Difference between pages "File:Ack4aFragment.jpg" and "File:HiroshiHasegawaAtTokyoOlympic3.jpeg"
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| + | [[Hiroshi Hasegawa]] at Tokyo Olympic 1964. |
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| − | Fragment of image http://mizugadro.mydns.jp/t/index.php/File:Ack4a600.jpg |
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| + | Family archive of [[Arase Tsugiko]] ([[あらせ つぎこ]]). |
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| − | [[Complex map]] of [[tetration]] to base $b\!=\!2$ |
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| + | [[Category:Arase Tsugiko]] |
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| − | $u\!+\!\mathrm i v=\mathrm{tet}_b(x\!+\!\mathrm i y)$ |
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| + | [[Category:Fragment]] |
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| − | |||
| + | [[Category:Japan]] |
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| − | ==Usage== |
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| + | [[Category:Kozo Okudaira]] |
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| − | This is fragment of image fig.3a (with improved resolution) of publication "Evaluation of holomorphic ackermanns", 2014. |
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| + | [[Category:Kyoko Okudaira]] |
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| − | <ref> |
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| + | [[Category:Okudaira]] |
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| − | http://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.14.pdf <br> |
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| − | http://mizugadro.mydns.jp/PAPERS/2014acker.pdf |
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| − | D.Kouznetsov. Evaluation of holomorphic ackermanns. Applied and Computational Mathematics. Vol. 3, No. 6, 2014, pp. 307-314. |
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| − | </ref> |
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| − | |||
| − | ==[[C++]] Generator of map== |
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| − | Files |
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| − | [[ado.cin]], |
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| − | [[conto.cin]], |
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| − | [[tet2f4c.cin]], |
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| − | [[Tet2f2048.inc]], |
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| − | [[GLxw2048.inc]] |
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| − | should be loaded to the working directory in order to compile the code below. |
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| − | <poem><nomathjax><nowiki> |
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| − | #include <math.h> |
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| − | #include <stdio.h> |
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| − | #include <stdlib.h> |
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| − | #define DB double |
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| − | #define DO(x,y) for(x=0;x<y;x++) |
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| − | #include <complex> |
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| − | #define z_type std::complex<double> |
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| − | #define Re(x) x.real() |
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| − | #define Im(x) x.imag() |
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| − | #define I z_type(0.,1.) |
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| − | |||
| − | #include "conto.cin" |
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| − | //#include "filog.cin" |
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| − | z_type b=2.; |
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| − | #include "tet2f4c.cin" |
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| − | |||
| − | int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; |
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| − | //z_type Zo=z_type(.31813150520476413, 1.3372357014306895); // This is for b=e, not used here.. |
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| − | //z_type Zc=z_type(.31813150520476413,-1.3372357014306895); |
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| − | int M=641,M1=M+1; |
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| − | int N=402,N1=N+1; |
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| − | DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. |
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| − | char v[M1*N1]; // v is working array |
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| − | // FILE *o;o=fopen("tet2m2.eps","w");ado(o,1604,804); |
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| − | // FILE *o;o=fopen("tettenm2.eps","w");ado(o,1604,804); |
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| − | // FILE *o;o=fopen("amsfig4dFragmen.eps","w");ado(o,1604,804); |
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| − | FILE *o;o=fopen("amsfig4aFragmen.eps","w");ado(o,1604,804); |
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| − | fprintf(o,"802 402 translate\n 100 100 scale 2 setlinecap 1 setlinejoin\n"); |
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| − | DO(m,M1)X[m]=-8.+.05*(m-.3); |
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| − | DO(n,200)Y[n]=-4.+.02*n; |
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| − | Y[200]=-.01; |
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| − | Y[201]= .01; |
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| − | for(n=202;n<N1;n++) Y[n]=-4.+.02*(n-1.); |
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| − | for(m=-8;m<9;m++){M(m,-4)L(m,4)} |
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| − | for(n=-4;n<5;n++){ M( -8,n)L(8,n)} |
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| − | fprintf(o,".008 W 0 0 0 RGB S\n"); |
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| − | DO(m,M1)DO(n,N1){g[m*N1+n]=990999; f[m*N1+n]=909999;} |
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| − | DO(n,N1){y=Y[n]; |
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| − | for(m=150;m<170;m++) |
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| − | {x=X[m]; //printf("%5.2f\n",x); |
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| − | z=z_type(x,y); |
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| − | // c=tetb(z); |
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| − | // c=F4TEN(z); |
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| − | c=F4(z); |
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| − | p=Re(c);q=Im(c); |
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| − | if(p>-99999. && p<99999. && q>-99999. && q<99999. ){ g[m*N1+n]=p;f[m*N1+n]=q;} |
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| − | d=c; |
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| − | for(k=1;k<31;k++) |
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| − | { m1=m+k*20; if(m1>M) break; |
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| − | // d=exp(a*d); |
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| − | d=exp(d*log(2.)); |
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| − | p=Re(d);q=Im(d); |
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| − | if(p>-99999. && p<99999. && q>-99999. && q<99999. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;} |
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| − | } |
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| − | d=c; |
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| − | for(k=1;k<31;k++) |
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| − | { m1=m-k*20; if(m1<0) break; |
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| − | // d=log(d)/a; |
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| − | d=log(d)/log(2.); |
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| − | p=Re(d);q=Im(d); |
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| − | if(p>-99999. && p<99999. && q>-99999. && q<99999. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;} |
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| − | } |
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| − | }} |
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| − | fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=20;q=1; |
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| − | for(m=-4;m<4;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".004 W 0 .6 0 RGB S\n"); |
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| − | for(m=0;m<4;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".004 W .9 0 0 RGB S\n"); |
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| − | for(m=0;m<4;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".004 W 0 0 .9 RGB S\n"); |
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| − | for(m=1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W .9 0 0 RGB S\n"); |
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| − | for(m=1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 .9 RGB S\n"); |
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| − | conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".03 W .6 0 .6 RGB S\n"); |
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| − | for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 0 RGB S\n"); |
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| − | fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); |
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| − | //system( "ggv fig3.eps"); |
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| − | system("epstopdf amsfig4aFragmen.eps"); |
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| − | system( "open amsfig4aFragmen.pdf"); |
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| − | getchar(); system("killall Preview"); |
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| − | } |
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| − | </nowiki></nomathjax></poem> |
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| − | |||
| − | ==[[Latex]] Generator of labels== |
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| − | <poem><nomathjax><nowiki> |
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| − | \documentclass{amsproc} |
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| − | \usepackage{graphicx} |
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| − | \usepackage{rotating} |
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| − | \usepackage{hyperref} |
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| − | \newcommand \sx {\scalebox} |
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| − | \newcommand \rme {{\rm e}} %% |
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| − | %\newcommand \rme {{e}} %% |
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| − | \newcommand \rmi {{\rm i}} %%imaginary unity \newcommand \ds {\displaystyle} |
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| − | \newcommand \rot {\begin{rotate}} |
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| − | \newcommand \ero {\end{rotate}} |
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| − | \newcommand \ing \includegraphics |
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| − | \usepackage{geometry} |
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| − | \topmargin -94pt |
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| − | \oddsidemargin -70pt |
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| − | \paperwidth 1666pt |
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| − | \paperheight 856pt |
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| − | \textwidth 1900px |
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| − | \textheight 900px |
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| − | \begin{document} |
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| − | \parindent 0pt |
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| − | |||
| − | \newcommand \mapax { |
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| − | \put(18,820){\sx{5}{$y$}} |
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| − | \put(18,730){\sx{5}{$3$}} |
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| − | \put(18,630){\sx{5}{$2$}} |
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| − | \put(18,530){\sx{5}{$1$}} |
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| − | \put(18,430){\sx{5}{$0$}} |
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| − | \put(-14,329){\sx{5}{$-1$}} |
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| − | \put(-14,229){\sx{5}{$-2$}} |
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| − | \put(-14,129){\sx{5}{$-3$}} |
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| − | \put(-14, 29){\sx{5}{$-4$}} |
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| − | \put(14, 0){\sx{5}{$-8$}} |
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| − | \put(114, 0){\sx{5}{$-7$}} |
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| − | \put(214, 0){\sx{5}{$-6$}} |
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| − | \put(314, 0){\sx{5}{$-5$}} |
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| − | \put(414, 0){\sx{5}{$-4$}} |
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| − | \put(514, 0){\sx{5}{$-3$}} |
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| − | \put(614, 0){\sx{5}{$-2$}} |
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| − | \put(714, 0){\sx{5}{$-1$}} |
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| − | \put(844, 0){\sx{5}{$0$}} |
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| − | \put(944, 0){\sx{5}{$1$}} |
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| − | \put(1044, 0){\sx{5}{$2$}} |
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| − | \put(1144, 0){\sx{5}{$3$}} |
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| − | \put(1244, 0){\sx{5}{$4$}} |
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| − | \put(1344, 0){\sx{5}{$5$}} |
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| − | \put(1444, 0){\sx{5}{$6$}} |
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| − | \put(1544, 0){\sx{5}{$7$}} |
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| − | \put(1634, 0){\sx{5}{$x$}} |
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| − | } |
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| − | %\flushright{$b=\mathrm e \approx 2.71$} |
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| − | |||
| − | {\begin{picture}(1620,850) %%% |
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| − | \put(50,40){\ing{amsfig4aFragmen}} \mapax |
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| − | \put(214,680){\sx{8}{$b=2$}} |
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| − | \put(76,798){\sx{4}{$u\!+\!\mathrm i v \approx 0.824678546142074 + 1.567432123849648 \,\mathrm i$}} |
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| − | \put(80,90){\sx{4}{$u\!+\!\mathrm i v \approx 0.824678546142074 - 1.567432123849648 \,\mathrm i$}} |
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| − | \put(60,434){\sx{4}{\bf cut}} |
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| − | \put(800,434){\sx{4}{$v\!=\!0$}} |
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| − | \multiput(380,610)(555,105){3}{\sx{4}{$u\!=\!1$}} |
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| − | \multiput(240,464)(555,105){4}{\sx{4}{$v\!=\!1$}} |
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| − | \multiput(240,404)(555,-105){4}{\sx{4}{$v\!=\!-1$}} |
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| − | |||
| − | \end{picture}} |
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| − | \end{document} |
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| − | </nowiki></nomathjax></poem> |
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| − | |||
| − | ==Refrences== |
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| − | <references/> |
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| − | |||
| − | http://www.ams.org/mcom/2009-78-267/S0025-5718-09-02188-7/home.html D.Kouznetsov. (2009). Solutions of F(z+1)=exp(F(z)) in the complex plane. [[Mathematics of Computation]], 78: 1647-1670. DOI:10.1090/S0025-5718-09-02188-7. |
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| − | |||
| − | https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br> |
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| − | http://mizugadro.mydns.jp/BOOK/202.pdf |
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| − | Д.Кузнецов. Суперфунцкии. [[Lambert Academic Publishing]], 2014. (In Russian) |
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| − | |||
| − | http://mizugadro.mydns.jp/BOOK/437.pdf |
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| − | D.Kouznetsov. Suparfunctions. Mizugadro, 2015. (In English) |
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| − | |||
| − | http://myweb.astate.edu/wpaulsen/tetration.html |
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| − | William Paulsen. Tetration is repeated exponentiation. (2016). We can define $^0b = 1, ^1b = b, ^2b = b^b$, &3b = b^{b^b}$, etc. .. |
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| − | |||
| − | [[Category:AMS]] |
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| − | [[Category:Applied and Computational Mathematics]] |
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| − | [[Category:Book]] |
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| − | [[Category:Bookmap]] |
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| − | [[Category:Complex map]] |
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| − | [[Category:C++]] |
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| − | [[Category:Latex]] |
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| − | [[Category:Superfunctions]] |
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| − | [[Category:Tetration]] |
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Latest revision as of 08:37, 1 December 2018
Hiroshi Hasegawa at Tokyo Olympic 1964.
Family archive of Arase Tsugiko (あらせ つぎこ).
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:10, 1 December 2018 |  | 3,457 × 1,776 (1.63 MB) | Maintenance script (talk | contribs) | Importing image file |
- You cannot overwrite this file.
File usage
The following 2 pages link to this file:
- File:Amsfig4aFragment.jpg (file redirect)
- File:Amsfig4aFragment.jpg (file redirect)
