File:Logiha300.jpg

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
// using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
#include "efjh.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  int M=302,M1=M+1;
  int N=51,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
//FILE *o;o=fopen("logi3e4a.eps","w");ado(o,304,204);
FILE *o;o=fopen("logihalf3.eps","w");ado(o,304,104);
fprintf(o,"152 2 translate\n 100 100 scale\n");
DO(m,M1) X[m]= -1.5+.02*(m-.5);
DO(n,N1) Y[n]=0.+.02*(n-.5);

for(m=-3;m<4;m++){if(m==0){M(.5*m,0)L(.5*m,1.04)} else{M(.5*m,0)L(.5*m,1)}}
for(n=0;n<3;n++){ M( -1.5 ,.5*n)L(1.5,.5*n)}
fprintf(o,".004 W 0 0 0 RGB S\n");

//maq(3.);
maq(3.);
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
// c=E(H(z))-1.;
// c=F(1.+E(0.1*z));
// c=F(z);
        c=F(.5+E(z));
        c=F(.5+E(c));
// c=boe(z);
// c=.5*(1.-cos(exp((z+1.)/LQ)));
// d=H(F(z-1.));
// p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.)-1.;
// if(p>-99 && p<20) g[m*N1+n]=p;
        p=Re(c);q=Im(c);
        if(p>-99 && p<99) {g[m*N1+n]=p;}
        if(q>-99 && q<99) {f[m*N1+n]=q;}
// if(q>-99 && q<99 && fabs(q)>1.e-11 ) {f[m*N1+n]=q;}
                        }}

fprintf(o,"1 setlinejoin 2 setlinecap\n");
p=2;q=.4;
//#include"plof.cin"
for(m=-2;m<2;m++)
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q, q);fprintf(o,".002 W 0 .6 0 RGB S\n");
for(m=0;m<2;m++)
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q);fprintf(o,".002 W .9 0 0 RGB S\n");
for(m=0;m<2;m++)
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q);fprintf(o,".002 W 0 0 .9 RGB S\n");

for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".006 W .9 0 0 RGB S\n");
for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 .9 RGB S\n");
for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 0 RGB S\n");

                  conto(o,f,w,v,X,Y,M,N, (0. ),-99,99); fprintf(o,".008 W .5 0 .5 RGB S\n");

fprintf(o,"0 setlinejoin 0 setlinecap\n");

//M(-3.02,0)L(0,0)
//M(1.-1./Q,0)L(3,0) fprintf(o,"0.01 W 1 1 1 RGB S\n");
M(0.7,0)L(3,0) fprintf(o,"0.01 W 1 1 1 RGB S\n");
//for(n=0;n<32;n++) {M(-.1*n,0)L(-.1*(n+.4),0)}
for(n=0;n<12;n++) { M(0.7+.07*(n+.3),0)
                        L(0.7+.07*(n+.7),0)}
fprintf(o,"0.014 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf logihalf3.eps"); // for linux
        system( "open logihalf3.pdf"); // for mac
        getchar(); system("killall Preview");
}

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
// using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
#include "efjh.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  int M=302,M1=M+1;
  int N=51,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
//FILE *o;o=fopen("logi3e4a.eps","w");ado(o,304,204);
FILE *o;o=fopen("logihalf4.eps","w");ado(o,304,104);
fprintf(o,"152 2 translate\n 100 100 scale\n");
DO(m,M1) X[m]= -1.5+.02*(m-.5);
DO(n,N1) Y[n]=0.+.02*(n-.5);

for(m=-3;m<4;m++){if(m==0){M(.5*m,0)L(.5*m,1.04)} else{M(.5*m,0)L(.5*m,1)}}
for(n=0;n<3;n++){ M( -1.5 ,.5*n)L(1.5,.5*n)}
fprintf(o,".004 W 0 0 0 RGB S\n");

//maq(3.);
maq(4.);
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
// c=E(H(z))-1.;
// c=F(1.+E(0.1*z));
// c=F(z);
        c=F(.5+E(z));
        c=F(.5+E(c));
// c=boe(z);
// c=.5*(1.-cos(exp((z+1.)/LQ)));
// d=H(F(z-1.));
// p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.)-1.;
// if(p>-99 && p<20) g[m*N1+n]=p;
        p=Re(c);q=Im(c);
        if(p>-99 && p<99) {g[m*N1+n]=p;}
        if(q>-99 && q<99) {f[m*N1+n]=q;}
// if(q>-99 && q<99 && fabs(q)>1.e-11 ) {f[m*N1+n]=q;}
                        }}

fprintf(o,"1 setlinejoin 2 setlinecap\n");
p=2;q=.4;
//#include"plof.cin"
for(m=-2;m<2;m++)
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q, q);fprintf(o,".002 W 0 .6 0 RGB S\n");
for(m=0;m<2;m++)
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q);fprintf(o,".002 W .9 0 0 RGB S\n");
for(m=0;m<2;m++)
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q);fprintf(o,".002 W 0 0 .9 RGB S\n");

for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".006 W .9 0 0 RGB S\n");
for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 .9 RGB S\n");
for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 0 RGB S\n");

                  conto(o,f,w,v,X,Y,M,N, (0. ),-99,99); fprintf(o,".008 W .5 0 .5 RGB S\n");

fprintf(o,"0 setlinejoin 0 setlinecap\n");

//M(-3.02,0)L(0,0)
//M(1.-1./Q,0)L(3,0) fprintf(o,"0.01 W 1 1 1 RGB S\n");
M(.96,0)L(3,0) fprintf(o,"0.01 W 1 1 1 RGB S\n");
//for(n=0;n<32;n++) {M(-.1*n,0)L(-.1*(n+.4),0)}
for(n=0;n<10;n++) { M(.96+.07*(n+.3),0)
                        L(.96+.07*(n+.7),0)}
fprintf(o,"0.014 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf logihalf4.eps"); // for linux
        system( "open logihalf4.pdf"); // for mac
        getchar(); system("killall Preview");
}

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
// using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
#include "efjh.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  int M=302,M1=M+1;
  int N=101,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
//FILE *o;o=fopen("logi3e4a.eps","w");ado(o,304,204);
FILE *o;o=fopen("logihal5.eps","w");ado(o,304,204);
fprintf(o,"152 102 translate\n 100 100 scale\n");
DO(m,M1) X[m]= -1.5+.02*(m-.5);
DO(n,N1) Y[n]=-1.+.02*(n-.5);

for(m=-3;m<4;m++){if(m==0){M(.5*m,-1.04)L(.5*m,1.04)} else{M(.5*m,-1)L(.5*m,1)}}
for(n=-2;n<3;n++){ M( -1.5 ,.5*n)L(1.5,.5*n)}
fprintf(o,".004 W 0 0 0 RGB S\n");

//maq(3.);
maq(5.);
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
// c=E(H(z))-1.;
// c=F(1.+E(0.1*z));
// c=F(z);
        c=F(.5+E(z));
        c=F(.5+E(c));
// c=boe(z);
// c=.5*(1.-cos(exp((z+1.)/LQ)));
// d=H(F(z-1.));
// p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.)-1.;
// if(p>-99 && p<20) g[m*N1+n]=p;
        p=Re(c);q=Im(c);
        if(p>-99 && p<99) {g[m*N1+n]=p;}
        if(q>-99 && q<99) {f[m*N1+n]=q;}
// if(q>-99 && q<99 && fabs(q)>1.e-11 ) {f[m*N1+n]=q;}
                        }}

fprintf(o,"1 setlinejoin 2 setlinecap\n");
p=2;q=.4;
//#include"plof.cin"
for(m=-2;m<2;m++)
for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q, q);fprintf(o,".002 W 0 .6 0 RGB S\n");
for(m=0;m<2;m++)
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q);fprintf(o,".002 W .9 0 0 RGB S\n");
for(m=0;m<2;m++)
for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q);fprintf(o,".002 W 0 0 .9 RGB S\n");

for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".006 W .9 0 0 RGB S\n");
for(m= 1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 .9 RGB S\n");
for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 0 RGB S\n");

                  conto(o,f,w,v,X,Y,M,N, (0. ),-99,99); fprintf(o,".008 W .5 0 .5 RGB S\n");

fprintf(o,"0 setlinejoin 0 setlinecap\n");

//M(-3.02,0)L(0,0)
//M(1.-1./Q,0)L(3,0)
M(1.25,0)L(3,0)
fprintf(o,"0.01 W 1 1 1 RGB S\n");
//for(n=0;n<32;n++) {M(-.1*n,0)L(-.1*(n+.4),0)}
for(n=0;n<4;n++) { M(1.25+.06*(n+.3),0)
                       L(1.25+.06*(n+.7),0)}
fprintf(o,"0.014 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf logihal5.eps"); // for linux
        system( "open logihal5.pdf"); // for mac
        getchar(); system("killall Preview");
}

\documentclass[12pt,a4paper,oneside]{book}
%\newcommand \EN[1] {{#1}} % make the English version
\newcommand \EN[1] {{}} % suppress the English version
\newcommand \RU[1] {{#1}} % make the Russian version (in this document not supported)
%\newcommand \RU[1] {{}} % suppress the Russian version
%The Japanese version is not yet supported. While \JP is used to suppress several lines at once.
\newcommand \JP[1] {{}} % ореsuppress some text
%\usepackage[space]{cite }% If exist.
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[russian]{babel}
\usepackage{latexsym,amsmath,amssymb,amsbsy,graphicx}

\usepackage{rotating}
\usepackage{hyperref}
\usepackage{wrapfig}
\usepackage{geometry}
%\renewcommand\baselinestretch{.94}
%\renewcommand\baselinestretch{.94}
%\renewcommand\baselinestretch{1.15}
%\renewcommand\baselinestretch{1.2}
%\renewcommand\baselinestretch{1.2}

\paperwidth150mm
%\paperheight 257mm
\paperheight 216mm
%\textwidth 175mm
\textwidth 150mm
%\oddsidemargin 5mm
\oddsidemargin -72pt
%\topmargin -17mm
\topmargin -103pt
\textheight 257mm
\pagestyle{empty}
\large

\usepackage{color}
\definecolor{rose}{rgb}{1,.9,1}
\renewcommand\thesection{\arabic{section}}
\renewcommand\figurename{Рис.}
%\renewcommand\refname{References}
%\renewcommand\figurename{Fig.}
\newcommand \be {\begin{eqnarray}}
\newcommand \ee {\end{eqnarray} }
\newcommand \sx {\scalebox}
\newcommand \rme {{\rm e}} %%makes the base of natural logarithms Roman font
%\newcommand \rme {{e}} %%makes the base of natural logarithms Italics font; choose one of these
\newcommand \rmi {{\rm i}} %%imaginary unity is always roman font
\newcommand \ds {\displaystyle}
\newcommand \bN {\mathbb{N}}
\newcommand \bC {\mathbb{C}}
\newcommand \bR {\mathbb{R}}
\newcommand \cO {\mathcal{O}}
\newcommand \cF {\mathcal{F}}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \nS {\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!}
\newcommand \pS {{~}~{~}}
\newcommand \fac {\mathrm{Factorial}}
\newcommand {\rf}[1] {(\ref{#1})}
\newcommand{\iL}[1] {~\label{#1}\pS \rm[#1]\nS} %make the labels visible
%\newcommand{\iL}[1] {\label{#1}} %make the labels invisible; choose one of these options
\newcommand \eL[1] {\iL{#1}\ee}
\newcommand \ing \includegraphics
\newcommand \tet {\mathrm{tet}}
\parindent 0pt
\begin{document}
\JP{
\color{red}
\begin{picture}(425,729.88)
\put(0,0){\rule{1pt}{729.88pt}}
\put(425,0){\rule{1pt}{729.88pt}}
\put(0,0){\rule{426pt}{1pt}}
\put(0,728.88){\rule{426pt}{1pt}}
\end{picture}
%\vskip -740pt
\vskip -729pt
\color{black}
}\hskip 2pt
\sx{1.32}{\begin{picture}(320,120)
\put(16,16){\ing{logihalf3}}
\put(8,112){\sx{1.2}{$y$}}
\put(8, 64.4){\sx{1.17}{$\displaystyle \frac{1}{2}$}}
\put(8, 14){\sx{1.2}{$0$}}
\put(60,5){\sx{1.2}{$-1$}}
\put(166,5){\sx{1.2}{$0$}}
\put(266,5){\sx{1.2}{$1$}}
\put(312,5){\sx{1.24}{$x$}}
\put(26,49.2){\sx{1.2}{\rot{12} $v\!=\!4$ \ero}}
\put(29,32){\sx{1.2}{\rot{6} $v\!=\!2$ \ero}}
\put(30,15){\sx{1.2}{$v\!=\!0$}}
\put(222.4,32){\sx{1.2}{\rot{90}$v\!=\!0$\ero}}
\put(238,24){\sx{1.2}{\rot{58}\bf cut \ero}}
\put(288,15){\sx{1.2}{\rot{0}\bf cut \ero}}
\put(170,113){\sx{1.2}{\rot{-20}$u\!=\!3$\ero}}
\put(161,100){\sx{1.2}{\rot{-30}$u\!=\!2$\ero}}
\put(151,87){\sx{1.2}{\rot{-41}$u\!=\!1$\ero}}
\put(136.6,76){\sx{1.2}{\rot{-54}$u\!=\!0$\ero}}
\put(125,68){\sx{1.2}{\rot{-72}$u\!=\!-1$\ero}}
\put(112,64){\sx{1.2}{\rot{-79}$u\!=\!-2$\ero}}
\put(97,59){\sx{1.2}{\rot{-81}$u\!=\!-3$\ero}}
\put(84,56){\sx{1.2}{\rot{-83}$u\!=\!-4$\ero}}
\end{picture}}
\vskip 4pt

\hskip 2pt
\sx{1.32}{\begin{picture}(320,120)
\put(16,16){\ing{logihalf4}}
\put(8,112){\sx{1.2}{$y$}}
\put(8, 64.4){\sx{1.17}{$\displaystyle \frac{1}{2}$}}
\put(8, 14){\sx{1.2}{$0$}}
\put(60,5){\sx{1.2}{$-1$}}
\put(166,5){\sx{1.2}{$0$}}
\put(266,5){\sx{1.2}{$1$}}
\put(312,5){\sx{1.24}{$x$}}
\put(26,40){\sx{1.2}{\rot{9} $v\!=\!4$ \ero}}
\put(29,27.7){\sx{1.2}{\rot{5} $v\!=\!2$ \ero}}
\put(30,15){\sx{1.2}{$v\!=\!0$}}
\put(222.4,32){\sx{1.2}{\rot{90}$v\!=\!0$\ero}}
\put(251,24){\sx{1.2}{\rot{69}\bf cut \ero}}
\put(288,15){\sx{1.2}{\rot{0}\bf cut \ero}}
\put(170,114){\sx{1.2}{\rot{-19}$u\!=\!4$\ero}}
\put(162,105){\sx{1.2}{\rot{-30}$u\!=\!3$\ero}}
\put(155,95){\sx{1.2}{\rot{-37}$u\!=\!2$\ero}}
\put(146,85){\sx{1.2}{\rot{-43}$u\!=\!1$\ero}}
\put(137,77){\sx{1.2}{\rot{-54}$u\!=\!0$\ero}}
\put(127.4,72){\sx{1.2}{\rot{-69}$u\!=\!-1$\ero}}
\put(117.6,65){\sx{1.2}{\rot{-75}$u\!=\!-2$\ero}}%
\put(106.6,62){\sx{1.2}{\rot{-78}$u\!=\!-3$\ero}}%
\put(97.6,59){\sx{1.2}{\rot{-82}$u\!=\!-4$\ero}}
\end{picture}}
\vskip 4pt

\hskip 2pt
\sx{1.32}{\begin{picture}(320,220)
\put(16,16){\ing{logihal5}}
\put(8,212){\sx{1.2}{$y$}}
\put(8,164.5){\sx{1.17}{$\displaystyle \frac{1}{2}$}}
\put(8,114){\sx{1.2}{$0$}}
\put(-2,64.5){\sx{1.16}{$\displaystyle-\frac{1}{2}$}}
\put(-1,14){\sx{1.2}{$-1$}}
\put(60,5){\sx{1.2}{$-1$}}
\put(166,5){\sx{1.2}{$0$}}
\put(266,5){\sx{1.2}{$1$}}
\put(312,5){\sx{1.24}{$x$}}
\put(26,137){\sx{1.2}{\rot{9} $v\!=\!4$ \ero}}
\put(29,125){\sx{1.2}{\rot{4} $v\!=\!2$ \ero}}
\put(30,114.5){\sx{1.2}{$v\!=\!0$}}
\put(28,105){\sx{1.2}{\rot{-4} $v\!=\!-2$ \ero}}
\put(25,94){\sx{1.2}{\rot{-9} $v\!=\!-4$ \ero}}
%
\put(172,201.8){\sx{1.2}{\rot{-22} $u\!=\!4$ \ero}}
\put(167,192.8){\sx{1.2}{\rot{-29} $u\!=\!3$ \ero}}
\put(159.8,183.8){\sx{1.2}{\rot{-36} $u\!=\!2$ \ero}}
\put(152,176){\sx{1.2}{\rot{-47} $u\!=\!1$ \ero}}
%
\put(82,21){\sx{1.2}{\rot{60} $u\!=\!-4$ \ero}}
\put(95,18){\sx{1.2}{\rot{56} $u\!=\!-2$ \ero}}
\put(110,17){\sx{1.2}{\rot{48} $u\!=\!0$ \ero}}
\put(130,17){\sx{1.2}{\rot{40} $u\!=\!2$ \ero}}
\put(156,17){\sx{1.2}{\rot{30} $u\!=\!4$ \ero}}
%
\put(263,124){\sx{1.2}{\rot{74}\bf cut \ero}}
\put(298,115){\sx{1.2}{\rot{0}\bf cut \ero}}
\put(222.4,102){\sx{1.2}{\rot{90}$v\!=\!0$\ero}}
\end{picture}}

\end{document}