File:Vladi11.jpg

From TORI
Revision as of 08:56, 1 December 2018 by Maintenance script (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

Original file ‎(2,902 × 2,055 pixels, file size: 721 KB, MIME type: image/jpeg)

Agreements at the substituiton of the numerical implementations of natural tetration tet and that of the natural arctetration ate into equations

$\mathrm{ate}(\mathrm{tet}(z))=z$

$\mathrm{tet}(\mathrm{ate}(z))=z$

Tetration is implemented as FSE.

Arctetration is implemented as FSL.

The agreements are

$ \displaystyle D_{\rm at}(z)= -\ln\left( \frac

\right) $ $ \displaystyle D_{\rm ta}(z)= -\ln\left( \frac
\right) $ Maps $D=D_{\rm at}(x\!+\!\mathrm i y)$ is shown at left, and map of $D=D_{\rm at}(x\!+\!\mathrm i y)$ is shown at right. In the central regions, the agreement with more than 14 digits takes place. Usage: this is figure 15.3 of the book Суперфункции (2014, In Russian) [1]; the English version is in preparation in 2015. First time published in the Vladikavkaz Matehmatical Journal[2].

Refereces

  1. ↑ https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0
    http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf
    http://mizugadro.mydns.jp/BOOK/202.pdf Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014.
  2. ↑ http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. Figure 11.


C++ generator of the left hand side map

ado.cin, conto.cin, fslog.cin fsexp.cin should be loaded in order to compile the code below.



#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
typedef std::complex<double> z_type;
//#include <complex.h>
//#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

//#include"superex.cin"
//#include"superlo.cin"
#include"fsexp.cin"
#include"fslog.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
z_type Zc=z_type(.31813150520476413,-1.3372357014306895);

int M=200,M1=M+1;
int N=300,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("figslosexp.eps","w");ado(o,0,0,404,604);
FILE *o;o=fopen("vladi11a.eps","w");ado(o,404,604);
fprintf(o,"202 302 translate\n 50 50 scale\n");

DO(m,M1) X[m]=-4+.04*m;
DO(n,N1) Y[n]=-6+.04*(n+.5);

for(m=-4;m<5;m++) { if(m==0){M(m,-6.1)L(m,6.1)}
                        else {M(m,-6)L(m,6)} }
for(n=-6;n<7;n++) {M( -4,n)L(4,n)} fprintf(o,".006 W 0 0 0 RGB S\n");

DO(m,M1)DO(n,N1){ g[m*N1+n]=9999;
                        f[m*N1+n]=9999; }
DO(m,M1){x=X[m]; printf("50 run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
        c=FSEXP(z);
        if(abs(c)<1.e128){ c=FSLOG(c);
                                d=z;
                                p=abs(c-d);
                                p=-log(p)/log(10.);
                        if(p>-99 && p<99) g[m*N1+n]=p;
                        }
        }}

p=40;q=8;
#include "plodi.cin"
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf vladi11a.eps");
        system( "open vladi11a.pdf");// linux
//getchar(); system("killall Preview");//macintosh
}

C++ generator of the right hand side map

ado.cin, conto.cin, fslog.cin fsexp.cin

should be loaded in order to compile the code below.


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#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"superex.cin"
//#include"superlo.cin"
#include"fsexp.cin"
#include"fslog.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
z_type Zc=z_type(.31813150520476413,-1.3372357014306895);

int M=200,M1=M+1;
int N=300,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("figslosexp.eps","w");ado(o,0,0,404,604);
FILE *o;o=fopen("vladi11b.eps","w");ado(o,404,604);
fprintf(o,"202 302 translate\n 50 50 scale\n");

DO(m,M1) X[m]=-4+.04*m;
DO(n,N1) Y[n]=-6+.04*(n+.5);

for(m=-4;m<5;m++) { if(m==0){M(m,-6.1)L(m,6.1)}
                        else {M(m,-6)L(m,6)} }
for(n=-6;n<7;n++) {M( -4,n)L(4,n)} fprintf(o,".006 W 0 0 0 RGB S\n");

DO(m,M1)DO(n,N1){ g[m*N1+n]=9999;
                        f[m*N1+n]=9999; }
DO(m,M1){x=X[m]; printf("50 run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
        c=FSLOG(z);
        if(abs(c)<1.e128){ c=FSEXP(c);
                                d=z;
                                p=abs(c-d);
                                p=-log(p)/log(10.);
                        if(p>-99 && p<99) g[m*N1+n]=p;
                        }
        }}

p=40;q=8;
#include "plodi.cin"

//M(Re(Zo),Im(Zo)) L(-2.02,Im(Zo)) M(Re(Zo),-Im(Zo)) L(-2.02,-Im(Zo))
//fprintf(o,".08 W 1 1 1 RGB S\n");
DO(m,14){ M(Re(Zo)-.31*(m ), Im(Zo)) L(Re(Zo)-.31*(m+.5), Im(Zo)) }
DO(m,14){ M(Re(Zo)-.31*(m ),-Im(Zo)) L(Re(Zo)-.31*(m+.5),-Im(Zo)) }
fprintf(o,"0 setlinecap .08 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf vladi11b.eps");
        system( "open vladi11b.pdf");// linux
//getchar(); system("killall Preview");//macintosh
}

Latex combiner


\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{geometry}
\paperwidth 418px
%\paperheight 134px
\paperheight 296px
\topmargin -96pt
\oddsidemargin -94pt
\pagestyle{empty}
\begin{document}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}

\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}


\newcommand \vladiEL {
\put(-18,590){\sx{2.3}{$y$}}
\put(-18,544){\sx{2.3}{4}}
\put(-18,494){\sx{2.3}{4}}
\put(-18,444){\sx{2.3}{3}}
\put(-18,394){\sx{2.3}{2}}
\put(-18,344){\sx{2.3}{1}}
\put(-18,294){\sx{2.3}{0}}
\put(-36,244){\sx{2.3}{$-1$}}
\put(-36,194){\sx{2.3}{$-2$}}
\put(-36,144){\sx{2.3}{$-3$}}
\put(-36, 94){\sx{2.3}{$-4$}}
\put(-36, 44){\sx{2.3}{$-5$}}
%\put(-20, -20){\sx{2.3}{$-4$}}
\put( 30, -20){\sx{2.3}{$-3$}}
\put( 80, -20){\sx{2.3}{$-2$}}
\put(130, -20){\sx{2.3}{$-1$}}
\put(196, -20){\sx{2.3}{$0$}}
\put(246, -20){\sx{2.3}{$1$}}
\put(296, -20){\sx{2.3}{$2$}}
\put(346, -20){\sx{2.3}{$3$}}
\put(391, -20){\sx{2.3}{$x$}}
}

%\begin{figure}[t]
%\begin{center}
\vskip 16pt
\hskip 16pt
%\sx{.54}{\begin{picture}(472,580)
\sx{.47}{\begin{picture}(456,580)
%\put(0,0){\includegraphics{figslosexp}}
\put(0,0){\includegraphics{vladi11a}}
\vladiEL
\put(110,520){\sx{2.8}{$10\!<\!D\!<\!12$}}
\put(154,420){\sx{2.4}{$12\!<D\!<\!14$}}
\put(160,310){\sx{2.8}{$D\!>\!14$}}
\put(154,168){\sx{2.4}{$12\!<D\!<\!14$}}
\put(110,64){\sx{2.8}{$10\!<\!D\!<\!12$}}
\put(20, 320){\sx{2.8}{$D\!<\!1$}}
\put(310,560){\sx{2.8}{$D\!<\!1$}}
\put(310,20){\sx{2.8}{$D\!<\!1$}}
\end{picture}}
\sx{.47}{\begin{picture}(388,580)
%\put(0,0){\includegraphics{figsexpslo}}
\put(0,0){\includegraphics{vladi11b}}
\vladiEL
\put( 20,379){\sx{2.5}{$12\!<\!D\!<\!14$}}
\put( 20,210){\sx{2.5}{$12\!<\!D\!<\!14$}}
\put(200,310){\sx{3}{$D\!>\!14$}}
%\put(204,373){\sx{1}{11}}
%\put(204,226){\sx{1}{11}}
\end{picture}}
\end{document}

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:14, 1 December 2018Thumbnail for version as of 06:14, 1 December 20182,902 × 2,055 (721 KB)Maintenance script (talk | contribs)Importing image file

You cannot overwrite this file.

There are no pages that use this file.

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:Vladi11.jpg&oldid=22222"