Dear.All

I'm a beginner of Maple 13. 

In MATLAB, there is a command 'sigmaplot' which draw the 'SINGULAR VALUE OF SYSTEM H(jw)' over all frequency range. 

I want to obtain the function of the 'sigmaplot' graph about frequency variable 'w'.

so I defined matrix A,B,C,D in Maple13. 

and specify H like following

H:= Multiply(C,Multiply(Inversematrix(s*IdentityMatrix(8)-A),B))+D              

          --> It is to express H=C*((sI-A)^-1)*B+D that is the state-space matrix of frequency domain form.

and Maple 13 gave me a very long formular expressed by 's'.

Then I try to 'SingularValues' command 

but there came up 'Error Message : Error. (in content/polynom) general case of floats not handled'

I couldn't resolve this problem.... 

So I'm requesting your advice like this.

Could you give some advice ? 

I wnat to print the polar that contain a part of loops,but it always contains all loops.

how do I solve this preblem?

Any one can help me,please?

Hi all,

I try  to plot phase portrait the below DAEs, 

diff(S(t), t)=-β*(1+δ*sin2Πt)*S(t)*I(t)-μ*S(t)+μ,

diff(I(t), t)=β*(1+δ*sin2Πt)*S(t)*I(t)-γ*I(t)-μ*I(t),

0=S(t)+I(t)+R(t)-1.

where

μ=0.01,

β=1510,

δ=0.02,

γ=50,

I really appreciate your help.

Hi,

  I have a loop code, such as

****

i_max:=10;

for i from 1 to i_max do
  blah blah blah

end do;

****

  I would like to clean memory, something like restart suppose to do, after each cycle. Restart could only work at top level. How should I do to clean memory after each cycle?

Dear all,

It's very convenient to define a DE or PDE through Differential Operator D, for example,

((D[1, 1]+D[1, 2]+D[2, 2])(z))(x, y) = exp(x)*sin(y)

Is it possible to realize Inverse Operator Method of Operator D? How to solve the following equation if we rewrite the pde through inverse operator method?

(z)(x, y)=((D[1, 1]+D[1, 2]+D[2, 2])^(-1))exp(x)*sin(y)

Thanks a lot.

When I try to export my data from a spreadsheet to Excel, instead of numbers I get a long text containing numbers. For example instead of having just "11625.7677908435" I get "Typesetting:-mprintslash([11625.7677908435], [HFloat(11625.767790843516)])". 

I want to get numerical solution of the Eqs.ode(see the folowlling ode and ibc）in Maple.However,when i run the following procedure,it prompts an error "Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution". How to solve the issue? Please help me.

restart:
n := 1.4; phi := 1; beta := .6931; psi := 1

> restart;
> n := 1.4; phi := 1; beta := .6931; psi := 1;

> s := proc (x) options operator, arrow; evalf(1+(phi*exp(beta*psi)*h(x))^n) end proc;

> Y := proc (x) options operator, arrow; evalf(f-(1/2-(1/2)/n)*ln(s(x))+2*ln(1-(1-s(x))^(-1+1/n))) end proc;

> ode := diff(h(x), `$`(x, 2))+(diff(Y(x), x))*(diff(h(x), x)+1) = 0;


> ibc := h(0) = 0, ((D(h))(10)+1)*s(10)^(-(1-1/n)*(1/2))*(1-(1-1/s(10))^(1-1/n))^2 = 0;

> p := dsolve({ibc, ode}, numeric);
Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution
>

Hi Maple friends.

expand( (a+b)^2 );

a^2+2*a*b+b^2

expand( (a+b)^3 );

a^3+3*a^2*b+3*a*b^2+b^3

expand( (a+4)^4 )

a^4+16*a^3+96*a^2+256*a+256 (???)

Pascal's triangle shows that 'expand( (a+4)^4 )' should have resulted in a^4+4*a^3*b+6*a^2*b^2+4*a*b^3+b^4

Where are the b variables in Maple's solution?

Thanks in advance.

Hi, I would like to know if there is a command on Maple 18 that can show all the decompositions of a given symbolic tensor.

Hallo,

how can I  construct a Permutationgroup with given GroupOrder and Degree.

for instance: GroupOrder 12 and Degree 5, I found by accident

G:=<(1,2,3),(1,5,2)>

Best Regards

Kurt Ewald

As I am trying to solve this integration:

restart; with(linalg); with(stats); with(plots); with(Statistics); with(LinearAlgebra); with(Optimization);
lambda0 := proc (t) options operator, arrow; gamma0+gamma1*t+gamma2*t^2 end proc;
lambda := lambda0(t)*exp(beta*s);
t1 := 145; t3 := 250; t2 := (t1+t3)*(1/2);
s := 1/(273.16+50); s1 := 1/(273.16+t1); s3 := 1/(273.16+t3); s2 := 1/(273.16+t2); gamma0 := 0.1e-3; gamma1 := .5; gamma2 := 0; beta := -3800;
c := 300; n := 200;
Theta := solve(1-exp(-(gamma0*tau1+(1/2)*gamma1*tau1^2+(1/3)*gamma2*tau1^3)*exp(beta*s1)) = 1-exp(-(gamma0*a+(1/2)*gamma1*a^2+(1/3)*gamma2*a^3)*exp(beta*s2)), a);

a := Theta[1];

Delta := solve(1-exp(-(gamma0*(a+tau2-tau1)+(1/2)*gamma1*(a+tau2-tau1)^2+(1/3)*gamma2*(a+tau2-tau1)^3)*exp(beta*s2)) = 1-exp(-(gamma0*b+(1/2)*gamma1*b^2+(1/3)*gamma2*b^3)*exp(beta*s3)), b);

b := Delta[1];

A1 := `assuming`([unapply(int(exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma0+gamma1*t+gamma2*t^`2`), t = N .. M), N, M)], [N > 0, M > 0]);
A2 := unapply(int(exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
A3 := unapply(int(exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);
B1 := `assuming`([unapply(int(t^2*exp(beta*s1)*exp(-(gamma0*t+(1/2)*gamma1*t^2+(1/3)*gamma2*t^3)*exp(beta*s1))/(gamma2*t^2+gamma1*t+gamma0), t = N .. M), N, M)], [N > 0, M > 0]);
B2 := unapply(int((a+t-tau1)^2*exp(beta*s2)*exp(-(gamma0*(a+t-tau1)+(1/2)*gamma1*(a+t-tau1)^2+(1/3)*gamma2*(a+t-tau1)^3)*exp(beta*s2))/(gamma0+gamma1*(a+t-tau1)+gamma2*(a+t-tau1)^2), t = N .. M), N, M);
B3 := unapply(int((b+t-tau2)^2*exp(beta*s3)*exp(-(gamma0*(b+t-tau2)+(1/2)*gamma1*(b+t-tau2)^2+(1/3)*gamma2*(b+t-tau2)^3)*exp(beta*s3))/(gamma0+gamma1*(b+t-tau2)+gamma2*(b+t-tau2)^2), t = N .. M), N, M);

F0 := A1(0, tau1)+A2(tau1, tau2)+A3(tau2, c);
F1 := B1(0, tau1)+B2(tau1, tau2)+B3(tau2, c);

NLPSolve(1/(n^3*(F0*F1-F1)), tau1 = 115 .. 201, tau2 = 237 .. 273);

I need to have tau1 tau2 as varibles to get there optimal values ..

But this error keeps coming :

Error, (in Optimization:-NLPSolve) integration range or variable must be specified in the second argument, got HFloat(1.0) = HFloat(158.0) .. HFloat(255.0)

Please Help ..

I am a problem with solve differential equation, please help me: THANKS 

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

              Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
                                   Error, (in dsolve) too many levels of recursion

I DONT KNOW ABOUT THIS ERROR

PLEASE HELP ME

THANKS A LOT

what conditions are necessary that a group G has stabilisers?

How can I get the Automorphism Group of a group G as a Permutationgroup?

Best regards

Kurt Ewald

Hello,

this is the second time I'm writing.

I posted this question in June http://www.mapleprimes.com/questions/201781-System-Of-Parametric-Equations.

This time I have  a similar problem because I'm trying to find a solution for a parametric system of equations but the number of equations and parameters is much bigger and using the tips you gave me last time I couldn't reach any result.

Here is the system:

1) alpha[1]=v*a*u*b ;
2) alpha[2]=v*a*u*(1-b);
3) alpha[3]= v*z*c*(1-a) ;
4) alpha[4]=v*z*(1-a)*(1-c) ;
5) alpha[11]=1/2*v*a* u* b* (-p*u*b+p*u*b*a+b*g-g);
6) alpha[22]=1/2*v*a*u*(1-b)* (p u b-p u b a-b g-p u+p u a);
7) alpha[33] =1/2*v*c*z*(1-a)* (c* (-z*p*a+q)-q);
8) alpha[44]=1/2*v*z*((1-a)*(1-c)* (c*z*p*a-z*p*a-q*c);
9) alpha[12]=v*a*u*b*(1- b)*(-p*u+p*u*a+g) ;
10) alpha[13]=v*a*u*b*z*c*p*(1-a) ;
11) alpha[14]=a*u*b*z*(1-a)*(1-c) ;
12) alpha[23]=a*u*z*c*(1-a)*(1-b);
13) alpha[24]=v*a*u*z*p*(1-a)*(1-b)*(1-c);
14) alpha[34]= v*c*z*(1-a)*(1-c)*(-z*p*a+q);

I have 14 equations/unknowns and 8 parameters (a, b, c, u, v, z, p, q).

I would like to write this system only in terms of alphas. In order to do so, I usually try to find the value for the parameters and the substitute them into the equations (and I have already found b,c,g,q using this technique) but I couldn't manage to find all of them. 

Howveer, as you suggested me, with Maple there is the command "eliminate" that implement exactly what I'm looking for but I can't make it work.

This is my code:

> sys := {alpha[1] = v*a*u*(1-b), alpha[2] = v*a*u*b, alpha[3] = v*z*c*(1-a), alpha[4] = v*z*(1-a)*(1-c), alpha[11] = (1/2)*v*a*u*(1-b)*(p*u*b-p*u*b*a-b*g-p*u+p*u*a), alpha[12] = v*a*u*b*(1-b)*(-p*u+p*u*a+g), alpha[13] =      z*c*a*u*(1-a)*(1-b), alpha[14] = v*z*a*u*p*(1-a)*(1-b)*(1-c), alpha[22] = (1/2)*v*a*u*b*(-p*u*b+p*u*b*a+b*g-g), alpha[23] = v*z*c*a*u*b*p*(1-a), alpha[24] = z*a*u*b*(1-a)*(1-c), alpha[33] = (1/2)*v*c*z*(1-a)*(c*(-z*p*a+q)-q), alpha[34] = v*c*z*(1-a)*(1-c)*(-z*p*a+q), alpha[44] = (1/2)*v*z*(1-a)*(1-c)*(c*z*p*a-z*p*a-q*c)};

> eliminate(sys, {a,b,c, p, q, u, v, z});

> simplify(%, size);

I also tries to substitute in the system the four parameters I already found but still I can't find a solution.

What am I doing wrong? Or the problem is that it is too complicated?

Thank you for your attention,

Elena