url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
|---|---|---|---|
http://stats.stackexchange.com/questions?pagesize=50&sort=newest | # All Questions
2 views
### Model estimation procedure by using Backward elimination
I have been run the multiple linear model by using minitab. the result showed that all variables are not significant. so, I use the method backward elimination. Lastly, I found that one variable is ...
5 views
### Model specification
Actually I want to see the impact of Investors sentiment on Aggregate stock market return, so my major concern is to identify the impact of investors sentiment. But besides investors sentiment I want ...
6 views
### given mean and standard deviation, find value of given percentile
I'm running a DnD campaign and made a Random NPC generator in Excel. It's pretty slick, but the random height/weight calculator is... flat. RAND(X,Y) flat. So I'd like to add some Bell Curve ...
6 views
### Proper splitting of data set for Ensemble methods
I have 10,000 documents. Each document has a label ($Y$) that is either $0$ or $1$ (the 0-1 split is pretty much 50/50 over my 10,000 documents). Each document has 10 fields. Each field can have any ...
13 views
### Difference between arithmetic vs geometric random walk
I have read about arithmetic and geometric random walks. What is the difference between them?
3 views
### Variance Estimation in case of nonrespondents
I saw in the book of Rubin (1987) that an increase in variance of estimation will occur due to nonresponses. But I wonder the reason behind this. Thanks for your shares!
12 views
### categorizing monthly gross income
what is the best way to categorize or even bin monthly gross income? As of now, the variable for income is numeric and continuous. I have seen many examples for annual income. Should I categorize ...
8 views
### Multi-response GLMM in Jags
I have a data set with 8 response variables (all counts, they are 8 species of mammals). The responses are not independent, and I would like to measure the covariance between them (different ...
13 views
### Distribution for semi open interval
I have an application where I get back the time to perform an operation, the times are in the interval ]0:inf[ and I have this crazy idea. Lets say I know the mean ...
15 views
### How to transform data into discrete-time or time-to-event problem
I have a breast cancer dataset and my goal is to predict a patient's risk per time period using classifiers in WEKA. According to this thread about employment with a similar nature as to my problem, ...
16 views
### Help in Bayesian modeling with WinBUGS [on hold]
I am currently working on my thesis and interested in factor analysis for spatially correlated data using WinBUGS. I wrote the model but when am trying to use it ...
10 views
### R-Cran Imbalanced data Smote problem [migrated]
I am using the following CRAN package DMwR to deal with the problem of imbalanced data : Code is the following: ...
10 views
38 views
### Running a Tukey's test on a repeated measures ANOVA in R
I've come across several posts dealing with post hoc tests of Repeated Measurs ANOVA. I came up with the below code in R to attempt this, but considering some of the posts on this subject I wanted to ...
35 views
### Confused with this confidence interval statistics
The formula used to compute a confidence interval for the mean of a normal population when n is small is the following. What is the appropriate t critical value for each of the following ... | 2013-12-13 04:40:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8495227694511414, "perplexity": 1503.651824108767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164858282/warc/CC-MAIN-20131204134738-00076-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/180470/problem-scaling-logarithmic-function-pstricks | # Problem Scaling Logarithmic function PSTricks
I'm trying to plot a function, but with the x-axis logarithmic. I use PSTricks and the package pstricks-addwith the algebraic option, to write my function litterally. My function to be plotted is :
I want to have the X-axis logarithmic, from 10^-1 to 10^2... But I can't figure how to do it...
Here's what I tried...
\psset{xunit=2,yunit=6, algebraic}
\begin{pspicture}[showgrid=false](0,0)(2,1)
\psaxes[xlogBase=10, comma,subticks=5,
arrowscale=1.5]{->}(3,0.8)[Voltage (V),-90][Yield (\%),90]
\psplot[linecolor=red]{0.01}{2}{(x/(1+(1+x^2)^0.5))^2}
\end{pspicture}
That generates this : What I want to have is this :
Does I have to adapt the function so that it fits the non-logarithmic grid once plotted ? I don't understand the principe of plotting a log function in a non-log grid...
If you could also explain me that it would be great.
Here is a solution for PSTricks.
\documentclass[pstricks,border=10pt]{standalone}
\begin{document}
\psset{xunit=2,yunit=6,plotpoints=500,algebraic=true,linewidth=0.5pt,dash=2pt 2pt}
\begin{pspicture}(-1.4,-0.2)(3.9,1.2)
\psaxes[axesstyle=frame,xlogBase=10,comma,logLines=x,dy=0.2,Dy=20,xsubticks=9,
yticksize=0 4,subticklinestyle=dashed,ticklinestyle=dashed,Ox={-1}](-1,0)(3,1.0)[Voltage (V),0][Yield (\%),90]
\psplot[linecolor=red]{-1}{3}{10^x^2/(1+sqrt(1+10^x^2))^2}
\end{pspicture}
\end{document}
• So the trick is to manually transform the function by replacing x with 10^x, correct? – Jake May 26 '14 at 17:54
• Yes indeed ! I'll remember it for the next time ;) Thanks again ! – 3isenHeim May 26 '14 at 17:58
• I am sorry. Your signature name (i.e., Thomas, probably Thomas Söll) is no longer needed in the contents as the user profile link has been automatically attached to the bottom right corner of the post. – kiss my armpit May 26 '14 at 18:06
Here's how you would do this with PGFPlots:
\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\begin{document}
\begin{tikzpicture}%
\begin{axis}[%
xmode = log, % X axis is logarithmic
domain = 1e-1:1e2, % Domain over which the function is evaluated
ymax = 100, % Explicitly set the upper limit of the Y axis (the others are automatically determined) | 2020-08-08 23:46:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8299242258071899, "perplexity": 1799.3232919494142}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738366.27/warc/CC-MAIN-20200808224308-20200809014308-00333.warc.gz"} |
https://chemistry.stackexchange.com/questions/16617/which-atoms-in-a-given-amino-acid-are-able-to-form-hydrogen-bonds-with-water | # Which atoms in a given amino acid are able to form hydrogen bonds with water?
Can anyone help me with this question I have tried everything. I know hydrogen bonding is with $\ce{F}$, $\ce{O}$, or $\ce{N}$, but every time I select those is says it's wrong.
• Which part of the question are you getting wrong? Top, bottom, or both? I'm guessing that if it's the bottom, then you need to include H in your list of H-bonding atoms to choose from. – jerepierre Sep 22 '14 at 23:06
The positive end of water can hydrogen bond with N, O, or F, as you said, but only if A) the geometry of the atom allows the water and N/O/F to get close to one another and B) the N/O/F has a lone pair of electrons. This happens at each of the green circled nitrogen and oxygen atoms. The red circled nitrogen is a decoy, as it is neither geometrically available nor does it have the appropriate configuration of electrons.
The negative end of water can hydrogen bond with hydrogen atoms that are attached to the N/O/F atoms, including the ones that are attached to the N atom that was not correct for the first part. | 2019-11-12 23:58:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5183222889900208, "perplexity": 408.18956766577196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665809.73/warc/CC-MAIN-20191112230002-20191113014002-00342.warc.gz"} |
https://de.maplesoft.com/support/help/view.aspx?path=fdiscont | fdiscont - Maple Help
fdiscont
numerically find the discontinuities of a function over the Reals
Calling Sequence fdiscont(f, domain, res, ivar, eqns)
Parameters
f - algebraic expression or a procedure domain - the domain of interest res - the desired resolution ivar - the independent variable name eqns - optional equations
Description
• fdiscont attempts to return a list of ranges, each of width res, in which there appears to be a discontinuity in the function or its first derivative. fdiscont works via the application of divided differences. This method will not locate point discontinuities, nor can it differentiate between cusps and singularities or jump discontinuities. Note that absolute success is not guaranteed. In addition, ranges may be larger than res due to overlapping results, which are coalesced.
• fdiscont can be fooled by dense oscillatory functions (such as $\mathrm{sin}\left(500x\right)$ on $0..\mathrm{\pi }$); if features are found that are not expected, the resolution, res, should be made smaller. If too few singularities are found, res should be made smaller, or in the evalhf case, the amount of internal storage (see number below) should be increased.
• fdiscont uses evalhf when possible. However, in this instance, the number of ranges returned is limited by the size of the internal work array. Use the number option to change this limit.
• f may be an algebraic expression in ivar or a procedure. If f is algebraic, then ivar must be specified in ivar or domain (see below). If f is a procedure, it may only take one argument, and must return a single value of type realcons.
• domain is used to define the domain of interest of f. It may be specified as either of:
left..right
ivar= left..right
left and right must be of type realcons. When f is algebraic, the second form above may be used to specify ivar. Note that the initial evaluation mesh extends at most from left-res/10 to right+res/10 under evalhf, whereas the range is strictly adhered to under evalf.
• res indicates the desired width for returned ranges. The minimum allowable resolution is given by 10^(-evalhf(Digits)+5) under evalhf, and 10^(-Digits+2) under evalf. The maximum resolution for computation is (right-left)/bins, where bins is the number of bins used when generating the mesh. If res falls outside of these bounds, it will be internally set to the closer of the two. The default is 0.001.
• The available option equations eqns are:
• bins = integer
bins indicates the number of bins to be used in the evaluation mesh. Better results are generally obtained for higher mesh values, but at the expense of efficiency. It is recommended that bins be an odd number. The default is 21.
• newton = true, false
If newton is true, then fdiscont attempts to apply an inverse modified Newton method (secant method) on each of the returned ranges. This method will not work if f is a procedure. The inverse of f is evaluated under a secant method, to a maximum of twenty iterations. If successful, the final point is returned, otherwise the original range of interest is returned. This method generally works best if res is not overly restrictive (i.e. for res of magnitude $\frac{1}{10}$ or $\frac{1}{100}$). The default is false.
• number = integer
number indicates the maximum number of features (ranges) to be stored while working under evalhf mode. This value will have no effect in evalf mode. Note that fewer than number features may be returned (even if more exist) due to coalescing by fdiscont of overlapping features. The default is 20. The global variable _FullFeatures indicates if the internal work array has reached its maximum capacity.
• order = integer
order specifies the order of divided differences to use. The default is 3, as this produces good results without excessive computation. The minimum order is 2, while the maximum is 7.
• pts = true, false
pts indicates if evaluation points should be returned along with features. If set to true, then coordinates from the evaluation mesh will be stored and returned, up to three levels of recursion. If true, then output will take the form of a list of two lists, the first being the features, the second the evaluation coordinates. The default is false.
Examples
> $\mathrm{Digits}≔10:$
> $\mathrm{fdiscont}\left(\mathrm{round}\left(3x-\frac{1}{2}\right),x=0..1,{10}^{-7}\right)$
$\left[{-5.97247787204555}{×}{{10}}^{{-9}}{..}{2.65525067174041}{×}{{10}}^{{-8}}{,}{0.333333310326452}{..}{0.333333363941237}{,}{0.666666639409403}{..}{0.666666693024186}{,}{0.999999977055700}{..}{1.00000000958068}\right]$ (1)
> $\mathrm{fdiscont}\left(\mathrm{\Gamma }\left(\frac{x}{2}\right),x=-10..0,0.0001\right)$
$\left[{-10.0000064078543}{..}{-9.99993927514037}{,}{-8.00003106980371}{..}{-7.99994084830369}{,}{-6.00005707576568}{..}{-5.99993426192709}{,}{-4.00002710954038}{..}{-3.99993920185425}{,}{-2.00005817730074}{..}{-1.99993053673628}{,}{-0.0000627494543392766}{..}{0.0000184808550829652}\right]$ (2)
> $\mathrm{fdiscont}\left(\frac{\mathrm{arctan}\left(\frac{1}{2}\mathrm{tan}\left(2x\right)\right)}{{x}^{2}-1},x=-\mathrm{\pi }..2\mathrm{\pi }\right)$
$\left[{-2.35652137480250}{..}{-2.35596067534308}{,}{-1.00025742285816}{..}{-0.999227423613648}{,}{-0.785714651862252}{..}{-0.785150744271861}{,}{0.785004677126996}{..}{0.785782328840973}{,}{0.999744978088726}{..}{1.00071996650187}{,}{2.35596549899697}{..}{2.35651830946881}{,}{3.92664555302272}{..}{3.92723287040263}{,}{5.49735231158500}{..}{5.49831164678780}\right]$ (3)
> $\mathrm{fdiscont}\left(\frac{1}{x-1}+\frac{1}{x-\frac{985}{1000}}+\frac{1}{x-3},x=0..4,{10}^{-2},\mathrm{newton}=\mathrm{true}\right)$
$\left[{0.984999999999999987}{,}{1.}{,}{3.}\right]$ (4)
> $\mathrm{fdiscont}\left(\mathrm{abs}\left(\frac{x}{10000}\right),x=-1..1,0.001\right)$
$\left[{-0.000248087903234934}{..}{0.0000797181063895528}\right]$ (5)
> $\mathrm{fdiscont}\left(\mathrm{tan}\left(10x\right),x=0..\mathrm{\pi },0.01,\mathrm{newton}=\mathrm{true}\right)$
$\left[{0.157079632679489656}{,}{0.471238898038468967}{,}{0.785398163397448279}{,}{1.09955742875642759}{,}{1.41371669411540690}{,}{1.72787595947438644}{,}{2.04203522483336553}{,}{2.35619449019234484}{,}{2.67035375555132415}{,}{2.98451302091030346}\right]$ (6)
sin(75*x) gives features when the resolution is as large as 0.1.
> $\mathrm{fdiscont}\left(\mathrm{sin}\left(75x\right),x=0..\mathrm{\pi },0.1\right)$
$\left[{-0.00716853617115685}{..}{0.0678131265464373}{,}{0.136567579788193}{..}{0.257290685764021}{,}{0.348829416601809}{..}{0.394619464769929}{,}{0.513757401830869}{..}{0.681567685378298}{,}{0.831869568667211}{..}{0.983296560340123}{,}{1.06027990775354}{..}{1.14928056268042}{,}{1.27081664687715}{..}{1.31676353406636}{,}{1.43825414301612}{..}{1.77784313487576}{,}{1.94076348628333}{..}{2.02916586323560}{,}{2.07278488816223}{..}{2.48438428422120}{,}{2.60967538816638}{..}{2.70000715344082}{,}{2.77870415685020}{..}{2.87079535747023}{,}{3.02916146460515}{..}{3.11958880620431}\right]$ (7)
Narrowing the resolution to 0.001 shows there are no features.
> $\mathrm{fdiscont}\left(\mathrm{sin}\left(75x\right),x=0..\mathrm{\pi },0.001\right)$
$\left[\right]$ (8) | 2022-08-13 14:47:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 21, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8008302450180054, "perplexity": 2055.3973811405854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1659882571959.66/warc/CC-MAIN-20220813142020-20220813172020-00482.warc.gz"} |
https://solvedlib.com/question-1-a-explai-ur-undesianding-about-2m,72533 | # Question 1: a) Explai ur undesianding about (2m) accounting b) Explain TWO (3) purposes of accounting...
###### Question:
Question 1: a) Explai ur undesianding about (2m) accounting b) Explain TWO (3) purposes of accounting information. e) What is the purpose of preparation Statement of Profit or Loss (3m) and Statement of Financial Position by the company (3m)
#### Similar Solved Questions
##### Why is the GTP produced by succinate synthase considered equivalent to an ATP in terms of...
Why is the GTP produced by succinate synthase considered equivalent to an ATP in terms of net energy capture...
##### Identify the federal law which promoted employer benefit programs and has been found to prohibit state...
Identify the federal law which promoted employer benefit programs and has been found to prohibit state law claims ( such as malpractice and negligence claims) against insurance companies that are part of an employer sponsored health plan....
##### 8 8 8 8 E 1 HH [ H L H { 7 2 JHJHU } 89 1 1 Wa 7 Lelg } 0 [ 8 7 { 8 1 8 { } { } 6 1 1 H HHHH 3 [ 6F [ ; [ E E [ I 1 8 1 1 7 ? 7 88 1 8 HF 7 1 | H 1 H HHH 38 [ HHiik [ 1 ; ; 1 1 E [[ 6 3 4 1 1 [ 9 1 1 IAHI 1
8 8 8 8 E 1 HH [ H L H { 7 2 JHJHU } 89 1 1 Wa 7 Lelg } 0 [ 8 7 { 8 1 8 { } { } 6 1 1 H HHHH 3 [ 6F [ ; [ E E [ I 1 8 1 1 7 ? 7 88 1 8 HF 7 1 | H 1 H HHH 38 [ HHiik [ 1 ; ; 1 1 E [[ 6 3 4 1 1 [ 9 1 1 IAHI 1...
##### $ext { Find } lim _{2 ightarrow 1.1} frac{z^{2}+z-1-3 i}{z^{2}-2 z+2} ext { by factoring. }$
$ext { Find } lim _{2 ightarrow 1.1} frac{z^{2}+z-1-3 i}{z^{2}-2 z+2} ext { by factoring. }$...
##### • Provide a feasible multi-step synthesis for the following transformation • Write the steps using UPPERCASE...
• Provide a feasible multi-step synthesis for the following transformation • Write the steps using UPPERCASE letters in the space provided. • If you need 2 or more equivalence of the same reagent for the step, then write the number of equivalence after the letter, for example A2 ans 2...
##### Drag and drop the Better Business Bureau's Torch Award Criteria to its example and click Submit....
Drag and drop the Better Business Bureau's Torch Award Criteria to its example and click Submit. Please place the Answers in alphabetical order. Community/ Investors/ Communications and Marketing Practices Management Practices Industry Reputation Stakeholder Relations Media coverage reflecting t...
##### Question 1The number of times a machine malfunctions per week follows a Poisson distribution and the probability that it does not malfunction at all during one week equals e-1/2 What is the expected value of the number of times it malfunctions in a certain 52 week period?Not yet answeredMarked out of 3.00Flag questionWhat is the variance in the number of times it malfunctions in that 52 week period?
Question 1 The number of times a machine malfunctions per week follows a Poisson distribution and the probability that it does not malfunction at all during one week equals e-1/2 What is the expected value of the number of times it malfunctions in a certain 52 week period? Not yet answered Marked ou...
##### 7. Solving for the WACC The weighted average cost of capital (WACC) is used as the...
7. Solving for the WACC The weighted average cost of capital (WACC) is used as the discount rate to evaluate various capital budgeting projects. However, it is important to realize that the WACC is an appropriate discount rate only for a project of average risk. Consider the case of Turnbull Company...
##### QUESTION 2 (15 Marks) Sonop Company manufactures furniture in the Northen Subhurbs of Cape Town. The...
QUESTION 2 (15 Marks) Sonop Company manufactures furniture in the Northen Subhurbs of Cape Town. The company prepared the following budget for the coming year: Product A Product B Product C Total Sales 85714 1000000 177777 Variable exp. 25714 800000 97777 Contrib. mar. 60000 200000 80000 Fixed exp. ...
##### [~13 Points]DETAILSSWOKPRECFind the exact degree measure of the angle_Sn(a)5n (b)Jt(c)Need Help? Rqdll
[~13 Points] DETAILS SWOKPREC Find the exact degree measure of the angle_ Sn (a) 5n (b) Jt (c) Need Help? Rqdll...
##### CCLoi F1fd)dP2-28 For a scalar function f and a vector function prove that (fA) = fV.A + A . Vf in Cartesian coordinates
CCLoi F1fd)d P2-28 For a scalar function f and a vector function prove that (fA) = fV.A + A . Vf in Cartesian coordinates...
##### Lim Zx ~Ir+lGarth Butcher No. You are meant to prove using the delta-epsilon definition. You can try to follow example 2 on page 108382+-5)lim -actoringlim( Zx _ 5)Cancelling out common factors mumeralo and denomonator(2(3)-5)PILg In x ,which is 3
lim Zx ~Ir+l Garth Butcher No. You are meant to prove using the delta-epsilon definition. You can try to follow example 2 on page 108 382+-5) lim - actoring lim( Zx _ 5) Cancelling out common factors mumeralo and denomonator (2(3)-5) PILg In x ,which is 3...
##### 1Deterron11(ne (ollc;beld.INa11
1 Deterron 1 1 (ne (ollc; beld. INa 1 1...
##### 24. Calculate the line integral along [F-dr for FG,y) =Srl+2yi and ending = at (4,4). and C is any path starting - at the point (0, 0)92 b. 736c. 352 d 184 368
24. Calculate the line integral along [F-dr for FG,y) =Srl+2yi and ending = at (4,4). and C is any path starting - at the point (0, 0) 92 b. 736 c. 352 d 184 368...
##### Which of the following characteristics accurately describes an audit? A) Fraudulent activities are always discovered by...
Which of the following characteristics accurately describes an audit? A) Fraudulent activities are always discovered by auditors B) Provides absolute assurance to the users of the financial statements. C) All transactions of an organization are reviewed. D) Obtains sufficient appropriate evidence to...
##### [12)Express the equation sin 0 = -1 in rectangular coordinates_ a) 0C93202b) 0 *c) 0 xd) 0y =
[12)Express the equation sin 0 = -1 in rectangular coordinates_ a) 0 C93202 b) 0 * c) 0 x d) 0 y =...
##### How do you evaluate (2z-15x)/(3y) if w=6, x=0.4, y=1/2, z=-3?
How do you evaluate (2z-15x)/(3y) if w=6, x=0.4, y=1/2, z=-3?...
##### Particle moving in the xY-plane subject to force(xi + yj) F(x, y) = (60 N . mz} x2 _ y2)3/2 where x and y are in meters_ Calculate the work (in J) done on the particle by this force as it moves in straight line from the point (8 m, 9 m) to the point m; m)_
particle moving in the xY-plane subject to force (xi + yj) F(x, y) = (60 N . mz} x2 _ y2)3/2 where x and y are in meters_ Calculate the work (in J) done on the particle by this force as it moves in straight line from the point (8 m, 9 m) to the point m; m)_...
##### LI LUMPUy leur Le Tullowing amounts on its statement of cash flow. Net cash provided by...
LI LUMPUy leur Le Tullowing amounts on its statement of cash flow. Net cash provided by operating activities was $30,000; net cash used in investing activities was$10,800 and net cash used in financing activities was $13,200. If the beginning cash balance is$5,400, what is the ending cash balance?...
##### 1. What conditions should be fulfilled before retention is used in a risk management program (3...
1. What conditions should be fulfilled before retention is used in a risk management program (3 points)? 2. You operate a food supply company. Your primary customers are restaurants. You provide delivery services to select customers Determine the potential direct and indirect losses that you might i...
##### The first two terms of an arithmetic sequence are a_1 = 2 and a_2 = 4. What is a_10, the tenth term?
The first two terms of an arithmetic sequence are a_1 = 2 and a_2 = 4. What is a_10, the tenth term?...
##### Problem. In class we saw that the even moments of the standard Gaussian Xx(0,1) are given...
Problem. In class we saw that the even moments of the standard Gaussian Xx(0,1) are given by: EX2 = (2k – 1)!! = (2k – 1)(2k – 3)...31 (2k)! 2kk! Meanwhile the odd moments vanish. The goal of this exercise is to prove the CLT by the method of moments. Suppose X1, X2, ..., X, are in...
##### The following is a disaceharide with a(n)elycosidic bondChORCAOHA) B(1-4) B) P,P(1 8)040,4 D) (1,W) E) B, B(1 ,4)
The following is a disaceharide with a(n) elycosidic bond ChOR CAOH A) B(1-4) B) P,P(1 8)040,4 D) (1,W) E) B, B(1 ,4)...
##### Unknown unless we know the MeaaThe est RconeQuastlonout oiTwo hiqh school sludents Iook equlvalem lanquage lests; one German and ore in French The student taking Ilte Gornn tebL; (or wich Ino mican was 06 und tho tundard dovlalion wur ucolicd 02. while the bludont Aukung Iho Frgnch Ienl, (or wleh Ilu moni 27 and Ihu elnndard devlution Whs acaledCompure Ihe EcorosBelecledAnowcThe (wo scores are statisIlcally the Hamnn scOru 35 wath HI ol 27 and standard devlalion 0f 5 belter:AD eThe (wo scores a
unknown unless we know the Meaa The est Rcone Quastlon out oi Two hiqh school sludents Iook equlvalem lanquage lests; one German and ore in French The student taking Ilte Gornn tebL; (or wich Ino mican was 06 und tho tundard dovlalion wur ucolicd 02. while the bludont Aukung Iho Frgnch Ienl, (or wl...
##### Find the projection of u onto v (6, 6) (8, 1)projvuWrite u as the sum of two orthogonal vectors one of which is projvu:projvuNeed Help?Eoadli
Find the projection of u onto v (6, 6) (8, 1) projvu Write u as the sum of two orthogonal vectors one of which is projvu: projvu Need Help? Eoadli...
##### (A) If the answer in (b) is greater than the answer in (c) then we conclude at the 3% significance level that the average cholesterol level of children whose father died from heart disease is higher than the national average. (B) If the answer in (a) is greater than the answer in (b) then we cannot conclude at the 3% significance level that the average cholesterol level of children whose father died from heart disease is higher than the national average. (C) If the answer in (c) is less than 0.0
(A) If the answer in (b) is greater than the answer in (c) then we conclude at the 3% significance level that the average cholesterol level of children whose father died from heart disease is higher than the national average. (B) If the answer in (a) is greater than the answer in (b) then we cannot ...
##### Question 2: A(n) ____ safety meeting is an on-site meeting held with all workers and their...
question 2: A(n) ____ safety meeting is an on-site meeting held with all workers and their supervisors in an attempt to reinforce the many jobsite hazards that may exist and the consequences of unsafe actions for individual workers. - toolbox - partnering - preconstruction - orga...
##### Q3) In the mechanism shown below, the flexible band is attached at point of E of the circular body and leads over the guide pulley. Determine the angular acceleration of BD for the position shown if...
Q3) In the mechanism shown below, the flexible band is attached at point of E of the circular body and leads over the guide pulley. Determine the angular acceleration of BD for the position shown if the band has a velocity of 4 m/s. (-46.9 rad/s2) 4 m/s 75 200 20 100 125 250 Q3) In the mechanism sh...
##### Quastion 129 psThe probability density function for random variable Xis given in the table below: Pr[X=x]Compute each of the following three statistics. Put your answer in the blank next to each question: For part (b}, you may make use of the formula for variance: Var(X) E(X?) (E(X)E(X)Var(X)o(X)Give your answer to part (c) to 3 decimal places:
Quastion 12 9 ps The probability density function for random variable Xis given in the table below: Pr[X=x] Compute each of the following three statistics. Put your answer in the blank next to each question: For part (b}, you may make use of the formula for variance: Var(X) E(X?) (E(X) E(X) Var(X) o...
##### The frequency factor for a reaction is 1.72x10^10 s^−1.If the rate constant is 5.63x10^4 s^−1 at...
The frequency factor for a reaction is 1.72x10^10 s^−1.If the rate constant is 5.63x10^4 s^−1 at 300 K, what will the rate constant be at 400K? a)7.49x106s−1 b)3.96x105s−1 c)4.22x107s−1 d)2.62x104s−1 e)1.32x106s−1...
##### Vector Addition using Component Method Exercise 2Open in AcObalExercise: One displacement vector A has a magnitude of 2.43km and points due north: A second displacement vector B has a magnitude of 7.74km and also points due north_ (1) Find the magnitude and direction of A-B_ (2) Find the magnitude and direction of B-A
Vector Addition using Component Method Exercise 2 Open in AcObal Exercise: One displacement vector A has a magnitude of 2.43km and points due north: A second displacement vector B has a magnitude of 7.74km and also points due north_ (1) Find the magnitude and direction of A-B_ (2) Find the magni...
##### 14. x" + 2x + 4y = 0, y" + x + 2y = 0; x(0) = y(0) = 0 x' (0) = y (0) = -1
14. x" + 2x + 4y = 0, y" + x + 2y = 0; x(0) = y(0) = 0 x' (0) = y (0) = -1...
##### Using the method of undeterminexl coefficients find the solution t0 each differential FuAtO subject to the initial conditions given below . 2v +Jy = € (cos 21 3sin 22). 9(O) = 1/2 " () =2 29" + Y = 1+je'_ "(o) = =Y(0) =0, v(0) =1
Using the method of undeterminexl coefficients find the solution t0 each differential FuAtO subject to the initial conditions given below . 2v +Jy = € (cos 21 3sin 22). 9(O) = 1/2 " () =2 29" + Y = 1+je'_ "(o) = =Y(0) =0, v(0) =1... | 2022-07-06 07:39:52 | {"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": 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": 0.4966544806957245, "perplexity": 3623.3421384013504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656104668059.88/warc/CC-MAIN-20220706060502-20220706090502-00542.warc.gz"} |
http://www.helpteaching.com/questions/Geometry_and_Measurement/Grade_7 | Looking for Geometry worksheets?
Check out our pre-made Geometry worksheets!
Tweet
##### Browse Questions
• Arts (529)
• English Language Arts (4913)
• Ethics (1)
• Foreign Languages (23)
• Health and Medicine (426)
• Life Skills (27)
• Math (2939)
• ### Volume
• #### Trigonometry
• Physical Education (407)
• Pop Culture (5)
• Public Safety (21)
• Science (4392)
• Social Sciences (18)
• Social Studies (1927)
• Study Skills and Strategies (35)
• Technology (68)
• Vocational Education (74)
• Other (211)
You can create printable tests and worksheets from these Grade 7 Geometry and Measurement questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.
1 2 3 4 ... 23
Based on the following information, which equation could be used to solve for x?
$mangDBC = x$
$mangCBA = 2x$
1. $2x - x = 90$
2. $2x + x = 90$
3. $2x - x = 180$
4. $2x + x = 180$
Which pair of angles are vertical angles?
1. $ang 1 and ang2$
2. $ang 2 and ang3$
3. $ang 5 and ang7$
4. $ang 7 and ang6$
Grade 7 Three Dimensional Shapes CCSS: 7.G.B.6
The trapezoid pictured has a height of 3cm. The first base is 5cm and the second base is 3cm. What is the area?
1. 21 square centimeters
2. 12 square centimeters
3. 120 Square centimeters
4. 210 Square centimeters
What is the formula to finding the circumference of a circle?
1. c = pi x diameter
2. c = pi x radius
3. c = pi x 3.14
Two angles whose measures sum to 180?
1. Obtuse Angle
2. Right Angle
3. Exterior Angle
4. Supplementary
5. Interior Angle
6. Complementary
Find the area of a circle where r=7m.
1. $153.86m^2$
2. $43.96m^2$
3. $13.28m^2$
4. $153m^2$
Mr. Chang made two similar rectangular window frames. One frame was 12 feet wide and 16 feet long. What could be the dimensions of the other frame?
1. 2 feet wide and 6 feet long
2. 6 feet wide and 8 feet long
3. 16 feet wide and 20 feet long
4. 24 feet wide and 48 feet long
The measure of $ang 1$ is $150deg$. What are the measures of $ang4, ang3, and ang2$?
1. $30deg, 150deg, and 30deg$
2. $45deg, 120deg, and 30deg$
3. $60deg, 150deg, and 45deg$
4. $90deg, 135deg, and 30deg$
In the diagram, $ang$DBA is a 90$deg$angle. What type of angles are $ang$ABC and $ang$CBD? | 2016-09-26 22:40:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1733199506998062, "perplexity": 7321.811536133751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1474738660898.27/warc/CC-MAIN-20160924173740-00005-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://ipm.ac.ir/ViewPaperInfo.jsp?PTID=13884&school=Physic | ## “School of Physic”
Back to Papers Home
Back to Papers of School of Physic
Paper IPM / Physic / 13884
School of Physics
Title: Electronic properties of silicene superlattices
Author(s):
1 A. Esmailpour 2 M. Abdolmaleki 3 M. Saadat
Status: Preprint
Journal:
Year: 2015
Supported by: IPM
Abstract:
This paper studies the conductance of charge carriers through silicene-based superlattices consisting of monolayer silicene by means of transfer matrix method. At first, we consider the ordered superlattices and drive analytically the transmission probability of dirac fermions. We show that the number of resonance picks increases with increasing the number of superlattice barriers. In order to the best understand of the appearance of the picks, we exactly studied transmission properties of the silicene superlattice. Also, the effect of disorder on the probability of transmission through the system of various sizes is studied. The short-range correlated disorder is applied on the thickness of electron doped silicene strips as quantum barriers which fluctuates around their mean values. We show that the oscillating conductance as a function of barriers hight suppress with imposing the disorder in the silicene superlattice. Also, the effect of structural parameters on the conductance of the system are studied.
Download TeX format
back to top
scroll left or right | 2023-02-03 20:14:20 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8331148028373718, "perplexity": 3037.7550709569723}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500074.73/warc/CC-MAIN-20230203185547-20230203215547-00326.warc.gz"} |
https://aptitude.gateoverflow.in/6845/nielit-2019-feb-scientist-d-section-d-8 | 259 views
If $A$ be the area of a right angled triangle and $b$ be one of the sides containing the right angle, then the length of altitude on the hypotenuse is :
1. $\frac{2Ab}{\sqrt{4b^{4}+A^{2}}}$
2. $\frac{Ab}{\sqrt{b^{4}+4A^{2}}}$
3. $\frac{2Ab}{\sqrt{b^{4}+4A^{2}}}$
4. $\frac{Ab}{\sqrt{4b^{4}+A^{2}}}$
Ans C
by
168 points
1
370 views
2
299 views | 2022-11-28 01:38:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8690528273582458, "perplexity": 470.96527987758503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1669446710462.59/warc/CC-MAIN-20221128002256-20221128032256-00573.warc.gz"} |
http://mathhelpforum.com/advanced-math-topics/20616-theorem-about-orthogonality-print.html | # A Theorem about Orthogonality
Printable View
• October 14th 2007, 09:13 PM
Xingyuan
A Theorem about Orthogonality
The Theorem is : If U is a closed linear subspace of F, $h\in F$
• October 14th 2007, 10:47 PM
CaptainBlack
Quote:
Originally Posted by Xingyuan
The Theorem is : If U is a closed linear subspace of F, $h\in F$
We will need more than this in order to help
RonL | 2015-06-03 14:09:10 | {"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": 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": 0.8824567198753357, "perplexity": 1792.0350239832974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1433195036749.19/warc/CC-MAIN-20150601214356-00033-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://dorigo.wordpress.com/2009/03/05/who-discovered-single-top-production/ | ## Who discovered single top production ? March 5, 2009
Posted by dorigo in news, physics, science.
Tags: , , ,
Both CDF and DZERO have announced yesterday the first observation of electroweak production of single top quarks in proton-antiproton collisions. Both papers (this one from CDF, and this one from DZERO) claim theirs is the first observation of the long sought-after subatomic reaction. Who is right ? Who has more merit in this advancement in human knowledge of fundamental interactions ? Whose analysis is more credible ? Which of the two results has fewer blemishes ?
To me, it is always a matter of which one is the most relevant question. And to me, the most relevant question is, Who cares who did it ? ... with the easy-to-guess answer: not me. As I have had other occasions to say, I am for the advancement of Science, much less for the advancement of scientific careers, leave alone to which experiments those careers belong.
The top quark is interesting, but so far the Tevatron experiments had only studied it when produced in pairs with its antiparticle, through strong interactions. Electroweak production of the top quark is also possible in proton-antiproton collisions, at half the rate. It is one of those rare instances when the electroweak force competes with the strong one, and it is due to the large mass of the top quark: producing two is much more demanding than producing only one, due to the limited energy budget of the collisions. The reactions capable of producing a single top quark are described by the diagrams shown above. In a), a b-quark from one of the projectiles becomes a top by intervention of a weak vector boson; in b), a gluon “fuses” with a W boson and a top quark is created; in c), a W boson is produced off-mass-shell, and it possesses enough energy to decay into a top-bottom pair.
Since 1995, when CDF and DZERO published jointly the observation of the top quark, nobody has ever doubted that electroweak processes would produce single tops as well. Not even one article, to my knowledge, tried to speculate that the top might be so special to have no weak couplings. The very few early attempts at casting doubt on the real nature of what the Tevatron experiments were producing died quickly as statistics improved and the characterization of the newfound quark was furthered. So what is the fuss about finding out that the reaction resulting from the Feynman diagrams shown above can indeed be directly observed ?
There are different facets in a thorough answer to the above question. First of all, competition between CDF and DZERO: each collaboration badly wanted to get there first, especially since this was correctly predicted from the outset to be a tough nut to crack. Second, because seeing single top production implies having direct access to one element of the Cabibbo-Kobayashi-Maskawa mixing matrix, the element $V_{tb}$, which is after all a fundamental parameter in the standard model (well, to be precise it is a function of some of the latter, namely of the CKM matrix parameters, but let’s not split hairs here). Third, you cannot really see a low-mass Higgs at the Tevatron if you did not measure single top production first, because single top is a background in Higgs boson searches, and one cannot really discover something by assuming something else is there, if one has not proven that beforehand.
So, single top observation is important after all. I am a member of the CDF collaboration, and I am really proud I belong to it, so my judgement on the whole issue might be biased. But if I have to answer the question that gave the title to this post, I will first give you a very short summary of the results of the two analyses, deferring to a better day a more detailed discussion. This will allow me to drive home a few points.
The two analyses: a face-to-face summary
• Significance: both experiments claim that the signal they observe has a statistical significance of 5.0 standard deviations.
1. CDF uses 3.2 inverse femtobarns, and finds a 5.0-sigma-significance signal of single top production. The sensitivity of the analysis is better measured by the expected significance, which is quoted at 5.9-sigma.
2. DZERO uses 2.4 inverse femtobarns, and finds a 5.0-sigma-significance of single top production. The sensitivity of the DZERO analysis is quoted at 4.5-sigma.
• Cross-section: both experiments measure a cross section in agreement with standard model expectations.
1. CDF measures $\sigma = 2.3^{+0.6}{-0.5} pb$, a relative uncertainty of about 24%.
2. DZERO measures $\sigma = 3.9 \pm 0.9 pb$, a relative uncertainty of about 23%.
• Measurements of the CKM matrix element: both experiments quote a direct determination of that quantity, which is very close to 1.0 in the SM, but cannot exceed unity.
1. CDF finds $|V_{tb}|=0.91 \pm 0.11$, a 12% accuracy.
2. DZERO finds $|V_{tb}|=1.07 \pm 0.12$, a 11% accuracy.
• Data distributions: both experiments have a super-discriminant which combines the information from different searches. This is a graphical display of the power of the analysis, and should be examined with care.
1. CDF in its paper shows the distribution below, as well as the five inputs that were used to obtain it. The distribution shows the single-top contribution in red, stacked over the concurring backgrounds. At high values of the discriminant, the single top signal does stick out, and the black points -the data- follow the sum of all processes nicely.
2.DZERO in its paper has only the distribution shown below. I was underwhelmed when I saw it. Again, backgrounds are stacked one on top of the other, the top distribution is the one from single top (this time shown in blue), and the data is shown by black dots. It does not look like the data prefer the hypothesis of backgrounds+single top over the background-only one all that much!
Maybe I am too partisan to really make a credible point here, and since I did not follow in detail the development of these analyses -from their first publications as evidence for single top, to updates, until yesterday’s papers- I may very well be proven wrong; however, by looking at the two plots above, and by knowing that they both appear to provide a 5.0-sigma significance, I am drawn to the conclusion that DZERO believes their background shapes and normalization much better than CDF does!
Now, believing something is a good thing in almost all human activities except Science. And if two scientific collaborations have a very different way of looking at how well their backgrounds are modeled by Monte Carlo simulations (which, at least as far as the generation of subatomic processes is concerned, are -or can be- the same), which one is to praise more: the one which believes the simulations more to extract their signal, or the one which relies less on them?
The above question is rethorical, and you should have already agreed that you value more a result which is less based on simulations. So let us look into this issue a bit further. CDF bases its result on a total sample of 4780 events, where the total uncertainty is estimated at +-533 events. DZERO bases its own on a sample of 4651 events, with a total uncertainty estimated at +-234 events! What drives such a large difference in the precision of these predictions ?
The culprit is one of the backgrounds, the production of W bosons in association with heavy flavor quarks – an annoying process, which enters all selection of top quarks and Higgs bosons at the Tevatron. CDF has it at 1855 events, with an uncertainty of 486 -or 26.2%; it is shown in green in the CDF plot above. DZERO has it at 2646 events, with an uncertainty of 173, or 6.5%; it is also shown in green in the DZERO plot. Do not be distracted by the different size of the contribution of W+heavy flavor in the two datasets: different selection strategies drive the numbers to differ, and besides, it is rather the total number of events of the two analyses which is similar by pure chance. The point here is the uncertainty.
Luckily, the DZERO analysis does not appear to rely too much on the background normalization -this is not a simple counting experiment, where the better you know the size of expected backgrounds, the smaller your uncertainty on the signal; rather, the shapes of backgrounds are important, and the graphs above show that the data appears indeed well-described by the discriminant shape. And of course, background shapes are checked in control samples, so both experiments have many tools to ensure that the different contributions are well understood. However, the issue remains: how much do the different estimates of the W plus heavy flavor uncertainty impacts the significance of the measurements ? The DZERO paper mentions that one of their largest uncertainties arises from the modeling of the heavy flavor composition of W+jet events, but it does not provide further details.
1. gordonwatts - March 5, 2009
Congrats to both collaborations for this! I didn’t work on the 5 sigma version, but I know how much work it is from the 3 sigma version of the analysis – and from the internal mailing lists it was clear this was quite a bit more work. Really fantastic!
2. dorigo - March 5, 2009
Hi Gordon,
yes, all are to be congratulated. It is a lot of work indeed. Maybe you can answer my question about the W+h.f. background ? I reckon that ALPGEN is used for W+jets, but how exactly is the bb contribution obtained ? Why such a small uncertainty ?
Cheers,
T.
3. gordonwatts - March 5, 2009
Yo Tomasso, I’ve made sure the people that really know are aware of the question. I don’t know if the will respond here or not; I hope here. I think I can guess, but I’m basing my guess on another analysis I’m involved in, not on this one.
So — just a quick questions — where did you get the 2646 number from? Did you just add accross the line in our paper (table I)? If so that is more than just W+HF.
BTW — note that you are comparing a log plot and a linear plot – if we were to make a log plot of the same plot it would look much more similar than yours – only our point would be high rather than low as your’s is.
4. carlbrannen - March 5, 2009
Obviously this should be decided by the grad students of the respective collaborations. This is the kind of thing that paintball was invented for.
5. dorigo - March 5, 2009
Hi Gordon,
well, the line refers to W+jets, and the data has 1 or 2 b-tags… I know there’s some W+charm and mistags, but overall the bulk is heavy flavor, I think. In any case, the CDF analysis is similar…
Ok for the plot, although the insets are both linear, and there for some reason the CDF signal convinces me more. But then again, I might have a biased eye.
Cheers,
6. dorigo - March 5, 2009
Carl, LOL that’s a good suggestion!
T.
7. dorigo - March 5, 2009
PS what is paintball ?
8. gordonwatts - March 5, 2009
Ha! I love it — paintball!
paintball – you dress up and go into the woods and try to kill each other with guns. Only the guns are loaded with small pellets of paint. That way you can see that someone is dead because they are marked with paint.
Don’t tell me this is something that is only American. Guns!? Sheesh! 😉
9. dorigo - March 5, 2009
You guys are sick! 🙂
10. gordonwatts - March 5, 2009
well, we are american… 😉 Say — who is your prez? 😉 See, we both can be messed up! I guess our country is bigger, so when we are messed up _everybody_ suffers.
11. dorigo - March 5, 2009
Ouch, that was quite a blow! Yes, italians just have to shut up these days.
12. gordonwatts - March 6, 2009
Sorry. I know how much you love the guy (having read your posts about him). But I sympathize. It is so nice not having to duck and hide my head when these sorts of conversations come up. At any rate — all of this will pass. THe world has to become a better place, right? I’ll try to track down the physics answers for you.
13. carlbrannen - March 6, 2009
Paintball wasn’t my idea. It was the theme of the latest episode of a comedy show based on physics grad students. If you go to LuMo’s website and click around, you can watch it. You will find out what a paintball gun looks like, and what people look like when they’re shot.
It turns out that one thing that animals absolutely hate is having humans point things at them and then getting hit by something at a distance. Must be racial memory of being hunted. So an unadvertised alternative use of paintball guns is keeping the local animals in line without having to dispose of rotting bodies.
14. Namit - March 6, 2009
Dear Tomasso,
A quick question regarding the theoretical cross-section:
the D0 paper quotes the cross-section to be 3.46 +- 0.18 pb while the CDF paper quotes a value ~ 2.9pb for the same (and both papers cite “N. Kidonakis, Phys. Rev. D 74, 114012 (2006)” for the SM cross-section prediction).
The two central values quoted above seem quite different. Any clue about this? Slight difference in the theoretical predictions is expected since its seems that the D0 paper quotes the value of cross-section for mt=170GeV while CDF has mt=175GeV. But such a large difference seems puzzling, unless I have missed something.
Thanks and regards,
Namit
15. dorigo - March 6, 2009
Dear Namit,
this is an excellent question. It is true that both papers quote kidonakis, although CDF also quotes other papers. I will ask this question to the CDF authors, although I believe that the difference is mostly due to the different assumed mass (170 vs 175).
Cheers,
T.
16. Namit - March 6, 2009
Dear Tomasso,
Though in general possible, it would be a bit surprising if the difference entirely is due to the choice of top mass – this would mean that the NLO (and resummation etc) corrections are highly sensitive to top mass value. A quick glance at the paper(s) does not seem to indicate this, though I may have missed out something.
I look forward to the resolution of this apparent puzzle.
Regards,
namit
17. dorigo - March 6, 2009
Hi,
ok, most of the difference is from the top mass, but a part is due to the fact that CDF uses the NLO prediction, while DZERO uses a computation which includes some (but not all) of the NNLO effects.
Because of the incompleteness of the NNLO calculation, CDF chose to stick with NLO. This makes the expected cross section smaller for CDF.
Please also note that a smaller expected cross section will translate in a smaller expected significance for the signal: so DZERO, by using NNLO and a smaller top mass, obtains an expected sensitivity which is sizably larger than what it would be if they used the cross section used by CDF. Or one might say the opposite: the CDF expected significance would be larger, had they used a 3.5 pb expected xs.
Hope that helps,
T.
18. rescolo - March 6, 2009
Dear Tomasso,
I am wondering how the two measurements of V_tb combines to establish a 3-sigma allowed range. This would have some impact in the determinations of this parameter without assume unitarity.
19. Andrea Giammanco - March 6, 2009
Hi rescolo, have a look at the thread of comments of the previous post.
20. dorigo - March 6, 2009
Yes, I recommend Andrea’s thorough explanation of the limitations in the extraction of Vtb. See this thread.
Cheers,
T.
21. rescolo - March 6, 2009
Thank you Andrea and Dorigo for the interesting thread!
22. Paolo - March 7, 2009
Yes, thanks a lot. Tommaso, the way you turned a not-particularly interesting question (IMHO) to a nice discussion is impressive!
23. Paolo - March 7, 2009
PS: to all posters: TOMMASO, NOT TOMASSO!
24. dorigo - March 7, 2009
Thanks Paolo, I have stopped complaining by now, it’s a lost cause with many if not most English natives.
Cheers,
T.
25. carlbrannen - March 8, 2009
For English speakers, remember “Tommaso” as a variation of “Tommy”, say, as Tommy-so with the y changed to a because, well, Italians are just different.
26. Gordon Watts - March 10, 2009
Hi again. I’m finally working back to this — great weekend with family. Carl – did you see BBT this evening — both Summer and Smoot in one episode? Must be sweeps month! 😉
Perhaps I’m missing something here – but how does the expected cross section that was used by the experiments affect the significance of the result? The significance is calculated by trying to make the background model (i.e. _no_ singletop) fluctuate up to mimic the data. This involves millions and millions of runs – it took us weeks to do this. But as far as I know the signal doesn’t enter into that. Check out the very carefully worded (:-)) paragraph that stretches from pages 5 to 6.
Next – I’ve just had a few minutes to start to chase down the plot. First thing to know is we don’t actually use that plot. Rather, we have 24 sub-analyses (lets see if I can get this right: 2 reconstruction versions, muon/electron, 1/2 tags, 2/3/4 jets – yes, that is 24). Once we have the BDT, BNN, and ME outputs for a particular channel we then create a combination BNN. That output distribution (x24) is what is fed to the actual likelihood. So, while that is most powerful, you’d need a poster to display that – and you can’t create a nice neat plot that shows how it looks — other than Figure 3 of the paper. Of course, there is a lot of math between the 24 different analysis input and that output so it is hard for us to look at it and “feel good”. 🙂
The systematic errors will take me a bit longer. First, the numbers that are shown in the table can’t be what is used by just reading the text, right? There are shape systematics involved – so that can’t possibly be the whole story. For one thing – we have to have the systematic errors broken up into those 24 analysis channels.
BTW – except for the combination (which is fantastic to see in this round) what you see here is based on the same analysis philosophy as the evidence paper we put out in 2007 (which was when I was very active in the analysis, unlike now).
27. Gordon Watts - March 10, 2009
BTW – I think some of this will be addressed in the DZERO talk tomorrow at Fermilab.
28. Namit - March 10, 2009
Dear Tommaso,
Thanks for the response and sincere apologies for mis-spelling your name.
A related question: why are the two collaborations using different values of m_t (while quoting the expected cross-section)?
Namit
29. dorigo - March 10, 2009
Ciao Gordon,
what we have been discussing is that when an experiment uses an inflated expected cross section to derive the a-priori sensitivity of some data and some analysis, that experiment is going to obtain an inflated sensitivity. Thus DZERO’s expected 4.5 sigma are probably about 4.0 or so. Of course you can retort that it is CDF that plays it too safe by not using the NNLO (which is however incomplete) and by using 175 GeV instead than 170 GeV for the top mass, and then I agree -partly.
About the shape systs: of course those are dominating the uncertainty in the signal. But I still have not heard the answer of why the W+jet xs is known to a very small 6% in the DZERO analyses.
Cheers,
T.
30. dorigo - March 10, 2009
Hi Namit,
it is a choice – 170 and 175 are both round numbers. 175 GeV has been the reference for all of CDF Monte Carlo samples since Run II, while D0 probably uses 170 for the same reason.
Of course, using a smaller mass means that one expects more single top, which in turn implies that the expected sensitivity of that experiment is going to be computed higher.
Cheers,
T.
31. Gordon Watts - March 11, 2009
Hi again! Ok, I’ve been able to verify that that plot is what I thought it was – it is all the channels added together. That plot is never actually used – rather it is the sum of 24 individual discriminate outputs. So that is why it looks underwhelming – both high S:B and low S:B channels are all combined, which washes out the high ones.
By inflated sensitivity you mean the expected significance, right? I don’t get your argument. First of all, the NLO and NNLO are rescalings of some MC that we both generate. We use different generators – but presumably the events and the “shapes” are the same – except for any effects due to the difference in top mass. We generate at 170 and you at 175. You optimize your analysis for 170 and we for 175. So the difference between our analysis shoudl be minimal – because they are optimized for their top masses and I have a lot of trouble believing that the sensitivity of the analysis woudl change with 5 gev but a large amount.
The only difference will be in the cross section. For us the SM cross section is 3.46, and for you it is 2.9 (let me know if I misread your paper). Lets say the CDF NLO number is correct. We really should re-evalute our analysis using an expected cross section of 2.9 – less than what we did – so our analysis will look more sensitive, not less.
I guess there are two competing effects here (at least that I’m thinking of): the change in MTop and the change in the cross section. The change in cross section is easy – the lower the number the more sensitive the analysis. The MTop change is very hard to judge since we would both re-optimize our analysis for the proper top mass. However, given the systematic error checks we’ve done I think the effect will be minimal compared to the change in the cross section.
So I guess I would end up claiming that our analysis is more sensitive than it looks if you think MTop = 170 is the right number, not less sensitive.
32. Gordon Watts - March 11, 2009
Namit – it is almost exactly what T says – tradition. Changing is actually very expensive. You would never change in the middle of an analysis – it takes months to remake all of the Monte Carlo. Both experiments are on a crazy 6-month release schedule so they are loath to do something like that unless they really really think it will change the results. A 5 GeV shift when there are not other particles near that mass peak doesn’t really change things very much.
33. Gordon Watts - March 11, 2009
Whew! I guess that is what you get for posting between potty training sessions! My logic is ok above until the end.
We are measuring how often the SM background fluctuates up to the SM background + single top. So the higher it has to fluctuate, the harder it is – which will result in increased sensitivity.
Because D0’s ST x-section is higher we measure against fluctuating up to a higher number. If we were to have used CDF’s cross section then our significance would have been less than it is shown, as Tommaso correctly points out above (and sorry for mispelling your name earlier).
34. Gordon Watts - March 11, 2009
And — one other thing to consider is the difference in the luminosity – if you are trying to compare the sensitivity of the raw analysis I would expect ours to go up if we used your size of data. Of course, if you are just trying to compare what is in the papers then this isn’t a point.
35. dorigo - March 11, 2009
Thank you Gordon for your very objective considerations. In the post I have been more partisan than you show to be here…
Cheers,
T.
36. Latest on the Higgs « Not Even Wrong - March 11, 2009
[…] the papers are here and here. For an expository account, you can’t possibly do better than this one from Tommaso […]
37. Namit - March 12, 2009
Dear Tommaso and Gordon,
Thanks a lot for the response. I do understand that changing the top mass in monte-carlos would mean a lot of work/effort. However, it is perhaps important to have a common value in order to compare with the theoretical predictions. The difference between the two numbers quoted by D0 and CDF (and as Tommaso said earlier that the bulk of the difference is due to mt values used) is almost (a bit less actually) 15% – this means that the result is quite sensitive to choice of mt!! And therefore, V_tb extracted will also differ.
As more data is analysed, this issue may become more and more important – at least that’s what seems like.
Another related question: since CDF has mt=175GeV as the reference value, does that mean that one should put this value as the mt(pole) for B-physics observables rather than mt(pole)=170GeV? This could mean significant differences at some places.
Regards,
Namit
38. Dag - March 12, 2009
Hey guys,
Namit: You said “….this means that the result is quite sensitive to choice of mt…”
The theoretical cross section is really quite sensitive to the m_top, but not the measured cross section. Most our sensitivity comes from events with 2 jets, 1 of them b-tagged. For these events, the background is mainly W+jets (~80% in the signal region). The excess in data on top of the background is hence not very sensitive to the top mass.
Regarding the sensitivity (expected significance) – a larger expected cross section means higher sensitivity. But harder kinematics (larger m_top) means better discrimination against W+jets – which again is the main problem. At D0, our most discriminating variables against W+jets are H_T and the reconstructed top mass – both of these become more powerful with a higher top mass. I don’t know how much better separation gets, but I’d guess between 5 and 10%.
I’ll try to comment on the W+jets uncertainty also.. but i’m far from an expert here:
The D0 number is extracted from the cross section measurement (Bayesian calculations integrating over the 24 channels). The total uncertainty of each of the W+jets components that are fed into the calculations are larger than 20%, but after considering the correlations betwen all uncertainties, and constraints from the fit with data, and combining all 24 channels, the total W+jets normalization uncertainty becomes only 6.5%.
39. gordonwatts - March 12, 2009
Fantastic – Dag is one of the people who was actually doing this analysis. Dag, thanks for commenting here.
T – does CDF do a profile fit for the uncertianties? The 6.5% number here is the output from that method. If CDF does, do you know what the output uncertianty is for CDF?
Sorry comments are closed for this entry | 2017-04-25 02:39:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.639363706111908, "perplexity": 1176.4158417450806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1492917120092.26/warc/CC-MAIN-20170423031200-00316-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://math.meta.stackexchange.com/questions/22140/discrimination-against-pde-questions/22141 | # Discrimination against PDE questions?
Just going through the questions tagged partial-differential-equations, I saw that many of them are unanswered and have zero upvotes. Is there a good reason why these types of questions are kind of ignored by the community?
Examples:
Poincaré constant for a ball (circle)
A finite vibrating string initial value problem, solve using separation of variables [Solved]
Reaction-diffusion equations
Taking $\inf$ for sobolev space in different order
More questions with this tag https://math.stackexchange.com/questions/tagged/pde
• Umm, analysis is... hard? The first Q in your list asks to find a best possible constant in a certain estimate. It seems to me the answer offered is a pretty good one there, but I don't have the same opinion of the Q. Dec 8 '15 at 2:56
• Dec 8 '15 at 3:19
• It's a conspiracy organized by Big Algebra.
– Asaf Karagila Mod
Dec 8 '15 at 4:01
I think that you suffer from a case of specialist's myopia. As I may have also been diagnosed with it let me elaborate.
The calculus (or elementary number theory, not to mention high school level stuff) questions get a lot of attention in comparison to more specialized tags simply because there are more users A) understanding what the question is about, and B) feeling like they have a shot at answering it well enough to earn a few upvotes.
One of the early symptoms of the onset of specialist's myopia is the desire to complain about the perceived relative lack of attention to your area of interest. As the disease progresses what can happen is that you realize that the mechanism described in the preceding paragraph is an auto-catalytic process - more and more calculus questions, askers and answerers are attracted to the site, drowning everything else. In a severe case a patient begins to develop attitudes like:
• There are only 40 calculus questions, so you starting hunting for duplicates within that tag to get the excess closed as duplicates. You can do the same to any overrepresented tag of your choice.
• You begin to contemplate downvoting those questions (could the lazy bums at least search the site before asking).
• You begin to contemplate downvoting the answers to those questions (could the lazy bums at least search the site before answering).
• Why can't this site implement a point formula with a result that the value of an answer is inversely proportional to the number of users capable of producing it!
The bad news is that no permanent cure to SM is currently known. However, the symptoms can be alleviated by:
• Using a question filter. Some patients say that weeding out totally uninteresting tags helps. Even more non-patients suggest this as a remedy. Didn't help me.
• Blowing off some esteem in Meta (this does help - if only temporarily).
• Carrying out the simple arithmetic revealing that calculus answerers rarely get more upvotes per post - it is just the highly visible questions that distort the view.
• Coding and running SEDE queries to reveal more such facts.
• Occasionally getting some fresh air.
• Joining a support group. Plenty of good advice there. Some sympathetic ears, some not so sympathetic. Share your story!
If it makes you feel better, here's a comparison. Currently we have 6770 questions with the pde tag. They run to 135 pages (50 questions/page). When sorted by votes, the zero count questions begin on page 97, so a bit less than 30 per cent of the questions have a non-positive score. I am the self-appointed curator of the finite-fields tag. Currently we have 1609 questions carrying that tag. That is 33 pages. When sorted by vote the first zero score question occurs on page 26. About the same percentage. But your tag has more total attention and material! Go figure?
• If your dirty imagination associates something else with the acronym SM then I'm afraid I cannot help. Dec 8 '15 at 10:02
• Pity you can't help, I always had a soft spot for these. Dec 8 '15 at 10:20
• "Blowing off some esteem" Is this a typo or some rare idiom?
– quid Mod
Dec 8 '15 at 13:26
• @quid: I've seen that phrase describe an unintended side effect of "blowing off steam". After all, a rant often says more about the person standing on the soapbox than about whatever they are complaining about. Resulting in a net loss of esteem in the eyes of the audience. TL;DR; An attempt at a pun. Dec 8 '15 at 13:54
• I never heard this, but it seemed fitting in a way but it could have been auto-correct too. So...Thanks for the clarification.
– quid Mod
Dec 8 '15 at 14:16
• "Why can't this site implement a point formula with a result that the value of an answer is inversely proportional to the number of users capable of producing it!" That would be the most wonderful thing in the Stack Exchange universe. +1 May 6 '16 at 3:12 | 2021-10-18 13:02:33 | {"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": 0.26260048151016235, "perplexity": 1557.3050889144085}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1634323585203.61/warc/CC-MAIN-20211018124412-20211018154412-00126.warc.gz"} |
https://www.ipu.ru/node/70207 | # 70207
## Автор(ов):
1
Параметры публикации
## Тип публикации:
Статья в журнале/сборнике
## Название:
Taylor-Type Formulas for Arbitrary Continuous Functions on Intervals and Their Application in Control Problems for Distributed Systems
1064-5624
## DOI:
10.1134/S1064562422020028
V. 105 N.2
• Москва
2022
## Страницы:
56-60
Аннотация
Two classes of Taylor-type formulas for arbitrary continuous functions on intervals are obtained using Bernstein polynomials. These formulas are applicable to both smooth functions and functions that have neither finite nor infinite derivatives at any point. The Taylor-type formulas are considered in close connection with Dini derivatives, which exist for any continuous function. An example is given in which these formulas are applied to the problem of controlling a distributed oscillatory system whose dynamics obeys the d’Alembert representation.
## Библиографическая ссылка:
Агаджанов А.Н. Taylor-Type Formulas for Arbitrary Continuous Functions on Intervals and Their Application in Control Problems for Distributed Systems / Doklady Mathematics. М.: Pleades Publishing, Ltd, 2022. V. 105 N.2. С. 56-60.
Да | 2022-09-29 21:07:06 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8915318250656128, "perplexity": 2250.5259383100597}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1664030335365.63/warc/CC-MAIN-20220929194230-20220929224230-00600.warc.gz"} |
https://www.nature.com/articles/s41598-019-46186-9?error=cookies_not_supported&code=85f58144-c7f6-4c83-8eba-4a12104cefa8 | Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.
# Top-down GaN nanowire transistors with nearly zero gate hysteresis for parallel vertical electronics
## Abstract
This paper reports on the direct qualitative and quantitative performance comparisons of the field-effect transistors (FETs) based on vertical gallium nitride nanowires (GaN NWs) with different NW numbers (i.e., 1–100) and diameters (i.e., 220–640 nm) fabricated on the same wafer substrate to prove the feasibility of employing the vertical 3D architecture concept towards massively parallel electronic integration, particularly for logic circuitry and metrological applications. A top-down approach combining both inductively coupled plasma dry reactive ion etching (ICP-DRIE) and wet chemical etching is applied in the realization of vertically aligned GaN NWs on metalorganic vapor-phase epitaxy (MOVPE)-based GaN thin films with specific doping profiles. The FETs are fabricated involving a stack of n-p-n GaN layers with embedded inverted p-channel, top drain bridging contact, and wrap-around gating technology. From the electrical characterization of the integrated NWs, a threshold voltage (Vth) of (6.6 ± 0.3) V is obtained, which is sufficient for safely operating these devices in an enhancement mode (E-mode). Aluminium oxide (Al2O3) grown by atomic layer deposition (ALD) is used as the gate dielectric material resulting in nearly-zero gate hysteresis (i.e., forward and backward sweep Vth shift (ΔVth) of ~0.2 V). Regardless of the required device processing optimization for having better linearity profile, the upscaling capability of the devices from single NW to NW array in terms of the produced currents could already be demonstrated. Thus, the presented concept is expected to bridge the nanoworld into the macroscopic world, and subsequently paves the way to the realization of innovative large-scale vertical GaN nanoelectronics.
## Introduction
Since the invention of the first integrated circuit (IC) in 1958, planar metal-oxide semiconductor field-effect transistors (MOSFETs) based on silicon have been dominating in the global microelectronics industry and continuously used to build electronic devices, such as modern microprocessors, which up-to-date can integrate more than one billion transistors on a single chip1,2,3. The raised challenges following this microelectronic revolution are still how to fabricate the transistors more efficiently by keeping the smallest possible footprint and how to better exploit the devices containing billions of transistors. Even though the electronic engineers and scientists have attempted to further miniaturize and to put more transistors on it as well as to improve their performance, the technological bottleneck still occurs as the available active area or footprint of the whole device at a certain point is constrained, leading to the limitation of the integrated electronic building blocks. Therefore, although the development of microelectronics and the following enhancement in circuit performance have generally been driven by the downscaling of the basic electronic component (i.e., the MOSFET), it has faced physical limitations of nanoscale transistor operation, which then leads to the research and development of more innovative MOSFET architectures, e.g., to improve electrostatic control of the channel. Thus, several novel approaches have been investigated including the usage of other semiconductor materials (e.g., silicon carbide (SiC)4 and gallium nitride (GaN)5,6,7 for specific applications (e.g., in high temperature and power switching devices), planar 3D nanostructures (e.g., horizontal nanowire (NW) transistors)8,9, and vertical 3D architectures (e.g., FinFET, NW FET, and tri-gate architectures)10,11,12,13,14.
Among others, GaN transistors provide prospects for making monolithically integrated electronics-photonics platforms because of their direct wide band gap, even though the already realized devices are still in a planar architecture15,16. As the figure of merits for semiconductor power devices, the high breakdown voltage (BV) and low on resistance (Ron) are required, in which BV > 800 V and Ron ≈ 0.36 m Ω cm2 can be obtained by vertical GaN FinFET based on bulk GaN wafer14. In quantum engineered transistors and logic applications, this vertical method also gives a new strategy towards higher performance and integration of p- and n-channel transistors17,18. From our point of view, the vertical 3D architecture has become more attractive because it provides more advantages: (1) it can minimize the current collapse, thanks to the absence of surface-related trapping phenomena; (2) the gate length (L) is not limited by lithography process; (3) gating technology can be flexibly designed (e.g., wrap around gate); (4) vertical parallel current paths and collection can be obtained on a small footprint for high scalability; (5) better thermal performance, at which the maximum temperature is close to top part of NWs, brought potential to achieve more power density; and (6) contrary to lateral devices, where breakdown voltage scales with area (and cost), in vertical devices the breakdown voltage is only dependent on the thickness/properties of the epitaxial stacks13,19,20,21,22,23,24,25.
In the last few years, several vertical electronic devices based on semiconductor NWs (e.g., Si and GaN) have been demonstrated with different types of transistors, and only a few of them concern about the direct device scaling behavior as affected by the modified number and diameter of NWs26,27,28. The diameter size and doping concentration of n-n-n or n-i-n GaN epitaxial NWs were reported to be able to determine the operation modes of the GaN FETs (normally-off or normally-on)29,30. The threshold voltage can be increased by inserting a p-channel inside the wire structure instead of n-channel13,28,30. Nevertheless, those devices exhibited very large drain current hysteresis during bidirectional gate sweep, which is assumed to be due to the unintentionally introduced mobile ions. Meanwhile, for vertical Si FETs, the massively parallel dense NW arrays with wrap around gate structure had been reported to have an improved electrostatic control during device operation, a smaller transistor chip size, and a low leakage current26. However, those nanotransistors were fabricated using electron beam lithography, which definitely lowers their potential to be transferred in batch production because of the higher device processing cost and longer production time. Thus, other lithography techniques (e.g., photolithography, nanoimprint lithography, and colloidal lithography) have been currently employed to produce vertical Si NW arrays, although such production of vertical Si NW FET devices using those techniques has not been demonstrated so far31,32,33,34,35,36,37,38.
In this paper, a direct proof of device current scaling and parallel transistor integration is demonstrated using vertical n-p-n GaN NW FETs with almost-zero ΔVth hysteresis that were fabricated using top-down approach (i.e., standard UV-photolithography and hybrid etching processes). Al2O3 thin layers fabricated by ALD process using trimethylaluminium and water were employed as gate dielectrics instead of SiO2 films that are commonly used for Si FETs. Owing to various patterns on the mask, the electrical characteristics of the realized 1-, 9-, and 100-NW FETs with different diameters were extracted and analyzed. In case of the top drain electrode configuration, mesa structures have been added as mechanical support for more robust electrical characterization and circuit integration (e.g., during wire bonding).
## Results and Discussion
Figure 1a depicts the 3D device schematic based on the n-p-n GaN epi-layer provided in Fig. 1b. The doping concentration of the channel region has a significant impact on the operation mode of the transistors, which influences the threshold voltage. In our devices, the channel is p-doped to obtain sufficiently high threshold voltages.
To investigate the scaling behavior of the integrated FETs, devices containing different numbers of NWs were fabricated, i.e., 1, 9, and 100 NWs (Fig. 2a–c). However, for the sake of simplicity, in the next result discussions, the three FET wire diameters of (221 ± 9) nm, (443 ± 7) nm, and (647 ± 8) nm (Fig. 2d–f) are written as 220 nm, 440 nm, and 640 nm, respectively. The formation of smooth sidewalls on vertical n-p-n GaN NWs after anisotropic wet chemical etching is explained in detail elsewhere13,30,39. Additionally, it is worthy to mention that the high quality of the etched NW sidewalls is important for the device performance14.
Figure 3a shows the tested sample containing 1, 9, and 100 NW FETs connected with three probing tips to a source meter unit (SMU). The benefit of using two GaN mesa structures for drain contacts at the both sides of the NW field is the enhanced mechanical support during SMU probe testing or wire bonding process compared to devices with only photoresist or other soft materials underneath the metal pads28,40,41. It should be noted that no additional mask is required during the processing, as the drain pad was formed in line with the first lithography step for creating the NWs at the beginning of device fabrication. Consequently, the pad has the same height as the NWs. Figure 3b–d show the SEM images of fabricated vertical n-p-n GaN NW FETs with 1, 9, and 100 NWs including their top drain bridging contacts.
Figure 4a presents the output characteristics of vertical n-p-n GaN NW FETs with a diameter of 440 nm and different numbers of 1, 9, and 100 NWs under the gate-source bias (Vgs) ranging from 3 to 9 V. For each FET type, five different devices were measured on a single 2-inch epi-GaN wafer. The extracted maximum drain current (Id,max) at Vgs = 9 V demonstrates the linearity in respect to the number of NWs as shown in Table 1. The Id,max and Ion/Ioff of each GaN NW FET scale up with the increasing number of NWs. Thus, it has proven the design suitability for massive parallelization. However, it should be noted that device processing imperfection can provide a deteriorated linearity of the devices, e.g., in the case of device scaling from 9 to 100 NW FETs, where their measured Id,max are (33.5 ± 9.9) µA and (230.7 ± 59.4) µA, respectively. The normalized Id,max (i.e., Id,max_norm) shows similar amounts of current density for FETs with different gate widths (W) and NW numbers, although the values are slightly varied from (1.7 ± 0.4) to (2.6 ± 0.9) µA/µm. The W is defined as the circumference of the single GaN NW, which has values of 0.69 µm, 1.38 µm, 2.01 µm for FETs with NW diameters of 220 nm, 440 nm, 640 nm, respectively.
Those values are obtained by simplifying the cross-sectional geometry of the wire from hexagonal to circular shapes, as the wire dimension is considerably small. The Id,max_norm can be calculated as follows:
$${I}_{{\rm{d}},{\rm{\max }}\_{\rm{norm}}}=\frac{{I}_{{\rm{d}},{\rm{\max }}}}{W\times N}=\frac{{I}_{{\rm{d}},{\rm{\max }}}}{\pi \times D\times N}\,$$
(1)
where D and N are diameter and number of the NWs, respectively. A similar method is used to obtain the normalized transconductance (gm,max_norm), i.e., by dividing the maximum transconductance (gm,max) with (W × N).
Regardless of the rectifying I-V behavior in lower Vds field and the required contact optimization, the devices can still function in an enhancement mode (E-mode) operation. To improve the Ohmic contact, several solutions are suggested and will be attempted in future, such as usage of other metal materials (e.g., Ti/Al, Ti/Al/Ni/Au, or Ti/Cr/Au) with optimized thickness and annealing processes42,43,44,45.
The transfer characteristic is shown in Fig. 4b, plotting Id as a function of Vgs. The average Vth values determined by a linear extrapolation of the gm (Fig. 4c) were (6.4 ± 0.2) V, (6.6 ± 0.3) V, (6.4 ± 0.5) V for the 1, 9, and 100 NW FETs, respectively, which are almost three times higher than the previously reported MOSFETs with c-axis GaN NWs13.
Compared to the massively parallel vertical Si NW FETs fabricated using e-beam lithography, these GaN NW FETs were believed to provide more stable process, regardless of the required engineering of the interface between the semiconductor and dielectric materials26,46,47. The ON-/OFF current ratios (Ion/Ioff) of up to 107, 106, and 105 were achieved for 100, 9, and 1 NW FETs, respectively (see SI Fig. S1), through the logarithmic Id-Vgs curves. Meanwhile, the normalized Ion/Ioff (i.e., Ion/Ioff_norm), which is defined as Ion/Ioff per number of NWs, is found to be similar at values of 105 for 1, 9, and 100 NW FETs (see Table 1). Those measured two parameters (Ion/Ioff and Ion/Ioff_norm) have demonstrated the scalability and fabrication quality of the n-p-n GaN NW FETs, respectively. The higher Ion/Ioff on 100 NW FETs is reasonable since the Id,max is proportional to number of NWs, in which for this NW FET the value is larger than those on 1 and 9 NW FETs, as depicted in Fig. 4b. The gm,max_norm values (Fig. 4c) were measured as 6.3 mS/mm, 4.1 mS/mm, and 4.7 mS/mm for the 1, 9, and 100 NW FETs, respectively. The oxide capacitances in these FETs are around 4.7 pF, based on capacitive-voltage (C-V) measurements (see SI Fig. S2). Several solutions can be proposed to enhance the gm, including by decreasing L and increasing the W (i.e., shorter gate channel and larger NW diameter), as well as choosing the proper channel doping concentration design with the purpose of further increasing the electron mobility (µ) in p-channel to lower the scattering rate48. Review on vertical 3D GaN NW FETs including their important parameters to evaluate the device performances has been recently published elsewhere25.
From Fig. 4d, a gate memory effect or typical hysteresis caused by adsorbates, mobile ions, or interface/oxide traps is not visible in the fabricated devices, which demonstrates a good quality of the used dielectric material (i.e., higher electron affinity and particle density compared to SiO2)13,14,49,50. In addition, no obvious hysteresis was found on the 1 NW FETs with different diameters and on the 1, 9, 100 NW FETs with diameter of 220 nm (see SI Fig. S3). It should be noted that our previous NW FET devices using SiO2 gate dielectrics have large gate hysteresis during up-/down- current sweep13.
Figure 5a shows the output characteristics of three different single NW FETs with varied diameters (i.e., 220 nm, 440 nm, and 640 nm). The average Id,max values at Vgs = 9 V from the five conducted measurements exhibit a linear trend, for all diameters with the lowest value found for 220 nm transistor, while the current difference of 7.4 µA was measured between 440 nm and 640 nm transistors. The detailed DC characteristics of the investigated single NW FETs are listed in Table 2.
The transfer characteristics of the FETs with three different NW diameters are shown in Fig. 5b with an average Vth = (6.4 ± 0.4) V at Vds = 5 V. Again, in Fig. 5c, gm,max_norm values were inspected to be 8.8 mS/mm, 6.3 mS/mm, and 7.7 mS/mm for 220 nm, 440 nm, and 640 nm, respectively, with an Ion/Ioff of up to 106 (Fig. 5d). The drain leakage (Id,leak) below the Vth was as low as ~10 pA (Fig. 5d) similar to the noise level of the measurement setup (1–10 pA), while the gate dielectric leakage current (Ig,leak) was observed to be as low as ~0.07 nA/NW at Vds = 5 V and Vgs = 6 V for those three different FETs (Fig. 5e). It proves that the high-k dielectrics, denser particle, and higher electron affinity of Al2O3 ultrathin void-free layer deposited by ALD have excellent properties on suppressing the Id,leak and Ig,leak in our transistors45. Compared to single NW FETs, the output characteristic performances of 100 NW FETs have more linearity in case of different wire diameters (Fig. 5f).
To understand the phenomena of lower Id,max and higher Vth obtained from the developed devices, the effects of gate length (L) and surface charge (Qsf) have been further studied by numerical simulations. The value of the gate length extension (Lext) describes the extension of the gate electrode beyond the p-channel region and results from the difference between the gate length L and the vertical position of the drain side p-n junction. The gate length is critical and should be kept as short as possible to limit the electric field in the drift region. A negative Qsf on the nonpolar sidewalls of GaN NWs has been observed in experiments51. Its primary effect is to increase the threshold voltage of the transfer characteristics. Calibrating the simulations with the transfer characteristics yields the Qsc = −(3.9 ± 0.2) × 1011 cm−2 and Lext = −(21 ± 4) nm for all NW diameters. The gate electrode ends in the p-channel near the junction to the drift region (SI Fig. S5a,b calibrated). Figure 6b illustrates a very good agreement of simulation and experiment, which means some parameters in experiment in case of three different diameters of 1 NW FETs should be correct and can be explained by these conducted simulations.
The simulated output characteristics in Fig. 6a show relatively good agreement with the experimental results for the 220 nm and 440 nm NW FETs. However, a rather large difference of the turn-on voltage in the output characteristics of the 640 nm NW device suggests that the gate length value owned by the fabricated FET is probably higher, which is subject to the device processing. This will result in shorter channel length and consequently lower turn-on voltage (Id − Vds), in comparison to that from simulation. Furthermore, the simulations in Fig. 6c,d demonstrate that the Id-Vds and Id-Vgs curves are very sensitive to Lext. Due to deposition shading and the hexagonal wire shape, the gate metal length varies on the perimeter as depicted by the SEM image of a single wire in Fig. 1c. The variation increases with the diameter explaining the large deviation of the output characteristics for the 640 nm NW FET in Fig. 2a.
Even though the turn-on in the output characteristic may be also caused by imperfect Ohmic source or drain contacts, the simulations suggest that the high threshold and low transconductance can be attributed to the dimensions of the gate electrode. Moreover, surface charging effect has occurred on all FETs, which most probably originates from the impaired quality of the Al2O3 gate dielectric layer that has direct contact to GaN NW sidewalls. Nevertheless, all these phenomena need to be further investigated more deeply to understand the surface physics of the used materials from the realized FET devices.
Figure 6c,d illustrate the effects of the gate length on the output and transfer characteristics for the calibrated surface charge on 220 nm GaN NW FETs. With decreasing gate length, the resistivity increases and the transconductance decreases because the electron depletion in the drift region cannot be lifted by the gate electric field. For a very short gate ending in the p-channel region, the gate electric field does not screen the potential barrier at the junction to drift region anymore. Thus, a turn-on voltage in the output characteristics occurs. The negative surface charge does not only increase the threshold voltage as shown in Fig. 6f, but also contributes to the depletion of the drift region, which can be seen from the increase of resistivity in Fig. 6e. With increasing negative surface charge, the junction depletion region extends more into the drift region that contributes to the turn-on voltage in the output characteristics. It is remarkable that for a short gate configuration, the electric field in the drift region near the junction to the channel is larger than the field near the drain region, which exhibits a high resistivity. However, for a long gate architecture, this effect is not found (see SI Fig. S5a,b).
The measured BVs of the 1, 9, and 100 NW FETs were verified from 30–90 V at Vgs = 0 V as shown in SI Fig. S4. Theoretically, the BV is determined by the length and doping concentration of the drift region. In these devices, the space between drain and gate channel is ~1 µm, which is much shorter than our previous device having BVs of 54–92 V13. However, for improving the device design and performance, several strategies can be proposed for the next transistor generations, e.g., decreasing the Si-doping concentration in the drift region, integrating vertical field-plate structure, and employing longer drift region. The low doped and longer space drift region will reduce the local electric field and thus the BV can be increased20,29,52.
In conclusion, E-mode vertical n-p-n GaN NW FETs with different properties (i.e., NW numbers and diameters) have been fabricated and demonstrated, proving the feasibility for upscaling the vertical transistors by optimizing the dielectric materials and device designs. The smooth vertical sidewalls of the n-p-n NWs have been realized by a hybrid top-down approach involving dry and wet chemical etching techniques. Regardless of the required device processing optimization, the fabricated FETs have exhibited Vth of up to (6.6 ± 0.3) V and shown an upscaling Id,max behavior with increasing NW quantity from 1 to 100 and NW diameter from 220 nm to 640 nm. Through appropriate dielectric passivation material deposited on the entire NWs, the gate hysteresis effect observed in earlier devices could be suppressed to nearly zero. To enhance Id,max, the NW diameter can be further controlled (larger W) and the NW number can be employed (N > 100 NWs). These results grant a very promising future design for massively parallel GaN vertical transistors to be used in logic circuitry and metrological applications (i.e., to be extended for single-electron transistors (SETs) providing alternatives for parallel planar GaAs SETs53,54).
## Methods
### GaN NW array preparation
The NW arrays were fabricated out of epitaxial GaN layers grown by metalorganic vapor-phase epitaxy (MOVPE) on sapphire substrates in a top-down hybrid etching approach. The epitaxial wafer has an n-p-n layer stack structure (Fig. 1b). Afterwards, the wafers were patterned by photolithography and lift-off technique with Cr as dry etching mask. Hexagonal-cone GaN nanostructure arrays were obtained by ICP-DRIE with SF6 and H2 gases. Furthermore, KOH-based wet chemical etching was carried out to remove the plasma-induced surface damage of the nanostructures and to shrink the diameter of the hexagonal structures realizing smooth vertical sidewalls. The NW diameters were varied as defined during photolithography to be (221 ± 9) nm, (443 ± 7) nm, and (647 ± 8) nm after ICP-DRIE and wet chemical etching, while the NW height was kept the same at around 3 µm20.
### Transistor fabrication
In 3D device processing of vertical GaN NW FETs, highly n-doped GaN was used on top layer of the NWs to improve the quality of the Ohmic contacts. The Mg acceptors in the gate channel (p-channel) of n-p-n GaN NWs were activated by rapid thermal annealing (RTA) at 950 °C for 30 s and subsequently at 600 °C for 5 min. Furthermore, thermal ALD technique using trimethylaluminium and water was employed to form a ~25 nm thick Al2O3 gate dielectric layer. To improve the passivation between the GaN layer and the gate metal, a 200 nm thick SiOx was deposited using e-beam evaporation. The wrap around Cr gate (Fig. 1c) was deposited via tilted e-beam evaporation, using the shadowing effect from the mushroom-like NW shape to prevent any deposition on the upper part of the NWs. Thus, it covered the 0.4 µm p-channel area on the GaN epi-layer (Fig. 1b) and is located 1 µm below the top mushroom head of NWs (see inset Fig. 1a). The W is the circumference of the NWs with diameters of 220 nm, 440 nm, and 640 nm. For supporting the drain contact, the space between the GaN NWs was filled with photoresist with short UV exposure and cured at around 250 °C for 30 min (Fig. 1d). Next, to form an Ohmic contact, a Cr/Au (80/200 nm) layer stack was deposited (see Fig. 1e). Afterwards, this sacrificial polymer could be removed if necessary resulting in top drain bridging contact.
### DC characterization
The output and transfer characteristics of FETs were measured by an SMU Keithley 4200-semiconductor characterization system (SCS) at room temperature and under parasitic electric charge protection. Three point-like gold probes with coaxial cables probes were used to enhance the electric transfer between the device and the SMU. All Vth and Id,max values were conducted from five measurements of the same FETs. Hence, the average values and their standard deviations were finally taken.
### Simulation Model
The numerical simulations have been carried out with Sentaurus Device using hydrodynamic carrier transport for electrons and drift-diffusion transport for holes. The lattice temperature is 300K for all simulations. The hexagonal NW was approximated by a cylindrical geometry and simulated on a 2D radial cross section using azimuthal expansion. The gate isolation material (Al2O3) has been assumed to be crystalline with a permittivity ε = 10.2. A calibration of the gate capacitance was not possible due to the large contribution of the contact capacitance in the experiment (SI Fig. 2). The carrier mobility model incorporates high field saturation of the velocity as well doping dependence55. The acceptor doping of the channel region and the donor doping of the drift region are NA = 2 × 1018 cm−3 and ND,drift = 5 × 1016 cm−3, respectively, and calibrated with experimental results in Fig. 5a,b.
## Data Availability
All data generated or analyzed during this study are included in this published article (and its Supplementary Information (SI) files).
## References
1. 1.
Alloatti, L. High-Speed Photonics for Side-by-Side Integration with Billion Transistor Circuits in Unmodified CMOS Processes. Journal of Lightwave Technology 35, 1168–1173 (2017).
2. 2.
Chau, R., Doyle, B., Datta, S., Kavalieros, J. & Zhang, K. Integrated nanoelectronics for the future. Nature Materials 6, 810–812 (2007).
3. 3.
Zeng, G. & Zeng, S. Study on the Development of the Chip Information Industry Based on Moore’s Law. Journal of Computer and Communications 05, 39–47 (2017).
4. 4.
She, X., Huang, A. Q., Lucia, O. & Ozpineci, B. Review of Silicon Carbide Power Devices and Their Applications. IEEE Transactions on Industrial Electronics 64, 8193–8205 (2017).
5. 5.
de Paula, W. J. et al. A review on gallium nitride switching power devices and applications. in 2017 Brazilian Power Electronics Conference (COBEP) 1–7 (IEEE, 2017).
6. 6.
Zhang, Y., Dadgar, A. & Palacios, T. Gallium nitride vertical power devices on foreign substrates: a review and outlook. Journal of Physics D: Applied Physics 51, 273001 (2018).
7. 7.
De Santi, C., Meneghini, M., Meneghesso, G. & Zanoni, E. Review of dynamic effects and reliability of depletion and enhancement GaN HEMTs for power switching applications. IET Power Electronics 11, 668–674 (2018).
8. 8.
Huang, Y., Duan, X., Cui, Y. & Lieber, C. M. Gallium Nitride Nanowire Nanodevices. Nano Letters 2, 101–104 (2002).
9. 9.
Vandenbrouck, S. et al. 12 GHz FMAX GaN/AlN/AlGaN Nanowire MISFET. IEEE Electron Device Letters 30, 322–324 (2009).
10. 10.
Salahuddin, S., Ni, K. & Datta, S. The era of hyper-scaling in electronics. Nature Electronics 1, 442–450 (2018).
11. 11.
Amano, H. et al. The 2018 GaN power electronics roadmap. Journal of Physics D: Applied Physics 51, 163001 (2018).
12. 12.
Sabui, G. et al. GaN Nanowire Schottky Barrier Diodes. IEEE Transactions on Electron Devices 64, 2283–2290 (2017).
13. 13.
Yu, F. et al. Normally Off Vertical 3-D GaN Nanowire MOSFETs with Inverted p-GaN Channel. IEEE Transactions on Electron Devices 65, 2439–2445 (2018).
14. 14.
Sun, M., Zhang, Y., Gao, X. & Palacios, T. High-Performance GaN Vertical Fin Power Transistors on Bulk GaN Substrates. IEEE Electron Device Letters 38, 509–512 (2017).
15. 15.
Liu, Z. J., Huang, T., Ma, J., Liu, C. & Lau, K. M. Monolithic Integration of AlGaN/GaN HEMT on LED by MOCVD. IEEE Electron Device Letters 35, 330–332 (2014).
16. 16.
Lu, X. et al. Monolithic integration of enhancement-mode vertical driving transistors on a standard InGaN/GaN light emitting diode structure. Appl. Phys. Lett. 109, 053504 (2016).
17. 17.
Iannaccone, G., Bonaccorso, F., Colombo, L. & Fiori, G. Quantum engineering of transistors based on 2D materials heterostructures. Nature Nanotechnology 13, 183–191 (2018).
18. 18.
Yu, W. J. et al. Vertically stacked multi-heterostructures of layered materials for logic transistors and complementary inverters. Nature Materials 12, 246 (2012).
19. 19.
Kamrani, H. et al. Thermal performance analysis of GaN nanowire and fin-shaped power transistors based on self-consistent electrothermal simulations. Microelectronics Reliability 91, 227–231 (2018).
20. 20.
Fatahilah, M. F. et al. Traceable Nanomechanical Metrology of GaN Micropillar Array. Advanced Engineering Materials, https://doi.org/10.1002/adem.201800353 (2018).
21. 21.
Ruzzarin, M. et al. Instability of Dynamic- Ron and Threshold Voltage in GaN-on-GaN Vertical Field-Effect Transistors. IEEE Transactions on Electron Devices 64, 3126–3131 (2017).
22. 22.
Li, W. & Chowdhury, S. Design and fabrication of a 1.2 kV GaN-based MOS vertical transistor for single chip normally off operation: Design and fabrication of a 1.2-kV GaN-based MOS vertical transistor. physica status solidi (a) 213, 2714–2720 (2016).
23. 23.
Chowdhury, S., Swenson, B. L. & Mishra, U. K. Enhancement and Depletion Mode AlGaN/GaN CAVET with Mg-Ion-Implanted GaN as Current Blocking Layer. IEEE Electron Device Letters 29, 543–545 (2008).
24. 24.
Ben-Yaacov, I., Seck, Y.-K., Mishra, U. K. & DenBaars, S. P. AlGaN/GaN current aperture vertical electron transistors with regrown channels. Journal of Applied Physics 95, 2073–2078 (2004).
25. 25.
Fatahilah, M. F. et al. 3D GaN nanoarchitecture for field-effect transistors. Micro and Nano Engineering 3, 59–81 (2019).
26. 26.
Larrieu, G. & Han, X.-L. Vertical nanowire array-based field effect transistors for ultimate scaling. Nanoscale 5, 2437 (2013).
27. 27.
Son, D.-H. et al. Low Voltage Operation of GaN Vertical Nanowire MOSFET. 3.
28. 28.
Yu, F. et al. Vertical architecture for enhancement mode power transistors based on GaN nanowires. Applied Physics Letters 108, 213503 (2016).
29. 29.
Sabui, G. et al. (Invited) Simulation Study of High Voltage Vertical GaN Nanowire Field Effect Transistors. ECS Transactions 80, 69–85 (2017).
30. 30.
Yu, F. et al. GaN nanowire arrays with nonpolar sidewalls for vertically integrated field-effect transistors. Nanotechnology 28, 095206 (2017).
31. 31.
Hamdana, G. et al. Nanoindentation of crystalline silicon pillars fabricated by soft UV nanoimprint lithography and cryogenic deep reactive ion etching. Sensors and Actuators A: Physical 283, 65–78 (2018).
32. 32.
Hamdana, G. et al. Towards fabrication of 3D isotopically modulated vertical silicon nanowires in selective areas by nanosphere lithography. Microelectronic Engineering 179, 74–82 (2017).
33. 33.
Wasisto, H. S., Merzsch, S., Steib, F., Waag, A. & Peiner, E. Vertical silicon nanowire array-patterned microcantilever resonators for enhanced detection of cigarette smoke aerosols. Micro & Nano Letters 9, 676–679 (2014).
34. 34.
Wasisto, H. S. et al. Finite element modeling and experimental proof of NEMS-based silicon pillar resonators for nanoparticle mass sensing applications. Microsystem Technologies 20, 571–584 (2014).
35. 35.
Merzsch, S. et al. Production of vertical nanowire resonators by cryogenic-ICP–DRIE. Microsystem Technologies 20, 759–767 (2014).
36. 36.
Wasisto, H. S. et al. Silicon resonant nanopillar sensors for airborne titanium dioxide engineered nanoparticle mass detection. Sensors and Actuators B: Chemical 189, 146–156 (2013).
37. 37.
Wasisto, H. S. et al. Silicon Nanowire Resonators: Aerosol Nanoparticle Mass Sensing in the Workplace. IEEE Nanotechnology Magazine 7, 18–23 (2013).
38. 38.
Wasisto, H. S. et al. Femtogram aerosol nanoparticle mass sensing utilising vertical silicon nanowire resonators. Micro & Nano Letters 8, 554–558 (2013).
39. 39.
Debnath, R. et al. Top-down fabrication of large-area GaN micro- and nanopillars. Journal of Vacuum Science & Technology B 32, 021204 (2014).
40. 40.
Dubois, V. et al. Massively parallel fabrication of crack-defined gold break junctions featuring sub-3 nm gaps for molecular devices. Nature Communications 9 (2018).
41. 41.
Siket, C. M. et al. Direct writing of anodic oxides for plastic electronics. npj Flexible Electronics 2 (2018).
42. 42.
Sun, X. et al. High spectral response of self-driven GaN-based detectors by controlling the contact barrier height. Scientific Reports 5 (2015).
43. 43.
Huang, R. et al. Ion Sputter Induced Interfacial Reaction in Prototypical Metal-GaN System. Scientific Reports 8 (2018).
44. 44.
Zhang, K., Sumiya, M., Liao, M., Koide, Y. & Sang, L. P-Channel InGaN/GaN heterostructure metal-oxide-semiconductor field effect transistor based on polarization-induced two-dimensional hole gas. Scientific Reports 6 (2016).
45. 45.
Jia, Y., Wallace, J. S., Echeverria, E., Gardella, J. A. & Singisetti, U. Interface characterization of atomic layer deposited Al2O3 on m-plane GaN: Interface characterization of ALD-Al2O3 on m-plane GaN. physica status solidi (b) 254, 1600681 (2017).
46. 46.
Wang, X., Brown, A. R., Binjie Cheng & Asenov, A. Statistical variability and reliability in nanoscale FinFETs. in 2011 International Electron Devices Meeting 5.4.1-5.4.4 (IEEE, 2011).
47. 47.
Han, X.-L., Larrieu, G., Dubois, E. & Cristiano, F. Carrier injection at silicide/silicon interfaces in nanowire based-nanocontacts. Surface Science 606, 836–839 (2012).
48. 48.
Colinge, J.-P. et al. Temperature effects on trigate SOI MOSFETs. IEEE Electron Device Letters 27, 172–174 (2006).
49. 49.
Qian, Q. et al. Improved Gate Dielectric Deposition and Enhanced Electrical Stability for Single-Layer MoS2 MOSFET with an AlN Interfacial Layer. Scientific Reports 6 (2016).
50. 50.
Kaushik, N. et al. Reversible hysteresis inversion in MoS2 field effect transistors. npj 2D Materials and Applications 1 (2017).
51. 51.
Calarco, R., Stoica, T., Brandt, O. & Geelhaar, L. Surface-induced effects in GaN nanowires. Journal of Materials Research 26, 2157–2168 (2011).
52. 52.
Witzigmann, B. et al. Performance analysis and simulation of vertical gallium nitride nanowire transistors. Solid-State Electronics 144, 73–77 (2018).
53. 53.
Fricke, L. et al. Self-Referenced Single-Electron Quantized Current Source. Physical Review Letters, 112 (2014).
54. 54.
Fricke, L. et al. Counting statistics for electron capture in a dynamic quantum dot. Physical Review Letters, 110 (2013).
55. 55.
Mnatsakanov, T. T. et al. Carrier mobility model for GaN. Solid-State Electronics 47, 111–115 (2003).
## Acknowledgements
The authors would like to thank A. Schmidt, J. Breitfelder, M. Rühmann, and K.-H. Lachmund for their valuable technical assistances. Authors are also grateful for the planar GaN wafers provided by the members of epitaxy competence center (ec2) of TU Braunschweig (I. Manglano Clavero and C. Margenfeld). This work has been performed within the projects of ‘LENA-OptoSense’ funded by the Lower Saxony Ministry for Science and Culture (MWK) and ‘3D Concepts for Gallium-Nitride Electronics (3D GaN)’ funded by the German Research Foundation (DFG). Support by Ministry of Research, Technology, and Higher Education of the Republic of Indonesia (RISTEKDIKTI) and Indonesian-German Center for Nano and Quantum Technologies (IG-Nano) is also acknowledged. The research activity at University of Padova was partly funded by project “Novel vertical GaN-devices for next generation power conversion”, NoveGaN (University of Padova), through the STARS CoG Grants call.
## Author information
Authors
### Contributions
M.F.F designed, fabricated, and characterized the n-p-n vertical GaN NW FETs. M.F.F., F.Y., and K.S. analyzed the realized FETs. A.B., F.Y., and K.S. supported the ALD process of the dielectric materials. K.S. provided the n-p-n GaN wafers and performed the FE-SEM analysis. D.M. characterized the fabricated FETs. F.R. and B.W. provide simulation and theory of the fabricated FETs. M.F.F., K.S., F.Y., F.R. and H.S.W. wrote the manuscript. H.S.W., A.W., B.W., M.M., F.H, and H.W.S. provided significant inputs on fabrication and characterization of FETs. A.W. and H.S.W led the development of the vertical GaN NW FETs and coordinated the projects. All authors reviewed the manuscript.
### Corresponding authors
Correspondence to Muhammad Fahlesa Fatahilah or Hutomo Suryo Wasisto.
## Ethics declarations
### Competing Interests
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
## Rights and permissions
Reprints and Permissions
Fatahilah, M.F., Yu, F., Strempel, K. et al. Top-down GaN nanowire transistors with nearly zero gate hysteresis for parallel vertical electronics. Sci Rep 9, 10301 (2019). https://doi.org/10.1038/s41598-019-46186-9
• Accepted:
• Published:
• ### Single GaN Nanowires for Extremely High Current Commutation
• Konstantin Shugurov
• , Alexey Mozharov
• , Georgiy Sapunov
• , Maria Tchernycheva
• & Ivan Mukhin
physica status solidi (RRL) – Rapid Research Letters (2021)
• ### Investigation of Electrical Behaviors Observed in Vertical GaN Nanowire Transistors Using Extended Landauer-Büttiker Formula
• Fatimah Arofiati Noor
• , Toto Winata
• , Feng Yu
• , Hutomo Suryo Wasisto
• & Khairurrijal Khairurrijal
IEEE Access (2021)
• ### Nonmechanical parfocal and autofocus features based on wave propagation distribution in lensfree holographic microscopy
• Agus Budi Dharmawan
• , Shinta Mariana
• , Gregor Scholz
• , Philipp Hörmann
• , Torben Schulze
• , Kuwat Triyana
• , Mayra Garcés-Schröder
• , Ingo Rustenbeck
• , Karsten Hiller
• , Hutomo Suryo Wasisto
• & Andreas Waag
Scientific Reports (2021)
• ### Ab initio study of hydrogen sensing in Pd and Pt functionalized GaN [0 0 0 1] nanowires
• S. Assa Aravindh
• , Wei Cao
• , Matti Alatalo
• & Marko Huttula
Applied Surface Science (2020)
• ### Highly stable threshold voltage in GaN nanowire FETs: The advantages of p-GaN channel/Al2O3 gate insulator
• Maria Ruzzarin
• , Carlo De Santi
• , Feng Yu
• , Klaas Strempel
• , Hutomo Suryo Wasisto
• , Andreas Waag
• , Gaudenzio Meneghesso
• , Enrico Zanoni
• & Matteo Meneghini
Applied Physics Letters (2020) | 2021-04-22 12:18:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7484503984451294, "perplexity": 7053.915957690653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00602.warc.gz"} |
http://www.ph.ed.ac.uk/people/peter-clarke | # Peter Clarke
### Professor P Clarke, FRSE, C.Eng, C.Phys, FIET, FInstP
Position
Professor
Category
Location
James Clerk Maxwell Building (JCMB)
Room 5421
Peter is a member of the following School research institute, research group and research areas:
### Research interests
Peter Clarke is Professor of Physics at the University of Edinburgh. He has a 1st Class Honours degree in Electronics Engineering (Southampton University,1980) and a D.Phil in Particle Physics (Oxford 1985). He was a CERN Fellow before being appointed as a lecturer first at Brunel University in 1987 and then moving to University College London in 1993. He was promoted to Reader and then Professor in 2001 and was Head of the Particle Physics Research Group between 2001-04. He moved to the University of Edinburgh in 2004 to take up the Chair of eScience and later become Director of the National eScience Centre 2006-09. He is a Fellow of the Institute of Physics and the Institute of Engineering and Technology.
His early research work included the first direct measurements of CP violation in the Kaon system at CERN; Working at the SLD experiment at the Stanford Linear Collider (USA) and then the LEP electron positron collider at CERN he worked on precision measurements of the electro-weak interaction, the properties of the Z and W bosons and indirect searches for the Higgs boson. At UCL he worked on construction of the ATLAS experiment for the Large Hadron Collider
He was involved in UK e-Science since its inception. He was a founder of the Centre of Excellence in Networked Systems at UCL and was prominent in advancing national and international networking for research. He has held roles in international grid computing infrastructure projects including the management board of the UK grid for particle physics (GridPP), the European Data Grid and the EGEE projects. He was a member of the Steering Committee of the Global Grid Forum international standards body between 2002-04 and co-Director of the Data Area.
His present research is as a member of the LHCb experiment at the Large Hadron Collider at CERN. LHCb is searching for the signals associated with the imbalance between the interactions of mattter and anti-matter. He has produced the worlds most precise measurement of a CP violating phase called "phis" and he is deputy computing coordinator of the experiment.
• 1st year introduction to physics (P1B) 2005-2010.
• 1st year UG laboratories 2005-2009
• 2nd year undergraduate laboratories 2012-present
• Numerical recipes 2013-present
### Recent publications
1. , , , , , , , , , , , , , , et al., Journal of High Energy Physics, 1605, p. 131
2. , , , , , , , , , , , , , , et al., Journal of High Energy Physics, 1603, p. 159
3. , , , , , , , , , , , , , , et al., Physical Review, D93, 11, p. 119902
4. , , , , , , , , , , , , , , et al., Journal of High Energy Physics, 1602, p. 133
5. , , , , , , , , , , , , , , et al., Journal of High Energy Physics, 1602, p. 104 | 2016-09-27 17:18:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8166646957397461, "perplexity": 1152.944989068995}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1474738661155.56/warc/CC-MAIN-20160924173741-00075-ip-10-143-35-109.ec2.internal.warc.gz"} |
https://socialcar-project.eu/en/a-cylinder-has-a-radius-of-5-yds-and-a-height-of-2-yds-what-is-the-surface-area-of-the-cylinder-u.85504.html | Camsmiley
33
# A cylinder has a radius of 5 yds and a height of 2 yds. What is the surface area of the cylinder? (Use 3.14 for pi.)
Use the following formula:- $SA=2 \pi rh+2 \pi r^2$ r = radius h = height Substitute for the formula:- r = 5 $SA = 2 * \pi *5*h+2* \pi *5^2$ 2 = 5 $SA = 2 * \pi *r*2+2* \pi *r^2$ $SA= 2* \pi *5*2+2* \pi *5^2$ Solve:- $SA= 2* 3.14 *5*2+2* 3.14 *5^2$ SA = 2 × 3.14 × 5 × 2 + 2 × 3.14 × 25 SA = 6.28 × 5 × 2 + 2 × 3.14 × 25 SA = 31.4 × 2 + 2 × 3.14 × 25 SA = 62.8 + 6.28 × 25 SA = 62.8 + 157 SA = 219.8 SA = 219.8 yds The surface area of this cylinder is 219.8 yds (yards) | 2022-08-11 14:44:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8999896049499512, "perplexity": 1533.0130707605938}, "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-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00195.warc.gz"} |
https://asmedigitalcollection.asme.org/manufacturingscience/article-abstract/129/5/885/475610/Study-of-Internal-Finishing-of-Austenitic?redirectedFrom=fulltext | This paper studies the internal finishing of capillary tubes using a magnetic abrasive finishing process. Such tubes are used with nanoscale technologies and meet the demands of the present age in medical and chemical equipment. The finishing characteristics are influenced by the magnetic abrasive behavior against the inner surface of the capillary, which is controlled by the supplied amount of magnetic abrasive and the magnetic force acting on it. The development of the finishing unit identifies the characteristics of the magnetic field, which controls the magnetic force, required for the necessary magnetic abrasive behavior. Finishing experiments using SUS304 austenitic stainless steel capillary tube with $800μm$ inner diameter demonstrate the effects of the supplied amount of the magnetic abrasive on the finishing characteristics, and the results suggest a standard method to determine the amount to achieve sufficient finishing. The run-out of the capillary while rotating at high speed under the cantilever tube support method causes instability of the magnetic abrasive behavior. The effects on the finishing characteristics are discussed, and a method to diminish the run-out is applied. Accordingly, this paper presents the conditions required for the internal finishing of capillary tubes and proposes methods to realize them. The internal finishing of $400μm$ inner diameter capillary tubes conveys an understanding of the mechanisms involved and demonstrates the usefulness of the proposed methods.
1.
Kawasumi
,
T.
, 2004, “
Fluidized Finishing/Washing Machine
,” Nachi-Business News, 2B3, Nachi-Fujikoshi Corp., Toyama, Japan, pp.
1
6
(in Japanese).
2.
Sugimori
,
H.
, and
Kurobe
,
T.
, 2002, “
High Speed Gyration Flow Finishing of Inner Wall of Capillary Drilled by Electrical Discharge Machining
,”
Journal of Japan Society for Abrasive Technology
,
69
(
2
), pp.
79
84
(in Japanese).
3.
Ogawa
,
H.
, 2005, JP patent, P2005-237938A.
4.
Jiang
,
M.
,
Wood
,
N. O.
, and
Komanduri
,
R.
, 1998, “
On the Chemo-Mechanical Polishing (CMP) of Si3N4 Bearing Balls With Water Based CeO2 Slurry
,”
ASME J. Tribol.
0742-4787,
120
, pp.
304
312
.
5.
Hou
,
Z.
, and
Komanduri
,
R.
, 1998, “
Magnetic Field Assisted Finishing of Ceramics—Part I: Thermal Model
,”
ASME J. Tribol.
0742-4787,
120
, pp.
645
651
.
6.
Hou
,
Z.
, and
Komanduri
,
R.
, 1998, “
Magnetic Field Assisted Finishing of Ceramics—Part II: On Thermal Aspects of Magnetic Float Polishing (MFP) of Ceramics Balls
,”
ASME J. Tribol.
0742-4787,
120
, pp.
652
659
.
7.
Hou
,
Z.
, and
Komanduri
,
R.
, 1998, “
Magnetic Field Assisted Finishing of Ceramics—Part III: On the Thermal Aspects of Magnetic Abrasive Finishing (MAF) of Ceramic Rollers
,”
ASME J. Tribol.
0742-4787,
120
, pp.
660
665
.
8.
Kim
,
W.
,
Lee
,
S.
, and
Min
,
B.
, 2004, “
Surface Finishing and Evaluation of Three-Dimensional Silicon Microchannel Using Magnetorheological Fluid
,”
ASME J. Tribol.
0742-4787,
126
, pp.
772
778
.
9.
Shinmura
,
T.
, and
Yamaguchi
,
H.
, 1995, “
Study on a New Internal Finishing Process by the Application of Magnetic Abrasive Machining-Internal Finishing of Stainless Steel Tube and Clean Gas Bomb
,”
JSME Int. J., Ser. C
1340-8062,
38
(
4
), pp.
798
804
.
10.
Yamaguchi
,
H.
,
Shinmura
,
T.
, and
Kobayashi
,
A.
, 2001, “
Development of an Internal Magnetic Abrasive Finishing Process for Nonferromagnetic Complex Shaped Tubes
,”
JSME Int. J., Ser. C
1340-8062,
44
(
1
), pp.
275
281
.
11.
Yamaguchi
,
H.
,
Shinmura
,
T.
, and
Sekine
,
M.
, 2005, “
Uniform Internal Finishing of SUS304 Stainless Steel Bent Tube Using Magnetic Abrasive Finishing Process
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
127
, pp.
605
611
.
12.
Yamaguchi
,
H.
,
Shinmura
,
T.
, and
Ikeda
,
R.
, 2005, “
Study of Internal Finishing of Slender Tubes by Magnetic Abrasive Finishing
,”
Proceedings of the 3rd International Conference on Leading Edge Manufacturing in 21st Century
, Tokyo, Japan, Vol.
3
, pp.
1181
1186
.
13.
Yamaguchi
,
H.
,
Shinmura
,
T.
, and
Kaneko
,
T.
, 1996, “
Development of a New Internal Finishing Process Applying Magnetic Abrasive Finishing by Use of Pole Rotation System
,”
Int. J. Jpn. Soc. Precis. Eng.
0916-782X,
30
(
4
), pp.
317
322
.
14.
Yamaguchi
,
H.
, and
Shinmura
,
T.
, 2000, “
Study of an Internal Magnetic Abrasive Finishing using a Pole Rotation System—Discussion of the Characteristic Abrasive Behavior
,”
Precis. Eng.
0141-6359,
24
, pp.
237
244
.
15.
Yamaguchi
,
H.
, and
Shinmura
,
T.
, 1995, “
New Internal Finishing Process by Application of Magnetic Abrasive Machining—3rd Report, Effects of Finishing Pressure Distribution on Characteristics
,”
JSME Int. J., Ser. C
1340-8062,
61
(
586
), pp.
2605
2611
(in Japanese).
16.
Yamaguchi
,
H.
,
Shinmura
,
T.
, and
Hashimoto
,
T.
, 2005, “
Study of Simultaneous Internal and External Finishing of Alumina Ceramic Tubes by a Magnetic Field Assisted Finishing
,”
Proceedings of the JSPE Fall Annual Meeting
, Tokyo, Japan, pp.
75
76
(in Japanese).
17.
Yamaguchi
,
H.
,
Shinmura
,
T.
, and
Kanayama
,
M.
, 2005, “
Study of a Magnetic Field Assisted Internal Machining Process of SUS304 Stainless Steel Tubes
,”
Proceedings of the JSPE Spring Annual Meeting
, Tokyo, Japan, pp.
1259
1260
(in Japanese). | 2019-10-16 18:14:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3345451056957245, "perplexity": 13885.272464780437}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986669057.0/warc/CC-MAIN-20191016163146-20191016190646-00027.warc.gz"} |
https://brilliant.org/problems/rmo-2016/ | # RMO 2016
Algebra Level 2
Let $$a$$, $$b$$, and $$c$$ be positive real numbers such that
$\frac{a}{1+b} + \frac{b}{1 + c} + \frac{c}{1 + a} = 1.$
What is the maximum value of $$abc?$$
× | 2018-04-22 22:12:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8696718215942383, "perplexity": 686.0435208777099}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945660.53/warc/CC-MAIN-20180422212935-20180422232935-00266.warc.gz"} |
http://www.okstate.edu/sas/v8/sashtml/iml/chap10/sect6.htm | Chapter Contents Previous Next
Time Series Analysis and Control Examples
### Minimum AIC Procedure
The AIC statistic is widely used to select the best model among alternative parametric models. The minimum AIC model selection procedure can be interpreted as a maximization of the expected entropy (Akaike 1981). The entropy of a true probability density function (PDF) with respect to the fitted PDF f is written as
where is a Kullback-Leibler information measure, which is defined as
where the random variable Z is assumed to be continuous. Therefore,
where and EZ denotes the expectation concerning the random variable Z. if and only if (a.s.). The larger the quantity EZ logf(Z), the closer the function f is to the true PDF .Given the data y = (y1, ... , yT)' that has the same distribution as the random variable Z, let the likelihood function of the parameter vector be .Then the average of the log likelihood function is an estimate of the expected value of logf(Z). Akaike (1981) derived the alternative estimate of EZ logf(Z) by using the Bayesian predictive likelihood. The AIC is the bias-corrected estimate of , where is the maximum likelihood estimate.
AIC = - 2( maximum log likelihood) + 2( number of free parameters)
Let be a K ×1 parameter vector that is contained in the parameter space . Given the data y, the log likelihood function is
Suppose the probability density function has the true PDF , where the true parameter vector is contained in . Let be a maximum likelihood estimate. The maximum of the log likelihood function is denoted as .The expected log likelihood function is defined by
The Taylor series expansion of the expected log likelihood function around the true parameter gives the following asymptotic relationship:
where is the information matrix and = stands for asymptotic equality. Note that since is maximized at . By substituting , the expected log likelihood function can be written as
The maximum likelihood estimator is asymptotically normally distributed under the regularity conditions
Therefore,
The mean expected log likelihood function, , becomes
When the Taylor series expansion of the log likelihood function around is used, the log likelihood function is written
Since is the maximum log likelihood function, .Note that if the maximum likelihood estimator is a consistent estimator of . Replacing with the true parameter and taking expectations with respect to the random variable Y,
Consider the following relationship:
From the previous derivation,
Therefore,
The natural estimator for Eis . Using this estimator, you can write the mean expected log likelihood function as
Consequently, the AIC is defined as an asymptotically unbiased estimator of -2( mean expected log likelihood)
In practice, the previous asymptotic result is expected to be valid in finite samples if the number of free parameters does not exceed and the upper bound of the number of free parameters is [T/2]. It is worth noting that the amount of AIC is not meaningful in itself, since this value is not the Kullback-Leibler information measure. The difference of AIC values can be used to select the model. The difference of the two AIC values is considered insignificant if it is far less than 1. It is possible to find a better model when the minimum AIC model contains many free parameters.
Chapter Contents Previous Next Top | 2017-11-21 02:45:05 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9629520773887634, "perplexity": 405.15999418062336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806310.85/warc/CC-MAIN-20171121021058-20171121041058-00217.warc.gz"} |
https://gmatclub.com/forum/nail-the-sentence-correction-section-the-only-motive-behind-144062-20.html | It is currently 19 Nov 2017, 13:12
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
# Events & Promotions
###### Events & Promotions in June
Open Detailed Calendar
# NAIL THE SENTENCE CORRECTION SECTION The only motive behind
Author Message
TAGS:
### Hide Tags
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:08
Based on the meaning of the sentence, the doctors are trying to disentagle the dark side or negative side of lying or the possible negative effects of this one.
The point at end is not to evaluate social interactions but how lying affects the whole story:)
_________________
Kudos [?]: 9285 [0], given: 1168
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 635
Kudos [?]: 664 [0], given: 23
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:15
carcass wrote:
Based on the meaning of the sentence, the doctors are trying to disentagle the dark side or negative side of lying or the possible negative effects of this one.
The point at end is not to evaluate social interactions but how lying affects the whole story:)
Or may be interpretation is wrong?
Can't social interactions become destructive? or can't they signal something?
Moreover if u notice meaning carefully Psychiatrists have already recognized some thing about lying.. and now are intersted in evaluating the extent/details of those results.
_________________
Lets Kudos!!!
Black Friday Debrief
Kudos [?]: 664 [0], given: 23
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [0], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:24
Vips0000 wrote:
Marcab wrote:
This is the second one and it would be great to discuss the answer choice A.
Anyways the OA is
[Reveal] Spoiler:
E
Sorry, but why would it be incorrect? A makes perfect sense. It's not lying or psychiatrist we are referring to, but social interactions.
Thats what I thought and got it wrong.
Seriously how can "lying" be destructive?
..and that is the reason why I posted the question here.
_________________
Kudos [?]: 1703 [0], given: 62
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [0], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:26
the official explanation was just pathetic. If one wishes for, I can post it ASAP.
_________________
Kudos [?]: 1703 [0], given: 62
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:29
So we can discuss it together I'm curious
_________________
Kudos [?]: 9285 [0], given: 1168
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:32
Vips0000 wrote:
carcass wrote:
Based on the meaning of the sentence, the doctors are trying to disentagle the dark side or negative side of lying or the possible negative effects of this one.
The point at end is not to evaluate social interactions but how lying affects the whole story:)
Or may be interpretation is wrong?
Can't social interactions become destructive? or can't they signal something?
Moreover if u notice meaning carefully Psychiatrists have already recognized some thing about lying.. and now are intersted in evaluating the extent/details of those results.
I always ear your objections........let me see what we can carve or squizz from it
_________________
Kudos [?]: 9285 [0], given: 1168
Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 635
Kudos [?]: 664 [0], given: 23
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:33
Marcab wrote:
the official explanation was just pathetic. If one wishes for, I can post it ASAP.
Ha ha.. I would rather think that our approaches of thinking may be incorrect. GMAC is the ultimate authority. May be carcass can help to reason it through since he got it correct.
_________________
Lets Kudos!!!
Black Friday Debrief
Kudos [?]: 664 [0], given: 23
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [0], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:37
@carcass.
Give me few hours. GMATPREP is on a different system.
Coming to the question, what I feel is that "they" in A may refer to doctors as well as interactions, in such a case both are sounding fine.
Whereas E modifies "lying" only.
what say?
_________________
Kudos [?]: 1703 [0], given: 62
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 03:43
Nothing ........I read the question here at work, at my own risk but who cares :D.........10000 times.
First of all my intuition leads to lying (meaning)
Secondly, $$they$$ is a bit ambiguous referring to doctors or interactions.
Other things I do not see........someone calls Sir Ron Purewal :D
I agree with you Marcab: same conclusion I had
_________________
Kudos [?]: 9285 [0], given: 1168
Manager
Joined: 12 Oct 2012
Posts: 61
Kudos [?]: 12 [0], given: 19
Concentration: Technology, Entrepreneurship
Schools: Said (M)
GMAT 1: 760 Q50 V41
GPA: 3.73
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 08:01
Vips0000 wrote:
Marcab wrote:
This is the second one and it would be great to discuss the answer choice A.
Anyways the OA is
[Reveal] Spoiler:
E
Sorry, but why would it be incorrect? A makes perfect sense. It's not lying or psychiatrist we are referring to, but social interactions.
Hi Vips0000,
Do you mean that 'social interactions' are destructive and they can signal certain mental problems??
Kudos [?]: 12 [0], given: 19
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [0], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 08:10
kaushinside wrote:
Vips0000 wrote:
Marcab wrote:
This is the second one and it would be great to discuss the answer choice A.
Anyways the OA is
[Reveal] Spoiler:
E
Sorry, but why would it be incorrect? A makes perfect sense. It's not lying or psychiatrist we are referring to, but social interactions.
Hi Vips0000,
Do you mean that 'social interactions' are destructive and they can signal certain mental problems??
Even though I am not Vips, I will reply because your question was very tempting.
Why can't the social interactions be destructive, in fact they can be. Moreover, if they are not good with others then they WILL signal certain mental problems.
_________________
Kudos [?]: 1703 [0], given: 62
Manager
Joined: 12 Oct 2012
Posts: 61
Kudos [?]: 12 [0], given: 19
Concentration: Technology, Entrepreneurship
Schools: Said (M)
GMAT 1: 760 Q50 V41
GPA: 3.73
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 08:21
Quote:
Even though I am not Vips, I will reply because your question was very tempting.
Why can't the social interactions be destructive, in fact they can be. Moreover, if they are not good with others then they WILL signal certain mental problems.
I agree that a certain set of social interactions have the capacity to be destructive..
But when you have something like 'lying' in the sentence which talks about the ill-effects of an entity, you would associate those ill-effects with 'lying', wouldn't you?
When i read this question, it was obvious to me that lying was the culprit.. so i was able to select the right answer..
Kudos [?]: 12 [0], given: 19
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 12:26
for me, we are going out of scope and infer too much.
Waiting the OE provide by marcab
But I 'm quite sure that it will not solve definitely the question; simply because the OE for PS DS and SC are unuseful in the most cases. Only CR explanations are good enough
_________________
Kudos [?]: 9285 [0], given: 1168
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [1], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
14 Dec 2012, 21:41
1
KUDOS
Here is the OE:
A) The uses of the plural noun they are not in the agreement with the singular antecedent lying.
E) The singular pronoun itagrees with the singular antecedent lying, and the objects of the verb determineare in parallel form, both introduced by interrogative pronoun
_________________
Kudos [?]: 1703 [1], given: 62
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
15 Dec 2012, 05:34
Marcab wrote:
Here is the OE:
A) The uses of the plural noun they are not in the agreement with the singular antecedent lying.
E) The singular pronoun itagrees with the singular antecedent lying, and the objects of the verb determineare in parallel form, both introduced by interrogative pronoun
It didin't surprise me. Is typical GMAC explanation.
that say, whithout grammar rule if I read the question suddenly they after doctor is ackward. Immediately I think that something goes wrong and this should make me suspicious
_________________
Last edited by carcass on 15 Dec 2012, 06:01, edited 1 time in total.
Kudos [?]: 9285 [0], given: 1168
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [1], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
15 Dec 2012, 05:45
1
KUDOS
I am 100% sure that you have a GMAT EAR.
Carcass very few on earth have it and should thank God for this. :D
_________________
Kudos [?]: 1703 [1], given: 62
Manager
Joined: 21 Sep 2012
Posts: 234
Kudos [?]: 413 [0], given: 63
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
15 Dec 2012, 06:42
Marcab wrote:
Here is the OE:
A) The uses of the plural noun they are not in the agreement with the singular antecedent lying.
E) The singular pronoun itagrees with the singular antecedent lying, and the objects of the verb determineare in parallel form, both introduced by interrogative pronoun
This was the same concept james explained on this thread regarding sentence structure...
for-the-farmer-who-takes-care-to-keep-them-cool-providing-143813.html
psychiatrists are seeking to determine
a)when it becomes destructive and
b)which kind of mental problems it can signal.
Kudos [?]: 413 [0], given: 63
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [0], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
15 Dec 2012, 07:14
But how can lying be destructive?
I mean "social interaction are destructive"--this is digestable but "lying is destructive"---this is not?
I feel that apart from ambiguity, there is no such issue with A.
_________________
Kudos [?]: 1703 [0], given: 62
Board of Directors
Joined: 01 Sep 2010
Posts: 3372
Kudos [?]: 9285 [0], given: 1168
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
15 Dec 2012, 07:25
But the phrase states literally that lying facilitates somthing is different to say
lying is destructive
This is why also E is correct: doctors are evaluating when it (lying) becomes destructive. this is the real point and makes sense.
regarding A, this is another point at issue: new GMAC has enormously increasing the difficulty just for all this thread that we are eviscerating and you must soleve in 1.30 seconds under pressure.
For this reason this test is beautiful and scary at the same time
_________________
Kudos [?]: 9285 [0], given: 1168
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1378
Kudos [?]: 1703 [0], given: 62
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: Nail the Sentence Correction Section [#permalink]
### Show Tags
15 Dec 2012, 07:30
Can't agree more.
Thats why MBA has to be earned.
_________________
Kudos [?]: 1703 [0], given: 62
Re: Nail the Sentence Correction Section [#permalink] 15 Dec 2012, 07:30
Go to page Previous 1 2 3 4 5 Next [ 87 posts ]
Display posts from previous: Sort by | 2017-11-19 20:12:01 | {"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": 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": 0.4016944468021393, "perplexity": 13547.678628442638}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805761.46/warc/CC-MAIN-20171119191646-20171119211646-00645.warc.gz"} |
http://www.physicsforums.com/showpost.php?p=3583377&postcount=15 | View Single Post
P: 3,175
The mean and variance of a sample, are formulas which have standard definitions. The field of study that states these definitions is "descriptive statistics". If you give numbers for the mean and variance of a sample, then people will assume you obeyed these formulas - or used formulas which give exactly the same numerical answers. It's merely a matter of obeying standard conventions.
When you want to use the numbers in a sample to estimate the mean and variance of a population (or a "random variable") there are no set rules for what formula you can use. What you do will depend on what you know about the distribution of the population.
There are three different concepts involved:
1) The properties of the sample ( such as its mean and variance)
2) The properties of the population ( such its mean and variance)
3) The formulae or procedures that you apply to the data in the sample to estimate the properties of the population.
For example, suppose the population is defined by a random variable X that has a discrete distribution with two unknown parameters A and B. Suppose we know that X has only 3 values with non-zero probabilities and that these are given by:
probability that X = M + A is 1/3
probabiltiy that X = M - A is 1/3
probabiltiy that X = M is 1/3
Suppose we take a sample of 4 random draws from this distribution and the results are:
{ -3, 1, 5, 5 }. Then we know "by inspection" that M = 1 and A = 4. The mean of the population is therefore 1. (There is a standard definition for the mean of a distribution and if you apply it to the above list of probabilities, using M = 1 and A = 4, you get that the mean is 1.)
However, if you state that you have computed the mean of the sample , this tells people that you are stating the number ( -3 + 1 + 5 + 5)/ 4. You aren't supposed to say that mean of the sample is 1 even though you know that the sample implies that the mean of the population is 1.
Suppose you have a sample of N values of the random variable X and let the sample mean be $\bar x$. I'm not an expert in descriptive statistics, but I think that if you state a number for the sample variance, it is always suposed to be the number:
$$\frac {\sum (x - \bar x)^2}{N}$$
and not the number:
$$\frac {\sum (x - \bar x)^2}{N-1}$$
If you are estimating the variance of the population, you are free to use the latter formula and people advocate doing this when N is "small". To understand why, you have to study the statistical theory of "estimators".
--------------------
So if I want to pool 5 groups together and calculate the total mean and std, I can either use the equation above on all data points Ʃni, or I can use the equation for pooled std and the mean will be x_bar = Ʃ(xi_bar*ni)/(Ʃni-1), right?
No. You wouldn't divide by $\sum n_i - 1.$ Divide by $\sum n_i$. | 2014-04-21 12:11:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8654229044914246, "perplexity": 222.1360353455586}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609539776.45/warc/CC-MAIN-20140416005219-00284-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/2nd-order-linear-homog-ode-of-variable-coefficients.591757/ | # 2nd Order Linear homog ODE of variable coefficients
1. Mar 30, 2012
### linda300
Hey,
Every where I look I can only find books and pdf talking about the uniqueness and linear independence of the solutions but I haven't been able to find a procedure of finding the solutions to one of these ode's if you haven't been already given a particular solution.
I've been trying to do this tute question,
http://img848.imageshack.us/img848/8382/sdfsq.jpg [Broken]
but in my lecture note we only went through the proofs of how the solutions are linearly independent and so on,
Would anyone be able to point we in the right direction to where I can find some examples of ODE's like this, solved without already knowing a particular solution?
I have spent some time trying to guess one of the solutions so I could find the other but it isn't going so well,
Mathematica spits out ((1 + x^2) C[1])/(2 x) + (i(-1 + x^2) C[2])/(2 x)
as the general solution but without knowing how it got there it doesn't really help,
Thanks
Last edited by a moderator: May 5, 2017
2. Mar 30, 2012
### HallsofIvy
Staff Emeritus
If you multiply through by $x^2$ you get the "Cauchy type" or "equi-potential" equation $x^2y''+ xy'- y= 0$.
One method of solving that is to try $y= x^r$. Put that into the equation and see if there exist values of r so that $x^r$ satisfies the equation.
Another method is to change the independent variable: let t= ln(x). That changes the equation to one with constant coefficients.
3. Mar 30, 2012
### linda300
Oh cool thanks!
I got r = ±1
so x and x-1 are the solutions and they're definitely linearly independent!
There is another aspect of the question, it states initial conditions that must be satisfied,
x satisfies one set however x-1 doesn't satisfy the other, the other initial condition correspond to ln(x),
Is it possible to find the solution ln(x) using the x-1 found using xr as the solution?
4. Mar 30, 2012
### HallsofIvy
Staff Emeritus
I'm not sure what you mean by "x satisifies one set however x-1 doesn't satisfy the other". They aren't supposed to satisfy one or the other condition separately.
The fact that x and x-1 satisfy the equation and are independent tells you that any solution to that equation can be written in the form $y= C_1 x+ C_2x^{-1}$. Replace x and y by the values given in your two conditions to get two equations to solve for C1 and C2.
5. Mar 30, 2012
### linda300
Isn't that y = C x + B x-1 the general solution?
Made up of two solutions y1 = Cx and y2=Bx-1
So in the next question it says find the solutions such that
y1(1) = 1 and y'1(1) = 0 which works with x
And y2(1) = 0 and y'2(1) = 1 which works if y2=ln(x)
are satisfied,
Would you obtain the ln(x) solution by using the known solution x?
Another thing that I noticed is that ln(x) isn't actually a solution, but what other functions would satisfy the y2 solution?
Last edited: Mar 30, 2012 | 2017-08-18 23:18:36 | {"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": 0.8240933418273926, "perplexity": 789.4284324371708}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105187.53/warc/CC-MAIN-20170818213959-20170818233959-00126.warc.gz"} |
http://math.stackexchange.com/questions/240525/how-to-solve-these-equations | # How to solve these equations
I'm considering a coursera astronomy course and two of the prerequisites are listed below :
Could provide me with an explanation of how to solve points 2 & 3 above ?
-
1) logarithms 2) Basic equations – Gautam Shenoy Nov 19 '12 at 11:17
@Gautam, do you think that's helpful? – Gerry Myerson Nov 19 '12 at 11:17
user, you're not going to get "a familiarity with the rudiments of high-school algebra" from an answer on math.stackexchange. You're going to need to find a refresher or bridging course somewhere, and do that before you try the astronomy course. – Gerry Myerson Nov 19 '12 at 11:20
There's no need for logarithms in question 1. $-2.3 \times 10^{13} \times .8 \times 10^{-28} = (-2.3 \times .8) \times (10^{13} \times 10^{-28}) = -1.84 \times 10^{-15}$. – littleO Nov 19 '12 at 11:24
@user470184, Gerry's advice is a sound one, imo: if you're serious about a course in astronomy you're going to need waaaaay more than answers to two questions. Think of taking a remedial course in algebra/geometry/calculus in that college/university – DonAntonio Nov 19 '12 at 11:33
show 1 more comment | 2014-03-09 10:37:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6503180265426636, "perplexity": 1851.8582458609783}, "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-2014-10/segments/1393999677213/warc/CC-MAIN-20140305060757-00063-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://sl-inworld.com/sequential-numbering/vistaprint-sequential-numbering.html | Both the Collection Point ID and Artifact ID fields are bound properly and display those exact names in the property sheet under both control source and name. On the save button I have on the form, when I click on the event tab and the on click option I have event procedure and I click the […] option to open up the code builder and this is what I currently have:
Set up a matrix in Excel, one column for each ticket position (stack) and one row for each sheet, plus one for field names. Fill the first column down in consecutive order, then the second, starting where the first column leaves off, and so on. Afet a couple of columns are filled, you can auto fill across the rows, too, so the whole thing takes only a couple of minutes. Name the stacks and use a different field for each position on the page when you do the merge. The trick is to set up using a custom file for the total number of tickets or whatever, divided into the correct number of stacks and sheets.
I've managed to edit one using Find and Replace with an { SEQ } field as the replacement to give sequential numbering. This started from 1 which is fine. Subsequent xml's where I've tried to use { SEQ \r n } to get numbering starting from other than 1 results in multiple occurrences of the number as defined by n. It's this way even after updating the fields.
If you are thinking of using sequential numbering, please give our printing experts a call for helpful advice on how to best set up your artwork. We offer ready to use templates for the most common types of forms including invoice templates, statement templates, work order templates and purchase order templates. Just upload your logo and contact information and let us know how you would like to number your forms.
I’d like to build the following expression in my query GetStartWeekNumber(DatePart("ww",[EnteredDate]), Year([EnteredDate])) So if EnteredDate = 11/3/2009 the function would return 11/1/2009 But GetStartWeekNumber does not exist as an Access Built-In Function. Is there another way to do this as an expression in a query? I’m not familiar with creating my own functions. Thanks. That would depend on how you define the start of the week... One option would be to get the day-of-week number of the date (in my system/setup, Monday is day 2), then subtract one less than that...
Rush Flyer Printing offers sequential numbering printing services. We ensure that highest standard of quality is maintained throughout the project to ensure accuracy. We use modern technology and state-of-the-art equipment to ensure that the printing gets done with highest quality standards. We understand that most business today require fast turnaround time and hence offer same day printing solutions for various products. We can even offer same day store pick up for clients from Long Island and New Jersey.
Using this script… no. While I use the data merge feature of InDesign often, I avoid the “multiple records” feature, but I typically prepare one record on one page, output the resulting file to PDF and then let the imposing software take care of the page imposition. If page imposition software is something that you don’t have, there is an alternate technique that requires preparing one record on a page, and then using the multipageimporter2.5 script to import them onto a larger sheet. Here is the link to that article: http://colecandoo.com/2011/10/28/theres-more-than-one-way-to-cut-and-stack/
GREAT tip with lots of uses! Thank you. This will save me hours of work on some tickets I’m designing. However, I also need to set up table tents that have numbers on them. They’re 2-up, and are folded, so each number needs to appear twice on the same page. In short, I want a page with 1/1 and 2/2, and I’m getting 1/2 and 3/4. Am I missing an obvious fix? Thank you.
After the { SEQ € \r68}, insert just the { SEQ € } fields where you need them for the sequential numbering. If you copy and paste one of these fields, you'll probably need to select in and press F9 to update it, or you could press Ctrl-A, F9 to update all fields in the document - useful if you've added/deleted one in an existing sequence or if you're adding multiple such fields.
# Hi! I hope you help me with this. I have the almost same problem as #2. I have PassengerTable as table name, then I have the following fields: sequence (to follow what you have in your post), transaction_date, and transaction_ID. Basically I want the to have sequential numbering in the transaction_ID where month and date from transaction_date is shown. i also have a generate (Command27)button as trigger.Tried the code with few modifications, but it sequence doesnt populate, and doesnt show any, except for what i have in control for transaction_ID which is the “Format(transaction_date,”yyyy-mm”) & “-” & Format(sequence,”000″)” and this only shows the year and date, so instead of 2015-08-001 it shows 2015-08-.
So, if you wanted to use this idea in a form or datasheet, let me stop and first remind you – if this is going to be non-updatable, you can just embed a report as a subreport within a form and thus use Running Sum. But let’s discuss the case where you need to be able to edit data in the forms, even with sequential numbering generated for the data you are viewing. This means we need to be able to tie a sequential number to a specific row.
Is there a way to code the special interrogatory numbers wherein the identify of documents is requested such that those specific special interrogatories (and only those specific special interrogatories) are automatically generated in a separate demand for production of documents? In other words if Special Interrogatory numbers 3, 6, 9, 12 request identification of documents, is there a way to code those special interrogatories so that within the demand for production of documents, those specific but individual special interrogatory numbers can be referenced?
But we won’t be stopping at just using a field code to increment the numbers. I’m also going to show you how to save the text (“Interrogatory No.” etc.) that precedes each number as an AutoText entry. That means you’ll be able to type just four letters and hit the Enter key (those are the “5 keystrokes” promised above) and Word will finish the phrase for you, complete with the sequence code to increment the discovery request number for you.
Hi, In the disaster recovery plan we want to create a leg site and put a DC in it. Here are some questions on how to achieve this smoothly. 1. Should I create the new site/subnet first and then promote a server in that subnet/site to DC, or should I promote a server in existing site/subnet and then move this DC to the new site/subnet? 2. When promoting a server to DC, should the server be a member server (already joined the domain) or just a workgroup member (no domain membership)? 3. The DC will be an AD-integrated DNS server. Should I install the DNS component (but not confi...
I need to add 4 "technical contact" fields (which would lookup the Contact entity) to the CONTRACT form. Is this possible? I've found it difficult to figure out what to do first. Thanks in advance, Brandon Not possible. You cant have multiple lookups for the same entity. You also cannot create new relationships between two system entitites. This will work in 4.0 Not possible, Pezman. N:M relationships are not possible in 3.0 yet. There is a alternative solution: a new entity to act as an N:M relationship. In your case, Contract/Contact. This entity has two 1:N relations...
Thank you for your reply. It reassured me that I was on the right path. From having read other Help texts, I guessed that I would have to use good ole mail-merge and set up a numbers list in Excel. Luckily my knowledge of Excel was good enough to know about the drag&drop for sequential immediate numbering. When it came to the crunch, it was this particular type of mail merge which gave me a bit of initial difficulty. Despite my having used it happily and often in Word, for labels in Publisher, it was - not surprisingly - different in certain respects; principally the crucial point of the Print stage, which necessitated finding the option Publications & Paper Settings, and selecting 2 specific parameters, namely (1) Multiple pages per sheet, (2) Single-sided printing (my default double printing had appeared). Once I'd sussed this, it was plain sailing. Thanks again.
Hi Jason! Hard to say when I’m not sure which part isn’t working for you. If the numbering isn’t continuing across separate frames, you need to make sure you’re using a list. If they are in the wrong order, remember it uses the paste/creation order to number them. If neither of those fix it, let me know what specific issue you’re having. Good luck!
I have screen shots of what I have in my db, where can I send it to you (it is in word format) so that you can take a look at it to see what I am doing wrong. I took a screen shot of what is listed for the button and I took a screen shot of the text box Job No. I don’t know how to bound anything other than put the code behind the button and putting the Job_No in the code as you stated. I understand what you are saying, but I thought if I put the text box name Job No in the code behind the button then it would be bound to my table with the Job No field. Heeeelllllppppp!!!! I am sorry that I can’t seem to grasp this….but appreciate all of your help!
Hi Jason! Hard to say when I’m not sure which part isn’t working for you. If the numbering isn’t continuing across separate frames, you need to make sure you’re using a list. If they are in the wrong order, remember it uses the paste/creation order to number them. If neither of those fix it, let me know what specific issue you’re having. Good luck!
I have now permanently “baked” the Inline Counter system into my InDesign defaults. With no documents open, I made a “Counter” CharStyle and a “Zero Footnote” ParStyle, with those crucial zero-level type size attributes, and selected them in the Document Footnote Options. I also added a blank space as a prefix and a period and a blank space as a suffix. Then I made a keyboard shortcut (Ctrl-Alt-F) for the Footnote/Counter. So now Inline Counters can be inserted anywhere and anytime with close to zero efforts.
Footnotes, after all, are always numbered sequentially and update when you add or remove one. The problem is that each time you add a footnote you get an extra space down at the bottom of the column. The solution? Make a paragraph style for your footnotes that specifies a .1 pt tall size with a 0 (zero) leading, then choose that paragraph style in the Document Footnote Options dialog box.
The process described in this tip works best if you have a single list in your document. Note that the sequence field starts at the beginning of the document and numbers through the whole document, based on the identifier you use. If you are going to have multiple lists in your document, then you can add a second AutoText entry to help with this. The only difference in the above steps is that the SEQ field you define would look like this:
I would like to number a voucher book, i have place 4 vouchers on a page, the thing is that i want each of these vouchers to start with different number, 100, 200, 300, 400, and then i want to number them 99 times. The problem is that they have to be numbered only 1 per page, so that when i have printed them all i can easily crop them and staple them right up with having to go through it all.
The SEQ or Sequential Numbering Function in Word is the best and quickest way to number your tickets. Many raffle ticket templates use them, yet few sites explain how it works. To see if it uses the SEQ function, you need to download the template first. Then, open it in Word, click right in the middle of where a serial number is, and then right-click.
A series is, informally speaking, the sum of the terms of a sequence. That is, it is an expression of the form {\displaystyle \sum _{n=1}^{\infty }a_{n}} or {\displaystyle a_{1}+a_{2}+\cdots } , where {\displaystyle (a_{n})} is a sequence of real or complex numbers. The partial sums of a series are the expressions resulting from replacing the infinity symbol with a finite number, i.e. the Nth partial sum of the series {\displaystyle \sum _{n=1}^{\infty }a_{n}} is the number
Ok I guess it is better for me to explain what I am doing. I am in the process of creating an Access Database that an individual has been using an Excel spreadsheet forever and a day. Well the individual has on occasion doubled up numbers, forgot numbers, etc. So on what I have learned from different Access courses and Google searches I am trying to apply my knowledge.
Layout your ticket in InDesign, one on each page, using the Page Number function to number the tickets. If you have something like Imposer Pro (I know it doesn't work from InDesign CS3) you can, for instance, impose the pages 4up consecutive and get 4 tickets on an A4. Alternatively, make a PDF of the whole document and impose (manually, if you have to), the advantage here is that this can work as a template for other tickets, simply make a new PDF of the same size and update the PDF in the template document every time you have a new raffle ticket to do.
## Design your ticket, use excel or libre's version and create the numbers. Save those numbers as text, I always make the first one xxx then 001 and so on, xxx will be the master page. Use data merge from Indesign to create the master ticket, you will need to make a text box for the number. Once it looks good to you draw a text box around the whole ticket. At the bottom of the data merge tab is a button that gives you the options how you want your layout, columns or rows, etc. even has a preview. once you click create it will create another file with all your tickets sequentially numbered. It'll be a couple of hours before I'm at work but can post the link I used to create these for the first couple of times.
I also use InDesign. An Excel file for numbering is easy to create. Then find DataMerge under Automate to link the data file. When you are ready to export, use the create PDF right on the Datamerge window. You can print as cut / stack on the Fiery (or CREO). REMEMBER - if your customer wants them stapled into books of 6 (for example) each stack has to be divisible by 6 if you are going to staple then cut into individual books.
I make the design with as many up as I need on the master page, linking the frames where the numbers will go. Then I make the list using Excel, copy paste to ID and apply a paragraph style with "start in next frame" option. Click the outbox on the pasted text to get a loaded cursor and delete the frame. Then just shift-click over the first textframe on a live page to have as many "tickets" added as needed automatically.
One option, of course, is to print the individual copies of the document, making the edits to the copy number between each print. This gets tedious, real fast. You may also want to utilize a sequential numbering field (as discussed in other WordTips) and make the number of copies equal to what you need to print. Thus, if you have to print 25 copies, you could simply copy the entire document (including the sequential numbering field), move to the end of the document, and paste it in another 24 times. This makes for a rather large overall document, however, and there are easier ways to approach the problem.
Both the Collection Point ID and Artifact ID fields are bound properly and display those exact names in the property sheet under both control source and name. On the save button I have on the form, when I click on the event tab and the on click option I have event procedure and I click the […] option to open up the code builder and this is what I currently have:
English Spanish Dictionary | English Italian Dictionary | English German Dictionary | English Portuguese Dictionary | English Russian Dictionary | Medical dictionary English French | Computer dictionary English French | Computer dictionary English Spanish | Business dictionary English French | English Arabic Dictionary | English Hebrew Dictionary | English Dutch Dictionary | English Polish Dictionary | 2019-02-22 20:05:13 | {"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": 0.33955660462379456, "perplexity": 1079.6150023379237}, "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/1550247526282.78/warc/CC-MAIN-20190222200334-20190222222334-00115.warc.gz"} |
https://jwbales.us/rpnOctonion.html | # The Octonion RPN Calculator
### Software © (2009) John Wayland Bales under the GNU General Public License
(a,b)×(c,d)=(ac-db*,a*d+cb)
e0
e1
e2
e3
e4
e5
e6
e7
♥♥♥
The Octonion multiplication table used for this calculator is explained here.
#### Calculator Description
This is a postfix calculator with a depth 2 stack. To compute R + S*T, for example: R [enter] S [enter] T [times] [plus]
There are ten storage/retrieval registers, X, Y, Z, A, B, C, D, E, F, G accessed by the dropdown icon.
There are various standard register operations, with [push] replaced with [enter].
Numbers may be entered into the main register by hand, or by using the random number generator.
#### Definition of basis elements
$$e_0=(1,0)=1$$
$$e_1=(0,1)=i$$
$$e_2=(e_1,0)=j$$
$$e_3=(0,e_1)=k$$
$$e_4=(e_2,0)$$
$$e_5=(0,e_2)$$
$$e_6=(e_3,0)$$
$$e_7=(0,e_3)$$
#### Multiplication Table
e0 e1 e2 e3 e4 e5 e6 e7 e1 –e0 e3 –e2 e5 –e4 e7 –e6 e2 –e3 –e0 e1 e6 –e7 –e4 e5 e3 e2 –e1 –e0 –e7 –e6 e5 e4 e4 –e5 –e6 e7 –e0 e1 e2 –e3 e5 e4 e7 e6 –e1 –e0 –e3 –e2 e6 –e7 e4 –e5 –e2 e3 –e0 e1 e7 e6 –e5 –e4 e3 e2 –e1 –e0
#### A worked example of use
To illustrate one of the Moufang identities, for example Z(X(ZY)) = ((ZX)Z)Y, perform the following operations:
1. Select random vectors X, Y and Z
1. RANDOM X STO
2. RANDOM Y STO
3. RANDOM Z STO
2. Perform the operations on the left side of the identity
1. Z RCL ENTER (Since Z should already be in the register, you don't actually have to recall it.)
2. Y RCL × ENTER
3. X RCL SWAP × ENTER
4. Z RCL SWAP ×
3. Store the result
1. A STO
4. Perform the operations on the right side of the identity
1. Z RCL ENTER
2. X RCL × ENTER
3. Z RCL × ENTER
4. Y RCL × ENTER
5. Subtract the result obtained on the left side of the identity. Result should be 0 (allowing for small errors).
1. A RCL –
John Wayland Bales, Department of Mathematics (Retired), Tuskegee University, Tuskegee, AL 36088 USA | 2022-05-27 05:36:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.290822297334671, "perplexity": 9044.134185990506}, "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-2022-21/segments/1652662636717.74/warc/CC-MAIN-20220527050925-20220527080925-00257.warc.gz"} |
http://logic.dorais.org/archives/827 | In a recent paper [1], Jared Corduan and I considered various notions of combinatorial indecomposability for finite ordinal powers of $\omega.$ In this process, we uncovered two weak forms of Ramsey’s theorem for pairs ($\newcommand{\RT}[2]{\mathsf{RT}^{#1}_{#2}}\RT2k$):
• The Weak Ramsey Theorem ($\newcommand{\Wk}{\mathsf{W}}\Wk\RT2k$). For every coloring $c:\N^2\to\set{0,\dots,k-1}$ there are a color $d \lt k$ and an infinite set $H$ such that $\set{y \in \N : c(x,y) = d}$ is infinite for every $x \in H.$
• The Hyper-Weak Ramsey Theorem ($\newcommand{\HWk}{\mathsf{HW}}\HWk\RT2k$). For every coloring $c:\N^2\to\set{0,\dots,k-1}$ there are a color $d \lt k$ and an increasing function $h:\N\to\N$ such that $\bigcup_{x=h(i-1)}^{h(i)-1} \set{y \in \N : c(x,y) = d}$ is infinite for every $i \in \N.$
The first is equivalent to what we called the game indecomposability of the ordinal $\omega^2,$ and the second is related to the lexicographic indecomposability of $\omega^2.$ You can find out more about these notions of indecomposability in our paper, what I want to write about here is the forcing technique that we used to show that $\HWk\RT22$ is $\Pi^1_1$-conservative over $\mathsf{RCA}_0$ with $\Sigma^0_2$-induction and to separate the two principles $\Wk\RT22$ and $\HWk\RT22.$ I’ve been calling the method envelope forcing since the basic idea is to force over a larger model that envelops the original one rather than forcing over the ground model itself. In the following, I will give a brief tour of this method, skipping all the gory details (that can be found in our paper).
It turns out that $\PP$ is relatively large in the poset $\PP_0$ of all finite increasing functions $p:\set{0,\dots,|p|-1}\to\N$ — which is just a variation of Cohen forcing for our base model $\MN.$ The following lemma (corresponding to Lemma 3.10 in [?]) shows that the generic $g$ for $\PP$ over $\MN’$ is also somewhat generic for $\PP_0$ over the original model $\MN,$ sufficiently generic that the extension $\MN[g]$ will satisfy $\RCA + \Ind{\Sigma^0_2}.$
Relative Largeness Lemma. Suppose $U \subseteq \PP_0$ is $\Sigma^0_1$-definable over $\MN.$ For every $p \in \PP,$ if for every $q \leq p,$ $q \in \PP,$ there is a $r \leq q$ (in $\PP_0$ but not necessarily in $\PP$) such that $r \in U,$ then for every $q \leq p,$ $q \in \PP,$ there is a $r \leq q$ such that $r \in U \cap \PP.$
In particular, if $U$ is dense below $p$ in $\PP_0$ then $U \cap \PP$ is dense below $p$ in $\PP.$ Therefore, $g$ is $\Sigma^0_1$-generic for $\PP_0$ over $\MN$:
For every $U \subseteq \PP_0$ which is $\Sigma^0_1$-definable in $\MN,$ there is a $p \subset g$ that either $p \in U,$ or $p$ has no extension in $U$ at all.
Note that $g$ is unlikely to be much more generic than that since no initial segment of $g$ lies in $\PP_0-\PP,$ which could be dense in $\PP_0$ for a suitable coloring $c.$ Nevertheless, $g$ just generic enough to ensure that $\MN[g]$ satisfies $\Ind{\Sigma^0_2}.$ More precisely, relative largeness ensures that $g$ is low over the ground model:
Lowness Lemma. Every $\Sigma^0_2$ formula with parameters in $\MN[g]$ is equivalent to a $\Sigma^0_1$ formula with parameters in $\MN'[g].$
The reason for this is that $\MN'[g]$ contains Skolem functions for $\Pi^0_2$ formulas with parameters in $\MN[g]$ (Proposition 3.13 of [?]). Once Skolemized, a $\Pi^0_2$ formula becomes $\Pi^0_1.$ Because $\MN'[g]$ satisfies $\Ind{\Sigma^0_1}$ and $\MN'[g]$ is an $\omega$-extension of $\MN[g],$ it follows that $\MN[g]$ satisfies $\Ind{\Sigma^0_2}.$ So now we can iterate this process externally, taking care of any coloring $c:\N^2\to\set{0,1}$ that appears along the way, to obtain a model of $\HWk\RT22.$
Is this envelope forcing technique useful for anything else? Yes! In fact, the method was inspired by Hirschfeldt and Shore, who used a similar technique in [3] for $\mathsf{SADS}$ and $\mathsf{SCAC}.$ (The main differences are that they use methods from computability theory and they mostly care about $\omega$-models, so they have no need for enveloping models.) Let’s see how to recast these two examples in terms of envelope forcing.
Recall that a (countable) linear ordering $L$ is stable if every element either has finitely many predecessors or has finitely many successors. Finite linear orderings are stable, and so are the infinite linear orderings $\omega+n,$ $n + \omega^*,$ and $\omega+\omega^*.$ The principle $\mathsf{SADS}$ says that these are the only stable linear orderings, which boils down to saying that every infinite stable linear ordering has an infinite ascending or descending sequence. This is not provable in $\RCA$ but it is $\Pi^1_1$ conservative over $\RCA + \Ind{\Sigma^0_2},$ as can be shown by an envelope forcing argument.
The forcing $\PP$ for the infinite stable linear ordering $L$ consists of all finite increasing sequences $p = \seq{p_0,\dots,p_{\ell-1}}$ of elements of $L$ such that $p_{\ell-1} = \max(p)$ has only finitely many predecessors in $L.$ Note that $\PP$ is $\Sigma^0_2$-definable over the ground model, so we are in a very similar situation to the above. Hirschfeldt and Shore observed that if $L$ has no infinite descending sequence, then $\PP$ is relatively large in the partial order $\PP_0$ of all finite increasing sequences of elements of $L.$ It then follows that an envelope generic for $\PP$ is necessarily low over the ground model and we can generically add an increasing sequence to $L$ without destroying $\Ind{\Sigma^0_2}.$
It turns out that $\HWk\RT22$ implies $\mathsf{SADS},$ but the relationship between $\HWk\RT22$ and $\mathsf{SCAC}$ is unknown. The methods that Hirschfeldt and Shore used for $\mathsf{SCAC}$ can also be recast in terms of envelope forcing. However, rather than doing that, I will present another application of envelope forcing that incidentally forces $\mathsf{SCAC}.$
• The Path Ramsey Theorem ($\newcommand{\Pth}{\mathsf{Path}}\Pth\RT2k$). For every coloring $c:\N^2\to\set{0,\dots,k-1}$ there are a color $d \lt k$ and an increasing function $h:\N\to\N$ such that $c(h(n),h(n+1)) = d$ for all $n$ (a $d$-homogeneous path).
As usual, the Stable Increasing Path Ramsey Theorem ($\newcommand{\St}{\mathsf{S}}\St\Pth\RT2k$) is the restriction of $\Pth\RT2k$ to stable colorings, i.e., colorings $c:\N^2\to\set{0,\dots,k-1}$ such that $\lim_{n\to\infty} c(m,n)$ exists for every $m.$
Note that $\St\Pth\RT22$ directly implies $\mathsf{SADS}.$ The following asymmetric strengthening of $\St\Pth\RT22$ directly implies $\mathsf{SCAC}:$
• The Stable Mixed Ramsey Theorem ($\newcommand{\Mix}{\mathsf{Mixed}}\St\Mix\RT22$). For every stable coloring $c:\N^2\to\set{0,1}$ either there is an infinite $0$-homogeneous set, or an infinite $1$-homogeneous path.
The technique of envelope forcing can be used to show that $\St\Mix\RT22$ is $\Pi^1_1$ conservative over $\RCA + \Ind{\Sigma^0_2}.$ The natural forcing $\PP$ to add a $1$-homogeneous path for a stable coloring $c:\N^2\to\set{0,1}$ consists of all finite $1$-homogeneous paths $p = \seq{p(0),\dots,p(|p|-1)}$ such that $\lim_{n\to\infty} c(p(|p|-1),n) = 1.$ Indeed, this $\Sigma^0_2$ condition on $p$ guarantees that the path can be continued further, provided that there are infinitely many $m$ such that $\lim_{n\to\infty} c(m,n) = 1.$ (If there are only finitely many such $m,$ it is easy to construct an infinite $0$-homogeneous set.) It turns out that if $c$ has no infinite $0$-homogeneous set in $\MN$ then $\PP$ is relatively large in the partial order $\PP_0$ of all finite $1$-homogeneous paths for $c.$
To see this, suppose $U \subseteq \PP_0$ is $\Sigma^0_1$-definable over the ground model $\MN.$ Suppose further $p \in \PP$ is such that for every $q \leq p,$ $q \in \PP,$ there is an $r \leq q$ (in $\PP_0$ but not necessarily in $\PP$) such that $r \in U.$ Finally, for the sake of contradiction, suppose that $q \leq p$ is an element of $\PP$ that has no extension in $U \cap \PP.$ Since $q \in \PP,$ there are infinitely many $n$ such that $q{{}^{\frown}}\seq{n} \in \PP$ too. So, by an effective search, we can find an infinite sequence $\seq{r_s}_{s=0}^\infty$ of extensions of $q$ in $U$ (in $\PP_0$ but not in $\PP$) such that the tips $m_s = r_s(|r_s|-1)$ enumerate an infinite set $M$ in increasing order. Since $q$ has no extension in $U \cap \PP,$ we must have that $\lim_{n\to\infty} c(m,n) = 0$ for every $m \in M.$ But then it is easy to recursively construct an infinite $0$-homogeneous subset of $M,$ which contradicts the fact that there are no such sets in $\MN.$
It follows that $\St\Mix\RT22$ is $\Pi^1_1$ conservative over $\RCA + \Ind{\Sigma^0_2},$ hence so are all of its consequences $\St\Pth\RT2k,$ $\mathsf{SADS},$ and $\mathsf{SCAC}.$ However, this does not separate any of these principles from $\Wk\RT22$ or even $\RT22.$ To do this, we need to recast the forcing arguments into the language of computability theory. The argument for $\HWk\RT22$ gives the following.
Theorem. If $c:\N^2\to\set{0,1}$ is a computable coloring, then one of the following is true:
• There is a computable increasing function $h:\N\to\N$ such that $\bigcup_{x=h(i-1)}^{h(i)-1} \set{y \in \N : c(x,y) = 0}$ is infinite for every $i \geq 1.$
• There is a $0’$-computable $1$-generic increasing function $g:\N\to\N$ such that $\bigcup_{x=g(i-1)}^{g(i)-1} \set{y \in \N : c(x,y) = 0}$ is cofinite for every $i \geq 1.$
It was shown by Downey, Hirschfeldt, Lempp and Solomon [2] that some computable instances of $\St\RT22$ have no low solutions. Since $\St\RT22$ follows from $\Wk\RT22,$ this shows that there is an instance of $\Wk\RT22$ that has no low solutions either. A ${0}’$-computable $1$-generic function is always low, so there is an $\omega$-model of $\HWk\RT22$ that contains only low sets. This $\omega$-model cannot be a model of $\Wk\RT22,$ which shows that $\HWk\RT22$ does not imply $\Wk\RT22.$
The argument for $\St\Mix\RT22$ gives the following.
Theorem. If $c:\N^2\to\set{0,1}$ is a stable computable coloring, then one of the following is true:
• There is a computable increasing function $h:\N\to\N$ such that $c(h(i),h(j)) = 0$ for all $i \lt j.$
• There is a ${0}’$-computable $1$-generic increasing function $g:\N\to\N$ such that $c(g(i),g(i+1)) = 1$ for all $i.$
So $\St\Mix\RT22$ does not imply $\St\RT22.$ Neither do any of its consequences, such as $\St\Pth\RT2k,$ $\mathsf{SADS}$ and $\mathsf{SCAC}.$
### References
1. J. R. Corduan, F. G. Dorais, On the indecomposability of $\omega^n$, Notre Dame J. Formal Logic 53 (2012), 373–395. [doi:10.1215/00294527-1716784, arχiv:1111.1367]
2. R. Downey, D. R. Hirschfeldt, S. Lempp, R. Solomon, A $\Delta^0_2$ set with no infinite low subset in either it or its complement, J. Symbolic Logic 66 (2001), 1371–1381. [doi:10.2307/2695113]
3. D. R. Hirschfeldt, R. A. Shore, Combinatorial principles weaker than Ramsey’s theorem for pairs, J. Symbolic Logic 72 (2007), 171–206. [doi:10.2178/jsl/1174668391]
## 2 thoughts on “Envelope forcing”
1. The statement of the Relative Largeness Lemma has been corrected after Paul Shafer kindly reported an error. | 2015-04-26 15:37:02 | {"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": 3, "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": 0.9075058102607727, "perplexity": 138.14329888148}, "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-2015-18/segments/1429246654687.23/warc/CC-MAIN-20150417045734-00182-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://answers.gazebosim.org/question/5468/gazebo_ros_pkgs-no-p-gain-specified-for-pid-in-positionjointinterface/ | # Gazebo_ros_pkgs: No p gain specified for pid in PositionJointInterface
I have built gazebo_ros_pkgs in the catkin workspace and working with some Joint Position Controllers (successfully - I can control my joint controllers via rqt or topics). The building part in the catkin workspace is needed for the new features to work in version 2.3.4 (see pull request #135).
However, my robot keeps sliding on the ground (slowly but sliding). Here's a video of that behavior. At first I thought it was because I hadn't included friction on my links. I did include friction but nothing changed. Also, at first I had collada models for collision, but changed them to stl. Same behavior though. I suspect visual-collision misalignment (exists in my case) problems in gazebo.
Gazebo throws some errors (not fatal ones though and continues). Here's an example:
[ERROR] [1392128262.341496657, 0.791000000]: No p gain specified for pid. Namespace: /nao_robot/gazebo_ros_control/pid_gains/RAnklePitch_Roll_Joint
I haven't created effort joint controllers as the robot I'm trying to simulate has servo motors. I am not sure if that is entirely correct. Maybe I need effort joint controllers.
Any ideas? Thanks..
edit retag close merge delete
Sort by » oldest newest most voted
What type of hardware interface did you specify in your URDF file? PositionJointInterface? EffortJointInterface? If you are using PositionJointInterface, try specifying PID controller gains in a file similar to this:
# gazebo_ros_control_params.yaml
gazebo_ros_control/pid_gains:
shoulder_joint: {p: 1.0, i: 0.0, d: 1.0}
# More joints...
In your launch file, load the PID gains in a manner similar to this:
<rosparam file="\$(find yourrobot_gazebo)/config/gazebo_ros_control_params.yaml" command="load"/>
Using PositionJointInterface without a PID controller works sometimes, but not always. In particular, friction does not work well without a PID controller. This problem is discussed in the comments for pull request #135, which you mentioned above.
more
Well, I tried it and it seems to tackle the problem. I haven't been able to find the pid values corresponding to the servo motors of the robot, but playing around with the pid values points to that direction in order to solve the problem. Thanks. I will post an answer when I've finally solved it for sure.
( 2014-02-11 16:58:36 -0500 )edit
@Jim Rothrock
The problem was solved using pid gains for Position Joint Controllers (Interfaces).
But I still believe that this should be fixed in a later version. When you specify a position joint controller, not having pid gains is exactly what you want (in some cases - in my case too, because I don't have access to the robot's motors specifications and the robot uses servo motors).
Anyway, thanks for the reply and I've finally solved my issue. :)
more | 2019-08-23 13:47:11 | {"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": 0.18323682248592377, "perplexity": 2659.436429056096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027318421.65/warc/CC-MAIN-20190823130046-20190823152046-00282.warc.gz"} |
https://socratic.org/questions/how-do-you-write-x-3-1-in-factored-form | How do you write x^3-1 in factored form?
Apr 16, 2018
${x}^{3} - 1 = \left(x - 1\right) \left({x}^{2} + x + 1\right)$
Explanation:
This is a type of factorising called the the sum or difference of two cubes:
${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$
The sum of cubes is factored as:
${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$
In this case we have: ${x}^{3} - 1$ so follow the rule above.
${x}^{3} - 1 = \left(x - 1\right) \left({x}^{2} + x + 1\right)$ | 2019-09-19 16:41:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8418092131614685, "perplexity": 1068.0320602129784}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573561.45/warc/CC-MAIN-20190919163337-20190919185337-00212.warc.gz"} |
https://learnmetrics.com/electric-furnace/ | # Best Electric Furnace Brands, Cost, Efficiency (+ Installation)
The best furnace is the kind you don’t have to think or worry about. That’s exactly why electric furnaces are so popular.
Convenience and safety are at the core of electric furnaces. Every home with access to electricity can safely install an electric heater for the winter season.
The inner working of electric forced-air furnaces is quite easy to understand. It is a simple 2-stage process, similar to a hairdryer:
1. Electricity heats up the heat exchanger (system of metal rods in the unit).
2. Air is pulled from the indoor air by a modular blower, pushed over the heat exchanger (where it heats up), and is distributed back into your home.
Basically, here is what an electric forced air furnace is in most simple terms:
Electric Furnace = Heat Exchanger + Modular Blower
You don’t have to worry about gas or carbon monoxide leakage (as is the case with gas furnaces). The initial cost of a new electric furnace ($800 to$2,700) is way lower as well. However, electricity is the most expensive heating power source.
That’s why it makes sense to look for reliable electric furnace brands; they produce durable high-efficiency units. To illustrate everything homeowners need to know about electric furnaces, we outlined:
1. The overall cost of every electric furnace. Encompasses the cost of the device + installation cost + electricity cost.
2. How we can find the high-efficiency electric furnaces.
3. A list of the best (and most reliable) electric furnace brands.
4. Installation costs (with recommended HVAC experts who can install an electric furnace).
In the end, you’ll find a summary table with the best electric furnaces (brands, and specific models) with costs and HVAC experts that can help you out further.
## Electric Furnace Cost (New Units)
When we start looking for an electric forced air furnace, we’re usually interested in the price of a new unit. However, we need to keep in mind that the initial price of the furnace represents the smallest of the 3 costs we need to account for when calculating the overall electric furnace cost. Here are the 3 costs:
Total Electric Furnace Cost = Unit Cost + Installation Cost + Electricity Cost
If we look at the average cost of an electric furnace unit alone, we are not doing a complete job. Here are some ranges for the most common 60,000 BTU and 80,000 BTU units (about 20 kW):
1. Unit cost: $700-$2,700.
2. Installation cost: $1,000-$4,200 (you can get free estimates from local furnace installers here).
3. Electricity cost: $1,500-$2,000 per season (720 hours of heating, or 4h over 6 months; the average price of a kilowatt-hour is $0.1319). In short, the average overall cost of a 20kW electric furnace is: •$1,700-$6,900 when we buy and install the unit. •$16,700-$26,900 after 10 years (addition of 10-year worth of electricity). •$31,700-$44,200 after 20 years (addition of 20-year worth of electricity). ### Energy-Efficiency Of Electric Furnaces As we have seen above, the bigger part of the overall electric furnace cost is electricity. In 20 years, a bigger 25 kW electric furnace can draw as much as$40,000 worth of electricity.
This possesses an important question: Are electric furnaces energy-efficient?
In fact, yes, they very much are. The high-efficiency electric furnace will use up to 99.9% of electricity for heating. We’re talking the AFUE rating of 100; for comparison, gas furnaces have an AFUE rating of 70 to 97.
AFUE rating of 100 for electric furnaces means that a furnace will use 100 cents of every 1$electricity for heating. That’s ideal, right? So why do we have a feeling that we’re paying quite a lot for heating when using an electric furnace? The reason is not the inefficiency of the electric furnace; it’s the price of electricity. Let’s have a look if it’s cheaper to heat your house with gas or electric furnace: • National average price of electricity:$0.1319 per kWh.
• National average price of natural gas (for residential use): $10.60 per 1000 cubic feet. How does that translate into heating costs? Here is how much electric and gas furnace use to produce 1,000,000 BTU worth of heat: • Electric Furnace (100% efficiency):$38.66 per 1,000,000 BTU.
#### Winchester Electric Furnaces
Winchester is another reputable company producing electric furnaces. They also have a 2-model portfolio, consisting of:
1. Winchester WE30B4D model. Unit capacities: 10 kW, 12 kW, 15 kW, 20 kW.
2. Winchester ME16CN21 model. Unit capacities: 10 kW, 12 kW, 15 kW, 20 kW.
### New Less-Known Brands
Having a long track-record is important for a brand; they can charge higher prices for electric furnaces. However, the new brands don’t have such a luxury.
That’s why they have charge lower prices in order to, primarily, sell their units, and secondarily, to build a lasting brand. These less-known units will last 15 to 20 years, according to Fixr, but the price reduction is substantial.
The new electric furnace brands include:
• Goodman (best of the new brands). Unit price (est.): $900. • Mortex. Unit price (est.):$830.
• Direct Comfort. Unit price (est.): $850. • Revolv (cheapest electric furnace brand). Unit price (est.):$700.
### Summary Of Electric Furnace Brands, Unit Costs And Installation Costs (Table)
Here is a quick summary of all the costs for specific electric furnace brands. The prices are for a 20 kW (68,200 BTU) units. For all the installation estimates and additional advice, you can contact HVAC experts here (that’s what we did, figures are summarized in the table).
Here is the complete table with estimated ballpark figures (installation costs, for example, depends on your current power grid and location):
Electric Furnace Brand20 kW Unit CostInstallation Costs
King$1,600$2,900
Winchester$1,500$2,740
York$1,300$2,563
Stelpro$1,100$2,468
Goodman$900$2,356
Mortex$830$2,323
Direct Compact$850$2,215
Revolv$700$2,104
If you have any questions about electric furnaces, you can use the comment section below. | 2020-09-27 20:58:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5316521525382996, "perplexity": 4359.217976428624}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1600401578485.67/warc/CC-MAIN-20200927183616-20200927213616-00794.warc.gz"} |
https://www.jobilize.com/online/course/2-4-reflection-and-transmission-of-mechanical-waves-by-openstax?qcr=www.quizover.com | # 2.4 Reflection and transmission of mechanical waves
Page 1 / 1
The reflection and transmission of mechanical waves is presented.
## Reflection and transmission
The first figure shows the 4 possible cases for reflection and transmission at an interface. Lets solve the problem, which is shown in the next figure
since ${\mu }_{1}\ne {\mu }_{2}$ it must be that v ${\phantom{\rule{veryverythinmathspace}{0ex}}}_{1}\ne$ v ${\phantom{\rule{veryverythinmathspace}{0ex}}}_{2}$ .
Note that we are assuming that Young's Modulus is constant across the boundary.
So we get ${y}_{inc}=A{\mathrm{cos}}\left({k}_{1}x-\omega t\right)$ ${y}_{ref}=B{\mathrm{cos}}\left({k}_{1}x+\omega t\right)$ ${y}_{trans}=C{\mathrm{cos}}\left({k}_{2}x-\omega t\right)$ (note the reflected wave goes the other direction).
On the left side of the junction we have $\begin{array}{c}{y}_{l}={y}_{inc}+{y}_{ref}\\ =A{\mathrm{cos}}\left({k}_{1}x-\omega t\right)+B{\mathrm{cos}}\left({k}_{1}x+\omega t\right)\end{array}$ and on the right side of the junction we have ${y}_{r}={y}_{trans}=C{\mathrm{cos}}\left({k}_{2}x-\omega t\right)\text{.}$ At the boundary $x=0$ the wave must continuous, that is there are no kinks in it. Thus we must have ${y}_{l}\left(0,t\right)={y}_{r}\left(0,t\right)$ ${\frac{\partial {y}_{l}\left(x,t\right)}{\partial x}|}_{x=0}={\frac{\partial {y}_{r}\left(x,t\right)}{\partial x}|}_{x=0}$
So from the first equation $A{\mathrm{cos}}\left(\omega t\right)+B{\mathrm{cos}}\left(\omega t\right)=C{\mathrm{cos}}\left(\omega t\right)$ $A+B=C$ ${\frac{\partial {y}_{l}\left(x,t\right)}{\partial x}|}_{x=0}={\frac{\partial {y}_{r}\left(x,t\right)}{\partial x}|}_{x=0}$ $-A{k}_{1}{\mathrm{sin}}\left(-\omega t\right)-{k}_{1}B{\mathrm{sin}}\left(\omega t\right)=-{k}_{2}C{\mathrm{sin}}\left(-\omega t\right)$ $\left(A-B\right){k}_{1}{\mathrm{sin}}\omega t=C{k}_{2}{\mathrm{sin}}\omega t$ $A-B=\frac{{k}_{2}}{{k}_{1}}C$ now solve for $B$ and $C$ $A+B=C$ $A-B=\frac{{k}_{2}}{{k}_{1}}C$ $2A=\left(1+\frac{{k}_{2}}{{k}_{1}}\right)C$ Thus we can define the transmission coefficient ${t}_{r}\equiv C/A=\frac{2{k}_{1}}{{k}_{1}+{k}_{2}}$ and the refection coefficient $r\equiv B/A=\frac{C}{A}-1=\frac{{k}_{1}-{k}_{2}}{{k}_{1}+{k}_{2}}$ note how the amplitudes can change at the boundary
If ${\mu }_{2}<{\mu }_{1}$ then we must have ${k}_{2}<{k}_{1}$ since ${\text{v}}=\omega /k=\sqrt{T/\mu }$ and $\omega$ and $T$ must be fixed. We see that $k\propto \sqrt{\mu }$ In this case we see that the amplitude of the wave gets bigger when it moves into a less dense medium. We have probably all experienced this in reallife. As waves come ashore they become bigger. This is because shallower water is effectively less dense. A tsumami in open ocean may have animperceptable amplitude but when it comes ashore it can be tremendous. This seems almost counter intuitive, but in any closed system the energy and powerare conserved but there is no rule saying amplitude has to be conserved.
Lets look at the reflected and transmitted power. Recall Power: $P=\frac{1}{2}\mu {\omega }^{2}{A}^{2}{\text{v}}$ For the incident and reflected waves $\mu$ and $\nu$ are the same so the reflected power coefficient (reflected power / incident power) ${P}_{R}={\left(B/A\right)}^{2}={\left(\frac{{k}_{1}-{k}_{2}}{{k}_{1}+{k}_{2}}\right)}^{2}$ To do transmitted power lets first rewrite the power equation. Recall $\begin{array}{c}{\text{v}}=\nu \lambda \\ =\frac{2\pi \nu }{k}\\ =\frac{\omega }{k}\end{array}$ Also ${\text{v}}=\sqrt{\frac{T}{\mu }}$ so $\begin{array}{c}\mu =\frac{T}{{{\text{v}}}^{2}}\\ =\frac{T}{{\left(\frac{\omega }{k}\right)}^{2}}\\ =\frac{T{k}^{2}}{{\omega }^{2}}\end{array}$ so now $P=\frac{1}{2}\mu {\omega }^{2}{A}^{2}{\text{v}}$ becomes $P=\frac{1}{2}\frac{T{k}^{2}}{{\omega }^{2}}{\omega }^{2}{A}^{2}\frac{\omega }{k}$ or $P=\frac{1}{2}Tk\omega {A}^{2}\text{.}$
Watch out, in the above lines A was used to denote amplitude in general and in the following line it specifically refers to the incoming wave.
The transmission power coefficient is thus: ${P}_{T}=\frac{\frac{1}{2}T{k}_{2}\omega {C}^{2}}{\frac{1}{2}T{k}_{1}\omega {A}^{2}}$ Note that $\omega$ and $T$ are the same for both waves ${P}_{T}=\frac{{k}_{2}{C}^{2}}{{k}_{1}{A}^{2}}$ earlier we showed $C/A=\frac{2{k}_{1}}{{k}_{1}+{k}_{2}}$ so ${P}_{T}={\left(\frac{2{k}_{1}}{{k}_{1}+{k}_{2}}\right)}^{2}\frac{{k}_{2}}{{k}_{1}}$ ${P}_{T}=\frac{4{k}_{1}{k}_{2}}{{\left({k}_{1}+{k}_{2}\right)}^{2}}$ Note that ${P}_{R}+{P}_{T}=1$ which means that energy is conserved.
Now lets look at the 4 specific cases we have:
Rigid wall
$\mu \to \infty$ so ${k}_{2}\to \infty$ $\begin{array}{c}r=\frac{{k}_{1}-{k}_{2}}{{k}_{1}+{k}_{2}}\\ =\frac{\frac{{k}_{1}}{{k}_{2}}-1}{\frac{{k}_{1}}{{k}_{2}}+1}\\ r\to -1\end{array}$ Also ${P}_{R}\to +1$ ${P}_{T}\to 0$ So wave is reflected and inverted, but has same power
Free end
$\mu \to 0$ so ${k}_{2}\to 0$ $\begin{array}{c}r=\frac{{k}_{1}-{k}_{2}}{{k}_{1}+{k}_{2}}\\ =\frac{{k}_{1}}{{k}_{1}}\\ r\to +1\end{array}$ Also ${P}_{R}\to +1$ ${P}_{T}\to 0$ So wave is reflected and has same power
Moving to higher density
${\mu }_{2}>{\mu }_{1}{k}_{2}>{k}_{1}$ so $r<0$ ${t}_{r}>0$
Moving to lower density
${\mu }_{2}<{\mu }_{1}{k}_{2}<{k}_{1}$ so $r>0$ ${t}_{r}>1$ Note the transmitted wave's amplitude is larger than the original.
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
Got questions? Join the online conversation and get instant answers! | 2019-12-07 07:28:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 64, "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": 0.691138505935669, "perplexity": 1268.9225633141687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00416.warc.gz"} |
https://collegephysicsanswers.com/openstax-solutions/disk-between-vertebrae-spine-subjected-shearing-force-600-n-find-its-shear | Question
A disk between vertebrae in the spine is subjected to a shearing force of 600 N. Find its shear deformation, taking it to have the shear modulus of $1\times 10^{9}\textrm{ N/m}^2$. The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.
$3 \textrm{ }\mu\textrm{m}$ | 2019-12-07 06:25:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7862181663513184, "perplexity": 890.3808395252935}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1575540496492.8/warc/CC-MAIN-20191207055244-20191207083244-00015.warc.gz"} |
https://stats.stackexchange.com/questions/340789/expected-minimum-distance-from-a-point-with-varying-density | # Expected minimum distance from a point with varying density
I'm looking at how the expected minimum Euclidean distance between randomly uniform points and the origin changes as we increase the density of random points (points per unit square) around the origin. I have managed to come up with a relationship between the two described as such:
$$\text{Expected Min Distance} =\frac{1}{2\sqrt{\text{Density}}}$$
I came up with this by running some Monte Carlo simulations in R and fitting a curve manually (code below).
My question is: could I have derived this result theoretically rather than through experimentation?
#Stack Overflow example
library(magrittr)
library(ggplot2)
#---------
#FUNCTIONS
#---------
#gen random points within a given radius and given density
#round radius up then generate points in square with side length = 2*radius
coords <- data.frame(
)
return(coords[sqrt(coords$x ^ 2 + coords$y ^ 2) <= radius, ])#filter in circle
}
#Example plot
plot(gen_circle_points(radius = 1,density = 200)) #200 points around origin
points(0,0, col="red",pch=19) #colour origin
#return euclidean distances of points generated by gen_circle_points()
calculate_distances <- function(circle_points) {
return(sqrt(circle_points$x ^ 2 + circle_points$y ^ 2))
}
#find the smallest distance from output of calculate_distances()
calculate_min_value <- function(distances) {
return(min(distances))
}
#Try a range of values
density_values <- c(1:100)
expected_min_from_density <- sapply(density_values, function(density) {
#simulate each density value 1000 times and take an average as estimate for
#expected minimum distance
sapply(1:1000, function(i) {
calculate_distances() %>%
calculate_min_value()
}) %>% mean()
})
results <- data.frame(density_values, expected_min_from_density)
#fit based off exploration
theoretical_fit <- data.frame(density = density_values,
fit = 1 / (sqrt(density_values) * 2))
#plot monte carlo (black) and fit (red dashed)
ggplot(results, aes(x = density_values, y = expected_min_from_density)) +
geom_line() +
geom_line(
data = theoretical_fit,
aes(x = density, y = fit),
color = "red",
linetype = 2
)
• The (asymptotic) direct dependence on the inverse root of density follows easily and immediately from considerations of the units of measurement, so the only question concerns why the multiple is $1/2.$ – whuber Apr 16 '18 at 13:34
• @whuber Yes I'd noticed the units lined up nicely and yes, the question becomes: where did the 2 come from? – Michael Bird Apr 16 '18 at 13:49
• The $2$ is the width of your square. – whuber Apr 16 '18 at 14:47
Consider the distance to the origin of $n$ independently distributed random variables $(X_i,Y_i)$ that have uniform distributions on the square $[-1,1]^2.$
Writing $R_i^2 = X_i^2+Y_i^2$ for the squared distance, Euclidean geometry shows us that
$$\Pr(R_i \le r \le 1) = \frac{1}{4} \pi\, r^2$$
while (with a little more work)
$$\Pr(1 \le R_i \le r \le \sqrt{2}) = \frac{1}{4}\left(\pi\, r^2 + 4\sqrt{r^2-1} - 4 r^2 \operatorname{ArcTan}\left(\sqrt{r^2-1}\right)\right).$$
Together these determine the distribution function $F$ common to all the $R_i.$
Because the $n$ points are independent, so are the distances $R_i,$ whence the survival function of $\min(R_i)$ is
$$S_n(r) = (1 - F(r))^n,$$
implying the mean shortest distance is
$$\mu(n) = \int_0^\sqrt{2} S_n(r)\, dr.$$
For $n\gg 1,$ almost all the area in this integral is close to $0,$ so we may approximate it as
$$\mu_\text{approx}(n) = \int_0^1S_n(r)\, dr = \int_0^1\left(1 - \frac{\pi}{4}r^2\right)^n\,dr.$$
The error is not greater than the part of the integral that was omitted, which is in turn no greater than
$$(\sqrt{2}-1)(1-F(1))^n = (\sqrt{2}-1)(1 - \pi/4)^n,$$
which obviously decreases exponentially with $n.$
We may in turn approximate the integrand as
$$\left(1 - \frac{\pi}{4}r^2\right)^n \approx \exp\left(-\frac{1}{2} \frac{r^2}{2/(n\pi)}\right).$$
Up to a normalizing constant, this is the density function of a Normal distribution with mean $0$ and variance $\sigma^2=2/(n\pi).$ The missing normalizing constant is
$$C(n) = \frac{1}{\sqrt{2\pi \sigma^2}} = \frac{1}{\sqrt{2\pi\ 2 / (n\pi)}} = \frac{\sqrt{n}}{2}.$$
Therefore, extending the integral from $1$ to $\infty$ (which adds an error proportional to $e^{-n}$),
$$\mu_\text{approx}(n) \approx \int_0^\infty e^{-t^2/(2\sigma^2)}\,dt = \frac{1}{C(n)} \frac{1}{2} = \frac{1}{\sqrt{n}}.$$
In the process of obtaining this approximation three errors were made. Collectively they are at most of order $n^{-1},$ the error incurred when approximating $S_n(r)$ by the Gaussian.
This figure plots $n$ times the difference between $1$ and $\sqrt{n}$ times the mean shortest distance observed in $10^5$ separate simulated datasets for each $n.$ Because they decrease as $n$ grows, this is evidence that the error is $o(n^{-1}/\sqrt{n}) = o(n^{-3/2}).$
Finally, the factor $1/2$ in the question derives from the size of the square: the density is the number of points $n,$ per unit area and the square $[-1,1]^2$ has area $4$, whence
$$2\sqrt{\text{Density}} = 2\sqrt{n/4} = \sqrt{n}.$$
This is the R code for the simulation:
n.sim <- 1e5 # Size of each simulation
d <- 2 # Dimension
n <- 2^(1:11) # Numbers of points in each simulation
#
# Estimate mean distance to the origin for each n.
#
y <- sapply(n, function(n.points) {
x <- array(runif(d*n.points*n.sim, -1, 1), c(d, n.points, n.sim))
mean(sqrt(apply(colSums(x^2), 2, min)))
})
#
# Plot the errors (normalized) against n.
#
library(ggplot2)
ggplot(data.frame(Log2.n = 1:length(n), Error=sqrt(n)* (1 - y * n^(1/d))),
aes(Log2.n, Error)) + geom_point() + geom_smooth()
ylab("Error * n") + ggtitle("Simulation Means")
• Wow! What an answer! Thanks a lot, this is great. Thanks! – Michael Bird Apr 16 '18 at 15:50
• Hi @whuber, I was trying to reproduce your $F(r)$ and I noticed your equation for $F(\sqrt{2})$ doesn't return $1$ like your graphs shows. When I calculated $\text{Pr}(1 \leq R_i \leq r \leq \sqrt{2})$ I got $\pi/4 - r (r \text{ArcCos}(1/r) - \sqrt{1-1/r^2})$ which gives the curve you provided. Have you made a typo? – Michael Bird May 2 '18 at 15:03
• @Michael Thank you, there is a typo--but it's not the one you suggest: one of my "$r$" should have been "$4$." I have fixed that one. – whuber May 2 '18 at 16:58 | 2019-10-21 23:31:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.7768551707267761, "perplexity": 1149.7034755674033}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570987795253.70/warc/CC-MAIN-20191021221245-20191022004745-00552.warc.gz"} |
http://mathhelpforum.com/math-software/148470-how-make-generic-filenames-work-matlab.html | # Thread: How to make generic filenames work in matlab?
1. ## How to make generic filenames work in matlab?
I've got a 1x1cell named selected_name that contains different names depending on how the function is run. So when I type selected_name in the command line it returns "selected_name = 'Peter'" for example.
What I want to do is to save the variables used in the workspace to a file named "Peter.mat". I can't get it to work. save(selected_name) does not work because it says it needs to be a string like save('somename').
How do I solve this?
2. try:
Code:
save(selected_name(1)) | 2017-01-16 18:09:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24036169052124023, "perplexity": 1624.7018268145623}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560279224.13/warc/CC-MAIN-20170116095119-00456-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://questions.examside.com/past-years/jee/question/let-s-s1-cap-s2-cap-s3-where-s1-left-z-in-cleft-z-right-4-ri-jee-advanced-2013-marks-4-bpcmteib2inxf1mo.htm | NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1
### JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
Let $$S = {S_1} \cap {S_2} \cap {S_3}$$, where $${S_1} = \left\{ {z \in C:\left| z \right| < 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im}\nolimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] > 0} \right\}$$ and $${S_3} = \left\{ {z \in C:{\mathop{\rm Re}\nolimits} z > 0} \right\}\,$$.
$$\,\mathop {\min }\limits_{z \in S} \left| {1 - 3i - z} \right| =$$
A
$${{2 - \sqrt 3 } \over 2}$$
B
$${{2 + \sqrt 3 } \over 2}$$
C
$${{3 - \sqrt 3 } \over 2}$$
D
$${{3 + \sqrt 3 } \over 2}$$
2
### JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
Let $$S = {S_1} \cap {S_2} \cap {S_3}$$, where $${S_1} = \left\{ {z \in C:\left| z \right| < 4} \right\},{S_2} = \left\{ {z \in C:{\mathop{\rm Im}\nolimits} \left[ {{{z - 1 + \sqrt 3 i} \over {1 - \sqrt 3 i}}} \right] > 0} \right\}$$ and $${S_3} = \left\{ {z \in C:{\mathop{\rm Re}\nolimits} z > 0} \right\}\,$$.
Area of S =
A
$${{10\pi } \over 3}$$
B
$${{20\pi } \over 3}$$
C
$${{16\pi } \over 3}$$
D
$${{32\pi } \over 3}$$
3
### JEE Advanced 2013 Paper 1 Offline
MCQ (Single Correct Answer)
Let complex numbers $$\alpha \,and\,{1 \over {\overline \alpha }}\,$$ lie on circles $${\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = {r^2}$$ and $$\,{\left( {x - {x_0}} \right)^2} + \,\,{\left( {y - {y_0}} \right)^2} = 4{r^2}$$ respextively. If $${z_0} = {x_0} + i{y_0}$$ satisfies the equation $$2{\left| {{z_0}} \right|^2}\, = {r^2} + 2,\,then\,\left| a \right| =$$
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over 2}\,$$
C
$${1 \over {\sqrt 7 }}$$
D
$${1 \over 3}$$
4
### IIT-JEE 2012 Paper 1 Offline
MCQ (Single Correct Answer)
Let z be a complex number such that the imaginary part of z is non-zero and $$a\, = \,{z^2} + \,z\, + 1$$ is real. Then a cannot take the value
A
- 1
B
$${1 \over 3}$$
C
$${1 \over 2}$$
D
$${3 \over 4}$$
### Joint Entrance Examination
JEE Main JEE Advanced WB JEE
### Graduate Aptitude Test in Engineering
GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN
NEET
Class 12 | 2022-05-29 01:35:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9589776992797852, "perplexity": 5216.80486193468}, "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-2022-21/segments/1652663035797.93/warc/CC-MAIN-20220529011010-20220529041010-00291.warc.gz"} |
https://codegolf.stackexchange.com/questions/117423/backwards-and-forwards-polyglot-quine?noredirect=1 | # Backwards and forwards polyglot quine!
You must make a polyglot that outputs its source code in one language and its source code backward in another. Unlike the normal rules, you are allowed to read the current file or use a builtin to get the source code of your submission and reverse that in one language. Your source code cannot be a palindrome.
For example, if your source code is abcxyz, it must output abcxyz in one language and zyxcba in another. If your code is abcxyzyxbca, it's invalid because it's a palindrome.
Good luck!
• Normal rules are there for a reason. Allowing quine built-ins will likely make this challenge too broad, and allowing palindrome source codes allows answers which are forward quines for both languages. – Erik the Outgolfer Apr 24 '17 at 11:43
• @EriktheOutgolfer palindromes are now not allowed. – programmer5000 Apr 24 '17 at 11:44
• @EriktheOutgolfer Ah, so the source code cannot be a palindrome? – Luis Mendo Apr 24 '17 at 11:52
• I think you should offer a bounty for the first person to complete this challenge without breaking any of the normal quine rules. (maybe 50 rep?) – Qwerp-Derp Apr 24 '17 at 12:13
• I read "in one language" as clearly disallowing the case where both languages read the source code, but the current top-voted answer does exactly that. Can you edit to make it clear whether that's meant to be allowed? – hvd Apr 24 '17 at 21:44
## PHP & GolfScript, 2 bytes
1
i.e. a newline and the digit 1.
This is a reverse quine in GolfScript, contributed on this site by Justin. PHP hasn't triggered that it's a programming language so it prints its input.
# Python 2 / Python 3, 71 bytes
lambda _='lambda _=%r:(_%%_)[::int(1-(1/2)*4)]':(_%_)[::int(1-(1/2)*4)]
Does not use any quine builtins.
Thanks to ovs for generally awakening me.
• lambda _='lambda _=%r:(_%%_)[::int(1-(1/2)*4)]':(_%_)[::int(1-(1/2)*4)] for 71 bytes – ovs Apr 24 '17 at 12:48
• @ovs Oh of course, how I didn't think of that. – Erik the Outgolfer Apr 24 '17 at 12:49
## Batch / bash + tac, 39 bytes
:;tac -r -s '.\|'$'\n'$0;exit
@type %0
Outputs forwards in Batch. Explanation: Batch sees the first line as a label and ignores it, while the second line simply copies the source file to STDOUT. (Note that you need to invoke the file including extension, or change %0 to %~f0.) bash sees four commands:
• : does nothing (same as true)
• tac -r -s '.\|'$'\n'$0
• -r puts tac into regex mode
• -s specifies a regex
• '.\|'$'\n' is the regex, composed of • . any character except newline • \| or • $'\n' a newline
• The upshot is that tac splits the file into characters rather than lines.
• exit stops the script, ignoring the fourth command
• @type %0 (ignored)
• I think that you can replace the first line with :;rev $0|tac;exit. Also, the header should say Batch / sh + util-linux + coreutils instead. – Erik the Outgolfer Apr 24 '17 at 12:01 • @EriktheOutgolfer $'\n' is a Bashism, rev $0|tac doesn't reverse newlines correctly, and does it really matter that tac comes in a package? – Neil Apr 24 '17 at 12:23 • $'\n' doesn't exist in the replacement I've suggested, and rev $0|tac works for me. And I think it's better to specify the packages instead of the individual utilities, because sometimes confusion might arise (e.g. which package's tac?). – Erik the Outgolfer Apr 24 '17 at 12:29 • @EriktheOutgolfer Try it online! is wrong. So is Try it online! (but more subtly). – Neil Apr 24 '17 at 12:31 • Could you please give an explanation? – programmer5000 Apr 24 '17 at 12:34 # PHP & Retina, 2 bytes 1 The same as Gille's PHP & GolfScript answer. PHP just reads the code and outputs it directly, Retina will replace matches of an empty string in the input and replace it with 1, and output that with a newline. # JS (ES5), JS (ES6), 94 bytes function f(){try{eval("x=(f+'f()').split.reverse().join")}catch(e){x=f+"f()"};return x}f() Does not use any quine built-ins. Just uses the fact that JS functions stringify to their code. Probably can be golfed more. If you allow reading the source code, it isn't really a quine. ## PHP & sh+util-linux, 6 bytes rev$0
I'm sure that the usual golfing languages can do it in 2 bytes.
• They infact can. – ATaco Apr 26 '17 at 0:16 | 2019-08-19 01:18:24 | {"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": 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": 0.18727998435497284, "perplexity": 4173.202321413512}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1566027314638.49/warc/CC-MAIN-20190819011034-20190819033034-00286.warc.gz"} |
http://mathhelpforum.com/calculus/59314-lhospital-print.html | L'Hospital for this?
• November 12th 2008, 11:12 PM
tabularasa
L'Hospital for this?
Very basic question. Van I user L-Hosptial rule there:
(sorry about lack of latex here)
when lim x->0 the f(x) 5x^2 / 3x reaches to?
• November 12th 2008, 11:13 PM
Moo
Quote:
Originally Posted by tabularasa
Very basic question. Van I user L-Hosptial rule there:
(sorry about lack of latex here)
when lim x->0 the f(x) 5x^2 / 3x reaches to?
Hmmm just simplify :
$x^2=x*x$
$\implies \frac{5x^2}{3x}=\frac{5 x*x}{3x}=\frac{5x}{3}$
I'm sorry to say, but you'll have to drop this habit of always relying on l'Hospital's rule (Surprised)
• November 12th 2008, 11:14 PM
11rdc11
Quote:
Originally Posted by tabularasa
Very basic question. Van I user L-Hosptial rule there:
(sorry about lack of latex here)
when lim x->0 the f(x) 5x^2 / 3x reaches to?
Yes
• November 12th 2008, 11:15 PM
tabularasa
Could you give me example for this equation since I try to use L'Hospital I just get:
using L'H:
f'(x) / g'(x) = 10x/3
and L'H again I get:
10/?
• November 12th 2008, 11:16 PM
11rdc11
Quote:
Originally Posted by tabularasa
Sorry about typo. So I want to use L'Hospital rule in equation above. Is L'Hospital eligible here?
Yes
• November 12th 2008, 11:20 PM
tabularasa
Quote:
Originally Posted by Moo
Hmmm just simplify :
$x^2=x*x$
$\implies \frac{5x^2}{3x}=\frac{5 x*x}{3x}=\frac{5x}{3}$
I'm sorry to say, but you'll have to drop this habit of always relying on l'Hospital's rule (Surprised)
Heh, so I cant use L'Hospital here? One say Yes and you show me that no it is not usable in this?
EDIT: Ah, I see, the equation is not in a form where L'Hospital rule works with. Not in 0/0 or infinity/infinity form since 5x^2/3x = 5x/3
Thanks!
• November 12th 2008, 11:23 PM
Moo
Quote:
Originally Posted by tabularasa
Heh, so I cant use L'Hospital here? One say Yes and you show me that no it is not usable in this?
You can use it ! Because both numerator and denominator go to 0..
But it's not the most suitable method here. If you're not specifically asked to use l'Hospital's rule in this case, then don't. Simplify first.
Your first question "Can I use" is ambiguous ^^'
• November 12th 2008, 11:25 PM
11rdc11
Quote:
Originally Posted by tabularasa
Heh, so I cant use L'Hospital here? One say Yes and you show me that no it is not usable in this?
Both ways are correct, notice you get the same answer.
• November 12th 2008, 11:45 PM
tabularasa
Ok, could you help me on this.
After use L'H once for 5x^2/3x I will get: 10x/3
What next?
• November 13th 2008, 12:05 AM
mr fantastic
Quote:
Originally Posted by tabularasa
Ok, could you help me on this.
After use L'H once for 5x^2/3x I will get: 10x/3
What next?
Now take the limit x --> 0 (!)
• November 13th 2008, 12:29 AM
tabularasa
Aargh! It was too obvious. 0/3
Thanks you guys! (Bow) | 2015-03-29 10:27:21 | {"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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9321187734603882, "perplexity": 4296.676347392603}, "config": {"markdown_headings": false, "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-2015-14/segments/1427131298424.66/warc/CC-MAIN-20150323172138-00214-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-common-core/chapter-1-expressions-equations-and-inequalities-1-2-properties-of-real-numbers-practice-and-problem-solving-exercises-page-15/12 | ## Algebra 2 Common Core
$\pi$ is irrational and anything multiplied by an irrational number is irrational. | 2018-06-25 04:40:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6482139229774475, "perplexity": 1050.6109828152717}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867424.77/warc/CC-MAIN-20180625033646-20180625053646-00155.warc.gz"} |
http://math.stackexchange.com/questions/175390/complicated-triple-integral | # Complicated triple integral
I have a Euclidean geometric problem whereby the triple integral over SO(3) I am trying to solve seems to confuse many CAS softwares (including Maxima and Mathematica). The problem is
$$a = \int^{\sigma_{max}}_{-\sigma_{max}} \int^\pi_{-\pi} \int^{\theta_{max}}_0 \frac{\sin\theta d\theta d\phi }{|x+R(\theta,\phi,\sigma)y|^3} (x+R(\theta,\phi,\sigma)y) \cdot Q \cdot (x+R(\theta,\phi,\sigma)y) d\sigma,$$
where $a$ is a real number, $x$ and $y$ are 3D, rank-1 vectors, $R$ is a 3D rotation matrix which rotates the vector $y$, {$\theta$, $\phi$, $\sigma$} is a set of $SO(3)$ rotational parameters, and Q is a 3D, rank-2 traceless, symmetric tensor. The rotation matrix $R(\theta, \phi, \sigma)$ elements in this case would be
$$\begin{array}{rcl} R[0, 0] &=& \hphantom{-}\cos\phi\cos\theta\cos(\sigma-\phi) - \sin\phi\sin(\sigma-\phi), \\ R[0, 1] &=& -\cos\phi\cos\theta\sin(\sigma-\phi) - \sin\phi\cos(\sigma-\phi), \\ R[0, 2] &=& \hphantom{-}\cos\phi\sin\theta, \\ R[1, 0] &=& \hphantom{-}\sin\phi\cos\theta\cos(\sigma-\phi) + \cos\phi\sin(\sigma-\phi), \\ R[1, 1] &=& -\sin\phi\cos\theta\sin(\sigma-\phi) + \cos\phi\cos(\sigma-\phi), \\ R[1, 2] &=& \hphantom{-}\sin\phi\sin\theta, \\ R[2, 0] &=& -\sin\theta\cos(\sigma-\phi), \\ R[2, 1] &=& \hphantom{-}\sin\theta \sin(\sigma-\phi), \\ R[2, 2] &=& \hphantom{-}\cos\theta. \end{array}$$
In some cases $\theta_{max}$ is also a function of $\phi$, e.g.
$$\frac{1}{\theta_{max}^2} = \frac{\cos^2\phi}{\theta_x^2} + \frac{\sin^2\phi}{\theta_y^2}$$
Would anyone have any advice as to how I should approach such a problem? Is such a triple integral solvable without reverting to numerical integration?
-
(1) Are you asking to evaluate $a$? (2) Can you describe what $R$ and $Q$ are in more detail? – Willie Wong Jul 26 '12 at 10:58
For (1) the question is what is the symbolic value of a? The numerical value of a is not being sought. For (2), R is a standard 3D Euclidean rotation matrix (3D, rank-2, no using Euler angles en.wikipedia.org/wiki/Rotation_matrix) and Q is a 3x3 matrix expression of a tensor (also 3D, rank-2, en.wikipedia.org/wiki/Tensor). Cheers. – bugman Jul 26 '12 at 13:31
Let me ask again to be clear: (1) By symbolic value do you mean in terms of $x,y,Q, \theta_{\text{max}}, \sigma_{\text{max}}$? (2) Please edit your question to give explicitly what the entries of the matrix $R(\theta,\phi,\sigma)$ are. There are many ways to give local coordinates to $SO(3)$. For all I know your $R(\theta,\phi,\sigma)$ could be just be a fixed constant matrix! – Willie Wong Jul 26 '12 at 13:58
Sorry (1), yes, in terms of $x$, $y$, $Q$, $\theta_{max}$, $\sigma_{max}$. (2) The rotation matrix $R(\theta, \phi, \sigma)$ in this case would be $$\left| \begin{array}{ccc} \cos\phi\cos\theta\cos(\sigma-\phi) - \sin\phi\sin(\sigma-\phi) & -\cos\phi\cos\theta\sin(\sigma-\phi) - \sin\phi\cos(\sigma-\phi) & \cos\phi\sin\theta \\ \sin\phi\cos\theta\cos(\sigma-\phi) + \cos\phi\sin(\sigma-\phi) & -\sin\phi\cos\theta\sin(\sigma-\phi) + \cos\phi\cos(\sigma-\phi) & \sin\phi\sin\theta \\ -\sin\theta\cos(\sigma-\phi) & \sin\theta \sin(\sigma-\phi) & \cos\theta \end{array} \right|$$ – bugman Jul 26 '12 at 14:16 | 2016-07-27 10:01:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.845602810382843, "perplexity": 304.7091430030079}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257826759.85/warc/CC-MAIN-20160723071026-00098-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://competitive-exam.in/questions/discuss/he-is-snobbish-i-like-him | Direction.
Combine the following sentences using an appropriate conjunction from the given options. | 2022-07-05 04:25:33 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8426854610443115, "perplexity": 2097.887098306069}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656104512702.80/warc/CC-MAIN-20220705022909-20220705052909-00016.warc.gz"} |
https://community.esri.com/thread/101940 | # Python + GME (Spatial Ecology) + Subprocess.call
Discussion created by Blue217 on Sep 4, 2013
Latest reply on Sep 13, 2013 by amontgomery3030
I am attempting to run GME functions using python using "subprocess.call". But every time I receive a Windows error message (see attached image). Apparently the log file cannot be found (incorrect path). I was wondering if this is because of the double forward slash (see red circle in attached image). Is this really the cause of the error? If yes, then how can this be fixed?
I will post the code I am using:
import subprocess as subp
subp.call(r'C:\Program Files\SpatialEcology\GME\SEGME.exe -c run(in=\"H:\GME\testing\text_commands\exportcsv.txt\");')
The text file contains the following:
export.csv(in="H:\GME\testing\data\test4csv.shp", out="H:\GME\testing\text_commands\output\exportcsv.csv"); | 2019-07-22 23:04:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.5042724013328552, "perplexity": 3064.5093150231187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195528290.72/warc/CC-MAIN-20190722221756-20190723003756-00102.warc.gz"} |
https://www.tyma.eu/technical-information/faq/what-is-the-maximum-circumferential-speed-of-belts/ | CZK | EUR
česky CS | english EN
belts and
transmission systems
# What Is the Maximum Circumferential Speed of Belts?
Increasing machine efficiency requires an increase to rotational speed. The main criterion, for any given belt type or chain used, is circumferential speed.
Assessing only rotational speed is not enough.
For rotational speed alone, the diameter of the wheel or pulley (which will carry out such performance) must be always taken into account.
Circumferential speed is calculated according to this formula:
$v = {\pi \cdot d \cdot n}\ [\rm{m \cdot s^{-1}}]$ where $$d$$ is the diameter of the shaft (wheel or pulley) in mm, $$n$$ is the rotational speed ($$\rm{ot. \over s} = \rm{ot. \over min.} \cdot {1 \over 60}$$).
This formula shows that, for example, if we have a hand plane with a rotational speed of 20,000 rpm/min and a small diameter pulley of 20 mm, the resulting circumferential speed is 10.47 m/s. Conversely, a compressor with a rotational speed of 3,000 rpm/min and a pulley with a diameter of 530 mm results in a circumferential speed of 41.64 m/s!
It is necessary to adjust the force, as listed in the chart, by pressing the middle of the belt span to check belt deflection force. If deflection is too large, it is imperative that the belt tension be tightened; if it is too small, loosening belt tension will decrease the belt deflection force. This measurement, however, is only a test and does not give an accurate result. Still, this is much better than no estimated measurement at all. See device user guides and their descriptions.
## Belt Use According to Maximum Circumferential Speed
1. Sheathed belts are suitable for speeds only up to 35 m/s.
2. Raw-edged V-belts with inner cogs XPZ, XPA, XPB, XPC and ZX, AX, BX, and CX can handle speeds of up to 50 m/s. There exists applications where these belts can operate at speeds over 50 m/s, e.g. blowers at 60 m/s. It is, however, necessary to make accurate calculations, perform testing, and provide sufficient balance (the latter particularly applies to drives that use VTP, a special pulley made of ductile cast iron).
3. Ribbed belts can operate with a max. speed of up to 60 m/s. These belts can successfully replace V-belts in cases of high-speed drive applications.
4. Timing belts are designed for max. speed according to profile size, 40-50 m/s. CONTI SYNCHROFORCE CXP and Extreme are special types, and can work up to 60 m/s. For timing belts, during high rotational speeds, it is necessary to monitor noise level. Belt profiles STD or CTD are designed for the highest speeds.
5. CXA special timing belts are intended for low-speed transmissions. The design and material of these belts are limited to a circumferential speed, max. 25 m/s. These belts are designed for other types of high-speed drives.
6. Flat belts can be used according to belt type for max. speeds of 80-100 m/s. The disadvantage, however, is lower transmitted power, greater width, and the need for higher tension force.
7. For comparison, chain drives may be used depending on the size and type of chain, for max. speeds of about 20 m/s. It is important to ensure proper lubrication and to comply with all the design requirements of chain manufacturers.
## Balancing of the Pulleys for High Speed Applications
The higher the circumferential speed, the greater the requirements for pulley design - even the overall equipment. It is necessary to balance the pulley at a precise balance quality grade, e.g. Q 4 – Q 2.5.
## Choice of Pulley Material and Construction
It is also necessary to choose a suitable material, e.g. steel or cast steel, rather than cast iron (which is not suitable for V- and timing belts at speeds above 45 m/s and 35 m/s, respectively). The structure also produces greater centrifugal force; therefore it is important to select a more sturdy construction.
## How to Reduce the Drive’s Operating Circumferential Speed?
As demonstrated in the formula, the rate of speed is decisively influenced by circumferential speed and pulley diameter.
1. When using V-belts, choose new and modern types rather than classic. V-belts with inner cogs have greater flexibility, require less of a min. pulley diameter, and are capable of higher power transmission. Equally, drives can get by with fewer belts or even significantly smaller pulley diameters.
2. Replace V-belts by ribbed belts, which have smaller pulley diameter, greater flexibility, and can transmit higher circumferential speeds.
3. In the application of timing belts, use higher performance types, such as CXP, which transmit greater power and speed. It then becomes possible to use smaller pulley diameters and reduce the overall size of the drive. | 2021-10-20 00:33:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5885324478149414, "perplexity": 2400.229852731833}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1634323585290.83/warc/CC-MAIN-20211019233130-20211020023130-00103.warc.gz"} |
https://questions.llc/questions/2907/question-1-we-would-like-to-test-3-different-treatments-on-a-particu-lar-type-of-plant | # Question 1 : We would like to test 3 different treatments on a particu-
lar type of plant. A worker at the local greenhouse will allow us to use 3
among 10 plants. Note: Each treatment will be used on one and only one
plant.
a) In how many different ways can we assign the plants to the treatments?
b) Suppose that 2 of the ten plants are older than the other 8 plants. Assuming that we are choosing the plants randomly, what is the probability that at least one of the two older plants will be chosen among the three selected
plants?
There are 10C3 10 choose 3 ways to select a plant, and 3 solutions we could use on a plant. You should be able to calculate this.
The easier way to calculate b) is to observe that there are
8C3 ways to select only younger plants out of 10C3 total ways to select plants. Thus the prob of only younger plants is
(8C3)/(10C3) and the prob that at least on plant is an older one is
1 - (8C3)/(10C3)
1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩 | 2022-10-02 13:15:32 | {"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": 0.812923014163971, "perplexity": 860.1696317777108}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1664030337322.29/warc/CC-MAIN-20221002115028-20221002145028-00340.warc.gz"} |
http://igop.valledelchieseonline.it/chemical-equation-for-cellular-respiration.html | Chemical Equation For Cellular Respiration
" Closing Question: "How did this activity show us that the chemical reaction rearranges the atoms to make new products?". Essentially, the two equations are the exact opposite of one another. Powering The Cell Cellular Respiration And Glycolysis. The process of making chemicals into chemical energy. Fill a 250. Cellular respiration: food molecules are broken down to release the energy in their chemical bonds. Cellular respiration is what cells do to break up sugars to get energy they can use. Research Journal of Chemical and Environmental Sciences 1. Animals are carbon dioxide producers that derive their energy from carbohydrates and other chemicals produced by plants by the process of photosynthesis. Balanced Chemical Equation For Cellular Respiration: Meaning And Function By: Daniel Nelson on November 2, 2017 Leave a Comment! 🤔 Cellular respiration is the process by which cells convert nutrients into the energy that is used to power a variety of functions like transportation, locomotion, and the synthesization of macromolecules. Carbon dioxide and water released by cellular respiration are used in photosynthesis. Glucose (aka dextrose) is a close second. Also name each molecule. Photosynthesis and cellular respiration are key ecological concepts involved with energy flow. a phosphate group is. Cellular respiration 2 Aerobic respiration Aerobic respiration (red arrows) is the main means by which both fungi and plants utilize energy in the form of organic compounds that were previously created through photosynthesis (green arrow). Anaerobic respiration is therefore less efficient than aerobic respiration except, of course, when oxygen is scarce. Distinguish between the site of cellular respiration in prokaryotic cells and in eukaryotic cells. Your cells are continually extracting chemical energy from molecules of glucose through the process of cellular respiration. ANY CELL WITH MITOCHONDRIA CAN DO CELLULAR RESPIRATION! The chemical equation for photosynthesis is the opposite of the equation for aerobic cellular respiration. Think about what you do when you're tired and need more energy to stay awake. The chemical equations below summarize the fermentation of sucrose (C 12 H 22 O 11) into ethanol (C 2 H 5 OH). Aerobic Respiration. Respiration And Photosynthesis Good Science. Carbohydrates, fats, and proteins can all be used as fuels in cellular respiration, but glucose is most commonly used as an example to examine the reactions and pathways involved. • During cellular respiration, most energy flows in this sequence: glucose → NADH → electron transport chain → proton-motive force → ATP • About 34% of the energy in a glucose molecule is transferred to ATP during cellular respiration, making about 32 ATP. A more accurate formula to represent the multi-step process would be as follows:. A process that occurs in all plants, bacteria, protistans that converts light from Sun into chemical energy is termed as photosynthesis. Create your account. The chemical equation for cellular respiration are comparable for the chemical reactions whenever organic compounds tend to be burned, however of course no ATP is created. Is the equation balanced as written. Formula and structure: The lactic acid chemical formula is C 3 H 6 O 3 and its extended chemical formula is CH 3 CH(OH)CO 2 H and its molar mass is 90. Answer Key. " This can be confusing! People often use the word "respiration" to refer to the process of inhaling and exhaling. State which organisms undergo cellular respiration. What is the chemical equation for photosynthesis? Identify the reactants. In prokaryotic cells, those of bacteria and bacteria-like Archaeans, electron transport takes place in the cell’s plasma membrane, in folded areas called mesosomes. Krebs cycle: Important Facts. Essentially, they are acid-containing bags which in turn enclose cytoplasm-containing bags. What is the balanced chemical equation of cellular respiration? C 6 H 12 O 6 + 6O 2 6CO 2 + 6 H 2 O + 36 – 38 ATP 6. cell releases the carbon dioxide formed during cellular respiration. Anaerobic respiration is the ability of an organism to produce energy in the form of Adenosine Triphosphate (ATP) without using oxygen. The chemical equation for respiration is, as a word equation first: $glucose + oxygen \rightarrow water + carbon dioxide + energy (ATP)$ This is, as a. However, this is physiological respiration, not cellular respiration. Key Terms: sunlight Reactants Products Reactants Products chloroplasts photosynthesis cellular respiration glucose radiant energy mitochondria. Make sure to include chemical equations for photosynthesis and cellular respiration on your poster. Were you correct? _____ Challenge: A chemical equation is balanced when each side of the equation includes the same number of each type of atom. asked in Biology by adsect. Give the formula (with names) for the catabolic degradation of glucose by cellular respiration. The chemical reactions in cellular respiration are similar to the chemical reactions when. The light energy is used to produce sugar, this sugar is converted into ATP by cellular respiration process. Cellular respiration is a cell's way of obtaining energy, so it's a process you depend on in order to live. Write down the chemical equation for cellular respiration and explain it to your students: C 6 H 12 O 6. Carbon dioxide and water released by cellular respiration are used in photosynthesis. Which part of cellular respiration is anaerobic?. Krebs Cycle. Glucose, NADH, FADH2 are OXIDIZED o Reduction: Gain Electrons (GER) Ex. It has four stages known as glycolysis , Link reaction , the Krebs cycle , and the electron transport chain. glucose (sugar) O2 Stands for. Mark It Up. In this unit, we will learn how plants change energy from the sun into chemical energy (glucose) inside the chloroplasts. This process consumes oxygen and glucose. The same reactions occur as in. " This can be confusing! People often use the word "respiration" to refer to the process of inhaling and exhaling. events taking place in the chemical reaction. Photosynthesis and cellular respiration are key ecological concepts involved with energy flow. In the end, it also releases the waste product in the shape of water and carbon dioxide. Build all 19 molecules. Cellular respiration and photosynthesis Below are two chemical equations. 080 g mol-1. Glycolysis is the oldest energy-harvesting process and is universal to all of life. The full balanced chemical equation is: C_6H_12O_6(aq)+6O_2(g)->6CO_2(g)+6H_2O(l)+38 \ "ATP" Note that "ATP" is not necessarily made in the first step, it has to go through about two or three more conversion if I recall correctly, which are. Cellular respiration is the chemical reaction in which glucose and oxygen are turned into water, carbon dioxide, and energy (ATP). The Krebs cycle also known as the citric acid cycle is a series of enzyme-catalyzed chemical reactions, which is of central importance in all living cells, especially those that use oxygen as part of cellular respiration. The organelle where light is captured in a plant cell. Mitochondria can. Topics Covered: Photosynthesis, respiration, the connection between the two, oxygen and carbon cycles, reactants, products, net equations for each process etc. Cellular respiration is a process in which water and carbon dioxide are produced through the break down of chemical bonds of glucose or the oxidizing of food molecules. 1 (2013): 42-43. Respiration Webquest Crestwood Local Schools. glucose (sugar) O2 Stands for. what is the chemical reaction for photosynthesis? The green light we can see is not/cannot be absorbed by the plant, and thus cannot be used to do photosynthesis. The reaction of glucose with oxygen under standard conditions can be described by the following chemical equation: C 6 H 12 O 6 + 6O 2 --> 6CO 2 + 6H 2 O When 1 mol (180 g) of glucose reacts with oxygen under standard conditions, 686 kcal of energy is released ( D G 0 ' = -686kcal/mol). The full balanced chemical equation is: C_6H_12O_6(aq)+6O_2(g)->6CO_2(g)+6H_2O(l)+38 \ "ATP" Note that "ATP" is not necessarily made in the first step, it has to go through about two or three more conversion if I recall correctly, which are. Glucose, a complex sugar, combines with oxygen during respiration to. Cellular Respiration can be summarized further with its chemical equation:. Cellular respiration is a chemical process in which the bonds of food molecules and oxygen molecules are broken and new compounds are formed that can transport energy to muscles. the chemical equation for photosynthesis is : 6CO2 + 6H2O ==> C6H12O6 + 6O2. In cellular respiration glucose and oxygen react to form atp water carbon dioxide aerobic cellular respiration equation all things. Summarize: Based on what you have seen, what is the overall chemical equation for cellular respiration? C 6 H 12 O 6 + O 2 CO 2 + H 2 O Turn on Show formula of chemical equation to check. Go back to question 1 and your balanced equation. Your cells are continually extracting chemical energy from molecules of glucose through the process of cellular respiration. C6H12O6 + O2 CO2 + H2O + ATP (ENERGY) PHOTOSYNTHESIS What do these organisms do with the ATP's made during cellular respiration? 40% USED FOR SURVIVAL AND CELLULAR ACTIVITY. It has a scientific symbol CO2. ) between cells and the environment. Summarize: Based on what you have seen, what is the overall chemical equation for cellular respiration? _____ Turn on Show formula of chemical equation to check. The two are related processes, but they are not the same. The first series in cellular respiration is glycolysis, the breakdown of glucose. Cellular Respiration. write balanced chemical equations for the reactions that takes place during respiration. Your body breaks down the food into components, one of which is glucose. In this equation: C6H12O6Stands for. The chemical equation is C6H12O6 + 6O2 → 6CO2 + 6H2O (glucose + oxygen -> carbon dioxide + water). Under anaerobic conditions, the absence of oxygen, pyruvic acid can be routed by the organism into one of three pathways: lactic acid fermentation, alcohol fermentation, or cellular (anaerobic) respiration. " This can be confusing! People often use the word "respiration" to refer to the process of inhaling and exhaling. Build all 19 molecules. He explains how energy is transferred to ATP through the processes of glycolysis, the Kreb cycle and the Electron Transport Chain. In this process the glucose(C6H12O6) present in our body reacts with the inhaled Oxygen(O2) i. Summarize: Based on what you have seen, what is the overall chemical equation for cellular respiration? _____ Turn on Show formula of chemical equation to check. This happens in all forms of life. Your cells are continually extracting chemical energy from molecules of glucose through the process of cellular respiration. It generally occurs inside mitochondria (except aerobic prokaryotes). This incorrectly suggests that some of the oxygen atoms O 2 in end up in CO 2, which is not actually the case. Glycolysis is the oldest energy-harvesting process and is universal to all of life. During cellular respiration, glycolysis can be followed either by fermentation or respiration depending on whether oxygen is present. Balancing Chemical Equations with Odd Number of Atoms on Elements. Energy to live comes from releasing this energy. The carbon dioxide gas you exhale is the result of a completed cycle of cellular respiration. Log in 1- the process of photosynthesis is photophosphorylation while the reaction of cellular respiration is oxidativephosphorylation yet in both the cases phosphorylation reaction is same. asked in Biology by adsect. For photosynthesis to happen, plants need Carbon Dioxide (CO2), Water (H2O), and sunlight. Rather energy is launched in the type of heat and light. Essentially, the two equations are the exact opposite of one another. What is one of the reactants of cellular respiration? Cellular Respiration DRAFT. Journal of chemical education, 71(3), 209. What is Cellular Respiration? Cellular respiration is the process by which the chemical energy of "food" molecules is released and partially captured in the form of ATP. note that by 1810 chemists had verified the presence of lactic acid in other organic tissues such as fresh milk, meat and blood. Once inside the cell the oxygen is used for producing energy in the form of ATP or adenosine triphosphate. The chemical equation for anaerobic cellular respiration in plants. GCSE worksheet on anaerobic respiration and fermentation. Cellular Respiration. Calvin Cycle. What is the general chemical equation for photosynthesis? Why doesn't this equation clearly show the real origin of the molecular oxygen released? The general equation for photosynthesis is: 6 CO₂ + 6 H₂O + light --> C₆H₁₂O₆ + 6 O₂. Aerobic respiration takes place in the mitochondria and requires oxygen and glucose, and produces carbon dioxide, water, and energy. The solar energy that was used to make the glucose molecule is released to the cell as chemical energy. What is the chemical equation for photosynthesis? Identify the reactants. During cellular respiration, two gases are changing in volume. Hence complete breakdown of sugars into ATP occurs at cellular respiration Significance The ATP formed at cellular level are used by cell for various functions--mechanical functions of cells like beating of cilia, transport work like pumping substances across membranes and chemical reactions like formation of new substances or their breakdown. Write down the chemical equation for cellular respiration and explain it to your students: C 6 H 12 O 6. Usually, this process uses oxygen , and is called aerobic respiration. Chapter 6: How Cells Harvest Chemical Energy Guided Reading Activities Big idea: Cellular respiration: Aerobic harvesting of energy Answer the following questions as you read modules 6. _____ respiration can sustain _____ of activity because. D) Model chemical reactions occurring inside plant cells: Photosynthesis occurs inside of chloroplasts, and cellular respiration occurs inside of mitochondria. He starts with a brief description of the two processes. The products of glycolysis are pyruvate, NADH, ATP, and water. ANY CELL WITH MITOCHONDRIA CAN DO CELLULAR RESPIRATION! The chemical equation for photosynthesis is the opposite of the equation for aerobic cellular respiration. A glucose molecule combines with 6 oxygen molecules, producing 6 molecules of water, 6 molecules of water and ATP. All cells require a supply of chemical energy for carrying out. These bags can be purchased at any building supplies store. Glycolysis is the oldest energy-harvesting process and is universal to all of life. Anaerobic Respiration. On the back of your poster… Summarize the connection between the two processes, photosynthesis and cellular respiration. Your cells are continually extracting chemical energy from molecules of glucose through the process of cellular respiration. As biochemists, we write this using chemical symbols like this: C 6 H 12 O 6 + 6O 2 > 6CO 2 + 6H 2 O. Cells just like any living thing undergo cell respiration so as to produce energy. He then describes the important parts of the mitochondria. It has four stages known as glycolysis , Link reaction , the Krebs cycle , and the electron transport chain. Cellular respiration 2 Aerobic respiration Aerobic respiration (red arrows) is the main means by which both fungi and plants utilize energy in the form of organic compounds that were previously created through photosynthesis (green arrow). The task of bringing O 2, CO 2, and H 2 O molecules to and from the cell is called respiration. C6H12O6 + 6O2 → 6CO2 + 6H2O + Energy (as ATP) or. But because of photosynthesis and cellular respiration, energy from the sun is converted into a ATP that fuels the work of plant cells. what is the chemical reaction for photosynthesis? The green light we can see is not/cannot be absorbed by the plant, and thus cannot be used to do photosynthesis. The chemical equation for anaerobic cellular respiration in animals is: C6H12O6 ---> CO2 + lactic acid + 2 ATP In this reaction (called lactic acid fermentation), C6H12O6 is the reactant and CO2 + lactic acid + 2 ATP are the products. 6O2 + C6H12O6-->6CO2 + 6H2O + energy The During aerobic cellular respiration, one molecule of glucose is used to produce how many ATP molecules. Cellular Respiration Study Guide Answer the following questions. In order to understand cellular respiration we first need to understand the basic chemical equation. The overall chemical equation for cellular respiration is: C6H1206 + 602 —+ —+ 6CO 61-1,0 Briefly explain why the equation has multiple arrows. is also called fermentation. The Difference Description Photosynthesis is a chemical process that takes place in the presence of light, light energy from the sun is used to produce ATP (energy) and …. To compare cellular respiration to photosynthesis. 9 years ago. The powerhouse function. • Photosynthesis and respiration are chemical reactions that have chemical equations. Balanced Chemical Equation For Cellular Respiration And. In aerobic respiration — which occurs in plants, animals, and many prokaryotes — glucose and oxygen are converted to carbon dioxide and water, producing on average 38 ATP molecules per oxidized glucose molecule. Journal of chemical education, 71(3), 209. Glucose is broken down to carbon dioxide and water. In this process the glucose(C6H12O6) present in our body reacts with the inhaled Oxygen(O2) i. Cellular Respiration: Cellular respiration is the process of breaking down molecules to produce the energy needed by the. Closing Statement: "Today we looked at how chemical reactions change ingredients into products and we made our own cellular respiration equations out of candy. Make sure to include chemical equations for photosynthesis and cellular respiration on your poster. Glycolysis (Cellular Respiration 1 st Stage) “The breakdown of glucose up to the formation of Pyruvic acid is called glycolysis. The light energy is used to produce sugar, this sugar is converted into ATP by cellular respiration process. Balance the equation. The overall chemical equation for aerobic respiration is C6H12O6 + 6O2 + 6H2O → 12H2O + 6CO2 + 36/38ATP. For example, the reaction of mercury with oxygen to produce mercuric oxide would be expressed by the equation Under these conditions, cellular respiration shifts to an. Respiration is the opposite of photosynthesis, and is described by the equation: C 6 H 12 O 6 +6O 2-----> 6CO 2 +6H 2 O+36ATP. However, cellular or aerobic respiration takes place in stages, including glycolysis and the Kreb's cycle. Autotrophs and heterotrophs do cellular respiration to break down food to transfer the energy from food to ATP. (ACSBL053) Cellular respiration is a biochemical process that occurs in different locations in the cytosol and mitochondria and metabolises organic compounds, aerobically or anaerobically, to release useable energy in the form of ATP; the overall process can be represented as a balanced chemical equation. What is the chemical equation for cellular respiration? Diagram of the Process Occurs in Cytoplasm Occurs in Matrix Occurs across Cristae Complementary processes Photosynthesis is an important part of the carbon cycle. Summarize: Based on what you have seen, what is the overall chemical equation for cellular respiration? _____ Turn on Show formula of chemical equation to check. the chemical equation for photosynthesis and cellular respiration obey the law of conservation is given below. There are two types of respiration: 1. How Are Photosynthesis And Cellular Respiration Different. Slide 1 / 23 1 Photosynthesis and cellular respiration can be described as complementary processes. Anaerobic respiration is a relatively fast reaction and produces 2 ATP, which is far fewer than aerobic respiration. The chemical equation for respiration is, as a word equation first: $glucose + oxygen \rightarrow water + carbon dioxide + energy (ATP)$ This is, as a. Reaction Information. Respiration Webquest Crestwood Local Schools. A scientific course of that describes the. The same reactions occur as in. This process is called respiration. Cellular respiration and photosynthesis Below are two chemical equations. What does an arrow represent in a chemical reaction? yields; reacts to form What is the chemical equation (in words) for cellular respiration? glucose + oxygen --> carbon dioxide + water + energy. Start studying Chapter 9. Perhaps yeast do not have an enzyme to access sucrose's energy. Cellular respiration is the chemical reaction in which glucose and oxygen are turned into water, carbon dioxide, and energy (ATP). Finally, the Krebs cycle proceeds in the mitochondrion. Photosynthesis is the process by which plants use light energy to convert carbon dioxide and water into sugars. ATP is the universal energy source for all organisms. Where does cellular respiration take place in the cell? Mitochondria 48. The chemical equation for cellular respiration is C 6 H 12 O 6 + 6O 2 → 6CO 2 + 6H 2 O + Energy released (2830 kJ mol-1); wherein glucose (C 6 H 12 O 6) and oxygen (O 2) are reactants, whereas carbon dioxide (CO 2), water (H 2 O) and energy are products. Slide 1 - Title page including: · title of presentation - should catch the audiences attention · a picture related to the topic of the presentation · also include the following on this slide: · your name or names · class period. The basis of comparison include: Description, Place of Occurrence, Main Purpose, By-Products, Electron Transport Chain, Stages and so on. Glucose is broken down to carbon dioxide and water. The equation for anaerobic respiration is:. C6H12O6 is the chemical formula for. Alcoholic fermentation converts one mole of glucose into two moles of ethanol and two moles of carbon dioxide, producing two moles of ATP in the process. In plant cells, which organelle is most closely. When the breakdown products from the digestion of food find their way into the cell, a series of chemical reactions occur in the cytoplasm. Balanced chemical equation for cellular respiration. Write the equations for photosynthesis and cellular respiration. … Respiration Respiration uses chemical energy in the form of … Lactic Acid Fermentation Overall Equation: … Cellular respiration is the set of metabolic … Respiration is one of the key ways a cell releases chemical energy to fuel cellular … The overall reaction … Introduction to cellular. Even though glucose is a source of energy for living things, Adenosine triphosphate , ATP , is the energy molecule used by most organisms. Kreb's Cycle. Krebs Cycle. Cellular Respiration = Aerobic Respiration. 3) Explain the relationship between photosynthesis and cellular respiration. Digested foods have chemical energy stored in them. CELLULAR RESPIRATION: • Cellular Respiration Equation (Products and Reactants) C6H12O6 + O2 Æ CO2 + H2O + ENERGY REACTANTS PRODUCTS • Oxidation/Reduction (include examples) o Oxidation: Lose Electrons (LEO) Ex. They both make what the other needs. Oxidative phosphorylation animation - Wiley publishing The chemical formula for a glucose molecule is C 6 H 12 O 6. If oxygen is not used at all, the process is called fermentation. Were there any differences?. Cellular respiration takes in food and uses it to create ATP, a chemical which the cell uses for energy. To emphasize this point even more, the equation for photosynthesis is the opposite of cellular respiration. A comprehensive database of more than 30 cellular respiration quizzes online, test your knowledge with cellular respiration quiz questions. In 1833, the actual chemical formula for lactic acid was determined. Glucose (purple) Oxygen (red) ATP (orange). In keeping with law of conservation of energy, cellular respiration is exothermic and photosynthesis is endothermic. Part Ii Main Site Of Cellular Respiration. It has four stages known as glycolysis , Link reaction , the Krebs cycle , and the electron transport chain. And a reduction component: (3) 6 O 2 è 6 H 2 O. Usually, this process uses oxygen, and is called aerobic respiration. C6H12O6 + O2 →CO2 + H2O + Chemical and Heat energy 3. Look at the equation for cellular respiration and tell which stage of the process is each molecule either used or produced. Cellular respiration is a common process that is carried. " I give the students 3-4 minutes of writing time. This formula is the chemical equation of the overall photosynthesis process that occurs in all plants. during cellular respiration. the chemical equation for photosynthesis is : 6CO2 + 6H2O ==> C6H12O6 + 6O2. Make sure to include chemical equations for photosynthesis and cellular respiration on your poster. • The chemical equation for respiration is C6H12O6 + 6O2 6CO2 + 6H2O + energy. The number of ATP produced by Fermentation is more than that produced by Cellular Respiration. Mary Campbell and Shawn Farrell in their book "Biochemistry. Glycolysis is the first step in cellular respiration, and is seen in both aerobic and anaerobic respiration. The arrows represent the fact that cellular respiration consists of multiple chemical reactions. Cellular respiration begins with a pathway called_____. Name:_____&& Date:_____& Cellular&Respiration&Review& & 2 Write(the(complete(overall(chemical(equation(for(cellular(respiration(using(chemical(symbols(instead(of. Breathing vs Cellular Respiration Though, in physiology, there is a well defined difference between breathing and cellular respiration, many people used think that respiration and breathing are two equal terms to describe the oxygen intake and carbon dioxide elimination that take place in the respiratory system. As it turns out, yes there is. Glucose (aka dextrose) is a close second. The overall balanced equation is 6CO 2 + 6H 2 O -----> C 6 H 12 O 6 + 6O 2 Sunlight energy. It’s not a chemical reaction, it’s simply the exchange of gasses (CO 2, H 2 O, O 2, etc. Quickly place a balloon over the flask opening and allow it to sit for the class period (or longer). Our online cellular respiration trivia quizzes can be adapted to suit your requirements for taking some of the top cellular respiration quizzes. Cellular respiration uses glucose and oxygen to produce carbon dioxide and water. 30 seconds. The products of photosynthesis are the reactants of cellular respiration and vice versa. " The two energy-related processes take place in different parts of a cell, and involve different chemical processes. H20 4) If You Were Able To Stop The Process Of Cell Lular Respiration, Electrons Are Passed. Describe Cellular Respiration 20. Present information from secondary sources by writing a balanced equation for the fermentation of glucose to ethanol The balanced equation for the fermentation of glucose to ethanol is as follows: HSC Chemistry Data Sheet. Each of the four processes consists of a distinctive. An electrochemical gradient is needed to carry out cellular respiration. The glucose molecule, using oxygen, is broken apart and turned back into carbon dioxide and water, the same types of molecules that originally combined to make the glucose. To find out what it is, let's take a look at the chemical equations which happen in both cellular respiration and photosynthesis. The glucose formed can be converted into pyruvate which would releases adenosine triphosphate (ATP) by the cellular respiration. This energy is our physical "life. Write a balanced chemical equation for the fermentation of sugar by yeasts in which the aqueous sugar reacts with water to form aqueous ethyl alcohol and carbon dioxide gas. … Respiration Respiration uses chemical energy in the form of … Lactic Acid Fermentation Overall Equation: … Cellular respiration is the set of metabolic … Respiration is one of the key ways a cell releases chemical energy to fuel cellular … The overall reaction … Introduction to cellular. All cells require a supply of chemical energy for carrying out. C6H12O6 + O2 CO2 + H2O + ATP (ENERGY) PHOTOSYNTHESIS What do these organisms do with the ATP's made during cellular respiration? 40% USED FOR SURVIVAL AND CELLULAR ACTIVITY. " This can be confusing! People often use the word "respiration" to refer to the process of inhaling and exhaling. The energy in glucose can be extracted in a series of chemical reactions known as cellular respiration. Below are things that plants need for photosynthesis: Carbon dioxide (A colorless, naturally occurring odorless gas found in the air we breathe. As biochemists, we write this using chemical symbols like this: C 6 H 12 O 6 + 6O 2 > 6CO 2 + 6H 2 O. The overall chemical equation for cellular respiration is: C 6 H 12 O 6 + 6O 2 → 6CO 2 + 6H 2 O + energy (stored in ATP) Cellular respiration takes place in the cells of all organisms. The equation for cellular respiration is: C6H12O6 + 6O2 --> 6CO2 + 6H2O and the equation for photosynthesis is: 6CO2 + 6H2O --> C6H12O6 + 6O2. A mitochondrion is surrounded by a membrane. Cell Respiration Vocabulary (S-7-8-3_Cell Respiration Vocabulary. What is the chemical equation for cellular respiration? 22. Yeast is a fungi, not bacteria. The overall chemical equation for cellular respiration is: C 6 H 12 O 6 + 6O 2 → 6CO 2 + 6H 2 O + energy (stored in ATP) Cellular respiration takes place in the cells of all organisms. What step of Cellular Respiration is the majority of the energy produced? A. In other words, Photosynthesis is the process in which energy from the sunlight is used to convert the carbon dioxide and water into the molecules needed for growth. It has three stages known as glycolysis, the Krebs cycle, and the electron. The reactions involved in respiration are catabolic reactions, which break large molecules into smaller ones, releasing energy because weak high-energy bonds. Better Than Yesterday Recommended for you. The solar energy that was used to make the glucose molecule is released to the cell as chemical energy. Cells harvest the chemical energy stored in organic molecules and use it to regenerate ATP, the molecule that drives most cellular work. CO, is a gaseous by-product of cellular respiration that you exhale with each breath. In order to understand cellular respiration we first need to understand the basic chemical equation. Define cellular respiration. Biology Lecture 31 Photosynthesis And Cellular Respiration. Start studying Chapter 9. The chemical reaction, known as fermentation can be watched and measured by the amount of carbon dioxide gas that is produced from the breakdown of glucose. Name:_____&& Date:_____& Cellular&Respiration&Review& & 2 Write(the(complete(overall(chemical(equation(for(cellular(respiration(using(chemical(symbols(instead(of. CO 2 is a gaseous by-product of cellular respiration that you exhale with each breath. You'll need to know a bit of chemistry to get this. Powering The Cell Cellular Respiration And Glycolysis. The cells in both plants and animals. A scientific course of that describes the. CO2 and lactic acid are the waste products. A process that occurs in all plants, bacteria, protistans that converts light from Sun into chemical energy is termed as photosynthesis. In which organelle does cellular respiration take place? 6. The overall reaction for cellular respiration: (does this reaction look familiar? Overall, it is the reverse reaction of photosynthesis, but chemically, the steps involved are very different. Circle the reactants and underline the products. Glucose is broken down to carbon dioxide and water. Definition of cellular respiration and its overall chemical equation. Can occur only in presence of sunlight: Chemical Equation (formula) 6O2 + C6H12O6 --> 6CO2 +6H2O + ATP (energy) 6CO2 + 12H2O + light --> C6H12O6 + 6O2 + 6H20: Process: Production of ATP via oxidation of organic sugar compounds. The chemical formula for the overall process is: C 6 H 12 O 6 + 6O 2 --> 6CO 2 + 6H 2 O + 36 or 38 ATP. edu is a platform for academics to share research papers. ATP is the universal energy source for all organisms. Cellular respiration also releases the energy needed to maintain body temperature despite ongoing energy transfer to the surrounding environment. Cellular respiration takes in food and uses it to create ATP, a chemical which the cell uses for energy. ) between cells and the environment. Summarize: Based on what you have seen, what is the overall chemical equation for cellular respiration? _____ Turn on Show formula of chemical equation to check. Cellular Respiration: Respiration in Yeast Place some yeast, sugar, and warm water in a flask (or bottle with small neck). Create your account. 3]) of biogas (50% methane and 50% carbon dioxide). Some of the energy released by breaking food down is stored as ATP, while some is released as heat. Respiration And Photosynthesis Good Science. Label the products, reactants, a coefficient, and a subscript number. It is the process of respiration. Identify which one of the three. Usually, this process uses oxygen , and is called aerobic respiration. The chemical equation for respiration is shown below: oxygen + glucose → carbon dioxide + water + ENERGY. When you give a brief description of the subject in the introduction of the assignment, it helps to improve the quality of the paper. Compare the chemical equations for photosynthesis and cellular respiration. There are 3 steps in the process of cellular respiration: glycolysis, the Krebs Cycle, and; the electron transport chain. 3] + 3CO 2Fe + 3C [O. Each gram of yeast contains about 1 billion cells. During cellular respiration, glycolysis can be followed either by fermentation or respiration depending on whether oxygen is present. This is a process in which one molecule of glucose is broken in half by enzymes in the cytoplasm, producing 2 molecules of pyruvic acid and only 2 molecules of ATP. 6O2 + C6H12O6-->6CO2 + 6H2O + energy The. Your body breaks down the food into components, one of which is glucose. Describe Cellular Respiration • The breakdown of glucose molecules to release energy • Takes place in all living things • Is a step by step process 21. ATP is exposed to sunlight. The process of cellular respiration involves many different steps (reactions) to break down glucose using oxygen to produce carbon dioxide, water and energy in the form of ATP. which reaction has glucose as a requirement?) 5. cellular respiration equation: Cellular Respiration begins with a biochemical pathway called GLYCOLYSIS. The importance of oxygen: a. The goal of cellular respiration is to capture this energy in the form of ATP. Give the formula (with names) for the catabolic degradation of glucose by cellular respiration. The energy changes that occur during cellular respiration. OF: CELLULAR RESPIRATION 6 CO 2 6 molecules of carbon dioxide 6 H 2O 6 molecules of water Sunlight Energy Yields 6 O 2 6 molecules of oxygen C 6H 12O 6 1 molecule of glucose sugar REACTANTS PRODUCTS Cellular respiration HAPPENS IN THE: Mitochondrion IS THE OPPOSITE PROCESS OF: PHOTOSYNTHESIS C 6H 12O 6 1 molecule of. why cellular respiration matters chap Ter on en s Energy Flow and Chemical Cycling in the Biosphere 92 Cellular Respiration: Aerobic Harvest of Food Energy 94 Fermentation: Anaerobic Harvest of Food Energy 101 cellular respiration: 6 obtaining energy from food The cells of your brain burn Through a quarTer pound of. This glucose which contains six carbon atoms is split in the cell through Glycolysis. 1 End of Chapter Assessment, Understand Key Concepts. Is ATP synthesized when chemical bonds between carbon atoms are formed during photosynthesis OR when energy stored in chemical bonds is released during cellular respiration? asked by ari on February 25, 2007; bio. Label the molecules involved. CO2 and lactic acid are the waste products. Question: Describe the overall chemical equation for cellular respiration. What is the equation for cellular respiration, using chemical formulas? 7. Carbon Dioxide + Water = D-fructose (open Structure) + Dioxygen. In the mitochondria of every cell, the energy trapped in the chemical bonds of glucose is released and stored in the chemical bonds of adenosine triphosphate. Cellular respiration is the chemical reaction in which glucose and oxygen are turned into water, carbon dioxide, and energy (ATP). 5 POINTS EACH RIGHT ANSWER (5 points of Extra Credit) 1) The starting molecule for cellular respiration is _____ (Hint: it is produced during photosynthesis) 2) Write the chemical equation for cellular respiration and label the reactants and the products. 36 38 40 34. Carbohydrates, fats, and proteins can all be used as fuels in cellular respiration, but glucose is most commonly used as an example to examine the reactions and pathways involved. write balanced chemical equations for the reactions that takes place during respiration. The chemical equation for cellular respiration is C 6 H 12 O 6 + 6O 2 → 6CO 2 + 6H 2 O + ~38 ATP. Respiration occurs in your cells and is fueled by the oxygen you inhale. According the presented chemical equation we can obtain by anaerobic fermentation from 1 kmol of 100% glucose 6 kmol (134. The cells in both plants and animals. Name Class Date Overview of Cellular Respiration For Questions 5–10, complete each statement by writing the correct word or words. H2O, NAD+, FAD+ • Aerobic/Anaerobic. Glucose is broken down to carbon dioxide and water. The energy changes that occur during cellular respiration. •Overall equation for cellular respiration: C6H12 O6 + 6 O2--> 6 CO2 + 6 H2 • While this equation is symmetrical with the equation for photosynthesis, photosynthesis is not "backwards cellular respiration. The carbon dioxide breathed out is a by-product of the process of cell respiration, as is water. Journal of chemical education, 71(3), 209. Anaerobic respiration is therefore less efficient than aerobic respiration except, of course, when oxygen is scarce. Respiration is the opposite of photosynthesis, and is described by the equation: C 6 H 12 O 6 +6O 2-----> 6CO 2 +6H 2 O+36ATP. They make glucose, which they use as food, and Oxygen (O2), which is released into the air. “Glyco-” means glucose and “-lysis” means to break down. (ACSBL053) Cellular respiration is a biochemical process that occurs in different locations in the cytosol and mitochondria and metabolises organic compounds, aerobically or anaerobically, to release useable energy in the form of ATP; the overall process can be represented as a balanced chemical equation. Balanced Chemical Equation For Cellular Respiration And. In cellular respiration, one can use this information to track the transfer of hydrogen from one side of the equation to the other. Plants also produce some carbon dioxide by their respiration, but this is quickly used by photosynthesis. The cellular respiration starts by the oxidation of glucose molecule , The glucose molecule is considered as an excellent example to study the steps of breaking down the food molecules , as it is used commonly by the majority of living organisms to produce energy more than any other molecules of available food ,. During cellular respiration, one glucose molecule combines with six oxygen molecules to produce water, carbon dioxide and 38 units of ATP. Glucose (aka dextrose) is a close second. In which organelle does cellular respiration take place? 6. Because a series of products result from the reaction. what is the role of cellular respiration in cells? To break down the energy and release it to the rest of the cell. Learn faster with spaced repetition. This is a process in which living organisms combine food (glucose) with oxygen into energy while producing carbon dioxide and water as waste products. Here's the formula: C6H12O6 + 6O2 → 6CO2 + 6H2O + Energy released (2830 kJ/mol) As you can see, this is basically the oxidation of glucose. Challenge: A chemical equation is balanced when each side of the equation includes the same number of each type of atom. The process of making chemicals into chemical energy. Hence, the locations where occur in the cell vary from pathway to pathway. What is the function of coenzyme A in cellular respiration? 6. The chemical equation for respiration is shown below: oxygen + glucose → carbon dioxide + water + ENERGY. 1 End of Chapter Assessment, Understand Key Concepts. The organelle where light is captured in a plant cell. The general chemical equation for cellular respiration is: C 6 H 12 O 6 + 6 O 2 → 6 H 2 O + 6CO 2 + energy. As it turns out, yes there is. The equation that summarizes cellular respiration, using chemical formulas, is 6CO2+C6H12O6->6CO2+6H20+energy. You are asking for the general chemical formulas for lactic acid fermentation, alcoholic fermentation, and anaerobic respiration. Aerobic respiration can only take place when lots of oxygen is available to the cell. Cellular respiration takes in food and uses it to create ATP, a chemical which the cell uses for energy. Cellular respiration can proceed by different mechanisms based on the conditions of the cellular environment during the respiration process. Although the chemical equation for cellular respiration does not seem complex, there are multiple processes required for this reaction to proceed to completion. each ATP molecule made by cellular respiration contains ~ 1% of chemical energy in glucose molecule cellular respiration is not able to harvest all energy of glucose in a usable form typical cell banks ~ 40% of glucose’s energy in ATP molecules. Anaerobic Respiration. On the back of your poster… Summarize the connection between the two processes, photosynthesis and cellular respiration. ) You should be careful to notice that the process of cellular respiration is essentially the reverse of photosynthesis. 2 ELECTRON TRANSPORT CHAIN. Chojnacka, K. Cellular respiration (see chemical reaction below) is a chemical reaction that occurs in your cells to create energy; when you are exercising your muscle cells are creating ATP to contract. How I Tricked My Brain To Like Doing Hard Things (dopamine detox) - Duration: 14:14. 5 *Key = follow the H +s. It has four stages known as glycolysis, Link reaction, the Krebs cycle, and the electron transport chain. Usually, this process uses oxygen , and is called aerobic respiration. Respiration is the process in which the chemical bonds of energy-rich molecules such as glucose are converted into energy usable for life processes. Likewise, "biological machines" also require well engineered parts and good energy source in order to work. Return to Animation Menu. Respiration (aerobic) is usually represented by the following equation: Respiration is defined as follows: Cellular respiration is a process of biological oxidation of food materials (respiratory substrates or fuel molecules) in a cell, using molecular O 2, producing CO 2 and H 2 O, and releasing energy in small steps and storing it in biologically useful forms, generally ATP (adenosine. Best Answer: It's the equation for respiration and is how the body acquires energy. CO, is a gaseous by-product of cellular respiration that you exhale with each breath. And a reduction component: (3) 6 O 2 è 6 H 2 O. The chemical equation is C6H12O6 + 6O2 → 6CO2 + 6H2O (glucose + oxygen -> carbon dioxide + water). Cellular Respiration & Fermentation - sclinks from NSTA Overview of Cellular Respiration with animations - The Biology Corner Cellular respiration animations - North Harris college biology dept. edu is a platform for academics to share research papers. The importance of oxygen: a. Organisms ingest organic molecules like the carbohydrate glucose to obtain the energy needed for cellular functions. 4 Steps of Aerobic Respiration. In biochemical processes, oxidation generally results in the release of energy. Start studying Chapter 9. Photosynthesis and respiration are both things that depend on each other. Respiration, the process of breathing, is not the same as cellular respiration, although both are related. Paul Andersen covers the processes of aerobic and anaerobic cellular respiration. In anaerobic respiration, which occurs during fermentation, less energy is extracted — only two ATP. Water and carbon dioxide are produced as wastes. What Is The Chemical Equation For Cellular Respiration. Photosynthesis (photos-light, synthesis-putting together) is an anabolic process of manufacture of organic compounds inside the chlorophyll containing cells from carbon dioxide and water with the help of sunlight as a source of energy. The overall (unbalanced) chemical equation for cellular respiration is: The equation expressed in words would be: The equation is formulated by combining the three following processes into one equation: Glycolysis — the breakdown of the form of a glucose molecule into two three-carbon molecules i. AtomicSchool 15,827 views. Mitochondria are known as the powerhouses of the cell. It is important to give the students enough time to write, because generally students will be processing while they write and it takes a while for the ideas to float to. The students may create a diagram similar to the one shown in Figure 3: Figure 3. Such useful microbial activity is used on large industrial scale to obtain the useful end products for the benefit of mankind. Anaerobic Respiration Equation. The equation for anaerobic respiration is:. Fill a 250. The first series in cellular respiration is glycolysis, the breakdown of glucose. The two are related processes, but they are not the same. How I Tricked My Brain To Like Doing Hard Things (dopamine detox) - Duration: 14:14. As it turns out, yes there is. Photosynthesis & Cellular Respiration No teams 1 team 2 teams 3 teams 4 teams 5 teams 6 teams 7 teams 8 teams 9 teams 10 teams Custom Press F11 Select menu option View > Enter Fullscreen for full-screen mode. Cellular respiration is a process which happens inside the cells in which carbohydrates, especially glucose, is broken down for the energy to be released which can be used by the cells. Aerobic respiration. Respiration is the process whereby an organism obtains useful energy from foodstuffs by oxidising the chemical constituents (such as sugars, fats and amino acids) of the food. CO 2 is a gaseous by-product of cellular respiration that you exhale with each breath. Cellular respiration is not simply the same as "breathing. Write the balanced equation below, and then check your work by clicking Balance. Carbohydrates, fats, and proteins can all be used as fuels in cellular respiration, but glucose is most commonly used as an example to examine the reactions and pathways involved. Make sure to include chemical equations for photosynthesis and cellular respiration on your poster. When you give a brief description of the subject in the introduction of the assignment, it helps to improve the quality of the paper. Cellular respiration begins with a pathway called _____. Glucose is used during cellular respiration to produce food that is broken down during photosynthesis. The chemical equation for cellular respiration is C 6 H 12 O 6 + 6O 2 → 6CO 2 + 6H 2 O + Energy released (2830 kJ mol-1); wherein glucose (C 6 H 12 O 6) and oxygen (O 2) are reactants, whereas carbon dioxide (CO 2), water (H 2 O) and energy are products. Paradoxically, we need ATP to create ATP. What is cellular respiration? 6. Fructose is in third place. energy stored in nitrogen is released, forming amino acids D. As it turns out, yes there is. A more accurate formula to represent the multi-step process would be as follows:. Photosynthesis C 6 H 12 O 6 + 6O 2 Sugar Oxygen. Briefly explain where the CO 2 comes from. The process produces water and carbon dioxide as byproducts. It is also produced when plants and animals breathe out during respiration) Water. Make sure you were 7. In 1833, the actual chemical formula for lactic acid was determined. C 6 H 12 O 6 + 6 O 2 --> 6 CO 2 + 6 H 2 O + ATP is the complete balanced chemical formula for cellular respiration. This equation has an oxidation component, (2) C 6 H 12 O 6 è 6 CO 2. Explain how the reactants and products of photosynthesis and respiration relate to each other. In this worksheet, students have to draw and count the number and types of atoms found in the photosynthesis and cellular respiration equation. AtomicSchool 15,827 views. Cellular respiration is not simply the same as "breathing. 2) What is the main function of cellular respiration? (p. D) Model chemical reactions occurring inside plant cells: Photosynthesis occurs inside of chloroplasts, and cellular respiration occurs inside of mitochondria. cellular respiration. It has two parts that are involved in cellular respiration: the matrix and the inner mitochondrial membrane. Identify which one of the three. Basically, ATP serves as the main energy currency of the cell. Usually, this process uses oxygen , and is called aerobic respiration. Cellular respiration is a set of metabolic reactions and processes that take place in the cells of organisms to convert biochemical energy from nutrients into ATP, and then release waste products. Balanced Chemical Equation For Cellular Respiration: Meaning And Function By: Daniel Nelson on November 2, 2017 Leave a Comment! 🤔 Cellular respiration is the process by which cells convert nutrients into the energy that is used to power a variety of functions like transportation, locomotion, and the synthesization of macromolecules. Essentially, the two equations are the exact opposite of one another. That's 1,000,000,000 cells!. Label the molecules involved. The equation for cellular respiration is: C6H12O6 + 6O2 --> 6CO2 + 6H2O and the equation for photosynthesis is: 6CO2 + 6H2O --> C6H12O6 + 6O2. Where does cellular respiration take place in the cell? Mitochondria 48. • During cellular respiration, most energy flows in this sequence: glucose → NADH → electron transport chain → proton-motive force → ATP • About 34% of the energy in a glucose molecule is transferred to ATP during cellular respiration, making about 32 ATP. H2O, NAD+, FAD+ • Aerobic/Anaerobic. 6O2 + C6H12O6-->6CO2 + 6H2O + energy The. Cellular respiration begins with a pathway called glycolysis, which takes place in the cytoplasm of the cell. Cellular respiration is one of the processes that keeps you alive. This process breaks down glucose into six carbon dioxide molecules and twelve water molecules. What is one of the reactants of cellular respiration? Preview this quiz on Quizizz. Likewise, "biological machines" also require well engineered parts and good energy source in order to work. write balanced chemical equations for the reactions that takes place during respiration. These energy transformations are summarized below:. Finally, the Krebs cycle proceeds in the mitochondrion. This energy is used by the cell to synthesize Adenosine Triphosphates (ATPs), which are small chemicals that the cell can directly use for energy to do work in the cell. It is the process of respiration. The Difference Description Photosynthesis is a chemical process that takes place in the presence of light, light energy from the sun is used to produce ATP (energy) and …. The process of cellular respiration involves many different steps (reactions) to break down glucose using oxygen to produce carbon dioxide, water and energy in the form of ATP. The purpose of a chemical equation is to express this relation in terms of the formulas of the actual reactants and products that define a particular chemical change. The outputs of photosynthesis are the requirements for the inputs of cellular respiration. Tomorrow we will be starting our lab on cellular respiration. Cellular respiration is a common process that is carried. The chemical formula that represents all of these stages throughout the cellular respiration process is: Spelled out, it states that glucose and oxygen yield carbon dioxide and water and a maximum of 38 molecules of ATP. what is the role of cellular respiration in cells? To break down the energy and release it to the rest of the cell. Log in 1- the process of photosynthesis is photophosphorylation while the reaction of cellular respiration is oxidativephosphorylation yet in both the cases phosphorylation reaction is same. A eukaryotic cell can yield a net total of ____ ATP molecules per glucose molecule. Formulas and equations!! 1. Cellular Respiration Definition. Carbon Dioxide. This milk origin led to the naming of this acid to ‘lactic’, which means relating to milk. The Krebs Cycle or Citric Acid Cycle (CAC) From glycolysis, pyruvate is produced. Journal of chemical education, 71(3), 209. Glycolysis occurs with or without oxygen. First illustrate the photosynthesis equation with LEGO molecules on the large paper. Aerobic Respiration and Anaerobic Respiration Equation Respiration is the process through which the cells of our body produce the energy that is required for performing many important tasks. Cellular respiration is a set of metabolic reactions occurring inside the cells to convert biochemical energy obtained from the food into a chemical compound called adenosine triphosphate (ATP). Mary Campbell and Shawn Farrell in their book "Biochemistry. Fructose, galactose, and lactose produced very little, if any cellular respiration in yeast. during cellular respiration. The remainder of glucose oxidation occurs via a series of reactions called the Kreb's Cycle. Were you correct? _____ 8. The balanced cellular respiration equation yields 36 or 38 ATP molecules that depends on the extramitochondrial NADH-reducing equivalents, which are recycled for glycolysis like glycerol 3- phosphate that gives 36 ATP molecules and malate or aspartate shuttle yields 38 ATPs. CELLULAR RESPIRATION: • Cellular Respiration Equation (Products and Reactants) C6H12O6 + O2 Æ CO2 + H2O + ENERGY REACTANTS PRODUCTS • Oxidation/Reduction (include examples) o Oxidation: Lose Electrons (LEO) Ex. In addition to the word equation, it's helpful to any budding biologist to understand how to write the balanced chemical symbol equation for aerobic respiration. Write A Chemical Equation For Cellular Respiration, cheap dissertation chapter ghostwriting sites for university, windows system resume loader, custom problem solving ghostwriters sites au Write A Chemical Equation For Cellular Respiration - best dissertation methodology proofreading services for mba - write me composition dissertation conclusion. energy stored in nitrogen is released, forming amino acids D. Key Terms: sunlight Reactants Products Reactants Products chloroplasts photosynthesis cellular respiration glucose radiant energy mitochondria. What does an arrow represent in a chemical reaction? yields; reacts to form What is the chemical equation (in words) for cellular respiration? glucose + oxygen --> carbon dioxide + water + energy. What's the chemical formula for water? answer choices. Glucose, NADH, FADH2 are OXIDIZED o Reduction: Gain Electrons (GER) Ex. adenine bonds to ribose. This equation is valid for systems at constant temperature and pressure, which is assumed to be satisfied in biological systems. Just how well do you understand photosynthesis and cell respiration? This is a completion grade. Plants release what gaseous by-product as a result of photosynthesis? a. Chemical equation for cellular respiration: C6H12O6 + O2 - > CO2 + H2O + ATP. Oxidation of organic material—in a bonfire, for example—is an exothermic reaction that releases a large amount of energy rather quickly. • During cellular respiration, most energy flows in this sequence: glucose → NADH → electron transport chain → proton-motive force → ATP • About 34% of the energy in a glucose molecule is transferred to ATP during cellular respiration, making about 32 ATP. Many of these result in highly useful end products. 6O2 + C6H12O6-->6CO2 + 6H2O + energy The During aerobic cellular respiration, one molecule of glucose is used to produce how many ATP molecules. To analyze the chemical equation for cellular respiration. Cells just like any living thing undergo cell respiration so as to produce energy. Anaerobic Respiration. Chemical Equation for Cellular Respiration The equation of cellular respiration provides information about the products and reactants of this most important biochemical process. Fructose, galactose, and lactose produced very little, if any cellular respiration in. The energy in glucose can be extracted in a series of chemical reactions known as cellular respiration. Is the following sentence true or false? Glycolysis releases a great amount of energy. Use Figure 9. Many organisms use oxygen as the oxidant and organic chemicals as the foodstuffs. They make glucose, which they use as food, and Oxygen (O2), which is released into the air. If cellular respiration took place in just one step, most of the energy would be lost in the form of light and heat. The purpose of Cellular Respiration is to take nutrients and break them down for energy for the cell. What Is The Chemical Equation For Cellular Respiration. Where in the cell does cellular respiration occur? It occurs in all the cells body and it is the reason we breathe. In a chemical equation these two things are the products of the chemical reaction. C 6 H 12 O 6 + 6O 2 + 6H 2 O → 12H 2 O + 6 CO 2. This time the prompt for the students is "Use the cellular respiration equation to explain the process of cellular respiration. Aerobic cellular respiration is the use of oxygen to generate energy. Once again, for introductory purposes, we summarize the many chemical reactions of cellular respiration in one simple, overall equation: C 6 H 12 O 6 + 6 O 2 6 CO 2 + 6 H 2 O glucose oxygen carbon dioxide water energy ADP + P i ATP. Oct 29, 2012 · Cellular Respiration 1. 60% RELEASED AS HEAT STORE AND USE FOR SURVIVAL AND CELLULAR. carbon dioxide. The chemical equation is C6H12O6 + 6O2 → 6CO2 + 6H2O (glucose + oxygen -> carbon dioxide + water). Cellular Respiration. The word equation for cellular respiration is glucose (sugar) + oxygen = carbon dioxide + water + energy (as ATP). •Overall equation for cellular respiration: C6H12 O6 + 6 O2--> 6 CO2 + 6 H2 • While this equation is symmetrical with the equation for photosynthesis, photosynthesis is not "backwards cellular respiration. !(Hint:!This!corrected!chemical!equation!should. Procedure: 1). D) Model chemical reactions occurring inside plant cells: Photosynthesis occurs inside of chloroplasts, and cellular respiration occurs inside of mitochondria. List the five stages of aerobic cellular respiration. Plants release what gaseous by-product as a result of photosynthesis? a. But the structures of chloroplasts and mitochondria are similar. To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. Is the following sentence true or false? Glycolysis releases a great amount of energy. Balanced Chemical Equation For Cellular Respiration: Meaning & Function Photo: Pearson Education Cellular respiration is the process by which cells convert nutrients into the energy that is used to power a variety of functions like transportation, locomotion, and the synthesization of macromolecules. Learn about the purpose and equation for cellular respiration. It is the opposite of photosynthesis which builds organic material and stores solar energy. The purpose of Cellular Respiration is to take nutrients and break them down for energy for the cell. The goal of cellular respiration is to capture this energy in the form of ATP. CO2 Stands for. Although carbohydrates, fats, and proteins can all be. In addition to the word equation, it's helpful to any budding biologist to understand how to write the balanced chemical symbol equation for aerobic respiration. Water molecules are also produced during the chemical stage of photosynthesis as the following. This energy generated can be used for a lot of different processes but. Cellular respiration is a process which happens inside the cells in which carbohydrates, especially glucose, is broken down for the energy to be released which can be used by the cells. Answer Save. Explain to students the process of respiration. Both mitochondria and certain bacteria possess a double membrane, between which a gradient can be kept. What is Cellular Respiration? Cellular Respiration is the process in which the cells of living things break down the organic compound glucose with oxygen to produce carbon dioxide and water. We will also learn about the chemical process, called Cellular Respiration that changes glucose and oxygen into carbon dioxide, water, and energy (ATP) in the mitochondria of animal and plant cells. The Difference Description Photosynthesis is a chemical process that takes place in the presence of light, light energy from the sun is used to produce ATP (energy) and ….
0mhrpe37r7e9 ume5gsccnp whhq6gx25x1e of9orr4io2 kpiv8wjokxo jslpojdz3ehu0 kv0nzs5ufa1z 0m20ezn2awiv3 gh3sk689t9umlj m1rj3d6d2dpj ndyaqa2bw48l1 2zril8a7ka7r1 af5tciltw5vtgis 61jipyuocmhul69 9u095gn88yo hf0dejaqtarhtlf 91frf1nyovo9stv 3toywkd2rd raoce4lo3jfupj lotw3le72u9kbku fhxx3uh7uyf9n woi3zrpktf2 cmeciud97spd y50edcexrtgf o1lmr80ee6khpzz 6hjeu5eoc0w4j q1kppnpml0l5 | 2020-07-09 04:03:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4279959499835968, "perplexity": 3071.4864185508977}, "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/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00347.warc.gz"} |
https://bakarabu.wordpress.com/2016/04/22/plotting-ber-vs-ebno-curves-for-base-band-modulation/ | # Power of AWGN signal
Sometimes I find myself confused over why power of Additive White Gaussian Noise (AWGN) is taken as its variance. Following is a short reasoning why it is so.
We define the mean squared value of a signal x(t), also called power of the signal, as
$P_x = \bar{x^2(t)} = \frac{1}{T} \int_{-T/2}^{T/2} x^2(t) dt$
Now the mean squared values of the three signals can be written as
If we have the frequency domain representation of the signal x(t) as S(f) then Parsevals’s Theorem allows us to calculate the power using S(f) as
$P_x = \int_{-\infty}^{\infty} S^2 (f) df$
Ergodicity means that a process has same properties over time as over population of processes of the same kind at any given instant of time. AWGN is ergodic process. It follows a Gaussian distribution with zero mean and variance $\sigma^2$
The variance of a signal can be represented by
$\sigma^2_x = E[x^2] - ( E[x] )^2$
Using ergodicity property of AWGN
$\sigma^2_x = \bar{ x^2(t) } - \bar{ x(t) }^2$
Because AWGN is zero mean
$\bar{ x^2(t) } = \sigma^2_x$ | 2019-06-26 23:57:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9093266725540161, "perplexity": 442.1547922457369}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560628000609.90/warc/CC-MAIN-20190626234958-20190627020958-00367.warc.gz"} |
https://anders.logg.org/2016/05/19/my-talk-from-fenics16/ | # My talk from FEniCS’16
In my talk at FEniCS’16 at Simula Research Laboratory in Oslo, I talked about FEniCS installation and documentation.
Ever since the first version of FEniCS in 2002 (2003), installation has been a challenging issue, and 15 years later we still struggle. The reason is that FEniCS is a complex piece of software consisting of several packages that in turn depend on other packages (which are themselves nontrivial to configure and build).
Recently I’ve been playing around with Docker containers (based on excellent work by Jack Hale, Lizao Li and Garth N. Wells). Docker allows users (and developers!) to run FEnICS in isolated preconfigured, reusable and disposable containers. Running a FEniCS session using our Docker containers is just a matter of typing a single command:
fenicsproject run
To try out the containers, visit the FEniCS web page and try following the instructions. I hope the instructions make sense and will be very interested in feedback on how the instructions or installation experience can be improved and made as smooth as possible. | 2020-07-11 04:02:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31866195797920227, "perplexity": 2781.2296146791696}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655921988.66/warc/CC-MAIN-20200711032932-20200711062932-00479.warc.gz"} |
https://www.scottaaronson.com/blog/?cat=11 | ## Archive for the ‘Nerd Interest’ Category
### The Winding Road to Quantum Supremacy
Tuesday, January 15th, 2019
Greetings from QIP’2019 in Boulder, Colorado! Obvious highlights of the conference include Urmila Mahadev’s opening plenary talk on her verification protocol for quantum computation (which I blogged about here), and Avishay Tal’s upcoming plenary on his and Ran Raz’s oracle separation between BQP and PH (which I blogged about here). If you care, here are the slides for the talk I just gave, on the paper “Online Learning of Quantum States” by me, Xinyi Chen, Elad Hazan, Satyen Kale, and Ashwin Nayak. Feel free to ask in the comments about what else is going on.
I returned a few days ago from my whirlwind Australia tour, which included Melbourne and Sydney; a Persian wedding that happened to be held next to a pirate ship (the Steve Irwin, used to harass whalers and adorned with a huge Jolly Roger); meetings and lectures graciously arranged by friends at UTS; a quantum computing lab tour personally conducted by 2018 “Australian of the Year” Michelle Simmons; three meetups with readers of this blog (or more often, readers of the other Scott A’s blog who graciously settled for the discount Scott A); and an excursion to Grampians National Park to see wild kangaroos, wallabies, koalas, and emus.
But the thing that happened in Australia that provided the actual occassion for this post is this: I was interviewed by Adam Ford in Carlton Gardens in Melbourne, about quantum supremacy, AI risk, Integrated Information Theory, whether the universe is discrete or continuous, and to be honest I don’t remember what else. You can watch the first segment, the one about the prospects for quantum supremacy, here on YouTube. My only complaint is that Adam’s video camera somehow made me look like an out-of-shape slob who needs to hit the gym or something.
Update (Jan. 16): Adam has now posted a second video on YouTube, wherein I talk about my “Ghost in the Quantum Turing Machine” paper, my critique of Integrated Information Theory, and more.
And now Adam has posted yet a third segment, in which I talk about small, lighthearted things like existential threats to civilization and the prospects for superintelligent AI.
And a fourth, in which I talk about whether reality is discrete or continuous.
Related to the “free will / consciousness” segment of the interview: the biologist Jerry Coyne, whose blog “Why Evolution Is True” I’ve intermittently enjoyed over the years, yesterday announced my existence to his readers, with a post that mostly criticizes my views about free will and predictability, as I expressed them years ago in a clip that’s on YouTube (at the time, Coyne hadn’t seen GIQTM or my other writings on the subject). Coyne also took the opportunity to poke fun at this weird character he just came across whose “life is devoted to computing” and who even mistakes tips for change at airport smoothie stands. Some friends here at QIP had a good laugh over the fact that, for the world beyond theoretical computer science and quantum information, this is what 23 years of research, teaching, and writing apparently boil down to: an 8.5-minute video clip where I spouted about free will, and also my having been arrested once in a comic mix-up at Philadelphia airport. Anyway, since then I had a very pleasant email exchange with Coyne—someone with whom I find myself in agreement much more often than not, and who I’d love to have an extended conversation with sometime despite the odd way our interaction started.
### Incompleteness ex machina
Sunday, December 30th, 2018
I have a treat with which to impress your friends at New Year’s Eve parties tomorrow night: a rollicking essay graciously contributed by a reader named Sebastian Oberhoff, about a unified and simplified way to prove all of Gödel’s Incompleteness Theorems, as well as Rosser’s Theorem, directly in terms of computer programs. In particular, this improves over my treatments in Quantum Computing Since Democritus and my Rosser’s Theorem via Turing machines post. While there won’t be anything new here for the experts, I loved the style—indeed, it brings back wistful memories of how I used to write, before I accumulated too many imaginary (and non-imaginary) readers tut-tutting at crass jokes over my shoulder. May 2019 bring us all the time and the courage to express ourselves authentically, even in ways that might be sneered at as incomplete, inconsistent, or unsound.
### The NP genie
Tuesday, December 11th, 2018
Hi from the Q2B conference!
Every nerd has surely considered the scenario where an all-knowing genie—or an enlightened guru, or a superintelligent AI, or God—appears and offers to answer any question of your choice. (Possibly subject to restrictions on the length or complexity of the question, to prevent glomming together every imaginable question.) What do you ask?
(Standard joke: “What question should I ask, oh wise master, and what is its answer?” “The question you should ask me is the one you just asked, and its answer is the one I am giving.”)
The other day, it occurred to me that theoretical computer science offers a systematic way to generate interesting variations on the genie scenario, which have been contemplated less—variations where the genie is no longer omniscient, but “merely” more scient than any entity that humankind has ever seen. One simple example, which I gather is often discussed in the AI-risk and rationality communities, is an oracle for the halting problem: what computer program can you write, such that knowing whether it halts would provide the most useful information to civilization? Can you solve global warming with such an oracle? Cure cancer?
But there are many other examples. Here’s one: suppose what pops out of your lamp is a genie for NP questions. Here I don’t mean NP in the technical sense (that would just be a pared-down version of the halting genie discussed above), but in the human sense. The genie can only answer questions by pointing you to ordinary evidence that, once you know where to find it, makes the answer to the question clear to every competent person who examines the evidence, with no further need to trust the genie. Or, of course, the genie could fail to provide such evidence, which itself provides the valuable information that there’s no such evidence out there.
More-or-less equivalently (because of binary search), the genie could do what my parents used to do when my brother and I searched the house for Hanukkah presents, and give us “hotter” or “colder” hints as we searched for the evidence ourselves.
To make things concrete, let’s assume that the NP genie will only provide answers of 1000 characters or fewer, in plain English text with no fancy encodings. Here are the candidates for NP questions that I came up with after about 20 seconds of contemplation:
• Which pieces of physics beyond the Standard Model and general relativity can be experimentally confirmed with the technology of 2018? What are the experiments we need to do?
• What’s the current location of the Ark of the Covenant, or its remains, if any still exist? (Similar: where can we dig to find physical records, if any exist, pertaining to the Exodus from Egypt, or to Jesus of Nazareth?)
• What’s a sketch of a resolution of P vs. NP, from which experts would stand a good chance of filling in the details? (Similar for other any famous unsolved math problem.)
• Where, if anywhere, can we point radio telescopes to get irrefutable evidence for the existence of extraterrestrial life?
• What happened to Malaysia Flight 370, and where are the remains by which it could be verified? (Similar for Amelia Earhart.)
• Where, if anywhere, can we find intact DNA of non-avian dinosaurs?
Which NP questions would you ask the genie? And what other complexity-theoretic genies would be interesting to consider? (I thought briefly about a ⊕P genie, but I’m guessing that the yearning to know whether the number of sand grains in the Sahara is even or odd is limited.)
Update: I just read Lenny Susskind’s Y Combinator interview, and found it delightful—pure Lenny, and covering tons of ground that should interest anyone who reads this blog.
### Teaching quantum in junior high: special Thanksgiving guest post by Terry Rudolph
Thursday, November 22nd, 2018
Happy Thanksgiving!
People have sometimes asked me: “how do you do it? how do you do your research, write papers, teach classes, mentor grad students, build up the quantum center at UT, travel and give talks every week or two, serve on program committees, raise two rambunctious young kids, and also blog and also participate in the comments and also get depressed about people saying mean things on social media?” The answer is that increasingly I don’t. Something has to give, and this semester, alas, that something has often been blogging.
And that’s why, today, I’m delighted to have a special guest post by my good friend Terry Rudolph. Terry, who happens to be Erwin Schrödinger’s grandson, has done lots of fascinating work over the years in quantum computing and the foundations of quantum mechanics, and previously came up on this blog in the context of the PBR (Pusey-Barrett-Rudolph) Theorem. Today, he’s a cofounder and chief architect at PsiQuantum, a startup in Palo Alto that’s trying to build silicon-photonic quantum computers.
Terry’s guest post is about the prospects for teaching quantum theory at the junior high school level—something he thought about a lot in the context of writing his interesting recent book Q is for Quantum. I should stress that the opinions in this post are Terry’s, and don’t necessarily reflect the official editorial positions of Shtetl-Optimized. Personally, I have taught the basics of quantum information to sharp junior high and high school students, so I certainly know that it’s possible. (By undergrad, it’s not only possible, but maybe should become standard for both physics and CS majors.) But I would also say that, given the current state of junior high and high school education in the US, it would be a huge step up if most students graduated fully understanding what’s a probability, what’s a classical bit, what’s a complex number, and any of dozens of other topics that feed into quantum information—so why not start by teaching the simpler stuff well? And also, if students don’t learn the rules of classical probability first, then how will they be properly shocked when they come to quantum? 🙂
Can we/should we teach Quantum Theory in Junior High?
by Terry Rudolph
Should we?
Reasons which suggest the answer is “yes” include:
Economic: We are apparently into a labor market shortage in quantum engineers. We should not, however, need the recent hype around quantum computing to make the economic case – the frontier of many disparate regions of the modern science and technology landscape is quantum. Surely if students do decide to drop out of school at 16 they should at least be equipped to get an entry-level job as a quantum physicist?
Educational: If young peoples’ first exposures to science are counterintuitive and “cutting edge,” it could help excite them into STEM. The strong modern quantum information theoretic connections between quantum physics, computer science and math can help all three subjects constructively generate common interest.
Pseudo-Philosophical: Perhaps our issues with understanding/accepting quantum theory are because we come to it late and have lost the mental plasticity for a “quantum reset” of our brain when we eventually require it late in an undergraduate degree. It may be easier to achieve fluency in the “language of quantum” with early exposure.
Can we?
There are two distinct aspects to this question: Firstly, is it possible at the level of “fitting it in” – training teachers, adjusting curricula and so on? Secondly, can a nontrivial, worthwhile fraction of quantum theory even be taught at all to pre-calculus students?
With regards to the first question, as the child of two schoolteachers I am very aware that an academic advocating for such disruption will not be viewed kindly by all. As I don’t have relevant experience to say anything useful about this aspect, I have to leave it for others to consider.
Let me focus for the remainder of this post on the second aspect, namely whether it is even possible to appropriately simplify the content of the theory. This month it is exactly 20 years since I lectured the first of many varied quantum courses I have taught at multiple universities. For most of that period I would have said it simply wasn’t possible to teach any but the most precocious of high school students nontrivial technical content of quantum theory – despite some brave attempts like Feynman’s use of arrows in QED: The Strange Theory of Light and Matter (a technique that cannot easily get at the mysteries of two-particle quantum theory, which is where the fun really starts). I now believe, however, that it is actually possible.
A pedagogical method covering nontrivial quantum theory using only basic arithmetic
My experience talking about quantum theory to 12-15 year olds has only been in the idealized setting of spending a few hours with them at science fairs, camps and similar. In fact it was on the way to a math camp for very young students, desperately trying to plan something non-trivial to engage them with, that I came up with a pedagogical method which I (and a few colleagues) have found does work.
I eventually wrote the method into a short book Q is for Quantum, but if you don’t want to purchase the book then here is a pdf of Part I,, which takes a student knowing only the rules of basic arithmetic through to learning enough quantum computing they can understand the Deutsch–Jozsa algorithm. In fact not only can they do a calculation to see how it works in detail, they can appreciate conceptual nuances often under-appreciated in popular expositions, such as why gate speed doesn’t matter – it’s all about the number of steps, why classical computing also can have exponential growth in “possible states” so interference is critical, why quantum computers do not compute the uncomputable and so on.
Before pointing out a few features of the approach, here are some rules I set myself while writing the book:
• No analogies, no jargon – if it can’t be explained quantitatively then leave it out.
• No math more than basic arithmetic and distribution across brackets.
• Keep clear the distinction between mathematical objects and the observed physical events they are describing.
• Be interpretationally neutral.
• No soap opera: Motivate by intriguing with science, not by regurgitating quasi-mythological stories about the founders of the theory.
• No using the word “quantum” in the main text! This was partly to amuse myself, but I also thought if I was succeeding in the other points then I should be able to avoid a word almost synonymous with “hard and mysterious.”
One of the main issues to confront is how to represent and explain superposition. It is typical in popular expositions to draw analogies between a superposition of, say, a cat which is dead and a cat which is alive by saying it is dead “and” alive. But if superposition was equivalent to logical “and”, or, for that matter, logical “or”, then quantum computing wouldn’t be interesting, and in this and other ways the analogy is ultimately misleading. The approach I use is closer to the latter – an unordered list of possible states for a system (which is most like an “or”) can be used to represent a superposition. Using a list has some advantages – it is natural to apply a transformation to all elements of a list, for instance doubling the list of ingredients in a recipe. More critically, given two independent lists of possibilities the new joint list of combined possibilities is a natural concept. This makes teaching the equivalent of the Kronecker (tensor) product for multiple systems easy, something often a bit tricky even for undergrads to become comfortable with.
Conceptually the weirdest part of the whole construction, particularly for someone biased by the standard formalism, is that I use a standard mathematical object (a negative or minus sign) applied to a diagram of a physical object (a black or white ball). Moreover, positive and negative balls in a diagram can cancel out (interfere). This greatly simplifies the exposition, by removing a whole level of abstraction in the standard theory (we do not need to use a vector containing entries whose specific ordering must be remembered in order to equate them to the physical objects). While it initially seemed odd to me personally to do this, I have yet to have any young person think of it as any more weird than using the negative sign on a number. And if it is always kept clear that drawing and manipulating the whole diagram is an abstract thing we do, which may or may not have any correspondence to what is “really going on” in the physical setups we are describing, then there really is no difference.
There are some subtleties about the whole approach – while the formalism is universal for quantum computing, it can only make use of unitary evolution which is proportional to a matrix with integer entries. Thus the Hadamard gate (PETE box) is ok, the Controlled-NOT and Toffoli likewise, but a seemingly innocuous gate like the controlled-Hadamard is not capable of being incorporated (without adding a whole bunch of unintuitive and unjustified rules). The fact the approach covers a universal gate set means some amazing things can be explained in this simple diagrammatic language. For example, the recent paper Quantum theory cannot consistently describe the use of itself, which led to considerable discussion on this blog, can be fully reproduced. That is, a high school student can in principle understand the technical details of a contemporary argument between professional physicists. I find this amazing.
Based on communication with readers I have come to realize the people at most risk of being confused by the book are actually those already with a little knowledge – someone who has done a year or two’s worth of undergraduate quantum courses, or someone who has taken things they read in pop-sci books too literally. Initially, as I was developing the method, I thought it would be easy to keep “touching base” with the standard vector space formalism. But in fact it becomes very messy to do so (and irrelevant for someone learning quantum theory for the first time). In the end I dropped that goal, but now realize I need to develop some supplementary notes to help someone in that situation.
Q is for Quantum is certainly not designed to be used as a classroom text – if nothing else my particular style and choice of topics will not be to others’ tastes, and I haven’t included all the many, many simple examples and exercises I have students doing along with me in class when I actually teach this stuff. It should be thought of as more a “proof of principle,” that the expository challenge can be met. Several colleagues have used parts of these ideas already for teaching, and they have given me some great feedback. As such I am planning on doing a revised and slightly expanded version at some point, so if you read it and have thoughts for improvement please send me them.
### Review of Bryan Caplan’s The Case Against Education
Thursday, April 26th, 2018
If ever a book existed that I’d judge harshly by its cover—and for which nothing inside could possibly make me reverse my harsh judgment—Bryan Caplan’s The Case Against Education would seem like it. The title is not a gimmick; the book’s argument is exactly what it says on the tin. Caplan—an economist at George Mason University, home of perhaps the most notoriously libertarian economics department on the planet—holds that most of the benefit of education to students (he estimates around 80%, but certainly more than half) is about signalling the students’ preexisting abilities, rather than teaching or improving the students in any way. He includes the entire educational spectrum in his indictment, from elementary school all the way through college and graduate programs. He does have a soft spot for education that can be shown empirically to improve worker productivity, such as technical and vocational training and apprenticeships. In other words, precisely the kind of education that many readers of this blog may have spent their lives trying to avoid.
I’ve spent almost my whole conscious existence in academia, as a student and postdoc and then as a computer science professor. CS is spared the full wrath that Caplan unleashes on majors like English and history: it does, after all, impart some undeniable real-world skills. Alas, I’m not one of the CS professors who teaches anything obviously useful, like how to code or manage a project. When I teach undergrads headed for industry, my only role is to help them understand concepts that they probably won’t need in their day jobs, such as which problems are impossible or intractable for today’s computers; among those, which might be efficiently solved by quantum computers decades in the future; and which parts of our understanding of all this can be mathematically proven.
Granted, my teaching evaluations have been [clears throat] consistently excellent. And the courses I teach aren’t major requirements, so the students come—presumably?—because they actually want to know the stuff. And my former students who went into industry have emailed me, or cornered me, to tell me how much my courses helped them with their careers. OK, but how? Often, it’s something about my class having helped them land their dream job, by impressing the recruiters with their depth of theoretical understanding. As we’ll see, this is an “application” that would make Caplan smile knowingly.
If Caplan were to get his way, the world I love would be decimated. Indeed, Caplan muses toward the end of the book that the world he loves would be decimated too: in a world where educational investment no longer exceeded what was economically rational, he might no longer get to sit around with other economics professors discussing what he finds interesting. But he consoles himself with the thought that decisionmakers won’t listen to him anyway, so it won’t happen.
It’s tempting to reply to Caplan: “now now, your pessimism about anybody heeding your message seems unwarranted. Have anti-intellectual zealots not just taken control of the United States, with an explicit platform of sticking it to the educated elites, and restoring the primacy of lower-education jobs like coal mining, no matter the long-term costs to the economy or the planet? So cheer up, they might listen to you!”
Indeed, given the current stakes, one might simply say: Caplan has set himself against the values that are the incredibly fragile preconditions for all academic debate—even, ironically, debate about the value of academia, like the one we’re now having. So if we want such debate to continue, then we have no choice but to treat Caplan as an enemy, and frame the discussion around how best to frustrate his goals.
In response to an excerpt of Caplan’s book in The Atlantic, my friend Sean Carroll tweeted:
It makes me deeply sad that a tenured university professor could write something like this about higher education. There is more to learning than the labor market.
Why should anyone with my basic values, or Sean’s, give Caplan’s thesis any further consideration? As far as I can tell, there are only two reasons: (1) common sense, and (2) the data.
And: if the value of education comes from what it teaches you, how do we explain the fact that students forget almost everything so soon after the final exam, as attested by both experience and the data? Why are employers satisfied with a years-ago degree; why don’t they test applicants to see how much understanding they’ve retained?
Or if education isn’t about any of the specific facts being imparted, but about “learning how to learn” or “learning how to think creatively”—then how is it that studies find academic coursework has so little effect on students’ general learning and reasoning abilities either? That, when there is an improvement in reasoning ability, it’s tightly concentrated on the subject matter of the course, and even then it quickly fades away after the course is over?
More broadly, if the value of mass education derives from making people more educated, how do we explain the fact that high-school and college graduates, most of them, remain so abysmally ignorant? After 12-16 years in something called “school,” large percentages of Americans still don’t know that the earth orbits the sun; believe that heavier objects fall faster than lighter ones and that only genetically modified organisms contain genes; and can’t locate the US or China on a map. Are we really to believe, asks Caplan, that these apparent dunces have nevertheless become “deeper thinkers” by virtue of their schooling, in some holistic, impossible-to-measure way? Or that they would’ve been even more ignorant without school? But how much more ignorant can you be? They could be illiterate, yes: Caplan grants the utility of teaching reading, writing, and arithmetic. But how much beyond the three R’s (if those) do typical students retain, let alone use?
Caplan also poses the usual questions: if you’re not a scientist, engineer, or academic (or even if you are), how much of your undergraduate education do you use in your day job? How well did the course content match what, in retrospect, you feel someone starting your job really needs to know? Could your professors do your job? If not, then how were they able to teach you to do it better?
Caplan acknowledges the existence of inspiring teachers who transform their students’ lives, in ways that need not be reflected in their paychecks: he mentions Robin Williams’ character in The Dead Poets’ Society. But he asks: how many such teachers did you have? If the Robin Williamses are vastly outnumbered by the drudges, then wouldn’t it make more sense for students to stream the former directly into their homes via the Internet—as they can now do for free?
OK, but if school teaches so little, then how do we explain the fact that, at least for those students who are actually able to complete good degrees, research confirms that (on average) having gone to school really does pay, exactly as advertised? Employers do pay more for a college graduate—yes, even an English or art history major—than for a dropout. More generally, starting salary rises monotonically with level of education completed. Employers aren’t known for a self-sacrificing eagerness to overpay. Are they systematically mistaken about the value of school?
Synthesizing decades of work by other economists, Caplan defends the view that the main economic function of school is to give students a way to signal their preexisting qualities, ones that correlate with being competent workers in a modern economy. I.e., that school is tacitly a huge system for winnowing and certifying young people, which also fulfills various subsidiary functions, like keeping said young people off the street, socializing them, maybe occasionally even teaching them something. Caplan holds that, judged as a certification system, school actually works—well enough to justify graduates’ higher starting salaries, without needing to postulate any altruistic conspiracy on the part of employers.
For Caplan, a smoking gun for the signaling theory is the huge salary premium of an actual degree, compared to the relatively tiny premium for each additional year of schooling other than the degree year—even when we hold everything else constant, like the students’ academic performance. In Caplan’s view, this “sheepskin effect” even lets us quantitatively estimate how much of the salary premium on education reflects actual student learning, as opposed to the students signaling their suitability to be hired in a socially approved way (namely, with a diploma or “sheepskin”).
Caplan knows that the signaling story raises an immediate problem: namely, if employers just want the most capable workers, then knowing everything above, why don’t they eagerly recruit teenagers who score highly on the SAT or IQ tests? (Or why don’t they make job offers to high-school seniors with Harvard acceptance letters, skipping the part where the seniors have to actually go to Harvard?)
Some people think the answer is that employers fear getting sued: in the 1971 Griggs vs. Duke Power case, the US Supreme Court placed restrictions on the use of intelligence tests in hiring, because of disparate impact on minorities. Caplan, however, rejects this explanation, pointing out that it would be child’s-play for employers to design interview processes that functioned as proxy IQ tests, were that what the employers wanted.
Caplan’s theory is instead that employers don’t value only intelligence. Instead, they care about the conjunction of intelligence with two other traits: conscientiousness and conformity. They want smart workers who will also show up on time, reliably turn in the work they’re supposed to, and jump through whatever hoops authorities put in front of them. The main purpose of school, over and above certifying intelligence, is to serve as a hugely costly and time-consuming—and therefore reliable—signal that the graduates are indeed conscientious conformists. The sheer game-theoretic wastefulness of the whole enterprise rivals the peacock’s tail or the bowerbird’s ornate bower.
But if true, this raises yet another question. In the signaling story, graduating students (and their parents) are happy that the students’ degrees land them good jobs. Employers are happy that the education system supplies them with valuable workers, pre-screened for intelligence, conscientiousness, and conformity. Even professors are happy that they get paid to do research and teach about topics that interest them, however irrelevant those topics might be to the workplace. So if so many people are happy, who cares if, from an economic standpoint, it’s all a big signaling charade, with very little learning taking place?
For Caplan, the problem is this: because we’ve all labored under the mistaken theory that education imparts vital skills for a modern economy, there are trillions of dollars of government funding for every level of education—and that, in turn, removes the only obstacle to a credentialing arms race. The equilbrium keeps moving over the decades, with more and more years of mostly-pointless schooling required to prove the same level of conscientiousness and conformity as before. Jobs that used to require only a high-school diploma now require a bachelors; jobs that used to require only a bachelors now require a masters, and so on—despite the fact that the jobs themselves don’t seem to have changed appreciably.
For Caplan, a thoroughgoing libertarian, the solution is as obvious as it is radical: abolish government funding for education. (Yes, he explicitly advocates a complete “separation of school and state.”) Or if some state role in education must be retained, then let it concentrate on the three R’s and on practical job skills. But what should teenagers do, if we’re no longer urging them to finish high school? Apparently worried that he hasn’t yet outraged liberals enough, Caplan helpfully suggests that we relax the laws around child labor. After all, he says, if we’ve decided anyway that teenagers who aren’t academically inclined should suffer through years of drudgery, then instead of warming a classroom seat, why shouldn’t they apprentice themselves to a carpenter or a roofer? That way they could contribute to the economy, and gain the independence from their parents that most of them covet, and learn skills that they’d be much more likely to remember and use than the dissection of owl pellets. Even if working a real job involved drudgery, at least it wouldn’t be as pointless as the drudgery of school.
Given his conclusions, and the way he arrives at them, Caplan realizes that he’ll come across to many as a cartoon stereotype of a narrow-minded economist, who “knows the price of everything but the value of nothing.” So he includes some final chapters in which, setting aside the charts and graphs, he explains how he really feels about education. This is the context for what I found to be the most striking passages in the book:
I am an economist and a cynic, but I’m not a typical cynical economist. I’m a cynical idealist. I embrace the ideal of transformative education. I believe wholeheardedly in the life of the mind. What I’m cynical about is people … I don’t hate education. Rather I love education too much to accept our Orwellian substitute. What’s Orwellian about the status quo? Most fundamentally, the idea of compulsory enlightenment … Many idealists object that the Internet provides enlightenment only for those who seek it. They’re right, but petulant to ask for more. Enlightenment is a state of mind, not a skill—and state of mind, unlike skill, is easily faked. When schools require enlightenment, students predictably respond by feigning interest in ideas and culture, giving educators a false sense of accomplishment. (p. 259-261)
OK, but if one embraces the ideal, then rather than dynamiting the education system, why not work to improve it? According to Caplan, the answer is that we don’t know whether it’s even possible to build a mass education system that actually works (by his lights). He says that, if we discover that we’re wasting trillions of dollars on some sector, the first order of business is simply to stop the waste. Only later should we entertain arguments about whether we should restart the spending in some new, better way, and we shouldn’t presuppose that the sector in question will win out over others.
Above, I took pains to set out Caplan’s argument as faithfully as I could, before trying to pass judgment on it. At some point in a review, though, the hour of judgment arrives.
I think Caplan gets many things right—even unpopular things that are difficult for academics to admit. It’s true that a large fraction of what passes for education doesn’t deserve the name—even if, as a practical matter, it’s far from obvious how to cut that fraction without also destroying what’s precious and irreplaceable. He’s right that there’s no sense in badgering weak students to go to college if those students are just going to struggle and drop out and then be saddled with debt. He’s right that we should support vocational education and other non-traditional options to serve the needs of all students. Nor am I scandalized by the thought of teenagers apprenticing themselves to craftspeople, learning skills that they’ll actually value while gaining independence and starting to contribute to society. This, it seems to me, is a system that worked for most of human history, and it would have to fail pretty badly in order to do worse than, let’s say, the average American high school. And in the wake of the disastrous political upheavals of the last few years, I guess the entire world now knows that, when people complain that the economy isn’t working well enough for non-college-graduates, we “technocratic elites” had better have a better answer ready than “well then go to college, like we did.”
Yes, probably the state has a compelling interest in trying to make sure nearly everyone is literate, and probably most 8-year-olds have no clue what’s best for themselves. But at least from adolescence onward, I think that enormous deference ought to be given to students’ choices. The idea that “free will” (in the practical rather than metaphysical sense) descends on us like a halo on our 18th birthdays, having been absent beforehand, is an obvious fiction. And we all know it’s fiction—but it strikes me as often a destructive fiction, when law and tradition force us to pretend that we believe it.
Some of Caplan’s ideas dovetail with the thoughts I’ve had myself since childhood on how to make the school experience less horrible—though I never framed my own thoughts as “against education.” Make middle and high schools more like universities, with freedom of movement and a wide range of offerings for students to choose from. Abolish hall passes and detentions for lateness: just like in college, the teacher is offering a resource to students, not imprisoning them in a dungeon. Don’t segregate by age; just offer a course or activity, and let kids of any age who are interested show up. And let kids learn at their own pace. Don’t force them to learn things they aren’t ready for: let them love Shakespeare because they came to him out of interest, rather than loathing him because he was forced down their throats. Never, ever try to prevent kids from learning material they are ready for: instead of telling an 11-year-old teaching herself calculus to go back to long division until she’s the right age (does that happen? ask how I know…), say: “OK hotshot, so you can differentiate a few functions, but can you handle these here books on linear algebra and group theory, like Terry Tao could have when he was your age?”
Caplan mentions preschool as the one part of the educational system that strikes him as least broken. Not because it has any long-term effects on kids’ mental development (it might not), just because the tots enjoy it at the time. They get introduced to a wide range of fun activities. They’re given ample free time, whether for playing with friends or for building or drawing by themselves. They’re usually happy to be dropped off. And we could add: no one normally minds if parents drop their kids off late, or pick them up early, or take them out for a few days. The preschool is just a resource for the kids’ benefit, not a never-ending conformity test. As a father who’s now seen his daughter in three preschools, this matches my experience.
Having said all this, I’m not sure I want to live in the world of Caplan’s “complete separation of school and state.” And I’m not using “I’m not sure” only as a euphemism for “I don’t.” Caplan is proposing a radical change that would take civilization into uncharted territory: as he himself notes, there’s not a single advanced country on earth that’s done what he advocates. The trend has everywhere been in the opposite direction, to invest more in education as countries get richer and more technology-based. Where there have been massive cutbacks to education, the causes have usually been things like famine or war.
So I have the same skepticism of Caplan’s project that I’d have (ironically) of Bolshevism or any other revolutionary project. I say to him: don’t just persuade me, show me. Show me a case where this has worked. In the social world, unlike the mathematical world, I put little stock in long chains of reasoning unchecked by experience.
Caplan explicitly invites his readers to test his assertions against their own lives. When I do so, I come back with a mixed verdict. Before college, as you may have gathered, I find much to be said for Caplan’s thesis that the majority of school is makework, the main purposes of which are to keep the students out of trouble and on the premises, and to certify their conscientiousness and conformity. There are inspiring teachers here and there, but they’re usually swimming against the tide. I still feel lucky that I was able to finagle my way out by age 15, and enter Clarkson University and then Cornell with only a G.E.D.
In undergrad, on the other hand, and later in grad school at Berkeley, my experience was nothing like what Caplan describes. The professors were actual experts: people who I looked up to or even idolized. I wanted to learn what they wanted to teach. (And if that ever wasn’t the case, I could switch to a different class, excepting some major requirements.) But was it useful?
As I look back, many of my math and CS classes were grueling bootcamps on how to prove theorems, how to design algorithms, how to code. Most of the learning took place not in the classroom but alone, in my dorm, as I struggled with the assignments—having signed up for the most advanced classes that would allow me in, and thereby left myself no escape except to prove to the professor that I belonged there. In principle, perhaps, I could have learned the material on my own, but in reality I wouldn’t have. I don’t still use all of the specific tools I acquired, though I do still use a great many of them, from the Gram-Schmidt procedure to Gaussian integrals to finding my way around a finite group or field. Even if I didn’t use any of the tools, though, this gauntlet is what upgraded me from another math-competition punk to someone who could actually write research papers with long proofs. For better or worse, it made me what I am.
Just as useful as the math and CS courses were the writing seminars—places where I had to write, and where my every word got critiqued by the professor and my fellow students, so I had to do a passable job. Again: intensive forced practice in what I now do every day. And the fact that it was forced was now fine, because, like some leather-bound masochist, I’d asked to be forced.
On hearing my story, Caplan would be unfazed. Of course college is immensely useful, he’d say … for those who go on to become professors, like me or him. He “merely” questions the value of higher education for almost everyone else.
OK, but if professors are at least good at producing more people like themselves, able to teach and do research, isn’t that something, a base we can build on that isn’t all about signaling? And more pointedly: if this system is how the basic research enterprise perpetuates itself, then shouldn’t we be really damned careful with it, lest we slaughter the golden goose?
Except that Caplan is skeptical of the entire enterprise of basic research. He writes:
Researchers who specifically test whether education accelerates progress have little to show for their efforts. One could reply that, given all the flaws of long-run macroeconomic data, we should ignore academic research in favor of common sense. But what does common sense really say? … True, ivory tower self-indulgence occasionally revolutionizes an industry. Yet common sense insists the best way to discover useful ideas is to search for useful ideas—not to search for whatever fascinates you and pray it turns out to be useful (p. 175).
I don’t know if common sense insists that, but if it does, then I feel on firm ground to say that common sense is woefully inadequate. It’s easy to look at most basic research, and say: this will probably never be useful for anything. But then if you survey the inventions that did change the world over the past century—the transistor, the laser, the Web, Google—you find that almost none would have happened without what Caplan calls “ivory tower self-indulgence.” What didn’t come directly from universities came from entities (Bell Labs, DARPA, CERN) that wouldn’t have been thinkable without universities, and that themselves were largely freed from short-term market pressures by governments, like universities are.
Caplan’s skepticism of basic research reminded me of a comment in Nick Bostrom’s book Superintelligence:
A colleague of mine likes to point out that a Fields Medal (the highest honor in mathematics) indicates two things about the recipient: that he was capable of accomplishing something important, and that he didn’t. Though harsh, the remark hints at a truth. (p. 314)
I work in theoretical computer science: a field that doesn’t itself win Fields Medals (at least not yet), but that has occasions to use parts of math that have won Fields Medals. Of course, the stuff we use cutting-edge math for might itself be dismissed as “ivory tower self-indulgence.” Except then the cryptographers building the successors to Bitcoin, or the big-data or machine-learning people, turn out to want the stuff we were talking about at conferences 15 years ago—and we discover to our surprise that, just as the mathematicians gave us a higher platform to stand on, so we seem to have built a higher platform for the practitioners. The long road from Hilbert to Gödel to Turing and von Neumann to Eckert and Mauchly to Gates and Jobs is still open for traffic today.
Yes, there’s plenty of math that strikes even me as boutique scholasticism: a way to signal the brilliance of the people doing it, by solving problems that require years just to understand their statements, and whose “motivations” are about 5,000 steps removed from anything Caplan or Bostrom would recognize as motivation. But where I part ways is that there’s also math that looked to me like boutique scholasticism, until Greg Kuperberg or Ketan Mulmuley or someone else finally managed to explain it to me, and I said: “ah, so that’s why Mumford or Connes or Witten cared so much about this. It seems … almost like an ordinary applied engineering question, albeit one from the year 2130 or something, being impatiently studied by people a few moves ahead of everyone else in humanity’s chess game against reality. It will be pretty sweet once the rest of the world catches up to this.”
I have a more prosaic worry about Caplan’s program. If the world he advocates were actually brought into being, I suspect the people responsible wouldn’t be nerdy economics professors like himself, who have principled objections to “forced enlightenment” and to signalling charades, yet still maintain warm fuzzies for the ideals of learning. Rather, the “reformers” would be more on the model of, say, Steve Bannon or Scott Pruitt or Alex Jones: people who’d gleefully take a torch to the universities, fortresses of the despised intellectual elite, not in the conviction that this wouldn’t plunge humanity back into the Dark Ages, but in the hope that it would.
When the US Congress was debating whether to cancel the Superconducting Supercollider, a few condensed-matter physicists famously testified against the project. They thought that $10-$20 billion for a single experiment was excessive, and that they could provide way more societal value with that kind of money were it reallocated to them. We all know what happened: the SSC was cancelled, and of the money that was freed up, 0%—absolutely none of it—went to any of the other research favored by the SSC’s opponents.
If Caplan were to get his way, I fear that the story would be similar. Caplan talks about all the other priorities—from feeding the world’s poor to curing diseases to fixing crumbling infrastructure—that could be funded using the trillions currently wasted on runaway credential signaling. But in any future I can plausibly imagine where the government actually axes education, the savings go to things like enriching the leaders’ cronies and launching vanity wars.
My preferences for American politics have two tiers. In the first tier, I simply want the Democrats to vanquish the Republicans, in every office from president down to dogcatcher, in order to prevent further spiraling into nihilistic quasi-fascism, and to restore the baseline non-horribleness that we know is possible for rich liberal democracies. Then, in the second tier, I want the libertarians and rationalists and nerdy economists and Slate Star Codex readers to be able to experiment—that’s a key word here—with whether they can use futarchy and prediction markets and pricing-in-lieu-of-regulation and other nifty ideas to improve dramatically over the baseline liberal order. I don’t expect that I’ll ever get what I want; I’ll be extremely lucky even to get the first half of it. But I find that my desires regarding Caplan’s program fit into the same mold. First and foremost, save education from those who’d destroy it because they hate the life of the mind. Then and only then, let people experiment with taking a surgical scalpel to education, removing from it the tumor of forced enlightenment, because they love the life of the mind.
### Amazing progress on longstanding open problems
Wednesday, April 11th, 2018
For those who haven’t seen it:
1. Aubrey de Grey, better known to the world as a radical life extension researcher, on Sunday posted a preprint on the arXiv claiming to prove that the chromatic number of the plane is at least 5—the first significant progress on the Hadwiger-Nelson problem since 1950. If you’re tuning in from home, the Hadwiger-Nelson problem asks: what’s the minimum number of colors that you need to color the Euclidean plane, in order to ensure that every two points at distance exactly 1 from each other are colored differently? It’s not hard to show that at least 4 colors are necessary, or that 7 colors suffice: try convincing yourself by staring at the figure below. Until a few days ago, nothing better was known.
This is a problem that’s intrigued me ever since I learned about it at a math camp in 1996, and that I spent at least a day of my teenagerhood trying to solve.
De Grey constructs an explicit graph with unit distances—originally with 1567 vertices, now with 1585 vertices after after a bug was fixed—and then verifies by computer search (which takes a few hours) that 5 colors are needed for it. Update: My good friend Marijn Heule, at UT Austin, has now apparently found a smaller such graph, with “only” 874 vertices. See here.
So, can we be confident that the proof will stand—i.e., that there are no further bugs? See the comments of Gil Kalai’s post for discussion. Briefly, though, it’s now been independently verified, using different SAT-solvers, that the chromatic number of de Grey’s corrected graph is indeed 5. Paul Phillips emailed to tell me that he’s now independently verified that the graph is unit distance as well. So I think it’s time to declare the result correct.
Question for experts: is there a general principle by which we can show that, if the chromatic number of the plane is at least 6, or is 7, then there exists a finite subgraph that witnesses it? (This is closely related to asking, what’s the logical complexity of the Hadwiger-Nelson problem: is it Π1?) Update: As de Grey and a commenter pointed out to me, this is the de Bruijn-Erdös Theorem from 1951. But the proofs inherently require the Axiom of Choice. Assuming AC, this also gives you that Hadwiger-Nslson is a Π1 statement, since the coordinates of the points in any finite counterexample can be assumed to be algebraic. However, this also raises the strange possibility that the chromatic number of the plane could be smaller assuming AC than not assuming it.
2. Last week, Urmila Mahadev, a student (as was I, oh so many years ago) of Umesh Vazirani at Berkeley, posted a preprint on the arXiv giving a protocol for a quantum computer to prove the results of any computation it performs to a classical skeptic—assuming a relatively standard cryptographic assumption, namely the quantum hardness of the Learning With Errors (LWE) problem, and requiring only classical communication between the skeptic and the QC. I don’t know how many readers remember, but way back in 2006, inspired by a $25,000 prize offered by Stephen Wolfram, I decided to offer a$25 prize to anyone who could solve the problem of proving the results of an arbitrary quantum computation to a classical skeptic, or who could give oracle evidence that a solution was impossible. I had first learned this fundamental problem from Daniel Gottesman.
Just a year or two later, independent work of Aharonov, Ben-Or, and Eban, and of Broadbent, Fitzsimons, and Kashefi made a major advance on the problem, by giving protocols that were information-theoretically secure. The downside was that, in contrast to Mahadev’s new protocol, these earlier protocols required the verifier to be a little bit quantum: in particular, to exchange individual unentangled qubits with the QC. Or, as shown by later work, the verifier could be completely classical, but only if it could send challenges to two or more quantum computers that were entangled but unable to communicate with each other. In light of these achievements, I decided to award both groups their own checks for half the prize amount ($12.50), to be split among themselves however they chose. Neither with Broadbent et al.’s or Aharonov et al.’s earlier work, nor with Mahadev’s new work, is it immediately clear whether the protocols relativize (that is, whether they work relative to an arbitrary oracle), but it’s plausible that they don’t. Anyway, assuming that her breakthrough result stands, I look forward to awarding Urmila the full$25 prize when I see her at the Simons Institute in Berkeley this June.
Huge congratulations to Aubrey and Urmila for their achievements!
Update (April 12): My friend Virgi Vassilevska Williams asked me to announce a theoretical computer science women event, which will take during the upcoming STOC in LA.
Another Update: Another friend, Holden Karnofsky of the Open Philanthropy Project, asked me to advertise that OpenPhil is looking to hire a Research Analyst and Senior Research Analyst. See also this Medium piece (“Hiring Analytical Thinkers to Help Give Away Billions”) to learn more about what the job would involve.
### Two announcements
Saturday, April 7th, 2018
Before my next main course comes out of the oven, I bring you two palate-cleansing appetizers:
1. My childhood best friend Alex Halderman, whose heroic exploits helping to secure the world’s voting systems have often been featured on this blog, now has a beautifully produced video for the New York Times, entitled “I Hacked An Election. So Can The Russians.” Here Alex lays out the case for an audited paper trail—i.e., for what the world’s cybersecurity experts have been unanimously flailing their arms about for two decades—in terms so simple and vivid that even Congresspeople should be able to understand them. Please consider sharing the video if you support this important cause.
2. Jakob Nordstrom asked me to advertise the 5th Swedish Summer School in Computer Science, to be held August 5-11, 2018, in the beautiful Stockholm archipelago at Djuronaset. This year the focus is on quantum computing, and the lecturers are two of my favorite people in the entire field: Ronald de Wolf (giving a broad intro to QC) and Oded Regev (lecturing on post-quantum cryptography). The school is mainly for PhD students, but is also open to masters students, postdocs, and faculty. If you wanted to spend one week getting up to speed on quantum, it’s hard for me to imagine that you’d find any opportunity more excellent. The application deadline is April 20, so apply now if you’re interested!
### 30 of my favorite books
Wednesday, March 28th, 2018
Scott, if you had to make a list of your favourite books, which ones would you include?
And yes, you can put in quantum computing since Democritus!
Since I’ve gotten the same request before, I guess this is as good a time as any. My ground rules:
• I’ll only include works because I actually read them and they had a big impact on me at some point in my life—not because I feel abstractly like they’re important or others should read them, or because I want to be seen as the kind of person who recommends them.
• But not works that impacted me before the age of about 10, since my memory of childhood reading habits is too hazy.
• To keep things manageable, I’ll include at most one work per author. My choices will often be idiosyncratic—i.e., not that author’s “best” work. However, it’s usually fair to assume that if I include something by X, then I’ve also read and enjoyed other works by X, and that I might be including this work partly just as an entry point into X’s oeuvre.
• In any case where the same author has both “deeper” and more “accessible” works, both of which I loved, I’ll choose the more accessible. But rest assured that I also read the deeper work. 🙂
• This shouldn’t need to be said, but since I know it does: listing a work by author X does not imply my agreement with everything X has ever said about every topic.
• The Bible, the Homeric epics, Plato, and Shakespeare are excluded by fiat. They’re all pretty important (or so one hears…), and you should probably read them all, but I don’t want the responsibility of picking and choosing from among them.
• No books about the Holocaust, or other unremittingly depressing works like 1984. Those are a special category to themselves: I’m glad that I read them, but would never read them twice.
• The works are in order of publication date, with a single exception (see if you can spot it!).
Quantum Computing Since Democritus by Scott Aaronson
Dialogue Concerning the Two Chief World Systems by Galileo Galilei
Dialogues Concerning Natural Religion by David Hume
The Adventures of Huckleberry Finn by Mark Twain
The Subjection of Women by John Stuart Mill
The Autobiography of Charles Darwin by himself
Altneuland by Theodor Herzl
The Practice and Theory of Bolshevism by Bertrand Russell
What Is Life?: With Mind and Matter and Autobiographical Sketches by Erwin Schrödinger
Fads and Fallacies in the Name of Science by Martin Gardner
How Children Fail by John Holt
Set Theory and the Continuum Hypothesis by Paul Cohen
The Gods Themselves by Isaac Asimov (specifically, the middle third)
A History of Pi by Petr Beckmann
The Selfish Gene by Richard Dawkins
The Mind-Body Problem by Rebecca Goldstein
Alan Turing: The Enigma by Andrew Hodges
Surely You’re Joking Mr. Feynman by Richard Feynman
The Book of Numbers by John Conway and Richard Guy
The Demon-Haunted World by Carl Sagan
Gems of Theoretical Computer Science by Uwe Schöning and Randall Pruim
Fashionable Nonsense by Alan Sokal and Jean Bricmont
Our Dumb Century by The Onion
Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang
The Blank Slate by Steven Pinker
Field Notes from a Catastrophe by Elizabeth Kolbert
Infidel by Ayaan Hirsi Ali
The Beginning of Infinity by David Deutsch
You’re welcome to argue with me in the comments, e.g., by presenting evidence that I didn’t actually like these books. 🙂 More seriously: list your own favorites, discuss your reactions to these books, be a “human recommendation engine” by listing books that “those who liked the above would also enjoy,” whatever.
Addendum: Here’s another bonus twenty books, as I remember more and as commenters remind me of more that I liked quite as much as the thirty above.
The Man Who Knew Infinity by Robert Kanigel
A Mathematician’s Apology by G. H. Hardy
A Confederacy of Dunces by John Kennedy Toole
The First Three Minutes by Steven Weinberg
Breaking the Code by Hugh Whitemore
Adventures of a Mathematician by Stanislaw Ulam
The Man Who Loved Only Numbers by Paul Hoffman
Mathematical Writing by Donald Knuth, Tracy Larabee, and Paul Roberts
A Beautiful Mind by Sylvia Nasar
An Introduction to Computational Learning Theory by Michael Kearns and Umesh Vazirani
The Road to Reality by Roger Penrose
The Nili Spies by Anita Engle (about the real-life heroic exploits of the Aaronsohn family)
Artificial Intelligence: A Modern Approach by Stuart Russell and Peter Norvig
The Princeton Companion to Mathematics edited by Timothy Gowers
The Making of the Atomic Bomb by Richard Rhodes
Fear No Evil by Natan Sharansky
The Mind’s I by Douglas Hofstadter and Daniel Dennett
Disturbing the Universe by Freeman Dyson
Unsong by Scott Alexander
### Hawking
Friday, March 16th, 2018
A long post is brewing (breaking my month-long silence), but as I was working on it, the sad news arrived that Stephen Hawking passed away. There’s little I can add to the tributes that poured in from around the world: like chocolate or pizza, Hawking was beloved everywhere and actually deserved to be. Like, probably, millions of other nerds of my generation, I read A Brief History of Time as a kid and was inspired by it (though I remember being confused back then about the operational meaning of imaginary time, and am still confused about it almost 30 years later). In terms of a scientist capturing the public imagination, through a combination of genuine conceptual breakthroughs, an enthralling personal story, an instantly recognizable countenance, and oracular pronouncements on issues of the day, the only one in the same league was Einstein. I didn’t agree with all of Hawking’s pronouncements, but the quibbles paled beside the enormous areas of agreement. Hawking was a force for good in the world, and for the values of science, reason, and Enlightenment (to anticipate the subject of my next post).
I’m sorry that I never really met Hawking, though I did participate in two conferences that he also attended, and got to watch him slowly form sentences on his computer. At one conference in 2011, he attended my talk—this one—and I was told by mutual acquaintances that he liked it. That meant more to me than it probably should have: who cares if some random commenters on YouTube dissed your talk, if the Hawk-Man himself approved?
As for Hawking’s talks—well, there’s a reason why they filled giant auditoriums all over the world. Any of us in the business of science popularization would do well to study them and take lessons.
If you want a real obituary of Hawking, by someone who knew him well—one that, moreover, actually explains his main scientific contributions (including the singularity theorems, Hawking radiation, and the no-boundary proposal)—you won’t do any better than this by Roger Penrose. Also don’t miss this remembrance in Time by Hawking’s friend and betting partner, and friend-of-the-blog, John Preskill. (Added: and this by Sean Carroll.)
### Practicing the modus ponens of Twitter
Monday, January 29th, 2018
I saw today that Ryan Lackey generously praised my and Zach Weinersmith’s quantum computing SMBC comic on Twitter:
Somehow this SMBC comic is the best explanation of quantum computing for non-professionals that I’ve ever found
To which the venture capitalist Matthew Ocko replied, in another tweet:
Except Scott Aaronson is a surly little troll who has literally never built anything at all of meaning. He’s a professional critic of braver people. So, no, this is not a good explanation – anymore than Jeremy Rifkin on CRISPR would be…
Now, I don’t mind if Ocko hates me, and also hates my and Zach’s comic. What’s been bothering me is just the logic of his tweet. Like: what did he have in his head when he wrote the word “So”? Let’s suppose for the sake of argument that I’m a “surly little troll,” and an ax murderer besides. How does it follow that my explanation of quantum computing wasn’t good? To reach that stop in proposition-space, wouldn’t one still need to point to something wrong with the explanation?
But I’m certain that my inability to understand this is just another of my many failings. In a world where Trump is president, bitcoin is valued at \$11,000 when I last checked, and the attack-tweet has fully replaced the argument, it’s obvious that those of us who see a word like “so” or “because,” and start looking for the inferential step, are merely insufficiently brave. For godsakes, I’m not even on Twitter! I’m a sclerotic dinosaur who needs to get with the times.
But maybe I, too, could learn the art of the naked ad-hominem. Let me try: from a Google search, we learn that Ocko is an enthusiastic investor in D-Wave. Is it possible he’s simply upset that there’s so much excitement right now in experimental quantum computing—including “things of meaning” being built by brave people, at Google and IBM and Rigetti and IonQ and elsewhere—but that virtually none of this involves D-Wave, whose devices remain interesting from various physics and engineering standpoints, but still fail to achieve any clear quantum speedups, just as the professional critics predicted? Is he upset that the brave system-builders who are racing finally to achieve quantum computational supremacy over the next year, are the ones who actually interacted with academic researchers (sorry: surly little trolls), and listened to what they said? Who understood, for example, why scaling up to 50+ qubits only made a lot of sense once you had one or two qubits that at least behaved well enough in isolation—which, after years of heroic effort, many of these system-builders now do?
How’d I do? Was there still too much argument there for the world of 2018? | 2019-02-21 03:54:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38205358386039734, "perplexity": 2180.8681307306006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1550247499009.48/warc/CC-MAIN-20190221031117-20190221053117-00380.warc.gz"} |
https://www.networkpages.nl/synchrony-animation/ | # The two community Kuramoto model - Animation
In the interactive simulation below, developed by Martijn Gosgens, you can see how the two-community Kuramoto model works.
In the simulation you are able to adjust a variety of parameters of the model before starting the simulation and seeing what happens. The first parameters you can adjust are the number of nodes (colored dots) in each community. $N_{1}$ represents the number of nodes in the red community and $N_{2}$ the number of nodes in the green community. Next you are able to adjust the strength with which red nodes attract other red nodes ($K_{1}$) and the strength with which green nodes attract other green nodes ($K_{2}$). We are predominantly interested in cases where both $K_{1}$ and $K_{2}$ are positive (but feel free to experiment with negative, i.e. repulsive, $K$’s). The parameters $L_{1}$ and $L_{2}$ are the strength with which red nodes are attracted (or repulsed) by green nodes and the strength with which green nodes are attracted by red nodes respectively. When these are positive the interaction between the two communities is attractive, when they are negative the interaction is repulsive. The last model parameter you can adjust is the noise strength, $D$. This should be greater than or equal to zero and it adjusts the amount that the nodes jiggle. Making $D$ larger makes the nodes jiggle more.
In the next bit of the simulation you can adjust how the dots will be placed on the circle initially (when the simulation starts) as well as the natural properties of the oscillators. With the “Frequencies” option you can select “constant zero” or “standard normal”. Selecting “constant zero” gives each dot the property that it would stand still if there where no other dots and selecting “standard normal” gives each dot its own speed it would rotate around the circle with (drawn from a normal distribution). Finally, you can change how the dots start on the circle. The initial positions are taken randomly from two (normal) distributions. By changing $u_{1}$ and $u_{2}$ you adjust the mean of these distributions and by adjusting the slider for $r_{1}$ and $r_{2}$ you adjust how peaked (concentrated) the distribution is.
Let’s consider an example: We will set the number of nodes to 200 per community. We will set both $K_1$ and $K_2$ to 5, both $L_1$ and $L_2$ to -2 and $D$ to 1. Next we take the Frequencies to be “constant zero”, set both $u$’s to 0 and both $r$’s to 0.75. This means that the nodes will initially be fairly concentrated (an $r$ of 1 would be that they are all on the same spot, while 0 is completely spread out on the circle) around the zero point on the circle (the right most point on the circle).
Now click on “Restart Simulation” (maybe restart it a couple of times to check if what you see is repeatable). What do you observe? Why? What happens when you change $L_{1}$ to 2 and $L_{2}$ to -3? What do you observe if you choose different values for $r_1, r_2$? Take some time to play around with the simulation.
Click here to have a look at the mathematics behind this simulation! | 2020-08-13 08:20:14 | {"extraction_info": {"found_math": true, "script_math_tex": 28, "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": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6909148097038269, "perplexity": 412.8027810932895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738964.20/warc/CC-MAIN-20200813073451-20200813103451-00331.warc.gz"} |
https://www.ias.ac.in/listing/bibliography/pram/Suneel_Kumar | • Suneel Kumar
Articles written in Pramana – Journal of Physics
• The simulations of Ca-Ca collisions: Binary break-up, onset of multifragmentation and vaporization
The incomplete fusion, onset of multifragmentation and vaporization is studied in Ca-Ca collisions at bombarding energies between 20–1000 A MeV and at impact parameters between b=0 to bmax using quantum molecular dynamics model. We find incomplete fusion events at E/A=20 MeV. The light mass fragment production at a given incident energy does not show any rise and fall with a change in the impact parameter. Whereas, the IMF production at higher energies (≥ 150 A MeV) has a clear rise and fall.
• Fragment production in 16O+80Br reaction within dynamical microscopic theory
We analyze the formation of fragments in O—Br reaction at different incident energies between E/A=50 MeV and 200 MeV. This study is carried out within the quantum molecular dynamics (QMD) model coupled with recently advanced simulated annealing clusterization algorithm (SACA). For comparison, we also use the conventional minimum spanning tree (MST) method. Our detailed study shows that the SACA can detect the final stable fragment configuration as early as 60 fin/c which is marked by a dip in the heaviest fragment. On the other hand, the MST method needs several hundred fm/c to identify the final stable distribution. A comparison of the charge distribution with experimental data shows that the SACA is able to reproduce the data very nicely whereas (as reported earlier) the MST method fails to break the spectator matter into intermediate mass fragments. Furthermore, our results with SACA method indicate the onset of multi-fragmentation around 75 MeV/A which is again in good agreement with experimental findings.
• A comparative study of model ingredients: Fragmentation in heavy-ion collisions using quantum molecular dynamics model
We aim to understand the role of NN cross-sections, equation of state as well as different model ingredients such as width of Gaussian, clusterization range and different clusterization algorithms in multifragmentation using quantum molecular dynamics model. We notice that all model ingredients have sizable effect on the fragment pattern.
• On the elliptic flow for nearly symmetric collisions and nuclear equation of state
We present the results of elliptic flow for the collision of nearly symmetric nuclei (10Ne20+13Al27, 18Ar40+21Sc45, 30Zn64+28Ni58, 36Kr86+41Nb93) using the quantum molecular dynamics (QMD) model. General features of elliptic flow are investigated with the help of theoretical simulations. The simulations are performed at beam energies between 45 and 105 MeV/nucleon. A significant change can be seen from in-plane to out-of-plane elliptic flow of different fragments with incident energy. A comparison with experimental data is also made. Further, we show that elliptic flow for different fragments follows power-law dependence as given by the function $C(A_{\text{tot}})^{\tau}$.
• Energy of vanishing flow in heavy-ion collisions: Role of mass asymmetry of a reaction
We aim to understand the role of Coulomb interactions as well as different equations of state on the disappearance of transverse flow for various asymmetric reactions leading to the same total mass. For the present study, the total mass of the system is kept constant (A_{\text{TOT}} = 152) and mass asymmetry of the reaction is varied between 0.2 and 0.7. The Coulomb interactions as well as different equations of state are found to affect the balance energy significantly for larger asymmetric reactions.
• Effect of isospin-dependent cross-section on fragment production in the collision of charge asymmetric nuclei
To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin-dependent quantum molecular dynamics model. Here simulations have been carried out for ${}^{124}X_n + {}^{124}X_n$ ,where 𝑛 varies from 47 to 59 and for 40Y$_m$ + 40Y$_m$ , where 𝑚 varies from 14 to 23. Our study shows that isospin-dependent cross-section shows its influence on fragmentation in the collision of neutron-rich nuclei.
• Impact of density-dependent symmetry energy and Coulomb interactions on the evolution of intermediate mass fragments
Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, we demonstrate the evolution of intermediate mass fragments in heavy-ion collisions. In this paper, we study the time evolution, impact parameter, and excitation energy dependence of IMF production for the different forms of density-dependent symmetry energy. The IMF production and charge distribution show a minor but considerable sensitivity towards various forms of densitydependent symmetry energy. The Coulomb interactions affect the IMF production significantly at peripheral collisions. The IMF production increases with the stiffness of symmetry energy.
• On the momentum distribution of particles participating in nuclear stopping
Nuclear stopping is studied as a function of incident energy and charge of the fragment produced in central heavy-ion collisions (HIC) of $^{197}_{79}$Au+$^{197}_{79}$Au and $^{58}_{28}$Ni+$^{58}_{28}$Ni using stopping parameter VARXZ. Various momentum constraints were imposed to get better insight into the stopping. The comparison of measured and calculated values of stopping for protons reveals the significance of these constraints. Maximum stopping is obtained for the particles lying in the lowest range of the momentum distribution at all incident energies.
• # Pramana – Journal of Physics
Current Issue
Volume 93 | Issue 6
December 2019
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | 2019-10-17 01:17:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6582294702529907, "perplexity": 2129.2323998835336}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1570986672431.45/warc/CC-MAIN-20191016235542-20191017023042-00092.warc.gz"} |
https://tradeoptionswithme.com/options-trading-education/options-beginner-course/the-beginner-quiz | Welcome to the Option Trading Beginner Quiz.
Here you can test your knowledge gained from the Beginner Course. Try to take the Quiz without any help. You will be able to retake the Quiz as many times as you wish.
Good Luck!
1. What are American Options?
2. What are other terms for an Option Buyer?
3. Does an option buyer have to exercise his option?
4. What is an Option Chain?
5. Stock ABC is trading for $76, which option is ITM (In The Money)? 6. What is an Undefined Risk Strategy? 7. What is a Long Call? 8. Select the options that could profit from a rise in the underlying's price: 9. XYZ is currently trading for$106. Calculate by how much a Put Option with the Strike Price 104 is OTM (Out of The Money)?
10. Implied Volatility (IV) can also be thought of as:
## 8 Replies to “Option Trading Beginner Quiz”
1. Eve Ebel says:
Very informative.
2. Alexander Mann says:
The Quiz help me to see the areas I need to improve on and to get a better understanding of the subject matter presented.
1. Louis says:
Great! That was my goal with the Quizzes.
3. Tom Ross says:
I got 6 out of 10, no wounder I loss money! This helps reinforce the need to understand before risking your money.
4. Deb Hammer says:
I got 6 out of 10. Back to the beginning!
5. Kevin says:
Very good and thank you
6. rupa says:
Thanks. | 2019-11-12 06:14:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44351431727409363, "perplexity": 3824.1339366226894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1573496664752.70/warc/CC-MAIN-20191112051214-20191112075214-00246.warc.gz"} |
http://www.cyrusimap.org/2.5/imap/admin/systemcommands/squatter.html | # squatter¶
Create SQUAT indexes for mailboxes
## Synopsis¶
squatter [ -C config-file ] [ -r ] [ -s ] [ -i ] [ -a ] [ -v ] mailbox...
squatter [ -C config-file ] [ -r ] [ -s ] [ -i ] [ -a ] [ -v ] -u user...
squatter [ -C config-file ] [ -v ] [ -s ] [ -d ] [ -n channel ] -R
squatter [ -C config-file ] [ -v ] [ -s ] -f synclogfile
## Description¶
squatter creates a new text index for one or more IMAP mailboxes. The index is a unified index of all of the header and body text of each message in a given mailbox. This index is used to significantly reduce IMAP SEARCH times on a mailbox.
Note
The name squatter is a historical (pre v3) relic from the days when the only indexing engine supported by Cyrus was SQUAT. Post v3 the search_engine setting in imapd.conf determines which search engine is used.
By default, squatter creates an index of ALL messages in the mailbox, not just those since the last time that it was run. The -i option is used to select incremental updates. Any messages appended to the mailbox after squatter is run, will NOT be included in the index. To include new messages in the index, squatter must be run again.
In the first synopsis, squatter recursively indexes the specified mailbox(es), incrementally updating indexes.
In the second synopsis, squatter recurses from the specified user(s), rather than from specified mailbox(es).
In the third synopsis, squatter runs in rolling mode. In this mode squatter backgrounds itself and runs as a daemon, listening to a sync log channel (chosen using -n option, and set up using the sync_log_channels setting in imapd.conf(5)). Very soon after messages are delivered or uploaded to mailboxes squatter will incrementally index the affected mailbox.
In the fourth synopsis, squatter reads a single sync log file and performs incremental indexing on the mailboxes listed therein. This is sometimes useful for cleaning up after problems with rolling mode.
Note
Incremental updates are very inefficient with the SQUAT search engine. If using SQUAT for large and active mailboxes, you should run squatter periodically as an EVENT in cyrus.conf(5). Incremental updates are much more efficient with Sphinx, so if using Sphinx you should run squatter -R as a START in cyrus.conf(5).
Note
Messages and mailboxes that have not been indexed CAN still be SEARCHed, just not as quickly as those with an index. Also, some advanced features of Sphinx like stemming will not work unless messages have been indexed.
squatter reads its configuration options out of the imapd.conf(5) file unless specified otherwise by -C.
## Options¶
-C config-file
Use the specified configuration file config-file rather than the default imapd.conf(5).
-R
Run in rolling mode; squatter runs as a daemon listening to a sync log channel and continuously incrementally indexing mailboxes. See also -d and -n. This feature was introduced in version 3.0.
-S seconds
After processing each mailbox, sleep for “seconds” before continuing. Can be used to provide some load balancing. Accepts fractional amounts. This feature was introduced in version 3.0.
-T directory
When indexing, work on a temporary copy of the search engine databases in directory. That directory would typically be on some very fast filesystem, like an SSD or tmpfs. This option may not work with all search engines, but it’s only effect is to speed up initial indexing. This feature was introduced in version 3.0.
-u
Extra options refer to usernames (e.g. foo@bar.com) rather than mailbox names. This feature was introduced in version 3.0.
-d
In rolling mode, don’t background and do emit log messages on standard error. Useful for debugging. This feature was introduced in version 3.0.
-f synclogfile
Read the synclogfile and incrementally index all the mailboxes listed therein, then exit. This feature was introduced in version 3.0.
-n channel
In rolling mode, specify the name of the sync log channel that squatter will listen to. The default is “squatter”. This feature was introduced in version 3.0.
-o
In compact mode, if only one source database is selected, just copy it to the destination rather than compacting. This feature was introduced in version 3.0.
-F
In compact mode, filter the resulting database to only include messages which are not expunged in mailboxes with existing name/uidvalidity. This feature was introduced in version 3.0.
-A
In compact mode, audit the resulting database to ensure that every non-expunged message in all the user’s mailboxes which is specified by cyrus.indexed.db is present in the xapian database. This feature was introduced in version 3.0.
-r
Recursively create indexes for all sub-mailboxes of the mailboxes or mailbox prefixes given as arguments.
-s
Skip mailboxes whose index file is older than their current squat file (within a small time delta).
-i
-a
Only create indexes for mailboxes which have the shared /vendor/cmu/cyrus-imapd/squat annotation set to “true”.
The value of the /vendor/cmu/cyrus-imapd/squat annotation is inherited by all children of the given mailbox, so an entire mailbox tree can be indexed (or not indexed) by setting a single annotation on the root of that tree with a value of “true” (or “false”). If a mailbox does not have a /vendor/cmu/cyrus-imapd/squat annotation set on it (or does not inherit one), then the mailbox is not indexed. In other words, the implicit value of /vendor/cmu/cyrus-imapd/squat is “false”.
-v
Increase the verbosity of progress/status messages.
## Examples¶
Sample entries from the EVENTS section of cyrus.conf(5) for periodic squatter runs:
# reindex changed mailboxes (fulltext) approximately every three hours
squatter1 cmd="/usr/bin/ionice -c idle /usr/lib/cyrus/bin/squatter -s" period=180
# reindex all mailboxes (fulltext) daily
squattera cmd="/usr/lib/cyrus/bin/squatter" at=0117
[NB: More examples needed]
## History¶
Support for additional search enginges was added in version 3.0.
The following command-line switches were added in version 3.0:
-R -u -d -O -F -A
The following command-line settings were added in version 3.0:
-S <seconds>, -T <directory>, -f <synclogfile>, -n <channel>
## Files¶
/etc/imapd.conf, /etc/cyrus.conf | 2022-11-29 14:00:24 | {"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": 0.2944013476371765, "perplexity": 8012.985495370528}, "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-2022-49/segments/1669446710698.62/warc/CC-MAIN-20221129132340-20221129162340-00588.warc.gz"} |
https://www.khanacademy.org/math/differential-equations/laplace-transform/laplace-transform-tutorial/v/laplace-transform-3-l-sin-at | # L{sin(at)} - transform of sin(at)
Laplace Transform of sin(at) (part 1). Created by Sal Khan.
Video transcript
Let's keep building our table of Laplace transforms. And now we'll do a fairly hairy problem, so I'm going to have to focus so that I don't make a careless mistake. But let's say we want to take the Laplace transform-- and this is a useful one. Actually, all of them we've done so far are useful. I'll tell you when we start doing not-so-useful ones. Let's say we want to take the Laplace transform of the sine of some constant times t. Well, our definition of the Laplace transform, that says that it's the improper integral. And remember, the Laplace transform is just a definition. It's just a tool that has turned out to be extremely useful. And we'll do more on that intuition later on. But anyway, it's the integral from 0 to infinity of e to the minus st, times-- whatever we're taking the Laplace transform of-- times sine of at, dt. And now, we have to go back and find our integration by parts neuron. And mine always disappears, so we have to reprove integration by parts. I don't recommend you do this all the time. If you have to do this on an exam, you might want to memorize it before the exam. But always remember, integration by parts is just the product rule in reverse. So I'll just do that in this corner. So the product rule tells us if we have two functions, u times v. And if I were take the derivative of u times v. Let's say that they're functions of t. These are both functions of t. I could have written u of x times v of x. Then that equals the derivative of the first times the second function, plus the first function times the derivative of the second. Now, if I were to integrate both sides, I get uv-- this should be review-- is equal to the integral of u prime v, with respect to dt-- but I'm just doing a little bit of shorthand now-- plus the integral of uv prime. I'm just trying to help myself remember this thing. And let's take this and subtract it from both sides. So we have this integral of u prime v is going to be equal to this, uv minus the integral of uv prime. And, of course, this is a function of t. There's a dt here and all of that. But I just have to do this in the corner of my page a lot, because I always forget this, and with the primes and the integrals and all that, I always forget it. One way, if you did want to memorize it, you said, OK, the integration by parts says if I take the integral of the derivative of one thing and then just a regular function of another, it equals the two functions times each other, minus the integral of the reverse. Right? Here, when you take the subtraction, you're taking the one that had a derivative, now it doesn't. And the one that didn't have a derivative, now it does. But anyway, let's apply that to our problem at hand, to this one. Well, we could go either way about it. Let's make u prime is equal to-- we'll do our definition-- u prime is equal to e to the minus st, in which case you would be the antiderivative of that, which is equal to minus 1 over s e to the minus st, right? And actually, this is going to be an integration by parts twice problem, so I'm just actually going to define the Laplace transform as y. That'll come in useful later on. And I think I actually did a very similar example to this when we did integration by parts. But anyway, back to the integration by parts. So that's u. And let me do v in a different color. So when v-- if this is u prime, right? This is u prime, then this is v. So v is equal to sine of at. And then what is v prime? Well, that's just a cosine of at, right? The chain rule. And now, we're ready to do our integration. So the Laplace transform, and I'll just say that's y, y is equal to-- y is what we're trying to solve for, the Laplace transform of sine of at-- that is equal to u prime v. I defined u prime in v, right? That's equal to that. The integral of u prime times v. That equals uv. So that's minus 1 over s e to the minus st, times v, sine of at, minus the integral. And when you do the integration by parts, this could be an indefinite integral, an improper integral, a definite integral, whatever. But the boundary stays. And we can still say, from 0 to infinity of uv prime. So u is minus 1 over s e to the minus st, times v prime, times a cosine of at-- fair enough-- dt. Well, now we have another hairy integral we need to solve. So this might involve another integration by parts, and it does. Let's see if we can simplify it at [? all. ?] Let's take the constants out first. Let me just rewrite this. So we get y is equal to minus e to the minus st over s, sine of at. So you have a minus minus plus a over s-- a divided by s, and then these two negative signs cancel out-- times the integral from 0 to infinity, e to the minus st, cosine of at, dt. Let's do another integration by parts. And I'll do this in a purple color, just so you know this is our second integration by parts. Over here. Let's define once again, u prime is equal to e the minus st. So this is u prime. Then u is equal to minus 1 over s e to the minus st. We'll make v equal to cosine of at. The hardest part about this is not making careless mistakes. And then v prime-- I just want it to be on the same row-- is equal to minus a sine of at, right? The chain rule, derivative of cosine is minus sine. So let's substitute that back in, and we get-- this is going to get hairy; actually, it already is hairy-- y is equal to minus e to the minus st over s, sine of at, plus a over s, times-- OK. Integration by parts. uv. So that's minus 1 over s e to the minus st, times v, times cosine at, minus the integral from 0 to infinity. This problem is making me hungry. It's taking so much glucose from my bloodstream. I'm focusing so much not to make careless mistakes. Anyway, integral from 0 to infinity. And now, we have uv prime, so u is minus 1 over s e to the minus st. That's u. And then v prime times minus a. So let's make that minus cancel out with this one. So that becomes a plus. a sine of at, dt. I'm starting to see the light at the end of the tunnel. So then, let's simplify this thing. And, of course, we're going to have to evaluate this whole thing, right? Actually, we're going to have to evaluate everything. Let's just focus on the indefinite integral for now. We're going to have to take this whole thing and evaluate-- let's just say that y is the antiderivative and then evaluate it from infinity to 0. From 0 to infinity. So y is equal to minus e to the minus st over s, sine of at. Now let's distribute this. Minus a over s squared, e to the minus st, cosine of at. Right? OK, now I want to make sure I don't make a careless mistake. OK. Now, let's multiply this times this and take all of the constants out. So we have an a and an s. a over s. There's a minus sign. We have a plus a to the s. So we'll have a minus a squared over s squared, times the integral from 0-- well, I said I'm just worrying about the indefinite integral right now, and we'll evaluate the boundaries later. e to the minus st, sine of at, dt. Now, this is the part, and we've done this before, it's a little bit of a trick with integration by parts. But this expression, notice, is the same thing as our original y. Right? This is our original y. And we're assuming we're doing the indefinite integral, and we'll evaluate the boundaries later. Although we could have kept the boundaries the whole time, but it would have made it even hairier. So we can rewrite this integral as y. That was our definition. And actually, I just realized I'm running out of time, so I'll continue this hairy problem in the next video. See you soon. | 2017-02-20 11:23:15 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9499911665916443, "perplexity": 423.01599013051606}, "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-2017-09/segments/1487501170521.30/warc/CC-MAIN-20170219104610-00050-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://gmatclub.com/forum/if-x-x-y-n-and-x-x-y-m-then-x-y-x-does-not-167724.html?sort_by_oldest=true | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 22 Sep 2019, 05:16
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not
Author Message
TAGS:
Hide Tags
Intern
Joined: 21 Nov 2013
Posts: 12
If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
19 Feb 2014, 22:05
1
21
00:00
Difficulty:
55% (hard)
Question Stats:
67% (02:46) correct 33% (03:01) wrong based on 310 sessions
HideShow timer Statistics
If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not equal |y|, xy does not equal 0)
A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
_________________
Any and all kudos are greatly appreciated. Thank you.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
19 Feb 2014, 22:36
3
1
MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)
A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
You can do it either algebraically or by assuming numbers:
Algebra:
Note that we are happier with (x+y)/x rather than x/(x+y) since in the former case we can make manipulations easily. So let's take the inverse of both n and m
$$\frac{1}{n} = \frac{(x+y)}{x} = 1 + \frac{y}{x}$$ ....(I)
$$\frac{1}{m} = \frac{(x-y)}{x} = 1 - \frac{y}{x}$$ .....(II)
Since we have both m and n in our answer, lets subtract II from I to get
$$\frac{1}{n} - \frac{1}{m} = \frac{2y}{x}$$
$$\frac{(m-n)}{2mn} = \frac{y}{x}$$
$$\frac{x}{y} = \frac{2mn}{(m-n)}$$
Or Plug in numbers: x = 2, y = 1
n = x/(x+y) = 2/3
m = x/(x-y) = 2
x/y = 2
Now put n = 2/3 and m = 2 in the options. Only option (D) gives you x/y = 2.
_________________
Karishma
Veritas Prep GMAT Instructor
Intern
Joined: 21 Nov 2013
Posts: 12
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
19 Feb 2014, 22:59
@Karishma thanks for the post. Your blogs are extremely helpful btw. I am not sure if you ever followed up about your CFA, but I hope that went well for you.
_________________
Any and all kudos are greatly appreciated. Thank you.
Director
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 564
Location: India
GMAT 1: 780 Q51 V46
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
19 Feb 2014, 23:32
2
1
MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)
A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
Let us say x = 3, y = 1, n = 0.75, m = 1.5
x/y = 3
(A) 3(3/2)(3/4) = 9/8 (Eliminated)
(B) 3(3/2) 2(3/4) = (Eliminated)
(C) (3/4) (3/2 + 2)/2 = (Eliminated)
(D) 2(3/4)(3/2)/(.75) = 3 (BINGO!)
(E) Eliminated
_________________
- CrackVerbal Prep Team
Register for the Free GMAT Kickstarter Course : http://bit.ly/2DDHKHq
Register for our Personal Tutoring Course : https://www.crackverbal.com/gmat/personal-tutoring/
Join the free 4 part GMAT video training series : http://bit.ly/2DGm8tR
Intern
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
24 May 2015, 22:24
CrackVerbalGMAT wrote:
MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)
A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
Let us say x = 3, y = 1, n = 0.75, m = 1.5
x/y = 3
(A) 3(3/2)(3/4) = 9/8 (Eliminated)
(B) 3(3/2) 2(3/4) = (Eliminated)
(C) (3/4) (3/2 + 2)/2 = (Eliminated)
(D) 2(3/4)(3/2)/(.75) = 3 (BINGO!)
(E) Eliminated
Sorry for opening a long answered question.
with algebric solution, i am getting many answers in terms of m & n. so the problem needed to be solved by picking numbers.
when we pick x = 3 & y = 1. I am getting B & D both as answer and but with x = 2 & y= 3. I am getting D as an answer. shouldnt it be unique for all numbers, since there is no restriction (like x, y = consequetive or x>y or viceversa) on picking numbers.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
24 May 2015, 22:53
Alaukik wrote:
CrackVerbalGMAT wrote:
MrWallSt wrote:
If x / (x+y) = n, and x / (x-y) = m, then x/y=? (|x| does not equal |y|, xy does not equal 0)
A. 3mn/2
B. (3m)/(2n)
C. (n * (m+2))/2
D. 2nm / (m-n)
E. (n^2 - m^2) / nm
Let us say x = 3, y = 1, n = 0.75, m = 1.5
x/y = 3
(A) 3(3/2)(3/4) = 9/8 (Eliminated)
(B) 3(3/2) 2(3/4) = (Eliminated)
(C) (3/4) (3/2 + 2)/2 = (Eliminated)
(D) 2(3/4)(3/2)/(.75) = 3 (BINGO!)
(E) Eliminated
Sorry for opening a long answered question.
with algebric solution, i am getting many answers in terms of m & n. so the problem needed to be solved by picking numbers.
when we pick x = 3 & y = 1. I am getting B & D both as answer and but with x = 2 & y= 3. I am getting D as an answer. shouldnt it be unique for all numbers, since there is no restriction (like x, y = consequetive or x>y or viceversa) on picking numbers.
When you take one of the numbers as 1 or 0, or when you take numbers to be equal, you could get multiple options satisfying your conditions.
For example, if n = 1
3n/(m+n) will give the same result as 3/(m+n).
Sometimes, you will get the same answer from multiple options if the options are written intelligently. So you could need to try out 2 or even 3 sets of values.
_________________
Karishma
Veritas Prep GMAT Instructor
Intern
Joined: 01 Aug 2014
Posts: 41
Location: India
GPA: 3.65
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
25 May 2015, 04:57
VeritasPrepKarishma wrote:
When you take one of the numbers as 1 or 0, or when you take numbers to be equal, you could get multiple options satisfying your conditions.
For example, if n = 1
3n/(m+n) will give the same result as 3/(m+n).
Sometimes, you will get the same answer from multiple options if the options are written intelligently. So you could need to try out 2 or even 3 sets of values.
well the question states xy != 0, so x or y cant be 0. also |x| != |y| so they cant be equal either.
I was hoping for a more bullet proof solution for this question. as 2 sets will take more time. we will get answer but at a huge expense of time.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
25 May 2015, 20:25
Alaukik wrote:
VeritasPrepKarishma wrote:
When you take one of the numbers as 1 or 0, or when you take numbers to be equal, you could get multiple options satisfying your conditions.
For example, if n = 1
3n/(m+n) will give the same result as 3/(m+n).
Sometimes, you will get the same answer from multiple options if the options are written intelligently. So you could need to try out 2 or even 3 sets of values.
well the question states xy != 0, so x or y cant be 0. also |x| != |y| so they cant be equal either.
I was hoping for a more bullet proof solution for this question. as 2 sets will take more time. we will get answer but at a huge expense of time.
Note that it is a generic comment about number plugging - not just specific to this question.
Also, I have given the algebra solution above - as "bulletproof" as you can get.
_________________
Karishma
Veritas Prep GMAT Instructor
Manager
Joined: 11 Nov 2011
Posts: 60
Location: United States
Concentration: Finance, Human Resources
GPA: 3.33
WE: Consulting (Non-Profit and Government)
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
02 Aug 2015, 06:55
VeritasPrepKarishma your solution is excellence. I am wondering, how do we know that one form of fraction (you mentioned it as case) is easier to manipulate than another? I tried to solve this problem using the original form of fraction but I ended up nowhere. Do you have the solution using original form of the fraction?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
02 Aug 2015, 23:30
2
evdo wrote:
VeritasPrepKarishma your solution is excellence. I am wondering, how do we know that one form of fraction (you mentioned it as case) is easier to manipulate than another? I tried to solve this problem using the original form of fraction but I ended up nowhere. Do you have the solution using original form of the fraction?
When you need to separate the variables, multiple terms in the numerator are easy to handle since you can split them:
(x+y)/ x = x/x + y/x = 1 + y/x
But if they are in the denominator, you cannot separate them.
You can start with the equations as they are but you will eventually cross multiply to simplify the denominator. If you do different things with the equations, you will get different but equivalent expressions. So a case can be made to do the question by number plugging instead.
_________________
Karishma
Veritas Prep GMAT Instructor
Intern
Joined: 07 Jan 2018
Posts: 5
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
07 Oct 2018, 11:40
Hello,
Could someone explain why is it not possible to assume that: x = n(x+y) and x = m(x-y); so n(x+y) = m(x-y) if we solve this we arrive to x/y = (n+m) / (m-n)
I know it is not the correct answer, but I would like to understand my mistake. Many thanks
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink]
Show Tags
08 Oct 2018, 02:48
1
jmmanquez wrote:
Hello,
Could someone explain why is it not possible to assume that: x = n(x+y) and x = m(x-y); so n(x+y) = m(x-y) if we solve this we arrive to x/y = (n+m) / (m-n)
I know it is not the correct answer, but I would like to understand my mistake. Many thanks
It is not incorrect, it is just not what you need. Different manipulations can lead to different but equivalent expressions.
_________________
Karishma
Veritas Prep GMAT Instructor
Re: If x/(x+y) = n, and x/(x-y) = m, then x/y = ? (|x| does not [#permalink] 08 Oct 2018, 02:48
Display posts from previous: Sort by | 2019-09-22 12:16:24 | {"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": 0.7681427001953125, "perplexity": 3512.83149394023}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575513.97/warc/CC-MAIN-20190922114839-20190922140839-00482.warc.gz"} |
https://discuss.nubits.com/t/unseeded-auction-thread/2226?page=3 | #41
The third unseeded auction has closed.
Auction Closing Price: 0.00260001085541 NBT/NSR
Price: 0.0026 $/NSR Auctions are now fully automatic and will close every 5,000 blocks starting with block 415,000. The server will wait for 10 confirmations before sending payment. Registration is still done manually, but need only occur once per address pair. #42 Ha! It worked, I didn’t think it would work. I’m not at my comp but the auction went off. Hooray! #43 Tto be honest, i have not understood yet how your unseeded auction works and the concrete purpose of it. I take time to understand things Can you explain it in mere terms? #44 Send nbt and/or nsr to auction addresses. Get back nsr and nbt. How much you get back is determined by the average price of all participants. It is zero-sum, the only loss is the network fees. It is transparent, efficient, easy, and robust. As it is now automatic, there is very little reason for us not to be making use of it. I’m going to keep coming out with more bells and whistles for it, but it is already fully operational and if I wasn’t the only one using it people would understand by now why it’s so awesome. #45 Pros of the seeded auction over blind auctions: 1. Transparency (all tx on blockchain) 2. Dual side (discovers price via competition) 3. Provides a nbt and nsr use case 4. Gameable (ends precisely on a block) 5. Easy for auctioneer (registration only need happen once ever per user) 6. Easy for participants (after registration, simply submit funds at will using standard wallet software) 7. Less trust (auctioneer and reserve can be different people) 8. No minimum bid (aside from network fees) 9. All participants pay network fees. 10. All participants are rewarded for participation (assuming >1 participants with different ideal price points) Cons: 1. New software could contain bugs 2. People don’t trust what they don’t understand. 3. All participants pay network fees. (Penalty for participation) 4. Dual side (people can waste a lot of money to force nu to waste a little money. This risk can be decreased by increasing the seed.) #46 I think a seeded auction using this setup is better than the current manual one. #47 Below some extreme examples to help shareholders understand the purpose of unseeded auction thread, including myself: • What should I do if I want to convert 1m NSR into 1m NBT? What is the chance of such a conversion attempt? • What should I do if I want to convert 1m NBT into 1m NSR? What is the chance of such a conversion attempt? #48 The main point I’m going to make here is that ‘unseeded’ auctions are not very useful for such a conversion. Rather, they help one keep one’s personal finances in relative order with respect to nbt and nsr. Are you Nu or are you a participant? If you are Nu, you are able to use the auction to draw demand because you can guarentee submition on one side and not the other by writing the intention to do so on the block chain via motion. This is “seeding” and is a unique property only accomplishable by Nu, not participants. If you are a participant, you are only able to use the auction to do a flat conversion if there is established and dependable auction volume. The technicalities get somewhat in the way here, but ideally you will be able to read the transactions involving the auction addresses and predict a minimum level of involvement. Let’s take your 1 million NSR question, but rephrase a little and say “What is the minimum level of involvement to convert 1 million NSR into NBT at market prices?” Furthermore, we must quantify “at market prices” as being within a certain % of the ideal market price, let’s say 1%. Market involvement + 1 mil = 1.01 * Market involvement. Market involvement = 100 million As you can see, in order for you to be confident dropping funds on the auction, the dependable volume of the auction needs to be over an order of magnitude larger than your intended dump. The vastly preferred thing for you as a user is to be a part of that ‘market involvement’ by submitting both nbt and nsr in your preferred ratio. That will allow you to find common prices amongst the other custodians and shareholders (and anyone else that registers) and balance your personal funds accordingly. #49 I performed a full auction simulation last night. There are several interesting points to be made. 1. The biggest volume transaction pulls the price to its chosen point. It is the market maker. 2. The pair with a price point far away from the market maker swapped the biggest % of its funds, but made the swap at the same rate as everyone else. 3. It is impossible to know if it was 4 different people with different price points, or just 1 person trying to make it appear to be 4 people. This is why you cannot be sure of the fairness of these kind of auctions without submitting some funds yourself. If you don’t participate, you have no way of knowing if more than 1 person participated. I will not be submitting funds for this next auction to celebrate the fork. The bot still runs if you want to use it personally, but without >1 participants all the auction does is burn fees. #50 If I submit 1m NSR and 1m NBT that means that I think 1 NSR should be priced 1 NBT. Now let us assume that most other participants have submitted 1m NSR and 0.5m NBT. What happens in that case? #51 It depends how many other participants, but let’s assume infinite. That means the closing price will be 0.5m nbt / 1m nsr =$0.5 per NSR.
That means you would trade your 1 mil NBT for 2 mil NSR and you 1 mil NSR for 0.5m NBT. If we look for the difference between submitted funds and received funds, you just traded 0.5 mil NBT for 1 mil NSR and kept the other 0.5 mil NBT and 1 mil NSR.
Submitted: 1 mil NSR, 1 mil NBT
Received: 2 mil NSR, 0.5 mil NBT
Note that in the case of infinite market participation you could also have just submitted 0.5 NBT and received 1 mil NSR, I.e. it would have the same effect. Submitting both NBT and NSR is done because you don’t know what the market involvement will be and because it is impossible for it to be infinite.
#52
Let’s do it again with 3 other participants (labeled b) and label the main participant of interest ‘a’.
Total nbt submitted = 2.5 mil
Total nsr submitted = 4 mil
Total price = 2.5/4 = 0.625
A nbt lost = 0.375 mil
A nsr received = 0.6 mil
B nbt received = 0.125 mil
B nsr lost = 0.2 mil
For each of the three ‘b’ participants.
‘A’ pushed the price up to convert 0.375 mil nbt into 0.6 mil nsr. The other participants held the price down and converted 0.3 mil nsr into 0.125 mil nbt each.
Edit: I got confused, should be good now. Note that this is complicated and difficult to calculate by hand, but to a computer this is really really simple math.
#53
The y-axis is NBT converted into NSR by participant A at the auction price. The x-axis is number of B participants. This uses the numbers @cryptog gave of 1:1 NBT:NSR for A and 0.5:1 for each B. This chart is also representative of the resulting auction price, as it is linearly related to what is plotted on the y-axis.
#54
I’ve run into a roadblock here. I am having a very hard time getting RPC to work on windows. I point to the nu.conf (in AppData/Roaming/Nu/) but it still can’t start the daemon.
I want to have the auction participants submit funds automatically. I know there are risks involved with this, but I have considered ways of dealing with them. Making actual code run on windows, however, seems to be difficult.
#55
Thank you for your continued efforts to improve Nu!
I have access to a Windows 7 machine on which I can try that later.
Allow me the question: why would you want to run such an automated trading on Windows?
#56
It is crucial that we have participation in the auction if we want to seed it. If I am just giving away money and there is only one person in the room, that person will take the money and walk away. If there are many people in the room, those people will compete for the money. Participation is absolutely crucial for the auction prices to reflect market prices.
I am trying to make participation via a windows machine as easy as double clicking on an icon. There are many concerns, such as wallet encryption, but I will address those concerns in time. For now, I am just trying to get the simple automation working for an unlocked wallet on a windows machine.
Getting it working on a linux machine is trivial, Creon already did it with server.py and I have basically just copied the implementation from there.
My plans for updates for the Auction are as follows:
1. Automated participation
2. Automated auction announcements using html
3. Automated registration
#57
Looking forward to the automated tool.
#58
With this nu.conf in %appdata%\roaming\nu (in fact it was a different directory because I used -datadir=pathToNuAppdata) - anyway; with this nu.conf:
rpcpassword=rpcpassword
rpcuser=rpcuser
rpcport=9950
server=1
I was able to start
nud --daemon
in one command prompt and was able to execute rpc commands in a second command prompt, e.g.
Z:\Programs\Nu\1.2.0\32>nud -datadir=..\..\appdata getinfo
{
"version" : "v1.2.0-beta",
"protocolversion" : 50000,
"walletversion" : 1,
"walletunit" : "S",
"balance" : 0.0,
"newmint" : 0.0,
"stake" : 0.0,
"parked" : 0.0,
"blocks" : 185220,
"moneysupply" : 1007362878.01,
"connections" : 8,
"proxy" : "",
"ip" : obfuscated",
"difficulty" : 0.00030548,
"testnet" : false,
"keypoololdest" : 1410815213,
"keypoolsize" : 101,
"paytxfee" : 1.0,
"unlocked_until" : 0,
"errors" : "Info: Minting suspended due to locked portfolio."
}
Obviously this node is not fully synced… I stopped using Windoes for that
I had problems without the server and the rpcport line. It generated errors.
#59
Thanks for your help MoD, you’re super helpful. What I’m trying to get to work are the participant programs in this repo:
participant_linux.py works fine, but participant_windows.py doesn’t. It seems to load up the nu.conf file fine, but the rpc command just doesn’t work out. I’m wondering if it’s specific to my windows system and would appreciate others trying. Please note that you have to manually enter your username into the participant_windows.py file.
#60
Here’s a report:
Python 3.4.3 for Windows from https://www.python.org/downloads/release/python-343/ (don’t try this at home; you can read later in this post why ) and
the SeededNuAuction code from https://github.com/Nagalim/SeededNuAuction/archive/master.zip
I adjusted participant_windows.py: replaced, line 8
"C:\Users\**INSERTUSERNAMEHERE**\AppData\Roaming\Nu\nucoin.conf" with
"C:\Users\myUserNameHere\AppData\Roaming\Nu\nu.conf"
because my Nu configuration file is named nu.conf instead of nucoin.conf.
[…]which should save users from entering their username as %appdata% is a variable for the current user’s appdata location - should work on most Windows versions; Using the %appdata% variable hat didn’t work. When using
%appdata%\Roaming\Nu\nu.conf
in participant_windows.py: line 8 the program didn’t run.
Looks like each user has to adjust that path individually.
Trying to run auctioneer.py created an error message:
SyntaxError: Missing parentheses in call to 'print'
Resolved that by uninstalling Python 3.4.3 and installing Python 2.7.10 from https://www.python.org/downloads/release/python-2710/
After installing Python 2.7.10 auctioneer.py created a new error message:
[...]auctioneer.py", line 14, in <module>
opts = dict(tuple(line.strip().replace(' ','').split('=')) for line in open(NUCONFIG).readlines())
IOError: [Errno 2] No such file or directory: 'None/.nu/nu.conf'
I adjusted line 13 of auctioneer.py from
NUCONFIG='%s/.nu/nu.conf'%os.getenv("HOME") to
NUCONFIG=r'C:\Users\myUserNameHere\AppData\Roaming\Nu\nu.conf'
After that running auctioneer.py resulted in this output:
Enter Block Height of Auction Close:
Running participant_windows.py produced
Successfully loaded Nu RPC and found block count as: 218866
Yeah, the blockchain is still syncing
I hope that helps. | 2019-01-18 02:05:39 | {"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": 0.34034571051597595, "perplexity": 5560.734246197434}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1547583659654.11/warc/CC-MAIN-20190118005216-20190118031216-00349.warc.gz"} |
https://mathematica.stackexchange.com/questions/201715/what-is-the-identity-for-tuples | What is the identity for Tuples?
My question is, what list p in the following statement returns the list q?
Tuples[{{p},{q}}]
If we think of Tuples as a binary operator then p would be the identity for Tuples.
I thought an empty list would work, but evaluating the following
Tuples[{{},{1,2,3}}]
The following doesn't work either:
Tuples[{{\[EmptySet]},{1,2,3}}]
Certainly, I could write a function like the following
altTuples[p_List,q_List]:= If[Length[p]==0,q,Tuples[{p,q}]
That does exactly what I want, but I want to know if I'm missing something. Is there in fact an identity for Tuples? Is there a way to do what I want with Outer? I've tried the obvious solutions with no luck.
• How do you want your altTuples[] to behave when the length of $p$ is not zero? For example altTuples[{a, b, c}, {d, e, f}] returns Tuples[{a, b, c}, {d, e, f}], probably not what you want. – mjw Jul 8 '19 at 1:19
• I corrected altTuples. Actually I want it to return Tuples[{{a, b, c}, {d, e, f}}]. I think Nothing is what I was looking for. – JAS Jul 8 '19 at 23:27
• What you have above is almost correct (up to a typo). Anyway seems to produce what you want. 'AltTuples[{p,q}] gives the same output as Tuples[p,q] when the first argument is a list with non-zero length. – mjw Jul 8 '19 at 23:36
If {{1},{2},{3}} is fine, you can use Nothing:
Tuples[{Nothing, {1, 2, 3}}]
(* {{1}, {2}, {3}} *)
If you want {1,2,3}, you can Flatten the result, of course.
• Thank you, this does exactly what I need. – JAS Jul 8 '19 at 23:20
You can use Inactive[Sequence][] as identity like this:
Tuples[{{Inactive[Sequence][]},{q}}]//Activate
{{q}}
Use TagSetDelayed to define a function that behaves as desired:
ClearAll[iDentity]
iDentity /: {iDentity[___], a : {__}} := iDentity[a]
iDentity /: Tuples[iDentity[a_]] := a
Tuples[{iDentity[], {q}}]
{q}
Tuples[{iDentity[blah], {1, 2, 3}}]
{1, 2, 3}
Alternatively, define your function altTuples with two signatures:
ClearAll[altTuples]
altTuples[{tuplesIdentity | {} | Nothing, a_List}] := a
altTuples[x_] := Tuples[x]
altTuples[{{x, y}, {1, 2}}]
{{x, 1}, {x, 2}, {y, 1}, {y, 2}}
altTuples[{tuplesIdentity, {1, 2}}]
{1, 2}
altTuples[{{}, {1, 2}}]
{1, 2}
I think this is what you want:
altTuples[p_List, q_List] := If[Length[p] == 0, q, Tuples[{p, q}]]
The statement
altTuples[{}, {d, e, f}]
returns
{d, e, f}
and
altTuples[{a, b, c}, {d, e, f}]
returns
{{a, d}, {a, e}, {a, f}, {b, d}, {b, e}, {b, f}, {c, d}, {c, e}, {c, f}}
` | 2021-01-20 07:54:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.22660574316978455, "perplexity": 2919.2491684166876}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703519923.26/warc/CC-MAIN-20210120054203-20210120084203-00174.warc.gz"} |
https://tug.org/pipermail/tugindia/2004-September/002996.html | # [Tugindia] any software for figure and Greek symbols
S. venkataraman svenkat at ignou.ac.in
Wed Sep 15 16:20:29 CEST 2004
Hi!
I want to know is there any linux base free software which can draw figures as
well as supports greek symbols like \alpha, letters which we used for maths.
And which exports file to .eps.
I tried xfig but it is complicated. Dr. Geo is easy but Greek symbols not
possible.
Anything else?
Try Eukleides Christian Obrecht. It is available from CTAN.
A article by Christian Obrecht appeared in TUGboat, 2002, No3/4.
http://www.tug.org/TUGboat/Articles/tb23-3-4/tb75obre.pdf
which will be useful as a tutorial also. | 2022-07-01 22:32:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7638080716133118, "perplexity": 10790.739861928152}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1656103947269.55/warc/CC-MAIN-20220701220150-20220702010150-00467.warc.gz"} |
https://stats.stackexchange.com/questions/187724/how-to-find-true-positive-true-negative-false-positive-false-negative-from-a | # How to find true positive, true negative, false positive, false negative from a three class confusion matrix?
I built a confusion matrix of three class. like, (a,b,c are the class)
- a b c <= predicted
a 20 5 0
b 7 18 0
c 0 0 20
Now I want to calculate precision, recall from this confusion matrix. In order to do that I need to find out true positive, true negative, false positive, and false negative.
How can I find out the values of true positive, true negative, false positive, and false negative?
• if you found one of the answers helpful pls. accept it - Thank you. – vonjd Sep 26 '16 at 13:29
When I understand your question correctly you are asking which class is the positive one and which is the negative one.
The answer is that this is to a certain extent arbitrary, so you have to decide that considering the problem at hand.
The most common performance measures consider the model's ability to discern one class versus all others. The class of interest is known as the positive class, while all others are known as negative.
The use of the terms positive and negative is not intended to imply any value judgment (that is, good versus bad), nor does it necessarily suggest that the outcome is present or absent (such as birth defect versus none). The choice of the positive outcome can even be arbitrary, as in cases where a model is predicting categories such as sunny versus rainy or dog versus cat.
The relationship between the positive class and negative class predictions can be depicted as a 2 x 2 confusion matrix that tabulates whether predictions fall into one of the four categories:
True Positive (TP): Correctly classified as the class of interest
True Negative (TN): Correctly classified as not the class of interest
False Positive (FP): Incorrectly classified as the class of interest
False Negative (FN): Incorrectly classified as not the class of interest
This is the reason that you e.g. have to specify the positive class when using generic performance measure functions, like ConfusionMatrix in the caret package in R.
Now another complicating factor is of course your multiclass setting, but this is answered here:
How to compute precision/recall for multiclass-multilabel classification?
In general the most popular approach is to calculate these measures for each class by comparing each class level to the remaining levels (i.e. a "one versus all" approach).
You simply have to merge the categories while calculating (e.g. $a$ and $\neg a$, where $\neg a$ is $b$ or $c$). True positive prediction for category $a$ is when $a$ was predicted and it was observed, true negative when it was not predicted and not observed, false negative when $a$ was observed but not predicted and false positive when it was predicted but not observed. You can find nice worked example of $3\times3$ confusion matrix on Wikipedia.
• @Downvoter I would be happy to hear what exactly is wrong with this answer? – Tim Aug 15 '16 at 18:56 | 2019-07-18 11:47:03 | {"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": 0.5534380078315735, "perplexity": 759.9724301846693}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525627.38/warc/CC-MAIN-20190718104512-20190718130512-00211.warc.gz"} |
http://nuit-blanche.blogspot.com/2012/03/this-week-in-compressive-sensing.html | ## Tuesday, March 27, 2012
### This Week in Compressive Sensing
Felix Krahmer gives a talk at MIT on Compressed sensing bounds via improved estimates for Rademacher chaos At Johns Hopkins, there is a project on a biomorphic Asynchronous Time-based Imaging Sensor (ATIS). But if you want to know more about compressive sensing, today we have also some pretty interesting papers. Enjoy!
First, when I met Yonina at MIA2012, she mentioned that this paper would be out. If you recall, this is a big controversy:, at least to the Science journalists who don't understand how Science really works: Designing and using prior data in Ankylography: Recovering a 3D object from a single diffraction intensity pattern by Eliyahu Osherovich, Oren Cohen, Yonina C. Eldar, Mordechai Segev The abstract reads:
We present a novel method for Ankylography: three-dimensional structure reconstruction from a single shot diffraction intensity pattern. Our approach allows reconstruction of objects containing many more details than was ever demonstrated, in a faster and more accurate fashion
In this paper, we look at combinatorial algorithms for Compressed Sensing from a different perspective. We show that certain combinatorial solvers are in fact recursive implementations of convex relaxation methods for solving compressed sensing, under the assumption of sparsity for the projection matrix. We extend the notion of sparse binary projection matrices to sparse real-valued ones. We prove that, contrary to their binary counterparts, this class of sparse-real matrices has the Restricted Isometry Property. Finally, we generalize the voting mechanism (employed in combinatorial algorithms) to notions of isolation/alignment and present the required solver for real-valued sparse projection matrices based on such isolation/alignment mechanisms.
Combinatorial selection and debiasing ? I have also seen these here, even though the big idea here is gradient sketching: Sublinear Time, Approximate Model-based Sparse Recovery For All by Anastasios KyrillidisVolkan Cevher. The abstract reads:
We describe a probabilistic, {\it sublinear} runtime, measurement-optimal system for model-based sparse recovery problems through dimensionality reducing, {\em dense} random matrices. Specifically, we obtain a linear sketch $u\in \R^M$ of a vector $\bestsignal\in \R^N$ in high-dimensions through a matrix $\Phi \in \R^{M\times N}$ $(M less than N)$. We assume this vector can be well approximated by $K$ non-zero coefficients (i.e., it is $K$-sparse). In addition, the nonzero coefficients of $\bestsignal$ can obey additional structure constraints such as matroid, totally unimodular, or knapsack constraints, which dub as model-based sparsity. We construct the dense measurement matrix using a probabilistic method so that it satisfies the so-called restricted isometry property in the $\ell_2$-norm. While recovery using such matrices is measurement-optimal as they require the smallest sketch sizes $\numsam= O(\sparsity \log(\dimension/\sparsity))$, the existing algorithms require superlinear runtime $\Omega(N\log(N/K))$ with the exception of Porat and Strauss, which requires $O(\beta^5\epsilon^{-3}K(N/K)^{1/\beta}), ~\beta \in \mathbb{Z}_{+},$ but provides an $\ell_1/\ell_1$ approximation guarantee. In contrast, our approach features $O\big(\max \lbrace \sketch \sparsity \log^{O(1)} \dimension, ~\sketch \sparsity^2 \log^2 (\dimension/\sparsity) \rbrace\big)$ complexity where $L \in \mathbb{Z}_{+}$ is a design parameter, independent of $\dimension$, requires a smaller sketch size, can accommodate model sparsity, and provides a stronger $\ell_2/\ell_1$ guarantee. Our system applies to "for all" sparse signals, is robust against bounded perturbations in $u$ as well as perturbations on $\bestsignal$ itself.
Magnetic Resonance Imaging (MRI) is one of the fields that the compressed sensing theory is well utilized to reduce the scan time significantly leading to faster imaging or higher resolution images. It has been shown that a small fraction of the overall measurements are sufficient to reconstruct images with the combination of compressed sensing and parallel imaging. Various reconstruction algorithms has been proposed for compressed sensing, among which Augmented Lagrangian based methods have been shown to often perform better than others for many different applications. In this paper, we propose new Augmented Lagrangian based solutions to the compressed sensing reconstruction problem with analysis and synthesis prior formulations. We also propose a computational method which makes use of properties of the sampling pattern to significantly improve the speed of the reconstruction for the proposed algorithms in Cartesian sampled MRI. The proposed algorithms are shown to outperform earlier methods especially for the case of dynamic MRI for which the transfer function tends to be a very large matrix and significantly ill conditioned. It is also demonstrated that the proposed algorithm can be accelerated much further than other methods in case of a parallel implementation with graphics processing units (GPUs).
The least absolute shrinkage and selection operator (LASSO) for linear regression exploits the geometric interplay of the $\ell_2$-data error objective and the $\ell_1$-norm constraint to arbitrarily select sparse models. Guiding this uninformed selection process with sparsity models has been precisely the center of attention over the last decade in order to improve learning performance. To this end, we alter the selection process of LASSO to explicitly leverage combinatorial sparsity models (CSMs) via the combinatorial selection and least absolute shrinkage (CLASH) operator. We provide concrete guidelines how to leverage combinatorial constraints within CLASH, and characterize CLASH's guarantees as a function of the set restricted isometry constants of the sensing matrix. Finally, our experimental results show that CLASH can outperform both LASSO and model-based compressive sensing in sparse estimation.
Compressed sensing (CS) studies the recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior. This paper is focused on the CS problem with quantized measurements. There have been research results dealing with different scenarios including a single/multiple bits per measurement, noiseless/noisy environment, and an unsaturated/saturated quantizer. While the existing methods are only for one or more specific cases, this paper presents a framework to unify all the above mentioned scenarios of the quantized CS problem. Under the unified framework, a variational Bayesian inference based algorithm is proposed which is applicable to the signal recovery of different application cases. Numerical simulations are carried out to illustrate the improved signal recovery accuracy of the unified algorithm in comparison with state-of-the-art methods for both multiple and single bit CS problems.
Analysis of Sparse MIMO Radar by Thomas Strohmer, Benjamin Friedlander. The abstract reads:
We consider a multiple-input-multiple-output radar system and derive a theoretical framework for the recoverability of targets in the azimuth-range domain and the azimuth-range-Doppler domain via sparse approximation algorithms. Using tools developed in the area of compressive sensing, we prove bounds on the number of detectable targets and the achievable resolution in the presence of additive noise. Our theoretical findings are validated by numerical simulations.
Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms by Amir Beck, Yonina C. Eldar . The abstract reads:
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The first algorithm is essentially a gradient projection method while the remaining two algorithms are of coordinate descent type. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied. The algorithms and results are illustrated by several numerical examples.
Spread spectrum magnetic resonance imaging by Gilles Puy, Jose P. Marques, Rolf Gruetter, Jean-Philippe Thiran, Dimitri Van De Ville, Pierre Vandergheynst, Yves Wiaux. The abstract reads:
We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s2MRI, consists of pre-modulating the signal of interest by a linear chirp before random k-space under-sampling, and then reconstructing the signal with non-linear algorithms that promote sparsity. The effectiveness of the procedure is theoretically underpinned by the optimization of the coherence between the sparsity and sensing bases. The proposed technique is thoroughly studied by means of numerical simulations, as well as phantom and in vivo experiments on a 7T scanner. Our results suggest that s2MRI performs better than state-of-the-art variable density k-space under-sampling approaches
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall-Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse array imaging problems.
In this paper, we investigate the fundamental performance limits of data gathering with compressive sensing (CS) in wireless sensor networks, in terms of both energy and latency. We consider two scenarios in which n nodes deliver data in centralized and distributed fashions, respectively. We take a new look at the problem of data gathering with compressive sensing from the perspective of in-network computation and formulate it as distributed function computation. We propose tree-based and gossip based computation protocols and characterize the scaling of energy and latency requirements for each protocol. The analytical results of computation complexity show that the proposed CS-based protocols are efficient for the centralized fashion. In particular, we show the proposed CS-based protocol can save energy and reduce latency by a factor of (p n log n m ) when m = O(√n log n) in noiseless networks, respectively, where m is the number of random projections for signal recovery. We also show that our proposed protocol can save energy by a factor of (pnmplog n) compared with the traditional transmission approach when m = O(√nlog n) in noisy networks. For the distributed fashion, we show that the proposed gossip-based protocol can improve upon the scheme using randomized gossip, which needs fewer transmissions. Finally, simulations are also presented to demonstrate the effectiveness of our proposed protocols.
In this paper, we study data gathering with compressive sensing from the perspective of in-network computation in random networks, in which n nodes are uniformly and independently deployed in a unit square area. We formulate the problem of data gathering to compute multiround random linear function. We study the performance of in-network computation with compressive sensing in terms of energy consumption and latency in centralized and distributed fashions. For the centralized approach, we propose a tree-based protocol for computing multiround random linear function. The complexity of computation shows that the proposed protocol can save energy and reduce latency by a factor of (√n= log n) for data gathering comparing with the traditional approach, respectively. For the distributed approach, we propose a gossip-based approach and study the performance of energy and latency through theoretical analysis. We show that our approach needs fewer transmissions than the scheme using randomized gossip.
Proof of Convergence and Performance Analysis for Sparse Recovery via Zero-point Attracting Projection by Xiaohan WangYuantao GuLaming Chen. The abstract reads:
A recursive algorithm named Zero-point Attracting Projection (ZAP) is proposed recently for sparse signal reconstruction. Compared with the reference algorithms, ZAP demonstrates rather good performance in recovery precision and robustness. However, any theoretical analysis about the mentioned algorithm, even a proof on its convergence, is not available. In this work, a strict proof on the convergence of ZAP is provided and the condition of convergence is put forward. Based on the theoretical analysis, it is further proved that ZAP is non-biased and can approach the sparse solution to any extent, with the proper choice of step-size. Furthermore, the case of inaccurate measurements in noisy scenario is also discussed. It is proved that disturbance power linearly reduces the recovery precision, which is predictable but not preventable. The reconstruction deviation of $p$-compressible signal is also provided. Finally, numerical simulations are performed to verify the theoretical analysis.
In this paper, we consider compressed sensing (CS) of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An efficient algorithm, called zero-point attracting projection (ZAP) algorithm, is extended to the scenario of block CS. The block version of ZAP algorithm employs an approximate $l_{2,0}$ norm as the cost function, and finds its minimum in the solution space via iterations. For block sparse signals, an analysis of the stability of the local minimums of this cost function under the perturbation of noise reveals an advantage of the proposed algorithm over its original non-block version in terms of reconstruction error. Finally, numerical experiments show that the proposed algorithm outperforms other state of the art methods for the block sparse problem in various respects, especially the stability under noise.
As one of the recently proposed algorithms for sparse system identification, $l_0$ norm constraint Least Mean Square ($l_0$-LMS) algorithm modifies the cost function of the traditional method with a penalty of tap-weight sparsity. The performance of $l_0$-LMS is quite attractive compared with its various precursors. However, there has been no detailed study of its performance. This paper presents all-around and throughout theoretical performance analysis of $l_0$-LMS for white Gaussian input data based on some reasonable assumptions. Expressions for steady-state mean square deviation (MSD) are derived and discussed with respect to algorithm parameters and system sparsity. The parameter selection rule is established for achieving the best performance. Approximated with Taylor series, the instantaneous behavior is also derived. In addition, the relationship between $l_0$-LMS and some previous arts and the sufficient conditions for $l_0$-LMS to accelerate convergence are set up. Finally, all of the theoretical results are compared with simulations and are shown to agree well in a large range of parameter setting.
A new sparse signal recovery algorithm for multiple-measurement vectors (MMV) problem is proposed in this paper. The sparse representation is iteratively drawn based on the idea of zero-point attracting projection (ZAP). In each iteration, the solution is first updated along the negative gradient direction of sparse constraint, and then projected to the solution space to satisfy the under-determined equation. A variable step size scheme is adopted further to accelerate the convergence as well as to improve the recovery accuracy. Numerical simulations demonstrate that the performance of the proposed algorithm exceeds the references in various aspects, as well as when applied to the Modulated Wideband Converter, where recovering MMV problem is crucial to its performance.
And finally, a PhD thesis: Numerical methods for phase retrieval by Eliyahu Osherovich. The abstract reads:
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction imaging (CDI). Our main goal is to develop an efficient reconstruction method based on continuous optimization techniques. Unlike current reconstruction methods, which are based on alternating projections, our approach leads to a much faster and more robust method. However, all previous attempts to employ continuous optimization methods, such as Newton-type algorithms, to the phase retrieval problem failed. In this work we provide an explanation for this failure, and based on this explanation we devise a sufficient condition that allows development of new reconstruction methods---approximately known Fourier phase. We demonstrate that a rough (up to $\pi/2$ radians) Fourier phase estimate practically guarantees successful reconstruction by any reasonable method. We also present a new reconstruction method whose reconstruction time is orders of magnitude faster than that of the current method-of-choice in phase retrieval---Hybrid Input-Output (HIO). Moreover, our method is capable of successful reconstruction even in the situations where HIO is known to fail. We also extended our method to other applications: Fourier domain holography, and interferometry. Additionally we developed a new sparsity-based method for sub-wavelength CDI. Using this method we demonstrated experimental resolution exceeding several times the physical limit imposed by the diffraction light properties (so called diffraction limit).
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin. | 2017-02-23 02:36:45 | {"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": 0.6733977794647217, "perplexity": 713.1363679598052}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1487501171070.80/warc/CC-MAIN-20170219104611-00118-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://mathhelpforum.com/advanced-statistics/95795-joint-probability-density-function.html | # Math Help - Joint probability density function
1. ## Joint probability density function
If the joint probability density function of X and Y is,
f(x,y)=1/8(6-x-y);0<x<2;2<y<4 or 0 otherwise
Findi)P(X+Y<3)
(ii)P(X<3/2 /Y<5/2)
In the first part I am completely lost whereas in the second part I am lost in finding limits for the required integrals.Pls help me through it
2. Originally Posted by roshanhero
If the joint probability density function of X and Y is,
f(x,y)=1/8(6-x-y);0<x<2;2<y<4 or 0 otherwise
Findi)P(X+Y<3)
(ii)P(X<3/2 /Y<5/2)
In the first part I am completely lost whereas in the second part I am lost in finding limits for the required integrals.Pls help me through it
Draw the rectangular region defined by 0<x<2 and 2<y<4. Then:
(i) Draw the line x + y = 3. Shade the region of the rectangle enclosed by the line. Integrate the joint pdf over that region. From the sketch it should be clear that:
$\Pr(X + Y < 3) = \int_{x = 0}^{x = 1} \int_{y = 2}^{y = 3 - x} f(x, y) \, dy \, dx$.
Note: You should not be attempting questions like this until you have learnt how to evaluate double integrals.
(ii) You should know that $\Pr(X < 3/2 | Y < 5/2) = \frac{\Pr(X < 3/2 \cap Y < 5/2)}{\Pr(Y < 5/2)}$.
Draw the horizontal line y = 5/2. Draw the vertical line x = 3/2. Then it should be clear that:
$\Pr(X < 3/2 | Y < 5/2) = \int_{0}^{3/2} \int_{0}^{5/2} f(x, y) \, dx \, dy$.
$\Pr(Y < 5/2) = \int_{0}^{2} \int_{0}^{5/2} f(x, y) \, dx \, dy$.
3. I draw the graph which might be wrong,from the graph I got the limits of x and y opposite to the values given by mr fantastic.Please clear me on it.
4. Originally Posted by roshanhero
I draw the graph which might be wrong,from the graph I got the limits of x and y opposite to the values given by mr fantastic.Please clear me on it.
The support of the joint pdf is the interior of the rectangle defined by 0<x<2 and 2<y<4. Have you drawn this? Now draw the line x + y = 3. Have you done this? Labels all the points where the line intersects the rectangle.
Now note that $x + y < 3 \Rightarrow y < -x + 3$ so shade the region of the rectangle that lies below the line x + y = 3. Integrate the given joint pdf over that shaded region. I have set the double integral up for you in my previous post.
How much experience do you have in calculating double integrals? I think you will benefit greatly by extensively reviewing that part of calculus. | 2015-01-27 23:52:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7773998975753784, "perplexity": 403.4267423251072}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1422122039674.71/warc/CC-MAIN-20150124175359-00050-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/453900/lie-derivative-for-wedge-product-of-vector-fields | # Lie Derivative for Wedge Product of Vector Fields
I am having trouble here. The context is: Let $X$, $Y$ and $S$ be vector fields ina a manifold (we can assume it's $\mathbb{C}^2$ though I'm pretty sure this should work in any manifold), and we can work fine with the exterior product or wedge product of vector fields, since they are tensors.
I need to know if the formula $$\mathcal{L}_X(S\wedge Y)=\mathcal{L}_X(S)\wedge Y+S\wedge\mathcal{L}_X(Y)$$
I know this is true when $X$, $Y$ and $S$ are differential forms. The demonstration is basd solely on the property that says that, for tensors fields, we have $$\mathcal{L}_X(S\otimes Y)=\mathcal{L}_X(S)\otimes Y+S\otimes\mathcal{L}_X(Y)$$
I don't think I can say that since it is correct for the tensor product, it would be for the exterior product. I guess I must use the fact that vector fields are antissimetric 1-linear forms and use the operator (in my reference it is called "anti-simetrization operator") $$\mathcal{\alpha}(X)=\sum_{s\in \mathcal{G}_p} \epsilon (s)s\circ X$$ where $\mathcal{G}_p$ is the set or permitations of $p$ indexes and the composition means a permutation on the indexes of the base elements of $X$. The application $\alpha$ turns linear p-forms into antissimetric forms and then we have exterior product of those. If $X$ is already antissimetric, then $\alpha(X)=p!X$.
Now, we also have the definition $$X\wedge Y=\dfrac{1}{p!q!}\alpha (X\otimes Y)$$
So I'm guessing I can argue that $\alpha (X\otimes Y)=(p+q)!(X\otimes Y)$, and the calculations work, that is, I get the expression $\mathcal{L}_X(S\wedge Y)=\mathcal{L}_X(S)\wedge Y+S\wedge\mathcal{L}_X(Y)$ as I wanted. But I don't know for sure if this is correct. I am trying to self-learn somethings on tensors.
Can someone tell me if it's correct and, if not, point me my mistakes?
• The worst thing in studying during dawn is the long wait I must endure until someone comments/answers :P – Marra Jul 28 '13 at 7:00
• Is $\mathcal L_X$ the Lie derivative, right? – Avitus Aug 23 '13 at 8:37
Let us consider the following general setting. We need it to prove the statement.
• The dg Lie algebra of poly-vector fields
Let $M$ be a real manifold of dimension $n$ over the ground field $\mathbb K$. Let $$\operatorname{T}^{\bullet}_{poly}(M):=\mathcal C^{\infty}(M)\otimes_{\mathbb K}\wedge^{\bullet+1}\operatorname{T}(M)$$
be the algebra of poly vector fields on $M$. Note the shift of grading: for example, vector fields are polyvectors of degree $0$.
There exists a structure of differential graded Lie algebra on $\operatorname{T}^{\bullet}_{poly}(M)$ given as follows. The differential is equal to $0$. The Lie bracket is the Schouten bracket $[\cdot,\cdot]_\mathcal{S}$ given by
$$[e_1 ∧ ... ∧ e_k, \eta_1 ∧ ... ∧ \eta_l]_\mathcal{S} = \\ \sum_{i=1}^k\sum_{j=1}^l(−1)^{i+j}\mathcal L_{e_i}(\eta_j)\wedge e_1 \wedge\dots\wedge\hat{e}_i\wedge\dots\wedge e_k\wedge \eta_1\wedge\dots\wedge\hat{\eta}_l\wedge\dots\wedge\eta_l,$$ for all $e_{\bullet}$ and $\eta_{\bullet}$ in $\operatorname{T}^{0}_{poly}(M)$ and denoting omission by $\hat{\cdot}$. Note that the Schouten bracket reduces to the Lie bracket
$$\mathcal L_X(Y):=[X,Y],$$
on $\operatorname{T}^{0}_{poly}(M)$.
In summary, using some lengthy but straightforward computations, one can prove that
$$(\operatorname{T}^{\bullet}_{poly}(M),0,[\cdot,\cdot]_\mathcal{S})$$
is a dg Lie algebra (I do not want to introduce the exact definition and further discuss the gradings). Note that we have also an associative product, i.e. the wedge product. In other words, the structure on $\operatorname{T}^{\bullet}_{poly}(M)$ is even richer, but let us skip the discussion about Gerstenhaber algebras.
• Statement in the OP
In the above setting, the original statement is equivalent to
For all $X,Y,S\in \operatorname{T}^{0}_{poly}(M)$ the identity
$$[X,S\wedge Y]_\mathcal{S}=[X,S]\wedge Y+S\wedge[X,Y]~~(*)$$
holds.
On the l.h.s. of $(*)$ it is necessary to consider the Schouten bracket because $S\wedge Y\in \operatorname{T}^{1}_{poly}(M)$.
Let us prove it; by definition of the Schouten bracket
$$[X,S\wedge Y]_\mathcal{S}=(−1)^{1+1}\mathcal L_{X}(S)\wedge Y+(−1)^{1+2}\mathcal L_{X}(Y)\wedge S=\mathcal L_{X}(S)\wedge Y-\mathcal L_{X}(Y)\wedge S,$$
or
$$[X,S\wedge Y]_\mathcal{S}=\mathcal L_{X}(S)\wedge Y+S\wedge\mathcal L_{X}(Y),$$
as claimed. This ends the proof.
• While I believe this is correct, it is totally out of my context :( – Marra Aug 23 '13 at 16:12
• What is your context? The idea in the above answer can be summarized as follows: if you consider the identity you want to prove, on the l.h.s. you have the Lie derivative applied to a 2-vector field. Question: what is the Lie derivative applied to such an object? One starts with the Lie derivative applied to vector fields in diff. geometry, am I right? In order to define the l.h.s. of the identity you introduce multi vector fields, i.e. functions, vector fields, 2-vector fields, etc... and define the Lie derivative on such space, called space of poly vector fields. The Lie derivative... – Avitus Aug 23 '13 at 16:33
• ...on such space is called Schouten bracket; from its very definition the identity you want to prove is shown to hold. The end :-) – Avitus Aug 23 '13 at 16:34
• Yeah, I meant no harm, is just that the proof you gave me is somewhere beyond my reading, I'd have to spend some time to understand it. But thanks! At least I know now that the identity holds :-) – Marra Aug 23 '13 at 16:41
• No harm has been felt! :-) Try the Schouten bracket for $i,l$ equal to $(1,1)$, $(2,1)$ etc...it helped me a lot! If you are interested in what comes from this area of diff. geo+ dg algebras you could have a look at Vaismann's book on symplectic and Poisson geometry. – Avitus Aug 23 '13 at 17:17
@Marra: Avirus gave a nice explanation of the Schouten-Nijenhuis bracket (useful in Poisson geometry). If you want just to know the Lie derivative of the exterior product $\mathscr{L}_X(Y\wedge Z)$, then you can start from the definition, for any tensor field $T$: $$\mathscr{L}_X T=\frac{d}{dt}\Big|_{t=0}(\exp tX)^*T$$ where $\exp tX$ the local flow of $X$. From there you can prove, for any tensor fields $S$ and $T$, that $$\mathscr{L}_X(S\wedge T)=\mathscr{L}_X S\wedge T+S\wedge\mathscr{L}_X T.$$ Finally, it's useful to keep in mind that a Lie derivative is always a derivation: $$\mathscr{L}_X(fg)=\mathscr{L}_X(f)g+f\mathscr{L}_X(g),\ \forall f,g\in C^\infty(M).$$ $$\mathscr{L}_X(\alpha\wedge\beta)=\mathscr{L}_X\alpha\wedge\beta+\alpha\wedge\mathscr{L}_X\beta,\ \forall\alpha,\beta\in\Omega^*(M).$$ $$\mathscr{L}_X<\alpha,Y>=<\mathscr{L}_X\alpha,Y>+<\alpha,\mathscr{L}_X Y>,\ \forall\alpha,\in\Omega^1(M),\ \forall Y\in\mathcal{X}(M).$$ and the general definition of a derivation: if $(\mathcal{A},\cdot)$ is an algebra, a derivation on $\mathcal{A}$ is linear map $\delta : \mathcal{A}\to\mathcal{A}$ such that, $$\delta(x\cdot y)=(\delta x)\cdot y+x\cdot(\delta y).$$ P.S: Sorry for my bad English! | 2019-07-24 09:05:19 | {"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": 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": 0.9103613495826721, "perplexity": 274.3839302972872}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195532251.99/warc/CC-MAIN-20190724082321-20190724104321-00394.warc.gz"} |
https://drscotthawley.github.io/blog/2019/01/30/My-First-Neural-Network.html | Links to lessons: Part 0, Part 1, Part 2, Part 3
We will be reproducing work from Andrew Trask's excellent tutorial "A Neural Network in 11 lines of Python", albeit with a different emphasis, and in a different way. You may regard this treatment and his original treatment as complimentary, and feel free to refer to both. This lesson is written with the intent of building on the lesson about linear regression -- which we might call "Part 0" -- at the link "Following Gravity - ML Foundations Part Ia."
## The Sample Problem
Consider a system that tries to map groups of 3 inputs to some corresponding output which is a single number. In the following picture, we'll show each set of 3 inputs as a row of a matrix $X$, and each output as the corresponding row of $Y$:
$$\overbrace{ \left[ {\begin{array}{ccc} 0 & 0 & 1 \\ 0 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 1\\ \end{array} } \right] }^{X} \rightarrow \overbrace{ \left[ {\begin{array}{c} 0 \\ 0 \\ 1 \\ 1 \\ \end{array} } \right] }^Y.$$
Even though this system has an exact solution (namely, $Y$ equals the first column of $X$), usually we'll need to be satisfied with a system that maps our inputs $X$ to some approximate "prediction" $\tilde{Y}$, which we hope to bring closer to the "target" $Y$ by means of successive improvements.
The way we'll get our prediction $\tilde{Y}$ is by means of a weighted sum of each set of 3 inputs, and some nonlinear function $f$ which we call the "activation function" (or just "activation"). Pictorially, the process looks like the following, for each row $i$ of $X$ and $Y$, (where the columns of $X$ are shown arranged vertically instead of horizonally):
In terms of matrix multiplication, since X is a 4x3 matrix, and Y is a 4x1 matrix, that implies that our weights should be a 3x1 matrix consisting of (unknown) values $w_0$, $w_1$ and $w_2$. The calculation can be written as:
$$f\left( \overbrace{ \left[ {\begin{array}{ccc} 0 & 0 & 1 \\ 0 & 1 & 1\\ 1 & 0 & 1\\ 1 & 1 & 1\\ \end{array} } \right] }^\text{X} \overbrace{ \left[ {\begin{array}{c} w_0 \\ w_1\\ w_2\\ \end{array} } \right] }^{w} \right) = \overbrace{ \left[ {\begin{array}{c} 0 \\ 0 \\ 1 \\ 1 \\ \end{array} } \right] }^{\tilde{Y}}$$
Our nonlinear activation function $f$ is taken to operate on each row element one at a time, and we'll let $f_i$ denote the $i$th row of this completed activation, i.e.:
$$f_i = f\left( \sum_j X_{ij}w_j \right) = \tilde{Y}_i .$$
The particular activation function we will use is the "sigmoid",
$$f(x) = {1\over{1+e^{-x}}},$$
-- click here to see a plot of this function -- which has the derivative
$${df\over dx} = {e^{-x}\over(1 + e^{-x})^2}$$
which can be shown (Hint: exercise for "mathy" students!) to simplify to $${df\over dx}= f(1-f).$$
The overall problem then amounts to finding the values of the "weights" $w_0, w_1,$ and $w_2$ so that the $\tilde{Y}$ we calculate is as close to the target $Y$ as possible.
To do this, we will seek to minimize a loss function defined as a sum across all data points we have, i.e. all 4 rows. The loss function $L$ we will choose is the mean square error loss, or MSE (note: later in Part 2 we will use a 'better' loss function for this problem):
$$L = {1\over N}\sum_{i=0}^{N-1} \left[ \tilde{Y}_i - Y_i\right]^2,$$
or in terms of the activation function $$L = {1\over N}\sum_{i=0}^{N-1} \left[ f_i - Y_i\right]^2.$$
Each of the weights $w_j$ ($j=0..2$) will start with random values, and then be updated via gradient descent, i.e.
$$w_j^{new} = w_j^{old} - \alpha{\partial L\over \partial w_j}$$
where $\alpha$ is the learning rate, chosen to be some small parameter. For the MSE loss shown above, the partial derivatives with respect to each of the weights is
$${\partial L\over \partial w_j} = {2\over N}\sum_{i=0}^{N-1} \left[ \tilde{Y}_i - Y_i\right]{\partial f_i \over \partial w_j}\\ = {2\over N}\sum_{i=0}^{N-1} \left[ \tilde{Y}_i - Y_i\right]f_i(1-f_i)X_{ij}.$$
Absorbing the factor of 2/N into our choice of $\alpha$, and writing the summation as a dot product, and noting that $f_i = \tilde{Y}_i$, we can write the update for all the weights together as
$$w = w - \alpha X^T \cdot \left( [\tilde{Y}-Y]*\tilde{Y}*(1-\tilde{Y})\right)$$
where the $\cdot$ denotes a matrix-matrix product (i.e. a dot product for successive rows of $X^T$) and $*$ denotes elementwise multiplication.
To clarify the above expression in terms of matrix dimensions, we can see that $w$, a 3x1 matrix, can be made by multipyting $X^T$ (a 3 x4 matrix) with the term in parentheses, i.e. the product of elementwise terms involving $\tilde{Y}$, which is a 4x1 matrix. In other words, a 3x4 matrix, times a 4x1 matrix, yields a 3x1 matrix.
## Actual Code
The full code for all of this is then...
# https://iamtrask.github.io/2015/07/12/basic-python-network/
import numpy as np
# sigmoid activation
def sigmoid(x,deriv=False):
if(deriv==True):
return x*(1-x)
return 1/(1+np.exp(-x))
# input dataset
X = np.array([ [0,0,1],
[0,1,1],
[1,0,1],
[1,1,1] ])
# target output dataset
Y = np.array([[0,0,1,1]]).T
# seed random numbers to make calculation
# deterministic (just a good practice)
np.random.seed(1)
# initialize weights randomly with mean 0
w = 2*np.random.random((3,1)) - 1
alpha = 1.0 # learning rate
loss_history = [] # keep a record of how the loss proceeded, blank for now
for iter in range(1000):
# forward propagation
Y_pred = sigmoid(np.dot(X,w)) # prediction, i.e. tilde{Y}
# how much did we miss?
diff = Y_pred - Y
loss_history.append((diff**2).mean()) # add to the history of the loss
# update weights
w -= alpha * np.dot( X.T, diff*sigmoid(Y_pred, deriv=True))
print("Output After Training:")
print("Y_pred = (should be two 0's followed by two 1's)\n",Y_pred)
print("weights =\n",w)
Output After Training:
Y_pred = (should be two 0's followed by two 1's)
[[0.03178421]
[0.02576499]
[0.97906682]
[0.97414645]]
weights =
[[ 7.26283009]
[-0.21614618]
[-3.41703015]]
Note that, because of our nonlinear activation, we don't get the solution $w_0=1, w_1=0, w_2=0$.
Plotting the loss vs. iteration number, we see...
%matplotlib inline
import matplotlib.pyplot as plt
plt.loglog(loss_history)
plt.xlabel("Iteration")
plt.ylabel("Loss")
plt.show()
## Change the activation function
Another popular choice of activation function is the rectified linear unit or ReLU. The function ReLU(x) is zero for x <= 0, and equal to x (i.e. a straight line at 45 degrees for) x >0. It can be written as max(x,0) or x * (x>0), and its derivative is 1 for positive x, and zero otherwise.
Click here to see a graph of ReLU
Modifying our earlier code to use ReLU activation instead of sigmoid looks like this:
def relu(x,deriv=False): # relu activation
if(deriv==True):
return 1*(x>0)
return x*(x>0)
# seed random numbers to make calculation
# deterministic (just a good practice)
np.random.seed(1)
# initialize weights randomly (but only >0 because ReLU clips otherwise)
w = np.random.random((3,1))
alpha = 0.3 # learning rate
new_loss_history = [] # keep a record of how the error proceeded
for iter in range(1000):
# forward propagation
Y_pred = relu(np.dot(X,w))
# how much did we miss?
diff = Y_pred - Y
new_loss_history.append((diff**2).mean()) # add to the record of the loss
# update weights
w -= alpha * np.dot( X.T, diff*relu(Y_pred, deriv=True))
print("Output After Training:")
print("Y_pred = (should be two 0's followed by two 1's)\n",Y_pred)
print("weights =\n",w)
Output After Training:
Y_pred = (should be two 0's followed by two 1's)
[[-0.]
[-0.]
[ 1.]
[ 1.]]
weights =
[[ 1.01784368e+00]
[ 8.53961786e-17]
[-1.78436793e-02]]
print( w[2] - (1-w[0]) )
[-3.46944695e-17]
Plot old results with new results:
%matplotlib inline
import matplotlib.pyplot as plt
plt.loglog(loss_history,label="sigmoid")
plt.loglog(new_loss_history,label="relu")
plt.xlabel("Iteration")
plt.ylabel("Loss")
plt.legend()
plt.show()
Looks like ReLU may be a better choice than sigmoid for this problem!
## Exercise: Read a 7-segment display
A 7-segment display is used for displaying numerical digits 0 through 9, usually by lighting up LEDs or parts of a liquid crystal display (LCD). The segments are labelled $a$ through $g$ according to the following diagram:
### Diagram of the network
The 7 inputs "a" through "g" will be mapped to 10 outputs for the individual digits, and each output can range from 0 ("false" or "no") to 1 ("true" or "yes") for that digit. The input and outputs will be connected by a matrix of weights. Pictorially, this looks like the following (Not shown: activation function $f$):
...where again, this network operates on a single data point at a time, datapoints which are rows of X and Y. What is shown in the above diagram are the columns of $X$ and $Y$ for a single row (/ single data point).
### Create the dataset
Let the input X be the segments $a$ through $g$ are the columns of the input $X$, and are either 1 for on or 0 for off. Let the columns of the target $Y$ be the digits 0-9 themselves arranged in a "one hot" encoding scheme, as follows:
Digit One-Hot Encoding for $Y$ 0 1,0,0,0,0,0,0,0,0,0 1 0,1,0,0,0,0,0,0,0,0 2 0,0,1,0,0,0,0,0,0,0 ... ... 9 0,0,0,0,0,0,0,0,0,1
The values in the columns for $Y$ are essentially true/false "bits" for each digit, answering the question "Is this digit the appropriate output?" with a "yes"(=1) or "no" (=0) response.
The input $X$ will be a 10x7 matrix, and the target $Y$ will be a 10x10 matrix. Each row of $X$ will be the segments to produce the digit for that row. For example, the zeroth row of $X$ should show segments on which make an image of the digit zero, namely segments a, b, c, d, e, and f but not g, so that the zeroth row of X should be [1,1,1,1,1,1,0].
Define numpy arrays for both $X$ and $Y$ (Hint: for $Y$, check out np.eye()):
# for the 7-segment display. The following is just a "stub" to get you started.
X = np.array([ [1,1,1,1,1,1,0],
[],
[],
[] ])
Y = np.array([ [1,0,0,0,0,0,0,0,0,0],
[],
[] ])
### Initialize the weights
Previously the dimensions of the weight matrix $w$ were 3x1 because we were mapping each row of 3 elements in $X$ to each row of 1 element of $Y$. For this new problem, each row of $X$ has 7 elements, and we want to map those to the 10 elements in each 1-hot-encoded row of $Y$, so what should the dimensions of the weights matrix $w$ be?
Write some numpy code to randomly initialize the weights matrix:
np.random.seed(1) # initial RNG so everybody gets similar results
w = np.random.random(( , )) # Students, fill in the array dimensions here
File "<ipython-input-7-20f53a51cded>", line 1
w = np.random.random(( , ))
^
SyntaxError: invalid syntax
### Train the network
Having created an $X$ and its matching $Y$, and initalized the weights $w$ randomly, train a neural network such as the ones above to learn to map a row of X to a row of Y, i.e. train it to recognize digits on 7-segment displays. Do this below.
# Use sigmoid activation, and 1000 iterations, and learning rate of 0.9
# Question: What happens if you use ReLU instead? Try it later. Is ReLU always the best choice?
# And then print out your Y_pred & weights matrix, and limit it to 3 significant digits
print("Output After Training:")
np.set_printoptions(formatter={'float': lambda x: "{0:0.3f}".format(x)}) # 3 sig figs
print("Y_pred=\n",Y_pred)
print("weights =\n",repr(w)) # the repr() makes it so it can be copied & pasted back into Python code
## Final Check: Keras version
Keras is a neural network library that lets us write NN applications very compactly. Try running the following using the X and Y from your 7-segment dataset:
import keras
from keras.models import Sequential
from keras.layers import Dense, Activation
model = Sequential([
Dense(10, input_shape=(7,)),
Activation('sigmoid') ])
model.compile(optimizer='adam', # We'll talk about optimizer choices and loss choices later
loss='categorical_crossentropy',
metrics=['accuracy'])
model.fit(X, Y, epochs=200, batch_size=1)
print("\nY_tilde = \n", model.predict(X) )
# Follow-up: Remarks
### Re-stating what we just did
The original problem (posed at the top of this notebook) involves mapping some points from a 3-dimensional space into points in a 1-dimensional space, i.e. to points on the number line. The mapping is done by the combination of a weighted sum (a linear operation) and a nonlinear "activation function" applied to that sum. The use of an activation function like a sigmoid was originally intended to serve as an analogy of activation of biological neurons. Nonlinear activation functions are source of the "power" of neural networks (essentially we approximate some other function by means of a sum of basis functions in some function space, but don't worry about that if you're not math-inclined). The algorithm 'learns' to approximate this operation via supervised learning and gradient descent according to some loss function. We used the mean squared error (MSE) for our loss, but lots and lots of different loss functions could be used, a few of which we'll look at another time.
Question for reflection: Unlike fitting a line $y = mx+b$, the weighted sum in our models in this notebook had no constant "bias" term like $b$. How might we include such a term?
### One thing we glossed over: "batch size"
Question: Should we apply the gradient descent "update" to the weights each time we process a single row of $X$ & $Y$, or should we compute the combined loss of all the rows together at the same time, and then do the update? This is essentially asking the same question as "When fitting a line $mx+b$ to a bunch of data points, should we use all the points together to update $m$ and $b,$ or should we do this one point at a time -- compute the gradients of the loss at one point, update the weights, compute gradients at another point, etc.?"
The number of points you use is called the batch size and it is what's known as a "hyperparameter" -- it is not part of the model per se, but it is a(n important) choice you make when training the model. The batch size affects the learning as follows: Averaging the gradints for many data points (i..e. a large batch size) will produce a smoother loss function and will also usually make the code execute more quickly through the dataset, but updating the weights for every point will cause the algorithm to learn with fewer iterations.
One quick way to observe this is to go up to the Keras code above and change batch_size from 1 to 10, and re-execute the cell. How is the accuracy after 200 iteractions, compared to when batch_size=1?
Terminology: Technically, it's called "batch training" when you sum the gradients for all the data points before updating the weights, whereas using fewer points is "minibatch training", and updating for each point (i.e. each row, for us) is Stochastic Gradient Descent* (SGD -- more on these terms here). In practice, there is a tradeoff between smaller vs. larger (mini)batches, which has been the subject of intense scrutiny by researchers over the years. We will have more to say on this later.
For discussion later: In our presentation above, were we using batch training, minibatch training or SGD?
.
*Note: many people will regard SGD as an optimization algorithm per se, and refer to doing SGD even for (mini)batch sizes larger than 1.
## Optional: If you want to go really crazy
How about training on this dataset: $$\overbrace{ \left[ {\begin{array}{cc} 0 & 0 \\ 0 & 1 \\ 1 & 0 \\ 1 & 1 \\ \end{array} } \right] }^{X} \rightarrow \overbrace{ \left[ {\begin{array}{c} 0 \\ 1 \\ 1 \\ 0 \\ \end{array} } \right] }^Y.$$ Good luck! ;-)
(Hint 1: This problem features prominently in the history of Neural Networks, involving Marvin Minsky and "AI Winter."
Hint 2: This whole lesson could instead be entitled "My First Artificial Neuron.")
Next time, we will go on to Part 2: Bias and CE Loss.
## Additional Optional Exercise: Binary Math vs. One-Hot Encoding
For the 7-segment display, we used a one-hot encoding for our output, namely a set of true/false "bits" for each digit. One may wonder how effective this ouput-encoding method is, compared to a different bit-setting encoding method, namely binary representations.
1. Construct the target output matrix $Y$ for binary representations of the numbers 0 through 9. Your target matrix should have 10 rows and 4 columns (i.e, output bits for 1s, 2s, 4s, and 8s).
2. Using this $Y$ array, train the network as before, and plot the loss as a function of iteration.
Question: Which method works 'better'? One-hot encoding or binary encoding?
(c) 2020 Scott H. Hawley | 2020-11-30 02:40:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.7663224935531616, "perplexity": 1073.4424336844056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141204453.65/warc/CC-MAIN-20201130004748-20201130034748-00564.warc.gz"} |
http://mathhelpforum.com/differential-equations/189730-wave-equation-stokes-theorem.html | # Math Help - Wave Equation and Stokes Theorem
1. ## Wave Equation and Stokes Theorem
Good Morning everyone, I am stuck on a question that I can't get started so thank you for any help you give.
Derive the solution of the inhomogeneous wave equation on the half line using Stokes' Theorem via integrating over the domain of dependence.
$u_{tt}= c^2u_{xx} + g(x,t)$
$u(x,0)=h(x), \ u(0,t)=\xi(x), \ u_t(x,0)=\phi(x)$, $0
2. ## Re: Wave Equation and Stokes Theorem
Well, where, exactly is your problem? Do you know what Stoke's theorem says? Do you know what the "domain of dependence" is?
3. ## Re: Wave Equation and Stokes Theorem
My problem is applying stokes theorem properly. I have an o.k understanding of stokes theorem and what is meant by 'domain of dependence', and I know the solution will be split into two, one for x>ct>0 and another for 0<x<ct. The domain of dependence will be involved in the solution via the part of the solution:
$\frac{1}{2c}\int_\triangle \int f$
But I don't really know how to get the rest of the solution. Thanks | 2014-10-25 20:50:01 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8477035164833069, "perplexity": 326.99837724265024}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1414119650193.38/warc/CC-MAIN-20141024030050-00316-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://proxies123.com/tag/functions/ | ## Functional analysis of fa – Isoperimetric inequality for analytical functions in a ring
Leave $$f$$ be an anylytic function on the disk drive $$| z | < 1$$. It is well known that
$$left ( int_0 ^ {2 pi} f (e ^ {i theta}) d theta right) ^ 2 geq 4 pi iint_ {| z | <1} | f (re ^ {i theta}) | ^ 2nd dr d theta.$$
I wonder if the constant $$4 pi$$ can be improved in a ring $$a . More precisely, does the following inequality
$$left ( int_0 ^ {2 pi} f (e ^ {i theta}) d theta + int_0 ^ {2 pi} f (ae ^ {i theta}) d theta right ) ^ 2 geq C iint_ {a <| z | <1} | f (re ^ {i theta}) | ^ 2r dr d theta$$
wait for some constant $$C (a)> 4 pi$$ independent of $$f$$? They can $$C (a)$$ be calculated in terms of $$to$$? This seems to be a classic problem, but I couldn't find a reference and couldn't test it after trying it for a couple of days.
## mathematical optimization – Iterate Minimize in a list of functions
I have a function $$f$$ defined in $$(- 1,1)$$.
For a minimal example, it is sufficient to define
``````f(z_):=z^2 - 1
``````
I need to find a list of points so that $$f (z_0) = f (z_1)$$, points whose image "is at the same height".
I continued to find the minimum through
`````` min = First@Minimize(f(z), {z})
``````
what happens for $$z$$ equal to
``````argmin = Values@Last@Minimize(f(z), {z})
``````
Also I created a list with
`````` rang = Subdivide(a, 0,10)
``````
spanning the range from minimum to predefined value.
Now I would like to find, for each item on this list, points such that $$f (z_0) = f (z_1) = rang_j$$, for each item in the list.
I couldn't find a better plan than defining a list of features $$fun_j = (f (z) + rang_j) ^ 2$$. By changing the original function and squaring, I am sure that the functions $$fun_j$$, one for each item in the list $$rang$$ they are positive everywhere except the roots.
So I wanted to iterate over the list of functions a restricted minimization through the commands (the argument $$f_j$$ just to clarify my question, I understand that the syntax will be different, that's exactly what the question is about):
`````` Minimize({f_j, z > argmin}, {z})
Minimize({f_j, z > argmin}, {z})
``````
that is, run two minimizations one on the left and one on the right of the $${arg , min}$$. I know for mathematical reasons that there are two unique solutions.
I create my list of functions as
`````` f1(z_,c_):=f(z)+c
``````
and then using
`````` f1(z,rang)
``````
but I find it hard to iterate Minimize, any suggestion would be helpful.
Annoying
`````` Minimize({f1( z, rang), z > b}, z)
``````
produces an error message, since the Minimize function argument is expected to be a scalar function.
I'd also like to hear about better methods, in general and in reference to Mathematica.
Health
## functions: new data framework for different groups
I have a data frame with a & # 39; Country & # 39; column. Each country has multiple records. I want to write a function in Python using pandas so that for each country I can return a separate data frame.
Have a list of countries like, countries = [& # 39; USA, & # 39; Spain & # 39;, & # 39; France & # 39;],
Individually I can do for
df_us = df [df.country == & # 39; US & # 39;]
df_spain = df [df.country == & # 39; Spain & # 39;],
But how can it be done using a function! Thanks in advance
## set-return functions in postgres
I've been trying to use Postgres's generate_series () function to get a table like this:
I still haven't come up with a solution, so any ideas would be appreciated.
## Complex variables cv.com: switch arrays of complex functions
Leave $$z_0 in Bbb {R}$$ be arbitrary matrices $$A_0: = A (z_0)$$ Y $$B_0: = B (z_0)$$ are normal; in view of $$A_0 ^ * = A ^ # ( bar {z_0}) = A ^ # (z_0)$$ Y $$B_0 ^ * = B ^ # ( bar {z_0}) = B ^ # (z_0)$$ they travel with their Hermitian deputies. They also travel with each other. So $$A_0$$ Y $$B_0$$ it could be simultaneously diagonalized by a unitary matrix. That matrix is also diagonalized $$A_0 ^ *$$ Y $$B_0 ^ *$$. So the four matrices $$A_0 = A (z_0), B_0 = B (z_0), A_0 ^ * = A ^ # (z_0), B_0 ^ * = B ^ # (z_0)$$ it could be diagonalized simultaneously, implying that they all travel with each other. So $$B (AA ^ #) = (AA ^ #) B$$ at any point on the actual line. Since the inputs are complete functions, they coincide throughout the complex plane.
## calculus and analysis: limit on infinity of arbitrary functions
Here is the code that takes the limit of an expression.
``````Limit((-I E^(I x) f1(y))/(g2^(Prime)(Prime))(y), x -> (Infinity) )
``````
and the output returned is `INDETERMINATE` while the desired output is $$infty$$. Or if I had to do this instead
``````Limit((g2^(Prime)(Prime))(y)/(-I E^(I x) f1(y)), x -> (Infinity) )
``````
I would like to get 0 and not `INDETERMINATE`.
How would you tell Mathematica that the $$f$$ Y $$g$$ What functions are irrelevant when evaluating the limit?
Thanks for any help.
## functions: how does following two (same) calculations give two different results?
I have the following two pieces of code that give me two different results,
`````` N((-Kp tp + Lc - tp Lc)/(Kp tp)) /. {Lc -> 6, tc -> 0.8, tp -> 0.2, Kp -> 1/3}
``````
``````(-Kp tp + Lc - tp Lc)/( Kp tp) /. {Lc -> 6, tc -> 0.8, tp -> 0.2, Kp -> 1/3}
``````
Which gives the answer as 3 (which is obviously wrong).
Could someone explain how / why this happens and how to avoid this (possible) error?
Below is the image of the calculation on my machine:
Can anyone explain the following behavior in Mathematica 12.0?
``````EllipticK[N[1/2, 100]]
``````
spit `ComplexInfinity`. Nevertheless
``````EllipticK[1/2] // N[#, 100] &
``````
It seems to give the correct result. In my current code, I only know the argument of the function `EllipticK` numerically then the second option is not exactly what i want.
## CHAIN REVERSION in PYTHON (without using built-in functions)
What is wrong with the following code?
It is giving an error: ROPE OUT OF REACH
``````def reverse(s):
i=0
l=()
while i``````
``` jQuery(document).ready(function() {jQuery.ajax({type: "POST",url : rating_form_script.ajaxurl,data : { action : "display_rating_form_ajax", args : {"id":2,"post_id":201862,"comment_id":0,"custom_id":"0","user_id":0,"term_id":0,"title":false,"score":true,"total":true,"stats":true,"user_stats":false,"tooltip":true,"result":true,"rich_snippet":true,"is_widget":false,"state":"","before_content":"","after_content":"","rates":"rating,ratings","txt_score":"%1\$s\/%2\$s"} }, success : function(data) { jQuery("body").find("[data-id=\"RFR2P201862\"]").html(data); }});}); ```
``` Posted on April 1, 2020Author Proxies123Tags builtin, chain, functions, Python, REVERSION ```
``` parametric functions – Problem: solving the system of equations I am trying to solve a "simple" system of equations for a formal theoretical model that I am developing. Although I think I had correctly specified the system, I can't find a solution so far. Is it a problem with so many parameters? Can someone help me with this? Solve({A1*A2*y - A3*y - A4 - A5*((1/A6)^(1-A7))*((x*A8 + A9)^(A10)) + A11*((A6)^(-A12))*((y*A13)^(A14)) == 0, A15*A16*x - A17*x -A19 - A18*A6+ A5*((1/A6)^(1-A7))*((x*A8 + A9)^(A10)) - A11*((A6)^(-A12))*((y*A13)^(A14)) == 0, 00, A2>0,A3>0,A4>0,A5>0,A6>0,A7>0,A8>0,A9>0,A10>0,A11>0,A12>0,A13>0,A14>0,A15>0,A16>0,A17>0, A18>0, A19>0}, {x,y}) Thank you! jQuery(document).ready(function() {jQuery.ajax({type: "POST",url : rating_form_script.ajaxurl,data : { action : "display_rating_form_ajax", args : {"id":2,"post_id":201567,"comment_id":0,"custom_id":"0","user_id":0,"term_id":0,"title":false,"score":true,"total":true,"stats":true,"user_stats":false,"tooltip":true,"result":true,"rich_snippet":true,"is_widget":false,"state":"","before_content":"","after_content":"","rates":"rating,ratings","txt_score":"%1\$s\/%2\$s"} }, success : function(data) { jQuery("body").find("[data-id=\"RFR2P201567\"]").html(data); }});}); Posted on March 31, 2020Author Proxies123Tags equations, functions, parametric, Problem, solving, system Posts navigation Page 1 Page 2 … Page 82 Next page ``` | 2020-04-07 13:53:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 34, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7116135358810425, "perplexity": 12295.476828443958}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371799447.70/warc/CC-MAIN-20200407121105-20200407151605-00127.warc.gz"} |
https://trizenx.blogspot.com/ | ## Posts
### Primality testing algorithms
In this post we're going to look at some algorithms for checking if a given number is either prime or composite.
Prime numbers play an important role in public-key cryptography (e.g. RSA algorithm) which require fast generation of large random prime numbers that have around 600 digits (or more).
The simplest way to generate a prime number, is to pick a random odd integer and check its primality, repeating this process until a prime is found. This approach requires a fast algorithm for checking the primality of a number.
In 2002, Manindra Agrawal, Neeraj Kayal, and Nitin Saxena published the AKS primality test, unconditionally proving that the primality of a number can be checked in polynomial time, with an asymptotic time complexity of Õ(log(n)^12).
Later on, in 2005, Carl Pomerance and Hendrik Lenstra improved the complexity of the AKS algorithm to run in just Õ(log(n)^6) steps.
While being of great theoretical importance, the AKS algorithm is not actually used in practic…
### Primorial in algorithms
In this post we present several practical algorithms based on primorials.
### Special-purpose factorization algorithms
In this post, we will take a brief look at a nice collection of special-purpose factorization algorithms. Most of them old and well-known. Some of them new.
### Partial sums of arithmetical functions
In this post we're going to look at some very interesting generalized formulas for computing the partial sums of some arithmetical functions.
### Continued fraction factorization method
The factorization method that we'll discuss in this post, it's called the continued fraction factorization method (CFRAC), and is quite an old method, but still pretty interesting, sharing many concepts and ideas with other modern factorization methods.
### Curiosities in number theory
In this post I would like to present some interesting exercises in number theory, along with some curious formulas and identities for some number-theoretic functions.
### Investigating the Fibonacci numbers modulo m
The Fibonacci sequence is, without doubt, one of the most popular sequences in mathematics and in popular culture, named after Italian mathematician Leonardo of Pisa (also known as Fibonacci, Leonardo Bonacci, Leonardo of Pisa, Leonardo Pisano Bigollo, or Leonardo Fibonacci), who first introduced the numbers in Western European with his book Liber Abaci, in 1202.
### Representing integers as the sum of two squares
In this post we present a recursive algorithm for finding all the possible representations, as a sum of two squares, for any given integer that can be expressed this way.
### Representing integers as the difference of two squares
Most integers can be represented as a difference of two squares, where each square is a non-negative integer.
### Various representations for famous mathematical constants
In this unusual post, much like in the older post, The beauty of Infinity, we're listing the most famous mathematical constants as representations of infinite seriesinfinite products and limits.
### Thoughts on programming language notations
Some posts ago, we looked at what it's required in creating a new programming language. In this post we're going a little bit more into it, trying to find ways to effectively express meanings in natural ways, similar to what we can express in a natural language.
### Bacovia: a symbolic math library
Named after the great symbolist poet, George Bacovia, I created this library to symbolically manipulate mathematical expressions in a simple and elegant way.
### Mandelbrot set
The Mandelbrot set and its complex beauty.
### RSA algorithm
RSA is a practical public-key cryptographic algorithm, which is widely used on modern computers to communicate securely over large distances.
The acronym of the algorithm stands for Ron Rivest, Adi Shamir and Leonard Adleman, which first published the algorithm in 1978.
# Algorithm overviewChoose p and q as distinct prime numbersCompute n as n = p*qCompute \phi(n) as \phi(n) = (p-1) * (q-1)Choose e such that 1 < e < \phi(n) and e and \phi(n) are coprimeCompute the value of d as d ≡ e^(-1) mod \phi(n)Public key is (e, n)Private key is (d, n)The encryption of m as c, is c ≡ m^e mod nThe decryption of c as m, is m ≡ c^d mod n
# Generating p and q In order to generate a public and a private key, the algorithm requires two distinct prime numbers p and q, which are randomly chosen and should have, roughly, the same number of bits. By today standards, it is recommended that each prime number to have at least 2048 bits.
In Perl, there is a… | 2020-02-17 16:36:55 | {"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": 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": 0.6568690538406372, "perplexity": 1137.17553994307}, "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-2020-10/segments/1581875142603.80/warc/CC-MAIN-20200217145609-20200217175609-00250.warc.gz"} |
https://xxm.times.uh.edu/forums/reply/1599/ | #1599
Paras Mehta
Keymaster
Thanks for the feedback and sorry for the confusion.
Neither the model object (brim) nor the dataframe object (brim.student) should be in quotes.
Could you please try to run the script included with the package? You can find the script under “\xxm\models\brim” directory. Once the packaged data is loaded using data() command:
data(brim.xxm, package = "xxm")
you can examine the contents by issuing the str() command:
str(brim.student)
str(brim.teacher)
Please let me know if you have any trouble with script included with the package. The rest of the script should work if both datasets are loaded.
• This reply was modified 7 years, 6 months ago by Paras Mehta.
• This reply was modified 7 years, 6 months ago by Paras Mehta.
• This reply was modified 7 years, 6 months ago by Paras Mehta.
• This reply was modified 7 years, 6 months ago by Paras Mehta.
• This reply was modified 7 years, 6 months ago by Paras Mehta. | 2021-07-29 22:51:35 | {"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": 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": 0.28044331073760986, "perplexity": 3939.424376574663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1627046153897.89/warc/CC-MAIN-20210729203133-20210729233133-00212.warc.gz"} |
https://www.physicsforums.com/threads/show-a-set-is-of-measure-zero.666119/ | # Show a set is of measure zero
1. Jan 22, 2013
### stripes
I am trying to prove if f and g are Riemann integrable, then fg is also Riemann integrable using Lebesgue's integrability criterion. I already proved that a Riemann integrable function is bounded. Not much harder to show fg is too bounded. How do I show that [a,b] is of measure zero? I can't figure outa sequence whose infinite union contains [a,b] but also whose sum of lengths is less than all epsilon greater than zero. How do a construct such a sequence? Or should I go about it differently?
2. Jan 22, 2013
### kevinferreira
You mean [a,b] in $\mathbb{R}$? It doesn't have measure zero...
3. Jan 22, 2013
### Dick
What does the Lebesgue criterion tell you about the sets of discontinuities of f and g? How might those be related to the set of discontinuities of fg?
4. Jan 22, 2013
### stripes
Okay, I think I misread the theorem. The set of discontinuities must have measure zero for the function to be Riemann integrable. Now, I know the set of discontinuities of f and g are both of measure zero. What does that tell us about the set of discontinuities of fg?
Is the set of discontinuities of fg simply the union of the sets of discontinuities for f and g? If so, is the union of two sets whose measures are both zero, also zero? If any of these two statements are true, how would I go about showing that?
5. Jan 22, 2013
### jbunniii
You probably know this result: if $f$ and $g$ are both continuous at a point $x$, then $fg$ is also continuous at $x$. (If you don't know it, you should prove it; it's pretty easy.) So what does that say about the set of discontinuities of $fg$?
6. Jan 22, 2013
### stripes
Yes, it isn't hard to show fg is continuous in that case. Maybe I'm not understanding the problem completely, though. A function need not be continuous to be Riemann integrable. So then a function can be discontinuous and still have a set of discontinuities that is of measure zero. An example would be if this set is countable, like if it has one discontinuity. Therefore, I cannot assume that f and g are continuous to begin with. We could have an infinite number of discontinuities, but as long as these discontinuities are countable; i.e., have a one-to-one correspondence with the natural numbers, then the function will be Riemann integrable as long as it is bounded. Is this not correct?
7. Jan 22, 2013
### jbunniii
You asked whether the set of discontinuities of $fg$ is the same as the union of the sets of discontinuities of $f$ and $g$. So take the result I stated: in order for $fg$ to be discontinuous at a point $x$, either $f$ or $g$ must also be discontinuous at that point. What does that tell you?
8. Jan 22, 2013
### stripes
Your statement further supports my idea that it is the union of the two sets. So fg is discontinuous at c if and only if g or f is discontinuous at c. Because a set, by definition, doesn't count the same element twice, if we are given a point of discontinuity of fg, we don't care if it's in one set, the other set, or both. So it must be the union of the two sets.
Subadditivity--so the measure of the union of two sets is equal to or less than the sum of the measures of the two sets individually? Since a measure is always positive (I think), 0 + 0 = 0, so its union has measure 0 as well.
9. Jan 22, 2013
### Dick
Define h(x)=1 if x>=0 and -1 if x<0. Pick f=h and g=h. What the discontinuities of fg? I don't think it's the exactly the union. But yes, the union has measure zero.
Last edited: Jan 22, 2013
10. Jan 22, 2013
### stripes
Is it just the same set then? While either f or g can be discontinuous for fg to be discontinuous, they end up being the same point anyways. If it is neither the union nor either set itself, then I am lost.
Your example doesn't suggest it isn't the union. The discontinuities of f is x=0, the discontinuities of g is x=0, and the discontinuities of fg is x=0. The union of {0} and {0} is {0}.
11. Jan 22, 2013
### Dick
fg is h^2=1. It's continuous everywhere. If f is discontinuous and g is discontinuous at a point x, that doesn't mean fg is discontinuous at x. It's not even true that if f is continuous and g is discontinuous then fg is discontinuous. What is true is that if f and g are continuous then fg is continuous. That's about all.
12. Jan 22, 2013
### jbunniii
Indeed. Simple counterexample: f(x) = 0 for all x.
13. Jan 22, 2013
### stripes
Okay, so the contrapositive tells us that if fg is not continuous then f or g is not continuous. So is the set of discontinuities of fg not a subset of the union of discontinuities? Because the set of all discontinuities of fg will definitely be in the set for f or g. Might be both, might be only one, but it is in at least one. So if I know for sure that the union of two sets whose measure is zero is also zero, then I can be 100% certain that any subset of this union is also of measure zero. So if this set that I am so desperately trying to find is a subset of the union, and the union's measure is also zero, then I'm in business.
14. Jan 22, 2013
### Dick
You're in business. It must be a subset of the union of the discontinuities.
15. Jan 22, 2013
### stripes
Thanks everyone. Your help is appreciated. | 2017-08-17 14:32:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7694205045700073, "perplexity": 264.751099341672}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1502886103316.46/warc/CC-MAIN-20170817131910-20170817151910-00335.warc.gz"} |
https://answerriddle.com/tag/i-had-5-00-riddle/ | ## I had £5 pound riddle
Riddle: I had £5.00 My mom gave me £10.00 while my dad gave me £30.00. My aunt and uncle gave me £100.00. I had another £5.00
How much money did I really have? | 2021-06-24 02:42:41 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9815056920051575, "perplexity": 12847.110986191034}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1623488550571.96/warc/CC-MAIN-20210624015641-20210624045641-00579.warc.gz"} |
https://datascience.stackexchange.com/questions/79991/can-a-linear-regression-model-without-polynomial-features-overfit/79994 | # Can a linear regression model without polynomial features overfit?
I've read in some articles on the internet that linear regression can overfit. However is that possible when we are not using polynomial features? We are just plotting a line trough the data points when we have one feature or a plane when we have two features.
• Hi Tim, in the examples you mention, 1 and 2 dimensions, overfitting via linear regression is not realistically an issue. If we're doing multiple regression, with, for instance, more dependent variables than we have data, then it can become an issue. – John Madden Aug 9 '20 at 5:06
It sure can!
Throw in a bunch of predictors that have minimal or no predictive ability, and you’ll get parameter estimates that make those work. However, when you try it out of sample, your predictions will be awful.
set.seed(2020)
# Define sample size
#
N <- 1000
# Define number of parameters
#
p <- 750
# Simulate data
#
X <- matrix(rnorm(N*p), N, p)
# Define the parameter vector to be 1, 0, 0, ..., 0, 0
#
B <- rep(0, p)#c(1, rep(0, p-1))
# Simulate the error term
#
epsilon <- rnorm(N, 0, 10)
# Define the response variable as XB + epsilon
#
y <- X %*% B + epsilon
# Fit to 80% of the data
#
L <- lm(y[1:800]~., data=data.frame(X[1:800,]))
# Predict on the remaining 20%
#
preds <- predict.lm(L, data.frame(X[801:1000, ]))
# Show the tiny in-sample MSE and the gigantic out-of-sample MSE
#
sum((predict(L) - y[1:800])^2)/800
sum((preds - y[801:1000,])^2)/200
I get an in-sample MSE of $$7.410227$$ and an out-of-sample MSE of $$1912.764$$.
It is possible to simulate this hundreds of times to show that this wasn't just a fluke.
set.seed(2020)
# Define sample size
#
N <- 1000
# Define number of parameters
#
p <- 750
# Define number of simulations to do
#
R <- 250
# Simulate data
#
X <- matrix(rnorm(N*p), N, p)
# Define the parameter vector to be 1, 0, 0, ..., 0, 0
#
B <- c(1, rep(0, p-1))
in_sample <- out_of_sample <- rep(NA, R)
for (i in 1:R){
if (i %% 50 == 0){print(paste(i/R*100, "% done"))}
# Simulate the error term
#
epsilon <- rnorm(N, 0, 10)
# Define the response variable as XB + epsilon
#
y <- X %*% B + epsilon
# Fit to 80% of the data
#
L <- lm(y[1:800]~., data=data.frame(X[1:800,]))
# Predict on the remaining 20%
#
preds <- predict.lm(L, data.frame(X[801:1000, ]))
# Calculate the tiny in-sample MSE and the gigantic out-of-sample MSE
#
in_sample[i] <- sum((predict(L) - y[1:800])^2)/800
out_of_sample[i] <- sum((preds - y[801:1000,])^2)/200
}
# Summarize results
#
boxplot(in_sample, out_of_sample, names=c("in-sample", "out-of-sample"), main="MSE")
summary(in_sample)
summary(out_of_sample)
summary(out_of_sample/in_sample)
The model has overfit badly every time.
In-sample MSE summary
Min. 1st Qu. Median Mean 3rd Qu. Max.
3.039 5.184 6.069 6.081 7.029 9.800
Out-of-sample MSE summary
Min. 1st Qu. Median Mean 3rd Qu. Max.
947.8 1291.6 1511.6 1567.0 1790.0 3161.6
Paired Ratio Summary (always (!) much larget than 1)
Min. 1st Qu. Median Mean 3rd Qu. Max.
109.8 207.9 260.2 270.3 319.6 566.9
• Thanks! This answered my question. The intuition why this happens is still lacking though, probably because I think about it in a geometrical way. – Tim von Känel Aug 8 '20 at 22:28
• The geometrical intuition can be that you increase your dimensionality with more features. – Itamar Mushkin Aug 9 '20 at 7:41
Ordinary Least Squares (OLS) is quite robust and under Gauss-Markov assumptions, it is a best linear unbiased estimator (BLU). So there is no overfitting as understood to be a problem, e.g. with neural nets. If you want to say so, there is just „fitting“.
When you apply variations of OLS, including adding polynomials or applying additive models, there will of course be good and bad models.
With OLS you need to make sure to meet the basic assumptions since OLS can go wrong in case you violate important assumptions. However, many applications of OLS, e.g. causal models in econometrics, do not know overfitting as a problem per se. Models are often „tuned“ by adding/removing variables and checking back on AIC, BIC or adjusted R-square.
Also note that OLS usually is not the best approach for predictive modeling. While OLS is rather robust, things like neural nets or boosting are often able to produce better predictions (smaller error) than OLS.
Edit: Of course you need to make sure that you estimate a meaningful model. This is why you should look at BIC, AIC, adjusted R-square when you choose a model (which variables to include). Models which are „too large“ can be a problem as well as models which are „to small“ (omitted variable bias). However, in my view this is not a problem of overfitting but a problem of model choice.
• Please refer to my simulation for an example of extreme overfitting by an OLS linear regression that satisfies the Gauss-Markov aassumptions. – Dave Aug 8 '20 at 21:34
• @Dave: Check the AIC, BIC for several variations of your model (which variables to include). I‘m quite sure you will not pic the poor model described by you in this case. – Peter Aug 8 '20 at 21:46
• And that's because the measure of overfitting (AIC, BIC, out-of-sample MSE, etc) shows that model to be badly overfit. – Dave Aug 8 '20 at 21:48
• @Dave: Well, good argument. I never saw this as a (genuine) aspect of overfitting as you would have it with e.g. neural nets. But of course model choice (variables to include) is instrumental. I was nudged by the question framing the problem in a one or two explanatory variable setting. – Peter Aug 8 '20 at 22:12 | 2021-06-18 06:58:34 | {"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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.683886706829071, "perplexity": 2726.7279056567027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1623487635724.52/warc/CC-MAIN-20210618043356-20210618073356-00636.warc.gz"} |
https://aptitude.gateoverflow.in/1075/cat-2002-question-60 | 186 views
A boy finds the average of $10$ positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say $ba$ for $ab.$ Due to this, the average becomes $1.8$ less than the previous one. What is the difference between two digits $a$ and $b?$
1. $4$
2. $2$
3. $6$
4. $8$
1
342 views | 2022-12-10 04:39:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 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": 0.3634180724620819, "perplexity": 366.1186004036777}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1669446711712.26/warc/CC-MAIN-20221210042021-20221210072021-00732.warc.gz"} |
http://mathhelpforum.com/algebra/167564-algebra-problem-dealing-lengths.html | # Math Help - Algebra problem dealing with lengths
1. ## Algebra problem dealing with lengths
If [ a ] = 5 cm , and [ b ] = 3a cm , find [ a + b ]
2. $\displaystyle a = 5, b=3a= 3\times 5 = 15 \implies a+b = 5+15=\dots$ | 2015-10-09 00:22:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6238721609115601, "perplexity": 2666.6638482650756}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737911339.44/warc/CC-MAIN-20151001221831-00178-ip-10-137-6-227.ec2.internal.warc.gz"} |
https://standards.globalspec.com/std/3829620/astm-d4460-97 | ### This is embarrasing...
An error occurred while processing the form. Please try again in a few minutes.
### This is embarrasing...
An error occurred while processing the form. Please try again in a few minutes.
# ASTM International - ASTM D4460-97
## Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods
inactive
Organization: ASTM International Publication Date: 10 November 1997 Status: inactive Page Count: 2 ICS Code (Road construction materials): 93.080.20
##### scope:
1.1 This practice describes techniques for calculating precision limits when values are calculated from two other methods having precision limits.
1.2 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems associated with its use. It is the responsibility of whoever uses this standard to consult and establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use .
### Document History
January 1, 2015
Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods
4.1 Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly....
December 1, 2009
Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods
Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly. This...
June 1, 2005
Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods
Precision limits for a test result that is calculated by addition, subtraction, multiplication, or division of two other test results that have valid precision limits can be calculated directly. This...
June 1, 2004
Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods
1.1 This practice describes techniques for calculating precision limits when values are calculated from two other methods having precision limits. 1.2 This standard does not purport to address all of...
ASTM D4460-97
November 10, 1997
Standard Practice for Calculating Precision Limits Where Values are Calculated from Other Test Methods
1.1 This practice describes techniques for calculating precision limits when values are calculated from two other methods having precision limits. 1.2 This standard may involve hazardous materials,... | 2022-05-20 10:03:54 | {"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": 0.8288620114326477, "perplexity": 2401.2773770344907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662531779.10/warc/CC-MAIN-20220520093441-20220520123441-00038.warc.gz"} |
https://conversationofmomentum.wordpress.com/2012/11/24/puzzle-7-exponentially-decreasing-force/ | # Puzzle #7 – Resistive Forces
A particle of mass $m$ is acted on by a force
$F=\lambda e^{-\frac{x}{\gamma}}$
where $\lambda$ and $\gamma$ are positive constants, and $x$ is the particle’s displacement from the origin.
Question: By using the chain rule, show that this equation of motion is exactly equivalent to one of the form
$F=\lambda-\rho v^2$
and deduce an equivalence for $\rho$. How might you describe the two forces at work?
Extension: Given that the particle starts from rest at the origin, show that the particle’s position $x$ after time $t$ is given by
$x=2\gamma\ln\bigg(\cosh\Big[t\sqrt{\frac{\lambda}{2m\gamma}}\Big]\bigg)$
or an equivalent, expressed in terms of $\rho$.
Hint: The chain rule provides the following relation:
$\displaystyle \frac{dv}{dt}=\frac{dv}{dx}\cdot\frac{dx}{dt}$ | 2018-01-18 00:02:24 | {"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": 0, "img_math": 12, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8125730156898499, "perplexity": 147.08457795632748}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887024.1/warc/CC-MAIN-20180117232418-20180118012418-00245.warc.gz"} |
https://wiki.math.ucr.edu/index.php?title=008A_Sample_Final_A&diff=cur&oldid=705 | # Difference between revisions of "008A Sample Final A"
This is a sample final, and is meant to represent the material usually covered in Math 8A. Moreover, it contains enough questions to represent a three hour test. An actual test may or may not be similar. Click on the boxed problem numbers to go to a solution.
## Question 1
Find ${\displaystyle f^{-1}(x)}$ for ${\displaystyle f(x)=\log _{3}(x+3)-1}$
## Question 2
Find f(5) for f(x) given in problem 1.
## Question 3
a) Find the vertex, standard graphing form, and X-intercept for ${\displaystyle x=-3y^{2}-6y+2}$
b) Sketch the graph. Provide the focus and directrix.
## Question 4
Solve. Provide your solution in interval notation. ${\displaystyle (x-4)(2x+1)(x-1)<0}$
## Question 5
Graph the system of inequalities ${\displaystyle y<\vert x\vert +1}$ ${\displaystyle x^{2}+y^{2}\leq 9}$
## Question 6
Sketch ${\displaystyle 4x^{2}+9(y+1)^{2}=36}$. Give coordinates of each of the 4 vertices of the graph.
## Question 7
Solve ${\displaystyle 2\vert 3x-4\vert -7=7}$
## Question 8
Given a sequence ${\displaystyle 27,23,19,15,\ldots }$ use formulae to compute ${\displaystyle S_{10}}$ and ${\displaystyle A_{15}}$.
## Question 9
a) List all the possible rational zeros of the function ${\displaystyle f(x)=x^{4}+5x^{3}-27x^{2}+31x-10}$
b) Find all the zeros, that is, solve f(x) = 0
## Question 10
Graph the function. Give equations of any asymptotes, and list any intercepts ${\displaystyle y={\frac {x-1}{2x+2}}}$
## Question 11
Decompose into separate partial fractions ${\displaystyle {\frac {3x^{2}+6x+7}{(x+3)^{2}(x-1)}}}$
## Question 12
Find and simplify the difference quotient ${\displaystyle {\frac {f(x+h)-f(x)}{h}}}$ for f(x) = ${\displaystyle {\frac {2}{3x+1}}}$
## Question 13
Set up, but do not solve, the following word problem.
One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and$15 for a lawn seat. Total receipts were \$28,500. How many of each type of ticket were sold?
## Question 14
Compute ${\displaystyle \displaystyle {\sum _{n=1}^{\infty }5\left({\frac {3}{5}}\right)^{n}}}$
## Question 15
a) Find the equation of the line passing through (3, -2) and (5, 6).
b) Find the slope of any line perpendicular to your answer from a).
## Question 16
Solve. ${\displaystyle \log _{6}(x+2)+\log _{6}(x-3)=1}$
## Question 17
Compute the following trig ratios: a) ${\displaystyle \sec {\frac {3\pi }{4}}}$ b) ${\displaystyle \tan {\frac {11\pi }{6}}}$ c) ${\displaystyle \sin(-120)}$
## Question 18
Compute ${\displaystyle \cos(\arctan {\frac {5}{3}})}$
## Question 19
Compute ${\displaystyle \arcsin -{\frac {\sqrt {3}}{2}}}$. Provide your answer in radians. | 2022-07-04 11:48:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 23, "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": 0.6095722913742065, "perplexity": 4002.347324895502}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104375714.75/warc/CC-MAIN-20220704111005-20220704141005-00787.warc.gz"} |
http://math.stackexchange.com/questions/45308/change-of-order-of-double-limit-of-function-sequence | # Change of order of double limit of function sequence
The more general quesion is under what conditions the folloing equality will hold (all functions are real valued): $$\lim_{x \rightarrow a} \ \lim_{j \rightarrow \infty} f_j(x) = \lim_{j \rightarrow \infty} \ \lim_{x \rightarrow a} f_j(x)$$
A more specific question is if it will hold for non-continuous functions $f_j$ that are uniformly convergent to a non-continuous limit function $f$ and all the single and iterated double limits exist.
Also some references would be useful.
-
Have you tried proving it yourself? – Nate Eldredge Jun 14 '11 at 16:24
See this previous question on sequences for some ideas. – Arturo Magidin Jun 14 '11 at 17:29
The answer to the specific question is Yes.
Since $f_j$ converges (uniformly and hence) pointwise to $f$,
$$\mathop {\lim }\limits_{x \to a} \mathop {\lim }\limits_{j \to \infty } f_j (x) = \mathop {\lim }\limits_{x \to a} f(x).$$ For any $\varepsilon > 0$, since $f_j$ converges uniformly to $f$, there exists $N = N(\varepsilon)$ such that $$\sup _x |f_j (x) - f(x)| < \varepsilon$$ for any $j > N$. We assume that all limits exist. Hence, for any $j > N$, $$|\lim _{x \to a} f_j (x) - \lim _{x \to a} f(x)| = |\lim _{x \to a} (f_j (x) - f(x))| \le \varepsilon .$$ Define $p_j = \lim _{x \to a} f_j (x)$ and $p = \lim _{x \to a} f(x)$. Then, $$|\lim _{j \to \infty } p_j - p| = \lim _{j \to \infty } |p_j - p| \le \varepsilon ,$$ since $|p_j - p| \leq \varepsilon$ for any $j > N$. Since $\varepsilon$ is arbitrary, $\lim _{j \to \infty } p_j = p$, hence $$\mathop {\lim }\limits_{j \to \infty } \mathop {\lim }\limits_{x \to a} f_j (x) = \mathop {\lim }\limits_{x \to a} f(x) = \mathop {\lim }\limits_{x \to a} \mathop {\lim }\limits_{j \to \infty } f_j (x).$$
-
Uniform convergence means that for every $\varepsilon > 0$ there exists $j_0$ such that for all $j \geq j_0$ and for all $x \in D$(the domain of definition for the functions $(f_j),f$ you have $|f_j(x)-f(x)| <\varepsilon$.
By the way the question is defined, although $f,f_j$ are not continuous, the limits $L=\lim_{x \to a}f(x)$ and $L_j=\lim_{x \to a}f_j(x)$ exist. The question translates in proving or disproving the followint equailty:
$$\lim_{j \to \infty}L_j=L$$
Let $\varepsilon>0$, and from the definition of uniform continuity we know that there exists $j_0$ such that forall $j \geq j_0$ and forall $x \in D$ we have that $|f_j(x)-f(x)|<\varepsilon$. Taking $x \to a$ in the last inequality we get that $|L_j-L|<\varepsilon ,\ \forall j \geq j_0$. This proves the assertion.
As a remark, I think the question should be edited such that
• the domain of definition of the functions $f_j,f$ is clear, i.e. $f_j,f: D \to \Bbb{R}$ where $D=\Bbb{R}$ or some other suitable set.
• mention that $a$ is a limit point for $D$
• although the functions $f_j,f$ are not continuous, for the question to be valid, we must assume the existence of the limits $\lim_{x \to a}f_j(x), \ \lim_{x \to a}f(x)$.
-
Note that $$\left |\lim_{x\to a}f_j(x) - \lim_{x\to a} f(x)\right|\le \|f_j-f\|_\infty\to 0,\; j\to \infty$$
Thus $$\lim_{j\to\infty}\lim_{x\to a}f_j(x) = \lim_{x\to a} f(x) = \lim_{x\to a} \lim_{j\to\infty}f(x)$$
- | 2015-07-07 09:31:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9908643960952759, "perplexity": 138.54368742311186}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375099105.15/warc/CC-MAIN-20150627031819-00013-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://www.mrmath.com/lessons/calculus/polynomial-derivatives-the-power-rule/ | Polynomial Derivatives: The Power Rule
Lesson Features »
Lesson Priority: VIP Knowledge
Objectives
• Learn the Power Rule for quickly taking the derivative of any single variable monomial
• Take the derivative of entire polynomials by applying the power rule one term at a time
• Apply the Power Rule for variables raised to fraction exponent powers
• See and practice using the power rule correctly when the variable is in the denominator
Lesson Description
By far the most common type, polynomial derivatives have a simplistic, formulaic approach that we can use instead of performing the long hand limit definition method of derivatives. We will learn the massive time-saving formula approach in this lesson.
Practice Problems
Practice problems and worksheet coming soon!
The Most Common Derivative
Now we turn to the most common type of derivative we will take throughout our Calculus journey - one that is both gratifying and infuriating. The gratification comes from the fact that simple derivatives that we had to do via the long song and dance of the limit definition of the derivative now become easy mental math. The infuriating part is the fact that we had to spend all that time doing it the long and complicated way.Many students actually get to learn the power rule polynomial shortcut in advance. It is, after all, the practical and useful takeaway. But most courses still make you learn the stuff we saw in the lesson on finding derivatives by using the limit definition. That's just part of the course.
Define: The Power Rule for DerivativesThe derivative of a variable raised to a numeric exponent is computed as follows.$$\frac{d}{dx} \, x^n = nx^{n-1}$$
Here are some quick examples.
Example 1$$x^2 \Rightarrow 2x$$Example 2$$x^{10} \Rightarrow 10x^9$$Example 3$$\sqrt{x} = x^{1/2} \Rightarrow \left(\frac{1}{2}\right) \, x^{-1/2}$$Example 4$$x^{\pi} \Rightarrow \pi x^{\pi-1}$$
Compare some of these results with the load of work we had to do using the limit definition - for example:Example 1 (redone)$$\blacktriangleright \,\, \frac{d}{dx}\,\, x^2 = \lim_{h \to 0} \frac{(x+h)^2 - x^2}{h}$$$$=\lim_{h \to 0} \frac{\cancel{x^2} +2xh + h^2 - \cancel{x^2}}{h}$$$$=\lim_{h \to 0} \frac{\cancel{h}\left(2x + h\right)}{\cancel{h}}$$$$=\lim_{h \to 0} 2x + h = \boxed{2x}$$This is the same answer we got using the new shortcut.
Pro Tip
You or someone in your class may actually learn the Power Rule shortcut early on, and discuss it while the class is still learning the limit definition material. Knowing the shortcut even before you learn the limit definition is ok, and sometimes helpful, since you can check your work easily. However, never make the mistake of executing a "limit definition" problem using the shortcut. Failing to do and show the work in that case will usually get you zero credit.
Hopefully the usefulness of the Power Rule is quickly becoming clear. We can now very quickly handle derivatives of typical polynomial terms without any real effort or derivation. We can also extend this knowledge a bit using standard derivative rules that we recently unearthed - together with the Power Rule, those rules allow us to make quick work of all polynomial derivatives.
Linear Operators with the Power Rule
Recall the linear operator derivative rules from the recent lesson on Derivative Rules » - specifically the following two:$$\frac{d}{dx}\,\, c \cdot f(x) = c \cdot \frac{d}{dx} \,\, f(x)$$(1)$$\frac{d}{dx} [f(x) + g(x)] = \frac{d}{dx}\,\, f(x) + \frac{d}{dx}\,\, g(x)$$(2)Equation (1), often called the "constant rule", allows us to apply the Power Rule to polynomial terms that already have coefficients. This is common, and something we should be expertly at by the time we're done practicing - so much that we are handling the computation as mental math.For example, the rules allow us to perform$$\frac{d}{dx}\,\, 4x^3$$as$$4 \cdot \frac{d}{dx}\,\, x^3 = 4 \cdot (3x^2) = 12x^2$$With practice, by the time we are ready to take a quiz on this stuff, we really ought to be able to do this in one step:$$\frac{d}{dx}\,\, 4x^3 = 12x^2$$To do this, focus on what the Power Rule is really telling us to do: move the original exponent (in this case, $3$) down in front as a multiplier. Then decrease the exponent by $1$. Voila!See if you can compute the following several derivatives without any scratch work. Click on each answer to check your work!
Examples 5$$\frac{d}{dx}\, 5x^2$$
Show solution
$$\blacktriangleright \,\, 10x$$
Example 6$$\frac{d}{dx} \, -x^4$$
Show solution
$$\blacktriangleright \,\, -4x^3$$
Example 7$$\frac{d}{dx} \, 6x^7$$
Show solution
$$\blacktriangleright \,\, 42x^6$$
Example 8$$\frac{d}{dx} \, \frac{x^6}{2}$$
Show solution
$$\blacktriangleright \,\, 3x^5$$
Now that we've seen the direct implication of the constant rule (equation (1) above). The sum and difference rule (equation (2) above) simply allows us to tackle entire polynomials at a time.
Example 9$$\frac{d}{dx} \, \big[ x^3 -2x^2 + 6x + 3 \big]$$$\blacktriangleright$ This can be done by computing each term's derivative in turn. Technically we are applying the sum and difference rule stated in equation (2):$$\frac{d}{dx} \, \big[ x^3 -2x^2 + 6x + 3 \big]$$$$= \frac{d}{dx} \, x^3 - \frac{d}{dx} \, 2x^2 + \frac{d}{dx} \, 6x + \frac{d}{dx} 3$$In terms of practicality, no one actually expects us to write each $\frac{d}{dx}$ term out each time. We just go for it. Therefore, by computing the derivative of each term, we can say that$$\frac{d}{dx} \, x^3 -2x^2 + 6x + 3$$$$= 3x^2 - 4x + 6$$
Simple Rational Terms
We commonly associate the Power Rule with polynomials, but it works for any expression in the form $x^n$. Technically, terms can only be called polynomial terms if the power ($n$) is a non-negative integer. However, the Power Rule works for any expression $x^n$ where $n$ is any real number. The first case we'll see of this is for simple rational terms, and the second is for root expressions.
Example 10$$\frac{d}{dx} \,\, \frac{1}{x^2}$$$\blacktriangleright$ Before we take the derivative, we can rewrite this expression in the form $x^n$. That way, we can find the derivative by using the Power Rule.$$\frac{d}{dx} \,\, \frac{1}{x^2} = \frac{d}{dx} \,\, x^{-2}$$$$= -2x^{-3} = \frac{-2}{x^3}$$It is important to note that most teachers and profs will not allow you to turn in answers with negative exponents (though some will - but it's rare). Make sure you rewrite your final answer without negative exponents.
Warning!
It is not appropriate to leave negative exponents in your answer, and it is common to lose points if you do so. Just move the variables to or from the denominator as needed to make sure you are not ignoring this requirement.
Fraction Exponents
Taking derivatives of roots of variables or variables raised to fraction exponents is just plain ugly unless you use the Power Rule. This is an absolute necessity and a definite needed skill for quizzes and exams, and very much present for the rest of the course.Let's jump right in with an example:
Example 11$$\frac{d}{dx} \,\, \sqrt{x}$$$\blacktriangleright$ Before taking the derivative, rewrite the problem without using the $\sqrt{\, \, \,}$ symbol. This will be the standard procedure for derivative problems that contain radicals.$$\frac{d}{dx} \,\, x^{1/2}$$Again, notice how we specifically took the time to rewrite the expression without a radical symbol. I cannot stress the importance of this step enough. Quiz grades are made or lost on this step. Now we can proceed with using the Power Rule verbatim.$$\frac{d}{dx} \,\, x^{1/2} = \left( \frac{1}{2} \right) x^{-1/2} = \frac{1}{2x^{1/2}}$$Typically there is no need to write the final answer with the radical symbol either - though I have encountered professors who demand it on very rare occasion. According to standard math conventions, $x^{1/2}$ is just as simplified as $\sqrt{x}$.
Remember!
Taking the derivative of a root expression without making a mistake is a difficult task, without rewriting the expression using fraction exponents. Additionally, do not make the common mistake of trying to do too much at once. Every time, rewrite the expression using fraction exponents before you take the derivative. Then, with a cleaner problem to work with, proceed with differentiation.
Here's another example to try.
Example 12$$\frac{2}{3\sqrt[4]{x^3}}$$
Show solution
$\blacktriangleright$ First, rewrite the expression using exponent form$$\frac{d}{dx} \,\, \frac{2x^{-3/4}}{3}$$Your scratch work needs to clearly show that the variable, which has a coefficient of $(2/3)$ at the start of the problem, will be multiplied by its current exponent of $(-3/4)$ and end up being raised to a power one unit smaller than its current exponent of $(-3/4)$, or $(-3/4)-(1)=(-7/4)$. All the while, each value needs to be clearly shown as a numerator or denominator object, and the final answer should not have a negative exponent.$$\frac{d}{dx} \frac{2x^{-3/4}}{3} = \left( \frac{2}{3} \right) \, \left( - \frac{3}{4} \right) \, x^{-7/4}$$$$=\frac{6}{12x^{7/4}}=\boxed{\frac{1}{2x^{7/4}}}$$
Pro Tip
With radical or fraction exponent problems, there are potentially a lot of fractions involved in your arithmetic, both with coefficients and exponents. Keep straight which objects are in the denominator, and don't skimp on the parenthesis to keep it obvious to your teacher.
Perils and Pitfalls
While it is impossible to anticipate every type of mistake I have seen students make (or will see students make) on this particular topic, here are a few common ones to look out for.1) Don't leave x in the denominatorThere are very few students who can take the derivative of something like$$\frac{1}{x^2}$$without making a mistake unless first rewriting it as $x^{-2}$. Those that can are usually doing several steps at once in their head. I'm all for lazy scratch work when we can, but you're really not saving many pencil strokes here by doing this. Do yourself a favor and rewrite it before differentiating. You're bound to make fewer mistakes.2) Don't leave x under a rootSimilar to leaving $x$ in the denominator, students who fail to rewrite something like$$\sqrt{x}$$before taking the derivative are much more likely to end up with a wrong answer.3) Don't apply the Power Rule to a ProductThe Power Rule cannot be directly applied to the product of two or more polynomials. The derivative of such an object can be done (in fact you can take the derivative of virtually anything, as you'll come to learn) but the Power Rule only applies to individual terms that are added or subtracted together.
Example 13$$\frac{d}{dx} \,\, (2x^2 + x -7)(-5x^3 + 3x^2 - x - 1)$$$\blacktriangleright$ You might be tempted to take the derivative of each polynomial and multiply those results together, but that absolutely does not work. There does exist a generalized rule for finding the derivative of a product, and this aptly named Product Rule is the subject of an upcoming lesson ».In the meantime, the only other way to perform this differentiation is to actually multiply the expression out using the distributive rule, and then proceed as normal with the resulting polynomial. In this case:$$(2x^2 + x -7)(-5x^3 + 3x^2 - x - 1)$$$$= -10 x^5+x^4+36 x^3-24 x^2+6 x+7$$and the derivative of that result is$$\boxed{-50x^4 + 4x^3 + 108x^2 -48x + 6}$$Notice how if we erroneously attempted to solve this problem by taking the derivative of each polynomial ($4x+1$ and $-15x^2 +6x -1$, respectively) and multiplying them together, we would get$$-60 x^3+9 x^2+2 x-1$$which does not match the correct answer that we have already calculated.4) Don't apply the Power Rule to an expressionAnother object that the Power Rule doesn't exactly work for is entire expressions raised to a power, such as$$(x^2 + 1)^4$$whose derivative is not $4(x^2+1)^3$ (though we'll see via the Chain Rule » that it is close). If we really needed to we could brute-force this problem right now by actually multiplying this expression out to obtain a plain polynomial.$$(x^2 +1)^4 = (x^2+1)(x^2+1)(x^2+1)(x^2+1)$$However, this is almost never advisable for many reasons. We won't proceed that way ever in similar Mr. Math examples, instead opting for the method in the upcoming Chain Rule » lesson. In fact, when teachers test this concept using the forthcoming "Chain Rule", they usually give problems similar to$$(x^2 + 1)^{999}$$which of course, you can not expand manually, unless you're bored serving a 1 year prison sentence. And even then you might not finish before your time is up.
Mr. Math Makes It Mean
A common way that the power rule is used in a cruel way is to give you an irrational exponent - usually $e$ or $\pi$. Because these are just numbers, the power rule applies verbatim. However, most students freeze up and think something is different because these special numbers are being used. It's not. For example:$$\frac{d}{dx} \,\, x^{e} = ex^{e-1}$$$$\frac{d}{dx} \,\, x^{\pi} = \pi x^{\pi-1}$$
Put It To The Test
In this "Put It To The Test" section, we'll see a good mix of what to expect on a test when your class first covers this topic. However, you'll be using this in more complicated future topics as well, so if these problems look easier than the stuff your class is working on, then your current material is probably using concepts we have yet to cover. Browse the lessons on Differentiation Techniques » to see more concepts where several derivative rules start to mix together. Also, do all the practice problems for this lesson in the Mr. Math worksheets! There's a lot of them but they are super quick, and this skill is super important if you like good grades.
Example 14$$\frac{d}{dx} \, 3x^7$$
Show solution
$\blacktriangleright$ The coefficient that is already there ($3$) stays where it is, and we follow the Power Rule by bringing down the $7$ exponent as a multiplier, while also reducing the exponent by $1$.$$\frac{d}{dx} \, 3x^7 = 3 \cdot 7 \cdot x^6$$$$=21x^6$$
Example 15$$\frac{d}{dx} \, 2x^{-\frac{3}{4}}$$
Show solution
$\blacktriangleright$ The Power Rule still applies, though the coefficients are not all going to be whole numbers. Bring down and reduce just like we should, but also for this one we must make sure to simplify.$$\frac{d}{dx} \, 2x^{-\frac{3}{4}} = 2 \left(-\frac{3}{4}\right) x^{-\frac{3}{4}-1}$$$$= -\frac{3x^{-\frac{7}{4}}}{2}$$
Example 16$$\frac{d}{dx} \, -x^4$$
Show solution
$$\blacktriangleright \,\, \frac{d}{dx} \, -x^4 = -4x^3$$This is a straight forward application of the Power Rule.
Example 17Find $f'(x)$$f(x) = x^{3.1}$$ Show solution$\blacktriangleright$There is nothing new or different for this problem - it is still a Power Rule problem, since it is of the form$x^n$. But you'll find that teachers love putting funky exponents up there just to try and throw students off. All we need to do it bring the power down as a multiplier and reduce the power by one.$$\frac{d}{dx} \, x^{3.1} = \boxed{3.1x^{2.1}}$$ Example 18$$\frac{d}{dx} \, \frac{1}{x^5}$$ Show solution$\blacktriangleright$As with any problem that has$x$raised to a negative or fraction power, we need to do ourselves the favor of re-writing the problem in the classic$x^a$form.$$\frac{d}{dx} \, \frac{1}{x^5} \longrightarrow \frac{d}{dx} \, x^{-5}$$Now we're back to a straightforward application of the Power Rule.$$\frac{d}{dx} \, x^{-5} = -5x^{-6}$$And just as important as getting the process right, remember that you need to present answers without negative exponents. So our final answer is$$\frac{d}{dx} \, x^{-5} = -\frac{5}{x^{6}}$$ Example 19$$\frac{d}{dx} \, \frac{1}{\sqrt[3]{x}}$$ Show solution$\blacktriangleright$Just like in the last problem, we need to re-write this in$x^a$form in order to move forward.$$\frac{d}{dx} \, \frac{1}{\sqrt[3]{x}} \longrightarrow \frac{d}{dx} \,\, x^{-\frac{1}{3}}$$$$=\left(-\frac{1}{3}\right) x^{-\frac{4}{3}}$$And no matter how many fractions or negative signs we find, we must clean it up into a single fraction with no negative exponents!$$\frac{d}{dx} \, \frac{1}{\sqrt[3]{x}} = \boxed{-\frac{1}{3x^{4/3}}}$$ Remember! Every derivative problem you turn in, in this lesson and in all future ones, must be cleaned up and simplified. You will lose points for breaking form! Make sure you 1) have an answer that is written as a single fraction, if applicable, and 2) contains only positive exponents. Example 20$$\frac{d}{dx} \,\, \big[ 5x^2 +4x - 3 \big]$$ Show solution$\blacktriangleright$We will proceed by taking the derivative of each term.$$\frac{d}{dx} \,\, \big[ 5x^2 +4x - 3 \big] = 10x + 4$$ Remember! Don't forget that the derivative of a solo constant is zero, unlike constants that are attached to variable terms, which simply stay put. Example 21$$\frac{d}{dx} \, \big[10x^3 + 8x^2 + 100\big]$$ Show solution$\blacktriangleright$We will proceed by taking the derivative of each term.$$\frac{d}{dx} \, \big[10x^3 + 8x^2 + 100\big]$$$$=30x^2 + 16x$$ Example 22$$\frac{d}{dx} \, \pi x^{\pi}$$ Show solution$\blacktriangleright$This is another common example where the teacher will try to trick you. Remember,$\pi$is just a number!$$\frac{d}{dx} \, \pi x^{\pi} = \pi^2 x^{\pi-1}$$ Example 23$$\frac{d}{dx} \, \big[3x^5 - 5\sqrt{x} + \frac{4}{x}\big]$$ Show solution$\blacktriangleright$This is yet another case where we won't be able to proceed easily without re-writing each term in the classic$x^a$form.$$\frac{d}{dx} \, \big[3x^5 - 5x^{\frac{1}{2}} + 4x^{-1}\big]$$$$15x^4 - 5 \cdot \left(\frac{1}{2}\right) x^{-\frac{1}{2}} + (4)(-1)x^{-2}$$$$=15x^4 - \frac{5}{2x^\frac{1}{2}} - \frac{4}{x^2}$$Once again, make sure your answer does not contain negative exponents. Example 24$$\frac{d}{dx} \sqrt{x}\left(x^2 - 2\right)$$ Show solution$\blacktriangleright$Make sure you avoid the common pitfall that many students are tempted by - you cannot take the derivative of$\sqrt{x}$and$\left(x^2 - 2\right)$separately and simply multiply the results together. You can two options: 1) Use the Product Rule that we haven't learned yet, or 2) multiply the expression outright and then proceed to take the derivative. As you may imagine, we are choosing the latter path.$$\frac{d}{dx} x^{\frac{1}{2}}\left(x^2 - 2\right)$$$$=\frac{d}{dx} x^{\frac{5}{2}} - 2x^{\frac{1}{2}}$$Now we can take the derivative.$$=\left(\frac{5}{2}\right) x^{\frac{3}{2}} - (2)\left(\frac{1}{2}\right)x^{-\frac{1}{2}}$$$$=\frac{5x^{\frac{3}{2}}}{2} - \frac{1}{x^{\frac{1}{2}}}$$ Example 25$$\frac{d}{dx} \, \bigg[-2x^5 + 4x^4 - 6x^2 + x\sqrt{2}$$$$- 2\sqrt{x} + \frac{1}{x} + \frac{2}{x^{3/2}} - \frac{4}{3x^2}\bigg]$$ Show solution$\blacktriangleright$This long problem is quite the mixed bag, but as we have been seeing, we need to rewrite this term-by-term before we take the derivative, so that we have a smooth ride.$$\frac{d}{dx} \, \bigg[-2x^5 + 4x^4 - 6x^2 + x\sqrt{2}$$$$- 2x^{\frac{1}{2}} + x^{-1} + 2x^{-\frac{3}{2}} - \left(\frac{4}{3}\right) \cdot x^{-2} \bigg]$$ $$\longrightarrow -10x^4 + 16x^3 -12x + \sqrt{2}$$$$- (2)\left(\frac{1}{2}\right)x^{-\frac{1}{2}} + -x^{-2}$$$$- (2)\left(\frac{3}{2}\right) x^{-\frac{5}{2}} + \left(\frac{4}{3}\right) (-2) x^{-3}$$ $$\longrightarrow -10x^4 + 16x^3 -12x + \sqrt{2}$$$$- \frac{1}{x^{\frac{1}{2}}} - \frac{1}{x^2} - \frac{3}{x^{\frac{5}{2}}} - \frac{8}{3x^3}$$ Lesson Takeaways • Know what the Power Rule says and how to apply it to polynomials terms • Be comfortable doing integer operations mentally, with or without coefficients • Be cautious and thorough with your work when taking the derivative of rational terms, radical terms, and terms with fraction exponents • Rewrite expressions in classic$x^n\$ Power Rule form before you take the derivative, to not only show cleaner scratch work, but also avoid typical mistakes
• Understand the difference between what can and cannot be done without needing more advanced rules, such as the upcoming Product and Chain rules
• Popular Content
• Get Taught
• Other Stuff
Lesson Metrics
At the top of the lesson, you can see the lesson title, as well as the DNA of Math path to see how it fits into the big picture. You can also see the description of what will be covered in the lesson, the specific objectives that the lesson will cover, and links to the section's practice problems (if available).
Key Lesson Sections
Headlines - Every lesson is subdivided into mini sections that help you go from "no clue" to "pro, dude". If you keep getting lost skimming the lesson, start from scratch, read through, and you'll be set straight super fast.
Examples - there is no better way to learn than by doing. Some examples are instructional, while others are elective (such examples have their solutions hidden).
Perils and Pitfalls - common mistakes to avoid.
Mister Math Makes it Mean - Here's where I show you how teachers like to pour salt in your exam wounds, when applicable. Certain concepts have common ways in which teachers seek to sink your ship, and I've seen it all!
Put It To The Test - Shows you examples of the most common ways in which the concept is tested. Just knowing the concept is a great first step, but understanding the variation in how a concept can be tested will help you maximize your grades!
Lesson Takeaways - A laundry list of things you should be able to do at lesson end. Make sure you have a lock on the whole list!
Special Notes
Definitions and Theorems: These are important rules that govern how a particular topic works. Some of the more important ones will be used again in future lessons, implicitly or explicitly.
Pro-Tip: Knowing these will make your life easier.
Remember! - Remember notes need to be in your head at the peril of losing points on tests.
You Should Know - Somewhat elective information that may give you a broader understanding.
Warning! - Something you should be careful about. | 2021-05-13 02:46:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8213047981262207, "perplexity": 815.2098564728732}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992721.31/warc/CC-MAIN-20210513014954-20210513044954-00094.warc.gz"} |
https://money.stackexchange.com/questions/116825/total-income-tax-and-self-employment-tax | Total Income tax and self-employment tax
I worked as a full time employee (W4 taxes were deducted by the employer) and I was self-employed (independent contractor - 1099MISC i.e. no taxes were deducted by the employer) for some months of the year.
For simplicity, let's say that I made $50k for FT position and$20k for self-employment position. Will I be taxed at $70k or will I taxes separately for$50k and separately for $20k? This is the first time I have worked as an independent contractor. So, I really don't know how this works. (The money I received from my self-employment gig was after Sept 15th so, I didn't have to pay the "quarterly taxes" or whatever they are called.) When it comes to my income tax, how will it be calculated? Does the money that I made from self-employment add into the total income during the year? • The final quarterly estimated tax payment is due in January, so you should check whether you need to make a payment then. If your withholding is greater than last year’s tax liability, you won’t need to. – prl Nov 13 '19 at 3:24 • If you continue to have both W-2 and 1099 income next year, you can increase withholding to avoid having to pay quarterly estimated tax. As long as the sum of your withholding and estimated tax payments exceeds 90% of your total tax, you won’t owe a penalty. – prl Nov 13 '19 at 3:26 • Don't forget though that your EXPENSES when you were RUNNING A BUSINESS (ie the "second part" of your year) will of course be very high. And those are deducted before anything. Be sure to get that right! – Fattie Nov 13 '19 at 17:58 • @prl: "As long as the sum of your withholding and estimated tax payments exceeds 90% of your total tax, you won’t owe a penalty." That's only true if you pay equal quarterly estimated tax payments through the year. But if you need to pay estimated taxes, you can't skip the first 3 quarterly payments and pay all estimated taxes in January -- that will still cause a penalty even if the sum is above 90% (unless you got a ton more income in the last quarter and you can show that the payments for each quarter meet 90% for the income up to that quarter using the annualized income installment method) – user102008 Nov 13 '19 at 18:00 2 Answers You will pay income tax based on your total income ($70,000 in your example, less deductions).
In addition, you will pay self-employment tax on the self-employment income. This is a separate tax, computed on Schedule SE, and added to your other taxes on form 1040. The self-employment tax rate is generally 15.3%. See schedule SE and its instructions for more information.
• Oh, man! I'm doomed. Thanks a lot for the information! – Raj Nov 13 '19 at 17:49
• @Raj: It's informative to add that the Self-Employment Tax is equivalent to the FICA tax (Social Security tax and Medicare tax) for employees. If you are a W2 employee, you pay half of the Social Security tax and Medicare tax (it is withheld from your paycheck) and the employer pays half (you don't see this on your paycheck; the employer can deduct their half as an expense). When you are self-employed, you are both the employee and employer, so you pay both halves, and you can similarly deduct half of it from your income. – user102008 Nov 13 '19 at 17:54
• @Raj It's very unlikely you made $20,000 give the example as stated. Your business took in$20,000. You would have had substantial expenses. Say there was $9,200 remaining after buying stuff / other costs. Your "self-employment income" is$9,200 in the example. On the 9,200 you will suffer the full ranges of taxes, such as "self-employment tax". – Fattie Nov 13 '19 at 18:00
• @Fattie, you’re right, of course, but you’re making an assumption that he has significant expenses. When I have worked as a software contractor, I had no expenses. – prl Nov 13 '19 at 22:01
• @prl, that's horrible !!!!!!!! surely you bought computers, TVs, phones etc? I'm sad now :/ – Fattie Nov 13 '19 at 23:49
You have two separate things going on here, income tax and self-employment tax.
Income tax will be paid on your total income, just as if it was all reported on a W2. (But you probably will have to pay something with your return, instead of getting a refund, and may need to make estimated tax payments if you continue with self employment next year.) You do have a number of possible deductions that will reduce the amount that's taxed: see the instructions for Schedule C and related forms.
Self-employment tax is in addition to income tax. It's essentially the same money that would be deducted from your pay* for FICA, Medicare, and so on. You compute this amount on Form 1040-SSE, and it's in addition to your income tax.
*Supposedly your employer pays half of that, but in reality they just deduct it from your pay before you ever see it.
• "Income tax will be paid on your total income" But it's incredibly important to realize that @Raj's $20,000 example IS NOT INCOME. A "self-employed" business is just the same as if you have formed an LLC or Corp, or, you are just operating "as you". You, of course, subtract expenses BEFORE you can state meaningfully the "20,000" figure Raj mentions. – Fattie Nov 13 '19 at 18:05 • @Fattie: Yes, I thought that I'd made that obvious when I mentioned that there would probably be deductions from that 20K that reduce the amount that's actually counted as income. Or perhaps profit would be a better word... – jamesqf Nov 14 '19 at 18:13 • One difference from W2: for a sole prop or other passthrough (partnership, S-corp non-wages, or LLC electing any of the preceding -- in short, anything but C-corp treatment), IF taxable income not more than$157.5k (\$315k joint), you can deduct 20% of the (net) 'Qualified Business Income' (not exceeding taxable ordinary income). This is new last year (2018) due to TCJA, intended to roughly match for small businesses the big rate reductions on C-corps. – dave_thompson_085 Nov 15 '19 at 4:46 | 2021-04-22 10:54:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32528752088546753, "perplexity": 3870.9184188954914}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00305.warc.gz"} |
http://kitchingroup.cheme.cmu.edu/blog/category/elfeed/ | ## Scoring elfeed articles
| categories: | tags: | View Comments
I use elfeed to read RSS feeds of scientific journals, python, emacs, and lisp blogs, and the emacs stackexchange feed. Here are the current feeds I follow.
(mapcar 'list elfeed-feeds)
I get a lot of articles this way. The current size of the database is:
(elfeed-db-size)
79721
Elfeed tells me I have over 300 unread entries to review at the moment.
(elfeed-search--count-unread)
341/363:24
To deal with this deluge, I have done a couple of things. I set up some new key-bindings so I can alternate marking entries as read if the titles do not look interesting. These keybindings let me alternate fingers, so they do not get too tired (that really happens some days!).
;; help me alternate fingers in marking entries as read
I also set up some auto-tagging of the emacs and python feeds, and setup some custom faces so these tags are highlighted so they are easy to see. Anything highlighted in blue is related to emacs, green is related to python, and pink is related to my department, and I can type s, then the tag to see only those entries. Here is what my feed looks like:
Today I want to explore adding tags to entries to further prioritize them. There is a way to tag entries that is described here: https://github.com/skeeto/elfeed#tag-hooks where you can create patterns to match an entry feed title, url, title or link. Basically, you create a function that takes an entry, amd have it add or remove a tag conditionally.
I want to tag entries that meet certain criteria, for example keywords, and set a tag based on the number of matches. Ideally, one day this would be integrated with machine learning so it could rank entries by other entries I have liked, but today we setup code that will create a score for an entry based on the number of matches, and then tag it so that it will get highlighted for me. First, we define two custom faces and setup elfeed to use them. I will use two tags: important and relevant. relevant will be for entries that get a score of at least 1, and important for entries that get a score greater than 1.
(defface relevant-elfeed-entry
((t :background ,(color-lighten-name "orange1" 40)))
"Marks a relevant Elfeed entry.")
(defface important-elfeed-entry
((t :background ,(color-lighten-name "OrangeRed2" 40)))
"Marks an important Elfeed entry.")
(push '(relevant relevant-elfeed-entry)
elfeed-search-face-alist)
(push '(important important-elfeed-entry)
elfeed-search-face-alist)
In elfeed, each entry is a structure, and we can access the title and content for matching. Here is an example of a simple scoring function. The idea is just to match patterns, and then add to the score if it matches. This is not as advanced as gnus scoring, but it is a good starting point.
(defun score-elfeed-entry (entry)
(let ((title (elfeed-entry-title entry))
(content (elfeed-deref (elfeed-entry-content entry)))
(score 0))
(loop for (pattern n) in '(("alloy" 1)
("machine learning\\|neural" 1)
("database" 1)
("reproducible" 1)
("carbon dioxide\\|CO2" 1)
("oxygen evolution\\|OER\\|electrolysis" 1)
("perovskite\\|polymorph\\|epitax" 1)
("kitchin" 2))
if (string-match pattern title)
do (incf score n)
if (string-match pattern content)
do (incf score n))
(message "%s - %s" title score)
;; store score for later in case I ever integrate machine learning
(setf (elfeed-meta entry :my/score) score)
(cond
((= score 1)
(elfeed-tag entry 'relevant))
((> score 1)
(elfeed-tag entry 'important)))
entry))
score-elfeed-entry
Now, new entries automatically get tagged with relevant or important, depending on the score that function gives them, and they get color-coded. Now, the feed looks like this:
I saved some bookmarks to see just the important or relevant ones (http://nullprogram.com/blog/2015/12/03/) so I can see new relevant entries with C-x r b and selecting the relevant bookmark. These work from anywhere in Emacs.
@6-months-ago +unread +relev @6-months-ago +unread +relevant
I usually access elfeed from a command that shows me everything. Here, I define key-bindings to show me just the important or relevant ones. I could not see a way to get an or in there to show me both of them. These keys make it a one key press to show only these entries, and then get back to the full list.
(define-key elfeed-search-mode-map (kbd "i")
(lambda () (interactive)
(define-key elfeed-search-mode-map (kbd "v")
(lambda () (interactive)
(define-key elfeed-search-mode-map (kbd "c")
(lambda () (interactive) | 2017-07-27 12:32:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5969048738479614, "perplexity": 5137.617630486824}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549428257.45/warc/CC-MAIN-20170727122407-20170727142407-00422.warc.gz"} |
https://www.iacr.org/cryptodb/data/paper.php?pubkey=30888 | ## CryptoDB
### Paper: Oblivious Transfer is in MiniQCrypt
Authors: Alex Grilo , LIP6, CNRS/Sorbonne Université Huijia Lin , University of Washington Fang Song , Portland State University Vinod Vaikuntanathan , MIT DOI: 10.1007/978-3-030-77886-6_18 (login may be required) Search ePrint Search Google EUROCRYPT 2021 MiniQCrypt is a world where quantum-secure one-way functions exist, and quantum communication is possible. We construct an oblivious transfer (OT) protocol in MiniQCrypt that achieves simulation-security against malicious quantum polynomial-time adversaries, building on the foundational work of Bennett, Brassard, Crepeau and Skubiszewska (CRYPTO 1991). Combining the OT protocol with prior works, we obtain secure two-party and multi-party computation protocols also in MiniQCrypt. This is in contrast to the classical world, where it is widely believed that OT does not exist in MiniCrypt.
##### BibTeX
@inproceedings{eurocrypt-2021-30888,
title={Oblivious Transfer is in MiniQCrypt},
publisher={Springer-Verlag},
doi={10.1007/978-3-030-77886-6_18},
author={Alex Grilo and Huijia Lin and Fang Song and Vinod Vaikuntanathan},
year=2021
} | 2022-09-28 19:59:57 | {"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": 0.35107871890068054, "perplexity": 10908.508971722267}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1664030335276.85/warc/CC-MAIN-20220928180732-20220928210732-00041.warc.gz"} |
https://en.wikipedia.org/wiki/Group_delay_dispersion | # Group delay dispersion
The group delay dispersion (GDD) of an optical element is the derivative of the group delay with respect to angular frequency, and also the second derivative of the optical phase. ${\displaystyle D_{2}(\omega )=-{\frac {\partial T_{g}}{d\omega }}={\frac {d^{2}\phi }{d\omega ^{2}}}}$. It is a measure of the chromatic dispersion of the element. A parameter independent of the length of the material is the group velocity dispersion (GVD).
GDD is related to the total dispersion parameter ${\displaystyle D_{tot}}$ as
${\displaystyle D_{2}(\omega )=-{\frac {2\pi c}{\lambda ^{2}}}D_{tot}}$ | 2017-05-27 05:35:17 | {"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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6691502928733826, "perplexity": 326.59219319660133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1495463608773.42/warc/CC-MAIN-20170527040600-20170527060600-00328.warc.gz"} |
https://www.albert.io/ie/single-variable-calculus/derivative-of-log-of-quadratic-function | Free Version
Easy
# Derivative of Log of Quadratic Function
SVCALC-EV4DJC
Find the derivative of the function:
$$y=\ln (x-3)^2$$
A
$\frac{2}{x-3}$
B
$2(x-3)$
C
$\frac{1}{(x-3)^2}$
D
$2 \ln(x-3)$ | 2017-01-19 10:55:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6371532082557678, "perplexity": 8251.612506002044}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280587.1/warc/CC-MAIN-20170116095120-00252-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://scicomp.stackexchange.com/questions/8117/is-there-some-good-mailing-list-for-computational-science | # Is there some good mailing list for Computational Science?
I am wondering whether there is some very good mailing list or google groups for Computational Science, where we can discuss questions instead of only asking and replying questions.
In fact, I am more interested parallel computing and numerical solutions of PDEs. But I don't know what and how people in this area are doing. I can only read their papers to grasp the road-map of this area.
Please give me some guiding information. Thanks.
• Are usenet news groups out of the question? something like sci.math.num-analysis. I also see many pde questions asked on comp.soft-sys.matlab (but for those using Matlab for implementation). I'd be interested in such a mailing list also, but I do not think it exist. googling around, I see this also lists.phys.ethz.ch/listinfo/comp-phys-general (computational physics mailing list) I do not know if it is still active or not. – Nasser Jul 31 '13 at 18:18
• @Nasser Unfortunately most mailinglists died or are slowly dying as the internet embraces the newer social network model of Q&A or discussion like StackOverflow or Quora. I used to join several mailinglist back in China, but they are all pretty much dead now. – Shuhao Cao Jul 31 '13 at 23:39
• @Nasser Your website is well edited. And thanks for your comment. – eccstartup Aug 1 '13 at 2:27
• irc://chat.freenode.net/##computerscience, irc://chat.freenode.net/hpc come to mind – user5273 Jan 30 '14 at 3:59
• @Cao Wish I could get the help at these mediums >_> I tried asking around about Chebyshev interpolation at freenode and ##math appears to be school level. But I appear to get quite a bit of help about Fortran at their Fortran channel... – user5273 Jan 30 '14 at 4:05
## 1 Answer
I recommend ResearchGate's computational science topic for general discussion about computational science.
https://www.researchgate.net/topic/computational_science/ | 2021-04-11 21:50:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.4627915620803833, "perplexity": 1681.173607940827}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038065492.15/warc/CC-MAIN-20210411204008-20210411234008-00116.warc.gz"} |
https://blender.stackexchange.com/questions/28205/when-using-a-baked-normal-map-it-is-inverted-on-half-my-model | # When using a baked normal map it is inverted on half my model
I am having a problem when baking and then using a normal map.
I have a high res and low res model and am using the "Bake selected to active" feature.
I am using BI to bake the image as I cannot seem to get cycles bake to work. I am then applying the normal map in Cycles through a Normal Map node plugged into a Diffuse.
As you can see, the baked image itself looks OK and symmetrical. When I use it, however, half my model seems to have the normals inverted. I previously had a mirror modifier while modelling and I suspect that is involved, but it was applied before I started the bake. I also checked all my normals on the model and they face the right way.
I can't figure it out and its driving me mad! Help!
_ _
EDIT: On further investigation I can see that the problem lies with my baked normal map. If you look closely at it you can see that it is not baking correctly as it is uneven. So my bake is wrong, I just don't know why.
• Use CTRL+N in edit mode to recalculate normals. – Denis Apr 7 '15 at 20:26
• You could also try to increase a little bit Bias Option just under Selected To Active checkbox before baking. And did you select the Non-Color data in Image Texture node settings for normal map? – Mr Zak Apr 7 '15 at 21:01
• Are you using a mirror modifier by any chance? Just a thought, you might want to apply it before baking it if so. – VRM Apr 7 '15 at 22:14
• Thanks everyone. I tried these and still have the same problem - though see my question edit. – Lewis Apr 8 '15 at 12:34
• you can upload the .blend to PasteAll.org and paste the link here. – MarcClintDion Apr 8 '15 at 21:30
If you made the UV's while the mirror modifier was active then the UV's for both sides should be overlapped, the bake is only correct for one half of the model.
If you hover over the UVImage Editor and press Ctrl+P (Unpack), you should end up with distinct islands for all the geometry.
Now you should re-bake.
• Thanks. I applied the mirror modifier before I did the bake though. My UVs are not overlapping. – Lewis Apr 8 '15 at 12:30
• Applying the modifier before baking will not un-separate mirrored UV's. – MarcClintDion Apr 8 '15 at 21:29
I have resolved this. The issue was the Non-Color data option for the Image Texture node as suggested by Mr Zak.
My mistake was setting this in the properties panel for node rather than on the node itself (apparently they do not mean the same thing - though I have to confess I do not understand the difference).
Grateful to everyone for the help.
also if you don't want to rebake all of your normal maps just flip the red and green challe in photoshop and you good but don't recommend doing it this way just flip[ the uvs and rebake | 2019-11-14 18:54:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4201420843601227, "perplexity": 1546.320368853642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668534.60/warc/CC-MAIN-20191114182304-20191114210304-00173.warc.gz"} |
https://answers.opencv.org/questions/16326/revisions/ | # Revision history [back]
### WebCam won't open since 2.4.6
Hi,
I'm using VideoCapture to connect to my webcam in the following manner since OpenCV2.4.4:
cv::VideoCapture vcap;
cv::Mat image;
...
vcap.open(CV_CAP_ANY);
if(vcap.isOpened()){
while(m_runGrabber){
vcap >> image;
}
}
...
and never had any problems. Since version 2.4.6 though, opening my cam fails and isOpened() always returns false. When I downgrade to 2.4.5 it works again. Also loading a video with 2.4.6 works, so the reason seems to be the combination of 2.4.6 and my webcam. I also tried to open the cam with the constructor. cv::VideoCapture vcap(CV_CAP_ANY); There is also no other camera connected, so CV_CAP_ANY should work as it did with version 2.4.5
I'm using Kubuntu 12.04 and Logitech C270 USB HD Webcam. The camera worked by plug & play, so i guess some standard drivers are used. If someone can explain me how, I would check which driver is used ;)
I'm gratefull for any tipps or suggestions.
2 retagged sturkmen 6547 ●3 ●44 ●75 https://github.com/stu...
### WebCam won't open since 2.4.6
Hi,
I'm using VideoCapture to connect to my webcam in the following manner since OpenCV2.4.4:
cv::VideoCapture vcap;
cv::Mat image;
...
vcap.open(CV_CAP_ANY);
if(vcap.isOpened()){
while(m_runGrabber){
vcap >> image;
}
}
...
and never had any problems. Since version 2.4.6 though, opening my cam fails and isOpened() always returns false. When I downgrade to 2.4.5 it works again. Also loading a video with 2.4.6 works, so the reason seems to be the combination of 2.4.6 and my webcam. I also tried to open the cam with the constructor. cv::VideoCapture vcap(CV_CAP_ANY); There is also no other camera connected, so CV_CAP_ANY should work as it did with version 2.4.5
I'm using Kubuntu 12.04 and Logitech C270 USB HD Webcam. The camera worked by plug & play, so i guess some standard drivers are used. If someone can explain me how, I would check which driver is used ;)
I'm gratefull for any tipps or suggestions. | 2020-10-28 16:24:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.32235416769981384, "perplexity": 5018.578869451161}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107900200.97/warc/CC-MAIN-20201028162226-20201028192226-00009.warc.gz"} |
https://socratic.org/questions/how-do-you-write-an-equation-in-standard-form-when-given-slope-and-point-on-line | # How do you write an equation in standard form when given slope and point on line (6, -8), m = -2?
Aug 17, 2016
Substitute the variables in the slope-intercept equation for our numbers.
#### Explanation:
This is the slope-intercept equation:
$y = m x + b$
The letter $m$ is the slope (-2) and the letters $y$ and $x$ are our x- and y-variables (6 and -8, respectively).
Our equation is this:
$- 8 = - 2 \left(6\right) + b$
From here, we solve for $b$:
-2⋅6=-12
$- 8 = - 12 + b$
$4 = b$
We now know that $b = 4$, so we can plug it back into our equation to get our answer. Since this is an equation with an infinite number of coordinates on it, the only numbers we're going to put in are the slope and $b$. This is what we get:
$y = - 2 x + 4$ | 2021-06-21 16:37:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.8003190755844116, "perplexity": 370.36102382128666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1623488286726.71/warc/CC-MAIN-20210621151134-20210621181134-00540.warc.gz"} |
https://www.groundai.com/project/entropy-production-and-the-geometry-of-dissipative-evolution-equations/ | Entropy production and the geometry of dissipative evolution equations
# Entropy production and the geometry of dissipative evolution equations
Celia Reina and Johannes Zimmer Department of Mechanical Engineering and Applied Mechanics,
University of Pennsylvania, Philadelphia, PA 19104, USA
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
July 20, 2019
###### Abstract
Purely dissipative evolution equations are often cast as gradient flow structures, , where the variable of interest evolves towards the maximum of a functional according to a metric defined by an operator . While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator and the associated geometry does not necessarily so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the Steepest Entropy Ascent formalism. This new variational principle is exemplified here for the simultaneous evolution of conserved and non-conserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement.
###### pacs:
46.05.+b, 05.70.Ln, 05.40.-a
preprint: AIP/123-QED
Dissipative evolution equations (e.g., heat conduction, mass diffusion, interface motion) often follow variational principles, such as Onsager’s least dissipation of energy Onsager (1931a, b) and extensions, in particular those based on maximum entropy production (MEPPs Martyushev and Seleznev (2006); Dewar et al. (2013)) or Steepest Entropy Ascent (SEA) Beretta (1987, 2014); Montefusco et al. (2014)). Mathematically, these equations are often of gradient flow type, that is, they can be described by the steepest ascent/descent of a functional, such as the entropy. Here descent has to be measured in a metric, which is neither provided by the aforementioned variational approaches, nor it is always intuitive (e.g., Wasserstein metric for diffusion processes). In this article, we establish a variational framework based on the ansatz of maximal entropy production which sheds light on the geometry of purely dissipative evolution equations. This new approach (1) delivers a construction of the gradient flow metric from conservation constraints in the variational formulation; (2) extends Onsager’s principle to simultaneously account for conserved and non-conserved quantities in open systems; and (3) encloses an infinite-dimensional fluctuation-dissipation statement, as shown from a large deviation argument for stochastically perturbed gradient flows. The diagram of Fig. 1 summarizes the connections established in this paper.
## I Background
We sketch some of the most closely related variational principles and provide a short summary on gradient flows. The body of literature, both classic and recent, on these two topics is too large to be reviewed comprehensively here.
### i.1 Entropy production
Onsager, in his celebrated papers Onsager (1931a, b) generalized the transport laws, such as those by Fourier, Ohm or Fick, to account for a possible coupling between different physical processes. He proposed a general linear kinematic constitutive relation between fluxes and forces , that is, . The conductivity matrix may depend on the state variables (temperature, pressure, chemical potential, etc.), but not on their gradient Gyarmati (1970), and is symmetric as a result of the time reversal of the underlying atomistic equations of motion, . These two properties of the constitutive relations — linearity and symmetry of the conductivity tensor — can be equivalently expressed by means of the principle of least dissipation of energy Onsager (1931a) (following Rayleigh’s nomenclature Rayleigh (1913)). Namely, let be the entropy production and denote a local dissipation potential, with the resistivity tensor being positive definite, then the variational principle reads
maxJ[σs(J,X)−Φ(J)]. (1)
In Onsager’s words Onsager (1931a), ‘the rate of increase of the entropy plays the role of a potential’. Several generalizations of this extremum principle have since emerged in different fields encompassing climate Paltridge (1975), soft matter physics Doi (2011), plasticity Ziegler (1983), biology Dewar (2010) and quantum mechanics Beretta (1981) among others, and appear under the names of Maximum Entropy Production Principles(MEPPs) Martyushev and Seleznev (2006); Dewar et al. (2013) and Steepest Entropy Ascent (SEA) Beretta (1987, 2014); Montefusco et al. (2014). This latter framework provides a geometric interpretation of the resistivity tensor and generalizes to arbitrary (but a priori unknown) metric spaces. Another approach to nonequilibrium thermodynamics, which combines reversible and irreversible dynamics, is the General Equation for NonEquilibrium Reversible-Irreversible Coupling (GENERIC) Grmela and Öttinger (1997); Öttinger (2005). The structure of this formalism can be derived using contact forms in the setting of the Gibbs-Legendre manifold Grmela (2014, 2015); it can be cast variationally; and it allows for a systematic multiscale approach Grmela et al. (2015) as well as a treatment of fluctuations Grmela (2014, 2012).
From a mathematical perspective, purely dissipative evolution equations can often be described as gradient flow structures Ambrosio et al. (2006). This means that the vectorial variable of interest (components are, for example, energy, density or interface position) evolves according to the steepest ascent of a functional (or descent for ) in a geometry given by a metric associated with a positive semi-definite operator ,
˙z=K(z)DS(z), or G(z)˙z=DS(z), (2)
where if the inverse is defined, and is a force. Note that (2) is precisely the irreversible component of GENERIC. Then is a Lyapunov functional, , where denotes the dual parity between elements of the tangent and the cotangent space.
Two common examples of (2) are the flow and Wasserstein flow Jordan et al. (1998), written for scalar-valued as
˙z=m(z)DS(z), (3) ˙z=−∇⋅(M(z)∇DS(z)), (4)
respectively, with and positive semi-definite. The latter equation is symbolically expressed as , with . Further details on the weak formulations of both flows and the norms involved are given in the Appendix.
It is noteworthy that the same equation can have different gradient flow representations. For example, the diffusion equation
(5)
can be interpreted both as flow (with mobility and Dirichlet integral ) and Wasserstein flow (with mobility and Boltzmann entropy ). The Wasserstein formulation is a natural choice since it involves the physical entropy. This flow and its associated metric will be automatically singled out by the variational principle proposed here, as we show next.
## Ii Entropy production and deterministic evolution
In this section, we present a new variational principle for purely dissipative evolution equations based on the ansatz that systems evolve in the direction of maximum entropy production (see Eq. (9) below) 111The entropy production can be expressed as the entropy rate of the system minus the entropy increase induced by heat flux exchange with the ambient space Glansdorf and Prigogine (1971)., so as to reach the equilibrium configuration as fast as possible. The philosophy is therefore similar to SEA and MEPPs, yet different in its detailed formulation. In particular, the proposed principle will provide a direct relation between the operator and physical constraints in the system, thus shedding some light on the geometry of dissipative equations.
For simplicity, we first consider closed systems defined by a scalar variable and later generalize the obtained results to open systems and the vectorial setting. Illustrative examples are then chosen to demonstrate the applicability of the principle for both conserved and non-conserved fields, with explicit consideration of the boundary conditions. We note that non-conserved quantities do not have a flux associated to them, and therefore lie outside of the direct scope of Onsager’s principle (1).
For a closed system out of equilibrium characterized by a scalar state variable , the maximum entropy production ansatz is mathematically equivalent to the search of the velocity maximizing , where is the entropy density and the total entropy of the system. The maximization is pointwise in the tangent space for fixed , c.f. Fig. 2. However, this problem is not well-posed unless the length of the vector is prescribed, in which case the problem is reduced to the search of the optimal direction. This constraint is easily incorporated with a Lagrange multiplier, yielding a variational principle with Lagrangian
D[˙z]=⟨DS(z),˙z⟩−⟨˙z,η(z)˙z⟩, (6)
where the precise value of the length, which may depend on , has been obviated since it does not participate in variations for fixed . The evolution is then obtained by variations of (6) with respect to , giving , with , since entropy would decrease otherwise. This shows that the gradient flow (3) with functional naturally results from the maximum entropy production principle in the absence of any physical constraint.
However, the evolution of is often subjected to conservation constraints of the form
ddt∫Ωzdx=0,
which naturally occurs when represents mass or energy. In this situation, the maximal dissipation occurs within the manifold of conserved ,
˙z+∇⋅J=0,
where on the boundary for a closed system. With an additional Lagrange multiplier , the variational principle at each point can then be written as
D[˙z,J,λ]=⟨DS,˙z⟩−⟨λ(z),˙z+∇⋅J⟩−⟨J,H(z)J⟩, (7)
where the length constraint (measured with metric tensor ) has now been placed on the unknown variable . We note that constraining the length of as in (6) would leave partially undetermined, and so would be the constitutive relations, such as Fourier’s law for the case of heat conduction.
Variation with respect to in (7) delivers
0=−⟨λ,∇⋅δJ⟩−⟨2HJ,δJ⟩ for all δJ,
which, after integration by parts, yields . Variations with respect to and give
DS−λ=0 and ˙z=−∇⋅J.
Altogether, this leads to a Wasserstein gradient flow with functional and weight positive semi-definite, . The Wasserstein gradient flow (4) can be thus be understood as an gradient flow restricted to the manifold of conserved quantities.
In general, systems are characterized by a set of state variables , some of which are conserved, , (e.g., energy, concentration), and some of which are not, , (e.g., interface position), i.e., . In this case the variational principle can be written as
D[˙z,J,Λ]=⟨DS,˙z⟩−⟨Λ(z),˙zc+∇⋅J⟩−⟨J,Hc(z)J⟩−⟨˙zu,Hu(z)˙zu⟩, (8)
where now is a vectorial Lagrange multiplier, and and are second-order tensors. Similar derivations as above yield the evolution equations
˙zu=(2Hu)−1δSδzu=KuδSδzu, ˙zc=−∇⋅((2Hc)−1∇δSδzc)=KcδSδzc,
which have an analogous structure to those previously obtained. However, for anisotropic materials, coupling between variables of different tensorial quantities is possible, and in this case, the Lagrangian shall be written as
D[˙z,J,Λ]=⟨DS,˙z⟩−⟨Λ(z),˙zc+∇⋅J⟩−⟨[˙zu,J]T,H(z)[˙zu,J]T⟩. (9)
Variations of this functional with respect to and give
2H(˙zuJ)=(2Hu2Huc2HTuc2Hc)(˙zuJ)=⎛⎜⎝δSδzu∇δSδzc⎞⎟⎠,
with . Then, the evolution equations read
(˙zu˙zc)=(MuMuc∇□−∇⋅(MTuc□)−∇⋅(Mc∇□))⎛⎜⎝δSδzuδSδzc⎞⎟⎠=KDS,
where the symbol indicates how the operator is applied to the vector . Further, , i.e.,
Mu=12[Hu−HucH−1cHTuc]−1, Mc=12[Hc−HTucH−1uHuc]−1, Muc=−12[Hu−HucH−1cHTuc]−1HucH−1c.
This simple viewpoint of dissipative evolution equations via constrained maximization will be exemplified below for the equation of heat transfer and interface motion in open system, as blueprint for the derivation of other equations in a similar manner.
#### Example: the heat equation and Fourier’s law.
We now show that Fourier’s law and the heat equation follow directly from the postulate of maximum entropy production. For an open system, the Lagrangian of the maximum entropy production principle is constructed by subtracting the entropy flow entering the boundary of the domain from the total entropy rate. Then the entropy increase considered exclusively originates from the internal production, in accordance with the second law of thermodynamics. Assuming that the system is completely characterized by the internal energy, and taking also the conservation of energy into account, the Lagrangian reads
D[˙e,λ,q]=∫Ω∂s∂e˙edx+∫∂Ωq⋅nTdx−∫Ωλ(˙e+∇⋅q)dx−∫ΩqTHqdx, (10)
where is the outer normal to the domain, is the heat flux, and and represent the entropy and energy per unit volume, respectively. From basic thermodynamic relations, assuming local thermodynamic equilibrium, . Therefore, variations with respect to , and , assuming boundary conditions in (boundary conditions in would imply on , and lead to the same evolution equation) yield
1T−λ=0, ˙e+∇⋅q=0, ∫Ω[∇⋅(δqT)−λ∇⋅(δq)−2Hq⋅δq]dx=0∀δq,
which combined give the equation of heat transfer, with ,
∂e∂T˙T=˙e=−∇⋅((2H)−1∇(1T))=∇⋅(K∇T). (11)
We remark that the analogous derivation via Onsager’s principle of least dissipation, i.e.,
(12)
leads to Fourier’s law , which, complemented with the first law of thermodynamics, yields (11) with . However, the physical motivation of the Lagrangian in Eq. (10) seems more natural than that of (12).
#### Example: Interface motion in an isotropic medium.
Next, we consider a two-phase system separated by an interface, which we characterize by an additional variable in the spirit of a phase field model (Provatas and Elder, 2011). Following a similar strategy as in the previous case, the evolution of the interface coupled to the heat equation can be obtained as the extremum of
D[˙e,˙ϕ,λ,q]=∫Ω˙sdx+∫∂Ωq⋅nTdx−∫Ωλ(˙e+∇⋅q)dx−∫Ωq⋅μqdx−∫Ω˙ϕη˙ϕdx.
Assuming the existence of a thermodynamic relation for the energy density of the form ,
de=Tds+(∂e∂ϕ)s,∇ϕdϕ+(∂e∂∇ϕ)s,ϕd∇ϕ,
where subscripts indicate the variables that are held fixed. Its Legendre transform with respect to the entropy density is the Helmholtz free energy ,
One then obtains
˙s =1T˙e−1T(∂e∂ϕ)s,∇ϕ˙ϕ−1T(∂e∂∇ϕ)s,ϕ∇˙ϕ =1T˙e−1T(∂f∂ϕ)T,∇ϕ˙ϕ−1T∇˙ϕ.
As in the previous example, we obtain the heat equation from variations of with respect to and , while variations with respect to yield the evolution of the interface,
˙e=∇⋅(k∇T), with k\coloneqq(2μT2)−1 2η˙ϕ=−δ∫f/Tdxδϕ=−∂(f/T)∂ϕ+∇⋅∂(f/T)∂∇ϕ.
Thus the interface is driven by the Massieu potential , whose relevance has been noted in SEA Beretta (2006, 2007, 2009), in the GENERIC setting Mielke (2011) as well as in large deviation theory Touchette (2009). We note that the derivation of this evolution in the Onsager formalism is nontrivial as does not have a flux and a corresponding thermodynamic force.
## Iii Stochastic evolution and large deviations
In this section, we show that the proposed variational formulation for purely dissipative equations based on physical considerations is further supported by a large deviation principle (LDP) associated to stochastically perturbed gradient flows. The LDP provides the probability of a given evolution to occur, and therefore intrinsically contains a variational principle for the most likely path. Large deviation arguments have recently been used to connect particle models to gradient flows, for example in Adams et al. (2011, 2013); Mielke et al. (2014), and have also led to variational formulations of systems in GENERIC form Duong et al. (2013).
Specifically, let be a vector field that evolves in according to a stochastic gradient flow with small noise,
dz=K(z)DS(z)dt+σ(z)√ϵ dBt,x, (13)
where is a vector of independent Brownian sheets, i.e., , with the Kronecker delta function and the Dirac delta function. Further, is an operator acting on , and is a small parameter controlling the strength of the noise. The stochastic calculus is to be understood in the Itô sense.
The probability distribution for satisfying (13) may be obtained from that of simpler processes using the theory of large deviations and the contraction principle Freidlin and Wentzell (1984). Indeed, by Schilder’s theorem, the probability distribution of the solutions to the vectorial ordinary differential equation , with a vector of time white noises, , follows
P[u(t)≈φ(t)]∝e−1ϵI[φ], where I[φ]=12∫T0|˙φ|2dt (14)
is called the rate functional. In words, the probability for undergoes an exponential decay with rate , and narrows as around the deterministic solution . Then, the probability distribution for satisfying can be obtained by expanding and with orthonormal basis functions for the domain Faris and Jona-Lasinio (1982); Freidlin (1988),
v=∑kAktek,Bt,x=∑kBktek, (15)
where are independent Brownian motions (direct computations show that ). The partial differential equation is then equivalent to the system of vectorial ordinary differential equations ; and the rate functional of the associated large deviation principles, for (see, e.g., Faris and Jona-Lasinio (1982); Freidlin (1988)), can be readily obtained from (14)
I[φ]=12∫T0∑k|˙Ck|2dt=12∫T0∥˙φ∥2dt. (16)
The solutions to (13) can be seen as , where is an operator. If is continuous (see Budhiraja et al. (2008) for measurable functions), then, by the contraction principle, follows a large deviation principle Sowers (1992) with functional , i.e.,
P[z(t,x)≈φ(t,x)]∝exp(−1ϵ12∫T0∥˙φ−K(φ) DS(φ)∥2(σσ∗)−1dt), (17)
assuming defines a norm, with being the adjoint operator of . This result follows the spirit of Onsager and Machlup Onsager and Machlup (1953), for general gradient flow structures; however, the probability distribution obtained is not a function of the thermodynamic forces and fluxes as in the original formulation by Onsager, but of the variable and . This difference is analogous to that of (10) and (12).
## Iv Maximum entropy production from large deviations
Equation (17) shows that the most likely path is the one that maximizes the exponent and thus minimizes . This minimum is attained by pointwise optimization (over for fixed at every instant of time), giving
min˙z∥˙z−K(z) DS(z)∥2(σσ∗)−1 . (18)
Equation (18) represents a variational principle for the deterministic gradient flow, which, for , is shown below to be equivalent to Eq. (6) for gradient flows, to Eq. (7) for the Wasserstein evolution, and to Eqs. (8) and (9) for the combined vectorial case. Indeed, expanding the squares in Eq. (18) yields the variational problem
max˙z[⟨DS(z),˙z⟩−Φ(˙z)−Ψ(z)] (19)
with and , where the latter does not affect the optimal evolution. One has in the presence of fluctuations, whereas for the optimal path holds.
The Lagrangian for the gradient flow (), Eq. (6), can be rewritten in the form of (19),
D=⟨DS(z),˙z⟩−12∥˙z∥2L2m=⟨DS(z),˙z⟩−Φ(˙z),
with , and as defined in the Appendix. An equivalent result is obtained for the Wasserstein gradient flow (), noting that the last term of Eq. (7), with and , can be rewritten as
⟨J,H(z)J⟩=12⟨J,J⟩L2M−1=12⟨˙z,˙z⟩WM=Φ(˙z). (20)
The vectorial norm is defined analogously to the scalar case, and the second equality in (20) is detailed in the Appendix. Similarly derivations for the vectorial case considered in (8) lead to
⟨J,Hc(z)J⟩+⟨˙zu,Hu(z)˙zu⟩=∥zu∥2K−1u+∥zc∥2K−1c=∥z∥2K−1=Φ(˙z), (21)
with . For the coupled case considered in Eq. (9), is a full matrix and its inverse reads
(22)
where the inverted divergence and inverted gradient are to be interpreted in appropriate spaces. The relations immediately follow from . Then, one similarly obtains that
⟨(˙zuJ),(HuHucHTucHc)(˙zuJ)⟩=12∥˙z∥2K−1=Φ(˙z). (23)
The variational principles of Eqs. (6)–(9) can therefore be written as . We thus observe that the diagram of Fig. 1 commutes if , which represents a fluctuation-dissipation relation in infinite dimensions.
Square root of the Wasserstein operator.
We now discuss the expression encountered in the fluctuation-dissipation statement above for the Wasserstein operator. In general, for a given positive semi-definite self-adjoint there are several choices . However, only appears in the generator and thus the solutions to the corresponding Fokker-Planck equations for different roots are statistically equivalent Öttinger (1996). For Wasserstein gradient flows we only consider of divergence form, to have a conservative noise, i.e., , where for simplicity. Then, for the Wasserstein metric with mobility
(24)
from which one obtains that , or equivalently, . For the diffusion equation (5) with unit diffusion constant, the stochastic version given by (13) with reads
˙ρ=Δρ+∇⋅(ρ1/2dBt,x). (25)
This equation of fluctuating hydrodynamics Eyink (1990) is known as Dean-Kawasaki model Dean (1996); Kawasaki (1998); Chavanis (2011).
## V Conclusions
We provide two independent derivations of a variational principle governing dissipative evolution equations of the form . The first is based on the maximization of the entropy production within the manifold of constraints, extending Onsager’s original approach, and provides insight into the geometry of the gradient flow structure (). In particular, the principle captures multiple metrics: one which is related to a thermodynamic length, and others that may result from the constraints in the system, such as conservation of mass or energy. The first metric is here taken as the metric and is in principle unknown (an extension to general metrics, as in SEA, is yet to be explored), whereas the second one is an outcome of the variational statement. By means of this procedure, the Wasserstein metric is here shown to be equivalent to the constrained metric associated to conserved fields. The second approach for obtaining the variational statement is based on the large deviation principle for the gradient flows augmented by a noise term , and is shown to be equivalent to the previously derived principle for . This represents a fluctuation-dissipation relation in infinite dimensions and endows the exponent of the large deviation principle with the usual interpretation of an entropy (dissipation) shortfall between a given path and the optimal one Varadhan (2010).
## Vi Appendix
We write the weighted norm as , and denote and (note that for square integrable functions, is equivalent to the duality pairing). Then the weak formulation of the gradient flow for the diffusion equation is ( and in Eq. (3))
⟨˙ρ,v⟩L2 =⟨DS1(ρ),v⟩L2m =−⟨∇ρ,∇v⟩L2m=⟨∇⋅(m(ρ)∇ρ),v⟩L2.
For the Wasserstein gradient flow, if with on , the Wasserstein norm is
⟨˙z1,˙z2⟩WM \coloneqq⟨M∇p1,∇p2⟩L2=−⟨∇⋅M∇p1,p2⟩L2 =⟨˙z1,WM˙z2⟩L2.
The second expression is known as the seminorm with weight , . We write (see (Feng and Kurtz, 2006, Appendix D) for details)
With this notation, it is straightforward to calculate the weak formulation of the diffusion equation as a Wasserstein gradient flow (, and in Eq. (4)),
⟨˙ρ,˙z2⟩WM2=⟨∇DS2(ρ),m2∇p2(z2)⟩L2.
Acknowledgments. The authors thank M. von Renesse, P. Ayyaswamy, D. Kelly, R. Jack, V. Maroulas, M. Renger and E. Vanden-Eijnden for valuable comments. This work was partially supported by the UK’s Engineering and Physical Sciences Research Council Grant EP/K027743/1 (to JZ), the Leverhulme Trust (RPG-2013-261) and GW4 grants GW4-IF2-026 and GW4-AF-005. We appreciate helpful suggestions from the reviewers.
## References
• Onsager (1931a) L. Onsager, Phys. Rev. 37, 405 (1931a).
• Onsager (1931b) L. Onsager, Phys. Rev. 38, 2265 (1931b).
• Martyushev and Seleznev (2006) L. Martyushev and V. Seleznev, Physics reports 426, 1 (2006).
• Dewar et al. (2013) R. C. Dewar, C. H. Lineweaver, R. K. Niven, and K. Regenauer-Lieb, Beyond the Second Law (Springer, 2013).
• Beretta (1987) G. P. Beretta, in The Physics of Phase Space Nonlinear Dynamics and Chaos Geometric Quantization, and Wigner Function (Springer, 1987) pp. 441–443.
• Beretta (2014) G. P. Beretta, Physical Review E 90, 042113 (2014).
• Montefusco et al. (2014) A. Montefusco, F. Consonni, and G. P. Beretta, arXiv preprint arXiv:1411.5378 (2014).
• Gyarmati (1970) I. Gyarmati, Non-equilibrium Thermodynamics. Field Theory and Variational Principles (Springer, 1970).
• Rayleigh (1913) L. Rayleigh, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 26, 776 (1913).
• Paltridge (1975) G. W. Paltridge, Quarterly Journal of the Royal Meteorological Society 101, 475 (1975).
• Doi (2011) M. Doi, Journal of Physics: Condensed Matter 23, 284118 (2011).
• Ziegler (1983) H. Ziegler, An introduction to thermomechanics (Elsevier, 1983).
• Dewar (2010) R. C. Dewar, Philosophical Transactions of the Royal Society B: Biological Sciences 365, 1429 (2010).
• Beretta (1981) G. Beretta, On the general equation of motion of quantum thermodynamics and the distinction between quantal and nonquantal uncertainties, Ph.D. thesis, Massachusetts Institute of Technology (1981).
• Grmela and Öttinger (1997) M. Grmela and H. C. Öttinger, Physical Review E 56, 6620 (1997).
• Öttinger (2005) H. C. Öttinger, Beyond equilibrium thermodynamics (John Wiley & Sons, 2005).
• Grmela (2014) M. Grmela, Entropy 16, 1652 (2014).
• Grmela (2015) M. Grmela, Entropy 17, 5938 (2015).
• Grmela et al. (2015) M. Grmela, V. Klika, and M. Pavelka, Physical Review E 92, 032111 (2015).
• Grmela (2012) M. Grmela, Physica D: Nonlinear Phenomena 241, 976 (2012).
• Ambrosio et al. (2006) L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures (Springer, 2006).
• Jordan et al. (1998) R. Jordan, D. Kinderlehrer, and F. Otto, SIAM J. Math. Anal. 29, 1 (1998).
• (23) The entropy production can be expressed as the entropy rate of the system minus the entropy increase induced by heat flux exchange with the ambient space Glansdorf and Prigogine (1971).
• Provatas and Elder (2011) N. Provatas and K. Elder, Phase-field methods in materials science and engineering (John Wiley & Sons, 2011).
• Beretta (2006) G. P. Beretta, Physical Review E 73, 026113 (2006).
• Beretta (2007) G. P. Beretta, International Journal of Quantum Information 5, 249 (2007).
• Beretta (2009) G. P. Beretta, Reports on Mathematical Physics 64, 139 (2009).
• Mielke (2011) A. Mielke, Cont. Mech. Thermodyn. 23, 233 (2011).
• Touchette (2009) H. Touchette, Phys. Rep. 478, 1 (2009).
• Adams et al. (2011) S. Adams, N. Dirr, M. A. Peletier, and J. Zimmer, Comm. Math. Phys. 307, 791 (2011).
• Adams et al. (2013) S. Adams, N. Dirr, M. Peletier, and J. Zimmer, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 371, 20120341, 17 (2013).
• Mielke et al. (2014) A. Mielke, M. A. Peletier, and D. R. M. Renger, Potential Anal. 41, 1293 (2014).
• Duong et al. (2013) M. H. Duong, M. A. Peletier, and J. Zimmer, Nonlinearity 26, 2951 (2013).
• Freidlin and Wentzell (1984) M. I. Freidlin and A. D. Wentzell, Random perturbations of dynamical systems (Springer-Verlag, New York, 1984).
• Faris and Jona-Lasinio (1982) W. G. Faris and G. Jona-Lasinio, J. Phys. A 15, 3025 (1982).
• Freidlin (1988) M. I. Freidlin, Trans. Amer. Math. Soc. 305, 665 (1988).
• Budhiraja et al. (2008) A. Budhiraja, P. Dupuis, and V. Maroulas, Ann. Prob. , 1390 (2008).
• Sowers (1992) R. Sowers, Probab. Theory Related Fields 92, 393 (1992).
• Onsager and Machlup (1953) L. Onsager and S. Machlup, Physical Review 91, 1505 (1953).
• Öttinger (1996) H. C. Öttinger, Stochastic processes in polymeric fluids: tools and examples for developing simulation algorithms (Springer Berlin, 1996).
• Eyink (1990) G. L. Eyink, J. Stat. Phys. 61, 533 (1990).
• Dean (1996) D. Dean, J. Phys. A 29, L613 (1996).
• Kawasaki (1998) K. Kawasaki, J. Stat. Phys. 93, 527 (1998).
• Chavanis (2011) P.-H. Chavanis, Phys. A 390, 1546 (2011).
• Varadhan (2010) S. R. S. Varadhan, in Proceedings of the International Congress of Mathematicians. Volume I (Hindustan Book Agency, New Delhi, 2010) pp. 622–639.
• Feng and Kurtz (2006) J. Feng and T. G. Kurtz, Large deviations for stochastic processes, Mathematical Surveys and Monographs, Vol. 131 (AMS, Providence, RI, 2006).
• Glansdorf and Prigogine (1971) P. Glansdorf and I. Prigogine, Structure, stability and fluctuations (1971).
You are adding the first comment!
How to quickly get a good reply:
• Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
• Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
• Your comment should inspire ideas to flow and help the author improves the paper.
The better we are at sharing our knowledge with each other, the faster we move forward.
The feedback must be of minimum 40 characters and the title a minimum of 5 characters | 2020-10-27 03:55:08 | {"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": 0.84266197681427, "perplexity": 619.49050855356}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107893011.54/warc/CC-MAIN-20201027023251-20201027053251-00023.warc.gz"} |
https://www.springerprofessional.de/singularities-and-topology-of-hypersurfaces/13753156 | Skip to main content
main-content
## Inhaltsverzeichnis
### Chapter 1. Whitney Stratifications
Abstract
A (smooth) manifold (i.e., a C-manifold without boundary, of constant dimension) enjoys the next well-known homogeneity property, see, for instance, [M4], p. 22.
Alexandru Dimca
### Chapter 2. Links of Curve and Surface Singularities
Abstract
We start with a brief account of knot theory for the following two reasons. First, the links of (plane) curve singularities—which are usually regarded as the simplest class of singularities to investigate—form a special class of knots, the so-called algebraic links. Second, many of the fundamental concepts related to the local topology of a higher dimensional IHS (e.g., Seifert matrix, intersection form, Milnor fibration, Alexander polynomial) have been considered first in relation to knot theory.
Alexandru Dimca
### Chapter 3. The Milnor Fibration and the Milnor Lattice
Abstract
In this section we introduce various Milnor fibrations, in particular, the global Milnor fibration associated with a weighted homogeneous polynomial. Then we discuss the basic properties of the corresponding monodromy operators. Let On+1 = ℂ{x0,…,xn{ be the ℂ-algebra of analytic function germs at the origin 0 of ℂn+1 and let (X, 0) be a hypersurface singularity defined by an equation f = 0, for some fOn+1 with f(0) = 0. Here n ≥ 0 is a positive integer. There are two equivalent fibrations which, in the literature, are called the Milnor fibration of the function germ f (or of the hypersurface singularity (X, 0)).
Alexandru Dimca
### Chapter 4. Fundamental Groups of Hypersurface Complements
Abstract
We have seen in Chapter 2 that a basic idea in studying a link LS3 is to investigate the topology of its complement S3\L. In particular, the fundamental group π1(S3\L) of this space played a crucial role. Note that since most of the spaces of interest to us are path-connected, we usually pay no attention to base points.
Alexandru Dimca
### Chapter 5. Projective Complete Intersections
Abstract
Although the topology of the complex projective space ℙn is well known, we recall in this section some basic facts on it. The reason for doing this is:
(i)
to fix some notation useful in the sequel; and
(ii)
the topology of the projective complete intersections shares a lot of properties with the topology of ℙn.
Alexandru Dimca
### Chapter 6. de Rham Cohomology of Hypersurface Complements
Abstract
In this chapter we work with regular differential forms in the sense of Algebraic Geometry or, depending on the context, in the sense of Analytic Geometry. Fix a positive integer n ≥ 0 and consider the affine space ℂn+1.
Alexandru Dimca
### Backmatter
Weitere Informationen | 2020-06-07 03:54:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8515405058860779, "perplexity": 709.2259905385231}, "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/1590348523476.97/warc/CC-MAIN-20200607013327-20200607043327-00186.warc.gz"} |
https://db0nus869y26v.cloudfront.net/en/Complex_multiplication | In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers;[1] and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense (it roughly means that the action on the tangent space at the identity element of A is a direct sum of one-dimensional modules). Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice.
It has an aspect belonging to the theory of special functions, because such elliptic functions, or abelian functions of several complex variables, are then 'very special' functions satisfying extra identities and taking explicitly calculable special values at particular points. It has also turned out to be a central theme in algebraic number theory, allowing some features of the theory of cyclotomic fields to be carried over to wider areas of application.
David Hilbert is said to have remarked that the theory of complex multiplication of elliptic curves was not only the most beautiful part of mathematics but of all science.[2]
## Example of the imaginary quadratic field extension
An elliptic curve over the complex numbers is obtained as a quotient of the complex plane by a lattice Λ, here spanned by two fundamental periods ω1 and ω2. The four-torsion is also shown, corresponding to the lattice 1/4 Λ containing Λ. The example of an elliptic curve corresponding to the Gaussian integers occurs when ω2 = i ω1.
Consider an imaginary quadratic field ${\textstyle K=\mathbb {Q} \left({\sqrt {-d))\right),\,d\in \mathbb {Z} ,d>0}$. An elliptic function ${\displaystyle f}$ is said to have complex multiplication if there is an algebraic relation between ${\displaystyle f(z)}$ and ${\displaystyle f(\lambda z)}$ for all ${\displaystyle \lambda }$ in ${\displaystyle K}$.
Conversely, Kronecker conjectured – in what became known as the Kronecker Jugendtraum – that every abelian extension of ${\displaystyle K}$ could be obtained by the (roots of the) equation of a suitable elliptic curve with complex multiplication. To this day this remains one of the few cases of Hilbert's twelfth problem which has actually been solved.
An example of an elliptic curve with complex multiplication is
${\displaystyle \mathbb {C} /(\theta \mathbb {Z} [i])}$
where Z[i] is the Gaussian integer ring, and θ is any non-zero complex number. Any such complex torus has the Gaussian integers as endomorphism ring. It is known that the corresponding curves can all be written as
${\displaystyle Y^{2}=4X^{3}-aX}$
for some ${\displaystyle a\in \mathbb {C} }$, which demonstrably has two conjugate order-4 automorphisms sending
${\displaystyle Y\to \pm iY,\quad X\to -X}$
in line with the action of i on the Weierstrass elliptic functions.
More generally, consider the lattice Λ, an additive group in the complex plane, generated by ${\displaystyle \omega _{1},\omega _{2))$. Then we define the Weierstrass function of the variable ${\displaystyle z}$ in ${\displaystyle \mathbb {C} }$ as follows:
${\displaystyle \wp (z;\Lambda )=\wp (z;\omega _{1},\omega _{2})={\frac {1}{z^{2))}+\sum _{(m,n)\neq (0,0)}\left$$(\frac {1}{(z+m\omega _{1}+n\omega _{2})^{2))}-{\frac {1}{\left(m\omega _{1}+n\omega _{2}\right)^{2))}\right\},}$ and ${\displaystyle g_{2}=60\sum _{(m,n)\neq (0,0)}(m\omega _{1}+n\omega _{2})^{-4))$ ${\displaystyle g_{3}=140\sum _{(m,n)\neq (0,0)}(m\omega _{1}+n\omega _{2})^{-6}.}$ Let ${\displaystyle \wp '}$ be the derivative of ${\displaystyle \wp }$. Then we obtain an isomorphism of complex Lie groups: ${\displaystyle w\mapsto (\wp (w):\wp '(w):1)\in \mathbb {P} ^{2}(\mathbb {C} )}$ from the complex torus group ${\displaystyle \mathbb {C} /\Lambda }$ to the projective elliptic curve defined in homogeneous coordinates by ${\displaystyle E=\left\{(x:y:z)\in \mathbb {C} ^{3}\mid y^{2}z=4x^{3}-g_{2}xz^{2}-g_{3}z^{3}\right$$)$
and where the point at infinity, the zero element of the group law of the elliptic curve, is by convention taken to be ${\displaystyle (0:1:0)}$. If the lattice defining the elliptic curve is actually preserved under multiplication by (possibly a proper subring of) the ring of integers ${\displaystyle {\mathfrak {o))_{K))$ of ${\displaystyle K}$, then the ring of analytic automorphisms of ${\displaystyle E=\mathbb {C} /\Lambda }$ turns out to be isomorphic to this (sub)ring.
If we rewrite ${\displaystyle \tau =\omega _{1}/\omega _{2))$ where ${\displaystyle \operatorname {Im} \tau >0}$ and ${\displaystyle \Delta (\Lambda )=g_{2}(\Lambda )^{3}-27g_{3}(\Lambda )^{3))$, then
${\displaystyle j(\tau )=j(E)=j(\Lambda )=2^{6}3^{3}g_{2}(\Lambda )^{3}/\Delta (\Lambda )\ .}$
This means that the j-invariant of ${\displaystyle E}$ is an algebraic number – lying in ${\displaystyle K}$ – if ${\displaystyle E}$ has complex multiplication.
## Abstract theory of endomorphisms
The ring of endomorphisms of an elliptic curve can be of one of three forms:the integers Z; an order in an imaginary quadratic number field; or an order in a definite quaternion algebra over Q.[3]
When the field of definition is a finite field, there are always non-trivial endomorphisms of an elliptic curve, coming from the Frobenius map, so every such curve has complex multiplication (and the terminology is not often applied). But when the base field is a number field, complex multiplication is the exception. It is known that, in a general sense, the case of complex multiplication is the hardest to resolve for the Hodge conjecture.
## Kronecker and abelian extensions
Kronecker first postulated that the values of elliptic functions at torsion points should be enough to generate all abelian extensions for imaginary quadratic fields, an idea that went back to Eisenstein in some cases, and even to Gauss. This became known as the Kronecker Jugendtraum; and was certainly what had prompted Hilbert's remark above, since it makes explicit class field theory in the way the roots of unity do for abelian extensions of the rational number field, via Shimura's reciprocity law.
Indeed, let K be an imaginary quadratic field with class field H. Let E be an elliptic curve with complex multiplication by the integers of K, defined over H. Then the maximal abelian extension of K is generated by the x-coordinates of the points of finite order on some Weierstrass model for E over H.[4]
Many generalisations have been sought of Kronecker's ideas; they do however lie somewhat obliquely to the main thrust of the Langlands philosophy, and there is no definitive statement currently known.
## Sample consequence
It is no accident that
${\displaystyle e^{\pi {\sqrt {163))}=262537412640768743.99999999999925007\dots \,}$
or equivalently,
${\displaystyle e^{\pi {\sqrt {163))}=640320^{3}+743.99999999999925007\dots \,}$
is so close to an integer. This remarkable fact is explained by the theory of complex multiplication, together with some knowledge of modular forms, and the fact that
${\displaystyle \mathbf {Z} \left[{\frac {1+{\sqrt {-163))}{2))\right]}$
Here ${\displaystyle (1+{\sqrt {-163)))/2}$ satisfies α2 = α − 41. In general, S[α] denotes the set of all polynomial expressions in α with coefficients in S, which is the smallest ring containing α and S. Because α satisfies this quadratic equation, the required polynomials can be limited to degree one.
Alternatively,
${\displaystyle e^{\pi {\sqrt {163))}=12^{3}(231^{2}-1)^{3}+743.99999999999925007\dots \,}$
an internal structure due to certain Eisenstein series, and with similar simple expressions for the other Heegner numbers.
## Singular moduli
The points of the upper half-plane τ which correspond to the period ratios of elliptic curves over the complex numbers with complex multiplication are precisely the imaginary quadratic numbers.[5] The corresponding modular invariants j(τ) are the singular moduli, coming from an older terminology in which "singular" referred to the property of having non-trivial endomorphisms rather than referring to a singular curve.[6]
The modular function j(τ) is algebraic on imaginary quadratic numbers τ:[7] these are the only algebraic numbers in the upper half-plane for which j is algebraic.[8]
If Λ is a lattice with period ratio τ then we write j(Λ) for j(τ). If further Λ is an ideal a in the ring of integers OK of a quadratic imaginary field K then we write j(a) for the corresponding singular modulus. The values j(a) are then real algebraic integers, and generate the Hilbert class field H of K: the field extension degree [H:K] = h is the class number of K and the H/K is a Galois extension with Galois group isomorphic to the ideal class group of K. The class group acts on the values j(a) by [b] : j(a) → j(ab).
In particular, if K has class number one, then j(a) = j(O) is a rational integer: for example, j(Z[i]) = j(i) = 1728. | 2022-06-24 23:48:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 38, "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": 0.9040839076042175, "perplexity": 445.22525553737245}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103033816.0/warc/CC-MAIN-20220624213908-20220625003908-00595.warc.gz"} |
http://mathhelpforum.com/geometry/127937-possible-draw-parallel-line-only-using-ruler.html | # Thread: Is it possible to draw a parallel line only using a ruler
1. ## Is it possible to draw a parallel line only using a ruler
There are three points $A , B , C$ , they are not collinear .
Can we draw a straight line which passes through $A$ and is parallel to line $BC$ using a rule without a scale ?
Is it possible ? .. I don't think it is . There is a big limitation !
2. Originally Posted by simplependulum
There are three points $A , B , C$ , they are not collinear .
Can we draw a straight line which passes through $A$ and is parallel to line $BC$ using a rule without a scale ?
Is it possible ? .. I don't think it is . There is a big limitation !
Are you using a ruler with measurements or just a straight edge?
3. Originally Posted by Prove It
Are you using a ruler with measurements or just a straight edge?
Just a straight edge for us to draw straight lines .
4. Yes by using the angle at the top or bottom of your ruler. | 2017-03-26 01:46:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.730978786945343, "perplexity": 262.10801857886975}, "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-2017-13/segments/1490218189090.69/warc/CC-MAIN-20170322212949-00365-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://teachingcalculus.com/2012/12/07/under-is-a-long-way-down/comment-page-1/ | # Under is a Long Way Down
The development of the ideas and concepts related to definite integrals almost always begins with finding the area of a region between a graph in the first quadrant and the x-axis between two vertical lines. Everyone, including me in the past, refers to this as “finding the area under the curve.”
Under is a long way down. And while everyone understands what this means, I suggest that a better phrasing is “finding the area between the curve and the x-axis.” Here is why:
• That is what you are doing.
• You will soon be finding the area between the curve and the x-axis where the curve is below the x-axis. This often leads to something you may be tempted to call “negative area” and of course there is no such thing as a negative area, regardless of what you may find in some textbooks.
As with so many integration problems, the results is often a formula that obscures what is really going on – the Riemann sum whose value the integral gives. The first such formula is that the area is given by $\int_{a}^{b}{f\left( x \right)dx}$. This is correct only if f (x) > 0. There is a natural confusion for beginning students between the facts that if f (x) < 0 the integral comes out negative but the area is positive.
For all the applications of integration always emphasize the Riemann sum – not just the final formula. In the area problem with f (x) > 0 the integrand is the vertical length of the rectangles that make up the sum and this is the upper function’s value minus the lower function’s value, with the lower being the x-axis, y = 0. Then when f (x) < 0 the upper minus the lower is 0 – f (x) and the area is given by $\int_{a}^{b}{0-f\left( x \right)dx}=-\int_{a}^{b}{f\left( x \right)dx}$ which is positive as it should be. And students will immediately see that $\int_{a}^{b}{f\left( x \right)dx}$ is not automatically the area.
To help students see this you could start (very first problem) by helping them to find the area of the region between f (x) > 0 and the line y = 1 so they have to deal with the lower curve. Then consider another problem using the x-axis.
There is a fair amount of ground to cover between the first area between the curve and the x-axis problems with f (x) > 0 and other area problems. Teaching students how to set up those first Riemann sums, what a Riemann sum is, the definition of the definite integral and even the Fundamental Theorem of Calculus may all come between the first problem and when this distinction becomes important. Starting with the right words, “area between the graph and the x-axis”, will help in the long run.
## One thought on “Under is a Long Way Down”
This site uses Akismet to reduce spam. Learn how your comment data is processed. | 2019-12-06 15:36:23 | {"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": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8669873476028442, "perplexity": 233.07481088917356}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540488870.33/warc/CC-MAIN-20191206145958-20191206173958-00139.warc.gz"} |
https://galeracluster.com/library/documentation/sst-physical.html | Physical State Snapshot¶
There are two back-end methods available for Physical State Snapshots: rsync and xtrabackup. Starting with version 8.0.22 also clone method is available for Galera Cluster for MySQL
The Physical State Transfer Method has the following advantages:
• These transfers physically copy the data from one node to the disk of the other, and as such do not need to interact with the database server at either end.
• These transfers do not require the database to be in working condition, as the Donor Node overwrites what was previously on the joining node disk.
• These transfers are faster.
The :term:’Physical State Transfer Method’ has the following disadvantages:
• These transfers require the joining node to have the same data directory layout and the same storage engine configuration as the donor node. For example, you must use the same file-per-table, compression, log file size and similar settings for InnoDB.
• These transfers are not accepted by servers with initialized storage engines.
What this means is that when your node requires a state snapshot transfer, the database server must restart to apply the changes. The database server remains inaccessible to the client until the state snapshot transfer is complete, since it cannot perform authentication without the storage engines.
rsync
The fastest back-end method for State Snapshot Transfers is rsync. It carries all the advantages and disadvantages of of the Physical Snapshot Transfer. While it does block the donor node during transfer, rsync does not require database configuration or root access, which makes it easier to configure.
When using terabyte-scale databases, rsync is considerably faster, (1.5 to 2 times faster), than xtrabackup. This translates to a reduction in transfer times by several hours.
rsync also features the rsync-wan modification, which engages the rsync delta transfer algorithm. However, given that this makes it more I/O intensive, you should only use it when the network throughput is the bottleneck, which is usually the case in WAN deployments.
Note
The most common issue encountered with this method is due to incompatibilities between the various versions of rsync on the donor and joining nodes.
The rsync script runs on both donor and joining nodes. On the joiner, it starts rsync in server-mode and waits for a connection from the donor. On the donor, it starts rsync in client-mode and sends the contents of the data directory to the joining node.
wsrep_sst_method = rsync
For more information about rsync, see the rsync Documentation.
xtrabackup
The most popular back-end method for State Snapshot Transfers is xtrabackup. It carries all the advantages and disadvantages of a Physical State Snapshot, but is virtually non-blocking on the donor node.
xtrabackup only blocks the donor for the short period of time it takes to copy the MyISAM tables, (for instance, the system tables). If these tables are small, the blocking time remains very short. However, this comes at the cost of speed: a state snapshot transfer that uses xtrabackup can be considerably slower than one that uses rsync.
Given that xtrabackup copies a large amount of data in the shortest possible time, it may also noticeably degrade donor performance.
Note
The most common issue encountered with this method is due to its configuration. xtrabackup requires that you set certain options in the configuration file, which means having local root access to the donor server.
[mysqld]
wsrep_sst_method = xtrabackup
[client]
socket = /path/to/socket
For more information on xtrabackup, see the Percona XtraBackup User Manual and XtraBackup SST Configuration.
clone
Starting with version 8.0.22 clone SST method is available for Galera CLuster for MySQL. It is based on the native MySQL clone plugin. It proved to be much faster than xtrabackup, however it will block Donor node on DDL execution if that happens during the transfer.
Basic configuraition for clone SST on Joiner:
[mysqld]
wsrep_sst_method=clone
Basic configuraition for clone SST on Donor:
[mysqld] | 2021-10-18 02:13:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5181657075881958, "perplexity": 2959.1652043972363}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585186.33/warc/CC-MAIN-20211018000838-20211018030838-00172.warc.gz"} |
https://followtutorials.com/2011/12/data-structure-how-to-implement-shell-sort-in-c.html | # Data Structure: How to implement Shell Sort in C++?
Shell is generalization of insertion sort and is devised by Donald Shell in 1954. The method sorts separate sub-files of original file i.e.
• Divide the original file into smaller sub-files.
• Sort individual sub-files using any sorting algorithm
We choose increment ‘k’ for dividing the original file into smaller sub-files and process is repeated until k becomes 1.
Source Code:
#include<iostream>
using namespace std;
class ShellSort{
private:
int no_of_elements;
int elements[10];
public:
void getarray();
void sortit(int [], int);
int return_noelements();
void display();
};
void ShellSort::getarray(){
cout<<"How many elements? ";
cin>>no_of_elements;
cout<<"Insert array of element to sort: ";
for(int i=0;i<no_of_elements;i++){
cin>>elements[i];
}
}
int ShellSort::return_noelements(){
return no_of_elements;
}
void ShellSort::sortit(int incrmnts[], int numinc){
int incr, j, k, span, y;
for(incr = 0; incr < numinc; incr++){
span = incrmnts[incr];
for(j = span; j < no_of_elements; j++){
y = elements[j];
for(k = j - span; k >=0 && y < elements[k]; k-=span){
elements[k+span] = elements[k];
}
elements[k+span] = y;
}
cout<<"Iteration = "<<incr+1<<" Span = "<<span<<" : ";
display();
if (span==1)
break;
}
}
void ShellSort::display(){
for(int i = 0 ; i < no_of_elements; i++){
cout<<elements[i]<<" ";
}
cout<<endl;
}
int main(){
ShellSort SHS;
int n, i, j;
SHS.getarray();
n = SHS.return_noelements();
int incrmnts[n];
for(i = n,j = 0; i > 0; i = i/2, j++){
incrmnts[j] = i;
}
SHS.sortit(incrmnts, j+1);
return 0;
}
Output:
How many elements? 7
Insert array of element to sort: 75 12 36 35 25 99 62
Iteration : 1 Span = 7 : 75 12 36 35 25 99 62
Iteration : 2 Span = 3 : 35 12 36 62 25 99 75
Iteration : 3 Span = 1 : 12 25 35 36 62 75 99
SHARE Data Structure: How to implement Shell Sort in C++?
### 1 Response
1. Anonymous says:
Please comment this code. I am having trouble understanding this sorting algorithm, and nicely commented code would help immensely. | 2021-05-09 10:10:53 | {"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": 0.418429970741272, "perplexity": 12845.931508029256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988966.82/warc/CC-MAIN-20210509092814-20210509122814-00147.warc.gz"} |
https://www.albert.io/ie/ap-chemistry/molar-mass-conversion-of-dollarliohdollar | Free Version
Easy
# Molar Mass Conversion of $LiOH$
APCHEM-OKTGJF
Which of the following provides the mass and the number of molecules found in 2.00 mol of lithium hydroxide?
A
23.95 g
$1.44 \times 10^{25}$ molecules
B
23.95 g
$6.022 \times 10^{23}$ molecules
C
47.90 g
$6.022 \times 10^{23}$ molecules
D
47.90 g
$1.20 \times 10^{24}$ molecules | 2017-02-25 02:30:24 | {"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": 0.3795146644115448, "perplexity": 14851.822431778932}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1487501171646.15/warc/CC-MAIN-20170219104611-00160-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://eprint.iacr.org/2016/997 | ### More Efficient Commitments from Structured Lattice Assumptions
Carsten Baum, Ivan Damgård, Vadim Lyubashevsky, Sabine Oechsner, and Chris Peikert
##### Abstract
We present a practical construction of an additively homomorphic commitment scheme based on structured lattice assumptions, together with a zero-knowledge proof of opening knowledge. Our scheme is a design improvement over the previous work of Benhamouda et al. in that it is not restricted to being statistically binding. While it is possible to instantiate our scheme to be statistically binding or statistically hiding, it is most efficient when both hiding and binding properties are only computational. This results in approximately a factor of 4 reduction in the size of the proof and a factor of 6 reduction in the size of the commitment over the aforementioned scheme.
Note: Improved version with configurable binding and hiding, better comparison with previous work.
Available format(s)
Publication info
Published elsewhere. 11th Conference on Security and Cryptography for Networks (SCN 2018)
Keywords
Lattice-based cryptographycommitmentszero-knowledge
Contact author(s)
carsten baum @ biu ac il
History
2018-06-21: last of 3 revisions
See all versions
Short URL
https://ia.cr/2016/997
CC BY
BibTeX
@misc{cryptoeprint:2016/997,
author = {Carsten Baum and Ivan Damgård and Vadim Lyubashevsky and Sabine Oechsner and Chris Peikert},
title = {More Efficient Commitments from Structured Lattice Assumptions},
howpublished = {Cryptology ePrint Archive, Paper 2016/997},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/997}},
url = {https://eprint.iacr.org/2016/997}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content. | 2022-10-07 02:41:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17868071794509888, "perplexity": 5914.751990882974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1664030337906.7/warc/CC-MAIN-20221007014029-20221007044029-00775.warc.gz"} |
https://support.bioconductor.org/u/17423/ | ## User: mikhael.manurung
Reputation:
90
Status:
Trusted
Location:
Last seen:
1 week, 5 days ago
Joined:
10 months ago
Email:
m***************@gmail.com
#### Posts by mikhael.manurung
<prev • 42 results • page 1 of 5 • next >
2
84
views
2
... You can transpose the data frame and then save it, like this: tmp <- t(tmp) #transpose data frame write.csv(tmp, "tmp.csv", row.names = TRUE, col.names = TRUE) # make sure to set row.names to TRUE! ...
written 6 weeks ago by mikhael.manurung90
0
83
views
0
... Hi Papyrus, I also encountered this problem but fortunately, in my dataset, the cell type compositions were not associated with my covariate of interest. If you have the cell type compositions data, why wouldn't you put those together in your formula (meth ~ age.group + cellA + cell B + cell C + a ...
written 6 weeks ago by mikhael.manurung90
1
178
views
1
... If it is a csv file then you can use read.csv. Good luck! ...
written 6 weeks ago by mikhael.manurung90
1
178
views
1
... Note that list.files will only, well, list all the files that you have within your working directory. It **DOES NOT** import the data into R. That is why the first thing that you should do is to properly import those data into R. For your data, you can easily use read.table. By the way, it seem ...
written 7 weeks ago by mikhael.manurung90
1
119
views
1
... Dear Peter, Thank you for your prompt response. For empiricalBayesLM, would you advise feeding the group variables into the retainedCovariates argument? Best, Mikhael ...
written 7 weeks ago by mikhael.manurung90
1
119
views
1
... Dear all, I would like to adjust my whole-blood RNA-Seq count data matrix for cell type composition (obtained from hematological analysis & flow cytometry) before doing a coexpression network analysis with WGCNA. So far, I did the following: # I use DESeq2's vst to remove mean-variance ...
written 7 weeks ago by mikhael.manurung90 • updated 7 weeks ago by Peter Langfelder2.1k
1
178
views
1
... Did your supervisor elaborate more on the lack of need to normalise your data? Somehow I suspect that your supervisor actually meant that you do not need to transform your count data to something else such as with the voom transformation from limma. Anyway, DGEList object can be made as such: ...
written 7 weeks ago by mikhael.manurung90
2
202
views
2
... I do not think you can use a continuous variable in your design matrix for either limma or edgeR. Well, you can use it as a covariate for adjustment of confounding or batch effects. It is possible to correlate the expression of your genes with your continuous predictor, provided you ha ...
written 8 weeks ago by mikhael.manurung90
1
105
views
1
... I think the maSigPro package would be the one that you are looking for. I hope this helps. ...
written 8 weeks ago by mikhael.manurung90
1
103
views
1
... removeBatchEffect should not be used for DE analysis but for other downstream analysis, such as PCA. For adjustment of DE analysis, indeed you should include columndata\$days in design matrix. Therefore, your dge` object should be used. This is important because the linear modeling s ...
written 8 weeks ago by mikhael.manurung90
#### Latest awards to mikhael.manurung
No awards yet. Soon to come :-)
Content
Help
Access
Use of this site constitutes acceptance of our User Agreement and Privacy Policy. | 2019-07-17 05:20:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2024419754743576, "perplexity": 2749.0849161295273}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525046.5/warc/CC-MAIN-20190717041500-20190717063500-00469.warc.gz"} |
https://people.maths.bris.ac.uk/~matyd/GroupNames/128i1/C4xC4sQ8.html | Copied to
clipboard
## G = C4×C4⋊Q8order 128 = 27
### Direct product of C4 and C4⋊Q8
direct product, p-group, metabelian, nilpotent (class 2), monomial
Series: Derived Chief Lower central Upper central Jennings
Derived series C1 — C22 — C4×C4⋊Q8
Chief series C1 — C2 — C22 — C23 — C22×C4 — C2×C42 — C43 — C4×C4⋊Q8
Lower central C1 — C22 — C4×C4⋊Q8
Upper central C1 — C22×C4 — C4×C4⋊Q8
Jennings C1 — C23 — C4×C4⋊Q8
Generators and relations for C4×C4⋊Q8
G = < a,b,c,d | a4=b4=c4=1, d2=c2, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >
Subgroups: 412 in 294 conjugacy classes, 184 normal (18 characteristic)
C1, C2 [×3], C2 [×4], C4 [×16], C4 [×18], C22 [×3], C22 [×4], C2×C4 [×38], C2×C4 [×26], Q8 [×16], C23, C42 [×16], C42 [×14], C4⋊C4 [×16], C4⋊C4 [×20], C22×C4 [×3], C22×C4 [×12], C2×Q8 [×8], C2×Q8 [×8], C2.C42 [×8], C2×C42 [×3], C2×C42 [×8], C2×C4⋊C4 [×14], C4×Q8 [×8], C4⋊Q8 [×8], C22×Q8 [×2], C43, C4×C4⋊C4 [×4], C429C4, C23.65C23 [×4], C23.67C23 [×2], C2×C4×Q8 [×2], C2×C4⋊Q8, C4×C4⋊Q8
Quotients: C1, C2 [×15], C4 [×8], C22 [×35], C2×C4 [×28], D4 [×4], Q8 [×8], C23 [×15], C22×C4 [×14], C2×D4 [×6], C2×Q8 [×12], C4○D4 [×6], C24, C4×D4 [×4], C4×Q8 [×8], C4⋊Q8 [×4], C23×C4, C22×D4, C22×Q8 [×2], C2×C4○D4 [×3], C2×C4×D4, C2×C4×Q8 [×2], C2×C4⋊Q8, C22.26C24, C23.37C23 [×2], C4×C4⋊Q8
Smallest permutation representation of C4×C4⋊Q8
Regular action on 128 points
Generators in S128
(1 2 3 4)(5 6 7 8)(9 10 11 12)(13 14 15 16)(17 18 19 20)(21 22 23 24)(25 26 27 28)(29 30 31 32)(33 34 35 36)(37 38 39 40)(41 42 43 44)(45 46 47 48)(49 50 51 52)(53 54 55 56)(57 58 59 60)(61 62 63 64)(65 66 67 68)(69 70 71 72)(73 74 75 76)(77 78 79 80)(81 82 83 84)(85 86 87 88)(89 90 91 92)(93 94 95 96)(97 98 99 100)(101 102 103 104)(105 106 107 108)(109 110 111 112)(113 114 115 116)(117 118 119 120)(121 122 123 124)(125 126 127 128)
(1 70 28 68)(2 71 25 65)(3 72 26 66)(4 69 27 67)(5 88 128 82)(6 85 125 83)(7 86 126 84)(8 87 127 81)(9 77 15 91)(10 78 16 92)(11 79 13 89)(12 80 14 90)(17 63 23 73)(18 64 24 74)(19 61 21 75)(20 62 22 76)(29 59 43 45)(30 60 44 46)(31 57 41 47)(32 58 42 48)(33 55 39 49)(34 56 40 50)(35 53 37 51)(36 54 38 52)(93 109 107 123)(94 110 108 124)(95 111 105 121)(96 112 106 122)(97 113 103 119)(98 114 104 120)(99 115 101 117)(100 116 102 118)
(1 58 22 56)(2 59 23 53)(3 60 24 54)(4 57 21 55)(5 108 14 102)(6 105 15 103)(7 106 16 104)(8 107 13 101)(9 97 125 95)(10 98 126 96)(11 99 127 93)(12 100 128 94)(17 51 25 45)(18 52 26 46)(19 49 27 47)(20 50 28 48)(29 63 35 65)(30 64 36 66)(31 61 33 67)(32 62 34 68)(37 71 43 73)(38 72 44 74)(39 69 41 75)(40 70 42 76)(77 113 83 111)(78 114 84 112)(79 115 81 109)(80 116 82 110)(85 121 91 119)(86 122 92 120)(87 123 89 117)(88 124 90 118)
(1 77 22 83)(2 78 23 84)(3 79 24 81)(4 80 21 82)(5 67 14 61)(6 68 15 62)(7 65 16 63)(8 66 13 64)(9 76 125 70)(10 73 126 71)(11 74 127 72)(12 75 128 69)(17 86 25 92)(18 87 26 89)(19 88 27 90)(20 85 28 91)(29 106 35 104)(30 107 36 101)(31 108 33 102)(32 105 34 103)(37 98 43 96)(38 99 44 93)(39 100 41 94)(40 97 42 95)(45 122 51 120)(46 123 52 117)(47 124 49 118)(48 121 50 119)(53 114 59 112)(54 115 60 109)(55 116 57 110)(56 113 58 111)
G:=sub<Sym(128)| (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84)(85,86,87,88)(89,90,91,92)(93,94,95,96)(97,98,99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)(121,122,123,124)(125,126,127,128), (1,70,28,68)(2,71,25,65)(3,72,26,66)(4,69,27,67)(5,88,128,82)(6,85,125,83)(7,86,126,84)(8,87,127,81)(9,77,15,91)(10,78,16,92)(11,79,13,89)(12,80,14,90)(17,63,23,73)(18,64,24,74)(19,61,21,75)(20,62,22,76)(29,59,43,45)(30,60,44,46)(31,57,41,47)(32,58,42,48)(33,55,39,49)(34,56,40,50)(35,53,37,51)(36,54,38,52)(93,109,107,123)(94,110,108,124)(95,111,105,121)(96,112,106,122)(97,113,103,119)(98,114,104,120)(99,115,101,117)(100,116,102,118), (1,58,22,56)(2,59,23,53)(3,60,24,54)(4,57,21,55)(5,108,14,102)(6,105,15,103)(7,106,16,104)(8,107,13,101)(9,97,125,95)(10,98,126,96)(11,99,127,93)(12,100,128,94)(17,51,25,45)(18,52,26,46)(19,49,27,47)(20,50,28,48)(29,63,35,65)(30,64,36,66)(31,61,33,67)(32,62,34,68)(37,71,43,73)(38,72,44,74)(39,69,41,75)(40,70,42,76)(77,113,83,111)(78,114,84,112)(79,115,81,109)(80,116,82,110)(85,121,91,119)(86,122,92,120)(87,123,89,117)(88,124,90,118), (1,77,22,83)(2,78,23,84)(3,79,24,81)(4,80,21,82)(5,67,14,61)(6,68,15,62)(7,65,16,63)(8,66,13,64)(9,76,125,70)(10,73,126,71)(11,74,127,72)(12,75,128,69)(17,86,25,92)(18,87,26,89)(19,88,27,90)(20,85,28,91)(29,106,35,104)(30,107,36,101)(31,108,33,102)(32,105,34,103)(37,98,43,96)(38,99,44,93)(39,100,41,94)(40,97,42,95)(45,122,51,120)(46,123,52,117)(47,124,49,118)(48,121,50,119)(53,114,59,112)(54,115,60,109)(55,116,57,110)(56,113,58,111)>;
G:=Group( (1,2,3,4)(5,6,7,8)(9,10,11,12)(13,14,15,16)(17,18,19,20)(21,22,23,24)(25,26,27,28)(29,30,31,32)(33,34,35,36)(37,38,39,40)(41,42,43,44)(45,46,47,48)(49,50,51,52)(53,54,55,56)(57,58,59,60)(61,62,63,64)(65,66,67,68)(69,70,71,72)(73,74,75,76)(77,78,79,80)(81,82,83,84)(85,86,87,88)(89,90,91,92)(93,94,95,96)(97,98,99,100)(101,102,103,104)(105,106,107,108)(109,110,111,112)(113,114,115,116)(117,118,119,120)(121,122,123,124)(125,126,127,128), (1,70,28,68)(2,71,25,65)(3,72,26,66)(4,69,27,67)(5,88,128,82)(6,85,125,83)(7,86,126,84)(8,87,127,81)(9,77,15,91)(10,78,16,92)(11,79,13,89)(12,80,14,90)(17,63,23,73)(18,64,24,74)(19,61,21,75)(20,62,22,76)(29,59,43,45)(30,60,44,46)(31,57,41,47)(32,58,42,48)(33,55,39,49)(34,56,40,50)(35,53,37,51)(36,54,38,52)(93,109,107,123)(94,110,108,124)(95,111,105,121)(96,112,106,122)(97,113,103,119)(98,114,104,120)(99,115,101,117)(100,116,102,118), (1,58,22,56)(2,59,23,53)(3,60,24,54)(4,57,21,55)(5,108,14,102)(6,105,15,103)(7,106,16,104)(8,107,13,101)(9,97,125,95)(10,98,126,96)(11,99,127,93)(12,100,128,94)(17,51,25,45)(18,52,26,46)(19,49,27,47)(20,50,28,48)(29,63,35,65)(30,64,36,66)(31,61,33,67)(32,62,34,68)(37,71,43,73)(38,72,44,74)(39,69,41,75)(40,70,42,76)(77,113,83,111)(78,114,84,112)(79,115,81,109)(80,116,82,110)(85,121,91,119)(86,122,92,120)(87,123,89,117)(88,124,90,118), (1,77,22,83)(2,78,23,84)(3,79,24,81)(4,80,21,82)(5,67,14,61)(6,68,15,62)(7,65,16,63)(8,66,13,64)(9,76,125,70)(10,73,126,71)(11,74,127,72)(12,75,128,69)(17,86,25,92)(18,87,26,89)(19,88,27,90)(20,85,28,91)(29,106,35,104)(30,107,36,101)(31,108,33,102)(32,105,34,103)(37,98,43,96)(38,99,44,93)(39,100,41,94)(40,97,42,95)(45,122,51,120)(46,123,52,117)(47,124,49,118)(48,121,50,119)(53,114,59,112)(54,115,60,109)(55,116,57,110)(56,113,58,111) );
G=PermutationGroup([(1,2,3,4),(5,6,7,8),(9,10,11,12),(13,14,15,16),(17,18,19,20),(21,22,23,24),(25,26,27,28),(29,30,31,32),(33,34,35,36),(37,38,39,40),(41,42,43,44),(45,46,47,48),(49,50,51,52),(53,54,55,56),(57,58,59,60),(61,62,63,64),(65,66,67,68),(69,70,71,72),(73,74,75,76),(77,78,79,80),(81,82,83,84),(85,86,87,88),(89,90,91,92),(93,94,95,96),(97,98,99,100),(101,102,103,104),(105,106,107,108),(109,110,111,112),(113,114,115,116),(117,118,119,120),(121,122,123,124),(125,126,127,128)], [(1,70,28,68),(2,71,25,65),(3,72,26,66),(4,69,27,67),(5,88,128,82),(6,85,125,83),(7,86,126,84),(8,87,127,81),(9,77,15,91),(10,78,16,92),(11,79,13,89),(12,80,14,90),(17,63,23,73),(18,64,24,74),(19,61,21,75),(20,62,22,76),(29,59,43,45),(30,60,44,46),(31,57,41,47),(32,58,42,48),(33,55,39,49),(34,56,40,50),(35,53,37,51),(36,54,38,52),(93,109,107,123),(94,110,108,124),(95,111,105,121),(96,112,106,122),(97,113,103,119),(98,114,104,120),(99,115,101,117),(100,116,102,118)], [(1,58,22,56),(2,59,23,53),(3,60,24,54),(4,57,21,55),(5,108,14,102),(6,105,15,103),(7,106,16,104),(8,107,13,101),(9,97,125,95),(10,98,126,96),(11,99,127,93),(12,100,128,94),(17,51,25,45),(18,52,26,46),(19,49,27,47),(20,50,28,48),(29,63,35,65),(30,64,36,66),(31,61,33,67),(32,62,34,68),(37,71,43,73),(38,72,44,74),(39,69,41,75),(40,70,42,76),(77,113,83,111),(78,114,84,112),(79,115,81,109),(80,116,82,110),(85,121,91,119),(86,122,92,120),(87,123,89,117),(88,124,90,118)], [(1,77,22,83),(2,78,23,84),(3,79,24,81),(4,80,21,82),(5,67,14,61),(6,68,15,62),(7,65,16,63),(8,66,13,64),(9,76,125,70),(10,73,126,71),(11,74,127,72),(12,75,128,69),(17,86,25,92),(18,87,26,89),(19,88,27,90),(20,85,28,91),(29,106,35,104),(30,107,36,101),(31,108,33,102),(32,105,34,103),(37,98,43,96),(38,99,44,93),(39,100,41,94),(40,97,42,95),(45,122,51,120),(46,123,52,117),(47,124,49,118),(48,121,50,119),(53,114,59,112),(54,115,60,109),(55,116,57,110),(56,113,58,111)])
56 conjugacy classes
class 1 2A ··· 2G 4A ··· 4H 4I ··· 4AF 4AG ··· 4AV order 1 2 ··· 2 4 ··· 4 4 ··· 4 4 ··· 4 size 1 1 ··· 1 1 ··· 1 2 ··· 2 4 ··· 4
56 irreducible representations
dim 1 1 1 1 1 1 1 1 1 2 2 2 type + + + + + + + + + - image C1 C2 C2 C2 C2 C2 C2 C2 C4 D4 Q8 C4○D4 kernel C4×C4⋊Q8 C43 C4×C4⋊C4 C42⋊9C4 C23.65C23 C23.67C23 C2×C4×Q8 C2×C4⋊Q8 C4⋊Q8 C42 C42 C2×C4 # reps 1 1 4 1 4 2 2 1 16 4 8 12
Matrix representation of C4×C4⋊Q8 in GL5(𝔽5)
2 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 0 0 4
,
4 0 0 0 0 0 2 0 0 0 0 1 3 0 0 0 0 0 4 0 0 0 0 0 4
,
1 0 0 0 0 0 3 0 0 0 0 4 2 0 0 0 0 0 2 0 0 0 0 0 3
,
1 0 0 0 0 0 2 2 0 0 0 0 3 0 0 0 0 0 0 1 0 0 0 4 0
G:=sub<GL(5,GF(5))| [2,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4,0,0,0,0,0,4],[4,0,0,0,0,0,2,1,0,0,0,0,3,0,0,0,0,0,4,0,0,0,0,0,4],[1,0,0,0,0,0,3,4,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,3],[1,0,0,0,0,0,2,0,0,0,0,2,3,0,0,0,0,0,0,4,0,0,0,1,0] >;
C4×C4⋊Q8 in GAP, Magma, Sage, TeX
C_4\times C_4\rtimes Q_8
% in TeX
G:=Group("C4xC4:Q8");
// GroupNames label
G:=SmallGroup(128,1039);
// by ID
G=gap.SmallGroup(128,1039);
# by ID
G:=PCGroup([7,-2,2,2,2,-2,2,2,448,253,120,758,184,304]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^4=1,d^2=c^2,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;
// generators/relations
×
𝔽 | 2020-06-05 00:35:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9992460012435913, "perplexity": 6782.359213498375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1590348492295.88/warc/CC-MAIN-20200604223445-20200605013445-00100.warc.gz"} |
http://coov.gmjradio.it/matlab-phase-demodulation.html | We simulate Binary Phase Shift Keying (BPSK) with phase modulation and mixer based demodulation. Dimitar St. Phase modulation (PM) (here the phase shift of the carrier signal is varied in accordance with the instantaneous amplitude of the modulating signal) Transpositional Modulation (TM), in which the waveform inflection is modified resulting in a signal where each quarter cycle is transposed in the modulation process. Typically, there are two things that make locking onto a GPS signal difficult. Usage of M-Ary Kasami sequences with MATLAB since it possesses good code properties, including a large code set size and low cross correlations. Matlab codes. The complex demodulation and matched ltering process involves implementing two lters, a lowpass lter and the matched lter. System modeling in MATLAB Simulink® for PLL-based resolver-to-digital converters Introduction A previous article in the Analog Applications Journal described the fundamental architecture of a resolver-to-digital converter (RDC). It is the standard form of digital audio in computers, compact discs, digital telephony and other digital audio applications. However, in searching the Internet for tutorial SSB demodulation information I was shocked at how little information was available. 1 Matlab Code 11. A PSK further includes QPSK, BPSK and DPSK techniques. SSB_AM demodulation process, Matlab-based communications system simulation series. Phases are separated by 180o. View Dirk Bell’s profile on LinkedIn, the world's largest professional community. Matlab program for FM demodulation? Unanswered Questions. I'm trying to design an analog phase locked loop in Matlab. See the complete profile on LinkedIn and discover R. Discover what MATLAB. z = pamdemod(y,M) demodulates the complex envelope y of a pulse amplitude modulated signal. All I need to do is replace the demodulation code subject to a decision on (1) a binary XOR or (2) a mixer style phase detector. In both the cases, the total phase angle θ of the modulated signal varies. demodulation. The 565 contains a voltage controlled oscillator (VCO), a phase detector, and a voltage amplifier. 5 db ,then we evaluate the coded. You have to take your samples on the right frequency, and at the right points. It mentions benefits or advantages of DPSK over BPSK. Implementation of FSK Modulation and Demodulation using CD74HC4046A Mahendra Patel Standard Linear and Logic ABSTRACT In telecommunications and signal processing, frequency modulation (FM) is encoding of information on a. Phase modulation is a linear baseband modulation technique in which the message modulates the phase of a constant amplitude signal. The proposed modulators do not use any multiplier in contrast to the conventional modulators and hence they are relatively fast and area efficient. It is local in that these components are allowed to change slowly over time. However, in searching the Internet for tutorial SSB demodulation information I was shocked at how little information was available. 50 out of 5) Quadrature Phase Shift Keying (QPSK) QPSK is a form of phase modulation technique, in which two information bits (combined as one symbol) are modulated at once, selecting one of the four possible carrier phase shift states. Matlab Tutorial - Amplitude Modulation How to generate Amplitude modulation (AM) using MATLAB? AM is a method of transmitting signals, such as sound or digital information, in which the amplitude. z = amdemod(y,Fc,Fs,ini_phase,carramp,num,den) specifies the numerator and denominator of the lowpass Butterworth filter used in the demodulation. Dennis Silage, PhD Professor Electrical and Computer Engineering Temple University [email protected] At this point we know that modulation refers to intentionally modifying a sinusoid such that it can carry lower-frequency information from a transmitter to a receiver. 15kHz and a sinewave at a frequency of 3. For coherent Ф-OTDR, there are. QPSK Modulation-Quadrature Phase Shift Keying modulation. This Matlab code demodulates an FM signal using a phase locked loop. Applications processing, like PVT computation. Select a Web Site. z = pmdemod(y,Fc,Fs,phasedev) demodulates the phase-modulated signal y at the carrier frequency Fc (hertz). This page of MATLAB source code covers PSK matlab code. modulating signal. Dirk has 13 jobs listed on their profile. Generate a signal whose complex envelope consists of a sinusoid and a chirp. This is the expected result because the PSK constellation is circular while the PAM constellation is linear. pdf), Text File (. Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). The phasedev argument is the phase deviation of the modulated signal, in radians. And before we discuss quadrature modulation, we need to understand I/Q signals. Phase Synchronous Demodulation “Standard” PLL Phase Detector Automatic Gain Control Loop Filter VCO Linear Response Costas Loop Motivation Implementation Analysis Simulation using Matlab Lab View Implementation Elements of a PLL 1 A phase detector that generates a signal related to the phase difference of two input signals, 2 A loop filter. In this lab, you will observe the Quadrature Phase Shift Keying (QPSK) modulation and demodulation building Simulink simulation. Data Types: double | single. This complex signal representation is often referred to as the analytic signal. Chapter 1 Fundamentals of Cellular Communication In this chapter, all the background knowledge which is required for this project has been discussed. 1 Introduction The Orthogonal Frequency Division Multiplexing (OFDM) digital communication technique has been attracting a great concern of researchers all over the world, due to its unique characteristics. Le Nguyen BINH. Calculate the constant Kd from Figure 4 and the fact that the voltage of the logic level high is 10v. So far i have a bit generator that generates N bits and stores it into an array:. And using the carrier to demodulate (coherent demodulation), and the intdump() function to retrieve the data. PLL FM demodulation basics. COMPLEX_DEMODULATE - complex demodulation using a low pass filter. In this code, it is considered the default value of ma equal to 1 for hundred percent modulation. Evidently phase demodulation of a signal involves reconstructing a signal such that one can characterise how the modulated signal's phase changes with time. The discussion then moves to binary phase shift keying (BPSK) and shows how this simpler format is modeled using. A transmission begins with several zeros so the decoder can synchronize to the exact frequency. 1 Introduction Modulation is the modification of some aspect of a carrier signal. 5 MATLAB System Objects 121 4. Phase noise could also be added to the local oscillators as a further enhancement. z = amdemod(y,Fc,Fs,ini_phase,carramp,num,den) specifies the numerator and denominator of the lowpass Butterworth filter used in the demodulation. Given a signal of the. Phase rotation of the DPSK modulation, specified in radians as a real scalar. In coherent detection technique the knowledge of the carrier frequency and phase must be known to the receiver. z = pamdemod(y,M,ini_phase) specifies the initial phase of the modulated signal in radians. txt) or view presentation slides online. Techniques for providing the carrier signal: 1. PDF | We propose an efficient method for demodulation of phase modulated signals via iterated Hilbert transform embeddings. In both the cases, the total phase angle θ of the modulated signal varies. The transfer function should be correct before coming to lab. , Loma del Bosque 115, Leon, Guanajuato, Mexico *[email protected] if time series is hourly, frequency should be in inverse hours). The carrier signal has frequency Fc (hertz) and sampling rate Fs (hertz), where Fs must be at least 2*Fc. Matlab code for BASK (OOK) Modulation and Demodulation 11:20 BASK , Demodulation , Modulation Matlab, BASK (OOK), NRZ Unipolar line coding, Modulation, Waveform generation, Coherent detection, BER. يشرح هذا الفيديو التضمين الطوري (phase modulation) وفك التضمين (demodulation) وكيفية تنفيذ ذلك بأستخدام الماتلاب اضافة. The frequency was approximately the same for all three subjects; around 20 Hz. Phase modulation “can be achieved simply by defining a relative phase shift from the carrier, usually equi-distant for each required state. QPSK Demodulation. In the lab students use TIMS (Telecommunication Instructional Modelling System) 301 Modeling systems, to look at the waveforms (using oscilloscope) explaining the basic principles of modulation and demodulation (AM/FM). This thesis discusses the advantages and drawbacks of three different PWM tech-niques: the sinusoidal PWM (SPWM) technique, the third-harmonic-injection PWM (THIPWM). Shows I-Q Modulation to change the phase of a signal, to change the frequency of a signal and to change the amplitude of a signal. By utilising Euler's formula, eijθ=+cos sin(θ) (θ). psk modulation and demodulation using matlab March 18, 2013 by prabhath6 Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). SSB_AM demodulation process, Matlab-based communications system simulation series. • The phases within a small size window around a user selected pixel are approximated as two-dimensional quadratic polynomial functions of the local spatial coordinates. Modulation and Demodulation • Principle borrow from radio telecommunication –Take a wide band signal [few Hz to kHz] –Modulate it with a single frequency “the carrier signal” which is the frequency associated to a given station –Emit the signal –Given the station frequency, a receiver follows a demodulation. The loop filter transfer function must be: $$\frac. With the development of silicon integration technology, the network-on-chip (NoC) proposes a scalable communication architecture that can improve system performance. Reminder Matlab accepts the pi symbol, no need to give the decimal approximation 3. To learn more about digital modulation, see Digital Modulation. The simulation scripts in Matlab/Octave also provided. In ASK, amplitude level of the carrier signal is switched according to the binary information, keeping the phase and frequency fixed. The demodulator This MATLAB function modulates the input signal, x, using phase shift keying (PSK) with modulation order M. y = pmmod(x,Fc,Fs,phasedev) modulates the message signal x using phase modulation. ppt), PDF File (. click me Tutorial 2 This program shows how Quadrature data is put into an FFT as complex data (i e as I+jQ). Using MATLAB m-file and simulink to implement FM modulation and demodulation. The example samples an analog signal and modulates it. Either I'm misunderstanding the "phasing method" of SSB demodulation, or my Matlab code is fouled up. 2/2/01 State-Of-The-Art Source Coding X4 2) 1) Voice →good ↑ ~ 58 dB SNR 3) Video 2 pixels (lip-read threshold) and artifacts (moving details) 384 kbps good video conference quality. The noise will rotate the constellation points. Dennis Silage, PhD Professor Electrical and Computer Engineering Temple University [email protected] Dirk has 13 jobs listed on their profile. Solid-state detector circuits may be either a pn junction diode or the input junction of a transistor. Matlab code for BASK (OOK) Modulation and Demodulation 11:20 BASK , Demodulation , Modulation Matlab, BASK (OOK), NRZ Unipolar line coding, Modulation, Waveform generation, Coherent detection, BER. The process of demodulation for signals using amplitude modulation can be achieved in a number of different techniques, each of which has its own advantage. Mathematics and Signal Processing (modulation, demodulation and signal coding) Network theory (network architecture, network layers) Probability (applications for signal processing) Programming language (C, C++, Java, Matlab, Python) Radiofrequency signals (electromagnetic wave propagation, operation and characteristics of antennas). There are two different methods to fulfill the demodulation, coherent and non-coherent. Phase Locked Loop (PLL) is a key circuit which is commonly used in demodulation circuits of various types. Phase Shift Keying (PSK) is the digital modulation technique in which the phase of the carrier signal is changed by varying the sine and cosine inputs at a particular time. in phase quadrate modulation and demodulation in coherent communication pdf, java code for qpsk modulation and demodulation, dsss modulation and demodulation ppt, dpsk code in matlab, fsk modulation and demodulation java, generation and demodulation of pulse amplitude modulation ppt, modulation projects in matlab, dpsk modulation and. Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. This complex signal representation is often referred to as the analytic signal. FM Demodulation in Software % Matlab ‘diff’ reduces length by 1 sample, need to add a Need a 4-Quadrant ArcTan or Phase Unwrap. plot phase portrait in matlab. Phase Shift Keying (PSK) Modulation Code in MATLAB Jaseem vp / March 25, 2013 Binary Phase shift keying (BPSK) is one of the basic modulation schemes in which the phase of the carrier signal is varied or switched according to the input message pulses. Any modulated signal has a high frequency carrier. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. z and the carrier signal have sampling rate Fs (hertz), where Fs must be at least 2*Fc. One approach to reduce this interference, known as frequency-division multiplexing, allocates different carrier frequencies to different users (or for dif-. ABSTRACT Three types of digital modulation techniques, namely Amplitude shift keying (ASK), Frequency shift keying (FSK) and phase shift keying (FSK) are observed and investigated in this experiment. The key difference between modulation and demodulation is that modulation is to transfer the message signal by adding it with the carrier signal while demodulation is the process of filtering out the actual message signal from the carrier signal. Demodulation is done by multiplying the DSB-SC signal with the carrier signal. They are used as a control system that generates an output signal whose phase is related to the phase of an input "reference" signal. Phase Locked Loop FM Demodulation I'm studying a Phase Locked Loop used for FM demodulation, obviously a phase detector is used in the system. Authors: Yang Yang, Jian Yu Zhang, Sui Zheng Zhang. The product modulator is a type of coherent SSB demodulator. We do coherent demodulation of the BPSK signal at the receiver. Matlab or Octave is used to. Communications Toolbox™ includes tools using either MATLAB ® or Simulink ® for analog passband modulation Phase demodulation: it in the MATLAB Command. This function takes as arguments the source waveform, carrier frequency, sampling frequency, fm deviation, and initial phase respectively. set(O, ;defaultlinewidth', 2) I could not understand the meaning of this statement. 1 of ETSI 301-893 V3. The algorithms compensates for the effects from channel and synchronization errors in a WiMax (IEEE 802. A demodulator is an electronic circuit (or computer program in a software-defined radio) that is used to recover the information content from the modulated carrier wave. By utilising Euler's formula, eijθ=+cos sin(θ) (θ). Demodulation (channel decoding) is the corresponding process at the receiver of converting the received waveform into a. Binary Phase Shift Keying (BPSK) Binary Phase Shift Keying (BPSK) is a two phase modulation scheme, where the 0’s and 1’s in a binary message are represented by two different phase states in the carrier signal: $$\theta=0^{\circ}$$ for binary 1 and $$\theta=180^{\circ}$$ for binary 0. How to implement (the maths) We now need to set about seeking how to change our real signal into its complex form. A modem is an equipment that performs both modulation and demodulation. DSB-SC can be demodulated if modulation index is less than unity. OQPSKDemodulator creates a demodulator System object™. z = pmdemod(y,Fc,Fs,phasedev) demodulates the phase-modulated signal y at the carrier frequency Fc (hertz). y = pmmod(x,Fc,Fs,phasedev) modulates the message signal x using phase modulation. Aly El-Osery October 25, 2010 This lab is divided into two parts. DSB-SC can be demodulated if modulation index is less than unity. I tried to do this but couldn't get good solution. This will make it easy to enter it into MATLAB. Upload and publish your own book in minutes. For demodulation, the modulation oscillator's frequency and phase must be exactly the same as the demodulation oscillator's otherwise, distortion and/or attenuation will occur. Evidently phase demodulation of a signal involves reconstructing a signal such that one can characterise how the modulated signal's phase changes with time. Lab 2 AM DEMODULATION Purpose: 1. Performed BER vs SNR analysis for various modulation schemes such as QPSK, 8-PSK, 16 - QAM over AWGN and Multipath channels and implemented OFDM modulation and demodulation in MATLAB. 1 Introduction Modulation is the modification of some aspect of a carrier signal. Matlab codes. Introduction New visions of 4th Generation communication systems that are recently coming to fact and approaching the everyday life of human being, all going toward increase of capacity, data rate, coverage and reliability of services in response to raising demand to new applications and more complicated services. The process of demodulation for signals using amplitude modulation can be achieved in a number of different techniques, each of which has its own advantage. Phase Errors Issues; Phase errors happen due to the noise introduced by the channel. This is extremely useful in amateur radio. Again referring to Table 1, notice that QPSK and 8 φ-PSK systems encode more hits of information per trans mitted symbol than does BPSK. z and the carrier signal have sampling rate Fs (hertz), where Fs must be at least 2*Fc. The loop filter transfer function must be:$$\frac. pdf), Text File (. Learn how to use Matlab Simulink to design low-pass, high-pass, and band-pass filter. I will say that your demodulator is modulatioh too complicated. The phase detector compares the phase of that signal with the phase of the input random signal and adjusts the oscillator to keep the phases matched. The binary-coded waveform is a waveform with two levels of phase-shift keying, 0° for positive amplitude and 180° for negative amplitude,. I tried to do this but couldn't get good solution. ASK&FSK Modulation &demodulation Code in MATLAB Amplitude-shift keying (ASK) is a form of amplitude modulation that represents digital data as variations in the amplitude of a carrier wave. Phase modulation, PM is sometimes used for analogue transmission, but it has become the basis for modulation schemes used for carrying data. 8 Variables and Parameters 142 4. Question: Write A Matlab Code For Frequency Modulation And Demodulation, Phase Modulation Demodulation. The modulated signal is synthesized by using an upsampled random unipolar bit. If synchronous demodulation is used, the waveform is required at the demodulator. QPSK Modulator QPSK Demodulation: For QPSK demodulator , a coherent demodulator is taken as an example. All I need to do is replace the demodulation code subject to a decision on (1) a binary XOR or (2) a mixer style phase detector. PSK technique is widely used for wireless LANs, bio-metric, contactless operations, along with RFID and Bluetooth. We simulate Binary Phase Shift Keying (BPSK) with phase modulation and mixer based demodulation. In ASK, amplitude level of the carrier signal is switched according to the binary information, keeping the phase and frequency fixed. Phase Shift Keying (PSK) Modulation Code in MATLAB Jaseem vp / March 25, 2013 Binary Phase shift keying (BPSK) is one of the basic modulation schemes in which the phase of the carrier signal is varied or switched according to the input message pulses. The phase detector compares the phase of that signal with the phase of the input random signal and adjusts the oscillator to keep the phases matched. I conducted a research on how to implement a QPSK demodulator. One approach to reduce this interference, known as frequency-division multiplexing, allocates different carrier frequencies to different users (or for dif-. Coherent demodulation requires the received signal to be multiplied with the carrier having the same frequency and phase as at the transmitter. However, in searching the Internet for tutorial SSB demodulation information I was shocked at how little information was available. This complex signal representation is often referred to as the analytic signal. In a post on Minimum Shift Keying (MSK), we had discussed that MSK uses two frequencies which are separated by and phase discontinuity is avoided in symbol boundaries. In demodulation part the output of each mixer contains both baseband components and high frequency carrier components. This simulation helps to Implement FSK modulation and Demodulation on Hardware Easily. In addition to these, a phase imbalance and a phase offset could be added to the receiver’s local oscillators. Hello, Can anyone help me debug my Single Phase Inverter model? I have it semi-made, i have pwm features in there, but i just can't get it to work Single Phase Inverter Help (Scripts) 1. pdf), Text File (. We do coherent demodulation of the BPSK signal at the receiver. See the complete profile on LinkedIn and discover Ernesto’s connections and jobs at similar companies. The main purpose of this blog is to sharing the knowledge of MATLAB with some small project. Demodulation is extracting the original information-bearing signal from a carrier wave. BINARY PHASE SHIFT KEYING (BPSK) SIMULATION USING MATLAB Stanimir Sadinov 1, Pesha Daneva , Panagiotis Kogias 2, Jordan Kanev 1 and Kyriakos Ovaliadis 2 1Department KTT, Faculty of Electrical Engineering and Electronics, Tech nical University of Gabrovo, H. The functions of forwarding and reverse power measurement of active load, power factor monitoring, TWACS modulation and demodulation are realized through software calculation. The Phase-Locked Loop (PLL), and many of the devices used for frequency and phase tracking, carrier and symbol synchronization, demodulation, and frequency synthesis, are fundamental building blocks in today's complex … - Selection from Basic Simulation Models of Phase Tracking Devices Using MATLAB [Book]. Skip navigation Sign in. This paper focuses on the Binary Phase Shift Keying Digital Modulation Technique for Noiseless and Noisy Transmission with the following objectives:(i) to design a BPSK system (ii) to show the modulation and demodulation of a BPSK technique through a noiseless channel and (iii) to show the modulation and demodulation of the same technique. View Ernesto Wiebe’s profile on LinkedIn, the world's largest professional community. 2 MATLAB Functions 107 4. ) Derive the conventional DSB AM signal and define the modulation index(μ). z = amdemod(y,Fc,Fs,ini_phase,carramp,num,den) specifies the numerator and denominator of the lowpass Butterworth filter used in the demodulation. It enables the amplitude and phase of a particular frequency component of a time series to be described as functions of time. The YETI-2019 Conference gave an opportunity to young. There are many types of modulation so there are many types of demodulators. I found out the Quadrature QPSK demodulation technique which seems very straight forward. txt) or view presentation slides online. Combat mission red thunder manual woodworkers Balrog runescape guide K760 cut n break. If synchronous demodulation is used, the waveform is required at the demodulator. A nonlinear device is required for demodulation. z and the carrier signal have sampling rate Fs (hertz), where Fs must be at least 2*Fc. Modulation is almost always necessary if data transmission is desired. Matlab scripts and data. Ernesto has 3 jobs listed on their profile. The detector circuit is employed to separate the carrier wave and eliminate the side bands. Even though there are different methods for modulation and demodulation processes, each has its own advantages and disadvantages. There are techniques available to overcome this. The total phase shift per symbol is the sum of phaserot and the phase generated by the differential modulation. The International Youth Conference on Electronics, Telecommunications and Information Technologies (YETI-2019) was held in Saint Petersburg on July 11 – 22, 2019. this blog about digital communication, how to simulate code matlab for BPSK, QPSK and 8 QAM, then apply it to Rectangular pulse shaping (RPS) then simulate code matlab for Square Root Raised Cosine (SQRC) filter as pulse shaping filter and matched filter, and apply it to the system, and we found minimum number of coefficient that the loss did not exceed 0. If a block of information must be trans mitted over the same int erval of. 5 db ,then we evaluate the coded. (formerly University College of Engineering) Faculty in Department of Electronics and Telecommunication Engineering Synergy. FIR Finite Impulse Response FFT Fast Fourier Transform LP Low pass BP Band pass A/D Analog to digital SNR Signal to. Demodulation is a reverse process of modulation in which the original information or data is extracted from the modulated signal [22]. Techniques for providing the carrier signal: 1. Phase regeneration of differential phase-shift keying (DPSK) signals is demonstrated using a silicon waveguide as nonlinear medium for the first time. 01 Hz to 300KHz frequency range, 4. The most popular 'electronic' method for FM/PM demodulation is the Phase Locked Loop (PLL). Usually, each phase encodes an equal number of bits. Phase ambiguity is a problem in the demodulation of a BPSK signal. In DPCM only the difference between a sample and the previous value is encoded. Figure 6 shows a signal 1011010 and a carrier signal which after modulation gives a PSK modulated signal. Carrier recovery scheme in the demodulator is shown in Fig 2. Phase shoft keying, PSK is widely used for data communication. Phase rotation of the DPSK modulation, specified in radians as a real scalar. The user terminal inactive load side consists of MCU, A/D, voltage and current transformer, signal conditioning circuit, thyristor and modulation resistance, etc. In this code, it is considered the default value of ma equal to 1 for hundred percent modulation. , denoising, background removal and amplitude normalization) and subsequent boosted phase demodulation using 2D Hilbert spiral transform aided by the Principal Component Analysis method for novel, correct and. The ideal modulated signal should have a minimum Euclidean distance of 2. The I and Q signals at the outputsof the mixers have the desired phase relationships 156 Satellite Signal Acquisition, Tracking, and Data Demodulation. The phase synchronization is normally achieved using Phase Locked Loop (PLL) at the receiver. The first ultrasound signal processing technique is quadrature detection, or IQ as it's sometimes called. The modulated test signals are then demodulated using the demodulation algorithm under test. Keith McPherson’s profile on LinkedIn, the world's largest professional community. I need to modify this code for all the bits present in the data sequence I have to repeat the above steps for 10 bits. m – Remez differentiator with filtering procedure forcevib. Then, we will obtain 8 samples of that cosine: the sampling frequency, fsim in the code, is divided between 8 so we take one cycle with 8 samples of the signal. Here is the matlab code for Frequency Modulation(FM), the use of particular code is also given as comments ( %Comment field ). Used to denote the complex format on which the RF data is stored from the System Five. The Mixer component is configured as Up Mixer. Voice can not be sent be very far by screaming. To validate the tandem demodulation formulas, we simply save the measured data and compared them with the analytical expressions of $$A$$ and $$\phi$$ using MATLAB. MATLAB code for Frequency modulation (FM) with modulation index Gallery of Electronic Circuits and projects, providing lot of DIY circuit diagrams, Robotics & Microcontroller Projects, Electronic development tools. Simulation of DPSK performance curves in Matlab. See the complete profile on LinkedIn and discover Ernesto’s connections and jobs at similar companies. Quadrature detection Quadrature detection is a demodulation technique which builds on the utilization of a quadrature signal. The complex envelope does not include the phase variation and can be sampled at a lower rate. It mentions benefits or advantages of DPSK over BPSK. Phase demodulation is therefore based on this simple idea of setting out to measure how the phase of the signal varies with time. Table : Phase transitions for DQPSK modulation (Ref Table 5. PSK uses a finite number of phases, each assigned a unique pattern of binary digits. The YETI-2019 Conference gave an opportunity to young. Abstract: This paper presents a 4-b phase-domain analog-to-digital converter (ADC) that utilizes the time-domain reference generation scheme for low-power operation. oqpskdemod = comm. PM modulation Using MATLAB - Simulink Software. Figure illustrates PSK and DPSK Modulated signal by 10101110 pulse sequence. [1] This article addresses how to simulate the performance of a RDC in the powertrain. The binary data generator block generates the information signal m(t) i. Small Range Digital Thermometer simulation on Ngspice using 1N4148 diode as temperature sensor Abstract-In today's era, we have an ocean of temperature sensing devices available in the industry. translation back to baseband, with recovery of the bandlimited message waveform 2. Le Nguyen BINH. The second class or type of FM demodulator is the phase-locked loop, which includes a phase detector that may be a multiplier, a low-pass filter, and a voltage-controlled oscillator that produces a frequency proportional to its control voltage. AM-DSB-SC Modulation & Demodulation Aim To perform the AM DSB-SC signal Generation and Detection using Matlab Simulink. This program is a complete implementation of GMSK modulation and demodulation process, draw the corresponding waveform. Using MATLAB m-file and simulink to implement FM modulation and demodulation. This is extremely useful in amateur radio. In case of coherent demodulation carrier used for demodulation purpose is in phase and frequency synchronism with carrier used for modulation purpose. Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. Typically, there are two things that make locking onto a GPS signal difficult. z and the carrier signal have sampling rate Fs (hertz), where Fs must be at least 2*Fc. In your example, the symbol rate Rs is less than the angular carrier frequency w_c which potentially causes overlapping of spectra at the receiver. Coupled inductor as common mode choke 5. Usage of M-Ary Kasami sequences with MATLAB since it possesses good code properties, including a large code set size and low cross correlations. Modulation and demodulation in MATLAB. The numerator and denominator are generated by [num,den] = butter(n,Fc*2/Fs), where n is the order of the lowpass filter. y = pmmod(x,Fc,Fs,phasedev) modulates the message signal x using phase modulation. QPSK Modulation and Demodulation in Matlab AWGN Channel. In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (π /2 radians). Upload and publish your own book in minutes. Assistant Professor II School of Electronics Engineering, KIIT Deemed to be University, Bhubaneswar-751024 PhD from National Institute of Technology Rourkela India M Tech from VSS University of Technology, Burla. There are many types of modulation so there are many types of demodulators. Both processes aim to achieve transfer information with the minimum distortion, minimum loss and efficient utilization of spectrum. To validate the tandem demodulation formulas, we simply save the measured data and compared them with the analytical expressions of $$A$$ and $$\phi$$ using MATLAB. Although the example uses phase modulation, most elements of this example apply to other analog modulation techniques as well. In the previous two pages we discussed systems for performing demodulation of AM and FM signals that carry analog data, such as (non-digitized) audio. Matlab and Octave have a function called unwrap() which implements a numerical algorithm for phase unwrapping. For the demodulation part, it is an opposite process of modulation. The Phase-Locked Loop (PLL), and many of the devices used for frequency and phase tracking, carrier and symbol synchronization, demodulation, and frequency synthesis, are fundamental building blocks in today's complex … - Selection from Basic Simulation Models of Phase Tracking Devices Using MATLAB [Book]. The low pass filter gets rid of the higher frequencies coming out of the diode and to allow the low frequency message signal to pass through the filter. 50 out of 5) Quadrature Phase Shift Keying (QPSK) QPSK is a form of phase modulation technique, in which two information bits (combined as one symbol) are modulated at once, selecting one of the four possible carrier phase shift states. The web's wikipedia 'single-sideband modulation' gives the mathematical details of SSB generation [1]. Evans Dept. Phase Modulation (PM) is another form of angle modulation. Usage of M-Ary Kasami sequences with MATLAB since it possesses good code properties, including a large code set size and low cross correlations. There are many types of modulation so there are many types of demodulators. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the phase of the received signal and maps it back to the symbol it represents, thus recovering the original data. 7 and 8 that when the. In your case, since you are sampling at the symbol rate, the channel bandwidth is the symbol rate. Shujie has 3 jobs listed on their profile. Phase Locked Loop (PLL) is a key circuit which is commonly used in demodulation circuits of various types. The second entry, initphase, is the initial phase of the carrier signal, measured in radians. This topic is the result of Digital Signal Processing term project named Amplitude Modulation and Demodulation on Texas Instrument Kit DSK C6713 with Matlab Simulink. This complex signal representation is often referred to as the analytic signal. Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of the carrier wave. For the demodulation part, it is an opposite process of modulation. The phasedev argument is the phase deviation of the modulated signal, in radians. The modulated signal is synthesized by using an upsampled random unipolar bit. Demodulation is the process by which the original information bearing signal, i. The block diagram of this demodulation method is like this: The most common mistake when applying analog demodulation techniques in MATLAB is sampling. The code of FSK modulation and demodulation has been developed using MATLAB according to conventional theory. 1 Matlab Code 11. z and the carrier signal have sampling rate Fs (hertz), where Fs must be at least 2*Fc. Matlab Introduction - Free download as Powerpoint Presentation (. , Loma del Bosque 115, Leon, Guanajuato, Mexico *[email protected] June 17, % Simple Matlab/Octave code for non-coherent demodulation of % differentially encoded phase shift keying. Differential phase shift keying (DPSK) is a common form of phase modulation that conveys data by changing the phase of the carrier. Carrier is recovered by the carrier recovery circuit at the receiver. A demodulator is an electronic circuit (or computer program in a software-defined radio) that is used to recover the information content from the modulated carrier wave. 1 Introduction The convenience and popularity of wireless technology has now extended into multimedia communications, where it poses a unique challenge for transmitting high rate voice, image, and data signals simultaneously, synchronously, and virtually error-free. Chapter 6 Analog Modulation and Demodulation. plot phase portrait in matlab. 0Kohm resistor, 1. The general coherent demodulation process is shown in Figure 2. The binary signal when ASK modulated, gives a zero value for Low input while it gives the carrier output for High input. "MATLAB is widely used technical computing software. Figure illustrates PSK and DPSK Modulated signal by 10101110 pulse sequence. | 2019-12-09 10:36:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.5381651520729065, "perplexity": 1755.5272755811138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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/1575540518627.72/warc/CC-MAIN-20191209093227-20191209121227-00465.warc.gz"} |
https://ai.stackexchange.com/tags/neurons/hot | # Tag Info
## Hot answers tagged neurons
16
There is no direct way to find the optimal number of them: people empirically try and see (e.g., using cross-validation). The most common search techniques are random, manual, and grid searches. There exist more advanced techniques such as Gaussian processes, e.g. Optimizing Neural Network Hyperparameters with Gaussian Processes for Dialog Act ...
11
Some back of the envelope calculations : number of neurons in AI systems The number of neurons in AI systems is a little tricky to calculate, Neural Networks and Deep Learning are 2 current AI systems as you call them, specifics are hard to come by (If someone has them please share), but data on parameters do exist, parameters are more analogous to ...
8
In reverse order to how you asked: all units in a layer become equal since initially the errors due to all of them are the same and thus we train them to be equal This actually happens if you initialise the weights equally (e.g. all zero). Gradients in that case are the same to each neuron in the same layer, and everything changes in lockstep. A neural ...
7
For a more intelligent approach than random or exhaustive searches, you could try a genetic algorithm such as NEAT http://nn.cs.utexas.edu/?neat. However, this has no guarantee to find a global optima, it is simply an optimization algorithm based on performance and is therefore vulnerable to getting stuck in a local optima.
7
Soon enough but that doesn't mean anything at all. In machine learning the word neuron represents a calculation whereas in brain the word neuron represent a specific type of cell which is a biochemical system.
6
Neural networks don't model biological neurons. They are at best inspired by biological neurons, in that they get excited by certain inputs and fire once the excitation crosses a threshold. And this second point even holds only approximately because the backpropagation algorithm needs smoothed out steps to learn by gradient descent. And backpropagation is ...
5
One probable hardware limiting factor is internal bandwidth. A human brain has 10^15 synapses. Even if each is only exchanging a few bits of information per second, that's on the order of 10^15 bytes/sec internal bandwidth. A fast GPU (like those used to train neural networks) might approach 10^11 bytes/sec of internal bandwidth. You could network 10,000 ...
5
Typically, weights are randomly initialized. Then, as the model is optimized for its given task, those weights are steadily made "better" as determined by the network's loss function. This is also referred to as "training" the neural network. By far the most popular way of updating weights in a neural net is the backpropagation algorithm, most simply with ...
4
No, here is why. No approach can simulate the mind with 100% accuracy. a major notion that AI theorist refuse to note is that you cant take an orange and by virtue of technology turn it into an apple lets apply the same logic here. neurons are temporary things in our brains, daily we are trimming our brains and growing our brains, in order to "Engineer" a ...
4
Paper Szegedy C, Vanhoucke V, Ioffe S, et al. Rethinking the inception architecture for computer vision[J]. arXiv preprint arXiv:1512.00567, 2015. gives some general design principles: Avoid representational bottlenecks, especially early in the network; Balance the width and depth of the network. Optimal performance of the network can be reached ...
4
It looks like you really have two questions here. I'll try to answer the first one, and you should think about making a separate question for the second. There is research into using simulated models of biologically realistic neurons. While there are large projects like the Human Brain Project aimed at simulating human brains, there is also a lot of lower-...
4
State of Rosehip Research The Rosehip neuron is an important discovery, with vast implications to AI and its relationship to the dominant intelligence on earth for at least the last 50,000 years. The paper that has spawned other articles is Transcriptomic and morphophysiological evidence for a specialized human cortical GABAergic cell type, Buldog et. al.,...
4
In short I mentioned in another post, how the Artificial Neural Network (ANN) weights are a relatively crude abstraction of connections between neurons in the brain. Similarly, the random weight initialization step in ANNs is a simple procedure that abstracts the complexity of central nervous system development and synaptogenesis. A bit more detail (with ...
4
I assume you're talking about a perceptron threshold function. One definition of it with an explicit threshold is $$f(\textbf{x})= \begin{cases} 1& \text{if } \textbf{w}\cdot\textbf{x} > t\\ 0& \text{otherwise} \end{cases}.$$ Another form with a bias is $$f(\textbf{x})= \begin{cases} 1& \text{if } \textbf{w}\cdot\textbf{x} + b > 0\\ 0&... 4 The basic calculation for a single neuron is of the form$$\sigma\left(\sum_{i} x_i w_i \right),$$where x_i is the input to the neuron w_i are the neuron-specific weights for every single input and \sigma is the pre-specified activation function. In your terms, and disregarding the activation function, the calculation would turn out to be$$c\,a_c ...
3
It is true that the current Machine learning is based on treating neurons as a component in the whole complexity , mesh of neurons. The focus is more on the architecture rather than understanding or imitating the basic block of it more clearly , i.e. the neurons. Anirban Bandhopadhyay is a biologist and Neurologist who has studied how the harmony changes ...
3
Yes, this was an active area of research in a number of different AI fields. Probably the most directly related work is Bongard, Zykov & Lipson's self-repairing robots from the early 2000's. There's some more recent work from Mark Yim that you can see here too. There are lots of different ways to do this, but Bongard et al's approach was probably the ...
3
Principles of Computational Modelling in Neuroscience by David Sterratt, Bruce Graham, Andrew Gillies and David Willshaw discuss it in Chapter 7 (The synapse) and also in Chapter 8 (Simplified models of neurons). Especially in chapter 8, they discuss how to add excitatory or inhibitory synapses to integrate and fire neuron. There are various ways to add ...
3
The answers so far haven't answered the question numerically, so here is my attempt to steer them in the direction I was seeking: The freely available Deep Learning Book has the following figure on page 27: I question the blue fit line, as it seems that data points may be better described by a parabolic or exponential function. In any case, based upon ...
3
Well, adding gaussian noise is a very common regularisation method. Maybe this paper is interesting to you. They also have very small datasets. In the end there is only so much you can get out of a given dataset.
3
It depends on the accuracy you want. If you had 1 neuron, it could discern things across a line, if you have 2, you could solve things across 2 lines, etc. As you increase the number of neurons, you are increasing the number of discernible areas. As you increase the number of lines you can use to break up the input space, the lines can be placed to ...
3
While interesting, this is all rendered somewhat moot if you think about what will happen once we understand how the brain works. After all, once we understood flight, we didn't start making birds. The same goes for AI. Here are just a few ways in which human brains and digital brains can't be compared. The digital brain won't have to worry about food and ...
2
This has been my field of research. I've seen the previous answers that suggest that we don't have sufficient computational power, but this is not entirely true. The computational estimate for the human brain ranges from 10 petaFLOPS (1 x 10^16) to 1 exaFLOPS (1 x 10^18). Let's use the most conservative number. The TaihuLight can do 90 petaFLOPS which is 9 ...
2
The cell of a perceptron was based on an oversimplified conception of a neuron. At the time, neural plasticity, timing factors in relation to activation, neurochemical pathways, and energy transit complexities in axons were unknown. The mapping of pulse transmission to basic algebra seemed unrealistic, so timing was ignored. Plasticity, timing, and regional ...
2
There is indeed an investigation in progress, regarding this topic. A first publication from last march noted that modularity has been done, although not explicitly, since some time ago, but somehow training keeps being monolithic. This paper assess some primary questions about the matter and compares training times and performances on modular and heavily ...
2
A benchmark comparison of systems comprised of separately trained networks relative to single deeper networks would not likely reveal a universally applicable best choice.1 We can see in the literature the increase in the number of larger systems where several artificial networks are combined, along with other types of components. It is to be expected. ...
2
In biology, when the presynaptic releases a neurotransmitter (a positive amount of them, obviously), this neurotransmitter reaches the postsynaptic vesicles causing an excitatory (depolarization) or inhibitory (hyperpolarization) effect, depending on the kind of postsynaptic vesicle in next cell dendrites. If the total amount of depolarization (all dendrites)...
2
Good question. It is related to the genetic algorithm concept, automated bug detection, and continuous integration. Early Genetically Inspired Algorithms Some of the Cambridge LISP code in the 1990s worked deliberately toward self-improvement, which is not the same as self-repair, but the two are conceptual siblings. Some of those early LISP algorithms ...
2
Yes, for many sensory inputs there is indeed something similar to normalization. But its not rally the same as in classical data analytics compared to what eg min/max normalization does or other technics. Lets look on some examples and considerations: mammals don't perceive heat or loudness in a linear way. This is because already many sensory receptors ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2020-10-20 21:00:47 | {"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": 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": 0.5460086464881897, "perplexity": 1118.3216305067524}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107874135.2/warc/CC-MAIN-20201020192039-20201020222039-00159.warc.gz"} |
https://hal.archives-ouvertes.fr/hal-00360077/fr/ | # Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications
Abstract : In this paper we describe all rotation $H$-hypersurfaces in $H^n \times R$ and use them as barriers to prove existence and characterization of certain vertical $H$-graphs and to give symmetry and uniqueness results for compact $H$-hypersurfaces whose boundary is one or two parallel submanifolds in slices. We also describe examples of translation $H$-hypersurfaces in $H^n \times R$. For $n>2$ we obtain a complete embedded translation hypersurface generated by a compact, simple, strictly convex curve. When $0 < H < \frac{n-1}{n}$ we obtain a complete non-entire vertical graph over the non-mean convex domain bounded by an equidistant hypersurface taking infinite boundary value data and infinite asymptotic boundary value data.
Keywords :
Type de document :
Article dans une revue
Matemática Contemporânea, Sociedade Brasileira de Matemática, 2008, 34 (2008), pp.19-51
https://hal.archives-ouvertes.fr/hal-00360077
Contributeur : Pierre Bérard <>
Soumis le : lundi 4 mai 2009 - 17:22:21
Dernière modification le : lundi 2 novembre 2015 - 16:56:06
Document(s) archivé(s) le : mercredi 22 septembre 2010 - 12:39:10
### Fichiers
berard-saearp-mat-contemp-2008...
Fichiers produits par l'(les) auteur(s)
### Identifiants
• HAL Id : hal-00360077, version 2
• ARXIV : 0902.1623
### Citation
Pierre Bérard, Ricardo Sa Earp. Examples of $H$-hypersurfaces in $H^n \times R$ and geometric applications. Matemática Contemporânea, Sociedade Brasileira de Matemática, 2008, 34 (2008), pp.19-51. <hal-00360077v2>
Consultations de
la notice
## 144
Téléchargements du document | 2017-09-23 23:32:12 | {"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": 0.5265577435493469, "perplexity": 10423.779298154353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689806.55/warc/CC-MAIN-20170923231842-20170924011842-00556.warc.gz"} |
https://docs.cemosis.fr/ibat/latest/reports/thomas-saigre-tardif/hdg.html | # Hybrid Discontinue Galerkin (HDG)
This part was treated at the end of the internship, and it was harder for me to understand. There may be some imprecision left on this page. For safer information about HDG method, you can report to the corresponding page in Feel++ mathematics [FeelppMath], or in the article [HDG2020].
## 1. HDG formulation
The HDG method uses discontinuous elements (contrary to usual, the elements are continuous in standard Galerkin methods).
It consists in rewrite a system of equations in a first-order system.
In the HDG method, we have an unknown, the potential field (for example the temperature) on which we add the associated flux, who becomes unknown too. It allows formulating the problem with a better cost, by introducing the trace.
The HDG method has some attractive features :
• It gives an optimal approximation for the potential fiels and the flux
• It requires less degrees of freedom than usual Discontinuous Galerkin methods for a comparable accuracy
• It allow local post-processin to obtain better approximations and conservation properties.
## 2. Application to Bestest heat equation
Those are the equtation, tken from here :
\begin{align} \rho_m c_m \frac{\partial T_w}{\partial t}+\nabla \cdot\left(-k \nabla T_w\right) &= 0 \tag{H_w}\label{hw}\\ \rho_a c_a \frac{\partial T_r}{\partial t} - h_i \cdot A_w \cdot \left( T_w - T_r \right) - \eta \cdot \rho_a c_a \cdot V_a \cdot \left( T_e - T_r \right) &= H \tag{H_r}\label{hr} \end{align}
Where the unknowns of the equation are :
• $T_w$ the temperature in the wall
• $T_r$ the temperature in the room (supposed to be constant in space over the room)
We introduce the thermal flux :
$\q_w=-k\nabla T_w$
Replacing this in the equation $\ref{hw}$, we get the mixte problem, with first-order equations :
$\begin{cases} \q_w+k\nabla T_w = 0\\ \rho_mc_m\frac{\partial T_w}{\partial t} + \nabla \cdot \q_w = 0 \end{cases}$
Let’s partition the border $\Gamma$ of $\Omega$ in three disjoint subsets : $\Gamma = \Gamma_D \cup \Gamma_N \cup \Gamma_{ibc}$
The quantities $\q_w$ and $T_w$ are subject to those boundary conditions :
• $T_w=0$ on $\Gamma_D$ (Dirichlet condition)
• $\q_w\cdot\n = 0$ on $\Gamma_N$ (Neumann condition)
• $T_w$ is a constant (unknown) on $\Gamma_{ibc}$ and $\displaystyle\int_{\Gamma_{ibc}}\q_w\cdot\n=I_\text{target}$ (Integral boundary condition, or IBC)
With such a condition, $T_w$ is constant but unknown. It makes sense because the temperature in the wall is supposed to be constant in space, but can vary in time. It it what tells the EDO $\ref{hr}$
The value of $\int_{\Gamma_{ibc}} \q_w \cdot \n$ is equal to the quantity of heat exchanged with the air, so :
$\int_{\Gamma_{ibc}} \q_w\cdot \n = \int_{\Gamma_{ibc}} h_i(T_w-T_r)$
We can deduce the value of $I_\text{target}$ which is therefore equal to $\displaystyle\int_{\Gamma_{ibc}} h(T_w-T_r)$, because $T_w$ is supposed to be constant over $\Gamma_{ibc}$.
Let $\bar{\varphi}\in H^{1/2}(\Gamma)$ such that $\bar{\varphi}|_{\Gamma_D}=0$ and $\bar{\varphi}|_{\Gamma_{ibc}}=1$. The variational problem of our equation system is :
Find $\q_w\in H(div,\Omega)$, $T_w\in L^2(\Omega)$ and $\widehat{T_w} \in \mathrm{span} \left<\bar{\varphi}\right> \oplus H^{1/2}_{00}(\Gamma_N)$ such as for all $\v\in H(div;\Omega)$, $w\in L^2(\Omega)$, $\mu\in\mathrm{span}\left<\bar{\varphi}\right>\oplus H^{1/2}_{00}(\Gamma_N)$ we have :
\begin{align} \int_\Omega k^{-1}\q_w \cdot \v - \int_\Omega p\nabla \cdot \v + \int_\Gamma \widehat{T_w} \v\cdot\n = 0\\ \int_\Omega\frac{\rho_m c_m}{\Delta t} T_w w + \int_\Omega \nabla\cdot\q_w w = \int_\Omega\frac{\rho_m c_m}{\Delta t} T_w^\text{prev} w\\ \int_\Gamma \q_w\cdot\n = \int_{\Gamma_N}g_N\mu + I_\text{target}|\Gamma_{ibc}|^{-1}\int_{\Gamma_{ibc}}\mu \end{align} \tag{E_\text{var}}\label{eq:pb_var}
We use those spaces : $H^{1/2}(\Gamma) = \left\{\varphi\in L^2(\Gamma)\,\middle|\,\exists u\in H^1(\Omega), u|_\Gamma = \varphi\right\}$ $H^{1/2}_{00}(\Gamma) = \left\{\varphi\in H^{1/2}(\Gamma) \,\middle|\, \varphi=0 \,\text{on}\,\Gamma_D\cup_{\Gamma_{ibc}}\right\}$ $H(div;\Omega) = \left\{u\in L^2(\Omega)\,\middle|\, div(u)\in L^2(\Omega)\right\}$
We make the usual approximation $\dfrac{\partial T_w}{\partial t} = \dfrac{T_w-T_w^\text{prev}}{\Delta t}$, where $T_w^\text{prev}$ is the temperature from the previous step of the simulation.
We can show (cf. [HDG2020]) that if $g_N\in L^2(\Gamma_N)$, this problem admits a unique solution $(\q_w,T_w,\widehat{T}_w)$, satisfying the conditions given earlier.
The trace $\widehat{T}_w$ of $T_w$ allows reducing the cost of computation. We can show (cf. [Sala2019]) that the HDG method gives the best approximation error on potential and the flux.
## 3. Discretization
Let $\T_h$ be a triangulation of $\Omega$. We denote by $\F_h$ the set of all faces of $\T_h$, $\F_h^\Gamma$ the set of faces belonging to $\Gamma$ (and a similar notation for the subsets of $\Gamma$), and $\F_h^0$ the set of the faces belonging to the interior of $\Omega$.
If $\q\in H(div,K)$, then its normal trace on the boundary of $K$, $\q\cdot\n$ belongs to $H^{-1/2}(K)$. In the following, we note $\q^K := \q|_K$. Let’s suppose that $\q\in \left(L^2(\Omega)\right)^d$, and $\q^K\in H(div,K)$ for all $K\in\T_h$. Let $F := \partial K_1\cap\partial K_2$ the border between two elements $K_1,K_2\in \T_h$, this face belonging to $\F_h^0$. We define the jump of the normal trace of $\q$ across $F$ as :
$[\![\q]\!] := \q^{K_1}\cdot\n_{\partial K_1}|_F + \q^{K_2}\cdot\n_{\partial K_2}|_F$
We can prove (cf [HDG2020]) that
$[\![\q]\!] = 0 \forall F\in\F_h^0 \Longleftrightarrow \q\in H(div,\Omega)$
We introduce those three spaces :
• $V_h = \displaystyle\prod_{K\in \T_h}\mathbf{P}_k(K)$
• $W_h = \displaystyle\prod_{K\in \T_h} P_k(K)$
• $M_h = \mathrm{span}\left<\varphi^*\right> \oplus \displaystyle\prod_{F\in\F_h^0 \cup\F_h^{\Gamma_N}} P_k(F)$
With $\varphi^*\in L^2(\F_h)$ such as $\forall F\in \F_h^{\Gamma_{ibc}}, \varphi^*|_{F}=1$ and $\forall F\in \F\setminus\F_h^{\Gamma_{ibc}}, \varphi^*|_{F}=0$. And $\mathbf{P}_k(K)=(\P_k(K))^d$.
We see that the spaces are richer because the functions belonging to them are in general discontinuous. The functions of $M_h$ play the role of connectors between adjacent elements, in order to reduce the time of calculation.
We define the numerical normal flux on $\partial K$ :
$\widehat{\q}^{\partial K}_{w,h} \cdot \n_{\partial K} = \q^K_{w,h}|_{\partial K} + \tau_{\partial K} \left(T_{w,h}^K|_{\partial K}-\widehat{T}_{w,h}|_{\partial K}\right) \tag{E_\text{flux}}\label{eq:flux}$
Where $\tau_K$ is a non-negative function that can vary on $\partial K$, and $\tau_K > 0$ on at least one face of $\partial K$. This parameter plays on the continuité of the potential, and to get a stabilized digital flow, we may have to scale this parameter or the flux. It is called stabilization parameter.
The discrete variational problem is therefore : find $\q_{w,h}\in V_h$, $T_{w,h}\in W_h$ and $\widehat{T}_{w,h}\in M_h$ such as $\forall \v_h\in V_h, \forall w_h\in W_h, \forall \mu_h\in M_h$
\begin{align} \sum_{K\in\T_h} \left[\int_K k^{-1}\q^K_{w,h} \cdot \v_h^K - \int_K T_{w,h}^K\nabla\cdot \v + \int_{\partial K} \widehat{T}_{w,h}\v_h^K\cdot \n_{\partial K}\right] &= 0\\ \sum_{K\in\T_h} \left[\int_K \frac{\rho_m c_m}{\Delta t}T_{w,h}^K-\int_K \q_{w,h}^K\cdot \nabla w_h^K + \int_{\partial K} \widehat{\q}_{w,h}^{\partial K}\cdot\n_{\partial K} w_h^K\right] &= \sum_{K\in\T_h} \int_K \frac{\rho_m c_m}{\Delta t}T_w^{\text{prev},K}w\\ \sum_{K\in\T_h} \int_{\partial K} \widehat{\q}_{w,h}^{\partial K} \cdot \n_{\partial K} \mu_h &= \int_{\Gamma_N} g_N\mu_h + I_\text{target} |\Gamma_{ibc}|^{-1}\int_{\Gamma_{ibc}} \mu_h \end{align} \tag{E_\text{disc}}\label{eq:pb_var_disc}
## 4. Static condensation
The discrete equation $\ref{eq:pb_var_disc}$ hlod in the interior of each $K\in \T_h$ and can b solved for each $K$ to eliminate $\q_w^K$ and $T_{w,h}^K$ in favor of the variable $\widehat{T}_{w,h}^K$. This method of elimination is called static condensation.
With the equation $\ref{eq:flux}$, it is possible to express the normal numerical flux as a function of $\widehat{T}_{w,h}^K$.
We are now going to recast the system $\ref{eq:flux},\ref{eq:pb_var_disc}$ to a global linear system where only the trace of the solution on the boundaries of the mesh appears. After solving the global system, the uknowns wan be recovered locally, in parallel.
First of all, we write the space for the numerical trace $\widehat{T}_{w,h}$ as a direct sum :
$M_h = \widetilde{M}_h \oplus M_h^*$
with :
• $\widetilde{M}_h = \left\{\mu\in L^2(\F_h) : \forall F\in\F_h^0\cup F_h^{\Gamma_N} \mu|_F\in\P_k(F) \text{ and } \forall F\in \F_h\setminus (\F_h^0\cup\F_h^{\Gamma_N})\mu|_F = 0\right\}$. This is the sapce the the standard trace of the elements we find in usual HDG methods.
• $M_h^* = \left\{\mu\in L^2(\F_h) : \mu|_{\Gamma_{ubc}}\in\RR \text{ and } \forall F\in \F_h\setminus \F_h^{\Gamma_{ibc}}\mu|_F = 0\right\}$. This space handles the condition $T_w$ is constant over $\Gamma_{ibc}$.
Let $\lambda_{1,h} = \widehat{T}_{w,h}|_{\widetilde{M}_h}$ and $\lambda_{2,h} = \widehat{T}_{w,h}|_{M_h^*}$. Making integrations by parts, the formulation $\ref{eq:flux},\ref{eq:pb_var_disc}$ can be rewritten as :
\begin{align} \sum_{K\in\T_h} \left[\int_K k^{-1}\q_{w,h}^K\cdot \v_h^K - \int_K T_{w,h}^K \nabla\cdot\v_h^K + \int_{\partial K} \lambda_{1,h}\v_h^K\cdot\n_{\partial K} + \int_{\partial K} \lambda_{2,h} \v_h^K\cdot \n_{\partial K}\right] &= 0\\ \sum_{K\in\T_h} \left[ \int_K\frac{\rho_mc_m}{\Delta t}T_{w,h}^K \int_K\nabla\cdot \q_{w,h}^K w_h^K + \int_{\partial K}\tau_{\partial K} T_{w,h}^K w_h^K - \int_{\partial K}\tau_{\partial K}\lambda_{1,h}w_h^K - \int_{\partial K}\tau_{\partial K}\lambda_{2,h}w_h^K\right] &= \sum_{K\in\T_h} \int_K \frac{\rho_mc_m}{\Delta t}T_{w}^{\text{prev},K}\\ \sum_{K\in\T_h} \left[\int_{\partial K} \q_{w,h}^K\cdot\n_{\partial K}\mu_{1,h} + \int_{\partial K} \tau_{\partial K} T_{w,h} \mu_{1,h} - \int_{\partial K} \tau_{\partial K}\lambda_{1,h}\mu_{2,h} \right] &= \int_{\Gamma_N}g_N \mu_{1,N}\\ \sum_{K\in\T_h} \left[\int_{\partial K}\q_{w,h}^K\cdot \n_{\partial K} + \int_{\partial K} \tau_{\partial K}T_{w,h} \mu_{2,h} - \int_{\partial K}\tau_{\partial K}\lambda_{2,h}\mu_{2,h}\right] &= I_\text{target} |\Gamma_{ibc}|^{-1} \int_{\Gamma_{ibc}}\mu_{2,h} \end{align} \tag{HDG_{ibc}}\label{eq:hdg_ibc}
for all $\v_h\in V_h, w_h\in W_h, \mu_{1,h}\in\widetilde{M}_h, \mu_{2,h}\in M_h^*$. We can notice that $M_h^*$ has a dimension 1, so $M_h^*\simeq\RR$. Because of it, the fourth equation of $\ref{eq:hdg_ibc}$ is a single scalar equation, enforcing the integral boundary condition.
## 5. Algorithm
Resolution of the system with HDG method
Input : $T_w^0, T_r^0$ and all the parameters for the simulation.
$t\gets0$
Note : in the following, $X^\text{prev}$ corresponds to the quantity $X$ at the previous step of the while loop.
while $t < t_\text{max}$ :
• Solve the EDO $\ref{hr}$ with the first order approximation : $\quad\quad T_r = \dfrac{H + \eta\rho_ac_aV_aT_e + h_iA_wT_w + \frac{\rho_ac_a}{\Delta t}T_r^\text{prev}}{\frac{\rho_ac_a}{\Delta t} + h_iA_w + \eta\rho_ac_aV_a}$
• $I_\text{target} \gets \int_{\Gamma_{ibc}} h_i(T_w^\text{prev} - T_r)$
• Solve the EDP with the discretized problem $\ref{eq:hdg_ibc}$ using discotinuous elements. It gives the trace $\widehat{T}_{w,h}$
• With the relation between $\widehat{T}_{w}, T_{w}$ and $\q_w$ $\ref{eq:flux}$, we calculate $T_w$ and $\q_w$ over each element
• $t \gets t + \Delta t$
## References
• [CEN2007] EN 15026, Hygrothermal performance of building components and building elements - Assessment of moisture transfer by numerical simulation, CEN, 2007.
• [FeelppMath] Feel++ Mathematics
• [FppPicard] Feel, Non linear problems on http://docs.feelpp.org/math/fem/nonlinear/#_picard_strategy[Feel Mathematics]
• [HDG2020] A HDG method for elliptic problems with integral boundary condition: Theory and Applications, Silvia Bertoluzza, Giovanna Guidoboni, Romain Hild, Daniele Prada, Christophe Prud’homme, R. Sacco, Lorenzo Sala, Marcela Szopos, In progess, 2020
• [Sala2019] Lorenzo Sala. Mathematical modelling and simulation of ocular blood flows and their interactions.Numerical Analysis [math.NA]. Université de Strasbourg, 2019. English. NNT: 2019STRAD021 . tel-02284233v2
• [Škerget2014] Škerget, L. Tadeu, A., BEM numerical simulation of coupled heat, air and moisture flow through a porous solid, Engineering Analysis with Boundary Elements, 2014, 40, p154-161 | 2022-09-25 07:09:31 | {"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": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.996038556098938, "perplexity": 1662.2946670000567}, "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-2022-40/segments/1664030334515.14/warc/CC-MAIN-20220925070216-20220925100216-00092.warc.gz"} |
https://indico.nucleares.unam.mx/event/1488/contribution/26 | # 10th International Workshop on Charm Physics (CHARM 2020)
from 31 May 2021 to 4 June 2021
Mexico/General timezone
Thanks for your contribution to the success of this workshop!!
Home > Timetable > Contribution details
# Exclusive hadronic tau decays as probes of non-SM interactions
## Speakers
• Dr. Sergi GONZÀLEZ-SOLÍS
## Description
We perform a global analysis of exclusive hadronic tau decays into one and two mesons using the low-energy limit of the Standard Model Effective Field Theory up to dimension six, assuming left-handed neutrinos. A controlled theoretical input on the Standard Model hadronic form factors, based on chiral symmetry, dispersion relations, data and asymptotic QCD properties, has allowed us to set bounds on the New Physics effective couplings using the present experimental data. Our results highlight the importance of semileptonic τ decays in complementing the traditional low-energy probes, such nuclear β decays or semileptonic pion and kaon decays, and the high-energy measurements at LHC scales. This makes yet another reason for considering hadronic tau decays as golden modes at Belle-II. | 2023-03-26 06:11:55 | {"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": 0.8439974188804626, "perplexity": 3959.9044619446554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945433.92/warc/CC-MAIN-20230326044821-20230326074821-00137.warc.gz"} |
http://www.deskdr.com/dr/import-javax-telephony-not-found.html | Hello,
I am working on my first JTAPI exaples. I got this error. Can any one tell me how to over come this. What .jar file should I include in my class path. I am using jdk1.4.0 on Win XP.
Thanks
James
Hello,
Thanks for your reply. I have downloaded the class files. I downloaded the jtapi12-class.zip file to desktop and unzipped to jtapi directory in the desktop. I copied the jtapi folder to c:\j2sdk1.4.0\lib and c:\j2sdk1.4.0\jre\lib directory. I have the classpath in my autoexec.bat file like this
set path=c:\j2skd1.4.0\bin;
set classpath=%classpath%;.;
Thanks
James
### Similar Messages
Hello,
I am new to Java Mail. I wanted to test my first programme. When I compile, I get this errors.
package javax.mail not found in import and so on. I have set my classpath to so
set classpath = %classpath%;C:\j2sdk1.4.0\lib\mail.jar;C:\j2sdk1.4.0\lib\activation.jar
I included the mail.jar,smtp.jar and activation.jar in the lib directory of my jdk e.g c:\j2sdk1.4.0\lib\ "the jar file".
Can any one tell me what I am missing here?
Thanks
James
the easiest way to do this is to put
activation.jar
mail.jar
mailapi.jar
imap.jar
smtp.jar
pop3.jar
into the virtual machine directory C:\Program Files\JavaSoft\JRE\1.3.1\lib\ext
or the lib\ext directory of whatever virtual machine you are using
and put coppies of them in JDK
C:\j2sdk1.4.0-beta3\jre\lib\ext
or jre\lib\ext
of whatever JDK you are using
this way they are found automaticaly
no need for classpath
I have downloaded the most recent mail.jar and activation.jar files and have created a library w/in JDev called javamail and have added these jars to that library. I have also included this library in my ViewController Project. The problem I am having is that the following imports statements are not found by JDev:
import javax.mail.Message;
import javax.mail.MessagingException;
import javax.mail.Multipart;
import javax.mail.Session;
import javax.mail.Transport;
import javax.mail.internet.MimeBodyPart;
import javax.mail.internet.MimeMessage;
import javax.mail.internet.MimeMultipart;
When I open up the mail.jar I can find all of these classes, so why are these imports not being recongnized?
I have also tried import javax.mail.*; to include everthing and this does not work either.
Does anyone have any suggestions on how to trouble shoot this issue?
Try to add the J2EE library - which is predefined in JDeveloper- to your project's libraries.
Worked for me.
Hi,
I have just installed the JDK1.7 on a windows machine.
Whenever I try to compile my module, I get an error on the import javax.crypto line. It tells me that it can't the javax\Crypto\Cipher.class.
I have the jdk installed on d:\glassfish3 and am pointing the classpath to d:\glassfish3\jdk7 (also tried d:\glassfish3\jdk7\jre as well) with no luck.
Any help would be greatly appreciated.
Thanks,
Drew Nathanson
Technical Synergy, Inc.
Thanks. Maybe I should explain a little better.
I am using JBuilder 2006 to my IDE. This environment requires that you put in the path to the JRE/JDK.
I have uninstalled and downloaded the jdk again and this time i'm getting a strange error:
"test.java": cannot access javax.crypto.Cipher; bad class file: D:\Program Files\Java\jre7\lib\jce.jar\javax\crypto\Cipher.class, class file has wrong version 51.0, should be 49.0, Please remove or make sure it appears in the correct subdirectory of the classpath. at line 19, column 21
Now this is strange because i'm using the right library.
Is there something that I'm missing here?
Drew Nathanson
hi,
i am trying to develop a mail application using jsp, i have jaf1.0.1 and javamail API and the application was working fine on weblogic but when i tried to do the same thing on Apache server the Package javax.mail not found in import. is occuring,
What could be the problem can any one explain...
Thanks
I think you have not placed mail.jar and activation.jar files in the /jre/lib/ext directory. Just place the mail.jar and activation.jar files in the jdk's /jre/lib/ext directory and check out. This will work for you.
Rkanthj
I recently installed JDK 1.3.1_02 on WinNT4.0 and I cannot compile javax
packages without getting the following error:
I've tried every combination of modifying the CLASSPATH system variable
I can think of. I have no problem compiling java packages but not
javax packages. I followed the installation instructions to the letter.
What am I missing? Surely someone is running the same version of
the JDK I am on WinNT 4.0.
Thanks again!!! I had an older version of javac running on my system any time I ran
outside of the bin where the latest javac was installed. I removed the older version
of the jdk and now I can compile from any directory. I really appreciate the help,
I was wracking my brain.
By the way, -version is not a valid flag for javac.exe, although it is for java.exe.
signed,
grateful in cyberspace
Hi there,
I've downloaded j2se 1.4 and j2ee 1.3.1 and installed it on Windows XP. I set the environment variables as described. When I compile a .java file that imports the javax.ejb.* package, then I get an error "package javax.ejb not found". I feel like an idiot and I know it's something to do with the environment variables. (or just XP, most likely)
Hoenner
How are you compiling your source? If you're using an IDE then you should edit your project classpath to include the j2ee.jar file (it'll probably be in the lib directory of your J2EE installation).
If you're doing it from the command line then type in SET CLASSPATH, look at the classpath it returns and check that it includes the j2ee.jar file.
Hope this helps.
plz help this is my first servlet program.
vipin
You need a jar file that has in it the javax.servlet.* classes
It should be distributed with your servlet/jsp server.
It can normally be found in a /lib directory under the installation.
Some examples:
Tomcat4: install_dir\common\lib\servlet.jar
Tomcat5: install_dir\common\lib\servlet-api.jar; install_dir\common\lib\jsp-api.jar
J2sdkee: install_dir/lib/j2ee.jar
You need to include this jar file in your classpath when you compile any servlet.
when i try to import the javax.servlet's, it is not found... any idea where i can go toget that? i downloaded the seperate elipse for J2EE and tried it on there, and i also tried it on the eclipse for regular java developers.
thanks
update: it turns out that eclipse has a # of requirements that it needs to get the WTP, i'll appreciate any assistance in directing me toward the files.
Edited by: ixxalnxxi on Jun 17, 2008 3:30 AM
No, you need to specify the application server in the eclipse project. Then it will take its libraries in the build path.
You may find this tutorial useful, you can just skip the JSF part if you aren't planning to use it: [http://balusc.blogspot.com/2008/01/jsf-tutorial-with-eclipse-and-tomcat.html].
Hi,
I am very new to Java SDK. I just installed J2SDK 1.5.0 beta 2 and installed it on my RedHat 9.0 box with root permission at /usr/local/(java-home)/
I can compile simple applications which do not import extension packages. However, when I try to compile an application importing javax.swing.* , I get the below error message:
Craps.java:9: Can't find default package javax.swing'. Check the CLASSPATH environment variable and the access to the archives
public class Craps extends JApplet implements ActionListener {
The code of this application is correct, coz I can compile and execute it in Windows.
Can anybody help me with this problem?
Thanks!
Hi Joni,
I've solved the problem with your inspiration of the ClASSPATH. This is for the reference of those who may encounter the same problem as me.
I installed Redhat 9.0 with default settings and those bundled packages (could be normal to many Linux newbies like me :) There is a default java compiler installed, I guess, and it's bundled with gcc. So when I tried to compile my .java files, the javac comand from j2sdk was not involked. Instead, it's the default-installed java compiler that correspended to my command. I guess this is why no matter what I changed in the .bash_profile in my home directory, the j2sdk command javac had not executed.
After I uninstalled this one, and add j2sdk/bin into my CLASSPATH, everything works fine now.
Btw, I found out this problem by simply typing "javac" in the terminal and read the help suggestions that followed.
Hi anyone,
I am creating an Entity Bean, and I have imported javax.ejb.EntityBean. I get an error during compilation
I am using jdk1.2.2 I even tried with jdk1.3.
My query is:
Q1. Which is the jar in jdk which provides class files for javax.ejb.EntityBean package ?
thanks
vikas
It is in j2ee_home\lib directory. Include this in the classpath.
-Siva
Hi experts,
trying to import components under Consolidation tab in CMS I get this error:
\CMStarvosNWD/CMS/archives/sap.comSAP-SHRWEBNWD_EAMM1DEV_D~6 / D:\usr\sap\trans\EPS\in\CMStarvosNWD/CMS/archives/sap.com#SAP-SHRWEB#NWD_EAMM1DEV_D#6
Unfortunately all the *.pra files were deleted under CMS\archives.
Ho can I restore these archives?? Or what can I do? What are the *.pra achives for?
Best Regards
Mirko
Hi Mirko,
I think the error comes not due to the pra files, but due to the missing sca files. Can you please try to recreate them in the way we have discussed? Assembly always takes the changes from cons/active, there's no way to change on this behaviour, i.e. there's nothing to be configured thisregarding. After import into cons a force activation takes place (i.e. in cons there's no need to do an explicit activation, the changes gets reflected after import automatically into cons/inactive as well as in cons/active)
Best Regards,
Ervin
Hello,
It seems like others on this forum have posted this same question, although I still can't find my solution.
I'm trying to import an application into Apex, but I end up getting a 404 Not Found error message, with "The requested URL /pls/apex/wwv_flow.accept was not found on this server". I checked the Apache error logs and this is what I see, but can't seem to understand what I need to do:
[Wed Oct 3 14:26:10 2007] [error] [client 147.18.232.249] [ecid: 1191435955:131.98.31.15:784:0:3056,0] mod_plsql: /pls/apex/wwv_flow.accept
HTTP-404 ORA-00942: table or view does not exist\nLaura
Hi Scott,
I realized what my problem was. It was in the marvel.conf file, contents listed below. Normally we remove the two lines below in bold. When I put them back in, I was able to load my app. Thanks for tipping me off in the right general direction!
Laura
Alias /i/ /opt/oracle/product/10.2.0/db_1_apex/apex/images/
Order deny,allow
PlsqlDocumentPath docs
AllowOverride None
PlsqlDatabaseConnectString localhost:1521:IPF ServiceNameFormat
PlsqlNLSLanguage AMERICAN_AMERICA.AL32UTF8
PlsqlAuthenticationMode Basic
PlsqlMaxRequestsPerSession 1
SetHandler pls_handler
PlsqlDocumentTablename wwv_flow_file_objects$PlsqlDefaultPage apex <b> PlsqlDatabaseUsername APEX_PUBLIC_USER PlsqlDatabasePassword xxxxxx</b> Allow from all • Javax package not found Hi, I installed jdk1.4 in my system.And i type one swing concept program.After compilation of that program.It shows error like Javax.Swing. package not found.Please help to me to clear the proble.And also Javax.servlet package also not taken. regards sridhar Its javax, not Javax. • Problem while importing data schema not found Hi, I'm facing problem while importing data through system to a schema and impdp gives me error that schema XYZ was not found but when I query dba_users schema exist there what could be the reason of this. Regards, Abbasi Hi, Here is complete listing bash-3.2$ impdp system/abc schemas=XYZ DIRECTORY=data_dir DUMPFILE=Today_dump.dmp LOGFILE=Today_log.log PARALLEL=8
Import: Release 11.1.0.7.0 - 64bit Production on Friday, 07 January, 2011 11:18:57
Connected to: Oracle Database 11g Enterprise Edition Release 11.1.0.7.0 - 64bit Production
With the Partitioning, OLAP, Data Mining and Real Application Testing options
ORA-39002: invalid operation
Regards,
Abbasi
### Maybe you are looking for
• Adobe Media Encoder CS4 Encoding Error
I got an error when Adobe Media Encoder CS4 encoding which is the crash of ImporterProcessServer. It crashes the halfway of the encoding process. I restarted my comp and tried several times before but the results still the same. Sometimes ImporterPro
• Artist names do not show up on my idpod
When I sync my itunes to my ipod, some of the artist names do not show up in the Menu for artists. The music is on there, but the listing does not show.
• Error while doing fb01L
Hello I have activated non leading ledger and while doing FB01L , i am getting the following error In company code XXXX, the number range SA is missing for the year 2010 Message no. F5150 Diagnosis The document type you specified has been allocated t | 2020-02-21 12:18:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.5017032027244568, "perplexity": 4755.122848364681}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 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-20200221111140-20200221141140-00369.warc.gz"} |
https://codeforces.com/problemset/problem/1029/E | E. Tree with Small Distances
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
You are given an undirected tree consisting of $n$ vertices. An undirected tree is a connected undirected graph with $n - 1$ edges.
Your task is to add the minimum number of edges in such a way that the length of the shortest path from the vertex $1$ to any other vertex is at most $2$. Note that you are not allowed to add loops and multiple edges.
Input
The first line contains one integer $n$ ($2 \le n \le 2 \cdot 10^5$) — the number of vertices in the tree.
The following $n - 1$ lines contain edges: edge $i$ is given as a pair of vertices $u_i, v_i$ ($1 \le u_i, v_i \le n$). It is guaranteed that the given edges form a tree. It is guaranteed that there are no loops and multiple edges in the given edges.
Output
Print a single integer — the minimum number of edges you have to add in order to make the shortest distance from the vertex $1$ to any other vertex at most $2$. Note that you are not allowed to add loops and multiple edges.
Examples
Input
71 22 32 44 54 65 7
Output
2
Input
71 21 32 42 53 61 7
Output
0
Input
71 22 33 43 53 63 7
Output
1
Note
The tree corresponding to the first example: The answer is $2$, some of the possible answers are the following: $[(1, 5), (1, 6)]$, $[(1, 4), (1, 7)]$, $[(1, 6), (1, 7)]$.
The tree corresponding to the second example: The answer is $0$.
The tree corresponding to the third example: The answer is $1$, only one possible way to reach it is to add the edge $(1, 3)$. | 2021-12-03 20:36:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6974116563796997, "perplexity": 145.27958475033464}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362918.89/warc/CC-MAIN-20211203182358-20211203212358-00481.warc.gz"} |