File:Ruble85210a.png

Update of file http://mizugadro.mydns.jp/t/index.php/File:Ruble85210.png

The new experimental data are added as blue dots, than become available 2014.01.11.

Red cuve is by

The black straight line represents the linear approximation from 2014.10.27. The pink arc represents the circular approximation from 2014.11.29.

The green spots represent the data available for 2014.11.29.

Equaitons
The circular approximation in the figure has the root singularity at time $x\approx 120$. This the similar simgularity can be reproduced within a simple model.

Assume, that Head of the mafia has the printing machine, that prints roubles in the amount he needs.

Assume, fue to inflation, this amount is inversely proportional to the value of rouble.

Assume, the market value of rouble $f=f(x)$ at time $x$ is inversely proportional to the amount of these roubles.

These assumptions lead to the following equation:

$f'=-a/f$

where $a$ is constant coefficient of proportionality. This equation is easy to solve:

$ff'=-a$

$(f^2)'/2=-a$

$(f^2)'=-2a$

$f^2= -2ax +b$

where $b$ is constant of integration.

$f=\sqrt{b-2ax}$

This function reproduces the same root singularity at $x=b/(2a)$, as the elliptic approximation shown in the figure.

C++ generatot of dots

 * 1) include
 * 2) include
 * 3) include
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)

void ado(FILE *O, int X, int Y) {      fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%'); fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y); fprintf(O,"/M {moveto} bind def\n"); fprintf(O,"/L {lineto} bind def\n"); fprintf(O,"/S {stroke} bind def\n"); fprintf(O,"/s {show newpath} bind def\n"); fprintf(O,"/C {closepath} bind def\n"); fprintf(O,"/F {fill} bind def\n"); fprintf(O,"/o {.2 0 360 arc C F} bind def\n"); fprintf(O,"/times-Roman findfont 20 scalefont setfont\n"); fprintf(O,"/W {setlinewidth} bind def\n"); fprintf(O,"/RGB {setrgbcolor} bind def\n");}

//#include"ado.cin" FILE *i,*o; int main{ int j,n,m,N=200; char d[N][16]; DB f[N]; int di; DB dr; int day;

o=fopen("dollarplo.eps","w"); ado(o,720,320); fprintf(o,"210 10 translate 10 10 scale\n"); for(n=0;n<31;n+=5) {M(-20,n)L(50,n)} for(n=-20;n<51;n+=5) {M(n,0)L(n,30)} fprintf(o,"0 0 0 RGB 2 setlinecap .1 W S\n"); //M(-20,0) L(50,0) M(0,-0.2) L(0,30) fprintf(o,"0 0 0 RGB .16 W S\n"); DB x,y;
 * 1) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
 * 3) define o(x,y) fprintf(o,"%6.2f %6.2f o\n",0.+x,0.+y);

/* Suppress lines DO(n,N){x=(day-n)/10.; y=1000./f[n]; if(n==0) M(x,y) else L(x,y) } fprintf(o,"0 1 0 RGB 1 setlinejoin 1 setlinecap 1 W S\n");

M(-12,30) L(50,0) fprintf(o,"0 0 0 RGB .2 W S\n");

fprintf(o,"0 0 1 RGB\n"); i=fopen("ddat.txt","r"); DO(n,1024){j=fscanf(i,"%lf%lf",&x,&y); if(j<2) break; if(x>-221.) o(.1*x,.1*y);} fclose(i); fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf dollarplo.eps"); system(   "open dollarplo.pdf"); printf("day of observaiton: %3d\n", day); //     getchar; system("killall Preview");//for mac }

Latex combiner with previous estimates
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} \usepackage{rotating} \usepackage{color} \definecolor{pink}{RGB}{255,127,255} \paperwidth 732pt \paperheight 332pt \textwidth 800pt \textheight 400pt \topmargin -92pt \oddsidemargin -84pt \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(730,306) %\put(-6,-8){\sx{.64}{\includegraphics{85210_original.png}}} \put(-6.4,-8.4){\sx{.64}{\includegraphics{85210_original.png}}} %%%%%%%% %\put(46,20){\sx{14.9}{\color{pink} \circle{50}}} \put(10,10){\includegraphics{dollarplo}} \put(-4,308){\sx{1.3}{Ruble}} \put(-4,296){\sx{1.3}{in cents}} \put(-4,282){\sx{1.3}{of USA}} \put(0,210){\sx{2.5}{2}} \put(0,110){\sx{2.5}{1}} \put(0,10){\sx{2.5}{0}} \put(80,-4){\sx{2.5}{$-100$}} \put(214,-4){\sx{2.5}{$0$}} \put(300,-4){\sx{2.5}{$100$}} \put(400,-4){\sx{2.5}{$200$}} \put(500,-4){\sx{2.5}{$300$}} %\put(600,-2){\sx{2.5}{$400$}} \put(640,-3){\sx{2.5}{$t$, days}} %\put(86,30){\sx{2.4}{\rot{90}{\bf 2014.05.31}\ero}} \put(130,30){\sx{2.4}{\rot{90}{\bf 2014.07.19}\ero}} \put(180,30){\sx{2.}{\rot{90}{\bf 2014.09.07}\ero}} \put(230,30){\sx{2.4}{\rot{90}{\bf 2014.10.27}\ero}} \put(280,30){\sx{2.}{\rot{90}{\bf 2014.12.16}\ero}} %\put(330,30){\sx{2.4}{\rot{90}{\bf 2015.02.04}\ero}} \put(380,192){\sx{2.}{\rot{90}{\bf 2014.03.26}\ero}} \put(430,172){\sx{2.4}{\rot{90}{\bf 2015.05.15}\ero}} \put(480,192){\sx{2.}{\rot{90}{\bf 2015.07.04}\ero}} \put(530,172){\sx{2.4}{\rot{90}{\bf 2015.08.23}\ero}} \put(630,172){\sx{2.4}{\rot{90}{\bf 2015.12.01}\ero}} \put(730,172){\sx{2.4}{\rot{90}{\bf 2016.03.10}\ero}} \end{picture} \end{document}