## Simplification of an expression...

Dear users!

Hope everyone should be fine here. I need the following simiplification. I did it step by step is there and maple command to do this.

(diff(theta(eta), eta, eta))*(Rd*T[infinity]^3*(`&theta;w`-1)^3*theta(eta)^3+3*Rd*T[infinity]^3*(`&theta;w`-1)^2*theta(eta)^2+(3*(Rd*T[infinity]^3+(1/3)*epsilon*k[nf]))*(`&theta;w`-1)*theta(eta)+Rd*T[infinity]^3+k[nf]) = (-3*Rd*T[infinity]^3*(`&theta;w`-1)^3*theta(eta)^2-6*Rd*T[infinity]^3*(`&theta;w`-1)^2*theta(eta)+(-3*Rd*T[infinity]^3-epsilon*k[nf])*(`&theta;w`-1))*(diff(theta(eta), eta))^2+(-(rho*c[p])[nf]*nu[f]*f(eta)-(rho*c[p])[nf]*nu[f]*g(eta))*(diff(theta(eta), eta))+a*nu[f]*mu[nf]*(diff(f(eta), eta))^2/((-`&theta;w`+1)*T[infinity])-2*a*nu[f]*mu[nf]*(diff(g(eta), eta))*(diff(f(eta), eta))/((`&theta;w`-1)*T[infinity])+a*nu[f]*mu[nf]*(diff(g(eta), eta))^2/((-`&theta;w`+1)*T[infinity])

(diff(theta(eta), eta, eta))*Rd*T[infinity]^3*(theta(eta)*`&theta;w`-theta(eta)+1)^3+(diff(theta(eta), eta, eta))*k[nf]*(epsilon*theta(eta)*`&theta;w`-epsilon*theta(eta)+1)+3*Rd*T[infinity]^3*(`&theta;w`-1)*(theta(eta)*`&theta;w`-theta(eta)+1)^2*(diff(theta(eta), eta))^2+epsilon*k[nf]*(`&theta;w`-1)*(diff(theta(eta), eta))^2

diff((theta(eta)*`&theta;w`-theta(eta)+1)^3*(diff(theta(eta), eta))*Rd*T[infinity]^3, eta)+diff((epsilon*theta(eta)*`&theta;w`-epsilon*theta(eta)+1)*(diff(theta(eta), eta))*k[nf], eta);

## Problem in partial derivative...

Hi Users!

Hope everyone in fine and enjoying good health. I am facing problem to differential the following expression with respect to first variable (mentioned as red). Please help me to fix this query

f(z*sqrt(a/nu[f]), U*t/(2*x))

## how to Solve this NonLinear equation?...

dS[c] := Gamma*(P*In[a]+R[a]+S[a])-rho*S[c]-S[c]*beta[h]*In[v]/(S[c]+In[c]+R[c]+S[a]+In[a]+R[a]+In[m])-mu[h]*S[c]; dIn[c] := S[c]*beta[h]*In[v]/(S[c]+In[c]+R[c]+S[a]+In[a]+R[a]+In[m])-rho*In[c]-gamma*In[c]-mu[h]*In[c]; dR[c] := gamma*In[c]-rho*R[c]-R[c]*mu[h]; dS[a] := rho*S[c]-S[a]*beta[h]*In[v]/(S[c]+In[c]+R[c]+S[a]+In[a]+R[a]+In[m])-mu[h]*S[a]; dIn[a] := rho*In[c]+S[a]*beta[h]*In[v]/(S[c]+In[c]+R[c]+S[a]+In[a]+R[a]+In[m])-gamma*In[a]-mu[h]*In[a]; dR[a] := gamma*In[a]+rho*R[c]-R[a]*mu[h]; dIn[m] := Gamma*In[a]*(1-P)-mu[m]*In[m]; dS[v] := Gamma[v]-S[v]*beta[v]*(In[c]+In[a]+In[m])/(S[c]+In[c]+R[c]+S[a]+In[a]+R[a]+In[m])-mu[v]*S[v]; dIn[v] := S[v]*beta[v]*(In[c]+In[a]+In[m])/(S[c]+In[c]+R[c]+S[a]+In[a]+R[a]+In[m])-mu[v]*In[v]; solve({dIn[a]=0, dIn[c]=0, dIn[m]=0, dIn[v]=0, dR[a]=0, dR[c]=0, dS[a]=0, dS[c]=0, dS[v]=0}, {In[a], In[c], In[m], In[v], R[a], R[c], S[a], S[c], S[v]}); Warning, solutions may have been lost

## Piecewise function - How plot function with piece...

Hi

I have the following piecewise function in Maple:

`sigmaP:=piecewise(u < -1,-1,u >1,1,u);`

Now we can plot this function:

`plot(sigmaP,u=-5..5,size=[1200,300],gridlines,discont=[showremovable]);`

Next, I define a new piecewise  function as

`sigmaF:=u->piecewise(u < -1,-1,u >1,1,u);`

and I use this function in

```Fun:=proc(x1,x2,u1,u2)
2*x1*(1+x2)*sigmaF(u1)+(1+x2^2)*sigmaF(u2);
end proc:```

Now I need to find a minimum of this function so I use the following code

`GlobalOptimization:-GlobalSolve(Fun,x1,x2,u1,u2);`

where

```x1:=-5..5;
x2:=-10..100;
u1:=-1..1;
u2:=-1..1;
```

And I have the problem with plot function Fun. How to plot function Fun???

Best

## Solution of second order differential equation...

Dear Users!

Hope you would be fine with everying. I want to solve the following 2nd order linear differential equation.

(1+B)*(diff(theta(eta), eta, eta))+C*A*(diff(theta(eta), eta)) = 0;
where A is given as

A := -(alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega+alpha*exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))*omega-alpha*omega+exp(-sqrt((omega+1)*omega*(M^2+alpha+1))*eta/(omega+1))-alpha-omega-1)/sqrt((omega+1)*omega*(M^2+alpha+1));
I want solution for any values of omega, alpha, M, B, C and L. The BCs are below:

BCs := (D(theta))(0) = -1, theta(L) = 0.

## pdsolve ignores "assuming real", how to get real s...

I try to get real solutions for a PDE, i.e. real-valued functions depending on real variables. Maple computer complex solutions, i.e. complex-valued functions depending on complex variables.

Here is the example in question: (the four function f1, f2, f3, f4 depend on the four unknowns lam, mu, l, m)

``assuming`([pdsolve([diff(f2(lam, mu, l, m), m)-(diff(f1(lam, mu, l, m), l))-(diff(f4(lam, mu, l, m), mu))+diff(f3(lam, mu, l, m), lam) = 0, diff(f1(lam, mu, l, m), m)+diff(f2(lam, mu, l, m), l)-(diff(f3(lam, mu, l, m), mu))-(diff(f4(lam, mu, l, m), lam)) = 0])], [real])`

How can I solve my problem and receive only real solutions to my PDE?

A similar problem had been posted before (see here), but I can only find a cached version of the post where no answers are displayed.

## Write expression in term of other expression...

Dear Users!

Hope you would be fine. In the following maple code, I want to write the derivative of psi in term of psi like it did manually in red portion. For higher M and k it very hard to do it manully. It there any command to fix my problem for any value of k and M.

restart; k := 2; M := 4;

with(linalg); with(LinearAlgebra);

printlevel := 2;

for i while i <= 2^(k-1) do

for j from 0 while j <= M-1 do

psi[M*i+j-M+1] := simplify(2^((1/2)*k)*sqrt(GAMMA(j+1)*(j+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(j+2*alpha)))*(sum((-1)^i1*GAMMA(j-i1+alpha)*(2*(2^k*x-2*i1+1))^(j-2*i1)/(GAMMA(alpha)*factorial(i1)*factorial(j-2*i1)), i1 = 0 .. floor((1/2)*j))));

`&psi;&psi;`[M*i+j-M+1] := simplify(diff(psi[M*i+j-M+1], x))

end do

end do; r := 2^(k-1)*M;

VV := Vector[column](r, proc (i) options operator, arrow; psi[i] end proc);

DV := Vector[column](r, proc (i) options operator, arrow; `&psi;&psi;`[i] end proc);

``&psi;&psi;`[2] := 8*sqrt((alpha+1)*(1/2))*sqrt(2)*sqrt(alpha*GAMMA(alpha)^2*4^alpha/GAMMA(2*alpha))/sqrt(Pi) = 8*sqrt((alpha+1)*(1/2))*psi[1];

`&psi;&psi;`[3] := 16*sqrt((2+alpha)*(alpha+1)/(1+2*alpha))/sqrt(2)*(2*sqrt(2)*sqrt((alpha+1)*GAMMA(alpha)^2*4^alpha/GAMMA(1+2*alpha))*alpha*(4*x+1)/sqrt(Pi)) = 16*sqrt((2+alpha)*(alpha+1)/(1+2*alpha))*psi[2]/sqrt(2)

I am waiting your response. Thanks

## Define a new matrix...

Dear Users!

Hope you would be fine with everything. I want to define a matrix F of M+1 by M+1 order having element of the following form:

I derived the F[r,s] but confuse who to generate matrix now.

restart; M := 5; printlevel := 3; for r from 2 while r <= M+1 do for s while s <= r-1 do if type(r+s, odd) then F[r, s] := 2^(k+1)*sqrt((2*r-1)*(2*s-1)) end if end do end do

## Generate a matrix and block matrix ...

Dear Users!

Hoped everyone fine with everything. I the following maple expression, I need a matrix A for each n. Like if I take k =1 I want A[1]; if I take k=2, I want A[1], A[2]; for k=3 I want A[1], A[2], A[3] and so on. A[i]'s is square matrix having order M-1 by M-1.

Further I want to generate a block matrix for k. Like for k=1 I want a block matrix as Vector(1, {(1) = A[1]}), for k=2 I want a block matrix as Matrix(2, 2, {(1, 1) = A[1], (1, 2) = 0, (2, 1) = 0, (2, 2) = A[2]}), for k =3 I want a block matrix as Matrix(3, 3, {(1, 1) = A[1], (1, 2) = 0, (1, 3) = 0, (2, 1) = 0, (2, 2) = A[2], (2, 3) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = A[3]}) and so on.

restart; alpha := 1;
k := 2; M := 3;
printlevel := 3;

for n while n <= 2^(k-1) do

for m from 0 while m <= M-1 do

for j from 0 while j <= M-1 do

Omega[m, j] := 2^((1/2)*k)*sqrt(GAMMA(j+1)*(j+alpha)*GAMMA(alpha)^2/(Pi*2^(1-2*alpha)*GAMMA(j+2*alpha)))*(sum((-1)^i*GAMMA(j-i+alpha)*2^(j-2*i)*(sum((1/2)*binomial(m, l)*(2*n-1)^(m-l)*(1+(-1)^(j-2*i+l))*GAMMA((1/2)*j-i+(1/2)*l+1/2)*GAMMA(alpha+1/2)/GAMMA(alpha+1+(1/2)*j-i+(1/2)*l), l = 0 .. m))/(GAMMA(alpha)*factorial(i)*factorial(j-2*i)), i = 0 .. floor((1/2)*j)))/2^(k*(m+1))

end do

end do;

A[n]:=???

end do;

I am waiting for your positive response.

Thanks

## Problem in writing a sigma notation ...

Dear Users!

Hoped everyone is good. I am facing problem to write the following sigma notation for any m.

## Pulling Numeric Values under a Root...

Say I have an expression

ex:=sqrt(x)/2h

what do I tell maple to pull the 2h into the sqrt

sqrt(x/4h^2)

## Problem to find integration...

Dear User!

Hoped you all are fine with everything. I am facing to determinte the integration of the following for n = 0 and for n>=1.

int(2*x^i*(x+n)^m*sqrt(-x^2+x), x = 0 .. 1)

## Problem in define a square matrix...

Dear Users!

Hoped everyone fine with everything! I want to define a square matrix P whose elements are

p[i,j]=<φ[i],ψψ[j]>

printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do varphi[i, j] := t^j end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do phi[M*i+j+1] := varphi[i, j] end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do psi[i, j] := 2^((1/2)*k)*sqrt(2*j+1)*(sum((-1)^(j+i1)*factorial(j+i1)*(2*t-i)^i1/(factorial(j-i1)*factorial(i1)^2), i1 = 0 .. j)) end do end do;
printlevel := 2; for i from 0 while i <= 2^k-1 do for j from 0 while j <= M-1 do `&psi;&psi;`[M*i+j+1] := psi[i, j] end do end do;

take k=2,M=3

## animation of the points in maple ...

Hello Guys, I hope you are all fine. I have been struggling with creating an animation of the points (x,y) in maple. I have tried this example
L := [[1, 1], [3, 2], [3.4, 6], [5, 3, 7], [3, 7, 9, 1], [2, 6, 8, 4, 5]];
animate(PointPlot, [L[trunc(t)]], t = 1 .. 6, frames = 150)
but in my case it shows two points at different location means it takes x and y seperate value and showed it on 1 and 2 on x axis but i want to animate it as the location of point. Please help me.
Thank you in anticipation.