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Difference between revisions of "User:Boris Tsirelson/sandbox2"

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Line 1: Line 1:
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<center><asy>
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import gsl;
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int N=30;
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picture whole;
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picture common;
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draw ((-0.3,0)--(1.45,0),Arrow);
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draw ((0,0)--(0,1.3));
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draw ((1,0)--(1,1.3));
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label("$x$",(1.6,0),E);
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add ( common, currentpicture );
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erase();
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add ( currentpicture, common );
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guide g;
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for (int k=floor(-0.2N); k<floor(1.2N); ++k) {
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  real x = k/N;
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  real y = cdf_gaussian_P(6*(x-0.5));
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  y = y+0.15;
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  g=g..(x,y);
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}
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draw(g,defaultpen+1.3);
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label("$\scriptstyle g(x)$",(0.33,0.8));
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add ( whole, shift(-60,0)*scale(40,33)*currentpicture );
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erase();
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add ( currentpicture, common );
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draw((-0.2,1)--(1.2,1));
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label("$1$",(-0.2,1),W);
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guide g1;
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guide g2;
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for (int k=floor(-0.2N); k<floor(1.2N); ++k) {
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  real x = k/N;
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  real y = sqrt(2pi) * pdf_gaussian(6*(x-0.5));
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  g1=g1..(x,y);
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  g2=g2..(x,1.3y);
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}
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draw(g1,defaultpen+1.3);
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draw(g2,defaultpen+1.3);
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label("$\scriptstyle \xi(x)$",(0.5,0.4));
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label("$\scriptstyle g'(x)$",(0.85,1.25), Fill(white));
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add ( whole, shift(60,0)*scale(40)*currentpicture );
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erase();
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label(whole,"\small Fig. a2: Some characterizing functions",(30,-20));
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shipout(scale(1.2)*whole);
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</asy></center>
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 +
 
<center><asy>
 
<center><asy>
 
import gsl;
 
import gsl;

Revision as of 18:42, 9 November 2014






[Calculus: ] the art of numbering and measuring exactly a thing whose existence cannot be conceived. (Voltaire, Letter XVII: On Infinites In Geometry, And Sir Isaac Newton's Chronology)

And what are these fluxions? The velocities of evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities? (Berkeley, The Analyst)


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How to Cite This Entry:
Boris Tsirelson/sandbox2. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox2&oldid=34425