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Name: jay
Title:
  speed of sound
Question:
c       Programme for speed of sound in SCQGP
c       Bannur       
        implicit real*8(a-h,o-z)
        pi=4.d0*datan(1.d0)
        tempc=0.275d0           !for nf=0
c
        do 300 ii=1,201
        tilde=1.d0 0.1d0*dfloat(ii-1)                
        temp=tilde*tempc
        tcd=temp/tempc        
        anf=0.d0
        anc=3.d0        !no of colors
c       alambda=0.037d0       !n_f=3
c       alambda=0.0805d0       !n_f=2
        alambda=0.1375d0       !n_f=0
        af=(16.d0 (21.d0*anf/2.d0))*pi**2/90.d0
        ent1=entemp(temp,tempc,anf,anc,alambda,tcd)
        ent=ent1*3.d0*af*temp**4
        ent4=ent/temp**4
        ptem=ptemp(temp,tempc,anf,anc,alambda,tcd)
        pt4=ptem/temp**4
        write(*,*)tilde,pt4
300      continue
        stop
        end
c       subprograme for energy density e(T)
        function entemp(temp,tempc,anf,anc,alambda,tcd)
        implicit real*8(a-h,o-z)
        Dimension pl(10000),pl1(10000)
        pi=4.d0*datan(1.d0)
        fac1=(6.d0*pi)
        fac2=(33.d0-2.d0*anf)*dlog(temp/alambda)
        fac3=3.d0*(153.d0-19.d0*anf)/((33.d0-2.d0*anf)**2)
        fac4=dlog(2.d0*dlog(temp/alambda))/dlog(temp/alambda)
        alpha=(fac1/fac2)*(1.d0-fac3*fac4)
c       alpha=fac1/(fac2*(1.d0 fac3*fac4))
        gsq=4.d0*pi*alpha       !g^2_s
        den1=(16.d0 (21.d0*anf/2))*(pi**2/90.d0)
        den=1.1d0*den1*temp**3                 !n
        rav=(3.d0/(4.d0*pi*den))**0.33333333333d0
        fact=(anc/3.d0) (anf/6.d0)
        amdLO=dsqrt(fact*gsq)*temp
c          debye=amdLO
c        Debye Mass(SU(3)_c)
          n=100
          am=0.890052d0
          bm=1.29752d0
          cm=-2.42922d0
          dm=3.60965d0
          ax=tilde              !T/T_c
          az=am*dexp(-(bm/tcd**2)-(cm/tcd**4)-(dm/tcd**6))
          do 20 k=1,n
          pl(k)=az**k/k**2
          pl1(k)=(-az)**k/k**2
20        continue
          sum=0.d0
          sum2=0.d0
          do 30 k=1,n
          sum=sum pl(k)
          sum2=sum2 pl1(k)
30        continue
c         write(*,*)sum
          sum1=sum
          sum3=sum2
          amad1=((anc/3.d0)*6.d0*sum1/pi**2)
            amad2=((anf/6.d0)*(-12.d0*sum3/pi**2))
c           amad=dsqrt((gsq*temp**2)*(amad1 amad2))     !full qcd
            amad=dsqrt((gsq*temp**2)*amad1)              !pure gluonic
c        write(*,*)tilde,amad
        sigma=0.184d0                !string tension(GeV^2)
c       
        potn1=(2.d0*sigma)/(amad**2)
        potn2=alpha
        potn3=potn1-potn2
        debrt=(amad*rav)
        potn4=potn3*dexp(-debrt)/rav
        potn5=(2.d0*sigma)/(amad**2*rav)
        potn6=(2.d0*sigma/amad)
        potn7=alpha*amad
        potnf=(potn4-potn5 potn6-potn7)
        gammaf=potnf/temp
        tau=abs(gammaf)
        enertau1=(1.d0/2.7d0)*(dsqrt(3.d0)/2.d0)
        enertau=1.d0-enertau1*tau**(3.d0/2.d0)
        entemp=enertau
        return
        end
c
c       subprograme in pressure
        function ptemp(temp,tempc,anf,anc,alambda,tcd)
        implicit real*8(a-h,o-z)
        dimension funtemp(1901)
        Dimension pl(10000),pl1(10000)
        pi=4.d0*atan(1.d0)
        af=(16.d0 (21.d0*anf/2.d0))*pi**2/90.d0
        alower=tempc
        aupper=temp
        numb=101
        dtau=(aupper-alower)/dfloat(numb-1)
c       Generation of integrand
        do 88 i=1,numb
        temp=alower dtau*dfloat(i-1)
        fac1=(6.d0*pi)
        fac2=(33.d0-2.d0*anf)*dlog(temp/alambda)
        fac3=3.d0*(153.d0-19.d0*anf)/((33.d0-2.d0*anf)**2)
        fac4=dlog(2.d0*dlog(temp/alambda))/dlog(temp/alambda)
        alpha=(fac1/fac2)*(1.d0-fac3*fac4)
c       alpha=fac1/(fac2*(1.d0 fac3*fac4))
        gsq=4.d0*pi*alpha       !g^2_s
        den1=(16.d0 (21.d0*anf/2))*(pi**2/90.d0)
        den=1.1d0*den1*temp**3                 !n
        rav=(3.d0/(4.d0*pi*den))**0.33333333333d0
         fact=(anc/3.d0) (anf/6.d0)
c        amdLO=dsqrt(fact*gsq)*temp
c          debye=amdLO
c        Debye Mass(SU(3)_c)
          n=100
          am=0.890052d0
          bm=1.29752d0
          cm=-2.42922d0
          dm=3.60965d0
          ax=tilde              !T/T_c
          az=am*dexp(-(bm/tcd**2)-(cm/tcd**4)-(dm/tcd**6))
          do 20 k=1,n
          pl(k)=az**k/k**2
          pl1(k)=(-az)**k/k**2
20        continue
          sum=0.d0
          sum2=0.d0
          do 30 k=1,n
          sum=sum pl(k)
          sum2=sum2 pl1(k)
30        continue
c         write(*,*)sum
          sum1=sum
          sum3=sum2
          amad1=((anc/3.d0)*6.d0*sum1/pi**2)
            amad2=((anf/6.d0)*(-12.d0*sum3/pi**2))
c           amad=dsqrt((gsq*temp**2)*(amad1 amad2))     !full qcd
            amad=dsqrt((gsq*temp**2)*amad1)              !pure gluonic
c        write(*,*)tilde,amad
        sigma=0.184d0                !string tension(GeV^2)
c       
        potn1=(2.d0*sigma)/(amad**2)
        potn2=alpha
        potn3=potn1-potn2
        debrt=(amad*rav)
        potn4=potn3*dexp(-debrt)/rav
        potn5=(2.d0*sigma)/(amad**2*rav)
        potn6=(2.d0*sigma/amad)
        potn7=alpha*amad
        potnf=(potn4-potn5 potn6-potn7)
        gammaf=potnf/temp
        tau=abs(gammaf)
        etau1=(1.d0/2.7d0)*(dsqrt(3.d0)/2.d0)
        enertau=1.d0-etau1*tau**(3.d0/2.d0)
        funtemp(i)=temp**2*enertau
88      continue
        call simson(alower,aupper,numb,funtemp,rr)
        plus=rr*3.d0*af*aupper
        ptauc=0.0707d0*(tempc**3)*aupper
        ptemp=plus ptauc
        return
        end
c
        subroutine simson(a,b,nmx,func,r)
        implicit real*8(a-h,o-z)
        dimension func(1901)
        cnum=nmx
        h=(b-a)/(cnum-1.d0)
        odd=0.d0
        even=0.d0
        index=0
        do 11 m=1,nmx
        if (index)3,3,4
3       odd=odd func(m)
        index=1
        go to 11
4       even=even func(m)
        index=0
11      continue
        tot=2.d0*odd 4.d0*even-func(1)-func(nmx)
        r=h*tot/3.d0
        return
        end
Answers:

Name: спт
var a,b,t,M,R: integer;
    Function F(x:integer): integer;
        begin 
            F := x*x   2*x   10
        end;  
begin 
    a := -10; b := 10; 
    M := a; R := F(a); 
    for t := a to b do begin 
        if (F(t) < R) then begin 
            M := t; 
            R := F(t) 
        end 
    end; 
    write(M) 
end.