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Line 26: Line 26:
 
path g=(0,-2)--(0,-0.25);
 
path g=(0,-2)--(0,-0.25);
 
draw(Label("$A\cap B$",0),g,Arrow);
 
draw(Label("$A\cap B$",0),g,Arrow);
 +
</asy>
 +
====Case 2====
 +
<asy>
 +
int M=30;
 +
real a = 0.07;
 +
real a0 = 0.15;
 +
real b = 0.02;
 +
real c = 0.6;
 +
real d = -0.2;
 +
real x0 = -0.22;
 +
real u = 0.2;
 +
real v = 0.32;
 +
 +
draw ((-0.7,0)--(0.3,0),Arrow);
 +
draw ((x0,-0.02)--(x0,1.2),Arrow);
 +
 +
label("$x$",(0.3,0),E);
 +
label(rotate(90)*"$y$",(x0,1.2),N);
 +
label("$x_0$",(x0,-0.02),S);
 +
 +
guide g1; guide g2; guide g3; guide g4; guide g5;
 +
for (int k=floor(-0.7M); k<floor(0.3M); ++k) {
 +
  real x = k/M;
 +
  real z = 1+3*x^2;
 +
  real y1 = 1/(z-2a-a0)+2b*(1+c*x)+d;
 +
  real y2 = 1/(z-a-a0)+b*(1+c*x)+d;
 +
  real y3 = 1/(z-a0)+d;
 +
  real y4 = 1/(z+a-a0)-b*(1+c*x)+d;
 +
  real y5 = 1/(z+2a-a0)-2b*(1+c*x)+d;
 +
  g1=g1..(x,y1);
 +
  g2=g2..(x,y2);
 +
  g3=g3..(x,y3);
 +
  g4=g4..(x,y4);
 +
  g5=g5..(x,y5);
 +
}
 +
draw(g1,defaultpen+1);
 +
draw(g2,defaultpen+1);
 +
draw(g3,defaultpen+1);
 +
draw(g4,defaultpen+1);
 +
draw(g5,defaultpen+1);
 +
 +
real x = x0;
 +
real z = 1+3*x^2;
 +
real y1 = 1/(z-2a-a0)+2b*(1+c*x)+d;
 +
real y2 = 1/(z-a-a0)+b*(1+c*x)+d;
 +
real y3 = 1/(z-a0)+d;
 +
real y4 = 1/(z+a-a0)-b*(1+c*x)+d;
 +
real y5 = 1/(z+2a-a0)-2b*(1+c*x)+d;
 +
path g = (x,y1)..(x-u,y2)..(x-v,y3)..(x-u,y4)..(x,y5);
 +
draw( g );
 +
 +
pair w = (0.1,-0.6);
 +
 +
pair p = point(g,0.5);
 +
dot ( p );
 +
draw( p--p-0.5w, dashed );
 +
label(rotate(90)*"$\Psi_{x_0}(y)$",p-0.5w,N);
 +
 +
draw( (x,y2)--(x-u,y2) );
 +
draw( (x,y3)--(x-v,y3) );
 +
draw( (x,y4)--(x-u,y4) );
 +
 +
draw( (x-u,y2+0.05)--(x-u,y4-0.05) );
 +
draw( (x-v,y2+0.1)--(x-v,y4-0.1) );
 +
 +
real x = -0.15;
 +
real z = 1+3*x^2;
 +
real y4 = 1/(z+a-a0)-b*(1+c*x)+d;
 +
dot( (x,y4) );
 +
draw( (x,y4)--(x,y4)+w, dashed );
 +
label("$\scriptstyle \underline f_\alpha(x)$",(x,y4)+w,SE);
 +
 +
real x = -0.05;
 +
real z = 1+3*x^2;
 +
real y3 = 1/(z-a0)+d;
 +
dot( (x,y3) );
 +
draw( (x,y3)--(x,y3)+w, dashed );
 +
label("$\scriptstyle \underline f_1(x)=\overline f_1(x)$",(x,y3)+w,SE);
 +
 +
real x = 0.05;
 +
real z = 1+3*x^2;
 +
real y2 = 1/(z-a-a0)+b*(1+c*x)+d;
 +
dot( (x,y2) );
 +
draw( (x,y2)--(x,y2)+w, dashed );
 +
label("$\scriptstyle \overline f_\alpha(x)$",(x,y2)+w,SE);
 +
 +
label("\small Fig. a4: Non-precise function",(x0,-0.2));
 +
 +
shipout(scale(250,120)*currentpicture);
 
</asy>
 
</asy>
 
===Tests November 4th===
 
===Tests November 4th===

Revision as of 15:31, 17 November 2014

Test Copy&Paste HTML

Test-copy-paste

Test

Test Asymptote

Tests November 17th

Case 1

Case 2

Tests November 4th

Case 1

Case 2

Case 3

Tests October 27th

Case 1

Case 2

Case 3

Case 4

Case 5

[asy] pair A,B,C,X,Y,Z; A = (0,0); B = (1,0); C = (0.3,0.8); draw(A--B--C--A); X = (B+C)/2; Y = (A+C)/2; Z = (A+B)/2; draw(A--X, red); draw(B--Y,red); draw(C--Z,red); [/asy]

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Example: Cite-Extension

Test MathJax

\begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy \end{align}


\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]


Some Text \( \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \)


Some Text \[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]

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How to Cite This Entry:
WikiSysop. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=WikiSysop&oldid=34563

Test January 12th 2015

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