{ issleduem giperbolu  }{apr.doc & apr.html v /pat}
uses dos, crt;
label l1,l2,l3,l4;{,l5;}
const  NN=10; {nas=7;} {v mlrd $}
var T, M1,M2,M3,X3,X2,T3,T2,Q1,Q2,Q3,Q4,mm1,mm2,mm3,mm4,mm5,T1,X1,M4,M5,xx,tau1,
tau2,tau3,tau4,dt,{X3max_nc,}h1,h2,T0,X0,M6,M7,C,p,q,a,b,k1,m,k,nas,sigma,
{tt,}KG,xX3,xx2,xX1,xX0,dd,   dk,VVP,Q0,mm0,Ton,Xon,Qon,Qi,dd0,k0,Xm : real;
i,j,{k,}kk,jj,N: word;  ch: char; F1,F2,F3,F4:boolean;
X,Y,Z: array [0..NN] of real;  {Y: array [0..NN] of real;}
Function Pwr(a,x:real):real;begin if a=0 then Pwr:=0 else Pwr:=Exp(x*Ln(a))
end; { "a" v stepeni "x"}
(*
Procedure Gip; label l5,{l6,}l7;
{giperbola nyzhna for opr. momentov vis_shih poryadkov}
begin {v procedure "p"-eto delta,sdvig, "dd", "q" - eto "k"}
p:=0.1;{dd - eto delta v programme}
for i:=200 to 1000 do begin q:=i/100;{iz r-va ln-mov nahodim ~ "k"}
   a:=ln(mm1*(q-1))/(1-q); b:=ln(mm2*(2*q-1))/(1-2*q); if a<b then goto l5;
end;  l5: p:= exp(ln(mm1*(q-1))/(1-q)); {po "k" nahodim sdvig ~ "dd" }
   p:=pwr(dd,k); p:=1/p; {max znach X} q:= pwr(1+dd,k); q:=1/q; {min znach X}
   mm1:=(pwr(p,1-q)-pwr(1+p,1-q))/(q-1);
   mm2:=(pwr(p,1-2*q)-pwr(1+p,1-2*q))/(2*q-1);
{   writeln('k=',k:5:3,' dd=',dd:5:3,' Xmax=',p:5:3,' Xmin=',q:5:3,
   ' mm1=',mm1:5:3,' mm2=',mm2:5:3);} {momenti parapboli & giperboli raznie}
l7:
i:=1; while mm1<M1 do begin  i:=i+1; {podgonyaem dd do r-va M.O.}
   dk:=i/10000; p:=p-dk; mm1:=(pwr(p,1-q)-pwr(1+p,1-q))/(q-1);
end;
   mm2:=(pwr(p,1-2*q)-pwr(1+p,1-2*q))/(2*q-1);
i:=1; while mm2>M2 do begin i:=i+1; {podgonyaem "k" do r-va 2-x momentov}
   dk:=i/10000; q:=q-dk; mm2:=(pwr(p,1-2*q)-pwr(1+p,1-2*q))/(2*q-1);
end;
   mm1:=(pwr(p,1-q)-pwr(1+p,1-q))/(q-1);  if mm1<M1 then goto l7;
end;{end of proceduri}
*)


BEGIN T:=1;  kk:=47; Q1:=0; mm1:=0;  N:=NN; nas:=7;    {   goto l4;}
writeln('probel-All World in 2011,1-USA,2-Portugalia,U-Ukraina,3-Egypt,R-Russia,H-Hungary');
writeln('4-Belarus,N-Namibiya,5-KNR,2-Portugaliya,0-Germaniya,B-Braziliya,K-Kazahstan');
writeln('E-Estoniya-Chuhoniya,F-Finland,P-Poland,S-South Koreya,T-Tayvan",Y-Yapan');
ch:=readkey;

case ch of   { VVP - nominal  }
'0':begin VVP:=3.86  ; KG:=0.319;Nas:=0.084;end; {Germania why is error by "G" not "0" ???}
'1':begin VVP:=25.46 ; KG:=0.411 ; Nas:=0.333 ; end;   {USA}
'2':begin VVP:=0.237 ; KG:=0.338  ;Nas:=0.0103;end; {Portugalia}
'3':begin VVP:=0.302 ; KG:=0.315 ; Nas:=0.106 ;  end;   {Egypt}
'4':begin VVP:=0.066 ; KG:=0.252 ; Nas:=0.0092 ;  end; {Belorus}
'5':begin VVP:=18.1  ; KG:=0.385 ; Nas:=1.411 ;  end;     {KNR}
'B':begin VVP:=1.839 ; KG:=0.539 ; Nas:=0.218 ;  end;      {Brazilia}
'K':begin VVP:=0.245 ; KG:=0.275;Nas:=0.0198;end; {Kazahstan}
'E':begin VVP:=0.039 ; KG:=0.304;Nas:=0.00136;end; {Estonia-Chuhonia}
'F':begin VVP:=0.281 ; KG:=0.271;Nas:=0.00518;end; {Finland}
'H':begin VVP:=0.181 ; KG:=0.306 ; Nas:=0.0097 ;  end; {Hungary}
'N':begin VVP:=0.014 ; KG:=0.591 ; Nas:=0.0025 ;  end; {Namibia}
'P':begin VVP:=0.688 ; KG:=0.319;Nas:=0.038;end; {Poland}
'R':begin VVP:=1.82  ; KG:=0.375 ; Nas:=0.146 ;  end; {Russia}
'S':begin VVP:=1.80  ; KG:=0.314 ; Nas:=0.051 ;  end; {S.Koreya}
'T':begin VVP:=0.761 ; KG:=0.336;Nas:=0.023;end; {Tayvan"}
'U':begin VVP:=0.151 ; KG:=0.261 ; Nas:=0.041 ;  end;   {Ukraina}
'Y':begin VVP:=5.08  ; KG:=0.329;Nas:=0.125;end; {Yapan}
else  VVP:=26.316{/0.57} {trln}  ; KG:=0.648 ; Nas:=6.5 ;{mlrd}

Y[0]:=0; Y[1]:=0.161; Y[2]:=0.421; Y[3]:=0.779; Y[4]:=1.279; Y[5]:=2.009;
Y[6]:=3.151; Y[7]:=4.858; Y[8]:=7.642; Y[9]:=12.803; Y[10]:=26.316;
(* write('Y='); for i:=1 to 10 do write(Y[i]:5:3,' ');writeln;  *)
{ naydem koef Gini }   {write('Z[i]=');}
Z[0]:=0; for i:=1 to 10 do begin Z[i]:=Y[i]/Y[N]; { write(Z[i]:5:3,' ');} end;
{writeln;}{Z-eto Y v otn. edinith}

xx:=0; for i:=1 to N do xx:=xx+(Z[i-1]+(Z[i]-Z[i-1])/2)/N; xx:=(0.5-xx)/0.5;
(*  writeln({'xx=',xx:5:3,}'   KG=',xx:5:3);  *)
end;{All World}

{  write('Ia: '); }
write('I: ');   k:=3.8;  i:=1;   dk:=0.001; k0:=0.01;
a:=pwr(k-1,1/(1-k));  b:=pwr(  (1-k)*(2-k)*(1-kg)/2,1/(2-k)  ); xx:=a/b;

while xx<1 do begin
a:=pwr(k-1,1/(1-k));  b:=pwr(  (1-k)*(2-k)*(1-kg)/2,1/(2-k)  );
xx:=a/b;    k:=k+dk; i:=i+1;
end;
dd:=pwr(k-1,1/(1-k));
write('ch=',ch,' KG=',KG:5:3,' k=',k:5:3,{' a=',a:5:3,' b=',b:5:3,}
' xx=', xx:5:3,' i=',i,' dd=',dd:5:3);
Qi:= (  pwr(dd+1,1-k) - pwr(dd,1-k)  )/(1-k);
xx:=pwr(dd,-k); writeln(' Qi=',Qi:5:3,' X(dd)=',xx:5:3);
{ podobrali dd & k pri (dd+T)^1-k = 0, pogr. 8% - dlya Belorussi   }

a:=( pwr(dd+T,1-k) - pwr(dd,1-k) ) /(1-k);
b:=2/( (1-k)*(2-k)*(1-KG) ); b:=b*( pwr(dd+T,2-k) - pwr(dd,2-k) );
{ pust" } b:=abs(b);
l2:
while a<1 do begin
dd:=dd-dk; a:=( pwr(dd+T,1-k) - pwr(dd,1-k) ) /(1-k);
end;

while b<1 do begin
b:=2/( (1-k)*(2-k)*(1-KG) ); b:=b*( pwr(dd+T,2-k) - pwr(dd,2-k) );
{ pust" } b:=abs(b); k:=k-k0;
end;
a:=( pwr(dd+T,1-k) - pwr(dd,1-k) ) /(1-k);
if a<1 then goto l2;
writeln('a=',a:5:3,' b=',b:5:3,' dd=',dd:5:3,' k=',k:5:3,' - posle podgonki');
{  write('Ib: '); }
M1:=(pwr(dd,1-k)-pwr(1+dd,1-k))/(k-1);
M2:=(pwr(dd,1-2*k)-pwr(1+dd,1-2*k))/(2*k-1);
M3:=(pwr(dd,1-3*k)-pwr(1+dd,1-3*k))/(3*k-1);
M4:=(pwr(dd,1-4*k)-pwr(1+dd,1-4*k))/(4*k-1);
M5:=(pwr(dd,1-5*k)-pwr(1+dd,1-5*k))/(5*k-1);
M6:=(pwr(dd,1-6*k)-pwr(1+dd,1-6*k))/(6*k-1);
M7:=(pwr(dd,1-7*k)-pwr(1+dd,1-7*k))/(7*k-1);
{writeln('M1=',M1:5:3,' M2=',M2:5:3,' M3=',M3:5:3,' M4=',M4:5:3,
' M5=',M5:5:3,' M6=',M6:5:3,' M7=',M7:5:3); }


write('II: ');  {nahodim paraetri 2-x stupeney po kvadratnomy uravneniyu}
   p:=-(M3-M1*M2)/(M2-M1*M1);
   q:=(M1*M3-M2*M2)/(M2-M1*M1);
   X1:=-p/2-sqrt(p*p/4-q); X2:=-p/2+sqrt(p*p/4-q);
   T2:=T*(M1-X1)/(X2-X1); T1:=T-T2;
   {mm1:=T3*X3+T2*X2; mm2:=T3*sqr(X3)+T2*sqr(X2);
   mm3:=T3*sqr(X3)*X3+T2*sqr(X2)*X2;  }
   {writeln('X1=',X1:6:3,' X2:=',X2:6:3,' T1:=',T1:6:3,' T2:=',T2:6:3);}


write('III:');  {nahodim paraetri 2-x stupeney iteraciyami}
  T2:=0;X2:=0;T1:=0;X1:=0;
for i:=1 to kk do begin
    T3:=T-T2;
    X3:=(T*M1-T2*X2)/T3;
    X2:=(T*M3-T3*sqr(X3)*X3)/(T*M2-T3*sqr(X3));
    T2:=(T*M2-T3*sqr(X3))/sqr(X2);
end;
   mm1:=T3*X3+T2*X2; mm2:=T3*sqr(X3)+T2*sqr(X2);
   mm3:=T3*sqr(X3)*X3+T2*sqr(X2)*X2;
   writeln;
{writeln('X3=',X3:5:3,' X2:=',X2:5:3,' T3:=',T3:5:3,' T2:=',
    T2:5:3,' X[1]=',X[1]:5:2,' X[N-1]=',X[N-1]:5:2,' X[N]=',X[N]:5:2); }


write('IV: ');   {nahodim paraetri 3-x stupeney}
for i:=1 to kk do begin
      T3:=T-T2-T1;
      X3:=(T*M1-T2*X2-T1*X1)/T3; if i=kk then goto l1;
      X2:=(T*M3-T3*sqr(X3)*X3-T1*sqr(X1)*X1)/(T*M2-T3*sqr(X3)-T1*sqr(X1));
      T2:=(T*M2-T3*sqr(X3)-T1*sqr(X1) )/sqr(X2);
      X1:=(T*M5-T3*sqr(X3)*sqr(X3)*X3-T2*sqr(X2)*sqr(X2)*X2)
       /(T*M4-T3*sqr(X3)*sqr(X3)-T2*sqr(X2)*sqr(X2)  );
    T1:=(T*M4-T3*sqr(X3)*sqr(X3)-T2*sqr(X2)*sqr(X2) ) /( sqr(X1)*sqr(X1)  );
end;
l1:
writeln('i=',i,' X3=',X3:5:3,' X2:=',X2:5:3,' X1:=',X1:5:3,
      ' T3:=',T3:5:3,' T2:=',T2:5:3,' T1:=',T1:5:3);
Q1:=(1/(1-k))*(1/pwr(dd+T1,k-1)-1/pwr(dd,k-1));
Q2:=(1/(1-k))*(1/pwr(dd+T1+T2,k-1)-(1/pwr(dd+T1,k-1)));
Q3:=(1/(1-k))*(1/pwr(dd+T1+T2+T3,k-1)-(1/pwr(dd+T1+T2,k-1)));
writeln('Q3=',Q3:5:3,' Q2=',Q2:5:3,' Q1=',Q1:5:3);


write('V : '); {  nahodim chislo oligarhov  }
X0:=( T*M7-T3*pwr(X3,7)-T2*pwr(X2,7)-T1*pwr(X1,7) )/
    (T*M6-T3*pwr(X3,6)-T2*pwr(X2,6)-T1*pwr(X1,6) );
writeln('X0=',X0:5:3);

                                                        X0:=abs(X0);
T0:=(T*M6-T3*pwr(X3,6)-T2*pwr(X2,6)-T1*pwr(X1,6) )/pwr(X0,6)  ;
Q0:=X0*T0;

write('X0=',X0:5:3,' T0=',T0:9,' Q0=',Q0:9 );
writeln(' eto - podarok sud"bi; oligarhov ',trunc(1e9*T0*Nas)  );
T0:=abs(T0);  Q0:=X0*T0;
xx:=trunc(1e9*T0*Nas);N:=trunc(xx); { eto - chislo oligarhov }

xx0:=1/pwr(dd+T0,k); xx1:=1/pwr(dd+T1,k); xx2:=1/pwr(dd+T1+T2,k);
xx3:=1/pwr(dd+T1+T2+T3,k);
writeln('X(t)min=xx3=',xx3:5:3,' xx2=',xx2:5:3,' xx1=',xx1:5:3,
' xx0=X(dd+T0)=',xx0:5:4,' X(dd)=',1/pwr(dd,k):5:4);
{xx3:=xx3*Y[N]/Nas; xx2:=xx2*Y[N]/Nas; xx1:=xx1*Y[N]/Nas; xx0:=xx0*Y[N]/Nas;}
writeln('X(t)min=xx3=',xx3*0.57*VVP/Nas:5:3,' xx2=',xx2*0.57*VVP/Nas:5:3,
' xx1=',xx1*0.57*VVP/Nas:5:3,' X(t)max=xx0=',xx0*0.57*VVP/Nas:5:3,' tis. $');

{writeln;}


write('VI:zakon Tsipfa'); { zakon Tsipfa  } if N=0 then goto l4;  dt:=T0/N;
Xm:=-Q0/(dt*ln(dt)); xx:= Xm*dT/T0; q:=-dt*Xm*ln(dt);
writeln(' Q0=',Q0:9,' dt=',dt:9,' Xm=',Xm:5:3,{' or Xm $=',Xm*0.57*VVP/Nas:9,}
{' tis $;',}' Xo(T0)=',xx:5:3,' q=',q:9);
(*  writeln('VII: zarabotok v tis $');
writeln('min na dushu=',xx3{*0.57*VVP/Nas}:5:3,
'; max 3 classa=',2*xx2{*0.57*VVP/Nas}:5:0,{oba rab}
'; max 2 classa=',4*xx1{*0.57*VVP/Nas}:5:0,{1 rab}
'; max 1 classa=',6*4*xx1{*0.57*VVP/Nas}:5:0,
'; 1-y oligarh poluchaet- ',4*Xm{*0.57*VVP/Nas}:9,' tis.$');
a:=dT*Xm/({6*4*}xx1); writeln('k-vo nast oligarhov=',round(a/dT));

write('VIa:'); Ton:=pwr(1*Xm*dT,1/2); writeln('Ton=',Ton:9);
*)



(*Xm:=-Q0/(dt*ln(dt)); {perehod ot Tsipfa k giperbole  }
dk:=0.01; k0:=1.06; { Xm max = 376 pri k0 ot 1.05 do 1.06};
Xm:=-Q0*(1-k0)/pwr(dt,2-k0); xx:=dt*Xm/pwr(T0,k0);{nizhnee znach krivoy Tsipfa}
q:= -dt*Xm*pwr(dt,1-k0)/(1-k0);
writeln('Xm=',Xm:5:3,' xx=',xx:5:3,' q=',q:9);
*)
write('VII: ot zakona Tsipfa k giperbole');
dk:=0.01; k0:=1;
while xx<xx0 do begin  k0:=k0-dk;
Xm:=Q0*(1-k0)/pwr(dt,2-k0); xx:=dt*Xm/pwr(T0,k0);

end;
 {writeln;}
writeln(' Xm=',Xm:5:3,' xx:=',xx:5:3,' k0=',k0:5:3);


writeln('VIIa: zarabotok v tis $:  min na dushu tis.$=',xx3*0.57*VVP/Nas:0:3);
writeln('max 3 classa=',2*xx2*0.57*VVP/Nas:0:0,{oba rab}
        '; max 2 classa=',4*xx1*0.57*VVP/Nas:0:0,{1 rab}
        '; max 1 classa=',2*4*xx0*0.57*VVP/Nas:0:0,' tis.$');

(*[]*)      l4:
writeln;
writeln('ITOG: ch=',ch,' KG=',KG:5:3,' VVP=',VVP:5:3,' Nas=',Nas:5:3);
writeln(
'xx3=',xx3*0.57*VVP/Nas:5:2,' xx3=',xx2*0.57*VVP/Nas:5:2,' (xx3)=',xx2*2*0.57*VVP/Nas:5:2,' T3=',100*T3:5:1,' Q3=',100*Q3:5:1);
writeln(
'xx2=',xx1*0.57*VVP/Nas:5:2,' (xx2)=',xx1*4*0.57*VVP/Nas:5:2,' T2=',100*T2:5:1,' Q2=',100*Q2:3:1);
writeln('xx1=',xx0*2*0.57*VVP/Nas:5:2,' (xx1)=',xx0*2*4*0.57*VVP/Nas:5:2,' T1=',100*T1:5:1,' Q1=',100*Q1:3:1);
(*{}*)

writeln('(dohod 1-go oligarha) - ',{4*Xm*0.57*VVP/Nas:9,' tis.$,t.e. ',}
4*Xm*0.57*VVP/Nas/1e6:5:3,' mlrd.(10^9) $',' Q0=',100*Q0:5,
' k-vo oligarhov 1/4=',trunc(1e9*T0*Nas/4) );








ch:=readkey; writeln;{writeln;}
END.