File:TaniaPlot.png

Explicit plot of the Tania function, $y=\mathrm{Tania}(x)$.

$f=\mathrm{Tania}$ is solution of the equaitons
 * $ \displaystyle f'(z)= \frac{f(z)}{1+f(z)}$
 * $f(0)=1$

Such an equation (and the solution) appears in the Laser science in the simplest model of the uniformly pumped gain medium.

Copyleft 2011 by Dmitrii Kouznetsov.

Generation of the figure
The curves are generated with the C++ code below in the Encapsulated Postscript format. The resulting taniaplot.eps is converted to taniaplot.pdf and used as input file by the Latex document, that adds labels.

C++ Generator of curve of TaniaPlot
File ado.cin should be loaded into the working directory for the compliation of the code below:

using namespace std; DB ArcTania(DB x){ return x+log(x)-1.;} main{ int j,k,m,n; DB x,y, a; FILE *o;o=fopen("tania.eps","w");ado(o,808,408); fprintf(o,"404 4 translate\n 100 100 scale\n"); for(m=-4;m<5;m++){ M(m,0)L(m,4)} for(n=0;n<5;n++){ M(-4,n)L(4,n)} fprintf(o,".01 W 0 0 0 RGB S\n"); for(n=0;n<380;n++){y=.02+.01*n; x=ArcTania(y); if(n==0)M(x,y) else L(x,y) } fprintf(o,".03 W 0 .5 0 RGB S\n"); fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf tania.eps"); system(   "open tania.pdf"); //these 2 commands may be specific for macintosh getchar; system("killall Preview");// if run at another operational sysetm, may need to modify }
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x convert TaniaPlot.pdf TaniaPlot.png % Copyleft 2011 by Dmitrii Kouznetsov% \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 810pt % \paperheight 426pt % \topmargin -103pt % \oddsidemargin -96pt % \textwidth 1200pt % \textheight 600pt % \pagestyle {empty} % \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \begin{document} % \sx{1}{ \begin{picture}(808,410) % \put(1,9){\ing{tania}} % \put(388,393){\sx{2.8}{$y$}} % \put(388,303){\sx{2.8}{$3$}} % \put(388,203){\sx{2.8}{$2$}} % \put(388,103){\sx{2.8}{$1$}} % \put( 86,-9){\sx{2.5}{$-3$}} % \put(186,-9){\sx{2.5}{$-2$}} % \put(286,-9){\sx{2.5}{$-1$}} % \put(400,-9){\sx{2.5}{$0$}} % \put(500,-9){\sx{2.5}{$1$}} % \put(600,-9){\sx{2.5}{$2$}} % \put(700,-9){\sx{2.5}{$3$}} % \put(796,-9){\sx{2.5}{$x$}} % \end{picture} % } % \end{document}