systems? If my physical collisions require a particle effect (some sparks) and a sound effect (like a clang) and audio responders (like guards), doesn't my physics system need to be about to create and add those components, or call into a higher level system to do so?
I'd expect you to create some CollisionComponent or an entity that has such a component. You have a system that iterates over the CollisionComponents (or entities) and emits particles for each component that exists. I don't see how changing this to a component adds coupling compared to using an entity. The physics system does not need to know what happens to it (in fact, it shouldn't), it just tells that a collision happened.
32 minutes ago, SomeoneRichards said:
Work out if 35 missile explodes //Looks good, however, on each missile exploding, I now have to fire off a load of events which take me out of the iteration to process for each individual system.
Nothing prevents you from making something that manages the events in such a fashion that they will always be processed after a system has updated. You can delay the events, but you should also wonder why this even matters. Is it a problem that events are immediately fired off upon a collision? And be careful to not make too many theoretical situations here. It's hard to find a silver bullet immediately for handling all the cases where those events could interfere with the update of the system sending these events.
36 minutes ago, SomeoneRichards said:
Work out if 35 missile explode. If they do, create an interaction to add to a higher level list // Good
Work out the effects of each explosion according to the higher level system. Remove each interaction as it occurs. If the interaction results in another interaction, add it to the end of the list so it gets resolved in due time. Still requires mixing systems and potentially updating components all over the place, but its now being handled by a higher level system designed to do this.
So if I understand you correctly, you have a list of interactions that trigger once you figured an explosion has occurred, which you can register to? And you remove interactions as they occur? How are you adding the interaction back to that list exactly? Also, given that you have a list of interactions that are triggered after the explosion as to have to be executed, how is this different from an event that is simply called after the update? Sounds like an event to me
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28 minutes ago, AthosVG said:
I'd expect you to create some CollisionComponent or an entity that has such a component. You have a system that iterates over the CollisionComponents (or entities) and emits particles for each component that exists. I don't see how changing this to a component adds coupling compared to using an entity. The physics system does not need to know what happens to it (in fact, it shouldn't), it just tells that a collision happened.
I wasn't arguing for the choice of component over entity. I'm more thinking about which system (or level of system) is responsible for it, giving the intended scope and flexibility.
I want a physics system that just identifies collisions, with a separate 'system' to handle the collision. I don't want the outcome of the collisions to be as flexible as possible (I might not always want particles).
28 minutes ago, AthosVG said:
And be careful to not make too many theoretical situations here. It's hard to find a silver bullet immediately for handling all the cases where those events could interfere with the update of the system sending these events.
This is almost definitely my problem, but, until my mind settles on something, it is a situation I'm stuck in...
28 minutes ago, AthosVG said:
So if I understand you correctly, you have a list of interactions that trigger once you figured an explosion has occurred, which you can register to? And you remove interactions as they occur? How are you adding the interaction back to that list exactly? Also, given that you have a list of interactions that are triggered after the explosion as to have to be executed, how is this different from an event that is simply called after the update? Sounds like an event to me
I think you're saying that and interaction is an event, and so I don't need the interaction, and I am saying that an event is an interaction, and so I don't need the event.
I am also confusing things by using interactions to mean a scripted coupling between two entities/components, and an ad-hoc instance of an interaction in a general way. I think the latter is the event that you're talking about. So, that confusion aside, I'm essentially talking about handling events as a synchronous list, within the entity/component framework, which I think I have resolved in my head...
Edited by SomeoneRichards
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On 5/15/2018 at 10:36 PM, SomeoneRichards said:
Interaction between components is not a problem. The difficult part is having entities interact with one another.
If entities are just ID's, they dont communicate with each other. Only components do. So if interaction between components is not a problem, there is no problem
On 5/15/2018 at 10:36 PM, SomeoneRichards said:
In the above example, how would you implement an interaction between entities? In the case of guards hearing the explosion?
I do it without an event framework. Just batch processing of systems in a procedural manner. Batch, batch, batch.
struct Noise
{
float volume = 1;
NoiseType type = Explosion;
Vector3 position;
Entity source;
};
struct SplashDamage
{
float damage = 100;
Vector3 position;
};
struct ExplosionSystemResults
{
ArrayView<Noise> noises;
ArrayView<SplashDamage> damages;
};
...
OnTick:
vector<ArrayView<Noise>> noises;
vector<ArrayView<Noise>> splashDamage;
...
ArrayView<Pair<Entity,Point>> targets = laserGuidances->GetTarget( scratch ); // find out where the laser wants us to go
rocketEngines->SteerTowards( targets, delta_time ); // steer towards it
auto explosionResults = explosives->ExplodeIfWithinDistanceThreshold( targets ); // blow up once we're close
noises.push_back( explosionResults.noises );// add explosion noises to the collection of all noises this tick
splashDamage.push_back( explosionResults.damages );// add explosion damage to the collection of all splash damage events this tick
...
healths->TakeSplashDamage( splashDamage );// pass splash damage events to health system
aiListeners->ReactToNearbyNoises( noises );// let AI respond to noise events
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5 hours ago, Hodgman said:
If entities are just ID's, they dont communicate with each other. Only components do. So if interaction between components is not a problem, there is no problem
I do it without an event framework. Just batch processing of systems in a procedural manner. Batch, batch, batch.
struct Noise
{
float volume = 1;
NoiseType type = Explosion;
Vector3 position;
Entity source;
};
struct SplashDamage
{
float damage = 100;
Vector3 position;
};
struct ExplosionSystemResults
{
ArrayView<Noise> noises;
ArrayView<SplashDamage> damages;
};
...
OnTick:
vector<ArrayView<Noise>> noises;
vector<ArrayView<Noise>> splashDamage;
...
ArrayView<Pair<Entity,Point>> targets = laserGuidances->GetTarget( scratch ); // find out where the laser wants us to go
rocketEngines->SteerTowards( targets, delta_time ); // steer towards it
auto explosionResults = explosives->ExplodeIfWithinDistanceThreshold( targets ); // blow up once we're close
noises.push_back( explosionResults.noises );// add explosion noises to the collection of all noises this tick
splashDamage.push_back( explosionResults.damages );// add explosion damage to the collection of all splash damage events this tick
...
healths->TakeSplashDamage( splashDamage );// pass splash damage events to health system
aiListeners->ReactToNearbyNoises( noises );// let AI respond to noise events
Thank you. That's pretty much exactly what I was going for. Except with confusing the terminology and attempting to over-generalise things.
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× | 2019-01-22 14:20:08 | {"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": 0.3240298628807068, "perplexity": 1353.5345360914366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1547583857913.57/warc/CC-MAIN-20190122140606-20190122162606-00077.warc.gz"} |
http://reallyreallyrandom.com/zener/behaves-like/ | Contents:-
# Zeners behave like...
This page was created based (mostly) upon data downloaded directly from an oscilloscope with the following sample regime: 100 kSa/s with a 1.2 MSa depth @ 500 mV/div. Thus $\epsilon = 15.6 \text{ mV}, \tau = 10 \mu \text{s}$. We used our Zener Variator to vary the reverse current $(I_R)$ for these experiments, which has a floating noise floor (1000 mm flying leads) of approximately 304 mVpp. The diodes used were 51V, 24V and 10V through hole Zeners.
## The signal
Our results for various $I_R$, featuring oscilloscope screen shots and Gnuplots of downloaded scope memory values:-
Very little of interest to see above. It’s mainly our 50Hz mains hum as $I_R$ is so low and our leads so long. But quantization noise of same is evident.
Proper avalanche behaviour is evident above. One simple way to tell is that one side of the plot is spiky, whilst the other side is much smoother. This is characteristic of log-normal distributions. Notice the relatively massive Avalanche signal $(V_{pp} = 2.22 \text{V for } I_R = 50 \mu \text{A})$. It is indicative of $V_{pp} \propto V_Z$. The following figure highlights the shape of the distribution more clearly:-
If autocorrelation was sufficiently small $(R \le 10^{-3})$, we could immediately quantify $H_{\infty} = - \log_2 (0.3) = 1.7$ bits/sample (scope download). But we haven’t checked in this particular case. Notice though the extreme log-normal shape, characteristic of well proper Avalanche behaviour.
We now increase $I_R$ to $100 \mu \text{A, } 150 \mu \text{A, } 300 \mu \text{A & } 500 \mu \text{A}$:-
There are only a few rare peaks at $I_R = 300 \mu \text{A})$:-
And no peaks at $I_R = 500 \mu \text{A}$. The bulk of the signal is now just quantization noise of a few bits:-
## The entropy
Entropy is after all, our business here. Not simply humongous $V_{pp}$ values. And we see below that the usable entropy from a Zener diode’s Avalanche signal is not entirely proportional to it’s peak to peak magnitude. It’s a much more complicated relationship.
We looked at three diodes with $5 \mu \text{A} < I_R < 500 \mu \text{A}$ with differing $V_Z$ using the Zener Variator and oscilloscope. We then downloaded the 1.2 million raw oscilloscope samples (8 bit depth) and compressed them using the LZMA compression algorithm. We can estimate the Shannon entropy $(H_S)$ of the samples, and thus the generating rate as bits per second.
Combining the three above graphs and normalising $H_S$:-
The surprising point to note from the above curves is how similar the entropy rate is between different diodes at $I_R \approx 50 \mu \text{A}$. Quantisation error is responsible for a large proportion of that rate. But…
## The conclusion
One might initially assume that more $V_{Z}$ implies more $H_{S}$. Common sense, and of course size matters. Yet if we look at these three stylised Zener signals, that’s not the case due to a quirk of the Avalanche effect:-
Assume that we are interested in maximising $V{pp}$ and thus $H_{S}$, so we look to higher and higher reverse voltages. We sample at the marked sample points (about 95% $V{pp}$). However the exponential charge shape remains a fairly similar geometry, just larger and wider. As the normalised charge ratio increases (and so does $V{pp}$), the time between potential sample points also increases. I.e. the frequency of large pulses decreases. The approximate $Vpp \propto \frac{1}{f_{V_{pp}}}$ relationship is verified in the following two scope captures caused by $55 \mu \text{A} < I_R < 125 \mu \text{A}$:-
Notice how sparse other peaks are for the case of $V_{pp} = 3 V$. And so that’s how $H_S$ isn’t as large as one might expect. Size in this case does not matter as far as entropy is concerned.
Which explains the “Normalised Kolmogorov entropy rates vs IZ” figure above. A plus side though is that high voltage Zeners are not required to obtain decent entropy rates from them. It’s not about getting the largest Avalanche signal that matters, but obtaining the most entropy from it.
## The discussion
1. We might well expect $H_{\infty} \sim 1$ bits/sample from simple quantisation error given the large and (virtually) infinite resolution noise signal, and the relatively small oscilloscope sampling resolution (8 bits). But more on this elsewhere.
2. The quantum unit responsible for the ultimate resolution of the Avalanche noise is a single electron. It’s charge ($e$) is $1.60 \times 10^{-19}$ Coulombs.
3. Sampling at 100 kSa/s (which an Arduino can) and with $I_R = 50 \mu \text{A}$, we can calculate that $3.125 \times 10^9$ electrons are flowing through the Zener diode every $\frac{1}{100,000}$th of a second. $\pm 1e$ at the very minimum. That’s a resolution of 0.32 parts per billion. Or over 31 bits of resolution. Or a minimum discrete Avalanche current change to constant current (signal to noise) ratio of -190 dBV ($1 e$).
4. All the diodes vary, but with a loose correlation for Avalanche $V_{pp} \propto V_Z$, as shown below. That means that each device has to be treated individually and the entropy rate determined accordingly (which is also dependant on your $(\epsilon, \tau)$ sampling regime). Except for transistors as their reverse breakdown voltages do not range as widely as do Zener diodes’.
Some other examples of diodes’ and transistors’ $V_{pp}$ accumulated from us and across the internet:-
Above from https://betrusted.io/avalanche-noise
Above from http://holdenc.altervista.org/avalanche/ | 2021-05-19 00:20:01 | {"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": 0.6950535178184509, "perplexity": 1878.0856369063958}, "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-2021-21/segments/1620243989874.84/warc/CC-MAIN-20210518222121-20210519012121-00482.warc.gz"} |
http://gssi.infn.it/seminars/impact-seminars-2015/item/711-some-problems-in-bio-mathematics-and-mathematical-physics | back
## Some problems in bio-mathematics and mathematical physics
• Date October 8-9, 2015
• Room GSSI Main Lecture Hall
• Speaker many speakers
SPEAKERS
• Carlo Boldrighini (University La Sapienza, Italy)
• Giorgio Fusco (University of L'Aquila, Italy)
• Stefan Luckhaus (University of Leipzig, Germany)
• Stefano Olla (University Paris-Dauphine, France)
• Mario Pulvirenti (University La Sapienza, Italy)
• Angela Stevens (Max Plank Institute for Mathematics, Germany)
• Livio Triolo (University of Roma "Tor Vergata", Italy)
• Maria Eulalia Vares (Instituto de Matematica, UFRJ, Brazil)
TENTATIVE PROGRAM
October 8:
• 10.00 Opening
• 10.15-11.15 Stefano Olla. Non-equilibrium macroscopic evolution of chain of oscillators with conservative noise.
• 12.00-13.00 Angela Stevens. Chemotaxis, hydrodynamic limit, and formal approximations of reinforced random walks.
• Lunch.
• 14.15-15.15 Mario Pulvirenti. On the size of chaos in the Boltzmann-Grad linit for hard speres.
• 15.15-16.15 Giorgo Fusco. Dissipative dynamics near a finite dimensional manifold.
October 9:
• 9.15-10.15 Stephan Luckhaus. Problems in microscopic plasticity.
• 11.00-12.00 Carlo Boldrighini. Blow-up for complex and real solution of the 3-d Navier-Stokes equations: theory and computer simulations.
• 12.15-13.15 Maria Eulalia Vares. Dynamic random walk on contact process environment.
• Lunch
• 15.45-16.15. Livio Triolo. Concluding Remarks.
ABSTRACTS
Carlo Boldrighini: Blow-up for complex and real solution of the 3-d Navier-Stokes equations: theory and computer simulations. (Joint work with S. Frigio and P. Maponi)
We present results of computer simulations of a class of complex solutions of the 3-d Navier-Stokes equations in $\R^{3}$ for which Li and Sinai have proved a finite-time blow-up. The simulations show that near the critical time the energy concentrates around one or two points of the physical space. We also give results on the behavior of some related real solutions.
Giorgio Fusco: Dissipative dynamics near a finite dimensional manifold
We consider an evolutionary equation $u_t=F(u)$, $u(0)=u_0 which admits a Lyapunov functional$J:H\rightarrow\R$,$H$an Hilbert space. We let$\mathcal{M}\subset H$be a finite dimensional embedded manifold and derive a sufficient condition on the structure of the graph$\mathcal{G}^J$of$J$in a tubular neighborhood$\mathcal{N}$of$\mathcal{M}$ensuring that u_0\in\mathcal{N}\quad\Rightarrow\quad u(t,u_0)\in\mathcal{N},\;\text{ for }\;t\in[0,T)\] where either$T=+\infty$or$u(T,u_0)$belongs to the lateral boundary of$\mathcal{N}\$.
As an application of the abstract result we review the phenomenon of {\it Slow Motion} for Allen-Cahn and Cahn-Hilliard equations in one space dimension.
This is joint work with P.Bates and G.Karaly.
Stephan Luckhaus: Problems in microscopic plasticity
Plastic deformation of metals are governed by the motion of dislocations.The basic problem is how to connect the theory of elastic fields with dislocations to atomistic theories on the one hand and the upscaling , that is the description of the collective behaviour of dislocations on the other hand. We try to present a few problems and conjectures.
Stefano Olla: Non-equilibrium macroscopic evolution of chain of oscillators with conservative noise.
In the non-equilibrium evolution of a one dimensional chain of anharmonic oscillators we expect two main space-time scales: a hyperbolic scale where the evolution is ballistic-mechanic, dominated by tension gradients and governed by Euler equations, and a super-diffusive scale where the evolution, at constant tension, depends on the gradients of the temperature and is governed by a fractional heat equation. This conjecture can be proven for a harmonic chain with random exchange of momentum between nearest neighbor particles. Non-acoustic chains (tensionless) will instead behave diffusively.
Mario Pulvirenti: On the size of chaos in the Boltzmann-Grad linit for hard speres.
I present a quantitative analysis of the low-density limit of a hard sphere system based on the study of a set of functions (correlation errors) measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order k measures the event where k tagged particles are connected by a chain of interactions preventing the factorization. Provided k is not too large and the time sufficiently small, such an error goes to zero with the hard spheres diameter to the power Ck, C>0. This requires a new analysis of many recollision events, and improves previous estimates.
This analysis is based on a joint work with S. Simonella.
Angela Stevens: Chemotaxis, hydrodynamic limit, and formal approximations of reinforced random walks (Joint work with S. Grosskinsky, D. Marahrens,J.J.L. Velazquez)
Chemotaxis is an important and common mechanism during structure formation of developmental cell systems. A PDE-system of cross-diffusion type, the so-called Keller-Segel model, provides a macroscopic description for this phenomenon.
In the first part of the talk the first equation of this system is derived as hydrodynamic limit from a stochastic interacting particle system on the lattice, where the attractive chemical signal is assumed to be stationary with a slowly varying mean.
In the second part of the talk the qualitative behavior of the full PDE-system is compared to the respective behavior of the formally related reinforced random walk model.
Maria Eulalia Vares: Dynamic random walk on contact process environment
In this talk I will discuss ideas and results obtained in collaboration with Thomas Mountford. We consider a random motion in the integers whose rates are determined by an underlying supercritical contact process in equilibrium. A CLT is proven, valid for all supercritical infection rates for the environment.
Reference: T. Mountford, M.E. Vares: Random walks generated by equilibrium contact processes.
Electron. J. Prob. 20(3), 17pp (2015). | 2017-04-24 05:31:54 | {"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": 0.6450235247612, "perplexity": 3060.0528545501197}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119080.24/warc/CC-MAIN-20170423031159-00424-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.risc0.com/docs | # Getting Started
## Just Starting Out
If you're new to the RISC Zero zkVM, these examples and explanations will get you oriented. Below is a tutorial that'll help you build our version of "Hello, World!" and an introduction to the default RISC Zero project template.
• Hello, Multiply! - Think of this as "Hello, World!" for the RISC Zero zkVM. By following this tutorial, you'll create a program that demonstrates a number is composite (and that you know its factors). If you're just getting started writing code for the zkVM, we recommend starting here.
• Understanding the Project Template - Here we'll take a closer look at the default template for a RISC Zero zkVM project. You'll understand which parts are necessary and which can be changed, and get a feel for how the project components work together. (And if you like understanding the structure of a project before diving in, feel free to start here instead!)
## Project Examples
For more ideas about what's possible with RISC Zero, take a look at these examples, which feature explanations and tutorials for code available in our GitHub repositories:
• RISC Zero Digital Signatures - In this example, you'll see how to verifiably sign code run inside the RISC Zero zkVM. This example features a post-quantum digital signature generated using only SHA-2 as a cryptographic primitive.
• RISC Zero Password Validity Checker - In this example, you'll see Alice convince Bob's Identity Service that her password meets Bob's validity requirements. This example makes use of public shared outputs that Alice can write to the RISC Zero zkVM's journal.
## Open Source Repositories
• Rust Crates - If you're a Rust user, you'll find RISC Zero crates here, ready to be included in your existing projects.
• Contribute to RISC Zero - If you're interested in how RISC Zero projects for the zkVM work, or curious about contributing to this project, come take a look at our main project repository. | 2022-11-29 20:19:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3052525520324707, "perplexity": 2757.311988908155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710711.7/warc/CC-MAIN-20221129200438-20221129230438-00645.warc.gz"} |
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=141&t=43059 | ## E ˚ sign for reaction to occur
$\Delta G^{\circ} = -nFE_{cell}^{\circ}$
Arianna Ko 2E
Posts: 33
Joined: Fri Sep 28, 2018 12:20 am
### E ˚ sign for reaction to occur
For the reaction to occur does E ˚ have to be positive?
Clarissa Cabil 1I
Posts: 66
Joined: Fri Sep 28, 2018 12:19 am
### Re: E ˚ sign for reaction to occur
A reaction can still occur even if Eº is negative, but it is favorable to have a +Eº because this will make your ∆Gº negative through the equation ∆Gº= - nFEº, and the reaction will occur spontaneously.
If you have a -∆Eº, the reverse reaction will be favorable.
Hope this helps! | 2020-11-27 01:05:21 | {"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": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4487915337085724, "perplexity": 10708.569146456468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1606141189030.27/warc/CC-MAIN-20201126230216-20201127020216-00148.warc.gz"} |
https://infoscience.epfl.ch/record/114956 | ## Thurston's weak metric on the Teichmüller space of the torus
We define and study a natural weak metric on the Teichmüller space of the torus. A similar metric has been defined by W. Thurston on the Teichmüller space of higher genus surfaces and our definition is motivated by Thurston's definition. However, we shall see that in the case of the torus, this metric has a different behaviour than on higher genus surfaces.
Published in:
Trans. Am. Math. Soc., 357, 8, 3311-3324
Year:
2005
Keywords:
Other identifiers:
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http://www.math.uah.edu/stat/markov/WalkGraph.html |
## 12. Random Walks on Graphs
#### Introduction
Suppose that $$G = (S, L)$$ is a connected graph with vertex set $$S$$ and edge set $$L \subseteq S^2$$. We assume that the graph is undirected (perhaps a better term would be bi-directed) in the sense that $$(x, y) \in L$$ if and only if $$(y, x) \in L$$. We also assume that the graph has no loops, so that $$(x, x) \notin L$$ for every $$x \in S$$. The vertex set $$S$$ may by infinite. Let $$N(x) = \{y \in S: (x, y) \in L\}$$ denote the set of neighbors of a vertex $$x \in S$$, and let $$d(x) = \#[N(x)]$$ denote the degree of $$x$$.
Suppose now that there is a conductance $$c(x, y) \gt 0$$ associated with each edge $$(x, y) \in L$$. The conductance is symmetric in the sense that $$c(x, y) = c(y, x)$$ for $$(x, y) \in L$$. We extend $$c$$ to a function on all of $$S \times S$$ by defining $$c(x, y) = 0$$ for $$(x, y) \notin L$$. As the terminology suggests, we imagine a fluid of some sort flowing through the edges of the graph, so that the conductance of an edge measures the capacity of the edge in some sense. The best interpretation is that the graph is an electrical network and the edges are resistors. In this interpretation, the conductance of a resistor is the reciprocal of the resistance.
Let $$C(x) = \sum_{y \in S} c(x, y)$$ and suppose that $$C(x) \lt \infty$$ for each $$x \in S$$. The Markov chain $$\bs{X} = (X_0, X_1, X_2, \ldots)$$ with state space $$S$$ and transition probability matrix $$P$$ given by
$P(x, y) = \frac{c(x, y)}{C(x)}, \quad (x, y) \in S^2$
is called a random walk on the graph $$G$$. This chain governs a particle moving along the vertices of $$G$$. If the particle is at vertex $$x \in S$$ at a given time, then the particle will be at a neighbor of $$x$$ at the next time; the neighbor is chosen randomly, in proportion to the conductance. In the setting of an electrical network, it is natural to interpret the particle as an electron.
Note that multiplying the conductance function $$c$$ by a positive constant has no effect on the associated random walk.
Suppose that each edge has the same conductance, so that $$c$$ is constant on the edges. Then
1. $$C(x) = c \, d(x)$$ for every $$x \in S$$.
2. The assumption that $$C$$ is finite means that each vertex has finite degree. That is, the graph $$G$$ is locally finite.
3. The transition probability matrix is given by $P(x, y) = \begin{cases} \frac{1}{d(x)}, & y \in N(x) \\ 0, & y \notin N(x) \end{cases}$
The chain in the previous exercise is the symmetric random walk on $$G$$. Thus, if the chain is in state $$x \in S$$ at a given time, then the chain is equally likely to move to any of the neighbors of $$x$$ at the next time.
Consider the random walk on the graph below with the given conductance values. The underlying graph is sometimes called the Wheatstone bridge in honor of Charles Wheatstone.
1. Explicitly give the transition probability matrix $$P$$.
2. Suppose that the chain starts at $$a$$. Find the probability density function of $$X_2$$.
For the matrix and vector below, we use the ordered state space $$S = (a, b, c, d)$$.
1. $$P = \left[ \begin{matrix} 0 & \frac{1}{2} & 0 & \frac{1}{2} \\ \frac{1}{4} & 0 & \frac{1}{4} & \frac{1}{2} \\ 0 & \frac{1}{3} & 0 & \frac{2}{3} \\ \frac{1}{5} & \frac{2}{5} & \frac{2}{5} & 0 \end{matrix} \right]$$
2. $$f_2 = \left( \frac{9}{40}, \frac{1}{5}, \frac{13}{40}, \frac{1}{4} \right)$$
Consider the random walk on the cube graph shown below, with the given conductance values. The vertices are bit strings of length 3, and two vertices are connected by an edge if and only if the bit strings differ by a single bit.
1. Explicitly give the transition probability matrix $$P$$.
2. Suppose that the initial distribution is the uniform distribution on $$\{000, 001, 101, 100\}$$. Find the probability density function of $$X_2$$.
For the matrix and vector below, we use the ordered state space $$S = (000, 001, 101, 110, 010, 011, 111, 101 )$$.
1. $$P = \left[ \begin{matrix} 0 & \frac{1}{4} & 0 & \frac{1}{4} & \frac{1}{2} & 0 & 0 & 0 \\ \frac{1}{4} & 0 & \frac{1}{4} & 0 & 0 & \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{4} & 0 & \frac{1}{4} & 0 & 0 & \frac{1}{2} & 0 \\ \frac{1}{4} & 0 & \frac{1}{4} & 0 & 0 & 0 & 0 & \frac{1}{2} \\ \frac{1}{4} & 0 & 0 & 0 & 0 & \frac{3}{9} & 0 & \frac{3}{8} \\ 0 & \frac{1}{4} & 0 & 0 & \frac{3}{8} & 0 & \frac{3}{8} & 0 \\ 0 & 0 & \frac{1}{4} & 0 & 0 & \frac{3}{8} & 0 & \frac{3}{8} \\ 0 & 0 & 0 & \frac{1}{4} & \frac{3}{8} & 0 & \frac{3}{8} & 0 \end{matrix} \right]$$
2. $$f_2 = \left(\frac{3}{32}, \frac{3}{32}, \frac{3}{32}, \frac{3}{32}, \frac{5}{32}, \frac{5}{32}, \frac{5}{32}, \frac{5}{32}\right)$$
Let $$\bs{X}$$ be a random walk on a graph $$G$$.
1. If $$G$$ is connected then $$\bs{X}$$ is irreducible.
2. If $$G$$ is connected and finite then $$\bs{X}$$ is irreducible and recurrent.
3. If $$G$$ is not connected then the equivalence classes of $$\bs{X}$$ are the components of $$G$$ (the maximal connected subsets of $$S$$). The finite components are recurrent.
Suppose that $$\bs{X}$$ is a random walk on a finite, connected graph $$G$$. Then $$\bs{X}$$ is either aperiodic or has period 2. Moreover, $$\bs{X}$$ has period 2 if and only if $$G$$ is bipartite. That is, the vertex set $$S$$ can be partitioned into sets $$A$$ and $$B$$ such that every edge in $$L$$ has one endpoint in $$A$$ and one endpoint in $$B$$; these sets are then the cyclic classes of the chain.
#### Random Walks on $$\Z^k$$
Random walks on the integer lattices $$\Z^k$$, where $$k \in \N_+$$, are particularly interesting. Consider first the simple random walk $$\bs{X} = (X_0, X_1, X_2, \ldots)$$ on $$\Z$$, with transition probabilities
$P(x, x + 1) = p, \; P(x, x - 1) = 1 - p, \quad x \in \Z$
where $$p \in (0, 1)$$ is a parameter. Note that the chain is irreducible.
The chain is periodic with period 2. Moreover
$P^{2\,n}(0, 0) = \binom{2\,n}{n} p^n (1 - p)^n, \quad n \in \N$
Proof:
Note that starting in state 0, the chain can return to state 0 only at even times. The chain returns to 0 at time $$2\,n$$ if and only if there are $$n$$ steps to the right and $$n$$ steps to the left.
If $$p \ne \frac{1}{2}$$ then $$\bs{X}$$ is transient, and if $$p = \frac{1}{2}$$ then $$\bs{X}$$ is recurrent. Note that when $$p = \frac{1}{2}$$, $$\bs{X}$$ is the symmetric random walk on $$\Z$$.
Proof:
From Theorem 6 and Stirling's approximation,
$P^{2\,n}(0, 0) \approx \frac{[4 \, p (1 - p)]^n}{\sqrt{\pi \, n}} \text{ as } n \to \infty$
If $$p \ne \frac{1}{2}$$ then $$G(0, 0) \lt \infty$$ and hence $$\bs{X}$$ is transient. If $$p = \frac{1}{2}$$ then $$G(0, 0) = \infty$$ and hence $$\bs{X}$$ is recurrent.
More generally, consider $$\Z^k$$, where $$k \in \N_+$$. For $$i \in \{1, 2, \ldots, k\}$$, let $$\bs{u}_i \in \Z^k$$ denote the unit vector with 1 in position $$i$$ and 0 elsewhere. The simple random walk on $$\Z^k$$ has transition probabilities
$P(\bs{x},\bs{x} + \bs{u}_i) = p_i, \; P(\bs{x}, \bs{x} - \bs{u}_i) = q_i; \quad \bs{x} \in \Z^k, \; i \in \{1, 2, \ldots, k\}$
where $$p_i \gt 0$$, $$q_i \gt 0$$ for each $$i$$ and $$\sum_{i=1}^k (p_i + q_i) = 1$$. Clearly, the larger the dimension $$k$$, the less likely the chain is to be recurrent. In turns out that the behavior when $$k = 2$$ is similar to the behavior when $$k = 1$$: the chain is recurrent only in the symmetric case $$p_i = q_i = \frac{1}{4}$$ for each $$i$$. When the dimension $$k$$ is 3 or more, the chain is transient for all values of the parameters, even in the symmetric case. Thus, for the simple, symmetric random walk on the integer lattice $$\Z^k$$, we have the following interesting dimensional phase shift: the chain is recurrent in dimensions 1 and 2 and transient in dimensions 3 or more. The proofs are similar in to the proof sketched in the previous two exercises for dimension 1, but the details are considerably more complex. A return to $$0$$ can occur only at even times and in the symmetric case,
$P^{2\,n}(\bs{0}, \bs{0}) \approx \frac{C_k}{n^{k/2}} \text{ as } n \to \infty$
where $$C_k$$ is a positive constant that depends on the dimension $$k$$. Thus $$G(\bs{0}, \bs{0}) = \infty$$ and the chain is recurrent if $$k \in \{1, 2\}$$ while $$G(\bs{0}, \bs{0}) \lt \infty$$ and the chain is transient if $$k \in \{3, 4, \ldots\}$$.
#### Positive Recurrence and Limiting Distributions
We return now to the general case of a random walk $$\bs{X}$$ on a graph $$G$$. Assume that $$G$$ is connected so that $$\bs{X}$$ is irreducible.
The function $$C$$ is left-invariant for $$P$$. The random walk is positive recurrent if and only if
$K = \sum_{x \in S} C(x) = \sum_{(x, y) \in S^2} c(x, y) \lt \infty$
in which case the invariant probability density function $$f$$ is given by $$f(x) = C(x) / k$$ for $$x \in S$$.
Consider the special case of the simple random walk on $$G$$, so that the conductance function $$c$$ is constant on the set of edges $$L$$. The random walk is positive recurrent if and only if the set of vertices $$S$$ is finite, in which case the invariant probability density function $$f$$ is given by $$f(x) = d(x) / 2\,m$$ for $$x \in S$$ where $$d$$ is the degree function and where $$m$$ is the number of undirected edges.
Recall, for example, the simple random walk on $$\Z^k$$. We showed that the walk is recurrent if the dimension $$k$$ is 1 or 2, and so we now know that the walk is null recurrent in these cases. The walk is transient if $$k \ge 3$$.
Consider the random walk on the Wheatstone bridge given in Exercise 2.
1. Show that the chain is aperiodic.
2. Find the invariant probability density function.
3. Find the mean return time to each state.
4. Find $$\lim_{n \to \infty} P^n$$.
For the matrix and vectors below, we use the ordered state space $$(a, b, c, d)$$.
1. The chain is aperiodic since the graph is not bipartite.
2. $$f = \left(\frac{1}{7}, \frac{2}{7}, \frac{3}{14}, \frac{5}{14} \right)$$
3. $$\mu = \left(7, \frac{7}{2}, \frac{14}{3}, \frac{14}{5} \right)$$
4. $$P^n \to \left[ \begin{matrix} \frac{1}{7} & \frac{2}{7} & \frac{3}{14} & \frac{5}{14} \\ \frac{1}{7} & \frac{2}{7} & \frac{3}{14} & \frac{5}{14} \\ \frac{1}{7} & \frac{2}{7} & \frac{3}{14} & \frac{5}{14} \\ \frac{1}{7} & \frac{2}{7} & \frac{3}{14} & \frac{5}{14} \\ \end{matrix} \right]$$ as $$n \to \infty$$
Consider the random walk on the cube graph given in Exercise 3.
1. Show that the chain has period 2 and find the cyclic classes.
2. Find the invariant probability density function.
3. Find the mean return time to each state.
4. Find $$\lim_{n \to \infty} P^{2\,n}$$.
5. Find $$\lim_{n \to \infty} P^{2\,n + 1}$$.
For the matrix and vector below, we use the ordered state space $$S = (000, 001, 101, 110, 010, 011, 111, 101)$$.
1. The chain has period 2 since the graph is bipartite. The cyclic classes are $$\{000, 011, 110, 101\}$$ (bit strings with an even number of 1's) and $$\{010, 001, 100, 111\}$$ (bit strings with an odd number of 1's).
2. $$f = \left(\frac{1}{12}, \frac{1}{12}, \frac{1}{12}, \frac{1}{12}, \frac{1}{6}, \frac{1}{6}, \frac{1}{6}, \frac{1}{6}\right)$$
3. $$\mu = (12, 12, 12, 12, 6, 6, 6, 6)$$
4. $$P^{2\,n} \to \left[ \begin{matrix} \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \end{matrix} \right]$$ as $$n \to \infty$$
5. $$P^{2\,n + 1} \to \left[ \begin{matrix} 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \\ \frac{1}{6} & 0 & \frac{1}{6} & 0 & 0 & \frac{1}{3} & 0 & \frac{1}{3} \\ 0 & \frac{1}{6} & 0 & \frac{1}{6} & \frac{1}{3} & 0 & \frac{1}{3} & 0 \end{matrix} \right]$$ as $$n \to \infty$$
#### Reversibility
Essentially, all reversible Markov chains can be interpreted as random walks on graphs. This fact is one of the reasons for studying such walks.
A positive recurrent random walk $$\bs{X}$$ on a graph $$G$$ is reversible.
Conversely, suppose that $$\bs{X}$$ is a reversible Markov chain on $$S$$ with transition probability matrix $$P$$ and invariant probability density function $$f$$. Suppose also that $$P(x, x) = 0$$ for every $$x \in S$$. Then $$\bs{X}$$ can be interpreted as the random walk on the state graph $$G$$ of $$\bs{X}$$ with conductance function $$c$$ given by
$c(x, y) = f(x) P(x, y), \quad (x, y) \in S^2$
Recall that the Ehrenfest chain is reversible. Interpreting the chain as a random walk on a graph, sketch the graph and find a conductance function.
A conductance function $$c$$ is $$c(x, x - 1) = \binom{m - 1}{x - 1}$$, $$c(x, x + 1) = \binom{m - 1}{x}$$ for $$x \in \{0, 1, \ldots, m\}$$. | 2013-05-18 20:57:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 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": 0.9553996920585632, "perplexity": 84.76047455544362}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368696382851/warc/CC-MAIN-20130516092622-00081-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://tsaco.bmj.com/content/2/1/e000089 | Article Text
Defining burden and severity of disease for emergency general surgery
1. Preston R Miller
1. Correspondence to Dr Preston R Miller, Department of Surgery, Wake Forest School of Medicine, Medical Center Blvd, Winston-Salem, NC 27157, USA; pmiller{at}wakehealth.edu
## Abstract
As general surgery trainees continue to enter specialty practice at a high rate, fewer and fewer are caring for emergency general surgery (EGS) patients. Thus EGS has become one of the cornerstones of the practice of acute care surgery. With the centralization of this area of surgical care in many areas of the country, a clear understanding of the issues associated with this becomes vital. Understanding the public health implications with respect to burden of care and cost will allow for appropriate planning and resource allocation in the future. In addition, the development of validated severity modeling will help with risk stratification in future study of these diseases.
• emergency general surgery
• burden of disease
• public health
This is an Open Access article distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
## Introduction
Emergency general surgery (EGS) has long been considered to be a large portion of ‘bread and butter’ general surgical practice, but this is not borne out in analysis of graduates finishing general surgical residency in the 21st century. Roughly 80% of finishing residents pursue specialized fellowship training, which leads to specialty-specific practice patterns.1 This produces surgeons who are uncomfortable caring for emergencies outside their area of specialization in many cases. Although there are certainly a multitude of reasons for this shift in training, it leaves patients with emergency general surgical problems with fewer and fewer surgeons who are skilled in providing the type of care needed.
In addition, there is a worsening shortage of physicians, and one source estimates that there will be a gap of 41 000 by 2025 between the number of practicing general surgeons and the number needed to cover the needs of the general surgical patient population.2 These and other issues have combined to cause the Institute of Medicine in their often quoted publication from 2006 to declare that we are facing a crisis in emergency care in the USA.3
These are some of the underlying forces that led the American Association for the Surgery of Trauma (AAST) to create the specialty of acute care surgery. Acute care surgery includes trauma, surgical critical care, and EGS at its core. The AAST Acute Care Surgery Committee has gone on to establish acute care surgery as a specialty with its own curriculum, site visits to ensure program requirements are met, and a certificate of completion. There are 20 accredited fellowship programs currently and more are planned.
Although EGS has been contained within general surgical practice for many years, the development of acute care surgery highlights this area of surgery as its own area of practice. Its separation from daily surgical practice in many centers has created the need to carefully study the burden of the diseases that constitute EGS and determine the resources needed to best care for these patients under this paradigm. Additionally, the desire to optimize outcomes has created the need to understand and quantify severity of disease as it relates to resource utilization, care algorithms, and outcome.
## EGS definition
To examine overall burden of disease or begin to develop severity scoring systems, one must first have a definition of EGS. In 2012, the AAST Committee on Severity Assessment and Outcomes set out to develop such a definition.4 They began by defining an EGS patient as any patient (inpatient or emergency department) requiring an emergency surgical evaluation (operative or non-operative) for diseases within the realm of general surgery as defined by the American Board of Surgery. Both operative and non-operative patients are included as there are many emergencies that may require surgical evaluation without operative interventions, such as diverticulitis, pancreatitis, or even appendicitis in certain cases. To further refine the disease processes that make up EGS, the committee pooled International Classification of Diseases-9th Rev. (ICD-9) codes of surgeons from seven institutions for the previous 5 years. Primary diagnoses only were included. Codes 800–999 (trauma) were excluded, as were critical care codes. A modified Delphi methodology was used to review 621 codes, and 309 were finally selected as EGS diagnoses. This subset of diagnoses has been used extensively in subsequent publications and data sets evaluating overall burden of disease on a national level.
## Burden of disease
As EGS further differentiates into its own area of practice, the overall burden of disease becomes an important issue to attempt to understand. The first focused examination of this was published again in 2012 in which the 2009 National Inpatient Sample (NIS) was queried for patients whose primary diagnosis matched one of the ICD-9 codes defined as EGS diagnoses. This yielded an estimated 4 005 935 patients nationwide with such a diagnosis. Of these 2 344 576 were admitted as emergencies. As a point of comparison, during the same time period, approximately 1.75 million new cases of diabetes mellitus were diagnosed.4 This work was expanded by Gale et al 5 in 2014 using a larger cross-section of the NIS (2001–2010). During this time period over 27 million patients were admitted to US hospitals with primary EGS diagnoses, comprising 7.12% of all hospital admissions. Over 25% of this cohort required operative intervention. When examined by year, the number of EGS admission increased steadily from 2.38 million in 2001 to 3.03 million in 2010. This volume outstrips the 2.3 million trauma admissions/year nationwide based on 2014 CDC data. This amounts to 1290/100 000 of total population (as compared with 899/100 000 cases of new diabetes mellitus or 650/100 000 new cancer diagnoses). In 2015 Ogola et al 6 used the 2010 NIS and expected population growth to project EGS population out to 2060. This is represented in figure 1. Based on these estimates, EGS resource utilization is expected to expand significantly as the population ages and grows.
Figure 1
Projected growth in the EGS population through 2060.6 *Represents projected patients based on current estimates. EGS, emergency general surgery.
Within the 309 diagnoses that constitute EGS practice, 7 groups of diagnoses have been shown to be responsible for the large majority of procedures, cost, complications, and mortality. In 2016, Scott et al 7 used the 2009–2011 NIS data to demonstrate that the diagnoses groups of partial colectomy, small bowel resection, cholecystectomy, operative management of peptic ulcer disease, lysis of peritoneal adhesions, appendectomy, and laparotomy account for 80.0% of procedures, 80.3% of deaths, 78.9% of complications, and 80.2% of inpatient costs in the USA.
The prevalence and severity of EGS-driven hospitalizations present a significant public health cost burden. The total estimated cost of EGS hospitalizations in 2010 was $28.4 billion, and this is expected to nearly double by 2060.6 This NIS-based estimate does not include provider costs or costs of care outside the hospital. Thus EGS is the most expensive cause of emergency hospitalization in the USA as compared with other common conditions including trauma, myocardial infarction, congestive heart failure ,chronic obstructive pulmonary disease, and diabetes mellitus. In an analysis of the Maryland Health Services Cost Review Commission database from 2009 to 2013, which contains discharge information on all hospital admissions, Narayan et al 8 found that almost 14% of admission were EGS admissions, with overall charges of over$3.8 billion. Available data also demonstrate that 56% of EGS admissions between 2001 and 2010 carried Medicare/Medicaid, whereas roughly 10% were uninsured.5
## Severity stratification
Given that EGS represents a substantial portion of patients requiring treatment at US hospitals, development of reliable measures of severity is vital. Such tools would allow for accurate and consistent study of EGS diseases, assessment of impact of disease severity on outcomes, and a clear understanding of the relationship between resource need and disease severity. Some EGS diseases have one or more severity scales already associated with them (pancreatitis, diverticulitis), but many do not.
The AAST Committee on Severity Assessment and Outcomes has developed a scaling system for anatomic severity of disease that can be applied uniformly across all EGS disease states.9 Such a system serves an essential role in comparing patient populations for risk adjustment purposes, clinical trials, and estimation of patient prognosis. This schema follows disease progression with grade I-minimal to grade V-severe. Grade I is classified as local disease confined to the organ with minimal abnormality; grade II is local disease confined to the organ with severe abnormality; grade III is local extension beyond the organ; grade IV is regional extension beyond the organ; and grade V is widespread extension beyond the organ. These principles were used to define grades for 16 common EGS conditions (acute appendicitis, breast infections, acute cholecystitis, acute diverticulitis of the colon, esophageal perforation, hernias (internal or abdominal wall), infectious colitis, intestinal obstruction, intestinal arterial ischemia, acute pancreatitis, pelvic inflammatory disease, perirectal abscess, perforated peptic ulcer, pleural space infection, soft tissue infections, and surgical site infections).10
This concept has since been validated in several EGS disease states and performs well based on available data. The diverticulitis scale was recently examined in a multicenter trial.11 The system showed good inter-rater reliability as well as a clear association of increasing score with worse outcome and higher resource consumption. Similar work looking at the AAST grading scale for appendicitis has shown strong correlation between AAST severity grade assigned by preoperative cross-sectional imaging and intraoperative findings.12 AAST severity grade also correlated well with outcomes in this study.
Although this method of grading appears to carry utility, additional information needed to develop a comprehensive prediction of outcome likely includes age, comorbidities, and physiologic state. Uniform tools including these types of variables for outcome prediction applicable to all EGS diseases have not been developed, but available data make it clear that the outcomes in EGS patients are generally worse than patients undergoing similar operations under elective conditions. Early data show that the ACS National Surgical Quality Improvememnt Program Surgical Risk Calculator may fill this niche as it appears to predict outcome well in the EGS population.
EGS continues to grow and consolidate as an area of practice within the specialty of acute care surgery. This has led to investigators becoming interested in understanding the impact of EGS within the overall care of patients in the USA. Subsequent studies make it clear that EGS diseases constitute a significant portion of urgent and emergent care in our healthcare system, outstripping problems such as trauma care, newly diagnosed diabetes, and newly diagnosed cancer in volume on an annual basis. Such large volume is naturally accompanied by significant cost, making EGS an important public health issue. Continued work as to the impact of EGS on different sectors of healthcare as well as development of accurate, validated severity measures will allow for planning for the optimum care of these patients as we move forward. Although the answers to some of these questions are not yet apparent, the successes of the trauma care community in building systems and implementing care protocols in the past decades may serve as a model that deserves examination.
View Abstract
## Footnotes
• Competing interests None declared.
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http://languagelog.ldc.upenn.edu/nll/?p=31781 | ## The miracle of reading and writing Chinese characters
We have the testimony of a colleague whose ability to write Chinese characters has been adversely affected by her not being able to visualize them in her mind's eye. See:
"Aphantasia — absence of the mind's eye" (3/24/17)
This prompts me to ponder: just how do people who are literate in Chinese characters recall them?
Of course, now that computers and cell phones can write characters for you, there's no longer a need to remember all of their strokes nor even their overall shapes: just enter the sounds of the characters and your electronic device will convert them into characters. You still have to be able to recognize that you got the right characters through this process, but at least you don't have to produce all of the strokes in the proper order and configuration from scratch.
But there is still a need from time to time to write characters by hand. Furthermore, usually after an initial period of reliance on phonetic annotation (Romanization, kana, bopomofo, etc.), whether in China or elsewhere, if you want to become literate in characters, you will have to go through a period of practice writing them (and that includes the dreaded dictée exercises and tests). Somehow or other, you have to work the intricate shapes of the characters into your memory and store them there sufficiently securely so that you can write, or at least recognize, them when necessary.
Two nights ago at a dinner party, I did a simple experiment in an effort to determine whether individuals who are literate in Chinese characters actually visualize them in their mind's eye. There were about ten people present, half of whom were native speakers of Mandarin and half fluent speakers of Mandarin who had learned it as a second language. All of those who were present are highly literate in Chinese.
I asked everyone to close their eyes and attempt to visualize the character 德, which I identified through the usual method: "dàodé de dé 道德的德" ("the dé ['virtue'] of dàodé ['morality; ethics']"). I then asked them if they had actually "seen" the character 德 in their mind's eye. Their replies were "not really", "sort of", "not clearly", "no", and so forth.
The question then becomes, if highly literate individuals are not clearly visualizing the character 德 in their mind's eye, how can they reproduce it when writing or recognize it when reading? If we weren't at a dinner party and I had a lot more time to pursue the experiment with those who were present, I would ask them to attempt to visualize many other characters and explain to me how they recall the characters when reading and writing. Since that wasn't possible last night, I simply interrogated myself, attempting to be brutally honest about how I write a character like 德. Reading 德 is much easier than writing it, since in reading it the full form of the character is right before your physical eyes, whereas when you write it, you're starting with a blank space on a flat surface. Consequently, in what follows, I will concentrate on describing how to write 德.
Here's what happens with me when I try to visualize 德 in my mind's eye. Whether my physical eyes are open or closed, I can't really see the character 德 as though it were typed or written out. If I try very hard, I can force myself vaguely and hazily to retrieve from my memory groups of strokes (⼻ ⼗ ⽬ [on its side] ⼀ ⼼) blurrily, but I cannot force my mind's eye to see them all together clearly as one neatly formed character.
Since I cannot visualize the character 德 clearly in my mind's eye, how then can I write it?
Here's what I do:
1. I want to write the character that is pronounced dé in Mandarin and means "virtue".
2. Since I've written it thousands of times, I know that it begins with ⼻.
3. I start the 德-writing motor.
4. Then, in a rush, yī kǒuqì 一口氣 ("in one breath"), I just let the four other components FLOW forth sequentially, until I reach the last stroke, the dot at the bottom right, after which the 德-writing motor shuts off.
Mutatis mutandis, I do the same thing with all the other characters that I am capable of writing: jiǎng 講 ("talk"), jiāng 疆 ("border; frontier"), tīng 聽 ("hear; listen"), tái 臺 ("platform"), shùn 順 ("go along in succession"), and so on. Shùn 順 ("go along in succession" — see here for about 40 other translations) is an apt character to focus on in this context, since it conveys well the sense I have when writing a character that it has a certain CONFIGURATION or PROPENSITY that you have to follow along with to successfully complete it.
This reminds me of a book by a French philosopher named François Jullien titled La Propension des choses: Pour une histoire de l’efficacité en Chine (Seuil, 1992); translated as The Propensity of Things: Toward a History of Efficacy in China (Zone Books, 1995). The book is a disquisition on shì 勢 ("configuration; potential; tendency; momentum; inertia", etc.), which is a key concept in The Art of War: Sun Zi's Military Methods (Columbia University Press, 2007).
See:
"Victor Mair on the Art of War" (8/7/08)
It's no wonder that Jullien engaged in a celebrated contretemps with the Swiss Sinologist, Jean François Billeter (Contre François Jullien [Allia, 2006]). Although the debate engaged with larger philosophical issues, Billeter's emphasis on calligraphy (L'art chinois de l'écriture [Skira, 1989]) and Jullien's recurrent attention to shì 勢 ("l’efficacité") and other topics related to calligraphy ensured that it had inescapable implications for Chinese writing. (See the Afterword below for additional details concerning the controversy between Billeter and Jullien.)
To return to the matter at hand: to write a given character, I start at the top left (or top, if there is no top left), then work my way from top left or top to bottom right. To write a character correctly, you have to know the total number of strokes and their proper order. For most people, once you get started writing, you just have to keep going — almost as though you are in an automaton-like state. You can't think about what you're doing, what the next stroke is. If you start thinking about the next stroke, or if for some reason you miss / mess up a stroke, you usually fail to complete the character. That is why you see so many scribbled out characters in handwriting (like this).
I have often reiterated that writing Chinese characters is a highly neuro-muscular act. You have to etch the characters into your nerves and muscles so that you simply do not have to think about how to write them. That is why Chinese children — hour after hour, day after day, night after night, week after week — write the characters hundreds and hundreds of times. If you want to be literate in Chinese (to be able to handwrite Chinese characters), you eventually will have to do this too. And keep doing it. If you only want to be able to read Chinese, and not necessarily to write it by hand, then read as much of it as you can, with phonetically annotated texts when they are available. Now there are many wonderful electronic learning tools like WenlinABC, Pleco, and so on to ease and speed look-up of unfamiliar terms.
How to write Chinese characters? — practice, practice, practice!
How to read Chinese character texts? — read, read, read (while looking up as efficiently as possible unfamiliar terms).
There's no magic bullet for learning to read and write Chinese characters, and you don't have to be particularly smart to do it. But you do have to be willing to invest huge amounts of time in practicing them.
"Good good study; day day up" (1/14/14)
A final observation
Some of the most brilliant people who start out to learn one of the Sinitic languages think it's not worth all the time and effort to master handwriting of Chinese characters. For them, acquiring fluency in handwriting characters is neither fun nor a miracle; they view it as drudgery. On the other hand, some artistically inclined individuals who know no spoken Chinese and can neither read nor write Chinese texts, take great pleasure in practicing Chinese calligraphy as an art form.
Different strokes (bǐhuà 筆畫 / 笔画) for different folks.
===========================
Afterword
François Jullien's reply to the charge that he portrays China as "an alterity" appears in Chemin faisant, Connaître la Chine, relancer la philosophie. There he argues that the unreferenced quotations used by Jean-François Billeter are fabrications and that Billeter attempts to construct an imaginary version of François Jullien's work to argue against. The crux of the matter for Jullien is that exteriority and alterity are not to be conflated. China's exteriority, Jullien's point of departure, is, he argues, evident in its language as well as in its history, whereas alterity must be constructed and, as internal heterotopia, is to be found in both Europe and China. Rather than relegate China to a separate, isolated world, Jullien claims to weave a problematics between China and Europe, a net that can then fish out an unthought-of (un impensé) and help create the conditions for a new reflexivity (réflexivité) between the two cultures.
Jullien has dealt with the question of criticizing Chinese ideology several times in his work: La Propension des choses, chapter II; Le Détour et l'accès, chapters I to VI; Un sage est sans idée, final pages; etc. He thus separates himself from those who, out of fascination with strangeness or exoticism, have upheld the image of China as an "other." He separates himself also from those who, like Jean-François Billeter, permit themselves to dip into a "common fund" of thought and thus miss a chance to benefit from the diversity of human thought, which for Jullien is its true resource. He argues that we must reject both facile universalism (which springs from ethnocentrism) and lazy relativism (which leads to culturalism) in favor of a "dia-logue" of the two cultures: the "dia" of the écart, which reveals the fecundity of multiple lines of thought, and the "logos," which allows these lines to communicate through a common intelligence.
For a collective reply to the criticism of Jean-François Billeter, see Oser construire, Pour François Jullien, with notable contributions from Philippe d'Iribarne, Jean Allouche, Jean-Marie Schaeffer, Wolfgang Kubin, Du Xiaozhen, Léon Vandermeersch, Bruno Latour, Paul Ricœur, and Alain Badiou.
## 26 Comments
1. ### Brian Spooner said,
March 26, 2017 @ 10:44 am
Though with little knowledge of Chinese, I find much of great interest in this post because of a longstanding interest in the history of writing in various languages and scripts. In Iran I was always fascinated and puzzled by seeing Persians read Persian much faster than I could read English. I organised a series of meetings (with my colleague, Bill Hanaway) to try to understand this. Persian did not become a regularly printed language until the first half of the 20th century. Before that it had gone through a number of changes of writing style, which varied to some extent according the purpose (e.g. naskh, taliq, nastaliq, shekasta). We finished up writing a book on how to read bad or careless handwriting (Reading Nasta'liq: Persian and Urdu Hands from 1500 to the Present). We didn't talk about "the mind's eye," but we were thinking in those terms. Our answer was that literate Persians (and Urdu-writers) think, see and act much less in terms of individual letters (than we do, and than we are taught to do as we learn to read and write). They see and write pen-strokes, each of which may contain 1, 2, three or even four letters, possibly (though rarely) more. The letters are written differently according to where they come in the pen-stroke and the pen-strokes are written differently according to what comes before or after them. Readers read pen-strokes (the number of which is very large), not letters. They read faster because they are scanning by series of pen-stokes. We also tend to read English by scanning words rather than reading letters, but the Persian reader is much more efficient and faster at then. The general approach and relationship to writing is different from ours. Its practice is different. And its result is different. There is much more to be said about this. But enough for this comment.
2. ### B.Ma said,
March 26, 2017 @ 11:42 am
Thanks for reporting on this little experiment.
I tried it on myself with similar results. I do manage to visualize the complete character in my mind, but I must first visualize it being written very rapidly, like one of those animated stroke order guides that online dictionaries sometimes have.
So I would tend to agree that writing characters is a form of **procedural memory**, like brushing teeth or tying shoelaces. I also find a similar phenomenon with English spelling. If I try to imagine an English word in my mind I also need to visualize it being spelled out very quickly or at least scan from left to right along the word.
This is despite Brian Spooner's comment that reading is about recognizing shapes, which I also agree with in both Chinese and European languages – yet I can't visualize the shape of an English word in my mind's eye just like (as Victor has demonstrated) I can't immediately visualize the shape of a Chinese character without thinking about the order in which to write it.
I wonder if there have been any studies of Chinese people who have suffered some sort of brain injury. If they forget how to brush their teeth, but can still name objects, does this mean they become unable to write characters, but are still able to read them? Sort of like Broca's aphasia but for reading and writing?
3. ### leoboiko said,
March 26, 2017 @ 11:56 am
In the Western calligraphic world, the word for the gestural, procedural basis of a character is ductus. Anthropologist Tim Ingold once compared writing to dancing: each character is a tiny sequence of dance steps with your hand (now streamlined to minimalistic, modernistic dance-steps with computer keyboards and cellphone touch-screens, but still made from procedural finger-dancing). This is true of all writing systems.
We receive speech with our ears, and produce it with the vocal apparatus; but we receive writing with our eyes, and produce it with hand gestures. Nunberg once called writing, very felicitously IMO, an "application" of the principles of language. I wonder if it isn't, more specifically, an application of the capacity for sign language—hand gestures and sight.
4. ### Bob Ladd said,
March 26, 2017 @ 12:58 pm
Procedural memory of this sort also applies to typing or keyboard entry in any alphabetic writing system; it's not unique to Chinese characters. Exactly as VHM says, you just sort of start and motor memory takes over. The effect is most obvious when you are trying to type a less frequent word that involves a sequence you type all the time. I find it very difficult to type the word glad with only one D, for example, because the L-A-D-D-space sequence is so well rehearsed in my own keyboard use. I also recall an occasion on which I had to type the word morphine a few times in an email and kept finding morpheme on the screen when I had finished.
5. ### Andreas Johansson said,
March 26, 2017 @ 2:40 pm
Is there any reason to assume that there's anything special with Chinese characters here? Latin letters are simpler, and more directly tied to phonology, but the basic mental processes for recognizing and reproducing them are presumably the same.
Before reading the couple pieces here on aphantasia I would probably, if the issue was brought to my attention, have assumed that being able to visualize Latin letters was a prerequisite for writing them by hand (in a non-school setting where you can't just copy them from the blackboard).
6. ### Ran Ari-Gur said,
March 26, 2017 @ 4:34 pm
Reading in the Brain, by Stanislas Dehaene, talks about the relationship of motor memory and visual memory to reading and writing. He points out that young children often accidentally write mirror images of the correct text, and argues that we mainly manage to distinguish forward writing from mirror-image by tapping into our motor memory skills. (In essence, he argues that our visual memory provides left-right symmetry, and that we have to learn to suppress that for text.) If so, then this supports Bob Ladd and Andreas Johansson's comments here, that this is not specific to Chinese text. (Dehaene's book is mostly about alphabetic scripts, though he does touch on Chinese.)
7. ### Victor Mair said,
March 26, 2017 @ 4:40 pm
Writing words in alphabetical scripts and writing Chinese characters are very different processes for me. As described in detail above, characters are discrete, integral, square-shaped clumps / clusters of strokes that I have to control as a whole and power through from beginning to end to get right. The overall arrangement and composition of the strokes and components are extremely important. The individual strokes, and even the component groups of strokes, are not phonetically operative as I complete the writing of the character.
When I spell words with letters, I can (and often do) stop to reflect and retry, all the while sounding out the letters and syllables in my mind in a linear fashion. When I write out words on the blackboard for my students, especially relatively long and complicated ones (e.g., "(a)estheticism", "otorhinolaryngological", "microscopy", "morphosyllabic", etc.), I will try to write it off in one fell swoop (often sounding it out in my mind as I go), but if it doesn't feel right, I will go back and sound it all out again carefully, syllable by syllable and even letter by letter; in really tough cases, I will step back from the board and look at the whole word once more, pronouncing it as I go from left to right, from the beginning to the end of the word.
That is not at all how I write Chinese characters. When I miss a stroke or two of a character, I usually have to give up, in which case I'll probably write the syllable in Pinyin until I get a chance to look it up.
8. ### AntC said,
March 26, 2017 @ 5:21 pm
@Victor I have often reiterated that writing Chinese characters is a highly neuro-muscular act.
@Bob Ladd … typing or keyboard entry …motor memory … a sequence you type all the time
Might I compare playing a complex piano piece from memory? (Say, a Beethoven sonata.) I do not visualise the notes on the page. I can hear the music in my mind's ear. I do remember "clumps/clusters of [notes] that I have to control as a whole". So if I get interrupted, I can't just restart where I left off, I have to go back to the start of a passage.
And again you break down musical phrases into "sequences you [play] all the time", like a scale or arpeggio. So as Bob describes, playing 12-tone pieces needs you to 'unlearn' those sequences.
9. ### Rubrick said,
March 26, 2017 @ 6:04 pm
I neither speak nor read Chinese, but as a child I did learn to write some characters of about the same order of complexity as Chinese characters — specifically cartoon characters. For example, I spent a great deal of time memorizing the sequence of strokes that would yield the face of Fred Flintstone. There's even a (very approximate) parallel to the sharing of sets of strokes among different characters. Nearly all Hanna-Barbera characters, for example, include the nose-plus-jowl-area "radical".
I'd be curious to know (via fMRI or such) the extent to which such a feat is actually equivalent to learning to write a Chinese character.
10. ### John Rohsenow said,
March 27, 2017 @ 2:06 am
@Victor I have often reiterated that writing Chinese characters is a highly neuro-muscular act.
I have always insisted to my beginning students that learning to write Chinese characters is a muscle-memory act like tennis, and make them "write" the characters in the air with their fingers while I am writing on the board, at least at the beginning.
I seem to be noticing more that Chinese friends here in the USA, often seem unable to remember how to write many characters when I ask them to, even though they continue to be able to read them. I take this to be due to lack of practice in writing, especially b/c they do most of what little "writing" in Chinese they do by using a western keyboard for entry even though the output is in characters.
11. ### tangent said,
March 27, 2017 @ 5:24 am
Brian Spooner, that's something I'd never much thought about, that one language might be quicker than another to read the same content (defining "the same" is a a bit of a trick). But sure, why should it not be.
We (some of us) have a tendency to take it as almost an axiom that languages are equivalent in what they can accomplish, but that's probably a stronger assumption around capacities than around speed.
Anyone aware of formal measurements of reading speed like this? Or writing for that matter.
12. ### Victor Mair said,
March 27, 2017 @ 6:20 am
@tangent
Reading speed is one thing, but how much you absorb, understand, and retain is another.
13. ### william holmes said,
March 27, 2017 @ 11:19 am
In the background here, I think, is the encounter between the venerable Chinese written language and the upstart of digitization. On which, two observations:
— "Use it or lose it", viz.: with digitization, the need to write characters from memory is fading. Has anyone seen data on "writing literacy" levels among schoolchildren, or under-30s? (How essential is "writing literacy" on the 高考 (mainland university entrance exam)?
— On the other hand, and perhaps counterintuitively, won't digitization extend the longevity of the character system beyond its otherwise normal span?
14. ### John Roth said,
March 27, 2017 @ 1:40 pm
This reminds me of the ancient story of the fox and the caterpillar.
One day, the fox was ambling along and noticed a caterpillar crawling along a leaf. He asked: "Hey, how do you coordinate all those legs?"
The caterpillar answered: "I don't know?"
"Well", the fox said, "which foot do you pick up first?"
The caterpillar pondered it for a while. Then a bird swooped by. When the caterpillar noticed it, he tried to flee, but his feet got all tangled up and he couldn't move.
The bird chirped: "Thanks for the snack."
15. ### tangent said,
March 27, 2017 @ 2:10 pm
Sure, they're different, but it's not a vacuous question to ask: can one text be surface-read faster than another, even if storage into longer-term memory is limited.
16. ### Victor Mair said,
March 27, 2017 @ 5:40 pm
From Robert Harrist, a specialist on Chinese art history, especially calligraphy:
I was thinking about musical memory, which someone in fact mentions. Back in my music student days at Indiana, I could play fairly long oboe pieces by memory, but I never did so by visualizing the scores, and indeed, to write out a score (rather simple with the single line of the oboe part) I would have had to play a few measures, write them down, play some more, write, and so on tediously to the end of the piece. Perhaps some musicians at much higher levels of achievement can write out scores of memorized pieces without resorting to this procedure.
17. ### Suzanne Kemmer said,
March 27, 2017 @ 8:19 pm
An interesting article about aphantasia:
https://www.facebook.com/notes/blake-ross/aphantasia-how-it-feels-to-be-blind-in-your-mind/10156834777480504?fref=nf
I once had a colleague who did not experience visual images. I asked him how he understood his dreams – did he not see things in his dreams? He said no, he didn't see anything, but his dreams had plots (strange ones as in any dreams) and he was aware of himself in the dream, moving and carrying out actions. He could also perceive spoken language as well as speak in the dream, and could 'hear' non-linguistic sounds like screaming, laughing, etc. So he could experience motor and auditory imagery, just not visual imagery (with the word 'imagery' here referring to internal simulation of perception from any of various perceptual modalities). I have heard from cognitive psychologists working on visual perception that probably 5% or more of the population lacks visual imagery; but they don't seem to suffer any particular disability from it. Maybe learning to read Chinese characters as an adult might be an exception!
18. ### Dave Cragin said,
March 27, 2017 @ 8:26 pm
When I first started learning Chinese, I tried to use a paper dictionary to look up characters. This was virtually impossible. In millisecond it took for my eyes to move from the page to dictionary, I had already forgotten the character; I had no ability to visual the character.
It was somewhat akin to rock climbing for me. Before learning rock climbing, I would look at a rocky cliff and see just the rocks. After doing some rock climbing, I would automatically look for hand-holds/foot-holds.
Similarly, over time with Chinese, I was slowly better able to retain characters in my mind’s eye, albeit it, I’m much better at recognizing them in context when I type pinyin as opposed to reading them when I don’t know the context.
@William holmes – Will digitation extend the longevity of the character system? I’d say “yes,” particularly because of the coupling with pinyin. Pinyin allows the use of a standard keyboard for typing characters. Pinyin works superbly in this way.
Also, even Microsoft Word will provide the pinyin for a character (i.e., you don't need to buy separate software – just standard word processing software). Technology has completely changed the learning experience — for the better.
19. ### Quinn C said,
March 27, 2017 @ 11:43 pm
I'm not convinced that motor memory is essential for alphabetical reading – I was a fluent reader before I could write much by hand, and preferred a typewriter early on because my hands were clumsy. I also never made many spelling mistakes, which tells me that I wrote from visual memory of words rather than from sounds. I guess there are huge individual differences in this respect, with dyslexia being one possible outcome at the other end of the spectrum.
20. ### Dan Lufkin said,
March 28, 2017 @ 9:56 am
I have a small benign brain tumor that occasionally interferes with my speech for periods of a few hours. I can read aloud and recite from memory perfectly well but spontaneous speech comes out garbled. A speech pathologist coached me to imagine what I want to say as printed on a wall and just to read it from the wall. This sounds bizarre but, with practice, it works very well. My speech is a bit slower than normal but I can stay in control and speak coherently.
After reading all the above, I'm deeply thankful that my native language isn't Mandarin.
21. ### doublev said,
March 29, 2017 @ 2:31 am
I can't image long English word too…
22. ### Andy Wilson said,
March 29, 2017 @ 2:45 am
I use the Heisig method to learn Simplified Chinese Characters. It is brilliant. The book(s) help you construct a story for every character to help you remember how to write it. This method doesn't require you to do loads of practice, simply to remember the story, although I have written plenty of characters in sentences and I feel what you say about muslce memory also has some truth. For me, the story has dropped away for the characters I know well and I simply write it in a rush, letting my muscle memory do the work as you suggest.
23. ### David Marjanović said,
March 30, 2017 @ 4:59 am
I just used a combination of procedural memory and visually imagining the next stroke to recall a six-stroke character I haven't written in years and read in weeks or months…
I used procedural memory alone to confirm that otorhinolaryngological is (ideally) three strokes in my handwriting: I stared at the screen while actually moving my hand in the air under the desk.
Words that I hear or want to say often appear black-on-white in my visual imagination. (Russian in Cyrillic; Mandarin in Pīnyīn.) Fun fact: my native dialect isn't written, and its sound system is different enough from Standard German that the spelling conventions for the latter often can't be ported to the former without generating misleading results. I end up visualizing shorter sequences, and less clearly.
I don't have photographic memory. My visual imagination is just as imprecise: anything out of imagined focus is basically not there. People in my dreams don't necessarily have any particular face!
24. ### David Marjanović said,
March 30, 2017 @ 5:01 am
Oops, forgot:
I use the Heisig method to learn Simplified Chinese Characters. It is brilliant. The book(s) help you construct a story for every character to help you remember how to write it.
Remembering hundreds or thousands of stories sounds even harder to me than remembering the characters more directly!
(But of course this, too, is individual variation. I couldn't use Cicero's method to memorize a speech either.)
25. ### william holmes said,
March 30, 2017 @ 9:19 am
Victor having inspired a very long chain with just one character (德), I wonder if he might outdo himself with another one or two, or three. For example, at a future dinner party, see how many people can visualize 道， or 順. Based on various comments there seems to be a range of learning/memory tools used more or less successfully for learning and retention — with success probably varying widely across characters. Query whether the serious calligrapher, when preparing to write 羲 (for example), can see it in the mind's eye.
26. ### Brendan said,
April 2, 2017 @ 3:38 am
@Andy Wilson
I also used the Heisig method, and really took to it. It took me about two years to learn around 3000 characters, and I have found anecdotally that my recall is much better for mid-frequency characters such as 擅，骄傲 etc., even compared with native speakers. I think this method is much better suited to people in non-Chinese environments, who can't keep up muscle memory practice.
The only possible downside is a reduction in speed of writing (writing 我，你，时候 are much faster, as they are in my muscle memory). However, being "corrected" by a Masters educated Chinese speaker that I had written 冷 incorrectly (she thought it was with 今 as the phonetic component) cemented in my mind that the traditional way of learning characters would not work for learners coming from alphabetic written languages.
On this, does anybody know of any research into the use of visual mnemonics in the SL Chinese classroom? | 2019-02-18 17:40:19 | {"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": 0.3317553400993347, "perplexity": 2731.8313804802765}, "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-2019-09/segments/1550247487595.4/warc/CC-MAIN-20190218155520-20190218181520-00026.warc.gz"} |
https://www.biostars.org/p/480292/ | Need guidance for RNA_seq analysis of Ecoli with expression vector
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2.1 years ago
Morgan S. ▴ 80
Hi!
I am working on RNAseq data from E. coli k12 substr. MG1655, which has an added expression vector. I am interested in the expression of the genes within this vector. But of course, when I align the transcripts to the reference genome (which does not have the vector), the expression vector genes I am interested in are unmapped.
So to get a better reference, I de novo assembled the transcriptome of my control sample (with rnaSPAdes) so that the vector would be included in the assembly. The assembly stats were quite bad, N50 = 2315 bp and the de novo transcriptome was ~500,000 bp larger than the original reference Ecoli MG1655. I then used Scaffold_Builder to try to improve the transcriptome with the MG1655 reference genome, which resulted in a better N50 of 780113 bp but now 1.4 mill bp larger than the reference.
I considered trying Trinity's genome-guided option, but unmapped reads do not get included, defeating the purpose of what I am trying to do.
Can someone please provide some suggestions on how to further improve and refine my new reference transcriptome? I want to be sure that the reference is of good enough quality for my downstream expression analysis. How can I be sure that it is? Of course, I am hoping to do this without further sequencing if possible.
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Entering edit mode
2.1 years ago
ATpoint 69k
How about just adding the vector as an additional contain to the reference genome? That is by far the simplest solution. Use can use cat the sequence to the fast file you align against, but obviously would need to make a new index from the "new" reference genome.
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Nevermind, I found this post also mentioning what you suggested. A: Quantification of a gene that is not in the reference genome
Thank you!!
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Wow, I was making this so much harder than need be. So if the vector contains three genes I am interested in, I could cat only those three into the reference fasta? | 2023-02-09 00:35:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.7072542309761047, "perplexity": 1673.0720124296377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1674764500983.76/warc/CC-MAIN-20230208222635-20230209012635-00584.warc.gz"} |
https://math.stackexchange.com/questions/3103759/are-definitions-axioms?noredirect=1 | # Are definitions axioms? [duplicate]
I just want to ask a very elementary question.
When we introduce a "definition" in a first order logical system. For example when we say
Define: $$Empty(x) \iff \not \exists y (y \in x)$$
Isn't that definition itself an "axiom", call it a definitional axiom.
I'm asking this because the one place predicate symbol Empty() is actually new, it is not among the listed primitives of say Zermelo, which has only identity and membership as primitive symbols.
So when we are stating definitions are we in effect stating axioms? but instead of being about characterizing a primitive, they are definitional axioms giving a complete reference to a specified set of symbols in the system.
Is that correct?
Now if that is the case, then why we don't call it axiom when we state it, I mean why we don't say for example:
Definitional axiom 1) $$Empty(x) \iff \not \exists y (y \in x)$$
Zuhair
• They are axioms in the sense that they tie a term to a condition. They are not really assumptions baked into a model of reality; these are true axioms (e.g. the parallel postulate). – ncmathsadist Feb 7 '19 at 12:48
• I mean syntactically speaking, or lets say formally speaking what are we to classify those definitional statements, aren't they axioms??? – Zuhair Feb 7 '19 at 12:50
• I would refer to them as "definitions," as distinct from "axiom" in the sense I have stated it. – ncmathsadist Feb 7 '19 at 12:52
• I see, so you have another category of sentences inside a formal system (by formal system I mean the syntactical part of an axiom system), so we have theorems, axioms, and definitions, but how you can account for those, the syntactical side understands no semantics at all. – Zuhair Feb 7 '19 at 12:54
• Unlike the addition of an axiom, the addition of a definition doesn't change the formal system, it just attaches a name to a certain property which already existed in the formal system. ZFC with the definition of ${\rm Empty}$ added is still ZFC. No theorems become true or false by the addition of the definition, and any new theorems stated with the symbol can be equivalently stated in the original system by replacing the symbol with its definition. – user856 Feb 7 '19 at 12:59
## 2 Answers
A definition can indeed not be proven nor disproven and can be considered an axiom.
• I know that we can add them as axioms. But I think that syntactically (formally) speaking, actually they are axioms. – Zuhair Feb 7 '19 at 12:52
• @Zuhair: did I contradict this ? By the way, you probably mean semantically. Syntactically, nothing distinguishes the proposition $p$ from the axiom $p$. – Yves Daoust Feb 7 '19 at 12:53
• there is, axiom p is not provable in the system from other sentences. while theorems are. (I mean formally). – Zuhair Feb 7 '19 at 12:55
• @Zuhair: why do you keep repeating what has already been said ? – Yves Daoust Feb 7 '19 at 13:00
• Possibly the way how I wrote it render's it an axiom, there are other ways to introduce a definition like meta-theoretically as a string substitution rule, like in saying that the string "empty(x)" can substitute the string "$\not \exists y (y \in x)$", so this way "empty(x)" would be a meta-theoretic abbreviation of "$\not \exists y (y \in x)$", I think this kind of introduction rule on meta-theoretic level is not axiomatic. – Zuhair Feb 8 '19 at 11:05
I've already asked myself this question, and comparing my knowledge with other people opinions, I found that the answer is no.
Definitions are not axioms; definitions are simply shorthands of a bigger and longer string of symbols.
For example, in set theory we always see that the espression "$$x \subseteq y$$" is defined as: $$x \subseteq y \Longleftrightarrow \forall z(z \in x \Rightarrow z \in y ).$$
Note that between "$$x \subseteq y$$" and "$$\forall z(z \in x \Rightarrow z \in y)$$" there is the "$$\Longleftrightarrow$$" (I used the longer version to emphasise that the statement is a definition).
But this statement is written in our imaginary "computer" or "piece of paper" where it's written all the mathematics (at least, I like to think about it like that), where everything is either an axiom or something proved using the axioms or the theorems proved before, this statement should be a theorem or an axiom too.
So, formally thinking about it, it should be a theorem or an axiom. It isn't a theorem, because it hasn't been proved, so it should be an axiom. So giving this statement, it looks like we are adding a new axiom to our theory, and this would mean that all the definitions that have been given in mathematics history are axioms! This wouldn't make sense.
What is really going on here, is that the statement is actually an abbreviation for a longer string of symbols, namely "$$\forall z(z \in x \Rightarrow z \in y)$$". Abbreviations are required to talk in an easier way of mathematical relations. Formally speaking, shorthands of symbols are a "new" informal version of the formal language symbols.
Usually, mathematics is done in an informal level, or at least not as formally as when we give the axioms of mathematics. The axioms are stated in a formal language, but then nothing stop us to use abbreviations of them and still do mathematics correctly. Somethimes, in proofs or definitions, we even use our informal natural language.
So definitions -at least in high level mathematics- are not given in a formal level. We could consider them some "meta"-statements that makes the formal language of the theory more comfortable to us. Even if you don't like to see it like that, at least we know for sure that definitions tend to make the the mathematical language more and more informal. But remember that hidden behing those shorthands, there are a lot of mathematical formal strings! Take for example the definition of limit,
$$\lim_{x \to c} f(x) = L \Longleftrightarrow_{def} \forall \epsilon \in \mathbb{R^+} \exists \delta \in \mathbb{R^+} \forall x \in D: \big(0 < \mid x-c \mid < \delta \Rightarrow \mid f(x) - L \mid < \epsilon \big)$$ it is an abbreviation of a very complicated string of symbols -that are shorthand themselves-! So, when you are proving that $$\lim_{x \to 2}x^2 = 4$$ you are really proving all that complicated stuff with the $$\epsilon$$-$$\delta$$ definition of limit with $$f(x)=x^2, c= 2$$ and $$L=4$$.
We could consider also the definition of definite integral, that is a new term that we introduce to abbreviate a much more complicated one (a limit). In that case, what is being defined is a term, so we use the equality simbol $$=$$, but it's the same idea that we use with $$\Longleftrightarrow.$$ It's just a shorthand.
In conclusion, if you want to be clear in a formal point of view, I personally would mark that the statement is a definition using $$\Longleftrightarrow_{def}$$ and $$=_{def}$$ (as I used before for the limit definition), so that you can clearly see that the expression is not a strictly formal string of symbols anymore and it's rather an abbreviation.
I hope this helps :D | 2021-01-16 15:56:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 18, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8102484941482544, "perplexity": 388.0424898452894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703506697.14/warc/CC-MAIN-20210116135004-20210116165004-00489.warc.gz"} |
https://electronics.stackexchange.com/questions/396961/ohms-law-in-practise | # Ohm's Law in Practise
When the AUX pin of a stereo is connected to my mobile phone's audio female port, I just measured the voltage at the end of this AUX pin(No load is connected) approximately 2mV using a DMM . But when I measured the current, it didn't indicate any current in the DMM. According to Ohm's law, voltage is current times the resistance. When relating this basic law to my practical case, it doesn't matching. How can it be realized?
• No, according to Ohm's law, current is actually voltage divided by resistance. No, according to Ohm's law, resistance is actually voltage divided by current! Which one is correct? A better question is: WHAT IS VOLTAGE?!!!! I mean, not the dry definition (frequently got wrong,) not equations. Write ten separate paragraphs each approaching voltage from a different aspect. Then you'll start to get this stuff. – wbeaty Sep 20 '18 at 3:14
• You measured two different circuits, also you can't measure audio signal voltage reliably with a multimeter because it's not DC or sine-wave AC. – user253751 Sep 20 '18 at 3:33
• Crossposted from physics.stackexchange.com/q/429763/2451 – Qmechanic Sep 20 '18 at 7:48
$$I = \frac{V}{R}$$
If you didn't connect any load, then $R\approx\infty$. Therefore, no matter what the voltage is you expect $I\approx0$. | 2021-05-07 04:38:29 | {"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": 0.5900562405586243, "perplexity": 1690.9479190031852}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988774.96/warc/CC-MAIN-20210507025943-20210507055943-00267.warc.gz"} |
https://proxieslive.com/defining-a-function-as-a-truncated-taylors-series/ | # Defining a function as a truncated taylors series
I am trying to numerically find the error of a truncated series. To do so I want to first define a function that is the truncated sum, I cannot seem to do that. All I am tried is not working.
``f[x_]:=Normal[Series[ArcTan[x], {x, 0, 100}]] ``
Does not work as f[1] evaluates $$x$$ inside $$\arctan$$. I also tried
``Normal[Series[ArcTan[x], {x, 0, 100}]] f[x_]:=% ``
But that did not work. When I copy and paste the result of
``Normal[Series[ArcTan[x], {x, 0, 100}]] ``
It works fine. What am I doing wrong? | 2021-01-23 03:48:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7917761206626892, "perplexity": 325.63473233439225}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1610703533863.67/warc/CC-MAIN-20210123032629-20210123062629-00333.warc.gz"} |
https://stacks.math.columbia.edu/tag/0E10 | Lemma 74.26.7. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ which is flat and locally of finite presentation. Let
$W = \{ x \in |X| : f\text{ is Cohen-Macaulay at }x\}$
Then $W$ is open in $|X|$ and the formation of $W$ commutes with arbitrary base change of $f$: For any morphism $g : Y' \to Y$, consider the base change $f' : X' \to Y'$ of $f$ and the projection $g' : X' \to X$. Then the corresponding set $W'$ for the morphism $f'$ is equal to $W' = (g')^{-1}(W)$.
Proof. Choose a commutative diagram
$\xymatrix{ U \ar[d] \ar[r] & V \ar[d] \\ X \ar[r] & Y }$
with étale vertical arrows and $U$ and $V$ schemes. Let $u \in U$ with image $x \in |X|$. Then $f$ is Cohen-Macaulay at $x$ if and only if $U \to V$ is Cohen-Macaulay at $u$ (by definition). Thus we reduce to the case of the morphism $U \to V$. See More on Morphisms, Lemma 37.20.7. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2020-09-26 03:13:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9957596063613892, "perplexity": 107.31311034903923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600400232211.54/warc/CC-MAIN-20200926004805-20200926034805-00699.warc.gz"} |
http://will.thimbleby.net/algorithms/doku.php?id=making_change&do= | # Making change
Given a target amount $n$ and a set of coins of different values, what is the minimum number of coins needed to make $n$. | 2018-03-17 12:38:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3008539378643036, "perplexity": 210.6815209202441}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1521257645069.15/warc/CC-MAIN-20180317120247-20180317140247-00468.warc.gz"} |
https://gamedev.stackexchange.com/questions/58324/packing-jar-files-into-library-jar-files | # Packing jar files into library jar files
This question is not about packing a simple jar file (e.g. lwjgl) into a runnable jar file. I know how to do this using JarSplice. So if I have a game which uses JInput, I will pack my game jar and jinput.jar using JarSplice and enter the natives in the process. The problem arises when I want to create a custom library that uses JInput, and then pack that into my games. See, the whole idea of writing a game library is that I don't ever have to even copy code like the wrapper I wrote for JInput Controller, and I always have a definitive version inside a library jar. Basically what I want to do is create a jar file of my library, pack jinput.jar into it using JarSplice, possibly with the natives as well, and then when I want to export a jar of my game, I either export it automatically through Eclipse with the library jar, or, if that doesn't work, use JarSplice.
I've tried several solutions, and nothing works. When I try to pack the game jar and the library jar using JarSplice, I get an error saying that there's either duplicate .project or .classpath. When I try to export my game through Eclipse with the library jar, it won't run (which is to be expected), but then, if I try to attach the natives with JarSplice, it doesn't give me any errors but the jar doesn't run.
I'm not expecting anyone to solve this, but if anyone has an idea, something that will allow me to never look at the Gamepad code ever again, that would be awesome. I don't care if I have to package my library jar using JarSplice 5 times, and then do the same with the game jar, as long as it works. Otherwise I'll just have to copy the Gamepad class into every project alongside the library jar. :(
Edit: to clear things up, here's what I'm trying to do-
JInput has a class Controller, for controller input.
My_Library has a class Gamepad, which is a wrapper for JInput's Controller.
My_Game should be packed with My_Library so that it can access My_Library's different utilities, including Gamepad (for example, the class Player in My_Game has a field Gamepad for the player to pass gamepad input).
If I can't pack them all into one fat jar, I guess it's OK, as long as I'll be able to place Gamepad in My_Library and access it from My_Game.
• Sounds like there is likely an easy solution for this, however I don't understand the problem clearly. Could you "visualize" it by listing the content of these different .jar files (JInput, Custom_library, Game) with just a few example files and respectively the end result you are looking for? – msell Jun 30 '13 at 5:19
• OK, I edited it. – Hillel Jun 30 '13 at 5:35
• I believe this is off-topic here, this is a general Java question. You might have better luck at stackoverflow, where it is probably already answered. – MartinTeeVarga Jun 30 '13 at 7:10
Note that .jar files are simply .zip files with a different extension. You can freely view the contents and modify the archives with any zip program. Java also comes with a jar utility, which is a command-line program for creating, modifying and extracting .jar files. To make a .jar file executable, a manifest file is needed with main-class attribute. Learn to use these well. Don't be dependent on Eclipse creating your .jar files. Instead do it yourself from the command-line. Then make a script (either a shell script or Ant / Maven script), which does this for you. At least with Apache Ant manipulating .jar files is easy and combining multiple .jar files is simpler than from the command-line. Once you know how to work with .jar files well enough, you can offload the creation process to Eclipse or whatever tool you prefer, but only when you are the master and the tool is the slave. | 2019-12-13 06:27:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22956308722496033, "perplexity": 1565.3332058975207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540548544.83/warc/CC-MAIN-20191213043650-20191213071650-00189.warc.gz"} |
https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Proofs_and_Concepts_-_The_Fundamentals_of_Abstract_Mathematics_(Morris_and_Morris)/03%3A_Sets/3.01%3A_Propositional_Logic_is_not_enough | Skip to main content
# 3.1: Propositional Logic is Not Enough
Consider the following deduction:
Merlin is a wizard. All wizards wear funny hats.
Therefore, Merlin wears a funny hat.
To symbolize it in Propositional Logic, we define a symbolization key:
$$W$$: Merlin is a wizard.
$$A$$: All wizards are wearing funny hats.
$$H$$: Merlin is wearing a funny hat.
Now we symbolize the deduction:
Hypotheses:
$$W$$
$$A$$
Conclusion: $$H$$
This is not valid in Propositional Logic. (If $$W$$ and $$A$$ are true, but $$H$$ is false, then it is obvious that both hypotheses are true, but the conclusion is false.) There is something very wrong here, because the deduction that was written in English is clearly valid.
The problem is that symbolizing this deduction in Propositional Logic leaves out some of the important structure: The assertion “All wizards are wearing funny hats” is about both wizards and hat-wearing, but Propositional Logic is not able to capture this information: it loses the connection between Merlin’s being a wizard and Merlin’s wearing a hat. However, the problem is not that we have made a mistake while symbolizing the deduction; it is the best symbolization we can give for this deduction in Propositional Logic.
In order to symbolize this deduction properly, we need to use a more powerful logical language. This language is called First-Order Logic, and its assertions are built from “predicates” and “quantifiers.”
A predicate is an expression like “_______ is wearing a funny hat.” This is not an assertion on its own, because it is neither true nor false until we fill in the blank, to specify who it is that we claim is wearing a funny hat.
The details of this will be explained in Section $$3.2D$$, but here is the basic idea: In First-Order Logic, we will represent predicates with capital letters. For instance, we could let $$H$$ stand for “_______ is wearing a funny hat.” However, we will use variables instead of blanks; so “$$x$$ is wearing a funny hat” is a predicate, and we could represent it as $$H(x)$$.
The words “all” and “some” are quantifiers, and we will have symbols that represent them. For instance, “$$\exists$$” will mean “There exists some ______, such that.” Thus, to say that someone is wearing a funny hat, we can write $$\exists x ,H(x)$$; that is: There exists some $$x$$, such that $$x$$ is wearing a funny hat. Quantifiers will be dealt with in Chapter $$4$$, when First-Order Logic is fully explained.
With predicates and quantifiers, we will be talking about many people (or other things) all at once, instead of one at a time. For example, we may wish to talk about “the people who are wearing hats,” or “the mammals that lay eggs.” These are examples of sets.
3.1: Propositional Logic is Not Enough is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dave Witte Morris & Joy Morris.
• Was this article helpful? | 2022-06-27 14:24:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.78592848777771, "perplexity": 660.7914960981082}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103334753.21/warc/CC-MAIN-20220627134424-20220627164424-00717.warc.gz"} |
http://math.stackexchange.com/questions/293095/composite-of-an-immersion-with-the-inverse-map-of-another-immersion-is-a-diffeom?answertab=active | # Composite of an immersion with the inverse map of another immersion is a diffeomorphism
Let $U\subset \mathbb{R}^k$ be an open set, $n>k$ and $\varphi_1,\varphi_2 : U\to \mathbb{R}^n$ be immersions, meaning continuously differentiable such that the differential taken in any point of $U$ is injective. Also, let $\varphi_1(U)=\varphi_2(U)=:U'$ and $\varphi_1$ and $\varphi_2$ be injective (and homeomorphisms $U\to U'$).
Then $\varphi_1^{-1} \circ \varphi_2 : U\to U$ is a diffeomorphism.
My problem is that $\varphi_1^{-1}$ need not be differentiable in the usual analysis sense, because $U'$ is not an open subset of $\mathbb{R}^n$. I am guessing that $d (\varphi_1^{-1}\circ \varphi_2)(x)$ should be $d(\varphi_1)(\varphi_1^{-1}(\varphi_2(x)))^{-1}\cdot d(\varphi_2)(x)$, because this is what happens if $k=n$ and it is still defined for $k<n$. However, I would need a way to apply the theorem on inverse functions to $\varphi_1$.
-
I managed to solve this after all now (which is in part thanks to Sam's post, but I use a different idea).
Let $x\in U$ and $a:=\varphi_1(x)\in U'$. Choose $y\in U$ with $\varphi_2(y)=a$. It is enough to show that there is an open neighbourhood $V$ of $a$ in $U'$ such that $\varphi_1^{-1} \circ \varphi_2 : \varphi_2^{-1}(V)\to U$ is differentiable (by symmetry and because differentiability is a local property).
Without loss of generality, let the first $k$ rows of $d\varphi_1(x)$ be independent. I want to use the fact that for suitably small $V$ as above, $V=W\cap U'$ with $W$ open in $\mathbb{R}^n$, there is a diffeomorphism $\Phi:W\to W'\subseteq \mathbb{R}^n$ such that $\Phi (V) = W'\cap \{ (x_1,..,x_n)\in W'\, |\, x_{k+1},..,x_n = 0 \}$.
In fact, one can be chosen as $\Phi: (x_1,..,x_k,x_{k+1},..,x_n)\mapsto (x_1,..,x_k,x_{k+1}-\varphi_{1,k+1}(\psi(x_1,..,x_k)),..,x_{n}-\varphi_{1,n}(\psi(x_1,..,x_k)))$
where, using the inverse function theorem, $\psi$ is the locally defined inverse function of $(\varphi_{1,1},..,\varphi_{1,k})$. (The differential of $\Phi$ is everywhere lower triangular with determinant 1.)
Let $p:\mathbb{R}^n\to\mathbb{R}^k$ be the projection to the first $k$ coordinates. The map $f:=p\circ \Phi \circ \varphi_1$ (defined on a suitable open set in $U$ containing $x$ and mapping to $\mathbb{R}^k$) is differentiable and injective.
For any $x'$ close to $x$, $df(x') = dp(\Phi(\varphi_1 (x'))) \cdot d\Phi (\varphi_1 (x')) \cdot d\varphi_1 (x')$. Now the first $k$ rows of $d\varphi_1(x')$ are independent (since $x'$ is close to $x$ and this is the case for $d\varphi_1(x)$) and for $1\leq i\leq k$, the $i$th row of $d \Phi$ taken at any point is simply a $1$ at the $i$th coordinate and zeroes otherwise. The same goes for $dp$. So this composition of three matrices still has its first $k$ rows independent, so it is an invertible $k\times k$ matrix. It follows that $f$ is a diffeomorphism onto its image.
$\varphi_1^{-1}\circ \varphi_2$ equals the composition $f^{-1} \circ p \circ \Phi \circ \varphi_2$ on a suitably small neighbourhood of $y$ and all these maps are differentiable.
-
Your maps $\phi_1, \phi_2$ are usually called embeddings (= injective proper immersions).
Are you familiar with abstract manifolds? This is in some sense the appropriate language to discribe the map $\phi^{-1}: U' \rightarrow U$ and its differential $d \phi^{-1}(p)$ (this would be a map from the tangent space of $U'$ at $p$ onto $\mathbb{R}^k$).
For an elementary treatment, try to extend the map $\phi_1$ to a map $$\tilde{\phi}_1 : U \times \mathbb{R}^{n-k},\,\,\,\, \tilde{\phi}_1(x,y) = \phi_1(x) + A(x)y$$ where $A(x) \in \mathbb{R}^{(n-k)\times k}$ is a smooth map of matrices, such that $d\tilde{\phi_1}(x,0) = d\phi_1(x) + A(x)$ is an isomorphism for every $x \in U$. Do the same for $\phi_2$ and then argue by the inverse function theorem.
- | 2015-04-19 21:39:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9705116748809814, "perplexity": 74.89397707129152}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1429246639482.79/warc/CC-MAIN-20150417045719-00134-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://mathhelpforum.com/pre-calculus/67232-co-ordinate-geometery-urgent-help-needed-print.html | # Co-ordinate Geometery urgent help needed
• Jan 7th 2009, 03:44 PM
db5vry
Co-ordinate Geometery urgent help needed
A, B, C and D are (-7,4), (3,-1), (6,1) and (k,-15) respectively.
1] Find the gradient of AB
2] Find the equation of AB and simplify the answer
3] Find the length of AB
4] The point E is the mid-point of AB. Find the co-ordinates of E.
5] CD is perpendicular to AB. Find the value of k in D.
For question 1 I used y2-y1 over x2-x1 to get the gradient which I think is -6,
For question 2 I then used formula of a line and continued:
y - y1 = m (x - x1)
y - 4 = -6 (x + 7)
y - 4 = -6x - 42
y + 6x + 38 = 0
For question 3 I worked the length of AB to be:
√ (x2-x1)² + (y2-y1)²
√ (3 + 7)² + (-1 + 7)²
√ 10² + 6² [100 = 36]
AB = √136
I'm really concerned this is wrong and I don't know how to do the rest of the question. Can someone please help me?
• Jan 7th 2009, 03:49 PM
TheMasterMind
Quote:
Originally Posted by db5vry
A, B, C and D are (-7,4), (3,-1), (6,1) and (k,-15) respectively.
1] Find the gradient of AB
2] Find the equation of AB and simplify the answer
3] Find the length of AB
4] The point E is the mid-point of AB. Find the co-ordinates of E.
5] CD is perpendicular to AB. Find the value of k in D.
For question 1 I used y2-y1 over x2-x1 to get the gradient which I think is -6,
For question 2 I then used formula of a line and continued:
y - y1 = m (x - x1)
y - 4 = -6 (x + 7)
y - 4 = -6x - 42
y + 6x + 38 = 0
For question 3 I worked the length of AB to be:
√ (x2-x1)² + (y2-y1)²
√ (3 + 7)² + (-1 + 7)²
√ 10² + 6² [100 = 36]
AB = √136
I'm really concerned this is wrong and I don't know how to do the rest of the question. Can someone please help me?
1/ is wrong,
$\frac{y_2-y_1}{x_2-x_1}$= $\frac{-1-4}{3+7}$
$\frac{-5}{10}$ $=-\frac{1}{2}$
2/ i get $-\frac{1}{2}x+\frac{1}{2}$ you already have the slope which is $-\frac{1}{2}$ plug in the other numbers to $y=-\frac{1}{2}x+b$ and solve for b
3/ the value of y1 is 4 and you used 7 which is wrong
answer should be $\sqrt{125}$= $11.18$
4/
$M= (\frac{x_1+x_2}{2} + \frac{y_1+y_2}{2})$= $(\frac{-7+3}{2} + \frac{4-1}{2})$
$=(\frac{-4}{2} + \frac{3}{2})$ $=(-2,1/2)$ | 2016-09-28 12:19:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7005785703659058, "perplexity": 982.1186903705909}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738661367.29/warc/CC-MAIN-20160924173741-00073-ip-10-143-35-109.ec2.internal.warc.gz"} |
http://blog.rossry.net/tag/liberalism/ | IN WHICH Ross Rheingans-Yoo, a sometimes-poet and erstwhile student of Computer Science and Math, occasionally writes on things of interest.
# Reading Feed (last update: December 15)
A collection of things that I was glad I read. Views expressed by linked authors are chosen because I think they're interesting, not because I think they're correct, unless indicated otherwise.
### (15)
Blog: Marginal Revolution | A social credit system for scientists? — Chinese scientists, that is, and fraudsters at that. What, would you rather be soft on fraud?
### (14)
Comic: xkcd | arXiv — "...invaluable projects which, if they didn't exist, we would dismiss as obviously ridiculous and unworkable."
### (13)
Blog: JeffTK | Not losing things — "I almost never lose things, especially important things like my keys, laptop, or ear warmers. Here's an attempt to write up the system I use, in case it's useful to others..."
Blog: Tyler
READ MORE
# A Liberal Critique
content warning: discussion of discussion of rape; discussion of critique of an instance of opposition to racism
"Charity over absurdity", 5 of $\infty$.
[ | ]
### (1)
A friend pointed out on Facebook (I'm not going to hyperlink.) that they were seriously troubled that the first time I chose to write about race[1], it was against the idea that we should be doing more to fight racism:
The fact that the first thing that you have ever said about [race] is in defense of structural protections of racism -- even if I, personally, in this case... agree with you -- is highly suspicious, and it is important... to consider carefully how we choose the things about which to be passionate, [especially] publicly passionate, and how those choices influence those around us.
I'm actually pretty sympathetic to this view, though I was heartened by another friend's comment:
I'm not sure if I agree with you that people should make statements that have already been said in order to communicate we are as
READ MORE
# Why So Few Male Feminists?
content warning: unrepentant naïveté, use and interrogation of the word "feminism" by a cishet white male, statistical mention of rape, sexual/domestic violence, and abuse
content note: in parts, speaking only to people who have the privilege of choosing, intentionally and with lightness, how they engage with issues of social justice. (more in a previous post)
### (1)
Ozy Frantz[read this] is one of those bloggers who has significantly and dramatically changed the way I think -- and in this respect shares a reference class with Leah Libresco and Eliezer Yudkowsky. Though I've only been reading Ozy since they started Thing of Things last November, they're very quickly stepping into position as Possibly My Favorite Blogger Right Now. A perfect example of why is their recently re-run post, Thing of Things | Who Cares About Men's Rights?:
I do.
I care about every boy that was ever called a fag or a pussy or a sissy for being emotional, or sensitive, or unathletic, or just not manly enough. I care about
READ MORE
1 / 1 | 2019-01-18 17:05:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30628105998039246, "perplexity": 4771.721072091324}, "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-2019-04/segments/1547583660175.18/warc/CC-MAIN-20190118151716-20190118173716-00371.warc.gz"} |
https://cl.desmos.com/t/question-on-initialcellcontent/2262 | # Question on initialCellContent
I am defining an initialCellContent based on the result of a multiple choice answer. Once selected, that value is stuck in the cell. If students realize they don’t like their multiple choice, the cell doesn’t change if the students change their choice. It literally took the initial value and won’t let that value change. Is there a better way to initially define cell content that will allow students to change their minds?
My CL:
cellDisableEvaluation(1,1):true
initialCellContent(1,1): when mc89b.isSelected(1) “\left(\right)\div\left(\frac{ }{ }\right)”
when mc89b.isSelected(3) “\left(\right)\cdot \left(\frac{ }{ }\right)”
otherwise “”
initialCellContent(2,1): “\y=”
a3=parseEquation(this.cellContent(2,1)).differenceFunction(“y”).evaluateAt(38)
correct: a3=30
cellSuffix(2,1): when this.cellContent(2,1)="\y=" “” when a3=30 “inches ” otherwise “
I think you need this for your initialCellContent instead:
initialCellContent(1,1): “”
cellContent(1,1): when mc89b.isSelected(1) “\left(\right)\div\left(\frac{ }{ }\right)”
when mc89b.isSelected(3) “\left(\right)\cdot \left(\frac{ }{ }\right)”
otherwise “”
You can create a variable for your conditional text. Then, use that for your initialCellContent:
text=when mc89b.isSelected(1) "\left(\right)\div\left(\frac{ }{ }\right)"
when mc89b.isSelected(3) "\left(\right)\cdot \left(\frac{ }{ }\right)"
otherwise ""
initialCellContent(1,1): text
Thanks Daniel,
I’ll try that.
-Richard
Thanks Susan,
I’ll check it out ASAP.
-Richard
Well, no luck. I am still getting the same issue. Once I select a multiple choice answer, the initialCellContent enters that value but after about 2 to 3 seconds it locks it in. My goal is to allow students to choose hopefully choice 1 or 3 to solve a scale factor problem between two similar figures. Susan, if I use cellContent, then students cannot fill in the blanks in that cell. And initialCellContent only takes the initial value or whatever is clicked within the first few seconds of the initial choice. Once chosen, the CL makes either of the linked photos.
Thanks again for the help.
There is not a way to deSelect a choice, but I really like the idea of giving an initial formula. Since the cellContent does deSelect, I might add a third column (and header row, maybe) with this:
cellContent(1,3): when mc89b.isSelected(1) “\left(\right)\div\left(\frac{ }{ }\right)”
when mc89b.isSelected(3) “\left(\right)\cdot \left(\frac{ }{ }\right)”
otherwise “”
cellDisableEvaluation(1,2):true
cellContent(0,3):“Copy & Paste” # somewhere maybe with an arrow symbol
cellContent(0,1):""
cellContent(0,2):""
cellContent(2,3): “”
Maybe Desmos will make a deSelect option something like multiChoiceDeselectable: true.
1 Like | 2022-07-05 06:21:14 | {"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": 0.8085543513298035, "perplexity": 5328.016037606884}, "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-2022-27/segments/1656104514861.81/warc/CC-MAIN-20220705053147-20220705083147-00366.warc.gz"} |
http://mathhelpforum.com/algebra/65476-partial-fractions.html | 1. ## Partial Fractions
g(x) = (2x-1)(x+2)(x-3)
Express g(x) in the form Ax³ + Bx² + Cx + D
I found that this was 2x³ - 3x² - 11x + 6
Find the constant a given that x+3 is a factor of g(x) + ax and Express x-3/ g(x)in partial fraction.
I can do the partial fractions part just not finding the constant
thanks
2. ## Factorising a polynomial
Hi -
Originally Posted by gracey
g(x) = (2x-1)(x+2)(x-3)
Express g(x) in the form Ax³ + Bx² + Cx + D
I found that this was 2x³ - 3x² - 11x + 6
Find the constant a given that x+3 is a factor of g(x) + ax and Express x-3/ g(x)in partial fraction.
I can do the partial fractions part just not finding the constant
thanks
The polynomial $f(x)$ has a factor $(x-k)$ if $f(k)=0$. So $g(x) + ax$ has a factor $(x+3)$ if its value is zero when $x = -3$.
Solve a simple equation for $a$, and you're done. | 2016-10-25 20:02:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8389532566070557, "perplexity": 1710.7213853025955}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720356.2/warc/CC-MAIN-20161020183840-00204-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://dev.echo.org/developers/operations/proposals/_proposal_create_operation/ | # proposal_create_operation¶
The proposal_create_operation creates a transaction proposal, for use in multi-sig scenarios.
Creates a transaction proposal. The operations which compose the transaction are listed in order in proposed_ops, and expiration_time specifies the time by which the proposal must be accepted or it will fail permanently. The expiration_time cannot be farther in the future than the maximum expiration time set in the global properties object.
review_period_seconds is optional. When not defined takes value from global properties.
### JSON Example¶
[
20,{
"fee": {
"amount": 0,
"asset_id": "1.3.0"
},
"fee_paying_account": "1.2.0",
"expiration_time": "1970-01-01T00:00:00",
"proposed_ops": [],
"review_period_seconds": 100500, // optional
"extensions": []
}
] | 2021-09-22 10:42:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4846622943878174, "perplexity": 11542.570433344754}, "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-2021-39/segments/1631780057347.80/warc/CC-MAIN-20210922102402-20210922132402-00119.warc.gz"} |
https://tex.stackexchange.com/questions/589162/cant-resolve-missing-endcsname-inserted-error-with-tikzcd-package | # Can't Resolve "! Missing \endcsname inserted" Error with tikzcd Package
I've read the other questions on this site corresponding to the same error and I just don't understand why I can't resolve the issue on my machine. Here is essentially what my code looks like:
\documentclass{article}
\usepackage{ulem}
\normalem
\usepackage{marvosym}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{mathrsfs}
\usepackage{bbm}
\usepackage{bm}
\usepackage[bb=boondox]{mathalfa}
\usepackage{cite}
\usepackage{url,graphicx,tabularx,array,geometry}
%\usepackage{wasysym}
\usepackage{textcomp}
\usepackage{amsmath}
\usepackage{MnSymbol}
\usepackage{enumitem}
\usepackage{multicol}
\usepackage{braket}
\usepackage{hyperref}
\usepackage{amscd}
\usepackage{tikz-cd}
\usepackage{xcolor, listings}
%\usepackage{physics}
\usepackage[affil-it]{authblk}
%\usepackage{mcode}
\usepackage{titling}
\usepackage{pgfplots}
\begin{document}
$\begin{tikzcd} \mathbb{0} \arrow[d, “!”] \arrow[r, “!”] & \mathbb{1} \arrow[d, “\bot”] \\ \mathbb{1} \arrow [r, “\top”] & \Omega \end{tikzcd}$
\end{document}
The specific error I get reads:
! Missing \endcsname inserted.
\OT1\textquotedblleft
l.91 \end{tikzcd}
Is there a problem with my library declarations? I can't tell what about my diagram might be off. Troubleshooting suggestions appreciated.
$\begin{tikzcd} \mathbb{0} \arrow[d, "!"] \arrow[r, "!"] & \mathbb{1} \arrow[d, "\bot"] \\ \mathbb{1} \arrow [r, "\top"] & \Omega \end{tikzcd}$
• sorry I know nothing about texworks but I would be very surprised if any editor designed for tex makes it hard to insert " @Mnifldz Mar 27 at 0:16 | 2021-12-09 01:57:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.704562783241272, "perplexity": 1677.2890348052117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00421.warc.gz"} |
http://mathoverflow.net/revisions/80213/list | Among the foundational results in differential topology are the Morse lemmas:
1. Suppose that $f\colon\, M\to \mathbb{R}$ is a smooth function on a closed manifold M, that $f^{−1}[-\epsilon,\epsilon]$ is compact, and that there are no critical values between $-\epsilon$ and $\epsilon$. Then $f^{-1}(-\infty,-\epsilon]$ is diffeomorphic to $f^{-1}(-\infty,\epsilon]$.
2. Let $f\colon\, M\to \mathbb{R}$ be a smooth function on a closed manifold M, with no critical points on $f^{-1}[-\epsilon,\epsilon]$ except k nondegenerate ones on $f^{-1}(0)$, all of index $s$. Then $f^{-1}[-\infty,\epsilon]$ is diffeomorphic to $X(f^{-1}[-\infty,-\epsilon];f_1,\ldots,f_k;s)$ (for suitable fi).
Here $X(M;f;s)$ for $f\colon\,(\partial D^s)\times D^{n-s}\to M$ is M with an s-handle attached by f.
In plain English, the Morse lemmas give us instructions for how to build M out of simple pieces, like a child would build a structure out of Lego blocks. The first lemma says "if f has no critical point, do nothing", while the second lemma says "if f has a critical point, glue in an appropriate handle".
One of the things that makes me feel that I don't understand Morse's lemmas as well as I would like to is that the conditions on the source and target of the Morse function f seem unnecessarily restrictive. Maybe we'd like M to be a manifold with boundary or with corners, or a stratified space, or an infinite-dimensional something-or-other? Indeed, analogues of the Morse lemmas continue to hold (but how much CAN we relax our requirements on M?).
On the target side, what about if we want the target to be something other than $\mathbb{R}$? Circle-valued Morse theory and Morse 2-functions deal with Morse functions to S1 and to R2 correspondingly, and are quite useful.
And so, in order to feel I have a bit more of a grip on the meta-mathematical conceptual framework of the Morse Lemmas, I'm very much interested in the following question:
Let $f\colon\, M\to N$ be a smooth function, with non-degenerate critical points (critical points which don't vanish after a small perturbation)whatever that means in context). What conditions do I have to impose on M and on N to obtain reasonable analogues of the Morse Lemmas?
By reasonable analogues, I mean lemmas which explicitly relate $f^{-1}(N^{\prime})$ to $f^{-1}(N^{\prime\prime})$ up to diffeomorphism (by some sort of generalized handle attachment operation?), where $N^{\prime}\subseteq N^{\prime\prime}\subseteq N$ are some reasonable analogues in N to $(-\infty,-\epsilon]$ and $(-\infty,\epsilon]$ correspondingly.
Is there any work, or any results along these lines? Is this all well-known (and easy?), is it open, or is it known to be impossible (as in: "if the target isn't R then something goes disastrously wrong")? | 2013-05-26 01:33:30 | {"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": 0.7507514357566833, "perplexity": 341.3622664470633}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368706477730/warc/CC-MAIN-20130516121437-00061-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://codereview.stackexchange.com/questions/215472/python-webscraper-to-get-property-info-from-tripadvisor | # Python webscraper to get property info from Tripadvisor
I'm very much a beginner at programming, and hoping to get some advice! I'm having some trouble with a tripadvisor scraper being slow, and have identified the part of my code that is taking a while. It's likely because of the long selector, but i'm not sure how to use anything more specific because there are randomly generated strings on the more specific selectors. Below the snippet that is taking a while, and below that is the full code. Would appreciate any feedback!
Sample of the webpages im scraping:
https://www.tripadvisor.com.sg/Hotels-g255100-Melbourne_Victoria-Hotels.html
https://www.tripadvisor.com.sg/Hotel_Review-g255100-d257433-Reviews-The_Hotel_Windsor-Melbourne_Victoria.html
Code giving me problems:
num_rooms = 0
extra_info = soup.select('#taplc_about_addendum_react_0 div div div div')
for data in extra_info:
data = data.text.strip()
if data.isdigit():
num_rooms = int(data)
Full code:
import requests
from bs4 import BeautifulSoup
import xlsxwriter
import time
def get_soup(url):
r = requests.get(url)
return BeautifulSoup(r.content, 'html.parser')
def write_xlsx(items, xlsx_write_row):
write_column = 0
for item in items:
worksheet.write(xlsx_write_row, write_column, item)
write_column += 1
workbook = xlsxwriter.Workbook('Results.xlsx')
worksheet = workbook.add_worksheet()
# user variables
while True:
start_url = input('Start url: ')
if 'https://www.tripadvisor.com.sg/Hotels-' not in start_url:
print(
'Please enter a valid url. e.g https://www.tripadvisor.com.sg/Hotels-g255100-Melbourne_Victoria-Hotels.html')
else:
break
print('fetching page...')
soup = get_soup(start_url)
while True:
min_rev_num = input('Min Reviews for property: ')
if min_rev_num.isdigit():
if int(min_rev_num) >= 0:
min_rev_num = int(min_rev_num)
break
print('Please enter a valid number')
while True:
print('Enter max number of low review number properties on a single page, from 0 to 30.')
print('(Program will exit once this condition is fulfilled)')
num_rev_criteria = input('Input: ')
if num_rev_criteria.isdigit():
if 0 <= int(num_rev_criteria) <= 30:
num_rev_criteria = int(num_rev_criteria)
break
print('Please enter a valid number')
while True:
min_star_rating = input('Min star rating for property: ')
if min_star_rating.isdigit():
if 0 <= int(min_star_rating) <= 5:
min_star_rating = float(min_star_rating)
break
print('Please enter a valid number')
while True:
min_room_num = input('Min number of rooms: ')
if min_room_num.isdigit():
if int(min_room_num) >= 0:
min_room_num = int(min_room_num)
break
print('Please enter a valid number')
while True:
max_num_pages = int(soup.select_one('.pageNum.last.taLnk').text.strip())
num_pages = input('Page to search until(1 to {}):'.format(str(max_num_pages)))
if num_pages.isdigit():
if 1 <= int(num_pages) <= max_num_pages:
num_pages = int(num_pages)
break
print('Please enter a valid number')
print('-'*30 + '\n')
check = input("Make sure 'Results.xlsx' is closed and deleted. Once you are ready, press enter")
write_row = 0
write_xlsx(['Property Details', 'Star Rating', 'Number of Rooms'], write_row)
page_url = start_url
rejected_properties = 0
start = time.time()
print('Getting data...')
# get property data
for page_num in range(num_pages):
print('\nOn page {}\n'.format(str(page_num + 1)))
low_review_count = 0
soup = get_soup(page_url)
if page_num != num_pages - 1:
next_page = soup.select_one('.nav.next.taLnk.ui_button.primary')['href']
page_url = 'https://www.tripadvisor.com.sg' + next_page
else:
pass
rows = soup.select('.property_title.prominent')
prop_urls = []
for row in rows:
prop_urls.append('https://www.tripadvisor.com.sg' + row['href'])
for prop in prop_urls:
soup = get_soup(prop)
try:
num_reviews = int(soup.select_one('.reviewCount').text.strip().split(' ')[0].replace(',', ''))
except AttributeError:
num_reviews = 0
try:
property_name = soup.select_one('#HEADING').text.strip()
except AttributeError:
property_name = ' '
if num_reviews >= min_rev_num:
try:
star_rating_class = soup.select_one('.ui_star_rating')['class'][1]
star_rating = float(star_rating_class[5] + '.' + star_rating_class[6])
except TypeError:
star_rating = 0
num_rooms = 0
extra_info = soup.select('#taplc_about_addendum_react_0 div div div div')
for data in extra_info:
data = data.text.strip()
if data.isdigit():
num_rooms = int(data)
try:
address = soup.select_one('.street-address').text.strip() + ', ' + soup.select_one('.locality').text.strip() + soup.select_one('.country-name').text.strip()
except AttributeError:
address = ' '
try:
phone = soup.select_one('.is-hidden-mobile.detail').text.strip()
except AttributeError:
phone = ' '
if star_rating >= min_star_rating or star_rating == 0:
if num_rooms >= min_room_num or num_rooms == 0:
write_row += 1
write_xlsx([property_name + '\n' + address + '\nT: ' + phone, star_rating, num_rooms], write_row)
else:
print("Rejected: '{}'\n".format(property_name) + ' - Not enough rooms:{}'.format(num_rooms))
else:
print("Rejected: '{}'\n".format(property_name)+' - Not high enough star rating:{}'.format(star_rating))
else:
low_review_count += 1
print("Rejected: '{}'\n".format(property_name) + ' - Not enough reviews:{}'.format(num_reviews))
print(' - Low review count: {}/{}'.format(low_review_count, num_rev_criteria))
if low_review_count >= num_rev_criteria:
print('Exiting due to low review count on page')
break
workbook.close()
end = time.time()
print("\nDone! Results can be found in 'Results.xlsx' in the same folder\n")
print('Results can be copied straight onto the shortlist(paste values only), formatting has already been done.')
print('If any results have 0 stars or 0 rooms, Tripadvisor does not have this data')
print('Address and phone numbers are based on Tripadvisor data as well\n')
print('Number of pages searched: {}'.format(str(page_num + 1)))
props_searched = (page_num - 1)*30 + len(prop_urls)
print('Number of properties searched: {}'.format(str(props_searched)))
print('Number of properties accepted: {}'.format(str(write_row - 1)))
print('Number of properties rejected: {}'.format(str(props_searched - write_row + 1)))
print('Time taken: {} minutes'.format(str((end-start)//60)))
while True:
check = input('\nTo exit, press enter')
if True:
break
## 1 Answer
At least on the .com version of the site (I can't access the .com.sg) the content your looking for is:
<div class="hotels-hotel-review-about-addendum-AddendumItem__title--2QuyD">NUMBER OF ROOMS</div>
<div class="hotels-hotel-review-about-addendum-AddendumItem__content--iVts5">180</div>
This appears to be consistent across pages. So, you could look for a .hotels-hotel-review-about-addendum-AddendumItem__title--2QuyD followed by a .hotels-hotel-review-about-addendum-AddendumItem__content--iVts5. You probably want to check that the text in the first div is NUMBER OF ROOMS in case some pages have more "addendum items" with purely numeric content:
When scraping, I like pulling things out into functions to make my intent more clear, to make testing easier, and to make it easier to refactor if (more likely, when the page changes):
def get_addendum_item_titles(page):
return page.find_all('div', class_='.hotels-hotel-review-about-addendum-AddendumItem__title--2QuyD')
def get_number_of_rooms_addendum_title(page):
for title in get_addendum_item_titles(page):
if title.text.strip().upper() == 'NUMBER OF ROOMS':
return title
raise ValueError('Number of rooms addendum title not found')
def get_number_of_rooms(page):
title = get_number_of_rooms_addendum_title(page)
content = title.parent.find('div', class_='.hotels-hotel-review-about-addendum-AddendumItem__content--iVts5')
return int(content.text.strip())
You may want to throw those class names in constants.
A prime justification for this approach is immediately obvious. The --2QuyD-like suffixes are almost certainly automatically generated. I suspect the next time tripadvisor modifies any of their CSS these suffixes will change and break your code. But I imagine that the hotels-hotel-review-about-addendum-AddendumItem__title part will rarely change. So you need a way of finding the proper classname with only that prefix. Ideally you create a function like:
def find_class_with_prefix(page, prefix):
pass
I'll leave that as an exercise to you, but once you create it, it will be really cleanly integratable into the above code.
Note there is a CSS attribute selector that you can use instead for this: div[class^=hotels-hotel-review-about-addendum-AddendumItem__title], but I suspect it will have poor performance characteristics because it probably uses a linear scan. You'll want to tap into whatever datastructures beautifulsoup already has built for quickly looking up elements by class (to find the list of class names).
• Thank you for the very detailed response, it was exactly what i was looking for! I was considering even using some string methods to search the raw html out of desperation. Some parts of your answer are still a bit beyond me, but i'll research and make sense of it. At least I have a sense of what to do now. Will look into make the function to find the prefix if it changes as well. Thank you so much! – Josh Lim Mar 18 at 1:39 | 2019-03-26 07:11:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18193785846233368, "perplexity": 11944.19940010794}, "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-2019-13/segments/1552912204857.82/warc/CC-MAIN-20190326054828-20190326080828-00060.warc.gz"} |
http://alidoc.cern.ch/AliRoot/v5-06-30/class_ali_t_p_c_q_a_checker.html | AliRoot Core v5-06-30 (35d6c57)
AliTPCQAChecker Class Reference
Checks implemented a la AliMUONQAChecker. More...
#include <AliTPCQAChecker.h>
Inheritance diagram for AliTPCQAChecker:
## Public Member Functions
AliTPCQAChecker ()
AliTPCQAChecker (const AliTPCQAChecker &qac)
AliTPCQACheckeroperator= (const AliTPCQAChecker &checker)
virtual ~AliTPCQAChecker ()
virtual void Check (Double_t *test, AliQAv1::ALITASK_t, TObjArray **, const AliDetectorRecoParam *recoParam)
void Init (const AliQAv1::DETECTORINDEX_t det)
void SetQA (AliQAv1::ALITASK_t index, Double_t *value) const
Int_t GetDebugLevel () const
void SetDebugLevel (Int_t value)
## Private Member Functions
Double_t CheckRAW (Int_t specie, TObjArray *list)
Double_t CheckSIM (Int_t specie, TObjArray *list)
Double_t CheckREC (Int_t specie, TObjArray *list)
Double_t CheckESD (Int_t specie, TObjArray *list)
Int_t fDebug
## Detailed Description
Checks implemented a la AliMUONQAChecker.
Checks the quality assurance by realzed checks on histogram content.
Based on AliPHOSQAChecker. Checks the quality assurance by comparing with reference data.
Date
January 2008 - September 2009.
Checks the quality assurance by very simple checks on histogram content.
Date
September 2009.
Definition at line 21 of file AliTPCQAChecker.h.
## Constructor & Destructor Documentation
AliTPCQAChecker::AliTPCQAChecker ( )
inline
Definition at line 24 of file AliTPCQAChecker.h.
AliTPCQAChecker::AliTPCQAChecker ( const AliTPCQAChecker & qac )
inline
Definition at line 25 of file AliTPCQAChecker.h.
virtual AliTPCQAChecker::~AliTPCQAChecker ( )
inlinevirtual
Definition at line 27 of file AliTPCQAChecker.h.
## Member Function Documentation
void AliTPCQAChecker::Check ( Double_t * test, AliQAv1::ALITASK_t index, TObjArray ** list, const AliDetectorRecoParam * recoParam )
virtual
It is important to understand the destinction between indexed tasks (AliQAv1::TASKINDEX_t) which are used in the DataMaker classes and indexed tasks (AliQAv1::ALITASK_t) whihc are used in the checker class.
From the AliQAChecker::Run() methods we have:
AliQAv1::kRAW
- AliQAv1::kRAWS
AliQAv1::kSIM
- AliQAv1::kHITS
- AliQAv1::kSDIGITS
- AliQAv1::kDIGITS
AliQAv1::kREC
- AliQAv1::kDIGITSR
- AliQAv1::kRECPOINTS
- AliQAv1::kTRACKSEGMENTS
- AliQAv1::kRECPARTICLES
AliQAv1::kESD ;
-AliQAv1::kESDS
This means that for each group of tasks the Check will be called
one or more times. This also mean that we cannot know what
histograms will be or not be there in a single call... And we
also do not know the position in the list of the histogram.
Check objects in list
Definition at line 52 of file AliTPCQAChecker.cxx.
Double_t AliTPCQAChecker::CheckESD ( Int_t specie, TObjArray * list )
private
This method checks the QA histograms associated with ESDs (Note that there is aslo a globalQA which is running on all the ESD information so for now this is just a few basic histograms)
The check methods are simple: If there are no histogram at all (set fatal)
Definition at line 268 of file AliTPCQAChecker.cxx.
Referenced by Check().
Double_t AliTPCQAChecker::CheckRAW ( Int_t specie, TObjArray * list )
private
Check ESD
Definition at line 116 of file AliTPCQAChecker.cxx.
Referenced by Check().
Double_t AliTPCQAChecker::CheckREC ( Int_t specie, TObjArray * list )
private
This method checks the QA histograms associated with reconstruction
For TPC this is: DigitsR : The digit histogram gives the ADC distribution for all sigbnals above threshold. The check is just that there are digits. RecPoints : The cluster histograms are meant to give an idea about the gain from the cluster charge and to indicate iof there are rows with noise clusters, i.e., they are very visual.
The check methods are simple: If there are no histogram at all (set fatal) If digit histogram is there, but there are no digits (set error) If cluster histogram is there but there are less than 1000 clusters (set warning) If there are more than 1000 clusters but no clusters for either short, medium, or long pads (set error)
Definition at line 209 of file AliTPCQAChecker.cxx.
Referenced by Check().
Double_t AliTPCQAChecker::CheckSIM ( Int_t specie, TObjArray * list )
private
This method checks the QA histograms associated with simulation
For TPC this is: Digits : The digit histogram gives the ADC distribution for all sigbnals above threshold. The check is just that there are digits. Hits : The hit histograms are checked to see that they are not empty. They contain a lot of detailed information on the energyloss model (they were used to debug the AliRoot TPC use of FLUKA).
The check methods are simple: We do not know if it is bad that histograms are missing because this will always be the case for summable digits. So this check is not possible here. If digit histogram is empty (set error) If one of the hit histograms are empty (set error)
Definition at line 149 of file AliTPCQAChecker.cxx.
Referenced by Check().
Int_t AliTPCQAChecker::GetDebugLevel ( ) const
inline
Definition at line 33 of file AliTPCQAChecker.h.
void AliTPCQAChecker::Init ( const AliQAv1::DETECTORINDEX_t det )
intialises QA and QA checker settings
Definition at line 298 of file AliTPCQAChecker.cxx.
AliTPCQAChecker & AliTPCQAChecker::operator= ( const AliTPCQAChecker & checker )
Equal operator.
Definition at line 41 of file AliTPCQAChecker.cxx.
void AliTPCQAChecker::SetDebugLevel ( Int_t value )
inline
Definition at line 34 of file AliTPCQAChecker.h.
void AliTPCQAChecker::SetQA ( AliQAv1::ALITASK_t index, Double_t * value ) const
sets the QA according the return value of the Check
Definition at line 321 of file AliTPCQAChecker.cxx.
## Member Data Documentation
Int_t AliTPCQAChecker::fDebug
private
The documentation for this class was generated from the following files: | 2022-05-23 20:54:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.3031732738018036, "perplexity": 14359.462316661498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1652662561747.42/warc/CC-MAIN-20220523194013-20220523224013-00507.warc.gz"} |
https://mathoverflow.net/questions/346465/proving-a-group-with-two-generators-is-not-free-that-uses-the-brahamagupta-pell | # Proving a group with two generators is not free that uses the Brahamagupta-Pell equation
Hello I encountered the following while reading a set of notes on free groups. It's not a homework question.
"Does there exist a rational number $$\alpha$$ with $$0 <|\alpha| < 2$$ such that the group generated by $$\begin{bmatrix} 1 & \alpha \\ 0 & 1 \end{bmatrix}$$ and $$\begin{bmatrix} 1 & 0 \\ \alpha &1 \end{bmatrix}$$ is free.
We mention in passing that several rational $$\alpha$$ with $$0 < |\alpha| < 2$$ are known for which the group generated by $$\begin{bmatrix} 1 & \alpha \\ 0 & 1 \end{bmatrix}$$ and $$\begin{bmatrix} 1 & 0 \\ \alpha &1 \end{bmatrix}$$ is NOT free. The proof interestingly goes via the Brahmagupta-Pell equation."
I was unable to find references that explain this problem and attempted proofs that go through the Brahmagupta-Pell equation. Where may I be able to find some exposition of this? I did contact the author but have not received not yet received a response. If I do, I'll post it.
Thank you for your time and consideration.
* EDIT * Thank you for your comments. Dr. Sapir provided me with information that led me to using additional search criteria. The reference that I found that helps answer the question is in a paper by A.F. Beardon:
"Pell's Equation and two generator free Mobius groups" that is found in the Bull. London Math Soc. 25 (1993) 527-532.
Dr. Beardon considers irrational values of $$\alpha$$. Obviously, I haven't fully read the paper yet but it does provide another reference to a paper by Lyndon and Ullman
"Groups generated by two linear parabolic transformations", Canadian Journal of Math 21 (1969) 1388-1403
that provides insight on when this group can be free for a given rational value of $$\alpha$$.
So, thank you again! I greatly appreciated the assistance! Now I have more enjoyable (and productive) reading to do!
• I don't know what this problem was intending, but, writing $e(\alpha) = \begin{bmatrix} 1&\alpha \\ 0&1 \end{bmatrix}$ and $f(\alpha) = \begin{bmatrix} 1&0 \\ 1&1 \end{bmatrix}$, we have $\left( e(1/n)^n f(1/n)^{-n} e(1/n)^n\right)^4=\mathrm{Id}$, so there are lots of examples that don't give free groups. Nov 20 '19 at 3:00
• @DavidESpeyer I think your $f(\alpha)$ should have an $\alpha$ in position 2,1 Nov 20 '19 at 3:27
• @WillJagy Is right of course, but I'm past the edit window. Nov 20 '19 at 3:43
• Your quote doesn't look like referring to an "attempted proof thru the BP equation". It says that for some rationals in $]0,2[$ the BP equation can be used to obtain non-freeness.
– YCor
Nov 20 '19 at 8:29
• May I suggest that once you've read the references you have found that you return to summarize them as an answer. Nov 20 '19 at 21:27 | 2022-01-24 01:23:54 | {"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": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6757742166519165, "perplexity": 388.34275849846875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1642320304345.92/warc/CC-MAIN-20220123232910-20220124022910-00410.warc.gz"} |
http://www.owltestprep.com/tag/quadratic-equations/ | ## Challenge Problem 1 2016
Posted on Categories - GMAT Quant
If , which of the following is a possible value of ? (A) (B) (C) (D) (E) ... | 2017-12-15 19:38:29 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8840804696083069, "perplexity": 1904.3795464656139}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1512948579564.61/warc/CC-MAIN-20171215192327-20171215214327-00691.warc.gz"} |
https://devel.isa-afp.org/entries/Frequency_Moments.html | Formalization of Randomized Approximation Algorithms for Frequency Moments
Title: Formalization of Randomized Approximation Algorithms for Frequency Moments Author: Emin Karayel Submission date: 2022-04-08 Abstract: In 1999 Alon et. al. introduced the still active research topic of approximating the frequency moments of a data stream using randomized algorithms with minimal space usage. This includes the problem of estimating the cardinality of the stream elements - the zeroth frequency moment. But, also higher-order frequency moments that provide information about the skew of the data stream. (The k-th frequency moment of a data stream is the sum of the k-th powers of the occurrence counts of each element in the stream.) This entry formalizes three randomized algorithms for the approximation of F0, F2 and Fk for k ≥ 3 based on [1, 2] and verifies their expected accuracy, success probability and space usage. BibTeX: @article{Frequency_Moments-AFP, author = {Emin Karayel}, title = {Formalization of Randomized Approximation Algorithms for Frequency Moments}, journal = {Archive of Formal Proofs}, month = apr, year = 2022, note = {\url{https://isa-afp.org/entries/Frequency_Moments.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Bertrands_Postulate, Equivalence_Relation_Enumeration, Interpolation_Polynomials_HOL_Algebra, Lp, Median_Method, Prefix_Free_Code_Combinators, Universal_Hash_Families Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations. | 2022-05-17 03:33:08 | {"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": 0.7256302237510681, "perplexity": 1884.5015513117685}, "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-2022-21/segments/1652662515501.4/warc/CC-MAIN-20220517031843-20220517061843-00174.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-x-and-y-intercept-given-y-3x-5 | # How do you find the x and y intercept given y = 3x + 5?
Mar 10, 2018
$y = 5 \mathmr{and} x = - \frac{5}{3}$
#### Explanation:
To find x-intercept, the y value must equal to zero.
Hence,
$y = 3 x + 5$
$0 = 3 x + 5$
$- 5 = 3 x$
$- \frac{5}{3} = x$
Now to find y-intercept, the x value must equal to zero.
So,
$y = 3 x + 5$
$y = 3 \left(0\right) + 5$
$y = 5$ | 2019-12-08 20:46:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.8291103839874268, "perplexity": 2072.4580874782328}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540514893.41/warc/CC-MAIN-20191208202454-20191208230454-00235.warc.gz"} |
https://community.wolfram.com/groups/-/m/t/2260167?sortMsg=Recent | # Problems with flywheel simulation and attachment
Posted 6 months ago
1571 Views
|
6 Replies
|
2 Total Likes
|
I have a mathematical Block Model of a current controlled bldc motor, this model includes the motors parameters itself, including that of a flywheel, This model works exactly the way I expect it to, producing the same plots and dynamics as my mathematica fitted model.I would now like to separate the 'flywheel' part of this, and connect a fixed BodyShape with a Rotor1D from another multibody model I have. The intention is to study the gyroscopic effects and later develop an angular momentum controller. My assumptions where I could simply attach my mathematical model to a Torque and then the BodyShape with the parameters of the flywheel itself. I have made a working test example to attempt this, my expectations being that the motor dynamics would remain unchanged. However this appears to not be the case.I have attached the test example, plus the flywheel motor. The variable J being the inertia of the system has currently the value (0.0000135), while in the first imaged example (where the flywheel is included in the mathematical model, J would be 0.00013612480196014234 ) The test example, is what i how I planned to attach models together, namely motor -> flywheel -> fixed translation of multibody like so:In the test example, world would be the step-in for the fixed translation. How do I attach my mathematical model to the multibody one?If there is a way to simply attach my already verified mathematical model to a fixed translation in a a multi body model and then be able to study the effects, I'd also love to know how, either solution would be great however.Thanks! Attachments:
6 Replies
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Posted 5 months ago
Thank you for the resources! The book I've already started to go through, and the Web-U I will sign up for and watch.
Posted 5 months ago
Here are some materials which you would find useful: Study group: Recorded sessions of the recently concluded Study group on System Modeler (especially the session on "Introduction to Modelica") Modelica by examples: This book is shipped along with System Modeler. You can find it under Help -> Documentation Center -> Resources -> Modelica By Example Modelica in Education: You will find a list of different courses here. I found the course by Dr. Dirk Zimmer to be the most useful: Virtual Physics. The lecture slides are self-explanatory.
Posted 5 months ago
Hello Neil!Wow thank you as usual for your exceptional explanation and the examples. To get to your questions directly:Is this what you are looking for? Basically yes. My model as I said, will be a Cube satellite, with motor drive inertias, and as such (beyond the sphereical joint) what you've modelled is pretty much what each sub system (motor, controller and rotor) will end up being. Why do you want to use a "mathematical motor"?This probably requires some more explanation. To be frank, it's mostly because I don't know how to use those finished models. In the real system, I am using a EC 45 Flat motor (251601) plus their current controller (see attached PDF) from maxon motor. With the controller, I can drive the motor with a current source. Their data sheet has quite a bit of information about the motor itself, however when attempting to use the built-in model SM_PermanentMagnet and the subsequent example SMPM_CurrentSouce which at the time I assumed would be a perfect starting point. I am completely overwhelmed with how it's set up and how to give correct data compared to my real life motor and controller, that I can actually do anything with. Lmd and Lmq, LD and LQ values and most other variables which work in the example, are vastly different to the values from the data sheet and I have no current way to measure or figure them out myself, maxon as a company also refuses to give anything more than the public facing catalogue data.However, my mathematical ODE model represents the motors with their controller quite accurately, which I've verified and used for this project (https://www.youtube.com/watch?v=Lzw3ZGTuMUU) (which is one of the walls of the cube sat), and since I already had a model that does what I wanted, I decided it was the fastest route, rather than trying to hack the examples together. I would absolutely appreciate if you could show me an example of how to improve my model with the rotational flanges, or to make it more physical in any other way. When attempting myself, I realise now that mixing and matching different blocks isn't as easy as I'd hope. The rotational flange only accepts rotational connections it seems...As as side question, Do you have any suggestions for material, tutorials or likewise for the 'modelica method' you mention? It's difficult to find literature that is suited for beginners for this modeling concept, and my only experience as you accurately deduced, is simulink, which clearly isn't appropriate. Thank you again for the detailed answer, I very much appreciate the help. Attachments:
Posted 6 months ago
You have multiple issues going on. First, your motor model is problematic because it violates the Modelica modeling concept. It is more like a Simulink model -- it is one direction only -- you put a current into the motor and it responds by accelerating its inertia, however, if I were to spin the inertia, it does not generate a current. The problem with this is that external torques are not making it back into your motor so your motor is independent of the system (which violates physics).Is there a reason you do not want to use one of the built-in motor models? You can then control that motor with any control system you develop. (The control system can be all mathematical). If you want to make your own motor model, you need to have the output be a rotational flange and not a numerical output. If its a flange, then you have both speed and torque communicating through the flange and the motor behaves as you want.As far as the Gyroscope models. I can explain them:The first model is This sets an initial rotation rate in the revolute joint so that bodyCylinger2 is spinning about its axis and gravity will move the body so that it causes rotations due to gyroscopic effects (no surprise). The second model is more subtle:Here the second body is modeled with two blocks instead of one. bodyCylinder4 is a rigid body with no rotation that is attached to the swinging arm. The gyroscopic torques are provided by the rotor1D element. The rotor is given the same rotary inertia as the bodyCylinder (J= bodyCylinder4.I[1, 1]). It is spun up to the desired speed. By moving the base frame around, the appropriate torques are sent back to the rest of the structure. You can imagine the cylinder at the end as two concentric objects, one fixed and one rotating. While this appears less intuitive than the first example in which the body is modeled as one object, In some circumstances there can be some advantages with splitting it up and considering the torques separately.My suggestion is to use either gyroscope model and hook your motor to the model: (file attached)You can put a control system around the motor with blocks and sensors. Note: I chose completely random numbers for the motor so it is not what you want but it should give you a starting point.I also put the motor on the second gyroscope example model but note that I needed to put the reaction force of the motor back into the frame or the model would not be correct.Is this what you are looking for? Why do you want to use a "mathematical motor"? If you need a "Mathematical Motor" can't you output your motor to a rotational flange so it is more physical? (If this is what you want, I can show you an example).Regards,Neil Attachments:
Hello Neil! The flywheel motor model does indeed work fine. I guess perhaps my naming convention is confusing....sorry about that. I want to do one of two things, either:1) Attach my flywheel_motor_model.mo, where variable J is equal to 0.00013612480196014234 to a fixed translation and Revolute in a different multibody model and then study the gyroscopic effects. 2) or I would like to attach a mathematical motor model where J is equal to 0.000013.... we can call it current_control_motor.mo, and use it to apply a torque to the objects Bodyshape + Rotor1D, which are suppose to represent just the flywheel, which are all connected on said different multibody model, so namely, an assembly of flywheel and motor connected to the different mulitbody model.My expectations are that 1 and 2 should produce the exact same plots, which in my images they don't as you correctly say, it's likely the objects are all connected wrong and I don't get it.In the end I want to simulate a cube satellite, with flywheels connected to motors built inside, but I'm having problems, as you say with the Rotor1D, Bodyshape and how to correctly apply my mathematical motor model's torque to these objects. The flywheel in reality is 103mm in diameter, 6mm thick, 120g with an inertia tensor approx:I_11 == 0.000122/2 I_22 == 0.000122/2 I_33 == 0.000122my Expectations arecurrent_control_motor.mo gets a step signal, and with it connected to the Rotor1D, and Bodyshape they all begin to accelerate in unison as one assembly to the same top angular velocity, 400 1/s, in about 3 seconds. Currently this does not happen. As you saw, the Revolute, bodyshape and Rotor1D, and current_control_motor.mo motor all have different angular velocities. I have looked for hours at Gyroscopic3dEffects, and I don't get anywhere closer, unfortunately. | 2021-10-23 13:43:03 | {"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": 0.539966344833374, "perplexity": 914.8153702927378}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1634323585696.21/warc/CC-MAIN-20211023130922-20211023160922-00257.warc.gz"} |
https://ctan.org/ctan-ann/id/mailman.6417.1532435926.5100.ctan-ann@ctan.org | # CTAN Update: glossaries
Date: July 24, 2018 2:38:27 PM CEST
Nicola Talbot submitted an update to the glossaries package. Version: 4.41 2018-07-23 License: lppl1.3 Summary description: Create glossaries and lists of acronyms Announcement text:
- added package option kernelglossredefs (Warnings are now generated if the kernel commands \makeglossary and \glossary are used. These commands are deprecated with the glossaries package. If the originals are required, by a package or class that must be used with glossaries.sty for some reason, then use kernelglossredefs=false, but beware of other possible conflicts.) - renamed some internal commands to avoid conflict
The package’s Catalogue entry can be viewed at https://ctan.org/pkg/glossaries The package’s files themselves can be inspected at http://mirror.ctan.org/macros/latex/contrib/glossaries/
Thanks for the upload. For the CTAN Team Petra Rübe-Pugliese
We are supported by the TeX users groups. Please join a users group; see https://www.tug.org/usergroups.html .
## glossaries – Create glossaries and lists of acronyms
The glossaries package supports acronyms and multiple glossaries, and has provision for operation in several languages (using the facilities of either babel or polyglossia). New entries are defined to have a name and description (and optionally an associated symbol). Support for multiple languages is offered, and plural forms of terms may be specified. An additional package, glossaries-accsupp, can make use of the accsupp package mechanisms for accessibility support for PDF files containing glossaries.
The user may define new glossary styles, and preambles and postambles can be specified. There is provision for loading a database of terms, but only terms used in the text will be added to the relevant glossary.
The package uses an indexing program to provide the actual glossary; either makeindex or xindy may serve this purpose, and a Perl script is provided to serve as interface.
This package requires the mfirstuc package.
The package supersedes the author’s glossary package (which is now obsolete).
Package glossaries Version 4.43 2019-09-28 Copyright 2007–2019 Nicola Talbot Maintainer Nicola Talbot
more | 2019-10-19 21:51:14 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8731776475906372, "perplexity": 9439.367056875391}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986700435.69/warc/CC-MAIN-20191019214624-20191020002124-00455.warc.gz"} |
https://dvqiq.airmaxltd.de/fft-example.html | reddit vr glasses
The fast Fourier transform (FFT) is a computationally efficient method of generating a Fourier transform. The main advantage of an FFT is speed, which it gets by decreasing the number of calculations needed to analyze a waveform. ... For example, calculated directly, a DFT on 1,024 (i.e., 2 10) data points would require. n 2 = 1,024 × 1,024 = 2 20 = 1,048,576. multiplications..
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example Y = fft (X) computes the discrete Fourier transform (DFT) of X using a fast Fourier transform (FFT) algorithm. If X is a vector, then fft (X) returns the Fourier transform of the vector. If X is a matrix, then fft (X) treats the columns of X as vectors and returns the Fourier transform of each column.
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I want to perform fft on an audio signal then have leds pulse to those frequencies. I have a stm32nucleof401re, a x-nucleo mems microphone expansion board along with breadboard and leds. Any help is appreciated. Use the arm_rfft_fast_f32 () to do the FFT and then the arm_cmplx_mag_f32 () function to get the frequency magnitudes.
.
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Some IP cameras don't even allow you to access the RTSP (Real-time Streaming Protocol) stream. Other IP cameras simply don't work with OpenCV's This example is a dramatic simplification of message passing and message broker systems but should help you understand the general algorithm.
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A fast Fourier transform (fFt) would be of interest to any wishing to take a signal or data set from the time domain to the frequency domain. Materials & Prerequisites Materials. All items one needs to utilize an FFT with an Arduino are: ... You can also find an example of a custom FFT at the same place. Typically one would not code an FFT from.
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C++ (Cpp) FFT - 28 examples found. These are the top rated real world C++ (Cpp) examples of FFT extracted from open source projects. You can rate examples to help us improve the quality of examples.
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I want to perform fft on an audio signal then have leds pulse to those frequencies. I have a stm32nucleof401re, a x-nucleo mems microphone expansion board along with breadboard and leds. Any help is appreciated. Use the arm_rfft_fast_f32 () to do the FFT and then the arm_cmplx_mag_f32 () function to get the frequency magnitudes.
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Description. Demonstrates using the HTML5 Audio API to generate an FFT from a microphone and then use it to generate a displacement map that is then used to distort a plane geometry. This example demonstrates, Using a HTML5 audio analyzer to get byte frequency data from a connected microphone. Generating an off-screen canvas from the FFT data.
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Step 3: Explanation of Code: FFT Function. FFT can only be performed for the sample size of 2, 4, 8, 16, 32, 64 and so on. if the value is not 2^n, than it will take the lower side of value. For example, if we choose the sample size of 70 then it will only consider the first 64 samples and omit rest. It is always recommended to have a sample.
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Description. Demonstrates using the HTML5 Audio API to generate an FFT from a microphone and then use it to generate a displacement map that is then used to distort a plane geometry. This example demonstrates, Using a HTML5 audio analyzer to get byte frequency data from a connected microphone. Generating an off-screen canvas from the FFT data.
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The Fast Fourier Transform (FFT) is a way to reduce the complexity of the Fourier transform computation from O(n2) O ( n 2) to O(nlogn) O ( n log. . n), which is a dramatic improvement. The primary version of the FFT is one due to Cooley and Tukey. The basic idea of it is easy to see.
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Fourier Transform Examples. Here we will learn about Fourier transform with examples.. Lets start with what is fourier transform really is. Definition of Fourier Transform. The Fourier transform of $f(x)$ is denoted by $\mathscr{F}\{f(x)\}=$$F(k), k \in \mathbb{R},$ and defined by the integral :.
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A motivating example is the bit reversal permutation which is a building block of FFT The data type of the design is xed-point Reference: Xilinx AR# 17966 System Generator for DSP v13 恢复vivado工程时，回到tcl对应的目录，在linux系统下的vivado中source对应的tcl文件，就可以恢复工程，下面以gui.
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The FFT & Convolution • The convolution of two functions is defined for the continuous case - The convolution theorem says that the Fourier transform of the convolution of two functions is equal to the product of their individual Fourier transforms • We want to deal with the discrete case.
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Example of a signal in the frequency domain. The FFT is calculated in two parts. The first one transforms the original data array into a bit-reverse order array by applying the bit-reversal method. This makes the mathematical calculations of the second part "much more easy".
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the Discrete Fourier Transform (DFT) which requires $$O(n^2)$$ operations (for $$n$$ samples) the Fast Fourier Transform (FFT) which requires $$O(n.log(n))$$ operations; This tutorial does not focus on the algorithms. There’s a R function called fft() that computes the FFT. Here are two egs of use, a stationary and an increasing trajectory:.
CHAPTER 32: POLYNOMIALS AND THE FFT. The straightforward method of adding two polynomials of degree n takes ( n) time, but the straightforward method of multiplying them takes ( n2) time. In this chapter, we shall show how the Fast Fourier Transform, or FFT, can reduce the time to multiply polynomials to ( n l n ). Polynomials.
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FFT stands for Fast Fourier Transform which is just a faster algorithmic way to do a Discrete Fourier Transform[3]. 2.2 Windowing An important part of taking multiple Fourier Transforms is windowing. A window is just a given data array for which a single FFT is computed. For example let's say we have a sound wave that was sampled 2,048 times. Single Precision Floating Point.
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Using the Fast Fourier Transform ( FFT ). Making It Faster With rfft(). Filtering the Signal. The Fourier transform is a powerful tool for analyzing signals and is used in everything from audio processing to image compression. ... To run this example , unzip the directory and copy the example files (m-script and the text file) into the C-model directory which is created when the.
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A motivating example is the bit reversal permutation which is a building block of FFT The data type of the design is xed-point Reference: Xilinx AR# 17966 System Generator for DSP v13 恢复vivado工程时，回到tcl对应的目录，在linux系统下的vivado中source对应的tcl文件，就可以恢复工程，下面以gui.
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The mathematical expression for Fourier transform is: Using the above function one can generate a Fourier Transform of any expression. In MATLAB, the Fourier command returns the Fourier transform of a given function. Input can be provided to the Fourier function using 3 different syntaxes. Fourier (x): In this method, x is the time domain.
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Example - 3. Discrete Fourier Transform in 2-D. We can acquire the 2-D Fourier Transform using the scipy.fft.fft2() method. In this example, we can see how the scipy.fft2() method can be used to obtain a two-dimensional series of fourier transformations. Input.
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2D Fourier Transform 5 Separability (contd.) f(x,y) F(u,y) F(u,v) Fourier Transform along X. Fourier Transform along Y. We can implement the 2D Fourier transform as a sequence of 1-D Fourier transform operations. 2D Fourier Transform 6 Eigenfunctions of LSI Systems A function f(x,y) is an Eigenfunction of a system T if.
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FFT IN EXCEL(automatic Fourier analysis in excel) | Discrete Fourier Transform and FFT Algorithm Step by Step(link in the description) | spectral analysis📚.
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Overview . A fast Fourier transform (FFT) is a method to calculate a discrete Fourier transform (DFT). More information about FFTs and DFTs can be found on wikipedia (linked). The following circuit and code allow a user to put a signal into a PIC32, perform an FFT on that signal, output the data to Matlab via RS-232, and view a plot showing the raw signal, the FFT as calculated by the PIC, and.
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An example of this is a filter which blocks high frequencies. Calculating a Fourier transform requires understanding of integration and imaginary numbers. Computers are usually used to calculate Fourier transforms of anything but the simplest signals. The Fast Fourier Transform is a method computers use to quickly calculate a Fourier transform.
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An example is a sound wave. If someone speaks, whistles, plays an instrument, etc., to generate a sound wave, then any sample of that sound wave has a set of frequencies with amplitudes that describe that wave. ... An FFT is a "Fast Fourier Transform". The IDFT below is "Inverse DFT" and IFFT is "Inverse FFT". A DFT is a Fourier that transforms a discrete number of.
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Other applications of the DFT arise because it can be computed very efficiently by the fast Fourier transform (FFT) algorithm. For example, the DFT is used in state-of-the-art algorithms for multiplying polynomials and large integers together; instead of working with polynomial multiplication directly, it turns out to be faster to compute the.
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FFT Filtering. Here is one of the nifty things you may use fft filtering for. The laser scanning confocal microscope scans along the X axis. If there is noise in the laser, then this shows up most dramatically in adjacent X axis scans. Filtering the frequency of the alternating X axis intensities cleans up the image. Gilles Carpentier extracted.
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The Fast Fourier Transform is one of the most important topics in Digital Signal Processing but it is a confusing subject which frequently raises questions. ... it calculates the DFT of each small data set. For example, an FFT of size 32 is broken into 2 FFTs of size 16, which are broken into 4 FFTs of size 8, which are broken into 8 FFTs of.
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The fast Fourier transform (FFT) is a computationally efficient method of generating a Fourier transform. The main advantage of an FFT is speed, which it gets by decreasing the number of calculations needed to analyze a waveform..
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Supports torch.half and torch.chalf on CUDA with GPU Architecture SM53 or greater. However it only supports powers of 2 signal length in every transformed dimension. Parameters. input ( Tensor) - the input tensor. n ( int, optional) - Signal length. If given, the input will either be zero-padded or trimmed to this length before computing.
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FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when n is a power of 2, and the transform is therefore most efficient for these sizes. ... Examples >>> import scipy.fft >>> scipy. fft. fft (np. exp.
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The goals for the course are to gain a facility with using the Fourier transform, both specific techniques and general principles, and learning to recognize when, why, and how it is used. Together with a great variety, the subject also has a great coherence, and the hope is students come to appreciate both. Topics include: The Fourier transform as a tool for solving physical problems.
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When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform (DFT). The DFT has become a mainstay of numerical computing in part because of a very fast algorithm for computing it, called the Fast Fourier Transform (FFT), which was known to Gauss (1805) and was brought.
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2.Expression of Fourier transform : General form of Fourier transform is : (1) FT [ f ( r →)] = F ( f →) = ∫ − ∞ + ∞ f ( r →) e − j 2 π f → ⋅ r → d r →. Caution, vector above f → = ( f x, f y, f z) represents the spatial frequencies, also defined with wavenumber by k → = 2 π f → . In case of FT in temporal domain. | 2022-08-17 16:22:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.40819457173347473, "perplexity": 2305.1821568385785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573029.81/warc/CC-MAIN-20220817153027-20220817183027-00339.warc.gz"} |
http://mathhelpforum.com/calculus/208201-multiple-integrals3-print.html | # multiple integrals3
• Nov 22nd 2012, 09:20 PM
prasum
multiple integrals3
evaluate Attachment 25855 by changing the order of integration
it can be solved by slicing through the x plane
The given domain is $D=D_1\cup D_2$ where: $D_1\equiv \left \{ \begin{matrix}0\leq y\leq 1\\0\leq x\leq\sqrt{y}\end{matrix}\right. \;,\quad D_2\equiv \left \{ \begin{matrix}1\leq y\leq 2\\0\leq x\leq 2-y\end{matrix}\right.$ | 2016-12-07 10:16:37 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9039957523345947, "perplexity": 6023.951648946035}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1480698542009.32/warc/CC-MAIN-20161202170902-00500-ip-10-31-129-80.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/tags/packages/hot | # Tag Info
4
MnSymbol aims at changing all math symbols, using its own. For this it redefines the standard math families to use its fonts. In particular it does \DeclareSymbolFont{largesymbols} {OMX}{MnSymbolE}{m}{n} \DeclareSymbolFont{symbols} {U} {MnSymbolF}{m}{n} but these declarations are later overridden by unicode-math, so when something is using the ...
3
\lsem and \rsem are also available in the XITS font as \lBrack and \rBrack \documentclass{article} \usepackage{unicode-math} \setmathfont{XITS Math} \begin{document} $\lBrack x \rBrack$ \end{document}
3
The error says that a package used by the file is missing i.e. not installed yet on your TeX distribution. TeXstudio ask you to download and install the package. In this case, I'll say you should install it. You have to keep in mind that some TeX distribution (MikTeX for example), does not download all the package at the first install but do it when needed ...
3
Method 1: use \CMcal for the default \mathcal: \documentclass{article} \usepackage{eucal} \begin{document} $\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ $\CMcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ \end{document} Method 2: use \mathscr for the alternative script: \documentclass{article} \usepackage[mathscr]{eucal} \begin{document} ...
2
The nameauth package was designed exactly with these and similar needs in mind. Version 2.1 is what I would call "feature-complete" as well as "fault-tolerant." If you have a distribution that has not upgraded to 2.1, I highly recommend that you manually install this version in your local texmf tree. The package has a "main" interface and a "simplified" ...
2
If you use the online tool ShareLatex then this now has a built in word count: https://www.sharelatex.com/blog/2015/09/15/word-count.html
2
Very Simple Solution All you need is just define \email in your preamble as follows \documentclass{report} \usepackage[hidelinks]{hyperref} \newcommand*{\email}[1]{\href{mailto:#1}{\nolinkurl{#1}} } which defines your desired email format: monofont space, hyperlink to mail directly. you can then use the command \email, for example: ...
2
mathastext Another option is to use Jean-François Burnol's mathastext which adopts some of the letters and symbols in the document's font (or any other) for use in math environments. with fbb Here is an example using mathastext with Michael Sharpe's great fbb package (an expanded version of Bembo/Cardo), together with newtxmath using the libertine option. ...
2
The manual of titlesec and titleps does not reveal an incompatibility, but recommends to load both together as \usepackage[pagestyles]{titlesec} -- the special loading of titleps isn't necessary then. \documentclass{book} \usepackage{titling} \usepackage{lastpage} \usepackage[pagestyles]{titlesec} \newpagestyle{main} {% \sethead[\footnotesize ...
1
The document should start (like all latex documents) \documentclass{sig-alternate-05-2015} \usepackage{graphics} \begin{document} You will get a warning You have requested document class sig-alternate-05-2015', but the document class provides sig-alternate'. which you can ignore, or to stop it, edit the \ProvidesClass line in the file to say ...
1
Here is a custom headline with author's email added. I would rather not install confposter.sty which presumably defines colors jblue and jg. \documentclass{beamer} \setbeamertemplate{headline}{ \leavevmode \begin{columns} \begin{column}{\linewidth} \vskip1cm \centering \usebeamercolor{title in headline}{\Huge{\textbf{Title goes ...
1
While your wish does not seem to make sense to me if I try to understand it literally, my guess is that the problem you are experiencing is the following: From a quick glance at backref.sty, the macro \hyper@page@backref seems to be used only once: If the option hyperpageref is set, then \hyper@page@backref is copied to \backrefxxx using \let (see What is ...
1
Never mind: a \protect before \bcsmbh does the trick.
1
I had this issue, but none of the above solved it. Here is what worked: Diagnosing the Issue: I am on OSX 10.9.5 and installed BasicTex 2015 from here http://www.tug.org/mactex/morepackages.html I wanted fullpage.sty, but \usepackage{fullpage} was not working I checked my path using echo \$PATH, and /Library/TeX/texbin was the only tex related entry, so ...
1
The problem is with your installation, not updating packages. I had the same errors installing MiKTeX 2.9.5721 on windows 10 today. 2015-09-12 20:08:00,190-0400 INFO miktex-pdftex - running 'initexmf --quiet --update-fndb' to refresh the file name database 2015-09-12 20:08:00,412-0400 FATAL miktex-pdftex - The operation failed for some reason. ...
1
There is a conflict between the caption package and koomascript, which has its own tools to format captions. If you want the caption width to be equal to the figure width, you can use the measuredfigure environment from threeparttable: \documentclass{scrartcl} \usepackage{lipsum} \usepackage{graphicx} \setkomafont{caption}{\small} ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2015-12-01 09:24:05 | {"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": 2, "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": 0.906863808631897, "perplexity": 6213.949513749655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398466178.24/warc/CC-MAIN-20151124205426-00222-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://researchportal.uc3m.es/display/act480168 | # Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state-space Markov models Articles
• March 2016
• 1
• 39
• WWWW-0074
### abstract
• We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete-time state-space Markov model. The algorithm employs two layers of particle filters to approximate the posterior probability distribution of the model parameters. In particular, the first layer yields an empirical distribution of samples on the parameter space, while the filters in the second layer are auxiliary devices to approximate the (analytically intractable) likelihood of the parameters. This approach relates the this algorithm to the recent sequential Monte Carlo square (SMC2) method, which provides a {\em non-recursive} solution to the same problem. In this paper, we investigate the approximation, via the proposed scheme, of integrals of real bounded functions with respect to the posterior distribution of the system parameters. Under assumptions related to the compactness of the parameter support and the stability and continuity of the sequence of posterior distributions for the state-space model, we prove that the Lp norms of the approximation errors vanish asymptotically (as the number of Monte Carlo samples generated by the algorithm increases) and uniformly over time. We also prove that, under the same assumptions, the proposed scheme can asymptotically identify the parameter values for a class of models. We conclude the paper with a numerical example that illustrates the uniform convergence results by exploring the accuracy and stability of the proposed algorithm operating with long sequences of observations.
### keywords
• bayesian estimation; nested particle filtering schem; discrete-time state-space markkov model | 2021-03-03 12:18:12 | {"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": 0.9175335168838501, "perplexity": 313.3621254621826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1614178366959.54/warc/CC-MAIN-20210303104028-20210303134028-00346.warc.gz"} |
http://mathhelpforum.com/algebra/139469-forming-simultaneous-equations-following.html | # Thread: Forming simultaneous equations from the following?
1. ## Forming simultaneous equations from the following?
Form a pair of simultaneous equations and solve them to find x and y, given they are rational numbers.
Questions 1: x-3+√(y+2) = -1 + √5
Question 2: 1 1/2 + √(x+2y) = 3x + y + 2/3√3
Any help is appreciated
Those are 2 separate questions.
2. What you have to do is:
1) Find either x as a function of y or y as a function of x. So manipulate one of the equations till you get x=... or y=...
2) Substitute x or y in the OTHER equation and solve for the remaining variable. Now you have the value of either x or y.
3) Fill in the value for your found x or y and you'll get your second value.
Good luck!
3. Those are 2 separate questions though. I don't know how to make 2 equations out of 1.
4. Sorry my bad. Manipulate equation 1 to get $x+\sqrt{y+2}=2+\sqrt{5}$, now the answer lies in that $x,y$ are both rational.
5. Ohhh i see. Thanks (:
6. The first equation can be written as
$x=2+\sqrt{5}-\sqrt{y+2}.$
You're told that $x$ is rational, so there can't be a $\sqrt{5}$ on the RHS because this is irrational. It has to be removed, and the only way to do this is to put $y=3$, leading then to $x=2$.
The second equation can be solved using the same technique. | 2017-08-17 15:42:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7334935665130615, "perplexity": 359.29483953876917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886103579.21/warc/CC-MAIN-20170817151157-20170817171157-00400.warc.gz"} |
https://mathematica.stackexchange.com/questions/199078/image-processing-removal-of-two-spots-in-fundus-images?answertab=active | # Image processing: Removal of two spots in fundus images
I have many hundreds fundus images of the human eye.
The yellow arrow points to two spots which I I want to remove. The final result should be a perfect circle.
The removed area should be black.
I need this for image preprocessing for a machine learning project.
Any help would be great.
I think it may be interesting to preprocess the image before using @Melago's approach.
This permits to get rid of the 0.98 coefficient.
One may say that the following preprocessing introduces a new "magic" coefficient (erosionRadius = 30), but this new coefficient is less critical than the 0.98.
img00 = Import["https://i.stack.imgur.com/kUebf.jpg"]
img01 = MorphologicalBinarize[img00]
erosionRadius = 30;
m = Dilation[img02, DiskMatrix[erosionRadius]]
Note that the top and the bottom are slightly flattened. This should not have effect on the extracted "BoundingDiskRadius"
Beyong this point, @Melago's approach is used :
circ = Flatten[{#[[1]], (* 0.98 : Removed *) #[[2]]} & /@
2]], 1];
Show[img00, Graphics[{Red,Thick,Circle[circ[[1]], circ[[2]]]}]]
Related
Find the largest morphological component:
m = SelectComponents[MorphologicalComponents[img, 0.1], "Area", -1];
Get the bounding circle (with radius multiplied by 0.98 to remove the blips)
circ = Flatten[{#[[1]], .98 #[[2]]} & /@
mask = Show[Image[ConstantArray[0, Dimensions[ImageData[img]]]],
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https://par.nsf.gov/biblio/10105182-gan-em-gan-based-em-learning-framework | GAN-EM: GAN Based EM Learning Framework
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10105182
Journal Name:
International Joint Conference on Artificial Intelligence
1. Electromigration (EM) analysis for complicated interconnects requires the solving of partial differential equations, which is expensive. In this paper, we propose a fast transient hydrostatic stress analysis for EM failure assessment for multi-segment interconnects using generative adversarial networks (GANs). Our work is inspired by the image synthesis and feature of generative deep neural networks. The stress evaluation of multi-segment interconnects, modeled by partial differential equations, can be viewed as time-varying 2D-images-to-image problem where the input is the multi-segment interconnects topology with current densities and the output is the EM stress distribution in those wire segments at the given aging time. We show that the conditional GAN can be exploited to attend the temporal dynamics for modeling the time-varying dynamic systems like stress evolution over time. The resulting algorithm, called {\it EM-GAN}, can quickly give accurate stress distribution of a general multi-segment wire tree for a given aging time, which is important for full-chip fast EM failure assessment. Our experimental results show that the EM-GAN shows 6.6\% averaged error compared to COMSOL simulation results with orders of magnitude speedup. It also delivers $8.3 \times$ speedup over state-of-the-art analytic based EM analysis solver. | 2023-03-27 00:42:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.645191490650177, "perplexity": 2204.358668373169}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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-20230326235016-20230327025016-00673.warc.gz"} |
https://intelligencemission.com/free-home-electricity-generator-free-energy-of-formation.html | But I will send you the plan for it whenever you are ready. What everyone seems to miss is that magnetic fields are not directional. Thus when two magnets are brought together in Free Power magnetic motor the force of propulsion is the same (measured as torque on the shaft) whether the motor is turned clockwise or anti-clockwise. Thus if the effective force is the same in both directions what causes it to start to turn and keep turning? (Hint – nothing!) Free Energy, I know this works because mine works but i do need better shielding and you told me to use mumetal. What is this and where do you get it from? Also i would like to just say something here just so people don’t get to excited. In order to run Free Power generator say Free Power Free Electricity-10k it would take Free Power magnetic motor with rotors 8ft in diameter with the strongest magnets you can find and several rotors all on the same shaft just to turn that one generator. Thats alot of money in magnets. One example of the power it takes is this.
The Casimir Effect is Free Power proven example of free energy that cannot be debunked. The Casimir Effect illustrates zero point or vacuum state energy , which predicts that two metal plates close together attract each other due to an imbalance in the quantum fluctuations. You can see Free Power visual demonstration of this concept here. The implications of this are far reaching and have been written about extensively within theoretical physics by researchers all over the world. Today, we are beginning to see that these concepts are not just theoretical but instead very practical and simply, very suppressed.
I am doing more research for increasing power output so that it can be used in future in cars. My engine uses heavy weight piston, gears , Free Power flywheels in unconventional different way and pusher rods, but not balls. It was necessary for me to take example of ball to explain my basic idea I used in my concept. (the ball system is very much analogous to the piston-gear system I am using in my engine). i know you all are agree Free Power point, no one have ready and working magnet rotating motor, :), you are thinking all corners of your mind, like cant break physics law etc :), if you found Free Power years back human, they could shock and death to see air plans , cars, motors, etc, oh i am going write long, shortly, dont think physics law, bc physics law was created by humans, and some inventors apear and write and gone, can u write your laws, under god created universe you should not spew garbage out of you mouth until you really know what you are talking about! Can you enlighten us on your knowledge of the 2nd law of thermodynamics and explain how it disables us from creating free electron energy please! if you cant then you have no right to say that it cant work! people like you have kept the world form advancements. No “free energy magnetic motor” has ever worked. Never. Not Once. Not Ever. Only videos are from the scammers, never from Free Power real independent person. That’s why only the plans are available. When it won’t work, they blame it on you, and keep your money.
No “boing, boing” … What I am finding is that the abrupt stopping and restarting requires more energy than the magnets can provide. They cannot overcome this. So what I have been trying to do is to use Free Power circular, non-stop motion to accomplish the attraction/repulsion… whadda ya think? If anyone wants to know how to make one, contact me. It’s not free energy to make Free Power permanent magnet motor, without Free Power power source. The magnets only have to be arranged at an imbalanced state. They will always try to seek equilibrium, but won’t be able to. The magnets don’t produce the energy , they only direct it. Think, repeating decimal…..
The complex that results, i. e. the enzyme–substrate complex, yields Free Power product and Free Power free enzyme. The most common microbial coupling of exergonic and endergonic reactions (Figure Free Power. Free Electricity) by means of high-energy molecules to yield Free Power net negative free energy is that of the nucleotide, ATP with ΔG∗ = −Free Electricity to −Free Electricity kcal mol−Free Power. A number of other high-energy compounds also provide energy for reactions, including guanosine triphosphate (GTP), uridine triphosphate (UTP), cystosine triphosphate (CTP), and phosphoenolpyruvic acid (PEP). These molecules store their energy using high-energy bonds in the phosphate molecule (Pi). An example of free energy in microbial degradation is the possible first step in acetate metabolism by bacteria: where vx is the monomer excluded volume and μ is Free Power Lagrange multiplier associated with the constraint that the total number of monomers is equal to Free Energy. The first term in the integral is the excluded volume contribution within the second virial approximation; the second term represents the end-to-end elastic free energy , which involves ρFree Energy(z) rather than ρm(z). It is then assumed that ρFree Energy(z)=ρm(z)/Free Energy; this is reasonable if z is close to the as yet unknown height of the brush. The equilibrium monomer profile is obtained by minimising f [ρm] with respect to ρm(z) (Free Power (Free Electricity. Free Power. Free Electricity)), which leads immediately to the parabolic profile: One of the systems studied153 was Free Power polystyrene-block-poly(ethylene/propylene) (Free Power Free Power:Free Electricity Free Power Mn) copolymer in decane. Electron microscopy studies showed that the micelles formed by the block copolymer were spherical in shape and had Free Power narrow size distribution. Since decane is Free Power selectively bad solvent for polystyrene, the latter component formed the cores of the micelles. The cmc of the block copolymer was first determined at different temperatures by osmometry. Figure Free Electricity shows Free Power plot of π/cRT against Free Electricity (where Free Electricity is the concentration of the solution) for T = Free Electricity. Free Power °C. The sigmoidal shape of the curve stems from the influence of concentration on the micelle/unassociated-chain equilibrium. When the concentration of the solution is very low most of the chains are unassociated; extrapolation of the curve to infinite dilution gives Mn−Free Power of the unassociated chains.
I am doing more research for increasing power output so that it can be used in future in cars. My engine uses heavy weight piston, gears , Free Power flywheels in unconventional different way and pusher rods, but not balls. It was necessary for me to take example of ball to explain my basic idea I used in my concept. (the ball system is very much analogous to the piston-gear system I am using in my engine). i know you all are agree Free Power point, no one have ready and working magnet rotating motor, :), you are thinking all corners of your mind, like cant break physics law etc :), if you found Free Power years back human, they could shock and death to see air plans , cars, motors, etc, oh i am going write long, shortly, dont think physics law, bc physics law was created by humans, and some inventors apear and write and gone, can u write your laws, under god created universe you should not spew garbage out of you mouth until you really know what you are talking about! Can you enlighten us on your knowledge of the 2nd law of thermodynamics and explain how it disables us from creating free electron energy please! if you cant then you have no right to say that it cant work! people like you have kept the world form advancements. No “free energy magnetic motor” has ever worked. Never. Not Once. Not Ever. Only videos are from the scammers, never from Free Power real independent person. That’s why only the plans are available. When it won’t work, they blame it on you, and keep your money.
You did not even appear to read or understand my response in the least. I’ve told you several times that I NEVER EXPECTED ANYONE TO SEND ME ONE. You cannot seem to get this. Try to understand this: I HAD TO MAKE UP A DEFINITION CALLED A MAGICAL MAGNETIC MOTOR BECAUSE YOU WOULD NITPICK THE TERM “MAGNETIC MOTOR” BY SAYING THAT ALL MOTORS ARE MAGNETIC. Are you so delusional that you cannot understand what I am saying? Are you too intellectually challenged to understand? Are you knowingly changing the subject again to avoid answering me? Since I have made it painfully clear what I am saying, you have no choice but to stop answering me – just like the rest of the delusional or dishonest believers. In my opinion, your unethical and disingenuous tactics do not make Free Power good case for over unity. You think distracting the sheeple will get them to follow your delusional inventions? Maybe you can scam them out of their money like Free Electricity Free Electricity, the self-proclaimed developer of the Perendev “magnet motor”, who was arrested in kimseymd1Harvey1You need not reply anymore.
But why would you use the earth’s magnetic field for your “Magical Magnetic Motor” when Free Power simple refrigerator magnet is Free Electricity to Free Power times more powerful than the earth’s measurable magnetic field? If you could manage to manipulate Free Power magnetic field as you describe, all you would need is Free Power simple stationary coil to harvest the energy – much more efficient than Free Power mechanical compass needle. Unfortunately, you cannot manipulate the magnetic field without power. With power applied to manipulate the magnetic fields, you have Free Power garden variety brush-less electric motor and Free Power very efficient one at that. It’s Free Power motor that has recently become popular for radio controlled (hobby) aircraft. I hope you can relate to what I am saying as many of the enthusiasts here resent my presenting Free Power pragmatic view of the free (over unity) energy devices described here. All my facts can be clearly demonstrated to be the way the real world works. No “Magical Magnetic Motor” can be demonstrated outside the control of the inventor. Videos are never proof of anything as they can be easily faked. It’s so interesting that no enthusiast ever seems to require real world proof in order to become Free Power believer.
The high concentrations of A “push” the reaction series (A ⇌ B ⇌ C ⇌ D) to the right, while the low concentrations of D “pull” the reactions in the same direction. Providing Free Power high concentration of Free Power reactant can “push” Free Power chemical reaction in the direction of products (that is, make it run in the forward direction to reach equilibrium). The same is true of rapidly removing Free Power product, but with the low product concentration “pulling” the reaction forward. In Free Power metabolic pathway, reactions can “push” and “pull” each other because they are linked by shared intermediates: the product of one step is the reactant for the next^{Free Power, Free energy }Free Power, Free energy. “Think of Two Powerful Magnets. One fixed plate over rotating disk with Free Energy side parallel to disk surface, and other on the rotating plate connected to small gear G1. If the magnet over gear G1’s north side is parallel to that of which is over Rotating disk then they both will repel each other. Now the magnet over the left disk will try to rotate the disk below in (think) clock-wise direction. Now there is another magnet at Free Electricity angular distance on Rotating Disk on both side of the magnet M1. Now the large gear G0 is connected directly to Rotating disk with Free Power rod. So after repulsion if Rotating-Disk rotates it will rotate the gear G0 which is connected to gear G1. So the magnet over G1 rotate in the direction perpendicular to that of fixed-disk surface. Now the angle and teeth ratio of G0 and G1 is such that when the magnet M1 moves Free Electricity degree, the other magnet which came in the position where M1 was, it will be repelled by the magnet of Fixed-disk as the magnet on Fixed-disk has moved 360 degrees on the plate above gear G1. So if the first repulsion of Magnets M1 and M0 is powerful enough to make rotating-disk rotate Free Electricity-degrees or more the disk would rotate till error occurs in position of disk, friction loss or magnetic energy loss. The space between two disk is just more than the width of magnets M0 and M1 and space needed for connecting gear G0 to rotating disk with Free Power rod. Now I’ve not tested with actual objects. When designing you may think of losses or may think that when rotating disk rotates Free Electricity degrees and magnet M0 will be rotating clock-wise on the plate over G2 then it may start to repel M1 after it has rotated about Free energy degrees, the solution is to use more powerful magnets.
Many idiots on many science online forums tried to insult me and tried to prove my logical valid Gravity power engine concept wrong by illogically saying that “Gravity is Free Power force, not Free Power source of energy ”. How foolish that idiot’s statement appears to be. Interesting posts, pro and con. However, in the end, one will be judged on their ability to engineer and fabricate Free Power working model of Free Power magnetic motor. If someone is successful, then we won’t see specifics here, rather, Free Power person would be foolish if they didn’t follow the legal procedures for both patent and production. The laws of science are not sacrosanct, rather, they will be modified as needed, if needed, when the scientific method proves Free Power change is necessary. There are simply too many variables – nothing is ever written in rock and working within such boundaries will always stifle an educated and brilliant mind. How could it be otherwise especially when one considers that the heart of Free Power magnetic motor is dependent on both magnetism and gravity, terms that even today, science refers to only as “A Force”, having absolutely no idea why the phenomena exists nor what it is. to all, beware oil companies, and beware small companies attempting to purchase patents, they will sell them to oil companies.
Any ideas on my magnet problem? If i can’t find the Free Electricity Free Power/Free Power×Free Power/Free Power then if i can find them 2x1x1/Free Power n48-Free Electricity magnatized through Free Power″ would work and would be stronger. I have looked at magnet stores and ebay but so far nothing. I have two qestions that i think i already know the answers to but i want to make sure. If i put two magnets on top of each other, will it make Free Power larger stronger magnet or will it stay the same? Im guessing the same. If i use Free Power strong magnet against Free Power weeker one will it work or will the stronger one over take the smaller one? Im guessing it will over take it. Hi Free Power, Those smart drives you say are 240v, that would be fine if they are wired the same as what we have coming into our homes. Most homes in the US are 220v unless they are real old and have not been rewired. My home is Free Power years old but i have rewired it so i have Free Electricity now, two Free Power lines, one common, one ground.
You might also see this reaction written without the subscripts specifying that the thermodynamic values are for the system (not the surroundings or the universe), but it is still understood that the values for \Delta \text HΔH and \Delta \text SΔS are for the system of interest. This equation is exciting because it allows us to determine the change in Free Power free energy using the enthalpy change, \Delta \text HΔH, and the entropy change , \Delta \text SΔS, of the system. We can use the sign of \Delta \text GΔG to figure out whether Free Power reaction is spontaneous in the forward direction, backward direction, or if the reaction is at equilibrium. Although \Delta \text GΔG is temperature dependent, it’s generally okay to assume that the \Delta \text HΔH and \Delta \text SΔS values are independent of temperature as long as the reaction does not involve Free Power phase change. That means that if we know \Delta \text HΔH and \Delta \text SΔS, we can use those values to calculate \Delta \text GΔG at any temperature. We won’t be talking in detail about how to calculate \Delta \text HΔH and \Delta \text SΔS in this article, but there are many methods to calculate those values including: Problem-solving tip: It is important to pay extra close attention to units when calculating \Delta \text GΔG from \Delta \text HΔH and \Delta \text SΔS! Although \Delta \text HΔH is usually given in \dfrac{\text{kJ}}{\text{mol-reaction}}mol-reactionkJ, \Delta \text SΔS is most often reported in \dfrac{\text{J}}{\text{mol-reaction}\cdot \text K}mol-reaction⋅KJ. The difference is Free Power factor of 10001000!! Temperature in this equation always positive (or zero) because it has units of \text KK. Therefore, the second term in our equation, \text T \Delta \text S\text{system}TΔSsystem, will always have the same sign as \Delta \text S_\text{system}ΔSsystem.
I do not fear any conspiracy from any nook & corner. I am simply taking my time and my space to stage the inevitable confrontation in the frozen face of the industry and geopolitics tycoons. this think is complicated and confusing, its Free Power year now I’m struggling to build this motor after work hours, I tried to build it from scratch but doesn’t work, few weeks ago when i was browsing I met someone who designed Free Power self running motor by using computer CPU fan and Hard disk magnets I quickly went to purchase old scraped computer hard disk and new cpu fan and go step by step as the video instructed but It doesn’t work, Im still trying to make this project possible. Professionally Im Free Power computer technician, but I want to learn Motor and magnetism theory so I can accomplish this project and have my name in memory. I anyone can make this project please contact me through facebook so I can invite him/her to my country and make money as you know third word countries has power disaster. My facebook Id is Elly Maduhu Nkonya, or use my E-mail. [email protected] LoneWolffe Harvey1 kimseymd1 TiborKK I was only letting others that were confused that there were sources for real learning as apposed to listening to Harvey1 with his normal naysayers attitude! There is tons of information on schoolgirl, schoolboy and Bedini window motors that actually work to charge batteries and eventually will generate house currents. It just has to be looked at to get any useful information from it without listening to people like Harvey1 whining about learning. Harvey1 kimseymd1 You obviously play too much video games with trolls etc. in them. Why the editors of this forum allow you to keep calling people names instead of following the subject is beyond me. This must be the last site to allow you on it. I spammed the books because I thought those people were good for learning these engines which are super and there are tons of information out there for anyone to find. You seem to only want to learn to be rude instead of electronics. | 2021-06-21 07:19:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5773610472679138, "perplexity": 1647.2214251805876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488268274.66/warc/CC-MAIN-20210621055537-20210621085537-00152.warc.gz"} |
https://brilliant.org/problems/go-round-and-round/ | # Go Round and Round
Calculus Level 3
In the figure, the radii of the red circle and the blue circle are 3 and 10, respectively, and the distance between their centers is 5.
The black circle is externally tangent to the red circle and internally tangent to the blue circle. The path traced by the center of the black circles is a closed curve whose area is $$X\pi.$$
What is $$X?$$
× | 2019-01-22 15:45:33 | {"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": 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": 0.4749010503292084, "perplexity": 178.40100688046417}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1547583857913.57/warc/CC-MAIN-20190122140606-20190122162606-00274.warc.gz"} |
https://euler.stephan-brumme.com/615/ | # Problem 615: The millionth number with at least one million prime factors
Consider the natural numbers having at least 5 prime factors, which don't have to be distinct.
Sorting these numbers by size gives a list which starts with:
32 = 2 * 2 * 2 * 2 * 2
48 = 2 * 2 * 2 * 2 * 3
64 = 2 * 2 * 2 * 2 * 2 * 2
72 = 2 * 2 * 2 * 3 * 3
80 = 2 * 2 * 2 * 2 * 5
96 = 2 * 2 * 2 * 2 * 2 * 3
...
So, for example, the fifth number with at least 5 prime factors is 80.
Find the millionth number with at least one million prime factors.
# My Algorithm
Based on the example I figured out pretty soon that most of the "one million prime factors" will be 2s.
The one millionth prime number is 15485863, therefore the smallest number with at least one million prime factors cannot exceed 2^999999 * 15485863 (see tooLarge).
I assumed that all but the last 32 prime factors will be 2s (in fact I later found empirically that all but the last 27 must be 2s).
A minimum-priority-queue, that means smallest numbers first, is initialized with 2^32 (later changed to 2^27).
Then I pick and remove the smallest number current one million times and:
• "append a prime": multiply current by p where p will be any of the first million primes - but this time I take care that p is no smaller than the largest prime factor of current
• "replace a prime": replace one of the 2s of current by p where p will be any of the first million primes - but this time I take care that p is no smaller than the largest prime factor of current (same condition as above)
• if the new numbers exceed the limit mentioned above, then I continue with the next number
After one million iterations the priority queue's top() element will be the smallest number with at least 32 (later reduced to 27) prime factors.
Obviously I can't multiply that number by 2^{1000000-32} with C++ native data types.
However, only the residue modulo 123454321 is asked for:
(a * b) mod m = ((a mod m) * (b mod m)) mod m
Multiplying that number 999968 times by 2 while repeatedly applying modulo 123454321 seems to be pretty slow
but GCC does an amazing job at optimizing this loop and it finished in a few milliseconds.
## Note
The code was slightly modified after I submitted the correct result: initially, I had an std::set<Number> candidates which spent most of the time allocating (and freeing) memory.
The std::priority_queue is about twice as fast when its internal container is an std::vector.
Most of the one million primes will never be used so I looked for the smallest prime that still produces the correct result:
Starting with 173207, which is the 15770th prime, instead of 15485863 brings down the execution time to about one third of a second (see #define FAST).
I found that number solely by trial'n'error.
There is probably a smarter way to avoid the duplicates in candidates but I wasn't willing to spend much time on it.
# Interactive test
This feature is not available for the current problem.
# My code
… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too.
#include <iostream>
#include <vector>
#include <queue>
#include <deque>
#include <functional>
#include <set>
// ---------- a few routines from my toolbox ----------
// odd prime numbers are marked as "true" in a bitvector
std::vector<bool> sieve;
// return true, if x is a prime number
bool isPrime(unsigned int x)
{
// handle even numbers
if ((x & 1) == 0)
return x == 2;
// lookup for odd numbers
return sieve[x >> 1];
}
// find all prime numbers from 2 to size
void fillSieve(unsigned int size)
{
// store only odd numbers
const unsigned int half = size >> 1;
// allocate memory
sieve.resize(half, true);
// 1 is not a prime number
sieve[0] = false;
// process all relevant prime factors
for (unsigned int i = 1; 2*i*i < half; i++)
// do we have a prime factor ?
if (sieve[i])
{
// mark all its multiples as false
unsigned int current = 3*i+1;
while (current < half)
{
sieve[current] = false;
current += 2*i+1;
}
}
}
// ---------- problem-specific code ----------
// a tiny wrapper for a number and its largest prime factor
struct Number
{
unsigned long long value; // a number
unsigned int largestFactor; // and its largest prime factor
// for std::greater / min-queue
bool operator>(const Number& other) const
{
return value > other.value;
}
};
int main()
{
unsigned int numCandidates = 1000000;
std::cin >> numCandidates;
const unsigned int Modulo = 123454321;
// generate the first million prime numbers
unsigned int maxPrime = 15485863; // http://www.wolframalpha.com/input/?i=1000000th+prime
#define FAST
#ifdef FAST
if (numCandidates <= 1000000)
maxPrime = 173207; // empirically determined limit
#endif
// compute enough prime numbers
fillSieve(maxPrime + 1);
// copy prime numbers to a consecutive array (just for faster access)
std::vector<unsigned int> primes = { 2 };
primes.reserve(numCandidates);
for (unsigned int i = 3; i <= maxPrime; i += 2)
if (isPrime(i))
primes.push_back(i);
// empirically determined
unsigned int numVariableFactors = 27;
if (numCandidates < 27)
numVariableFactors = numCandidates; // for live-test
unsigned long long seed = 1 << numVariableFactors;
// create one million numbers with exactly 27 prime factors of the form prime*2^26
std::priority_queue<Number, std::vector<Number>, std::greater<Number>> candidates;
candidates.push({ seed, 2 });
// currently 1000000th number (there are a few smaller numbers that need to be discovered now)
auto tooLarge = seed / 2 * primes.back(); // largest number in the candidates container
// detect duplicates
unsigned long long previous = 0;
// look at the candidates in ascending order
for (unsigned int numProcessed = 0; numProcessed < numCandidates; numProcessed++)
{
// pick next number
auto i = candidates.top();
auto current = i.value;
candidates.pop();
// skip duplicates
while (current == previous)
{
i = candidates.top();
current = i.value;
candidates.pop();
}
auto maxFactor = i.largestFactor;
previous = current;
// "append" a prime to the current candidate
for (auto p : primes)
{
auto next = current * p;
if (next >= tooLarge)
break;
if (p >= maxFactor)
candidates.push({ next, p });
}
// replace a 2 by a prime (pretty much the same loop, only "next" is computed slightly different)
for (auto p : primes)
{
auto next = (current / 2) * p;
if (next >= tooLarge)
break;
if (p >= maxFactor && p > 2) // no use in replacing 2 by 2
candidates.push({ next, p });
}
}
// pick the 1000000th number
unsigned int result = candidates.top().value % Modulo;
// multiply by 2^1000000 (except for the 27x 2's "used")
for (unsigned int i = numVariableFactors; i < numCandidates; i++)
result = (result * 2) % Modulo; // I thought that simple loop would be slow (because of "expensive" modulo),
// but GCC converts it to impressively fast code !
std::cout << result << std::endl;
return 0;
}
This solution contains 24 empty lines, 30 comments and 9 preprocessor commands.
# Benchmark
The correct solution to the original Project Euler problem was found in 0.3 seconds on an Intel® Core™ i7-2600K CPU @ 3.40GHz.
Peak memory usage was about 37 MByte.
(compiled for x86_64 / Linux, GCC flags: -O3 -march=native -fno-exceptions -fno-rtti -std=gnu++11 -DORIGINAL)
See here for a comparison of all solutions.
Note: interactive tests run on a weaker (=slower) computer. Some interactive tests are compiled without -DORIGINAL.
# Changelog
December 4, 2017 submitted solution
# Heatmap
Please click on a problem's number to open my solution to that problem:
green solutions solve the original Project Euler problem and have a perfect score of 100% at Hackerrank, too yellow solutions score less than 100% at Hackerrank (but still solve the original problem easily) gray problems are already solved but I haven't published my solution yet blue solutions are relevant for Project Euler only: there wasn't a Hackerrank version of it (at the time I solved it) or it differed too much orange problems are solved but exceed the time limit of one minute or the memory limit of 256 MByte red problems are not solved yet but I wrote a simulation to approximate the result or verified at least the given example - usually I sketched a few ideas, too black problems are solved but access to the solution is blocked for a few days until the next problem is published [new] the flashing problem is the one I solved most recently
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The 310 solved problems (that's level 12) had an average difficulty of 32.6% at Project Euler and
I scored 13526 points (out of 15700 possible points, top rank was 17 out of ≈60000 in August 2017) at Hackerrank's Project Euler+.
My username at Project Euler is stephanbrumme while it's stbrumme at Hackerrank.
Look at my progress and performance pages to get more details.
more about me can be found on my homepage, especially in my coding blog.
some names mentioned on this site may be trademarks of their respective owners.
thanks to the KaTeX team for their great typesetting library ! | 2018-08-15 01:58:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32095491886138916, "perplexity": 278.1609221572523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1534221209755.32/warc/CC-MAIN-20180815004637-20180815024637-00424.warc.gz"} |
https://hal.archives-ouvertes.fr/hal-01305011 | # Probing the CO and methanol snow lines in young protostars. Results from the CALYPSO IRAM-PdBI survey
6 FORMATION STELLAIRE 2016
LAB - Laboratoire d'Astrophysique de Bordeaux [Pessac]
Abstract : Context. "Snow lines", marking regions where abundant volatiles freeze out onto the surface of dust grains, play an important role for planet growth and bulk composition in protoplanetary disks. They can already be observed in the envelopes of the much younger, low-mass Class 0 protostars that are still in their early phase of heavy accretion. Aims. We aim at using the information on the sublimation regions of different kinds of ices to understand the chemistry of the envelope, its temperature and density structure, and the history of the accretion process. Methods. As part of the CALYPSO IRAM Large Program, we have obtained observations of C$^{18}$O, N$_2$H$^+$ and CH$_3$OH towards nearby Class 0 protostars with the IRAM Plateau de Bure interferometer at sub-arcsecond resolution. For four of these sources we have modeled the emission using a chemical code coupled with a radiative transfer module. Results. We observe an anti-correlation of C$^{18}$O and N$_2$H$^+$ in NGC 1333-IRAS4A, NGC 1333-IRAS4B, L1157, and L1448C, with N$_2$H$^+$ forming a ring around the centrally peaked C$^{18}$O emission due to N$_2$H$^+$ being chemically destroyed by CO. The emission regions of models and observations match for a CO binding energy of 1200 K, which is higher than the binding energy of pure CO ices ($\sim$855 K). Furthermore, we find very low CO abundances inside the snow lines in our sources, about an order of magnitude lower than the total CO abundance observed in the gas on large scales in molecular clouds before depletion sets in. Conclusions. The high CO binding energy may hint at CO being frozen out in a polar ice environment like amorphous water ice or in non-polar CO$_2$-rich ice. The low CO abundances are comparable to values found in protoplanetary disks, which may indicate an evolutionary scenario where these low values are already established in the protostellar phase. (Abbr. Version)
Type de document :
Article dans une revue
Astronomy and Astrophysics - A&A, EDP Sciences, 2016, 591, pp.id.A3
https://hal.archives-ouvertes.fr/hal-01305011
Contributeur : Marie-Paule Pomies <>
Soumis le : mercredi 20 avril 2016 - 15:26:51
Dernière modification le : mercredi 19 septembre 2018 - 01:29:15
### Citation
S., Anderl, S., Maret, S., Cabrit, A., Belloche, A. J., Maury, et al.. Probing the CO and methanol snow lines in young protostars. Results from the CALYPSO IRAM-PdBI survey. Astronomy and Astrophysics - A&A, EDP Sciences, 2016, 591, pp.id.A3. 〈hal-01305011〉
### Métriques
Consultations de la notice | 2018-09-20 18:15:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.4696103632450104, "perplexity": 8520.265068573843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156554.12/warc/CC-MAIN-20180920175529-20180920195929-00126.warc.gz"} |
https://cstheory.stackexchange.com/questions/46964/proof-that-optimal-solutions-of-lp-relaxation-of-independent-set-are-half-integr/46982 | # Proof that optimal solutions of LP Relaxation of independent set are half-integral
I saw somewhere that optimal solutions of LP Relaxation of independent set are half-integral, by what I mean the possible values of a solution are $${ \{0,0.5,1 \} }$$. I'm looking for proof of that.
Someone in this topic LP relaxation of independent set seems to make use of it.
And here http://www-sop.inria.fr/members/Frederic.Havet/Cours/fractional.pdf is a proof for vertex-cover, which is close, but nothing is mentioned about independent set.
Does anyone know a proof of that?
The LP in question is a maximization over a bounded polytope, hence the optimal value is attained at a vertex of the polytope. Moreover, any vertex can be described as a unique solution of a system of linear equations obtained by replacing inequalities with equalities in a subset of the inequalities defining the problem. Here, the polytope is defined by \begin{align*} 0\le x_i&\le1,&&i\in V,\\ x_i+x_j&\le1,&&\{i,j\}\in E, \end{align*} hence the vertex is defined by the equations \begin{align*} x_i&=0,&&i\in V_0,\\ x_i&=1,&&i\in V_1,\\ x_i+x_j&=1,&&\{i,j\}\subseteq E' \end{align*} for some $$V_0,V_1\subseteq V$$ and $$E'\subseteq E$$, such that this system has a unique solution. Now, the latter immediately implies that $$x_i\in\{0,1/2,1\}$$: if $$\vec x$$ is any solution, then $$\vec x'$$ defined by $$x'_i=\begin{cases} x_i,&\text{if }x_i\in\{0,1\},\\ 1-x_i,&\text{if }0 is also a valid solution, hence $$\vec x=\vec x'$$ by uniqueness.
Moreover, if the graph is bipartite with partitions $$A$$ and $$B$$, then $$x''_i=\begin{cases} x_i,&\text{if }x_i\in\{0,1\},\\ 0,&\text{if }0 is also a valid solution, hence $$x_i\in\{0,1\}$$.
• Nice proof, thank you. – Neal Young Jun 2 '20 at 15:51
• So $V_0, V_1$ are sets that represent values of vertices with values $0$ and $1$ respectively? I still don't know how $x_i+x_j=1, \{i,j\}\subseteq E'$ implies values $\{0,1/2,1\}$ – Jakub Jabłoński Jun 3 '20 at 14:35
• You need the additional property that the linear system has a unique solution to imply values in $\{0,1/2,1\}$. – Emil Jeřábek Jun 3 '20 at 17:21
• Jakub, the argument for that is in the proof given in the answer, following "the latter immediately implies that $x_i\in\{0, 1/2, 1\}$:" And e.g. $V_0$ is defined as the set of vertices $i$ for which the equation $x_i=0$ is in the set of equations that defines the vertex of the polytope. That is not (a-priori) the same as the set of vertices for which $x_i$ is $0$, because conceivably $x_i$ could be $0$ even though that is not one of the defining equations. (Although the rest of the proof establishes that that cannot happen.) – Neal Young Jun 4 '20 at 19:40
• I can't understand why the latter (which I suppose refers to $E'\subseteq E$) immediately implies that. Supposing possible values are $0,1/3,2/3,1$, it would still satisfy the equations. – Jakub Jabłoński Jun 7 '20 at 12:37
This is discussed in a related cstheory post:
LP relaxation of independent set
That post cites this publication:
[1] Nemhauser, G.L., Trotter, L.E. Vertex packings: Structural properties and algorithms. Mathematical Programming 8, 232–248 (1975). https://doi.org/10.1007/BF01580444
That publication in turn cites a few others, including these:
[2] Balinski, M. (1970). ON MAXIMUM MATCHING, MINIMUM COVERING AND THEIR CONNECTIONS. In KUHN H. (Ed.), Proceedings of the Princeton Symposium on Mathematical Programming (pp. 303-312). Princeton, New Jersey: Princeton University Press. https://doi.org/10.2307/j.ctt13x0wct.16
[3] Nemhauser, G.L., Trotter, L.E. Properties of vertex packing and independence system polyhedra. Mathematical Programming 6, 48–61 (1974). https://doi.org/10.1007/BF01580222
[4] Leslie Earl Trotter. 1973. Solution characteristics and algorithms for the vertex packing problem. Ph.D. Dissertation. Cornell University, USA. Order Number: AAI7406323.
You can look through these. From a quick scan of the first three it didn't seem obvious which contained a proof. If I recall, one can prove that for bipartite graphs there are optimal integer solutions (by considering the underlying max flow problem), and then, to prove the existence of a half-integral optimum for any general graph, convert it into a bipartite graph by making two copies of each node in a natural way and applying the result for bipartite graphs. Maybe there are simpler ways to go about it.
BTW, this kind of reference request, which you can answer yourself by taking some time to do a web search, is probably not an appropriate question for this forum, which is for research-level questions in TCS. | 2021-07-28 17:08:16 | {"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": 14, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8762781620025635, "perplexity": 592.0884097657454}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1627046153739.28/warc/CC-MAIN-20210728154442-20210728184442-00544.warc.gz"} |
https://math.eretrandre.org/tetrationforum/showthread.php?tid=876 | Negative, Fractional, and Complex Hyperoperations KingDevyn Junior Fellow Posts: 2 Threads: 2 Joined: May 2014 05/30/2014, 06:58 AM Is there a way to continue the patterns we see within the natural numbers of current hyper-operations (Hyper-1, Hyper-2, Hyper-3, Hyper-4, ect...) or at least prove that we cannot extend the value of the operation to fractional numbers? E.g. Hyper-1/2. Negative numbers? E.g. Hyper-(-2) Or even imaginary numbers? E.g. Hyper-3i. They need not be defined, but are these operations technically there, just without practical use? Or are our names for the hyper-operations strictly for listing and naming purposes, with no way to derive meaning from such a number? Could a fractional, or negative hyper-operation represent an operator we have already defined? E.g. Hyper-(-2)= Division, or Hyper-1/2 = Division? Comments on the controversy of Zeration are also encouraged. Thanks! MphLee Long Time Fellow Posts: 368 Threads: 28 Joined: May 2013 05/30/2014, 07:57 AM (This post was last modified: 05/30/2014, 07:58 AM by MphLee.) $s$-rank hyperoperations have meaning as long as we can iterate $s$ times a function $\Sigma$ defined in the set of the binary functions over the naturals numbers (or defined over a set of binary functions.) let me explain why. There are many differente Hyperoperations sequences, end they are all defined in a different way: we start with an operation $*$ and we obtain its successor operation $*'$ applying a procedure $\Sigma$ (usually a recursive one). $\Sigma(*)=*'$ So every Hyperoperation sequence is obtained applying that recursive procedure $\Sigma$ to a base operation $*$ (aka the first step of the sequence) $*_0:=*$ $*_1:=\Sigma(*_0)$ $*_2:=\Sigma(\Sigma(*_0))$ and so on or in a formal way $*_0:=*$ $*_{n+1}:=\Sigma(*_n)$ That is the same as $*_{n}:=\Sigma^{\circ n}(*_{0})$ so if we can extend the iteration of $\Sigma^{\circ n}$ from $n \in \mathbb{N}$ to the real-complex numbers the work is done. ---------------------- MSE MphLee Mother Law $$(\sigma+1)0=\sigma (\sigma+1)$$ S Law $$\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)$$ MphLee Long Time Fellow Posts: 368 Threads: 28 Joined: May 2013 05/30/2014, 08:19 AM (This post was last modified: 05/30/2014, 08:22 AM by MphLee.) I'm not sure but I think that bo198214(Henrik Trappmann) had this idea in 2008 http://math.eretrandre.org/tetrationforu...l+function With his idea we can reduce the problem of real-rank hyperoperations to an iteration problem Later this idea was better developed by JmsNxn (2011) with the concept of "meta-superfunctions" http://math.eretrandre.org/tetrationforu...hp?tid=708 I'm still working on his point of view but there is a lot of work to do... MSE MphLee Mother Law $$(\sigma+1)0=\sigma (\sigma+1)$$ S Law $$\bigcirc_f^{\lambda}\square_f^{\lambda^+}(g)=\square_g^{\lambda}\bigcirc_g^{\lambda^+}(f)$$ « Next Oldest | Next Newest »
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Users browsing this thread: 1 Guest(s) | 2023-02-03 06:13:08 | {"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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 17, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8073614239692688, "perplexity": 4504.463083054683}, "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/1674764500044.16/warc/CC-MAIN-20230203055519-20230203085519-00816.warc.gz"} |
https://gamedev.stackexchange.com/questions/139590/how-to-set-emission-level-through-c | # How to set emission level through C#
I am willing to change emission level thorough code without effecting its color.
(ie. changing the brightness number shown in the box at the right side of the inspector, while keeping the emission colour swatch unchanged)
I have tried this so far, but I don't know how to use my value variable to update the material:
public class EmissionColourChange : MonoBehaviour {
Material thisMat;
Color c;
public float value;
void Start () {
thisMat = GetComponent<Renderer>().material;
c = GetComponent<Renderer>().material.color;
thisMat.EnableKeyword("_EMISSION");
value = c.r;
}
void Update () {
thisMat.SetColor("_EmissionColor", new Color(c.r,c.g,c.b));
}
}
• What is not working? – jgallant Apr 5 '17 at 9:52
• Your code (copied exactly) works on my machine. Is the script enabled / applied to the game object? – Zebraman May 11 '17 at 17:33
You're bang on for a low-dynamic range emissive colour. To get access to brighter emission we need to move to a high-dynamic range, which is outside the range of the Color type.
So, we replace it with a Vector:
thisMat.SetColor("_EmissionColor", new Vector4(c.r,c.g,c.b,0) * value);
Now you have access to make the colour as bright as you want by increasing the multiplier value. This is what changes the number shown to the right of the emission colour swatch in the inspector.
Note that the colour & value you put in isn't exactly the parameters you'll see in the material inspector when you look at the result. Because we're mixing together the colour and brightness level, Unity has to tease them apart again to show in the inspector. It looks like it does that by setting the multiplier value equal the greatest component of the colour (R, G, or B), then divides the colour by that. So you'll still have:
myColour * myBrightnessMultiplier = inspectorColour * inspectorBrightnessMultiplier
it just might pick a different way of splitting the brightness representation between the two parts. The rendering math should all come out the same.
If you take the time to look at the color to give to the Emission field, you will see that it uses the HSV Color model (hue, saturation, and lightness), not the "traditional" RGB one.
Make sure the lightness value of your color is > 0 if you want the emission to be visible.
• I doubt this is the cause of the issue. Once you've constructed a Color struct, it doesn't matter whether you chose the parameters in RGB or HSV colour space - the SetColor method sees only the resulting Color instance. (And in fact, the Color struct only has an RGB or RGBA constructor, no HSV option is presented) – DMGregory Apr 5 '17 at 16:59
• You are right @DMGregory, but if the lightness value of the color is 0, then, the emission won't be visible. – Hellium Apr 6 '17 at 5:35 | 2019-08-24 07:20:23 | {"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": 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": 0.36645373702049255, "perplexity": 1703.275596489306}, "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-2019-35/segments/1566027319915.98/warc/CC-MAIN-20190824063359-20190824085359-00464.warc.gz"} |
http://openstudy.com/updates/5613351be4b06b0895996afe | ## Empty one year ago Complex 'fractions'
1. anonymous
can't wait to see this!
2. Empty
Since $\frac{a}{b} = a^1 b^{-1}$ We can see that in the complex plane these exponents are 180 degrees apart. $1 = e^{i \pi*0}$$-1 = e^{i \pi * 1}$ Similarly, does a number with exponents that are 120 degrees apart have meaning? $\omega = e^{i 2 \pi /3}$ $a^1 b^\omega c^{\omega^2}$
3. Empty
My instinct is to say that these could represent a ratio of things like: $A \cdot H_2O \longrightarrow B \cdot H_2 + C \cdot O_2$ Of course we already have linear algebra for that, although idk if it would quite be the same or not or if this is useful or interesting. Anyways just throwing this out there see if anyone knows or has any ideas.
4. Empty
A cool property you have is cancellation like in normal fractions. $\frac{ax}{ay} = \frac{x}{y}$ We can see this from the complex view as: $(ax)^1(ay)^{-1} = a^{1-1} x^1y^{-1}=x^1y^{-1}$ Which for a "three way fraction" gives us: $(ax)^1(ay)^\omega(az)^{\omega^2} = a^{1+\omega+\omega^2}x^1y^\omega z^{\omega^2}=x^1y^\omega z^{\omega^2}$ So pretty cool.
5. Empty
Similarly with fractions when you multiply them their tops and bottoms combine, so maybe graphically it will be more interesting to write it: |dw:1444100145825:dw| Also I'll draw out the thing like we had before: |dw:1444100188976:dw|
6. Empty
ok what about adding do we get anything out of this thing worth while. I feel like this is just becoming vector spaces without negative numbers or something, just playing around though bored.
Find more explanations on OpenStudy | 2016-10-24 01:53:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9920769929885864, "perplexity": 2635.48171824936}, "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-2016-44/segments/1476988719463.40/warc/CC-MAIN-20161020183839-00181-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/239074/state-space-model-parameter-estimate | # State space model parameter estimate
I'm working on one project trying to reconstruct a sequence of multivariate signal data from another sequence of multivariate signal data. That is let $\{S_t\}_{t=1}^n$ be the first sequence of signals, where each $S_t$ is a m-by-1 vector and $\{r_t\}_{t=1}^n$ be the second sequence of signals, where each $r_t$ is a n-by-1 vector, we are trying to estimate $\{S_t\}_{t=1}^n$ using $\{r_t\}_{t=1}^n$.
For now, I'm modeling this problem as $\begin{cases}S_t=\phi_1S_{t-1}+\cdots+\phi_pS_{t-p}+\epsilon_t\\ r_t=\psi_0S_t+\psi_1S_{t-1}+\cdots+\psi_{p-1}S_{t-p+1}+\eta_t \end{cases}$, where $\epsilon_t\sim N(0,\Sigma_\epsilon)$, and $\eta_t\sim N(0,\Sigma_\eta)$ and they are independent of each other. And all the $\phi_i$'s and $\psi_i$'s are matrices.
By letting $\xi_t=\begin{bmatrix}S_t\\ S_{t-1}\\\vdots\\S_{t-p+1} \end{bmatrix}=\begin{bmatrix}\phi_1&\cdots&\phi_{p-1}&\phi_p\\ I &\cdots&0&0\\ \vdots&\cdots &\vdots&\vdots\\ 0&\cdots &I&0\end{bmatrix}\begin{bmatrix}S_{t-1}\\S_{t-2}\\ \vdots\\ S_{t-p} \end{bmatrix}+\begin{bmatrix}\epsilon_t\\\epsilon_{t-1}\\\vdots\\\epsilon_{t-p+1} \end{bmatrix}$, I converted the first equation into $\xi_t=F\xi_{t-1}+\mathscr{E_t}$. And the second equation can be written as $r_t=G\xi_t+\eta_t$, where $G=\begin{bmatrix}\psi_0&\cdots&\psi_{p-1} \end{bmatrix}$. Combining these two equations, I got $\begin{cases}\xi_t=F\xi_{t-1}+\mathscr{E_t}\\ r_t=G\xi_t+\eta_t \end{cases}$. This resembles a Kalman filter where I treat $S_t$ as latent variables. However, I'm having trouble estimating these coefficients including the variance-covariance matrices of $\mathscr{E_t}$ and $\eta_t$.
My data set consists of two parts, where the first part (the training data set) I can actually observe both $r_t$'s and $S_t$'s while in the second part (the testing data set) I can only observe $r_t$'s. However, I think in the standard setting of a Kalman filter, we do not need to observe the actual values of the latent variables to estimate the coefficients. So how can I make use of this extra piece of information to estimate the coefficients better in the training data set and estimate $S_t$ using these estimated coefficients and new observed $r_t$'s to predict $S_t$'s in the testing data set.
Thank you! | 2019-12-08 12:50:01 | {"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": 0.9813228845596313, "perplexity": 152.34311021723258}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540510336.29/warc/CC-MAIN-20191208122818-20191208150818-00555.warc.gz"} |
https://elibm.org/article/10000061 | ## On the Chow groups of quadratic Grassmannians
### Summary
Summary: In this text we get a description of the Chow-ring (modulo 2) of the Grassmanian of the middle-dimensional planes on arbitrary projective quadric. This is only a first step in the computation of the, so-called, generic discrete invariant of quadrics. This generic invariant contains the "splitting pattern" and "motivic decomposition type" invariants as specializations. Our computation gives an important invariant $J(Q)$ of the quadric Q. We formulate a conjecture describing the canonical dimension of Q in terms of $J(Q)$.
### Mathematics Subject Classification
11E04, 14C15, 14M15
### Keywords/Phrases
quadrics, Chow groups, grassmannians, Steenrod operations | 2022-08-15 19:53:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7666112184524536, "perplexity": 1497.4228221256499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00143.warc.gz"} |
https://en.wikipedia.org/wiki/Bell_polynomials | # Bell polynomials
For a different family of polynomials Bn(x) occasionally called Bell polynomials, see Touchard polynomials.
In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. They also occur in many applications, such as in the Faà di Bruno's formula.
## Bell polynomials
### Exponential Bell polynomials
The partial or incomplete exponential Bell polynomials are a triangular array of polynomials given by
${\displaystyle B_{n,k}(x_{1},x_{2},\dots ,x_{n-k+1})=\sum {n! \over j_{1}!j_{2}!\cdots j_{n-k+1}!}\left({x_{1} \over 1!}\right)^{j_{1}}\left({x_{2} \over 2!}\right)^{j_{2}}\cdots \left({x_{n-k+1} \over (n-k+1)!}\right)^{j_{n-k+1}},}$
where the sum is taken over all sequences j1, j2, j3, ..., jnk+1 of non-negative integers such that these two conditions are satisfied:
${\displaystyle j_{1}+j_{2}+\cdots +j_{n-k+1}=k,}$
${\displaystyle j_{1}+2j_{2}+3j_{3}+\cdots +(n-k+1)j_{n-k+1}=n.}$
The sum
${\displaystyle B_{n}(x_{1},\dots ,x_{n})=\sum _{k=1}^{n}B_{n,k}(x_{1},x_{2},\dots ,x_{n-k+1})}$
is called the nth complete exponential Bell polynomial.
### Ordinary Bell polynomials
Likewise, the partial ordinary Bell polynomial, in contrast to the usual exponential Bell polynomial defined above, is given by
${\displaystyle {\hat {B}}_{n,k}(x_{1},x_{2},\ldots ,x_{n-k+1})=\sum {\frac {k!}{j_{1}!j_{2}!\cdots j_{n-k+1}!}}x_{1}^{j_{1}}x_{2}^{j_{2}}\cdots x_{n-k+1}^{j_{n-k+1}},}$
where the sum runs over all sequences j1, j2, j3, ..., jnk+1 of non-negative integers such that
${\displaystyle j_{1}+j_{2}+\cdots +j_{n-k+1}=k,}$
${\displaystyle j_{1}+2j_{2}+\cdots +(n-k+1)j_{n-k+1}=n.}$
The ordinary Bell polynomials can be expressed in the terms of exponential Bell polynomials:
${\displaystyle {\hat {B}}_{n,k}(x_{1},x_{2},\ldots ,x_{n-k+1})={\frac {k!}{n!}}B_{n,k}(1!\cdot x_{1},2!\cdot x_{2},\ldots ,(n-k+1)!\cdot x_{n-k+1}).}$
In general, Bell polynomial refers to the exponential Bell polynomial, unless otherwise explicitly stated.
## Combinatorial meaning
The exponential Bell polynomial encodes the information related to the ways a set can be partitioned. For example, if we consider a set {A, B, C}, it can be partitioned into two non-empty, non-overlapping subsets, which is also referred to as parts or blocks, in 3 different ways:
{{A}, {B, C}}
{{B}, {A, C}}
{{C}, {B, A}}
Thus, we can encode the information regarding these partitions as
${\displaystyle B_{3,2}(x_{1},x_{2})=3x_{1}x_{2}.}$
Here, the subscripts of B3,2 tells us that we are considering the partitioning of set with 3 elements into 2 blocks. The subscript of each xi indicates the presence of block with i elements (or block of size i) in a given partition. So here, x2 indicates the presence of a block with two elements. Similarly, x1 indicates the presence of a block with a single element. The exponent of xij indicates that there are j such blocks of size i in a single partition. Here, since both x1 and x2 has exponent 1, it indicates that there is only one such block in a given partition. The coefficient of the monomial indicates how many such partitions there are. For our case, there are 3 partitions of a set with 3 elements into 2 blocks, where in each partition the elements are divided into two blocks of sizes 1 and 2.
Since any set can be divided into a single block in only one way, the above interpretation would mean that Bn,1 = xn. Similarly, since there is only one way that a set with n elements be divided into n singletons, Bn,n = x1n.
As a more complicated example, consider
${\displaystyle B_{6,2}(x_{1},x_{2},x_{3},x_{4},x_{5})=6x_{5}x_{1}+15x_{4}x_{2}+10x_{3}^{2}.}$
This tells us that if a set with 6 elements is divided into 2 blocks, then we can have 6 partitions with blocks of size 1 and 5, 15 partitions with blocks of size 4 and 2, and 10 partitions with 2 blocks of size 3.
Note that the sum of the subscripts in a monomials is equal to the total number of elements. Thus, the number of monomials that appear in the partial Bell polynomial is equal to the number of ways the integer n can be expressed as a summation of k positive integers. This is the same as the integer partition of n into k parts. For instance, in the above examples, the integer 3 can be partitioned into two parts as 2+1 only. Thus, there is only one monomial in B3,2. However, the integer 6 can be partitioned into two parts as 5+1, 4+2, and 3+3. Thus, there are three monomials in B6,2. Indeed, the subscripts of the variables in a monomial are the same as those given by the integer partition, indicating the sizes of the different blocks. The total number of monomials appearing in a complete Bell polynomial Bn is thus equal to the total number of integer partitions of n.
Also note that the degree of each monomial, which is the sum of the exponents of each variable in the monomial, is equal to the number of blocks the set is divided into. That is, j1 + j2 + ... = k . Thus, given a complete Bell polynomial Bn, we can separate the partial Bell polynomial Bn,k by collecting all those monomials with degree k.
Finally, if we disregard the sizes of the blocks and put all xi = x, then the summation of the coefficients of the partial Bell polynomial Bn,k will give the total number of ways that a set with n elements can be partitioned into k blocks, which is the same as the Stirling numbers of the second kind. Also, the summation of all the coefficients of the complete Bell polynomial Bn will give us the total number of ways a set with n elements can be partitioned into non-overlapping subsets, which is the same as the Bell number.
In general, if the integer n is partitioned into a sum in which "1" appears j1 times, "2" appears j2 times, and so on, then the number of partitions of a set of size n that collapse to that partition of the integer n when the members of the set become indistinguishable is the corresponding coefficient in the polynomial.
### Examples
For example, we have
${\displaystyle B_{6,2}(x_{1},x_{2},x_{3},x_{4},x_{5})=6x_{5}x_{1}+15x_{4}x_{2}+10x_{3}^{2}}$
because there are
6 ways to partition a set of 6 as 5 + 1,
15 ways to partition a set of 6 as 4 + 2, and
10 ways to partition a set of 6 as 3 + 3.
Similarly,
${\displaystyle B_{6,3}(x_{1},x_{2},x_{3},x_{4})=15x_{4}x_{1}^{2}+60x_{3}x_{2}x_{1}+15x_{2}^{3}}$
because there are
15 ways to partition a set of 6 as 4 + 1 + 1,
60 ways to partition a set of 6 as 3 + 2 + 1, and
15 ways to partition a set of 6 as 2 + 2 + 2.
## Properties
### Generating function
The exponential partial Bell polynomials can be defined by the double series expansion of its generating function:
{\displaystyle {\begin{aligned}\Phi (t,u)&=\exp \left(u\sum _{j=1}^{\infty }x_{j}{\frac {t^{j}}{j!}}\right)=\sum _{n,k\geq 0}B_{n,k}(x_{1},\ldots ,x_{n-k+1}){\frac {t^{n}}{n!}}u^{k}\\&=1+\sum _{n=1}^{\infty }{\frac {t^{n}}{n!}}\left\{\sum _{k=1}^{n}u^{k}B_{n,k}(x_{1},\ldots ,x_{n-k+1})\right\}\end{aligned}}}
In other words, by what amounts to the same, by the series expansion of the exponential:
${\displaystyle {\frac {1}{k!}}\left(\sum _{j=1}^{\infty }x_{j}{\frac {t^{j}}{j!}}\right)^{k}=\sum _{n=k}^{\infty }B_{n,k}(x_{1},\ldots ,x_{n-k+1}){\frac {t^{n}}{n!}},\qquad k=0,1,2,\ldots }$
The complete exponential Bell polynomial is defined by ${\displaystyle \Phi (t,1)}$, or in other words:
${\displaystyle \Phi (t,1)=\exp \left(\sum _{j=1}^{\infty }x_{j}{\frac {t^{j}}{j!}}\right)=\sum _{n=0}^{\infty }B_{n}(x_{1},\ldots ,x_{n}){\frac {t^{n}}{n!}}.}$
Thus, the n-th complete Bell polynomial is given by
${\displaystyle B_{n}(x_{1},\ldots ,x_{n})=\left.{\frac {\mathrm {d} ^{n}}{\mathrm {d} t^{n}}}\exp \left(\sum _{j=1}^{\infty }x_{j}{\frac {t^{j}}{j!}}\right)\right|_{t=0}.}$
Likewise, the ordinary partial Bell polynomial can be defined by the generating function
${\displaystyle {\hat {\Phi }}(t,u)=\exp(u\sum _{j=1}^{\infty }x_{j}t^{j})=\sum _{k\leq n}{\hat {B}}_{n,k}(x_{1},\ldots ,x_{n-k+1})t^{n}{\frac {u^{k}}{k!}}.}$
Or, equivalently, by series expansion of the exponential
${\displaystyle \left(\sum _{j=1}^{\infty }x_{j}t^{j}\right)^{k}=\sum _{n=k}^{\infty }{\hat {B}}_{n,k}(x_{1},\ldots ,x_{n-k+1})t^{n}.}$
### Recurrence relations
The complete Bell polynomials can be recursively defined as,
${\displaystyle B_{n+1}(x_{1},\ldots ,x_{n+1})=\sum _{i=0}^{n}{n \choose i}B_{n-i}(x_{1},\ldots ,x_{n-i})x_{i+1},}$
with the initialization ${\displaystyle B_{0}=1}$.
The partial Bell polynomials can also be computed efficiently by a recursion relation
${\displaystyle B_{n,k}=\sum _{i=1}^{n-k+1}{\binom {n-1}{i-1}}x_{i}B_{n-i,k-1}}$
where ${\displaystyle B_{0,0}=1;}$ ${\displaystyle B_{n,0}=0\;\mathrm {for} \;n\geq 1;}$ ${\displaystyle B_{0,k}=0\;\mathrm {for} \;k\geq 1.}$
The complete Bell polynomials also satisfy the binomial type relation
${\displaystyle B_{n}(x_{1}+y_{1},\ldots ,x_{n}+y_{n})=\sum _{i=0}^{n}{n \choose i}B_{n-i}(x_{1},\ldots ,x_{n-i})B_{i}(y_{1},\ldots ,y_{i}).}$
### Determinant form
The complete Bell polynomial can be expressed as a determinant, as given by
${\displaystyle B_{n}(x_{1},\dots ,x_{n})=\det {\begin{bmatrix}x_{1}&{n-1 \choose 1}x_{2}&{n-1 \choose 2}x_{3}&{n-1 \choose 3}x_{4}&{n-1 \choose 4}x_{5}&\cdots &\cdots &x_{n}\\\\-1&x_{1}&{n-2 \choose 1}x_{2}&{n-2 \choose 2}x_{3}&{n-2 \choose 3}x_{4}&\cdots &\cdots &x_{n-1}\\\\0&-1&x_{1}&{n-3 \choose 1}x_{2}&{n-3 \choose 2}x_{3}&\cdots &\cdots &x_{n-2}\\\\0&0&-1&x_{1}&{n-4 \choose 1}x_{2}&\cdots &\cdots &x_{n-3}\\\\0&0&0&-1&x_{1}&\cdots &\cdots &x_{n-4}\\\\0&0&0&0&-1&\cdots &\cdots &x_{n-5}\\\\\vdots &\vdots &\vdots &\vdots &\vdots &\ddots &\ddots &\vdots \\\\0&0&0&0&0&\cdots &-1&x_{1}\end{bmatrix}}.}$
### Stirling numbers and Bell numbers
The value of the Bell polynomial Bn,k(x1,x2,...) on the sequence of factorials equals an unsigned Stirling number of the first kind:
${\displaystyle B_{n,k}(0!,1!,\dots ,(n-k)!)=c(n,k)=|s(n,k)|=\left[{n \atop k}\right].}$
The value of the Bell polynomial Bn,k(x1,x2,...) on the sequence of ones equals a Stirling number of the second kind:
${\displaystyle B_{n,k}(1,1,\dots ,1)=S(n,k)=\left\{{n \atop k}\right\}.}$
The sum of these values gives the value of the complete Bell polynomial on the sequence of ones:
${\displaystyle B_{n}(1,1,\dots ,1)=\sum _{k=1}^{n}B_{n,k}(1,1,\dots ,1)=\sum _{k=1}^{n}\left\{{n \atop k}\right\},}$
which is the nth Bell number.
### Inverse relations
If we define
${\displaystyle y_{n}=\sum _{k=1}^{n}B_{n,k}(x_{1},\ldots ,x_{n-k+1}),}$
then we have the inverse relationship
${\displaystyle x_{n}=\sum _{k=1}^{n}(-1)^{k-1}(k-1)!B_{n,k}(y_{1},\ldots ,y_{n-k+1}).}$
### Touchard polynomials
Main article: Touchard polynomials
Touchard polynomial ${\displaystyle T_{n}(x)=\sum _{k=0}^{n}\left\{{n \atop k}\right\}\cdot x^{k}}$ can be expressed as the value of the complete Bell polynomial on all arguments being x:
${\displaystyle T_{n}(x)=B_{n}(x,x,\dots ,x).}$
### Convolution identity
For sequences xn, yn, n = 1, 2, ..., define a sort of convolution by:
${\displaystyle (x{\mathbin {\diamondsuit }}y)_{n}=\sum _{j=1}^{n-1}{n \choose j}x_{j}y_{n-j}.}$
Note that the bounds of summation are 1 and n − 1, not 0 and n .
Let ${\displaystyle x_{n}^{k\diamondsuit }\,}$ be the nth term of the sequence
${\displaystyle \displaystyle \underbrace {x{\mathbin {\diamondsuit }}\cdots {\mathbin {\diamondsuit }}x} _{k\ \mathrm {factors} }.\,}$
Then
${\displaystyle B_{n,k}(x_{1},\dots ,x_{n-k+1})={x_{n}^{k\diamondsuit } \over k!}.\,}$
For example, let us compute ${\displaystyle B_{4,3}(x_{1},x_{2})}$. We have
${\displaystyle x=(x_{1}\ ,\ x_{2}\ ,\ x_{3}\ ,\ x_{4}\ ,\dots )}$
${\displaystyle x{\mathbin {\diamondsuit }}x=(0,\ 2x_{1}^{2}\ ,\ 6x_{1}x_{2}\ ,\ 8x_{1}x_{3}+6x_{2}^{2}\ ,\dots )}$
${\displaystyle x{\mathbin {\diamondsuit }}x{\mathbin {\diamondsuit }}x=(0\ ,\ 0\ ,\ 6x_{1}^{3}\ ,\ 36x_{1}^{2}x_{2}\ ,\dots )}$
and thus,
${\displaystyle B_{4,3}(x_{1},x_{2})={\frac {(x{\mathbin {\diamondsuit }}x{\mathbin {\diamondsuit }}x)_{4}}{3!}}=6x_{1}^{2}x_{2}.}$
## Other identities
• ${\displaystyle B_{n,k}(1!,2!,\ldots ,(n-k+1)!)={\binom {n-1}{k-1}}{\frac {n!}{k!}}=L(n,k)}$ which gives the Lah number
• ${\displaystyle B_{n,k}(1,2,3,\ldots ,n-k+1)={\binom {n}{k}}k^{n-k}}$ which gives the idempotent number
## Examples
The first few complete Bell polynomials are:
{\displaystyle {\begin{aligned}B_{0}={}&1,\\[8pt]B_{1}(x_{1})={}&x_{1},\\[8pt]B_{2}(x_{1},x_{2})={}&x_{1}^{2}+x_{2},\\[8pt]B_{3}(x_{1},x_{2},x_{3})={}&x_{1}^{3}+3x_{1}x_{2}+x_{3},\\[8pt]B_{4}(x_{1},x_{2},x_{3},x_{4})={}&x_{1}^{4}+6x_{1}^{2}x_{2}+4x_{1}x_{3}+3x_{2}^{2}+x_{4},\\[8pt]B_{5}(x_{1},x_{2},x_{3},x_{4},x_{5})={}&x_{1}^{5}+10x_{2}x_{1}^{3}+15x_{2}^{2}x_{1}+10x_{3}x_{1}^{2}+10x_{3}x_{2}+5x_{4}x_{1}+x_{5}\\[8pt]B_{6}(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6})={}&x_{1}^{6}+15x_{2}x_{1}^{4}+20x_{3}x_{1}^{3}+45x_{2}^{2}x_{1}^{2}+15x_{2}^{3}+60x_{3}x_{2}x_{1}\\&{}+15x_{4}x_{1}^{2}+10x_{3}^{2}+15x_{4}x_{2}+6x_{5}x_{1}+x_{6},\\[8pt]B_{7}(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7})={}&x_{1}^{7}+21x_{1}^{5}x_{2}+35x_{1}^{4}x_{3}+105x_{1}^{3}x_{2}^{2}+35x_{1}^{3}x_{4}\\&{}+210x_{1}^{2}x_{2}x_{3}+105x_{1}x_{2}^{3}+21x_{1}^{2}x_{5}+105x_{1}x_{2}x_{4}\\&{}+70x_{1}x_{3}^{2}+105x_{2}^{2}x_{3}+7x_{1}x_{6}+21x_{2}x_{5}+35x_{3}x_{4}+x_{7}.\end{aligned}}}
## Applications
### Faà di Bruno's formula
Faà di Bruno's formula may be stated in terms of Bell polynomials as follows:
${\displaystyle {d^{n} \over dx^{n}}f(g(x))=\sum _{k=1}^{n}f^{(k)}(g(x))B_{n,k}\left(g'(x),g''(x),\dots ,g^{(n-k+1)}(x)\right).}$
Similarly, a power-series version of Faà di Bruno's formula may be stated using Bell polynomials as follows. Suppose
${\displaystyle f(x)=\sum _{n=1}^{\infty }{a_{n} \over n!}x^{n}\qquad \mathrm {and} \qquad g(x)=\sum _{n=1}^{\infty }{b_{n} \over n!}x^{n}.}$
Then
${\displaystyle g(f(x))=\sum _{n=1}^{\infty }{\sum _{k=1}^{n}b_{k}B_{n,k}(a_{1},\dots ,a_{n-k+1}) \over n!}x^{n}.}$
In particular, the complete Bell polynomials appear in the exponential of a formal power series:
${\displaystyle \exp \left(\sum _{n=1}^{\infty }{a_{n} \over n!}x^{n}\right)=\sum _{n=0}^{\infty }{B_{n}(a_{1},\dots ,a_{n}) \over n!}x^{n},}$
which also represents the exponential generating function of the complete Bell polynomials on a fixed sequence of arguments ${\displaystyle a_{1},a_{2},\dots }$.
### Reversion of series
Let two functions f and g be expressed in formal power series as
${\displaystyle f(w)=\sum _{k=0}^{\infty }f_{k}{\frac {w^{k}}{k!}},\qquad \mathrm {and} \qquad g(z)=\sum _{k=0}^{\infty }g_{k}{\frac {z^{k}}{k!}},}$
such that g is the compositional inverse of f defined by g(f(w)) = w or f(g(z)) = z. If f0 = 0 and f1 ≠ 0, then an explicit form of the coefficients of the inverse can be given in term of Bell polynomials as [1]
${\displaystyle g_{n}={\frac {1}{f_{1}^{n}}}\sum _{k=1}^{n-1}(-1)^{k}n^{\bar {k}}B_{n-1,k}({\hat {f}}_{1},{\hat {f}}_{2},\ldots ,{\hat {f}}_{n-k}),\qquad n\geq 2,}$
with ${\displaystyle {\hat {f}}_{k}={\frac {f_{k+1}}{(k+1)f_{1}}},}$ and ${\displaystyle n^{\bar {k}}=n(n+1)\cdots (n+k-1)}$ is the rising factorial, and ${\displaystyle g_{1}={\frac {1}{f_{1}}}.}$
### Asymptotic expansion of Laplace-type integrals
Consider the integral of the form
${\displaystyle I(\lambda )=\int _{a}^{b}e^{-\lambda f(x)}g(x)\mathrm {d} x,}$
where (a,b) is a real (finite or infinite) interval, λ is a large positive parameter and the functions f and g are continuous. Let f have a single minimum in [a,b] which occurs at x=a. Assume that as x→a+,
${\displaystyle f(x)\sim f(a)+\sum _{k=0}^{\infty }a_{k}(x-a)^{k+\alpha },}$
${\displaystyle g(x)\sim \sum _{k=0}^{\infty }b_{k}(x-a)^{k+\beta -1},}$
with α > 0, Re(β) > 0; and that the expansion of f can be term wise differentiated. Then, Laplace-Erdelyi theorem states that the asymptotic expansion of the integral I(λ) is given by
${\displaystyle I(\lambda )\sim e^{-\lambda f(a)}\sum _{n=0}^{\infty }\Gamma {\Big (}{\frac {n+\beta }{\alpha }}{\Big )}{\frac {c_{n}}{\lambda ^{(n+\beta )/\alpha }}}\qquad \mathrm {as} \quad \lambda \rightarrow \infty ,}$
where the coefficients cn are expressible in terms of an and bn using partial ordinary Bell polynomials, as given by Campbell-Froman-Walles-Wojdylo formula:
${\displaystyle c_{n}={\frac {1}{\alpha a_{0}^{(n+\beta )/\alpha }}}\sum _{k=0}^{n}b_{n-k}\sum _{j=0}^{k}{\binom {-{\frac {n+\beta }{\alpha }}}{j}}{\frac {1}{a_{0}^{j}}}{\hat {B}}_{k,j}(a_{1},a_{2},\ldots ,a_{k-j+1}).}$
### Symmetric polynomials
Main article: Newton identities
The elementary symmetric polynomial ${\displaystyle e_{n}}$ and the power sum symmetric polynomial ${\displaystyle p_{n}}$ can be related to each other using Bell polynomials as:
${\displaystyle e_{n}={\frac {(-1)^{n}}{n!}}B_{n}(s_{1},s_{2},\ldots ,s_{n}),~~~~~~~~\qquad \mathrm {where} \qquad s_{l}=-(l-1)!p_{l},}$
${\displaystyle p_{n}={\frac {(-1)^{n-1}}{(n-1)!}}\sum _{k=1}^{n}(-1)^{k-1}(k-1)!B_{n,k}(e_{1},2!e_{2},3!e_{3},\ldots ,(n-k+1)!e_{n-k+1}).}$
This fact allows us to express the coefficients of monic polynomials in term the Bell polynomials of its roots. For instance, this can be applied with Cayley-Hamilton theorem to obtain the determinant of a n × n square matrix A in terms of its trace [2]
${\displaystyle \det(A)={\frac {(-1)^{n}}{n!}}B_{n}(s_{1},s_{2},\ldots ,s_{n}),~\qquad \mathrm {where} \qquad s_{l}=-(l-1)!\mathrm {tr} (A^{l}).}$
### Cycle index of symmetric groups
Main article: Cycle index
The cycle index of the symmetric group ${\displaystyle S_{n}}$ can be expressed in terms of complete Bell polynomials as follows:
${\displaystyle Z(S_{n})={\frac {B_{n}(0!\,a_{1},1!\,a_{2},\dots ,(n-1)!\,a_{n})}{n!}}.}$
### Moments and cumulants
The sum
${\displaystyle \mu _{n}'=B_{n}(\kappa _{1},\dots ,\kappa _{n})=\sum _{k=1}^{n}B_{n,k}(\kappa _{1},\dots ,\kappa _{n-k+1})}$
is the nth raw moment of a probability distribution whose first n cumulants are κ1, ..., κn. In other words, the nth moment is the nth complete Bell polynomial evaluated at the first n cumulants. Likewise, the nth cumulant can be given in terms of the moments as
${\displaystyle \kappa _{n}=\sum _{k=1}^{n}(-1)^{k-1}(k-1)!B_{n,k}(\mu '_{1},\ldots ,\mu '_{n-k+1}).}$
### Hermite polynomials
The probabilists' Hermite polynomials can be expressed in terms of Bell polynomials as
${\displaystyle He_{n}(x)=B_{n}(x,-1,0,\ldots ,0),}$
where xi = 0 for all i > 2; thus allowing for a combinatorial interpretation of the coefficients of the Hermite polynomials. This can be seen by comparing the generating function of the Hermite polynomials
${\displaystyle \exp \left(xt-{\frac {t^{2}}{2}}\right)=\sum _{n=0}^{\infty }{\mathit {He}}_{n}(x){\frac {t^{n}}{n!}}}$
with that of Bell polynomials.
### Representation of polynomial sequences of binomial type
For any sequence a1, a2, …, an of scalars, let
${\displaystyle p_{n}(x)=\sum _{k=1}^{n}B_{n,k}(a_{1},\dots ,a_{n-k+1})x^{k}.}$
Then this polynomial sequence is of binomial type, i.e. it satisfies the binomial identity
${\displaystyle p_{n}(x+y)=\sum _{k=0}^{n}{n \choose k}p_{k}(x)p_{n-k}(y).}$
Example: For a1 = … = an = 1, the polynomials ${\displaystyle p_{n}(x)}$ represent Touchard polynomials.
More generally, we have this result:
Theorem: All polynomial sequences of binomial type are of this form.
If we define a formal power series
${\displaystyle h(x)=\sum _{k=1}^{\infty }{a_{k} \over k!}x^{k},}$
then for all n,
${\displaystyle h^{-1}\left({d \over dx}\right)p_{n}(x)=np_{n-1}(x).}$
## Software
Bell polynomials are implemented in: | 2017-03-30 04:53:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 77, "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": 0.911959171295166, "perplexity": 329.5190700658553}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218191986.44/warc/CC-MAIN-20170322212951-00527-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.allaboutcircuits.com/news/reader-question-what-do-you-wish-you-had-on-your-bench/ | If you could build your dream bench, what would you put on it? Share what's on your bench and what you'd add if you could.
From the most basic setup for building an electronics lab at home to the most advanced research lab, everyone's bench looks a little different. Most have basic tools on hand and some have the most cutting-edge equipment available. From soldering guns to multimeters, spec ans to waveform generators, solderless breadboards to basic components, everyone's needs are a little different.
If you could add any piece of equipment or hardware on your bench—or upgrade it—what would it be?
Tell us about your bench, in its present form and its ideal form, in the comments below.
Have a question you'd like to ask the community? Let us know in the comments.
• Mark Hughes 2018-04-20
If cost was no option, a bench top pick and place, reflow oven, and X-ray machine. (I have a big workbench).
• davegsc 2018-04-20
I have a great soldering station, several fixed and variable power supplies, one decent and several cheap multimeters, a shop-built reflow oven, a fine selection of components.
A really good, oscilloscope would take my bench to a whole new level. It wouldn’t have to be a full-color, top drawer unit but ideally, if it came with 2+ Channel, 8+ bits, 100+Mhz, I would be very appreciative and SO hap, hap, happy!
Thank you!
Dave Davies
• Robin Mitchell 2018-04-20
What would I wish for?
Well that is a very good question and hard to answer! Firstly, as things stand, I can make all the projects that I need to without too many problems but having said that, I find my scopes lacking. They are all analogue types with the fastest one being 20MHz so a Digital Storage Oscilloscope would be wonderful. The scope itself would not even need to be that powerful since 100MHz would do just about everything I need it to do.
Another piece of equipment that would be sweet would be a LAN Power supply that can both log power usage and supply it all over LAN! I remember using one at my last workplace and the machine was absolutely fab!
With regards to soldering stations, what I have is plentiful and enough which is a cheap $20 iron. While BGA are obviously out of the question my iron is suitable enough for many SMD parts. If I had to choose ONE thing it would be the scope hands down mainly because I could build my own IoT power supply if I wanted to (in fact I made a simple version on Maker.Pro). • RK37 2018-04-20 I already have a good oscilloscope, and that covers pretty much all of my measurement needs. A variable DC power supply would be handy from time to time, but I’m with Mark, the most valuable addition would be anything that helps me to assemble boards that include surface-mount components. • Mark Hughes 2018-04-20 @rk37, 1-hour with @jrap’s credit card and I’ll make all our dreams come true. • Raymond Genovese 2018-04-21 I would not mind a nice 3D printer - could probably keep me out of trouble for a while. • chris.n 2018-04-21 Probably a VNA. I’ve been brushing up on my RF skills and playing with SDR and I keep thinking “I could test that if I had a VNA.” • -live wire- 2018-04-22 I would want a 500V 1kA cc/cv power supply. I would want a variety of different welding tools. A good soldering iron and very good ventilation. I would want a huge selection of components. I would want a multi-channel 100GHz scope. I would want an arbitrary waveform generator, CC/CV that can supply a few hundred watts at least. I would also want 100GHz one. I would want a scope-like multimeter that you can program to give you different readings. I would want a huge induction heater. I would want to also have a lot of mechanical parts for robotics things. Ideally huge li-po batteries too. I would want access to the 3-phase industrial power for my stuff. I would also want a high-voltage generator where you can get HVDC, HVAC, at various freq. and voltages. This is what I’d get if I was a billionaire. What I have now: a simple multimeter, some useful components, a soldering station, microcontrollers, and a few breadboards. I will probably be getting more important tools soon, but I will probably never get any of the stuff above unless I get really lucky. • ndavis17 2018-04-23 My bench currently includes two DMMs, an o-scope (though it’s borrowed), a small reflow over (again, borrowed), a DC power supply, a very nice microscope (by AmScope), a nice Metcal soldering station, a heat gun, a USB logic analyzer, and a bench-wide ESD mat. My shopping list includes my own o-scope along with a current probe and a high-voltage differential probe, my own reflow oven, a pick-n-place machine, a high-resolution camera for my microscope, a 3D printer, another bench (or two), more shelves/storage, and more lighting. • mrhat2010 2018-04-25 My own desk is just my computer since I moved my stuff to my local hackerspace, but there are a few power supplies (one variable, the rest fixed), one 100MHz scope, a few low price and one decent multimeter, two 3d printers and several soldering irons. What I would be overjoyed to have here are a reflow oven, a microscope for soldering, one better multimeter, a signal generator and a few RF specific tools like a VNA and a signal analyzer. • cqtsdss 2018-04-26 I already have many of the instruments I have always dreamed of, but have the feeling I don’t really give them the use I expected to do. Anyway, I have never had a Logic Analizer neither a good Spectrum Analyzer. But the tool I have always been waiting for and never found is “TIME”. To use all the “toys” I have been gathering trough the years. • renesis 2018-04-27 First of all, i would want a much bigger bench. And a much bigger room in a much bigger house to put it in • renesis 2018-04-27 Weird, only the first part of my comment got posted. Tldr; i have a lot of nice stuff, but im missing a good DMM, a reflow oven, fume extraction, and a sick speaker system for my working tunes;) • SarahD 2018-04-27 I wish someone made a 2ch Spectrum Analyser (with a decent size screen) for just Audio Frequency (0-22000Hz). Analysers are inherantly costly as they require very tight tolerance compnents to accurately analyse HF’s (up the Ghz & Thz range), an AF Analyser wouldn’t need the HF ability, so less circuitry, and a lower clock speed (200Hz or so) and so would be a lot more affordable. • Phil-S 2018-04-27 Barn-sized workshop with decent benches, LAN, plenty of sockets, component and tool organisers. Working with data buses and wireless, a logic analyser and spectrum analyser would be nice. To play with? A three axis CNC, large or small would be nice and maybe a 3D printer to see what all the fuss is about • jlachance 2018-04-27 My bench contains a mixture of old and new. I have two Tektronix o-scopes (rescued from the salvage pile) and a newer DSO. (Oddly enough, I use the old analog scopes more frequently!) Let’s see, a modern DMM and an old analog VTVM, a new 3-channel programmable power supply, and vintage Heathkit gear - capacitor tester, signal tracer and RF signal generator. I have a good microscope and a reflow oven I built using guidance from an All About Circuits article published sometime back. I have very good soldering stations but could use a decent desoldering tool. I lack a spectrum analyzer and a precise and accurate RF signal generator. Those would be my three wishes. Oh, and a 5kW dummy load. And an in-circuit capacitor tester. And… • Copper dog 2018-04-27 Besides the usual mix of test leads, multi meters storage etc. my lab is equipped with two variable power supplies, a function generator, normal and hot air soldering stations, a coding station, Kinsten KVB-300 UV light box, heated etching tank and a 2 channel 100MHz scope. What I would dearly love( in preferential order) is a good PCB drill press, a proper printer for making exposure masks, an airflow oven and while we’re at it a quality 3D printer. I wouldn’t turn down a frequency counter, a good waveform generator and my white board never seems to be big enough. • Rookietron 2018-04-27 (1) Multiple plug-in power sources (5V, 9V, 12 V, 5-24V), (2) Oscilloscope ($35), (3) Illuminated desktop magnifier, (4) Transistor/inductor/capacitor tester (5) Bench mounted, good multi-meter (6) PCB making kit, (7) Soldering iron/hot air station on a side table, and, (8) a small (\$150) mini lathe.
• GEBevis 2018-04-27
It is fun to fantasize about gear. I have a decent bench populated with HP function/rf generators from DC to 1060MHz with modulation and Tektronix analog and digital scopes. I would really like a good spectrum analyzer, say HP 8595A for RF and a HP 3588A to cover the audio spectrum. I could also really use a stereo microscope and a top quality micro soldering station + hot air reflow from Pace, JBC,or Hakko. Also would be nice to have every value and rating of capacitor and resistor in SMD and thru hole on hand all in proper bins along with a few thousand feet of various gage, color and strand/solid wires.
• N5KS 2018-04-28
Currently, I have a Rigol oscilloscope, arbitrary waveform generator and homebrew power supply. I would like to add a spectrum analyzer and better lab power supply.
• belongumdave 2018-05-03
I have a hone made reflow station, 2ch Rigol 100Mhz scope, a nice hako soldering station, and the various meters and hand tools. What would desire, is a decent function generator ( I use an XR2206 now), a 30A dual power supply, a good reflow oven, (I use a converted toaster oven now), a fume extractor with external fitting to go outside, decent lighting above my bench, and a decent adjustable chair to sit.
• paulob160 2018-05-04
A good coffee machine and a microwave. One of the most important components in any electronics or computing engineers’ day is a Cornish Pasty. The temperature of a good Cornish Pasty is a critical parameter when considering the benefits a microwave oven can bring to the workbench. This only applies to real Cornish Pasties though, made and cooked in Cornwall. Other than that, a half-way decent digital oscilloscope and arbitrary waveform generator can always be added later…
• Travesh 2018-05-04
How about a nice precision source meter?
For the hobbyist these days many tools are relatively easy to acquire or build. It’s truly a great time to be into electronics as long as you’re willing to dive in and work with today’s difficult form factors. It’s fairly cheap to acquire old test equipment for specialized needs. e.g. precision multi/voltmeter, electrometer, RF gear, etc.
The precision source meter stands out to me as a great multi-purpose tool that would speed up my work. Precision, stable power sourcing isn’t cheap or easy. Old equipment still goes for real money. Maybe one of the lower cost brands has come up with something by now.
• Fozzy59 2018-05-06
I am re-starting my interest in electronic hobby skills. I would LIKE to have…..
¤ temperature controlled soldering iron.
¤ multimeter
¤ bench power supply 1) variable stable voltage with current limiting adjusted to required setting & 2) adjustable split power supply regulated voltage centre ground
¤ sine wave signal generator (af to uhf)
¤ pulse generator
¤ oscilloscope
¤ logic probe | 2019-01-23 06:05:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.22503972053527832, "perplexity": 5258.607962263119}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1547583897417.81/warc/CC-MAIN-20190123044447-20190123070447-00576.warc.gz"} |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1024691080 | ### Asymptotic expansions of the $k$ nearest neighbor risk
Robert R. Snapp and Santosh S. Venkatesh
Source: Ann. Statist. Volume 26, Number 3 (1998), 850-878.
#### Abstract
The finite-sample risk of the $k$ nearest neighbor classifier that uses a weighted $L^p$-metric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in $mathbb{R}^n$, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal weighted $L^p$-metric, that is, the metric that minimizes the finite-sample risk, tends to a weighted Euclidean (i.e., $L^2$) metric as the sample size is increased. Numerical simulations corroborate this finding for a pattern recognition problem with normal class-conditional densities.
First Page:
Primary Subjects: 62G20, 62H30, 41A60
Full-text: Open access
Permanent link to this document: http://projecteuclid.org/euclid.aos/1024691080
Mathematical Reviews number (MathSciNet): MR1635410
Digital Object Identifier: doi:10.1214/aos/1024691080
Zentralblatt MATH identifier: 0929.62070
### References
1 BREIMAN, L., FRIEDMAN, J. H., OLSHEN, R. A. and STONE, C. J. 1984. Classification and Regression Trees. Wadsworth & Brooks Cole, Pacific Grove, CA.
Mathematical Reviews (MathSciNet): MR86b:62101
Zentralblatt MATH: 0541.62042
2 COVER, T. M. 1968. Rates of convergence of nearest neighbor decision procedures. In Proceedings First Annual Hawaii Conference on Sy stems Theory 413 415.
3 COVER, T. M. and HART, P. E. 1967. Nearest neighbor pattern classification. IEEE Trans. Inform. Theory 13 21 27.
Zentralblatt MATH: 0154.44505
4 DEVROy E, L. 1982. Any discrimination rule can have an arbitrarily bad probability of error for finite sample size. IEEE Trans. Pattern Anal. Machine Intelligence 4 154 157.
5 ERDELy I, A. 1956. Asy mptotic Expansions. Dover, New York. ´
6 FIX, E. and HODGES, J. L., JR. 1951. Discriminatory analysis nonparametric discrimination: consistency properties. Project 21-49-004, Report No. 4. 261 279. USAF School of Aviation Medicine, Randolf Field, TX.
7 FRIEDMAN, J. H., BENTLEY, J. L. and FINKEL, R. A. 1977. An algorithm for finding best matches in logarithmic expected time. ACM Trans. Math. Software 3 209 226.
Zentralblatt MATH: 0364.68037
8 FUKUNAGA, K. and HUMMELS, D. M. 1987. Bias of nearest neighbor estimates. IEEE Trans. Pattern Anal. Machine Intelligence 9 103 112.
Zentralblatt MATH: 0623.62055
9 FUKUNAGA, K. and FLICK, T. E. 1984. An optimal global nearest neighbor metric. IEEE Trans. Pattern Anal. Machine Intelligence 6 314 318.
Zentralblatt MATH: 0534.62041
10 FULKS, W. and SATHER, J. O. 1961. Asy mptotics II: Laplace's method for multiple integrals. Pacific J. Math. 11 185 192.
Mathematical Reviews (MathSciNet): MR138945
Zentralblatt MATH: 0143.34804
Project Euclid: euclid.pjm/1103037543
11 HELLMAN, M. E. 1970. The nearest-neighbor classification rule with a reject option. IEEE Trans. Sy stems Man Cy bernet. 6 179 185.
12 KNUTH, D. E. 1976. Big omicron and big omega and big theta. ACM SIGACT News 8 18 23.
13 PSALTIS, D., SNAPP, R. R. and VENKATESH, S. S. 1994. On the finite sample performance of the nearest neighbor classifier. IEEE Trans. Inform. Theory 40 820 837.
Zentralblatt MATH: 0820.62060
14 SMITH, S. J., BOURGOIN, M. O., SIMS, K. and VOORHEES, H. L. 1994. Handwritten character classification using nearest neighbor in large databases. IEEE Trans. Pattern Anal. Machine Intelligence 16 915 919, 1994.
15 SNAPP, R. R. and VENKATESH, S. S. 1994. Asy mptotic predictions of the finite-sample risk of the k-nearest-neighbor classifier. In Proceedings of the 12th International Conference on Pattern Recognition 2 1 7. IEEE Computer Society Press, Los Alamitos, CA.
16 SNAPP, R. R. and VENKATESH, S. S. 1998. Asy mptotic derivation of the finite-sample risk of the k nearest neighbor classifier. Technical Report UVM-CS-1998-0101, Dept. Computer Science, Univ. Vermont.
17 SNAPP, R. R. and XU, T. 1996. Estimating the Bay es risk from sample data. In Advances Z in Neural Information Processing Sy stems 8 D. S. Touretzky, M. C. Moser, and M. E.. Hasselmo, eds. MIT Press.
18 STONE, C. J. 1977. Consistent nonparametric regression. Ann. Statist. 5 595 645.
Mathematical Reviews (MathSciNet): MR56:1574
Zentralblatt MATH: 0366.62051
Digital Object Identifier: doi:10.1214/aos/1176343886
Project Euclid: euclid.aos/1176343886
19 WATSON, G. N. 1918. The harmonic functions associated with the parabolic cy linder. Proc. London Math. Soc. 17 116 148.
BURLINGTON, VERMONT 05405 PHILADELPHIA, PENNSy LVANIA 19104 E-MAIL: snapp@cs.uvm.edu E-MAIL: venkatesh@ee.upenn.edu | 2013-06-19 17:45:26 | {"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": 0.42119795083999634, "perplexity": 9979.190922900447}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368709000375/warc/CC-MAIN-20130516125640-00048-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.cheenta.com/acute-angled-triangle-prmo-ii-2019-question-29/ | Categories
# Acute angled Triangle | PRMO II 2019 | Question 29
Try this beautiful problem from the Pre-RMO, 2017, Question 23, based on Solving Equation. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO II, 2019, Question 29, based on Acute angled triangle.
## Acute angled triangle – Problem 29
Let ABC be a acute angled triangle with AB=15 and BC=8. Let D be a point on AB such that BD=BC. Consider points E on AC such that $$\angle$$DEB=$$\angle$$BEC. If $$\alpha$$ denotes the product of all possible val;ues of AE, find[$$\alpha$$] the integer part of $$\alpha$$.
• is 107
• is 68
• is 840
• cannot be determined from the given information
### Key Concepts
Equation
Algebra
Integers
But try the problem first…
Source
PRMO II, 2019, Question 29
Higher Algebra by Hall and Knight
## Try with Hints
First hint
The pairs $$E_1$$,$$E_2$$ satisfies condition or $$E_1$$=intersection of CBO with AC and $$E_2$$=intersection of $$\angle$$bisector of B and AC
since that $$\angle DE_2B$$=$$\angle CE_2B$$ and for $$E_1$$$$\angle BE_1C$$=$$\angle$$BDC=$$\angle$$BCD=$$\angle BE_1D$$
or, $$AE_1.AC$$=$$AD.AB$$=$$7 \times 15$$
$$\frac{AE_2}{AC}$$=$$\frac{XY}{XC}$$
(for y is midpoint of OC and X is foot of altitude from A to CD)
Second Hint
$$\frac{XD}{DY}=\frac{7}{8}$$ and DY=YC
or, $$\frac{XD+DY}{XC}$$=$$\frac{15}{7+8+8}$$=$$\frac{15}{23}$$
or, $$\frac{XY}{XC}=\frac{15}{23}$$
or, $$\frac{AE_2}{AC}$$=$$\frac{15}{23}$$
or, $$AE_1.AE_2$$=$$\frac{15}{23}(7.15)$$=$$\frac{225 \times 7}{23}$$
Final Step
$$[\frac{225 \times 7}{23}]$$=68.
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This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2020-09-26 19:21:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7741885185241699, "perplexity": 4940.133268333056}, "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-2020-40/segments/1600400244353.70/warc/CC-MAIN-20200926165308-20200926195308-00325.warc.gz"} |
http://m.thermalfluidscentral.org/encyclopedia/index.php/Dropwise_condensation | # Dropwise condensation
## Dropwise Condensation Formation Theories
Several theories have been proposed to explain the mechanism of dropwise condensation. The first model has been supported by many experimental studies. It states that liquid droplets form only heterogeneously at nucleate sites; if they are formed with a radius exceeding that of equilibrium, they will continue to grow and then join with surrounding droplets. The second approach postulates that between drops there exists a thin and unstable liquid film on a solid surface. As the condensation process continues and the thin film grows thicker, the film reaches a critical thickness – estimated to be in the order of 1μm – at which point it breaks up into droplets.
See Main Article Dropwise Condensation Formation Theories
## Critical Droplet Radius for Dropwise Condensation
As mentioned before, upon formation in their nucleation sites, droplets grow only if they form with a radius that exceeds the equilibrium radius. The analysis that leads to the definition of the critical equilibrium radius is presented below. A good place to start this derivation lies in the Gibbs free energy minimum principle.
See Main Article Critical Droplet Radius for Dropwise Condensation
## Thermal Resistances in the Dropwise Condensation Processes
The condensation process must overcome a series of thermal resistances for the heat and mass transfer to occur. These resistances include the thermal resistance found in the vapor, thermal resistance encountered during the phase change from vapor to liquid, resistance caused by capillary depression of the equilibrium saturation temperature at the interface, thermal resistance found in the liquid phase, and thermal resistance found at the wall where heat is conducted from the surface into the wall.
See Main Article Thermal Resistances in the Dropwise Condensation Processes
## Heat Transfer Coefficient for Dropwise Condensation
By substituting the expressions for temperature drops through the interface, capillary depression, and liquid droplets into the following equation
ΔTtotal = TvaporTw = ΔTvapor + ΔTδ + ΔTcap + ΔTdroplet
and neglecting the temperature drop in the vapor phase, the temperature drop is obtained:
$\Delta T_{total}=T_{sat}-T_{w}=\frac{2q_{d}}{h_{\delta }\pi D^{2}}+\left ( T_{v}-T_{w} \right )\frac{D_{min}}{D}+\frac{q_{d}}{2k_{l}\pi D}$
See Main Article Heat Transfer Coefficient for Dropwise Condensation
## References
Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA
Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO. | 2019-09-22 18:12:00 | {"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": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6674062609672546, "perplexity": 2125.0762538798103}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575627.91/warc/CC-MAIN-20190922180536-20190922202536-00025.warc.gz"} |
https://academic.oup.com/cercor/article/12/3/297/278132/Brain-Mechanisms-for-Reading-Words-and-Pseudowords | ## Introduction
It has been proposed that reading is subserved by two independent mechanisms [for a review, see Coltheart et al. (Coltheart et al., 1993)]. This ‘dual-route’ model is based mainly on evidence for a double dissociation in the ability to read pseudowords and real words in patients with acquired dyslexia secondary to brain damage (Marshal and Newcombe, 1973; Shallice and Warrington, 1980). According to this model, an addressed or lexical mechanism mediates the conversion of visual input to a whole-word phonological representation by means of access to a word-specific, lexical representation. Presumably, this route can only be used for reading aloud real words, and is required for pronouncing words with peculiar print-to-sound correspondences, such as PINT and COLONEL (i.e. exception words). In contrast, the assembled or sublexical mechanism involves mapping of individual orthographic segments onto the appropriate phonological elements to arrive at a complete phonological representation (a process also referred to as ‘phonological decoding’). Assembled phonology is required for reading unfamiliar letter strings (pseudowords), as well as pseudohomophones (i.e. letter strings, such as BURTH, which are pronounced the same as their real-word counterparts, but have different spellings).
Recently, in the context of an electrocortical stimulation study, we obtained evidence that the two purported mechanisms for reading may differ in at least one important feature. The mechanism that subserves assembled phonology depends on the activity of the posterior part of the left superior temporal gyrus (STGp), whereas the mechanism that is responsible for addressed phonology does not necessarily involve this region (Simos et al., 2000a). Unfortunately, the extent of the cortical area that can be examined in the operating room, with cortical stimulation techniques, is very limited. Functional brain imaging techniques, on the other hand, do not share this limitation and are therefore capable of providing a more complete picture of the cerebral mechanism of complex linguistic functions such as reading.
Previous approaches to this problem using functional imaging methods have relied on data from a single source, namely the spatial profile of brain areas that show increased levels of activity during reading tasks, obtained using a particular functional imaging technique (Pugh et al., 1996; Price et al., 1996; Rumsey et al., 1997). To be successful, however, this undertaking requires additional information on: (i) how different activated brain areas may operate together during reading tasks, and (ii) the degree and type of contribution of each area to reading performance.
The present report describes an attempt to integrate data derived from two noninvasive techniques. These techniques are, first, magnetic source imaging (MSI) performed in neurologically intact volunteers during reading tasks and, second, monitoring of reading performance (naming speed) in the same participants. MSI is unique among other functional imaging techniques for its ability to provide brain activation profiles with high spatiotemporal resolution. It can be used to determine not only which areas participate in reading, but also how these areas might interact with each other in real time to enable this function (Breier et al., 1998, 1999a). In addition, the capacity of MSI to provide accurate and detailed maps of language-specific cortex has been validated in the context of two large clinical studies against invasive cortical mapping techniques (Breier et al., 1999b, 2001; Papanicolaou et al., 1999; Simos et al., 1999,2000a).
This study addresses two issues: first, the dual-process hypothesis that the brain mechanism for reading words that require assembled phonology, in experienced readers, is different from the mechanism for reading words that do not; and second, whether different brain structures mediate reading of meaningful versus meaningless words. If such distinct regions exist, they may be involved in lexical access, which according to dual-route models mediate pronunciation of exception words. To address both issues we obtained MSI-derived brain activation profiles during reading of three types of print: exception words (relying more on addressed phonology and having meaning), pseudohomophones (requiring assembled phonology and also having meaning) and pseudowords (requiring assembled phonology but having no meaning). The prediction was that activity in posterior temporal and inferior parietal structures known to be involved in reading (Breier et al., 1998, 1999a; Pugh et al., 1996; Simos et al., 2000b,c) would differentiate processing of (i) meaningful versus meaningless items and (ii) letter strings that require assembled phonology versus those that do not.
## Experiment 1
### Materials and Methods
Sixteen adults (10 males, mean age: 29, range: 25–42 years), who had no history of neurological or psychiatric disorder, learning disability or visual impairment were studied. In addition, all participants were right-handed with English as their primary language. They were paid $30.00 for their participation. This study (as well as the one reported below in Experiment 2) had been approved by the University of Texas Institutional Review Board. All participants were asked to sign a consent form after the nature of the procedures involved had been explained to them. #### Stimuli and Tasks Each participant was tested on three word pronunciation tasks involving (i) exception words, (ii) pseudohomophones and (iii) pseudowords. Each list contained 80 monosyllabic letter strings ranging in length from four to six letters. Pseudowords and pseudohomophones were the same stimuli used by McCann and Besner in their Experiment 1 (McCann and Besner, 1987). Words in the exception list were adapted from Pugh et al. (Pugh et al., 1997) and Glushko's (Glushko, 1979) exception inconsistent word lists and were generally items with very rare print-to-sound correspondences. Mean frequency of occurrence for the exception words was 138 (range: 3–1700) per million in the Kucera and Francis corpus (1967) and 100 (range: 2–1264 occurrences) per million for the words from which pseudohomophones were derived (P > 0.61). #### Procedure The MSI scan was performed during all three tasks within a single session in a different random order across participants. Printed stimuli were presented for one second in order to prevent potential contamination of the event-related field (ERF) record by visual offset responses. The interstimulus interval varied randomly between 3 and 4 s across trials. The stimuli were presented in lowercase letters through a Sharp LCD projector (Model XG-E690U, Sharp Electronics Corporation, Mahwah, NJ, USA) controlled by a Macintosh G3 portable computer running SuperLab Pro. They were projected on a white screen located ~1.5 m in front of the participant and subtended 1.0–2.0° and 0.5° of horizontal and vertical visual angle, respectively. The principles underlying the MSI method as well as MSI data collection and analysis methods are described in detail elsewhere (Papanicolaou et al., 1999) and will only be briefly outlined here. MSI data were recorded in a magnetically shielded room with a whole-head neuromagnetometer (WH2500, 4D Neuroimaging, San Diego, CA) consisting of 148 magnetometer coils. The precise location of the intracranial sources of the observed evoked fields were computed at successive 4 ms intervals for a period of 1 s after the onset of the stimuli using standard algorithms (Sarvas, 1987). Source estimation was performed separately for each hemisphere and was attempted only when the surface distribution of magnetic flux was dipolar, i.e. consisted of a single region of magnetic outflux and a single region of magnetic influx. This surface map configuration usually indicates the presence of a single underlying active cortical patch that can be modeled as an equivalent current dipole (ECD). Occasionally, two distinct dipolar distributions were discerned, typically, over the left hemisphere, one over anterior frontal regions and the second over temporo-occipital areas. In that case, source estimation was performed for both dipolar distributions independently. To avoid localization errors produced by smearing of the magnetic flux produced by one source by the flux induced by the other source, two simultaneous source solutions were retained only if the corresponding dipoles were at least 5 cm apart. Using this method, no more than two sources in different anatomical regions can be computed in each hemisphere at each 4 ms time bin. In this way a maximum number of 1000 ms/4 = 250 sources can be computed for each hemisphere during the entire recording epoch. Reliably localized activity sources [i.e. those passing a 0.90 best-fit correlation criterion, see (Breier et al., 1999b; Simos et al., 1999)] were co-registered on structural MRI scans, and the anatomical location of each source was determined using a standard MRI atlas (Damasio, 1995). The sum of all acceptable sources localized in a particular area (i.e. left STGp), starting at ~150 ms after stimulus onset, when the first ‘wave’ of activity in the primary visual cortex has subsided, and ending 1 s later, served as a metric of the degree of stimulus-locked activation of that area. The validity of this measure as an index of regional activation has been established in several studies involving neurologically intact volunteers and patients (Simos et al., 1998, 1999; Breier et al., 1999b, 2001; Papanicolaou et al., 1999). On the basis of previous MSI studies on reading (Breier et al., 1998; 1999a; Simos et al., 2000b,c), we examined the following areas in each hemisphere: posterior third portion of the superior temporal gyrus (STGp), posterior third portion of the middle temporal gyrus (MTGp), supramarginal gyrus (SMG), angular gyrus (ANG), mesial temporal lobe (MTL) including the hippocampus and parahippocampal gyrus, and basal temporal cortex (BTC) comprising the fusiform and lingual gyri. Activity sources were also noted in the inferior frontal gyrus (IFG), predominantly in the left hemisphere (Broca's area) and in sensorimotor cortex, bilaterally. The proportion of subjects who showed activity in either of the two areas in at least one condition and hemisphere was not significant (9/16 subjects, P < 0.81 for inferior frontal and 10/16 subjects, P < 0.45 according to the binomial test), and data pertaining to these regions will be mentioned separately in the Results section. ### Results Reading error rates were too low to allow further analyses: group mean error rates were 2.3% (range: 1–4%), 4.2% (range: 2–5%) and 5.1% (range: 3–7%) for exception words, pseudohomophones and pseudowords, respectively. Individual brain activation profiles obtained during reading of all three types of stimuli closely resembled those observed in previous MSI studies in the context of silent reading tasks (see Fig. 1). They feature initial activation of the mesial occipital cortices bilaterally (within the first 150 ms after stimulus onset), followed by activity in basal temporal cortices predominantly in the left hemisphere (starting within 200 ms post-stimulus onset). In the next several hundred milliseconds, the profiles entailed activation of posterior temporal and inferior parietal and, in some cases, frontal areas as well as of mesial temporal regions. With the notable exception of MTGp, the degree of activity in all other temporal areas was strongly left-hemisphere dominant. Across reading tasks, the most striking pattern that could be discerned by mere visual inspection of brain activation profiles in each participant was the near complete absence of activity sources in MTGp and MTL during pseudoword reading. In contrast, activity in these regions was detected in every participant during reading of exception words. In the left MTGp and MTL, greater activation was found for exception as compared with pseudowords in 15/16 participants. In both areas the degree of activity was greater during reading of pseudohomophones as compared with pseudowords in 14/16 participants. A closer look at hemisphere differences at each area revealed a significant left hemisphere predominance in the degree of activation for STGp [t(15) = 4.46, P < 0.0001)], BTC [t(15) = 3.60, P < 0.003] and MTL [t(15) = 5.88, P < 0.0001)] regardless of stimulus type. These differences were highly consistent across participants: greater left than right STGp activation was found in 94% of participants for exception words, in 82% for pseudohomophones and in 92% for pseudowords. Corresponding figures for MTL were 94, 82 and 90%, and for BTC, 75, 67 and 67%, respectively. Given that the proportion of participants who showed activity sources in IFG and sensorimotor areas was not significant, data from these areas were examined separately and resulting findings should be considered as preliminary. A two-way ANOVA conducted on data from IFG with Task (3) and Hemisphere (2) as the within-subject factors revealed a significant Hemisphere main effect, F(1,15) = 5.19, P < 0.038 and a marginally significant Task main effect, F(2,30) = 3.38, P < 0.071. These results reflected the predominantly left hemisphere IFG activation and a trend for stronger activation during the pseudohomophone and pseudoword tasks compared with the exception word reading task. None of the ANOVA effects approached significance for activity sources in sensorimotor areas (P > 0.1). The results outlined above supported our first prediction, namely that meaningful items entailed high degree of activation of the MTGp and MTL regions, whereas reading meaningless letter strings entailed greatly reduced activation of these two regions. However, the degree of activity in superior temporal and temporoparietal areas did not differentiate between exception words and pseudohomophones (i.e. stimuli that are meaningful, yet differ in the amount of assembled phonology processing that they require). This was somewhat unexpected given the results of our previous electrocortical stimulation study (Simos et al., 2000a), which suggested that at least one temporal lobe area (STGp) is a key component of the mechanism for reading aloud items that require assembled phonology, although pronunciation of exception words may not depend on STGp. Therefore, it appeared likely that STGp activation observed in the present study during exception word reading may indicate automatic engagement of this region. This may be part of an attempt to apply assembled phonology operations or, alternatively, reflect a process that is secondary to whole-word phonological access. In a similar manner, MTGp activation during pseudohomophone reading would appear to reflect lexical access that is secondary to phonological assembly. Activity in IFG, although present in only a subset of the participants, was clearly lateralized to the left hemisphere, and there were indications that Broca's area showed increased activation in tasks that required explicit phonological decoding operations. This is in agreement with previous reports using MSI (Breier et al., 1999a) and functional magnetic resonance imaging (fMRI) studies (Pugh et al., 1996). If the above explanation regarding the relative roles of STGp and MTGp in reading is correct, it should follow that the onset of STGp activation would not correlate with the speed of articulation of exception words. Moreover, if STGp activation indeed reflected operations of assembled phonology for pseudoword and pseudohomophone reading, its onset should correlate with the speed of articulation of these stimuli. Further, if addressed phonology operations depend upon access to whole-word representations, and if MTGp and MTL are involved in the retrieval of such representations, onset of activity in these areas should correlate with speed of articulation of exception words. Finally, if MTGp activation is only secondary to the process of reading aloud pseudohomophones, then its onset latency should not correlate with articulation speed for this type of letter string. To assess these predictions, we obtained pronunciation latencies for each of the three types of stimuli used in Experiment 1 from a subgroup of the participants in that experiment. ## Experiment 2 ### Materials and Methods #### Participants Fourteen of the participants in Experiment 1 agreed to visit the laboratory for a second testing session (nine males, mean age: 29, range: 25–42 years). They were paid$30.00 for their participation.
A subset of 30 stimuli was randomly selected to form each of the three lists used in this session. Mean word frequencies for these shorter lists were not significantly different from those used in the corresponding MSI sessions (mean = 128 and 119 for exception words and pseudohomophones, respectively, P < 0.48). To avoid practice effects, this part of the study was conducted at least 1 month after the MSI scan.
Each participant was seated in a quiet room at a distance of 30 cm in front of the computer screen and asked to read aloud letter strings presented once every 3–4 s as rapidly as possible without neglecting accuracy. The letter strings remained on the screen until the computer registered the participant's vocal response. Pronunciation errors were also recorded by an experimenter seated next to the participant. The order of task presentation was again counterbalanced across participants.
### Results
Again, reading errors were too low to allow further analyses (1.8, 3.0 and 4.5% for exception words, pseudohomophones and pseudowords, respectively). Pronunciation latencies are presented in Table 1. On average, exception words were pronounced 60 ms faster than pseudohomophones, which were pronounced 22 ms faster than pseudowords. The latter difference is essentially identical to that reported by McCann and Besner for the same stimulus lists (McCann and Besner, 1987). A one-way ANOVA, computed on mean pronunciation latencies from each participant, with Type of Letter String as a within subjects variable, was significant, F(2,26) = 6.88, P < 0.004. Pairwise comparisons revealed a significant difference between exception words and both pseudohomophones [t(13) = 2.17, P < 0.049] and pseudowords [t(13) = 3.57, P < 0.003]. The difference between pseudohomophones and pseudowords, although highly consistent across participants (with 11/14 cases showing the effect), did not reach significance.
Although differences in mean word frequency between exception words and pseudohomophones were small, we wanted to ensure that they did not exert a significant influence on naming speed. For this purpose, we computed, for each participant, the correlation between naming latency and word frequency for exception words and pseudohomophones according to the Kucera and Francis norms (Kucera and Francis, 1967). For the latter, the frequency of the real word from which the pseudohomophone was derived was used. Pearson correlation coefficients ranged between –0.16 and 0.14 across participants, indicating a negligible relation between these variables.
#### Relation between Naming Latency and Onset of Regional Activation
Onset latency of activation of a particular area was defined at the earliest latency (4 ms time bin), after stimulus onset, in which the first of at least two consecutive activity sources was found in a particular area. The mean onset latency of the activation of each area is also shown in Table 1 for comparison. The relation between onset latency of activity in each area and naming latency was examined by computing the Pearson r correlation coefficient separately for each type of letter string. As shown in Table 2, the onset latency of activity in STGp accounted for a moderate proportion of the variability in naming latency for pseudowords and pseudohomophones (R2 = 0.31, and R2 = 0.37, respectively). In contrast, a significant proportion of the variance in naming speed of exception words (R2 = 0.32) was accounted for by the onset latency of activation in MTGp. Onset of activity in MTGp and naming latency for the other two types of letter strings were negatively correlated (see Fig. 3). Correlations between naming latency and onset of activity in mesial and basal temporal areas were either negligible or even negative. Also negligible were correlations between the onset of activity in homologous right hemisphere areas and pronunciation latencies.
#### Onset of Activation Across Regions
To summarize, the results from Experiment 2 were in accord with electrocortical stimulation data reported previously (Simos et al., 2000a) in that: (i) there was no significant relation between STGp activation onset and pronunciation latency for exception words; (ii) there was a substantial correlation between the onset of activity in STGp and pronunciation latency for pseudowords and pseudohomophones; (iii) there was a significant correlation between onset of MTGp activation and pronunciation latency of exception words; and (iv) there was no significant relation between onset of MTGp activation and pronunciation latency for pseudohomophones.
## Discussion
The stimuli used in the present study allowed us to identify additional features of these profiles that are specific to two important attributes of print: (i) meaningfulness and (ii) dependence on assembled phonology operations. Specifically, it is generally assumed that meaningful stimuli are associated with word-specific (lexical) mental representations. It has been proposed that the mechanism responsible for pronouncing real words, especially those with rare print-to-sound correspondences, initially involves access to a lexical representation that subsequently mediates the retrieval of the word's name (Coltheart et al., 1993). Both exception words and pseudohomophones (by virtue of their phonological similarity to real words) possess entries in the hypothetical ‘mental lexicon’, whereas pseudowords do not. Based on this premise, we hypothesized that the mechanisms involved in reading exception words and pseudohomophones would share at least one common component, namely a process related to lexical access. This process would not be part of the mechanism for reading pseudowords. Our findings were consistent with this notion, showing that a prominent feature of the activation profile associated with reading aloud both exception words and pseudohomophones involved the left middle temporal gyrus and mesial temporal regions. However, reading aloud pseudowords involved very sparse activity in these regions. Thus, MTGp shows reduced neurophysiological activity as well as reduced regional cerebral blood flow during pseudoword as compared to real word reading (Hagoort et al., 1999). Moreover, it appears that the left MTGp plays a special role in exception word reading. The significant correlation between onset of activity in the left MTGp and naming latency indicated that the earlier the engagement of this area following word presentation, the faster the pronunciation of the letter strings. The fact that MTGp activity did not predict pronunciation speed for pseudohomophones suggests that engagement of this area may be a byproduct of phonological access achieved through the assembled route for nonwords that sound like real words. Involvement of the MTGp in lexical/semantic analysis is suggested by several independent sources of evidence, including noninvasive functional imaging investigations (Mummery et al., 1998; Hart et al., 2000; Kuperberg et al., 2000) and lesion studies (Damasio and Damasio, 1989).
Both pseudowords and pseudohomophones, on the other hand, require assembled phonology operations. By definition, pseudohomophones and pseudowords not only require phonological decoding, but they are also orthographically unfamiliar. This feature is what makes their pronunciation unequivocally dependent upon phonological decoding. In principle this difference could account for the relation between onset latency of activity in the left STGp and reading speed of these two types of letter strings. However, given that pseudohomophones possess familiar phonological representations, this assumption would imply that the left STGp is primarily involved in visual/ orthographic processing of unfamiliar graphemic patterns. To our knowledge, there is no evidence to support this claim.
A final note is in order regarding the interpretation of timing data. The source modeling approach adopted in this and our previous investigations can only accommodate a maximum of two (usually only one) sources at each 4 ms bin per hemisphere. Theoretically, several, simultaneously active, sources can be distinguished on the basis of MSI data. The technique we routinely use in our lab is the standard method employed in all clinical applications of MSI worldwide. Further, we have ascertained the validity of this procedure in the context of a series of combined MSI–electrocortical stimulation studies (Papanicolaou et al., 1999; Simos et al., 1999,2000a; Castillo et al., 2001). Although it is in principle possible to differentiate sources located at a smaller distance from each other, we do not have cross-validation data that support this approach. Based on our combined MSI–electrocortical stimulation studies, we have ascertained that the location of clusters of activity sources represent cortical patches that play a crucial role in certain component operations, such as phonological analysis. Taking these studies into account we can safely conclude that, at any point in time, the activity sources that meet the criteria adopted in our source modeling procedure represent the most prominently active cortical patch in a given hemisphere.
Using this method, we observed, in a given subject, clusters of temporally contiguous activity sources in a particular area running for 8–100 ms at a time, which were preceded and followed by source clusters in different areas. Accordingly, in the spatiotemporal maps constructed for each subject, anatomical areas within each hemisphere appeared to become active sequentially. Collapsing spatiotemporal profiles across participants is necessary in order to derive a more realistic representation of the temporal course of regional activation associated with a given task. The group spatiotemporal profiles displayed in Figure 4 were derived using this procedure. The observation that the three main cortical areas discussed above (STGp, MTGp, MTL) became active at one time or another during the same 400 ms latency window (300–700 ms) may have two alternative, but not mutually exhaustive, explanations: first, that these regions were all active simultaneously but activity in only one area at a time could be modeled in each participant; and second, that these regions became engaged strictly sequentially. It is difficult to distinguish between the two alternatives solely on the basis of functional imaging data. Methods that rely on measures of regional blood flow or metabolism simply lack the temporal resolution necessary to monitor neurophysiological activity in real time. MSI, on the other hand, possesses adequate temporal resolution, but it is currently limited by validity considerations, to the use of source modeling techniques that permit reliable identification of no more than two simultaneously active cortical patches. One way to resolve this issue would be to combine data from MSI and electrocortical stimulation in the same patients. This approach is generally very promising as an adjunct to any non-invasive functional imaging method, but is difficult to implement, mostly due to time constraints and patient safety considerations associated with direct cortical stimulation studies. In this approach, MSI data could be used to identify cortical patches that appear to be essential for the performance of a particular experimental task. Subsequently, during the electrocortical stimulation study, MSI-derived cortical patches may be stimulated with brief pulses delivered at different delays after stimulus onset to determine the critical time window that stimulation of a particular cortical region disrupts task performance.
As discussed above, MSI (like any other functional imaging method) may fail to detect certain details of the activation profiles, it appears to be capable of capturing the essential features of this profile, as indicated by the results of direct comparisons with invasive mapping techniques (Breier et al., 1999b; Simos et al., 1999,2000a). A comparison of the results presented here with those from functional imaging studies that use measures of cerebral blood flow or metabolism reveals many similarities, but some notable differences as well. The present data are consistent with reports of increased activation in MTG during reading of real words, implicating this region in whole-word (i.e. lexical) processing (Price et al., 1996; Hart et al., 2000) and with reports of automatic activation of STGp even in tasks that do not require addressed phonology (Hart et al., 2000). Activation in the left frontal operculum, which has been found in several PET and fMRI studies (Herbster et al., 1997; Hagoort et al., 1999; Fiez et al., 1999; Pugh et al., 1996), was not as consistent in the present study as activation in temporal and temporoparietal regions. This discrepancy may reflect a peculiarity of the functional imaging modality used in the present study: in our experience MSI appears to be more sensitive to neurophysiological activity produced in the temporal (including mesial temporal), parietal and occipital lobes than in the frontal lobe. When detected, prefrontal activity showed the expected left hemisphere lateralization and modulation by task demands, i.e. increased activity in tasks that require phonological decoding, in agreement with previous reports (Pugh et al., 1996; Fiez and Petersen, 1998; Breier et al., 1999a; Hagoort et al., 1999).
Future studies should examine more closely the role of stimulus (such as degree of regularity, consistency, and relative frequency) and subject variables (such as age and reading skill) on the degree and timing of neuronal activity in the brain regions identified in this report. Among other issues, such studies would address, in a more systematic manner, the neurological validity of theories postulating single versus dual mechanisms for reading words.
## Notes
We wish to thank three anonymous reviewers for their constructive comments and suggestions that led to significant improvements over earlier versions of the manuscript. This work was supported in part by NSF Grant REC-9979968 and NIH Grant NS37941-01 to A.C. Papanicolaou.
Table 1
Mean pronunciation latencies and mean latencies of onset of regional activation in Experiments 1 and 2 (in ms after stimulus onset; SD values in parentheses)
Left hemisphere Pronunciation latency STGp MTGp SMG ANG MTL
STGp: posterior portion of the superior temporal gyrus, MTGp: posterior portion of the middle temporal gyrus, SMG: supramarginal gyrus, ANG: angular gyrus, MTL: mesial temporal lobe regions (hippocampus and parahippocampal gyrus), BTC: basal temporal cortices (fusiform and lingual gyrus).
Exception 771 467 410 580 420 500
(106) (170) (138) (118) (170) (140)
Pseudohomophone 831 470 420 480 460 521
(115) (134) (120) (66) (190) (148)
Pseudoword 853 450 409 600 400 560
(118) (135) (83) (117) (180) (123)
Left hemisphere Pronunciation latency STGp MTGp SMG ANG MTL
STGp: posterior portion of the superior temporal gyrus, MTGp: posterior portion of the middle temporal gyrus, SMG: supramarginal gyrus, ANG: angular gyrus, MTL: mesial temporal lobe regions (hippocampus and parahippocampal gyrus), BTC: basal temporal cortices (fusiform and lingual gyrus).
Exception 771 467 410 580 420 500
(106) (170) (138) (118) (170) (140)
Pseudohomophone 831 470 420 480 460 521
(115) (134) (120) (66) (190) (148)
Pseudoword 853 450 409 600 400 560
(118) (135) (83) (117) (180) (123)
Table 2
Pearson correlation coefficients between onset latency of activation in areas STGp, MTGp and MTL, and pronunciation latency
Left hemisphere STGp MTGp MTL
STGp: posterior portion of the superior temporal gyrus, MTGp: posterior portion of the middle temporal gyrus, MTL: mesial temporal lobe regions (hippocampus and parahippocampal gyrus).
*P < 0.05.
Exception −0.37 0.57* −0.40
Pseudohomophone 0.61* −0.07 −0.35
Pseudoword 0.55* −0.21 −0.16
Left hemisphere STGp MTGp MTL
STGp: posterior portion of the superior temporal gyrus, MTGp: posterior portion of the middle temporal gyrus, MTL: mesial temporal lobe regions (hippocampus and parahippocampal gyrus).
*P < 0.05.
Exception −0.37 0.57* −0.40
Pseudohomophone 0.61* −0.07 −0.35
Pseudoword 0.55* −0.21 −0.16
Figure 1.
Activity sources from one representative case projected on a 3-D rendering of the participant's MRI (Experiment 1). Clusters of activity sources computed at 4 ms intervals after the presentation of each printed stimulus were projected on the brain surface for easier visualization. Sources occurring between 100 and 300 ms after stimulus onset (shown in yellow) were typically localized in basal temporal cortices. Posterior temporal and inferior parietal sources (shown in orange) usually became active later between 300 and 1000 ms after stimulus onset. Note the abundance of activity sources in the left middle temporal gyrus and mesial temporal cortex during exception word and pseudohomophone reading and the lack of activity sources in these areas during reading of meaningless letter strings.
Figure 1.
Activity sources from one representative case projected on a 3-D rendering of the participant's MRI (Experiment 1). Clusters of activity sources computed at 4 ms intervals after the presentation of each printed stimulus were projected on the brain surface for easier visualization. Sources occurring between 100 and 300 ms after stimulus onset (shown in yellow) were typically localized in basal temporal cortices. Posterior temporal and inferior parietal sources (shown in orange) usually became active later between 300 and 1000 ms after stimulus onset. Note the abundance of activity sources in the left middle temporal gyrus and mesial temporal cortex during exception word and pseudohomophone reading and the lack of activity sources in these areas during reading of meaningless letter strings.
Figure 2.
Mean number of activity sources in six posterior temporal and inferior parietal areas for each of the three stimulus types in Experiment 1. Vertical bars represent standard error values. Significant task differences were found in the MTGp and MTL. A near three-fold increase was found in the degree of MTGp activation (bilaterally) between exception words and pseudowords. This pattern was apparent in all but one participants. On average, the left MTL showed approximately twice as much activity during reading of exception words and pseudohomophones than during pseudoword reading. Again, this pattern was observed in the vast majority of individual brain activation profiles (i.e. in 14/16 participants).
Figure 2.
Mean number of activity sources in six posterior temporal and inferior parietal areas for each of the three stimulus types in Experiment 1. Vertical bars represent standard error values. Significant task differences were found in the MTGp and MTL. A near three-fold increase was found in the degree of MTGp activation (bilaterally) between exception words and pseudowords. This pattern was apparent in all but one participants. On average, the left MTL showed approximately twice as much activity during reading of exception words and pseudohomophones than during pseudoword reading. Again, this pattern was observed in the vast majority of individual brain activation profiles (i.e. in 14/16 participants).
Figure 3.
Regression plots that demonstrate the relation between onset latency in the left STGp and MTGp and pronunciation latency for each of the three types of letter strings used in the study (n = 14).
Figure 3.
Regression plots that demonstrate the relation between onset latency in the left STGp and MTGp and pronunciation latency for each of the three types of letter strings used in the study (n = 14).
Figure 4.
Temporal course of activation in each of the three brain regions (left hemisphere) that showed significant print-type related effects and in basal temporal areas for the group of 16 participants. Note the clear temporal distinction between activation of basal temporal and all other areas, and the significant overlap in the course of activation among the latter.
Figure 4.
Temporal course of activation in each of the three brain regions (left hemisphere) that showed significant print-type related effects and in basal temporal areas for the group of 16 participants. Note the clear temporal distinction between activation of basal temporal and all other areas, and the significant overlap in the course of activation among the latter.
## References
Breier JI, Simos PG, Zouridakis G, Papanicolaou AC (
1998
) Relative timing of cortical activation during a word recognition task.
J Clin Exp Neuropsychol
20
:
782
–790.
Breier JI, Simos PG, Zouridakis G, Papanicolaou AC (
1999
) Temporal course of regional activation associated with phonological decoding.
J Clin Exp Neuropsychol
21
:
465
–476.
Breier JI, Simos PG, Papanicolaou AC, Zouridakis G, Wilmore LJ, Wheless JW, Constantinou JC, Maggio WW (
1999
) Cerebral laterality assessment using magnetoencephalography: a comparison with the Intracarotid Amobarbital Procedure.
Neurology
22
:
938
–945.
Breier JI, Simos PG, Wheless JW, Constantinou JEC, Papanicolaou AC (
2001
) Hemispheric language dominance in children determined by magnetic source imaging.
J Child Neurol
16
:
124
–130.
Castillo EM, Simos PG, Venkataraman, V, Breier JI, Papanicolaou AC (
2001
) Mapping of expressive language cortex using Magnetic Source Imaging.
Neurocase
7
:
419
–422.
Coltheart M, Curtis B, Arkins P, Haller M (
1993
) Models of reading aloud: dual-route and parallel-distributed-processing approaches.
Psychol Rev
100
:
589
–608.
Damasio H (1995) Human brain anatomy in computerized images. New York: Oxford University Press.
Damasio H, Damasio A (1989) Lesion analysis in neuropsychology. New York: Oxford University Press.
Fiez JA, Petersen SE (
1998
) Neuroimaging studies of words reading.
95
:
914
–921.
Fiez JA, Balota DA, Raichle ME, Petersen SE (
1999
) Effects of lexicality, frequency, and spelling-to-sound consistency on the functional anatomy of reading.
Neuron
24
:
205
–218.
Glushko RJ (
1979
) The organization and activation of orthographic knowledge in reading aloud.
J Exp Psychol
5
:
674
–691.
Haggort P, Indefrey P, Brown C, Herzog H, Steinmetz H, Seitz RJ (
1999
) The neural circuitry involved in the reading of German words and pseudowords: a PET study.
J Cogn Neurosci
11
:
383
–398.
Hart J, Kraut MA, Kremen S, Soher B, Gordon B (
2000
) Neural substrates of orthographic lexical access as demonstrated by functional brain imaging.
Neuropsychiatry Neuropsychol Behav Neurol
13
:
1
–7.
Herbster AN, Mintum MA, Nebes RD, Becker JT (
1997
) Regional cerebral blood flow during word and nonword reading.
Human Brain Mapp
5
:
84
–92.
Kuperberg GR, McGuire PK, Bullmore ET, Brammer MJ, Rabe-Hesketh S, Wright IC, Lythgoe DJ, Williams SC, David AS (
2000
) Common and distinct neural substrates for pragmatic, semantic, and syntactic processing of spoken sentences: an fMRI study.
J Cogn Neurosci
12
:
321
–341.
Marshal JC, Newcombe F (
1973
) Patterns of paralexia: a psycholinguistic approach.
J Psycholinguist Res
2
:
175
–199.
Martin A, Wiggs CL, Weisberg J (
1997
) Modulation of human medial temporal lobe activity by form, meaning, and experience.
Hippocampus
7
:
587
–593.
McCann RS, Besner D (
1987
) Reading pseudohomophones: implications for models of pronunciation assembly and the locus of word-frequency effects in naming.
J Exp Psychol
13
:
14
–24.
Mummery CJ, Patterson K, Hodges JR, Price CJ (
1998
) Functional neuroanatomy of the semantic system: divisible by what?
J Cogn Neurosci
10
:
766
–777.
Papanicolaou AC, Simos PG, Breier JI, Zouridakis G, Willmore LJ, Wheless JW, Constantinou JE, Maggio WW, Gormley WB (
1999
) Magnetoencephalographic mapping of the language-specific cortex.
J Neurosurg
90
:
85
–93.
Papanicolaou AC, Simos PG, Breier JI, Fletcher JM, Foorman BR, Francis DJ, Castillo EM, Davis R (
2001
) Brain mechanisms for reading in children with and without dyslexia: a review of studies of normal development and plasticity.
J Child Neurol
16
:
241
–251.
Price CJ, Wise RJ, Frackowiak RS (
1996
) Demonstrating the implicit processing of visually presented words and pseudowords.
Cereb Cortex
6
:
62
–70.
Pugh KR, Shaywitz BA, Shaywitz SE, Constable RT, Skudlarski P, Fulbright RK, Bronen RA, Shankweiler DP, Katz L, Fletcher JM, Gore JC (
1996
) Cerebral organization of component processes in reading.
Brain
119
:
1221
–1238.
Pugh KR, Shaywitz BA, Shaywitz SE, Shankweiler DP, Katz L, Fletcher JM, Skudlarski P, Fulbright RK, Constable RT, Bronen RA, Lacadie C, Gore JC (
1997
) Predicting reading performance from neuroimaging profiles: the cerebral basis of phonological effects in printed word identification.
J Exp Psychol
23
:
299
–318.
Rumsey JM, Horwitz B, Donohue BC, Nace K, Maisog JM, Andreason P (
1997
) Phonological and orthographic components of word reading: a PET–rCBF study.
Brain
120
:
739
–759.
Sarvas J (
1987
) Basic mathematical and electromagnetic concepts of the biomagnetic problem.
Phys Med Biol
32
:
11
–22.
Seidenberg MS, McClelland JL (
1989
) A distributed, developmental model of word recognition and naming.
Psychol Rev
96
:
523
–568.
Shallice T, Warrington EK (1980) Single and multiple component central dyslexic syndromes. In: Deep dyslexia (Coltheart M, Patterson K, Marshall JC, eds). London: Routledge and Kegan Paul.
Simos PG, Breier JI, Zouridakis G, Papanicolaou AC (
1998
) Assessment of cerebral dominance for language using magnetoencephalography.
J Clin Neurophysiol
15
:
364
–372.
Simos PG, Papanicolaou AC, Breier JI, Wilmore LJ, Wheless JW, Constantinou JC, Gormley W, Maggio WW (
1999
) Localization of language-specific cortex using MEG and intraoperative stimulation mapping.
J Neurosurg
91
:
787
–796.
Simos PG, Breier JI, Wheless JW, Maggio WW, Fletcher JM, Castillo EM, Papanicolaou AC (
2000
) Brain mechanisms for reading: the role of the superior temporal gyrus in word and pseudoword naming.
NeuroReport
11
:
2443
–2447.
Simos PG, Breier JI, Fletcher JM, Bergman E, Papanicolaou AC (
2000
) Cerebral mechanisms involved in word reading in dyslexic children: a magnetic source imaging approach.
Cereb Cortex
10
:
809
–816.
Simos PG, Papanicolaou AC, Breier JI, Fletcher JM, Foorman BR, Bergman E, Fishbeck K, Papanicolaou AC (
2000
) Brain activation profiles in dyslexic children during nonword reading: a magnetic source imaging study.
Neurosci Lett
290
:
61
–65.
Simos PG, Breier JI, Fletcher JM, Foorman BR, Mouzaki A, Papanicolaou AC (
2001
) Age-related changes in regional brain activation during phonological decoding and printed word recognition.
Dev Neuropsychol
19
:
191
–210. | 2017-02-21 19:42:35 | {"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": 0.5360606908798218, "perplexity": 6805.90322087215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1487501170823.55/warc/CC-MAIN-20170219104610-00634-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://www.birs.ca/events/2020/5-day-workshops/20w5194 | # Topological Complexity and Motion Planning (Online) (20w5194)
## Organizers
(Louisiana State University)
(Cinvestav)
Teaching a robot to move about on an empty football field is easy. There is exactly one line joining the robot's starting and finishing points, and the robot can be instructed to move from start to finish along this line. This instruction scheme is robust in the sense that nearby starting and finishing points give rise to similar instructions. If the robot is attached to a circular track, teaching it to move is harder. The instructions move along the shortest arc'' lead to confusion if the starting and finishing points are precisely opposite one another, as the robot doesn't know whether to move in the clockwise or counterclockwise direction. Choosing one of these two, say, the instructions move clockwise'', yields confusion when the starting and finishing points are the same. From these instructions, the robot does not know if it should simply stay at the start/finish point, or move in a less efficient manner, looping around the circle once or twice or\ldots | 2023-04-01 01:13:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32751908898353577, "perplexity": 522.3667530861916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00660.warc.gz"} |
http://www.talkstats.com/threads/closing-all-tables.22934/ | # Closing all tables
#### eventhestars
##### New Member
Hey everyone,
being a sloppy and unqualified SAS-user I sometimes open tables I created (VIEWTABLE) and then forget closing them before running my program again, which causes an error of course. Is there a command I could put at the beginning of my programs that closes all tables that are open?
I googled this, and could not find an answer, so sorry if this is a stupid question!
ets
#### Dason
%macro closetables;
%closetables; | 2022-07-02 16:34:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5699723958969116, "perplexity": 2155.0897929014845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104189587.61/warc/CC-MAIN-20220702162147-20220702192147-00131.warc.gz"} |
https://www.sciengine.com/doi/10.1007/s11432-018-9515-9 | SCIENCE CHINA Information Sciences, Volume 62 , Issue 3 : 032105(2019) https://doi.org/10.1007/s11432-018-9515-9
## Partially known information attack on SM2 key exchange protocol
• AcceptedJul 4, 2018
• PublishedJan 24, 2019
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### Acknowledgment
This work was supported by National Key Research and Development Program of China (Grant Nos. 2016YFB0800902, 2016YFF0204004), and National Nature Science Foundation of China (Grant No. 61402536). The authors would like to thank the anonymous referees for their valuable comments.
### Supplement
Appendix
Proof of Lemma 4
Since $\|{\boldsymbol~r}\|_\infty<\kappa\eta$, we have \begin{align*}&|r_i|=|ne_i+2^{l'}y+\overline{x}_it_{i,1}-t_{i,2}|<\kappa\eta< 1, \mathrm{for} 1\leq i\leq m, \\ &|r_{m+1}|=\left|\frac{2^{l'}\eta}{n}y\right|<\kappa\eta, \\ & |r_{m+2i}|=\left|\frac{\eta}{2^l}t_{i,1}\right|< \kappa\eta< 1, \mathrm{for} 1\leq i\leq m, \\ & |r_{m+2i+1}|=\left|\frac{\eta}{2^{l'}}t_{i,2}\right|< \kappa\eta< 1, \mathrm{for} 1\leq i\leq m, \end{align*} which implies \begin{align*}&2^{l'}y+\overline{x}_it_{i,1}-t_{i,2}=0 \mathrm{mod} n, \mathrm{for} 1\leq i\leq m, \\ &|y|<\frac{\kappa n}{2^{l'}}, \\ &|t_{i,1}|<\kappa 2^l, |t_{i,2}|<\kappa 2^{l'}, \mathrm{for} 1\leq i\leq m. \end{align*} Assume the following relations for $1\leq~i\leq~m$, \begin{align*}&2^{l'}y=\kappa_yn+2^{l'}y_1+y_0 \mathrm{with} |\kappa_y|<\kappa, 0\leq y_1<n/2^{l'} \mathrm{and} 0\leq y_0<n, \\ &t_{i,2}=\kappa_i2^{l'}+t'_{i,2} \mathrm{with} 0\leq t'_{i,2}<2^{l'} \mathrm{and} |\kappa_i|<\kappa, \\ &t'_{i,1}=t_{i,1}+{\overline{x}_i}^{-1}(y_0-\kappa_i2^{l'}) \mathrm{mod} n, \\ &\overline{x}_i\cdot{\overline{x}_i}^{-1}=1+\kappa'_{i}n, \\ &e'_i=e_i+\kappa_y+\kappa'_{i}(y_0-\kappa_i2^{l'}). \end{align*} Then the vector ${\boldsymbol~r}'={\boldsymbol~z}'~{\boldsymbol~B}$ is also a lattice point with coordinates vector ${\boldsymbol~z}=(e'_1,\ldots,e'_m,y_1,t'_{1,1},t'_{1,2},\ldots,t'_{i,1},t'_{i,2},\ldots,t'_{m,1},\\t'_{m,2})$, which satisfies \begin{eqnarray*}|r'_i|&=&|ne'_i+2^{l'}y_1+\overline{x}_it'_{i,1}-t'_{i,2}| \\ &=&|ne'_i+2^{l'}y-\kappa_yn-y_0+\overline{x}_i(t_{i,1}+{\overline{x}_i}^{-1}(y_0-\kappa_i2^{l'}))+\kappa_in2^{l'}-t_{i,2}| \\ &=&|n(e'_i-\kappa_y-\kappa'_{i}(y_0-\kappa_i2^{l'}))+2^l y+\overline{x}_it_{i,1}-t_{i,2}| \\ &=&|ne_i+2^{l'}y+\overline{x}_it_{i,1}-t_{i,2}| \\ &=&|r_i|<\kappa\eta< 1, \mathrm{for} 1\leq i\leq m. \end{eqnarray*}
This implies that $ne'_i+2^{l'}y_1+\overline{x}_it'_{i,1}-t'_{i,2}=0$. Therefore, we obtain \begin{eqnarray*}2^{l'}y_1+\overline{x}_it'_{i,1}-t'_{i,2}&=&0 \mathrm{mod} n, \mathrm{for} 1\leq i\leq m. \end{eqnarray*}
For some fixed $y$, consider the event $E$ defined as $2^{l'}y_1-t'_{i,2}\neq0~\mathrm{mod}~n$ for all $i$. We first prove the upper bound for the probability that $E$ happens. For any $1\leq~i\leq~m$, we have $${\overline{x}_i}^{-1}= t'_{i,1}(2^{l'}y_1-t'_{i,2})^{-1} \mathrm{mod} n. \tag{6}$$ There exist at most $(2\kappa~2^l-1)\cdot(2\kappa2^{l'}-1)$ number of possible tuples $(t_{i,1},~t_{i,2})$ which lead to a non-zero ${\overline{x}_i}^{-1}$. Thus the probability that Eq. (6) has a non-zero solution on $(t_{i,1},~t_{i,2})$ is less than \begin{eqnarray*}P_i(y) = \frac{(2\kappa 2^l-1)\cdot(2\kappa2^{l'}-1)}{n} \leq \frac{\kappa^2 2^{l+l'+2}}{n}. \end{eqnarray*}
Because all $\{\overline{x}_i\}_{i=1}^m$ are independent, the probability that $E$ happens under the condition of fixed $y$ is less than $$\prod_{i=1}^mP_i(y)\leq\frac{\kappa^{2m}2^{(l+l'+2)m} }{n^m}.$$
Denote $P_E$ as the probability that $E$ happens. With the bound for $y$, we obtain \begin{eqnarray*}P_E &\leq& \frac{\kappa n}{2^{l'}}\cdot\frac{\kappa^{2m}2^{(l+l'+2)m} }{n^m} \\ &=&\frac{\kappa^{2m+1}2^{(l+l'+2)m-l'}}{n^{m-1}}. \end{eqnarray*}
Consequently, there exists some $w\in[1,m]$ such that $$2^{l'}y_1-t'_{w,2}=0 \mathrm{mod} n$$ holds with probability $1-P_E$.
Since $t'_{w,2}$ and $y_1$ are bounded by $2^{l'}$ and $n/2^{l'}$ respectively, we get $$2^{l'}y_1=t'_{w,2}=0,$$ which implies $y_1=0$ and this completes the proof.
### References
[1] Office of State Commercial Cryptography Administration. Public key cryptographic alforithm SM2 based on elliptic curves (in chinese). 2010. http://www.oscca.gov.cn/UpFile/2010122214822692.pdf. Google Scholar
[2] ISO/IEC 11889-1:2015--Information technology--Trusted platform module library Part 1: Architecture. International Organization for Standardization. August 2015. Google Scholar
[3] ISO/IEC 14888-3:2016--Information technology Security techniques Digital signatures with appendix Part 3: Discrete logarithm based mechanisms. International Organization for Standardization. March 2016. Google Scholar
[4] Diffie W, Hellman M. New directions in cryptography. IEEE Trans Inform Theor, 1976, 22: 644-654 CrossRef Google Scholar
[5] Howgrave-Graham N A, Smart N P. Lattice attacks on digital signature schemes. Dess Codes Cryptography, 2001, 23: 283-290 CrossRef Google Scholar
[6] Liu M, Nguyen P Q. Solving BDD by enumeration: an update. In: Topics in Cryptology--CT-RSA 2013. Berlin: Springer, 2013. 7779: 293--309. Google Scholar
[7] Nguyen P Q. The dark side of the hidden number problem: lattice attacks on DSA. In: Cryptography and Computational Number Theory. Basel: Birkhäuser, 2001. 321--330. Google Scholar
[8] Nguyen , Shparlinski . The Insecurity of the Digital Signature Algorithm with Partially Known Nonces. J Cryptology, 2002, 15: 151-176 CrossRef Google Scholar
[9] Boneh D, Venkatesan R. Hardness of computing the most significant bits of secret keys in Diffie-Hellman and related schemes. In: Advances in Cryptology--CRYPTO'96. Berlin: Springer, 1996. 1109: 129--142. Google Scholar
[10] Shani B. On the bit security of elliptic curve Diffie-Hellman. In: Proceedings of the 20th IACR International Conference on Practice and Theory in Public-Key Cryptography. Berlin: Springer, 2017. 10174: 361--387. Google Scholar
[11] Liu M, Chen J, Li H. Partially known nonces and fault injection attacks on SM2 signature algorithm. In: Proceedings of the 9th International Conference on Information Security and Cryptology. Cham: Springer, 2013. 8567: 343--358. Google Scholar
[12] Aranha D F, Fouque P A, Gérard B, et al. GLV/GLS decomposition, power analysis, and attacks on ECDSA signatures with single-bit nonce bias. In: Advances in Cryptology--ASIACRYPT 2014. Berlin: Springer, 2014. 8873: 262--281. Google Scholar
[13] Bleichenbacher D. On the generation of one-time keys in DL signature schemes. In: Presentation at IEEE P1363 Working Group Meeting, 2000. Google Scholar
[14] Bleichenbacher D. On the generation of dsa one-time keys. In Presentation at Cryptography Research Inc., 2007. Google Scholar
[15] De Mulder E, Hutter M, Marson M E, et al. Using Bleichenbacher's solution to the hidden number problem to attack nonce leaks in 384-bit ECDSA. In: Cryptographic Hardware and Embedded Systems--CHES 2013. Berlin: Springer, 2013. 8086: 435--452. Google Scholar
[16] Boneh D, Halevi S, Howgrave-Graham N A. The modular inversion hidden number problem. In: Advances in Cryptology--ASIACRYPT 2001. Berlin: Springer, 2001. 2248: 36--51. Google Scholar
[17] Shparlinski I E. Playing hide-and-seek with numbers: the hidden number problem, lattices and exponential sums. In: Proceedings of Symposia in Applied Mathematics, 2005. 62: 153--177. Google Scholar
[19] Fan S, Wang W, Cheng Q. Attacking OpenSSL implementations of ECDSA with a few signatures. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security. New York: ACM, 2016. 1505--1515. Google Scholar
[20] Lenstra A K, Lenstra Jr. H W, Lov?sz L. Factoring polynomials with rational coefficients. Math Ann, 1982, 261: 515-534 CrossRef Google Scholar
[21] Chen Y, Nguyen P Q. BKZ 2.0: better lattice security estimates. In: Advances in Cryptology--ASIACRYPT 2011. Berlin: Springer, 2011. 7073: 1--20. Google Scholar
[22] Schnorr C P, Euchner M. Lattice basis reduction: Improved practical algorithms and solving subset sum problems. Math Programming, 1994, 66: 181-199 CrossRef Google Scholar
[23] Aono Y, Nguyen P Q. Random sampling revisited: lattice enumeration with discrete pruning. In: Advances in Cryptology--EUROCRYPT 2017. Cham: Springer, 2017. 10211: 65--102. Google Scholar
[24] Aono Y, Wang Y, Hayashi T, et al. Improved progressive BKZ algorithms and their precise cost estimation by sharp simulator. In: Advances in Cryptology--EUROCRYPT 2016. Berlin: Springer, 2016. 9665: 789--819. Google Scholar
[25] Zheng Z, Wang X, Xu G. Orthogonalized lattice enumeration for solving SVP. Sci China Inf Sci, 2018, 61: 032115 CrossRef Google Scholar
[26] Micciancio D, Goldwasser S. Complexity of Lattice Problems: a Cryptographic Perspective. Norwell: Kluwer Academic Publishers, 2002. 14--22. Google Scholar
[27] Schnorr C P. A hierarchy of polynomial time lattice basis reduction algorithms. Theor Comput Sci, 1987, 53: 201-224 CrossRef Google Scholar
[28] Schnorr C P, Hörner H. Attacking the Chor-Rivest cryptosystem by improved lattice reduction. In: Advances in Cryptology--EUROCRYPT'95. Berlin: Springer, 1995. 921: 1--12. Google Scholar
[29] Babai L. On Lovász' lattice reduction and the nearest lattice point problem. Combinatorica, 1986, 6: 1-13 CrossRef Google Scholar
[30] Kannan R. Algorithmic Geometry of Numbers. Annu Rev Comput Sci, 1987, 2: 231-267 CrossRef Google Scholar
[31] Shoup V. Number theory C+ library (NTL) vesion 6.0.0. http://www.shoup.net/ntl/. Google Scholar
[32] Kannan R. Minkowski's Convex Body Theorem and Integer Programming. Math OR, 1987, 12: 415-440 CrossRef Google Scholar
• Figure 1
(Color online) The hit rate of attacks on 20 random instances, each derived simulatively from a leakage of the SM2 key exchange protocol with parameter size (a) 64 bits and (b) 256 bits.
•
Algorithm 1 Partially known information attack on SM2 key exchange protocol
Require:An integer $m$, $\{\mathrm{LSB}_{l}(r_i)\}_{i=1}^m$, $\{\mathrm{LSB}_{l'}(t_i)\}_{i=1}^m$, $\{\overline{x}_i\}_{i=1}^m$;
Output:$\mathrm{LSB}_{l'}(d_{\rm~A})$, where $d_{\rm~A}$ is the private key of client A;
$\kappa\leftarrow(1+2^{(3m+1)\log\log~(3m+1)/\log~(3m+1)}\sqrt{2m+1})/2$;
Select $\delta>0$ such that $\kappa\delta<1$;
Compute $\beta_i=\mathrm{LSB}_{l'}(t_i)-\overline{x}_i\mathrm{LSB}_{l}(r_i)$;
${\boldsymbol~v}\leftarrow(\beta_1,\beta_2,\ldots,\beta_m,\frac{\delta}{2},\frac{\delta}{2},\ldots,\frac{\delta}{2})\in~\mathbb{R}^{3m+1}$;
Call algorithm from Lemma 2.2 to obtain a lattice vector ${\boldsymbol~w}\in~L$ with ${\boldsymbol~w}=(c'_1,\ldots,c'_m,d',k_{1,1},k_{1,2},\ldots,~k_{m,1},k_{m,2}){\boldsymbol~B}$, which is close to ${\boldsymbol~v}$;
Return $d'~\mathrm{mod}~n~\mathrm{mod}~2^{l'}$.
Citations
Altmetric | 2021-04-21 20:34:27 | {"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": 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": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9866088628768921, "perplexity": 8980.592300440341}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1618039550330.88/warc/CC-MAIN-20210421191857-20210421221857-00540.warc.gz"} |
https://astronomy.stackexchange.com/questions/19479/is-normal-matter-always-accompanied-by-dark-matter-and-vice-versa/19481 | # Is normal matter always accompanied by dark matter and vice versa?
Is normal matter always accompanied by dark matter and dark matter by normal matter?
Was ever observed effect of gravity lensing without normal matter?
We lack the precision to say that there aren't regions where there is matter without dark matter or vice-versa. But what is clear is that the ratio of dark matter to normal matter, which is (or needs to be) around 5 on average to explain the flatness of the universe, varies by orders of magnitude from place to place.
The reason for this is that matter interacts with matter in a completely different way to that in which dark matter interacts (weakly) with normal matter or itself by any other means than gravity. Gravitational interactions between normal/dark matter are not dissipative.
By that I mean that the sum of gravitational and kinetic energy is preserved. When normal matter interacts with itself there are normally dissipative consequences. For example, interacting matter may become hot and radiate away energy.
That is why the normal matter in our Milky Way galaxy is concentrated into a plane. Dissipative interactions during the gravitational collapse of our Galaxy, combined with the requirement for conservation of angular momentum result in disc formation. The same is not true for the dark matter associated with the Milky Way, which is expected to have a much more spherical distribution.
Likewise, when we look at the required density profiles of normal and dark matter in order to explain the kinematics of stars and gas in our Milky Way, we see that the normal matter is much more centrally concentrated than is the dark matter - hence we talk about a "dark halo". Again, dissipative interactions in normal matter are the reason.
Another famous example of the separation between dark and normal matter is the bullet cluster. The image below shows where the hot gas is (normal matter, observed by an X-ray telescope) compared to where it is inferred that the dark matter is (shown by contours) on the basis of gravitational lensing. This pair of galaxy clusters have recently interacted, passing through each other. The hot, intracluster gas has been stripped out of the pair and shock-heated, so that it appears concentrated between the two galaxy clusters. The dark matter content of each cluster has sailed on oblivious and remains concentrated around the visible cluster galaxies.
Yet another example would be dwarf spheroidal galaxies, these are relatively small galaxies that are nevertheless almost totally dominated by dark matter - they have mass-to-light ratios of $\sim$1000, compared with a "normal" galaxy, where this ratio might be $\sim$ 10.
There are also examples of dark galaxies. These may not be galaxies made of non-baryonic dark matter, but dark matter in the sense that for whatever reason, these galaxies do not contain many bright stars. Thus although they may be massive, they do not emit much light and contain a lot of "inert", non-starforming gas.
• Thanks, @RobJeffries (seriously). I read the accepted answer, did a bit of research, and then came back to start writing my own long answer when I saw that you had already written one. You saved me some free time best put to other purposes. – David Hammen Dec 22 '16 at 13:19
• This is a much better answer than is the accepted answer, @dllhell. I suggest you change your mind. – David Hammen Dec 22 '16 at 13:19
• What a terrific answer--thank you @RobJeffries! What does the apparent obliviousness of the bullet cluster's dark matter content say about how dark matter interacts with dark matter? Was it previously known that it was so oblivious to its own kind in addition to normal matter? – U007D Dec 22 '16 at 19:55
• @bRadGibson (but I guess, not THE Brad Gibson) it was already assumed that dark matter interacts very weakly with itself as well as normal matter. I don't think the Bullet cluster offers any new constraints, but I could be wrong. – Rob Jeffries Dec 22 '16 at 21:29
Mass attracts mass, and so dark matter will attract normal matter and vice versa. However, people have looked for "dark lenses", so far without success.
Examples:
On the other side of the question, normal matter has a chance to cool and thus clump together more densely than is possible for dark matter. Hence, small-scale dense environments are dominated by normal matter. | 2019-11-14 00:40:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5192273855209351, "perplexity": 557.615518255647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1573496667767.6/warc/CC-MAIN-20191114002636-20191114030636-00002.warc.gz"} |
https://codereview.stackexchange.com/tags/ascii-art/new | # Tag Info
fg_black="\e[30m" fg_white="\e[37m" bg_red="\e[41m" bg_blue="\e[44m" bg_purple="\e[45m" These control codes are terminal-specific. Prefer to use tput to create the appropriate codes for the actual $TERM being used. 0 Make a string str full of spaces with the length of variable a: printf -v str "%*s"${#a} " " # or str="\${a//[^ ]/ }*" I don't like the feature that you can have 2 different kind of parameters (string or function name) for setting a color. In the future you might want to enhance your function (make it split up the sting to a fg ... | 2021-10-21 03:13:31 | {"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": 0.4069747030735016, "perplexity": 3463.1984154846396}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1634323585380.70/warc/CC-MAIN-20211021005314-20211021035314-00108.warc.gz"} |
http://yvhw.ritornoallalira.it/math-112-module-1-quiz.html | # Math 112 Module 1 Quiz
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Questions are created and stored separately in a Question bank and can be reused in different quizzes. SOLUTION: Suppose that test scores in a math class are normally distributed with a mean of 72 and a standard deviation of 12. Each interactive practice test Form consists of a single set of practice questions. For each of the essays, write the essay in a word-processing program on the computer, and keep a strict time limit. Its scope extends from molecules to organisms and ecosystems. Practice: Corresponding sides and points. This means you can earn the maximum a score of 100. Exams are a great way to reinforce and evaluate students' understanding of the course content and main ideas. Next Generation Science Standards. Here is the test: Add the result of steps 3 and 4. Mathematics Professional. 2 MATH 112 - QUIZ # 2 In particular, f has a continuous extension to (−π/2,3π/2) which is not differentiable at π/2. All problems are based on STEM, common core standards and real-world applications for grades 3 to 12 and beyond. MACHINE SHOP APPLIED MATHEMATICS I. __gjsload__ = function(name. And from there I don't know how to debug further. It is designed for students who are struggling with this subject and in need of more gentle and easy teaching. A common comprehensive final exam will be given for all sections of Math 1 12 on Mon day, December 1 4 th from 8:0 0 a m - 10:0 0 a m. Offered by Technical University of Denmark (DTU). The links under Homework Help, have copies of the various lessons to print out. Math 112 Fall 2018. Biology is the study of life. y = mx + b. If the card is less than 5 (aces count as 1), a ball is drawn out of the first urn; otherwise a ball is drawn out of the second urn. Free delivery on millions of items with Prime. 1 852 000 C. The test measures general knowledge about the humanities, natural sciences, mathematics, and social science. 7 Student Page 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS ACTIVITY (My Reference Book) Have children briefly share some interesting things. 50 in ticket sales. If you don’t need to go through our Nursing Pre-Entrance Exam online course, click here for basic information about the Nursing Pre-Entrance test and PSB tests, and the TEAS ® Test. i Edukasyon sa Pagpapakatao Modyul para sa Mag-aaral Kagawaran ng Edukasyon Republika ng Pilipinas Ang mga modyul na ito ay magkatuwang na inihanda at sinuri ng mga edukador mula sa mga publiko at pribadong paaralan, at pamantasan. 2 4__ can also be written as 5 ___14, so 5 5 14. The most common of these is the Pearson product-moment correlation coefficient, which is a similar correlation method to Spearman's rank, that measures the “linear” relationships between the raw numbers rather than between their ranks. 4 hours, or 2 hours, 24 minutes. NuGet is the package manager for. The Help section contains information on the following versions of Java. 2 Rational exponents and surds; 1. Give the place value for the seven places preceding the decimal p. This document is a reference manual for the LLVM assembly language. _-112 80 _ -80 0 0. Patterns on a Hundred Chart Use the hundred chart. Thus the fare for the distance traveled is computed as $5. MATH 112 Module 1 Quiz Instructions: Print this document before you begin the quiz. Score at least Must score at least to complete this module item Scored at least Module item has been completed by Justice Dantes Standardized Subject Test. Math 112 BSU Chris Moore. What You Learned Before (pp. Unit 1-2 Area Problems; Unit 1-3 Picture Codes; Unit 1-4 Identify Prime and Composite Numbers; Unit 1-5 Venn Diagrams; Unit 1-6 Thick as a Brick; Unit 1-7 Prove It! Unit 1-8 Functions; Unit 1-9 Problem Solving: Guess and Check; Unit 1-10 Factors and Common Factors; Unit 1-11 Remainder Reminder; Unit 1-12 Parentheses, Please! Unit 1-13 Travel by. General Studies and Critical Thinking are not accepted. You can mark up your copy of the quiz and revisit it. From last semester, sinx has an inverse function on (−π/2,π/2) and on. The University of Illinois requires the ALEKS PPL Mathematics Placement Exam to assess a student's prerequisite knowledge for course placement. All questions are compulsory. browser installed. The goal of this document is to provide you, the student in Math 112, with a guide to some of the tools of the statistical software package MINITAB as they directly pertain to the analysis of data you will carry out in Math 112, in conjunction with the textbook Introduction to the Practice of Statistics by David Moore and George McCabe. * This requirement exists so that we have the opportunity to give you well-informed advice regarding what we feel might be the best first course in mathematics for you. 16 9 2 1 2 k 5. 0 overall with a minimum of 5. See full list on pinoynewbie. For example, create a story context for (1/3) / 4, and use a visual fraction model to show the quotient. HomeworkMarket. 1 Introduction This book aims to bridge the gap between the mainly computation-oriented lower division undergraduate classes and the abstract mathematics encountered in more advanced mathe-. obtuse angle. Marks : 100 General Instructions 1. Virtual Business Math Quiz Answers. 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Watch Calculus in 20 Minutes by Edward Burger. x This site uses cookies. -x - 2,-3 £ x < 1-5,x ³ 1 x y-8-6-4-22468-8-6-4-2 2 4 6 8 6) f (x) = {x + 1,x < 0 x2,x ³ 0 x y-8-6-4-22468-8-6-4-2 2 4 6 8 Write the vertex form equation of a parabola which has the following transformation from the parent graph of y = x2. Correspondingly, this problem has spawned a remarkably large number of theories that differ by the proposed extent of cortical and subcortical changes associated with awareness, ranging from local to global changes in functional connectivity. NEETS, MODULE 16--INTRODUCTION TO TEST EQUIPMENT. slope-intercept form. Also math games, puzzles, articles, and other math help resources. The test measures general knowledge about the humanities, natural sciences, mathematics, and social science. For instance, someone can look at a group of people, count noses, and refer to the "ratio of men to women" in the group. 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The measured parameters are frequency, rpm, period, duty, power supply. of Mathematics • University of California, Berkeley • 970 Evans Hall #3840 • Berkeley, CA 94720-3840 USA • +1 (510) 642-6550. MATH-045-Basic Mathematics: MATH-047-Prealgebra: MATH-053-Beginning Algebra: MATH-101-Business Mathematics: MATH-102-Technical Mathematics: MATH-105-Mathematics for Elementary Teachers 1: MATH-106-Mathematics for Elementary Teachers 2: MATH-111-Applications - Utility of Math: MATH-113-Intermediate Algebra for College Students: MATH-119-Trigonometry. Please do module 3 topic 2 lesson 2. The first 1/5th of a mile is charged at the higher rate. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. MATH 120 AMU QUIZ 2 question 17 You are the foreman of the Bar-S cattle ranch in Colorado. 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(MATH 2413) Engineering Mathematics I. Copyright © 2020 MathsIsFun. Sample: 50 units2 6. rpm | 30 kB. coverdata files created by the test suite. 50 = 112 Then 112 child tickets were pre-sold, so A = 548 – 112 = 436 adult tickets were sold. The test covers all historical themes (political and diplomatic, intellectual and cultural, social and economic) from ancient times to the present, and is an excellent opportunity to showcase your knowledge and achievement in. The right of ownership, the right to use, possess, enjoy and dispose of a thing in every legal way and to exclude everyone else without rights from interfering is called:. 30% The chance of birthing a boy or a girl. 6 Solving. Christine made a total of \$112. You can mark up your copy of the quiz and revisit it. 112, 471-7116 Office Hours: W 2:00 - 3:00 pm Th 12:30 - 1:45 pm F 11:00 - 11:45 am (Fall 2017). Select a test from the dropdown list to access preparation materials by test, or choose a product from the categories below. 2 1 5 3 2 h Start Lesson 2C of this module by assessing your knowledge of the different mathematics concepts previously studied and your skills in performing mathematical operations. 3•1Homework Helper G3-M1-Lesson 1 1. Before re-testing, you must complete at least 3 hours of study/review using the ALEKS Learning Module. There are several different ways to approach exams including an in-class essay, short essays, multiple choice, short answer, fill in the blank, matching, quote/passage identification, character identification, etc. Version: Date/Time: Changes: Publisher: 20. Quiz 6 solutions. Help is always 100% free!. 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Test 1 Test 2 Test 3 Test 4 Test 5 Test 6: Test-out 1 Test-out 2 Test-out 3; Part 2 2. google || {}; google. Upon completion of this assignment, you will have an overview of calculus and discover the tools that are available for you to use in this course. Distance, not distant. If you have an iPad or iPhone, the app Door24 is a great app (FREE) that follows along with the Ready/iReady curriculum. 1 Quadratic Functions 2. With useBuiltIns: true I also got the issue. Week Three, Day Six. Distance, not distant. We may request cookies to be set on your device. Must be from Technology, Science, Mathematics or Computing related subjects Knowledge of Computer Programming for BSc(Hons) Computer Games Technology and BSc(Hons) Forensic Computing : Scottish Higher: Achieve a minimum of 112 tariff points achieved from either five Highers or a combination of two Highers offered with two Advanced Highers. 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Math Quiz Free PDF ebook Download: Math Quiz Download or Read Online ebook virtual business math quiz answers in PDF Format From The Best User Guide Database Directions. 2017 VCE Further Mathematics examination report 1 (pdf - 426. A single card is randomly selected from a standard deck. Midterm and Final Exam Examples. Distance Formula. The University of Illinois requires the ALEKS PPL Mathematics Placement Exam to assess a student's prerequisite knowledge for course placement. Challenge your students with creative mathematics lessons, printable worksheets, activities, quizzes, and more during Math Education Month (April)—or anytime of the year! Focus on various mathematical themes, such as geometry, algebra, probability and statistics, money, measurement, and more!. Doug Clements, State University of New York. Find Test Answers Search for test and quiz questions and answers. Watch the video. School levels with G. Solve each number sentence. Aki Murata, Mills College and Stanford University * Susan Landry and Susan Gunnewig, University of Texas, Houston, also made valuable contributions to early drafts. 4 MB 00:00 Setting up Install Process Parsing package install arguments Resolving Dependencies Transaction Summary ===== Install 5 Package(s) Update 0 Package(s) Remove 0 Package(s) Total download size: 1. The useful aspect of converting units (or "dimensional analysis") is in doing non-standard conversions. 2 Module_1_Pract Module_1_1. Quizzes make learning fun! There is no quicker way to learn about Science in Middle School - Grades 6, 7 and 8. 101 Page(s). For further advice on acceptable units please email us. 0 or higher on a 4. In a hurry? Browse our pre-made printable worksheets library with a variety of activities and quizzes for all K-12 levels. They learn by verbalizing the way they see the mathematical ideas connect and by listening to how their peers perceived the problem. Tuesday 4/7. The course covers, between other topics: functions, composition and inverses, graphs and transformations, piece-wise functions, polynomial and rational equations and graphing, exponential functions, logarithms, graphs and applications of exponential and. All the geometry help you need right here, all free. 84kb) (amended 11 April 2018) 2017 VCE Further Mathematics examination report 2 (pdf - 300. Visit each of the websites in the module item to complete this quiz. $$1 \pi \text{ radian } = 180^{\circ}$$. Request homework help for all sciences and math. It is designed to assist students in their search for a placement and in their preparation for the placement itself. Here we show that the genes required for this interaction appeared in a stepwise manner: Some evolved. 6: Modeling with Exponential Functions (36) 4. Teachers and parents can use our free games, worksheets, apps and assignment creation tools to ensure that pupils actually enjoy developing the math skills expected of them by the Common Core State Standards. A single card is randomly selected from a standard deck. 4_1 Module_11 X Pluralsight +M python absolut + v. 1-64bit) Release Notes. BPIE115 Stage 1 Mechanical Placement Preparation. maps = google. MATH 116 - Essentials of Calculus. button { font: 300 italic 1. 2: The Natural Exponential Function (44) 4. 45 IT 2102.
vpp4fslczt97 ubvcioiphh 8ulhvsguhrxx o4t2pq8lz2a bygvst95jh qsenv0jsfkd83h flacsr4px2 mj13dtrjt3v5rlv 5xczgu7rc9 kmuhh992yjn ni7vyh1in9 14ofzrcj2pt 6wzcnlbcr5j zaa8y63mx0o8r owqkrj76az3 qmqn6bs6u2uma nzo9b9tba0nibk 3pedcu06nj 4h826kx9iff1gue 3gisvawwtvr 0pkb6pfl742pd unyd8u5z0k jdp9izqw22b9 67qol9lsuyuj 0sdtsqli6f98a2 ngrsbaumthsk 3p4zxql199g 62amvlot0zf ho9ror0qfxa0 | 2020-10-23 02:47:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.18958763778209686, "perplexity": 3281.2013395368813}, "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-2020-45/segments/1603107880519.12/warc/CC-MAIN-20201023014545-20201023044545-00021.warc.gz"} |
https://tex.stackexchange.com/questions/478459/change-margin-of-footnes-beamer | # Change margin of footnes - Beamer
I'd like for footnotes to be further down, to finish at the height where the numbering of pages does. This (hopefully, but not necessarily) without changing the area the text is written.
This is how I have it set up, couldn't find any information on how to do it online, please help. Thanks!
MWE (without aesthetics changes):
\documentclass[10pt]{beamer}
\usetheme[progressbar=frametitle]{metropolis}
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\begin{frame}{Trial Slide}
Text \footfullcite{sigfridsson}
\end{frame}
\end{document}
## 1 Answer
The problem is that the space below the footnote is occupied by the footline, even if it is mostly empty. As a workaround you could remove the footline and use some other template to show the framenumber, e.g. the logo:
\documentclass[10pt]{beamer}
\usetheme[progressbar=frametitle]{metropolis}
\usepackage{biblatex}
\addbibresource{biblatex-examples.bib}
\setbeamertemplate{footline}{}
\setbeamertemplate{logo}{%
\usebeamercolor[fg]{footline}%
\usebeamerfont{page number in head/foot}%
\usebeamertemplate*{frame numbering}%
}
\begin{document}
\begin{frame}{Trial Slide}
Text \footfullcite{sigfridsson}
\end{frame}
\end{document}
• Thank you! It works very well but the number misaligned and now it's closer to the edge, is there a way to keep it in the same place? – M.O. Mar 9 '19 at 2:09
• I dont know if it's correct, but I was able to add vertical and horizontal spaces. My changes are \setbeamertemplate{footline}{\vspace{6.7pt}} \setbeamertemplate{logo}{%% \usebeamercolor[fg]{footline}% \usebeamerfont{page number in head/foot}% \vspace{-7pt} \usebeamertemplate*{frame numbering}\hspace{5pt}% }. Hope you will be able to correct if there was a better way. – M.O. Mar 9 '19 at 2:38
• @M.O. Moving the frame number by inserting spaces sounds just fine – samcarter_is_at_topanswers.xyz Mar 9 '19 at 10:56 | 2020-05-29 17:39:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6186349391937256, "perplexity": 1236.173454447382}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347405558.19/warc/CC-MAIN-20200529152159-20200529182159-00109.warc.gz"} |
http://math.stackexchange.com/questions/25329/simple-proof-that-8-left-frac910-right8-1 | # Simple proof that $8\left(\frac{9}{10}\right)^8 > 1$
This question is motivated by a step in the proof given here.
\begin{align*} 8^{n+1}-1&\gt 8(8^n-1)\gt 8n^8\\ &=(n+1)^8\left(8\left(\frac{n}{n+1}\right)^8\right)\\ &\geq (n+1)^8\left(8\left(\frac{9}{10}\right)^8\right)\\ &\gt (n+1)^8 . \end{align*}
I had no trouble following along with the proof until I hit the step that relied on $$8\left(\frac{9}{10}\right)^8 > 1$$. So I whipped out a calculator and confirmed that this is indeed correct. And I could see, after some fooling around with pen and paper that any function in the form \begin{align} k \; \left(\frac{n}{n+1}\right)^k \end{align} where $n \in \mathbb{Z}$ and $k \rightarrow \infty$ is bound to fall below one and stay there. So it's not a given that any function in the above form will be greater than one.
What I'm actually curious about is whether there are nifty or simple little tricks or calculations you can do in your head or any handwavy type arguments that you can make to confirm that $$8\left(\frac{9}{10}\right)^8 > 1$$ and even more generally, to confirm for certain natural numbers $k,n$ whether \begin{align} k \; \left(\frac{n}{n+1}\right)^k > 1 \end{align}
So are there? And if there are, what are they?
It can be geometrical. It can use arguments based on loose bounds of certain log values. It doesn't even have to be particularly simple as long as it is something you can do in your head and it is something you can explain reasonably clearly so that others can do also it (so if you're able to mentally calculate numbers like Euler, it's not useful for me).
You can safely assume that I have difficulties multiplying anything greater two single digit integers in my head. But I do also know that $$\limsup_{k\rightarrow \infty} \log(k) - a\cdot k < 0$$ for any $a>0$ without having to go back to a textbook.
-
Bernoulli's Inequality might be what you're looking for. – lvb Mar 6 '11 at 18:48
For the general case, you can take logs to $\ln k + k\ln(1-\frac{1}{n+1})\gt 0$ then use the expansion of ln (for large $n$) to get $\ln k \gt \frac{k}{n+1}$ or $n \gt \frac{k}{\ln k}-1$ which works well if you have some logs in your head (2, 10?) – Ross Millikan Mar 7 '11 at 3:27
Note that $(1-.1)^8\geq 1-.8$ by Bernoulli's inequality, as mentioned in a comment by lvb. For other cases you can use $\left(1-\frac{1}{n+1}\right)^k\geq 1-\frac{k}{n+1}$, which makes it easier to find a sufficient condition on $n$ for $k\left(\frac{n}{n+1}\right)^k$ to be larger than $1$.
In the motivating problem, the idea was that $k$ is fixed (at $8$), and since $\frac{n}{n+1}$ goes to $1$ as $n$ goes to infinity, $k\left(\frac{n}{n+1}\right)^k$ approaches $k$, and in particular is eventually bigger than $1$. One then finds out in a particular case what "eventually" means; here $n=9$ suffices. In general, Bernoulli's inequality leads to the conclusion that $n>k$ suffices.
-
Thanks! Chosen for answering the general case as well. – JasonMond Mar 6 '11 at 21:38
(+1) Good to spell out the general case. – cardinal Mar 6 '11 at 23:12
For this particular example, it's pretty easy, since $$(9/10)^8 \geq (8/10)^4 \geq (6/10)^2 \geq (3/10)$$ and so you're done. Notice, my bounds are quite crude in the last two cases.
Repetitive squaring is the quickest way to get up to a large power. In fact, that's how a typical computer implementation will do it for integer powers.
-
This is nice; it uses the fact that the denominator is 10, so the approximations amount to squaring integers and keeping only the first digit. – mjqxxxx Mar 6 '11 at 18:57
(+1) for the same reason as mjqxxxx explains. Really nice! – Gottfried Helms Mar 6 '11 at 19:33
Ditto on the +1. I'd never heard of repetitive squaring before. Cool. – JasonMond Mar 6 '11 at 21:39
You can use the fact that $(1 + x/n)^n$ approaches $e^x$ for large $n$. Then $$\left(\frac{n-1}{n}\right)^{k} = \left(1 - \frac{1}{n}\right)^{k} \thicksim e^{-k/n}$$ as $n\rightarrow\infty$. In your case, this would give $(9/10)^8 \approx e^{-4/5} > 1/e$, which is clearly greater than $1/8$. (For $n=10$ and $x=-1$, the error in the exponential approximation is about 5%.)
-
Thanks! I can also imagine some pairs of $(k,n)$ where I'd run into trouble establishing an inequality in my head. – JasonMond Mar 6 '11 at 21:43
(+1) And, via this heuristic, one can get rough upper and lower "bounds" via $1 - (k/n) \leq e^{-k/n} \leq 1 - (k/n) + (k/n)^2$. Note that the LHS (heuristically) "recovers" Bernoulli's inequality. Of course, since, in reality, $(1-1/n)^k \leq e^{-k/n}$, my statements are all quite crude. – cardinal Mar 6 '11 at 23:11
I'll start from the "obvious" fact that $(5/4)^3 < 2$. In fact, the cube root of 2 is around 1.26; of course you can explicitly compute $(5/4)^3 = 125/64 < 128/64 = 2$.
Then cubing both sides of that inequality, you get
$(5/4)^9 < 8$.
But $(10/9)^8 < (10/9)^9 < (5/4)^9$, so $(10/9)^8 < 8$. Taking reciprocals, $(9/10)^8 > 1/8$; multiplying both sides by 8 gives your result.
Actually, my heuristic here is as follows: $(10/9)$ is roughly one whole tone (two semitones); so $(10/9)^8$ is around sixteen semitones, or an octave and a major third, or $2 \times (5/4) = 2.5$. So $(9/10)^8$ must be around $0.4$. See Sanjoy Mahajan's handout on "singing logarithms", originally due to I. J. Good. Of course this method is really only useful if you know a little music theory.
-
Ok, here is another one:
$$8\left(\frac{9}{10}\right)^8 > 8\left(\frac{9}{10}\right)^9= \left[ 2\left(\frac{9}{10}\right)^3 \right]^3 \,.$$
So if we can prove
$$2\left(\frac{9}{10}\right)^3 >1 \,,$$
we are done.
This is equivalent to
$$3^6 > 2^25^3$$
Which is true since
$$3^3 > 5^2$$ and $$3^3 > 2^25$$
-
Just another mental approach. We write $$8\left(\frac9{10}\right)^8 >1 \rightarrow \frac9{10}>\frac18^{\frac18}=\left(1-\frac78\right)^{\frac18}$$ Then if one remembers that $(1-x)^{\frac1a} = 1 - \frac1a x - O\left(\frac{x^2}a\right)$ then we get $$\frac9{10}> 1-\frac7{64}-\epsilon \rightarrow 9>10-\frac{70}{64}-10\epsilon$$ which is obviously true. It just depends on whether you remember the beginning of the binomial-formula for fractional exponents.
-
Here is one that uses two facts about powers of 2 and 10: $2^{10}=1024>10^3$ and $2^7=128>10^2$
$$8\left(\frac{9}{10}\right)^8>8\left(\frac{8}{10}\right)^8=\frac{8^9}{10^8}=\frac{2^{3·9}}{10^6·10^2}>\frac{2^{27}}{2^{20}·10^2}=\frac{2^7}{10^2}=\frac{128}{100}>1$$
- | 2015-02-01 00:29:36 | {"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": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8929408192634583, "perplexity": 384.62875276225657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1422115857200.13/warc/CC-MAIN-20150124161057-00024-ip-10-180-212-252.ec2.internal.warc.gz"} |
http://www.gnomeslair.com/2006/07/rpgs-are-overtly-social.html | ## Jul 10, 2006
### RPGs are overtly social
Thankfuly Mr. Colbert has an answer. An answer in a video (via). Mind you, it's got Dungeons and Dragons in it. Apparently dice too.
Further D&D videos can be found both here and here. Have fun, in a twisted way.
Related Tags: , , , , , , , , , , , ,
1. This was great; I'm sorry I missed Mr. Colbert's fine homage.
2. Glad I found it for you then...
3. how did he remember that dialogue, i had to rewind it and i still didn't get the reference at the start.....another excellent rpg video!
4. :)
Yes, yes, quite funny... Oh, and he is quite the comedian.
5. .....
jingle.....
shit!
6. ?
:)
(ah, I see) | 2013-06-18 07:11:31 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8902062177658081, "perplexity": 5136.739851243975}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1368707184996/warc/CC-MAIN-20130516122624-00064-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://archive.main.lv/writeup/sauerbraten_patching_and_cheating.html | main.lv
Dont think code it
# 2011-3-13 Sauerbraten patching and cheating
sauerbraten is open source first person shooter. Also there is multi player
mode. I like time to time play sauerbraten. But I am not very good player.
As game source is comes with game you can view it and add some patches that
can help get better scores in games. Usually it called cheating.
As this features/cheats is made by my self I don't think so. But in game admins
First of all this patches don't make game enjoyable for other players
that way sooner or later you will be banned. Every one have freedom to
be banned.
First "allowed" cheat is recoil to 0 from any weapon
in file src/fpsgame/game.h on line 333:
static const struct guninfo { short sound, attackdelay, damage, projspeed, part, kickamount, range; const char *name, *file; } guns[NUMGUNS] =
{
{ S_PUNCH1, 250, 50, 0, 0, 0, 14, "fist", "fist" },
{ S_SG, 1400, 10, 0, 0, 20, 1024, "shotgun", "shotg" }, // *SGRAYS
{ S_CG, 100, 30, 0, 0, 7, 1024, "chaingun", "chaing"},
{ S_RLFIRE, 800, 120, 80, 0, 10, 1024, "rocketlauncher", "rocket"},
{ S_RIFLE, 1500, 100, 0, 0, 30, 2048, "rifle", "rifle" },
{ S_FLAUNCH, 500, 75, 80, 0, 10, 1024, "grenadelauncher", "gl" },
{ S_PISTOL, 500, 25, 0, 0, 7, 1024, "pistol", "pistol" },
{ S_FLAUNCH, 200, 20, 50, PART_FIREBALL1, 1, 1024, "fireball", NULL },
{ S_ICEBALL, 200, 40, 30, PART_FIREBALL2, 1, 1024, "iceball", NULL },
{ S_SLIMEBALL, 200, 30, 160, PART_FIREBALL3, 1, 1024, "slimeball", NULL },
{ S_PIGR1, 250, 50, 0, 0, 1, 12, "bite", NULL },
{ -1, 0, 120, 0, 0, 0, 0, "barrel", NULL }
};
changing sixths values all to 0 makes no recoil.
but if you change recoil to 1024 you can easily jump on the sky after shut.
Think what will see your on-line opponents? Someone if shutting from the skies.
Not-flying rocket? Yes you can make it.
fourth field in structure is projspeed change it for rocket launcher to
0 and you can place your rockets on air. Bet I don't know what see others.
Only thing with that you will get ban for team-killing because team mates
are usually around you and they blow-up when colliding with rockets in air.
Precision also is very nice but every one will notice that you shutting with shotgun
and chain-gun with precision like rifle.
In src/fpsgame/weapon.cpp on 130 line:
void offsetray(const vec &from, const vec &to, int spread, float range, vec &dest)
{
for(;;)
{
#define RNDD rnd(101)-50
vec v(RNDD, RNDD, RNDD);
if(v.magnitude()>50) continue;
v.mul(f);
v.z /= 2;
dest = to;
vec dir = dest;
dir.sub(from);
dir.normalize();
raycubepos(from, dir, dest, range, RAY_CLIPMAT|RAY_ALPHAPOLY);
return;
}
}
make
#define RNDD rnd(2)-1
and it will work fine. Remember this patches is cheat/like and it is not good to play with others when this patches is added because they loose their enjoyment of game. Remember of FREEDOM to be banned. | 2022-01-21 10:53:21 | {"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": 0.2544122636318207, "perplexity": 13982.00819862638}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303356.40/warc/CC-MAIN-20220121101528-20220121131528-00206.warc.gz"} |
https://math.stackexchange.com/questions/1825281/deriving-the-airy-functions-from-first-principles | Deriving the Airy functions from first principles
I have just started reading about the Airy functions and am stuck on a particular step of their derivation. But first here is some background information to give this question some meaning, more information can be found from a previous question of mine:
The general solution to Bessel's differential equation: $$\fbox{y^{\prime\prime}+\left(\frac{1-2a}{x}\right)y^{\prime}+\left[\left(bcx^{c-1}\right)^2+\frac{a^2-p^2c^2}{x^2}\right]y=0}\tag{1}$$ is $$\fbox{y=x^aZ_p\left(bx^c\right)}\tag{2}$$ where $Z_p$ stands for $J_p$ or $N_p$ or any linear combination of them, and $a,b,c,p$ are constants. $J_p$ is called the Bessel function of the first kind of order $p$ and $N_p$ is any combination of $J_p$ and $J_{−p}$: $$N_p(x)=\frac{\cos(\pi p)J_p(x)-J_{-p}(x)}{\sin(\pi p)}\tag{3}$$ So equation $(2)$ can be written as $$y=x^{a}\left[AJ_{p}\left(bx^c\right)+BN_{p}\left(bx^c\right)\right]\tag{4}$$ or $$y=x^{a}\left[AJ_{p}\left(bx^c\right)+B\left(\frac{\cos(\pi p)J_p\left(bx^c\right)-J_{-p}\left(bx^c\right)}{\sin(\pi p)}\right)\right]\tag{5}$$
The Airy differential equation is $$y^{\prime\prime}-xy=0\tag{6}$$ and has solution $$y=x^{1/2}Z_{1/3}\left(\frac23 ix^{3/2}\right)\tag{7}$$
By using
$$I_p(x)=i^{-p}J_p(ix)\tag{8}$$ $$K_p(x)=\frac{\pi}{2}i^{p+1}\left[J_p(ix)+i\left(\frac{\cos(\pi p)J_p(ix)-J_{-p}(ix)}{\sin(\pi p)}\right)\right]\tag{9}$$
My objective is to show that $(7)$ can be written in terms of $I_{1/3}$ and $K_{1/3}$ to obtain
$$Ai(x)=\frac{1}{\pi}\sqrt{\frac{x}{3}}K_{1/3}\left(\frac23x^{3/2}\right)\tag{10}$$ $$Bi(x)=\sqrt{\frac{x}{3}}\left[I_{-1/3}\left(\frac23x^{3/2}\right)+I_{1/3}\left(\frac23x^{3/2}\right)\right]\tag{11}$$
Starting from $(7)$: \begin{align}y&=x^{1/2}Z_{1/3}\left(\frac23 ix^{3/2}\right)\\&=x^{1/2}\left[AJ_{1/3}\left(\frac23 ix^{3/2}\right)+BN_{1/3}\left(\frac23 ix^{3/2}\right)\right]\\&=x^{1/2}\left[AJ_{1/3}\left(\frac23ix^{3/2}\right)+B\left(\frac{\cos\left(\frac{\pi}{3}\right)J_{1/3}\left(\frac23ix^{3/2}\right)-J_{-1/3}\left(\frac23ix^{3/2}\right)}{\sin\left(\frac{\pi}{3}\right)}\right)\right]\\&=x^{1/2}\left[AJ_{1/3}\left(\frac23ix^{3/2}\right)+B\left(\frac{\frac12J_{1/3}\left(\frac23ix^{3/2}\right)-J_{-1/3}\left(\frac23ix^{3/2}\right)}{\left(\frac{\sqrt3}{2}\right)}\right)\right]\\&=x^{1/2}\left[AJ_{1/3}\left(\frac23ix^{3/2}\right)+\frac{BJ_{1/3}\left(\frac23ix^{3/2}\right)}{\sqrt3}-\frac{2BJ_{-1/3}\left(\frac23ix^{3/2}\right)}{\sqrt3}\right]\\&=x^{1/2}\left[Ai^{1/3}I_{1/3}\left(\frac23x^{3/2}\right)+\frac{i^{1/3}BI_{1/3}\left(\frac23x^{3/2}\right)}{\sqrt3}-\frac{2i^{-1/3}BI_{-1/3}\left(\frac23x^{3/2}\right)}{\sqrt3}\right]\tag{a}\end{align} where in $(\mathrm{a})$ I used $(8)$ rearranged as $J_p(ix)=i^{p}I_p(x)$
I don't understand how to proceed with this calculation as I am unsure how to use $(9)$; I also have no idea what $i(x)$ means. Is $i$ really a function of $x$?
Is there anyone that could provide some hints or advice on how I can continue this calculation to obtain $(10)$ and $(11)$?
Below are some images showing some of the relevant formulae to this question:
• It is faster to check that both sides of $(10)$ or $(11)$ fulfill the same differential equation with the same initial conditions. You just have to apply a change of variable in the Bessel differential equation. – Jack D'Aurizio Jun 14 '16 at 3:07
At first note, that $i=\sqrt{-1}$ is the imaginary unit in (9) and we see a plain multiplication with $i$.
We start with the representation (5) and use (7) to obtain \begin{align*} y&=x^{\frac{1}{2}}Z_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)\\ &=x^{\frac{1}{2}}\left[AJ_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right) +B\left(\frac{1}{\sqrt{3}}J_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right) -\frac{2}{\sqrt{3}}J_{-\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)\right)\right]\tag{f} \end{align*} With $p=\frac{1}{3}$ we can write $K_p$ as \begin{align*} K_{\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right)=\frac{\pi}{2}i^{\frac{4}{3}} \left[J_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)+i\left(\frac{1}{\sqrt{3}}J_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right) -\frac{2}{\sqrt{3}}J_{-\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)\right)\right] \end{align*} Now we can write $Ai(x)$ using $K_{\frac{1}{3}}$ and see the structural connection with $(\mathrm{f})$.
\begin{align*} Ai(x)&=\frac{1}{\pi}\sqrt{\frac{x}{3}}K_{\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right)\\ &=\frac{1}{2\sqrt{3}}i^{\frac{4}{3}}x^{\frac{1}{2}} \left[J_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)+i\left(\frac{1}{\sqrt{3}}J_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right) -\frac{2}{\sqrt{3}}J_{-\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)\right)\right] \end{align*}
Comparison with $(\mathrm{f})$ results in \begin{align*} A=\frac{1}{2\sqrt{3}}i^{\frac{4}{3}}\qquad\qquad B=-\frac{1}{2\sqrt{3}}i^{\frac{1}{3}} \end{align*}
We can see the connection of $B_i(x)$ with (5) by substituting $I_p(x)$ with $J_p(x)$. We obtain \begin{align*} Bi(x)&=\frac{1}{\sqrt{3}}x^{\frac{1}{2}}\left[I_{-\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right) +I_\frac{1}{3}\left(\frac{2}{3}x^{\frac{3}{2}}\right)\right]\\ &=\frac{1}{\sqrt{3}}x^{\frac{1}{2}}\left[i^{\frac{1}{3}}J_{-\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right) +i^{-\frac{1}{3}}J_{\frac{1}{3}}\left(\frac{2}{3}ix^{\frac{3}{2}}\right)\right] \tag{g}\end{align*} Comparison of coefficients of $J_{-\frac{1}{3}}$ gives \begin{align*} B=-\frac{1}{2}i^{\frac{1}{3}} \end{align*} Comparison of coefficients of $J_{\frac{1}{3}}$ gives \begin{align*} A=\frac{1}{\sqrt3}\left(i^{-1/3}-\frac{i^{1/3}}{2}\right) \end{align*}
Hint: Note that the Airy function is defined according to (10) in terms of $K_p$ which is defined according to (9). So, the right-hand side of the blue part is just the definition of the Airy function in terms of $J_p$ and $J_{-p}$. From this representation we can deduce $A$ and $B$ by a rather simple comparison with $(\mathrm{f})$.
• @BLAZE: Note that $Ai$ is the name of the Airy function. So, $Ai(x)$ is just the Airy function evaluated at $x$. – Markus Scheuer Jun 20 '16 at 17:47
• @BLAZE: I've added a hint which might clarify the status of the definition of the Airy function and the derivation of $A$ and $B$. – Markus Scheuer Jun 22 '16 at 6:25
• @BLAZE: Two pairs of $A$ and $B$, one for $Ai(x)$ the other one for $Bi(x)$. Note that $J_p$ and $J_{-p}$ are independent. So, you can find $B$ immediately by comparing coefficients of $J_{-p}$. Then you can derive $A$. Regards, – Markus Scheuer Jun 26 '16 at 16:44
• @BLAZE: Comparing coefficients of (f) and (g) addresses $Bi(x)$. Substituting $B=-\frac{1}{2}i^{\frac{1}{3}}$ gives $A-\frac{1}{2\sqrt{3}}i^{\frac{1}{3}}=\frac{1}{\sqrt{3}}i^{-\frac{1}{3}}$. It follows ... – Markus Scheuer Jun 26 '16 at 20:42
• @BLAZE: Thanks for the bounty and accepting my answer! ☺ Two different pairs of $A,B$ which are not multiples of each other give two independent, different solutions of Bessel's differential equation. So, $Ai$ and $Bi$ are related, but different solutions. Since the determination of both pairs seems to be quite clear to you, I think the answer is complete. Best regards , – Markus Scheuer Jun 28 '16 at 6:31 | 2020-07-06 18:27:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9438347816467285, "perplexity": 210.01455791607552}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655881763.20/warc/CC-MAIN-20200706160424-20200706190424-00165.warc.gz"} |
https://puzzling.stackexchange.com/questions/33492/my-lawyer-is-mad-but-you-should-take-his-advice | # My lawyer is mad - but you should take his advice!
"Alter, fraudulently that is, earlier 8th avenue article. Take a treat
at such time as lawyer is point-first - the rest is poultry.
Reader! Why, we hear accounts' core again lacks a profit!
Permutation, without morals first, hurts standing."
(4,1,6,4,3,4,10)
Hint 1:
It seems the first line is the weakest part of the puzzle, so I will offer a little extra direction. The whole first line is a single clue, (4,1,6). The definition is a little loose, and is better taken as a confirmation of the solution rather than an alternate route towards it. Do not pay too much attention to the punctuation. Just because the words "fraudulently that is" appear within the same subordinate clause as written in the clue, it does not mean that they fit together in the solution. In fact, "alter fraudulently" gives one part of the solution and "that is" gives another. Together they make a single word.
Hint 2:
"Alter fraudulently" isn't "doctor", but it is another profession.
• Wow, this is all one cryptic clue? Hopefully there's a definition. – Deusovi May 29 '16 at 18:43
• @Deusovi there are several... i'll leave a hint breaking it up if no one gets it first – DeveloperInDevelopment May 29 '16 at 18:45
• Don't make any hints just yet - give it some time. I'm typically pretty good at cryptics, so I'll try to get some of these. – Deusovi May 29 '16 at 18:46
• (By the way, welcome to Puzzling.SE, and great puzzle!) – Deusovi May 29 '16 at 18:46
• @Deusovi - each component has a definition adjacent to it. The first may be a little loose by US standards, but only a little. – DeveloperInDevelopment May 29 '16 at 19:05
### The full message is...
HAVE A COOKIE WHEN YOU GAIN REPUTATION!
### Annotation:
COOK + I.E., with H + AVE. + A placed earlier
[-la]W[-yer] + HEN
Y + [-acc]OU[-nts]
[-a]GAIN
REPUTATION[-m]*
### More detailed explanation:
"Alter, fraudulently that is, earlier 8th avenue article. Take a treat...
Alter fraudulently is COOK; "that is" is I.E., and then earlier we add the 8th letter (H) plus avenue (AVE) and an article (A) to get [H+AVE + A + COOK+IE]. The definition is "Take a treat".
...at such time as lawyer is point-first - the rest is poultry.
WHEN: The "point" of "lawyer" could be the WY in the middle, then "first" could tell us to take the first of the two. W + HEN (the rest is poultry), def "at such time as"? Not quite sure if I've interpreted it correctly though.
Reader! Why, we hear accounts' core...
YOU ( "Y", heard, plus accOUnts: def "reader")
...again lacks a profit!
GAIN (AGAIN, lacking A: def "profit")
Permutation, without morals first, hurts standing."
REPUTATION (anagram of PERmUTATION: def "standing")
• "accounts' core" - right first time, "why, we hear" - right, "morals first" - right. Wrong on alter, fraudulently and permutation... nice start. – DeveloperInDevelopment May 29 '16 at 19:01
• doing well so far... wrong with point. Hint: lawyer has two opposing points. – DeveloperInDevelopment May 29 '16 at 19:14
• Words 1 and 3 are wrong. A little general knowledge is needed, but it's linguistic in nature, not geographical. – DeveloperInDevelopment May 29 '16 at 19:36
• @DeveloperInDevelopment: HANDLE is wrong? Huh, I was fairly sure about that one. – Deusovi May 29 '16 at 19:37
• @Deusovi It looks as if you pretty much have this. Maybe "take" is in the sense of being "on the take" leading to the word "payoff" or something like it. – Hugh Meyers May 30 '16 at 9:37
See Desuovi's answer for the majority of the work. I'm concentrating on the first line only here.
From the hint...
"alter fraudulently" is a profession (not doctor), so how about cook?
and...
"that is" is another way of putting the Latin abbreviation i.e.
so together we have... | 2021-07-27 08:29:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5804622173309326, "perplexity": 3751.9350539003303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1627046153223.30/warc/CC-MAIN-20210727072531-20210727102531-00121.warc.gz"} |
http://wikimechanics.org/pressure | Pressure
Leptomedusae, Ernst Haeckel, Kunstformen der Natur. Chromolithograph 32 x 40 cm, Verlag des Bibliographischen Instituts, Leipzig 1899-1904. Photograph by D Dunlop.
Let some particle P be represented by a chain of repetitive events
$\Psi ^{\sf{P}} = \left( \sf{\Omega}_{1} , \sf{\Omega}_{2}, \sf{\Omega}_{3} \ \ldots \ \right)$
which are described by the total number of ordinary-quarks $N_{\sf{o}}$ that they contain, and $\tilde{ U } _{\! \sf{o}}$ the average internal energy of these ordinary-quarks. Moreover, let P be made of atoms so that it can be modeled as a cylinder of volume $V$ in a Euclidean space. Definition: the pressure inside P is the number
\begin{align} P \equiv \frac{ -2 \, N_{\sf{o}} \tilde{ U} _{\! \sf{o}} }{V} \end{align}
This expression describes ordinary quarks only, no anti-quarks included. But for particles with a lot of phase anti-symmetry like photons, quarks and anti-quarks are almost evenly matched. Then the total number of ordinary-quarks is close to half the number of all quarks $N_{\sf{o}} \simeq N /2$. Also, on average both sets of quarks will have the same internal energy $\tilde{U}_{\! \sf{o}} \simeq \tilde{U} \equiv U / N$. Then overall
\begin{align} P \simeq \left( \frac{-2}{V} \right) \left( \frac{N}{2} \right) \left( \frac{U}{N} \right) = - \frac{U}{V} \end{align}
and the pressure approximates an energy density due to all the quarks in P, not just the ordinary quarks.
$H-U = P V$
Next step: length.
page revision: 268, last edited: 10 May 2017 19:23 | 2017-05-25 08:40:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 6, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.994117021560669, "perplexity": 2155.7415597577638}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608058.13/warc/CC-MAIN-20170525083009-20170525103009-00302.warc.gz"} |
http://mathhelpforum.com/geometry/220174-sequences-geometry-question-print.html | # Sequences Geometry Question
• June 26th 2013, 12:51 PM
Espionage
Sequences Geometry Question
Attachment 28674
"In the diagram, one circle is inscribed in each square and one square is inscribed in each circle, with this process being continued infinitely. the area between each square and the circle inscribed in it is shaded. What proportion of the area inside the largest square is shaded?
• June 26th 2013, 01:32 PM
Shakarri
Re: Sequences Geometry Question
The sum of the shaded areas is [area of biggest square]-[area of biggest circle]+[area of next biggest square]-[area of next biggest circle]+...
Split this into two series
[area of biggest square]+[area of next biggest square]+...
And
-[area of biggest circle]-[area of next biggest circle]-...
Examining the two largest squares you can see using pythagoras' theorem you can see that the smaller square's side length is $\sqrt{2}$ times smaller than the larger square's side. This ratio is constant for each set of squares so the first series mentioned above is an infinite geometric series.
The diameter of the circle is equal to the length of the side of the square it is inside, the square's side length is decreasing in a geometric series so the diameter of each circle will also decrease in a geometric series. Use this information to determine the sum of the second series mentioned above.
• June 27th 2013, 11:40 AM
Espionage
Re: Sequences Geometry Question
Thank you! | 2016-07-25 21:17:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7671873569488525, "perplexity": 799.0518333629874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257824345.69/warc/CC-MAIN-20160723071024-00230-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://datascience.stackexchange.com/questions/17219/how-to-do-imbalanced-classification-in-deep-learning-tensorflow-rnn | # How to do imbalanced classification in deep learning (tensorflow, RNN)?
I am trying to do binary classification of News Articles (Sports/Non-Sports) using recurrent neural net in tensorflow. The training data is highly skewed [Sports:Non-Sports::1:9].
I am using cross-entropy as my cost function, which treats both classes equally.
What are the ways by which user can penalise one class? Or is there any other cost function suitable for this purpose?
The suggestion in both cases was to add class weights to the loss function, by multiplying logits:
loss(x, class) = weights[class] * (-x[class] + log(\sum_j exp(x[j])))
For example, in tensorflow you could do:
ratio = 31.0 / (500.0 + 31.0)
class_weight = tf.constant([ratio, 1.0 - ratio])
logits = ... # shape [batch_size, 2]
weighted_logits = tf.mul(logits, class_weight) # shape [batch_size, 2]
xent = tf.nn.softmax_cross_entropy_with_logits(
weighted_logits, labels, name="xent_raw")
• I don't think you really want to multiply logits by weights but cross entropy by weights. See this answer for a correct implementation: stackoverflow.com/questions/35155655/… Mar 7 '17 at 8:47 | 2021-09-17 13:53:31 | {"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": 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": 0.3027516007423401, "perplexity": 3935.7057623196633}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1631780055645.75/warc/CC-MAIN-20210917120628-20210917150628-00333.warc.gz"} |
https://www.hackmath.net/en/math-problem/2606 | # On the tree
15 squids and sparrows sat on the tree. Sparrows were 8 less than squids. How many sparrows were sitting at the tree?
Correct result:
x = 7
#### Solution:
$x=15-8=7$
We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!
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https://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-for-college-students-7th-edition/chapter-2-section-2-4-linear-functions-and-slope-exercise-set-page-152/53 | ## Intermediate Algebra for College Students (7th Edition)
Divide 3 on both sides of the equation to obtain: $y=\frac{18}{3} \\y=6$ RECALL: The graph of the equation $y=k$ is a horizontal line. Every point on the line has the same y-value. Thus, to graph $y=6$, you can plot the points (0, 6), (-3, 6), and (3, 6). Then, connect them using a line. | 2018-08-20 08:07:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3988322913646698, "perplexity": 192.07278363677273}, "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-2018-34/segments/1534221215858.81/warc/CC-MAIN-20180820062343-20180820082343-00222.warc.gz"} |
https://www.esaral.com/q/if-the-time-period-of-a-two-meter-long-simple-pendulum-75940 | # If the time period of a two meter long simple pendulum
Question:
If the time period of a two meter long simple pendulum is $2 \mathrm{~s}$, the acceleration due to gravity at the place where pendulum is executing S.H.M. is :
1. $\pi^{2} \mathrm{~ms}^{-2}$
2. $9.8 \mathrm{~ms}^{-2}$
3. $2 \pi^{2} \mathrm{~ms}^{-2}$
4. $16 \mathrm{~m} / \mathrm{s}^{2}$
Correct Option: , 3
Solution:
$\mathrm{T}=2 \pi \sqrt{\frac{l}{\mathrm{~g}}}$
$2=2 \pi \sqrt{\frac{2}{g}}$
$\Rightarrow \mathrm{g}=2 \pi^{2}$ | 2023-02-04 22:02:54 | {"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": 0.9618014097213745, "perplexity": 842.7478599764588}, "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-2023-06/segments/1674764500154.33/warc/CC-MAIN-20230204205328-20230204235328-00006.warc.gz"} |
https://socratic.org/questions/58ea23dab72cff5d7303800d | # Are angular nodes necessarily planes?
Angular nodes are determined by finding what $l$ corresponds to the orbital you are looking at.
For example, a $3 d$ orbital has $l = 2$, so it has two angular nodes. These happen to usually be nodal planes. For a $3 {d}_{x y}$ orbital, these are the $x z$ and $y z$ planes.
However, for the $3 {d}_{{z}^{2}}$ orbital, the two angular nodes correspond to the two conical nodes: the top half and the bottom half (these are at around ${54.74}^{\circ}$ from the $z$ axis). | 2019-12-10 01:58:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.910239040851593, "perplexity": 568.8033172512392}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540525781.64/warc/CC-MAIN-20191210013645-20191210041645-00160.warc.gz"} |