Hi. I am trying to identify mode shapes (phi(x)) and natural frequencies  of non-uniform euler-bernoulli beam. There are number of numerical methods to solve ODE with certain boundary conditions (i.e. Runge Kutta method). Problem is that I am newbie here. I am interested in particularly first vibration mode and its frequency. Is there anyone acquainted with it and would be able to help me?  Non-unif.mw

Hi,

Since i already have a working eclipse environment, I want to ask whether Maple IDE is available as an Eclipse Plugin. Also is there any trial version available. Is it possible to use Maple IDE with maple worksheet environment so for example i prepare a document inside maple and write codes procedures separately in maple IDE file and call them where ever i want inside the worksheet. Also what file format Maple IDE supports (Sorry the only files in maple i have used is .mw). Moreover can i use Maple IDE without relying on maple worksheet enviroment in other words is maple graphics (like plots viewable in Maple IDE like for R programming Language, R Eclipse Plugin has graphics section inside eclipse as well).

Thanks

I am writing a big numerical code in maple. I need to write the results in each step in a file. I mean in the first step of loop it writes the results in the first line of a text file, in the second step writes in the second line and to the end. when I use writedata command, it needs to write a complete array or matrix and it is not what i need. In  other words I want to save data for each steps of iteration during the calculation and when it goes to ther next step it writes the result in the next line.

Can you help me to perform it?

Thanks

I am trying to find out the stiffness matrix of composite by using iterative loop that sums over each laminate and adds the result to the previously calculated matrix 

D=null matrix

for i to 4 do Dply := evalf(evalm((1/3)*Q[i]*(z(i+1)^3-z(i)^3))); D := evalm(D+Dply) end do;
evalm(D);

although the values are coming out fine but in the diagonalm elements, it shows the true value + _rtable[4456495426] which I am not able to figure out why is it coming?

hi,

I want to solve this to data table , i can plot but i need data in table 

sol1 := dsolve([diff(u(theta),theta) = 427.2461*u(theta)+385620.123/u(theta)-25671.3871, u(0) = .6], numeric);

plots[odeplot](sol1, 0..0.18, color = red);

thanks.

how i can trust in DirectSearch solution result.is there any creteria?

my variable is intensity.

this is my code:

ep0 := 1/(4*3.14); el := 8.54*10^(-2); hbar := 1; vf := 1/300; kb := 1; tem := 2.586*10^(-2); ci := 1; p := 1.458*10^16; beta := 2; ai := 7.1*10^(-4); bi := ai/sqrt(3); enph := .196; d := enph/(kb*tem); n0 := 1/(exp(enph/(kb*tem))-1); gama := hbar*vf; intensity := 10000001; w := 1.55; impurity := 7.2*10^3;

g := hbar*beta/(bi^2*sqrt(2*p*enph)); aa := g^2*(n0+1)/(2*Pi*hbar*gama^2); bb := g^2*n0/(2*Pi*hbar*gama^2); cc := 2/(Pi*gama^2); l := (1*hbar)*w/(2*kb*tem);u := el^2*intensity/(32*w*hbar^2);

DirectSearch:-SolveEquations([op([((enph*ln(1+exp(c+enph/(kb*tem)))/(kb*tem)-polylog(2, -exp(c))+polylog(2, -exp(c+enph/(kb*tem))))*enph*(kb*tem)^2-(enph^2*ln(1+exp(c+enph/(kb*tem)))/(kb^2*tem^2)+2*enph*polylog(2, -exp(c+enph/(kb*tem)))/(kb*tem)+2*polylog(3, -exp(c))-2*polylog(3, -exp(c+enph/(kb*tem))))*(kb*tem)^3+(-exp(b)*enph*ln(1+exp(c+enph/(kb*tem)))+exp(c+d)*enph*ln(1+exp(b-d+enph/(kb*tem)))+exp(b)*kb*tem*polylog(2, -exp(c))-exp(c+d)*kb*tem*polylog(2, -exp(b-d))-exp(b)*kb*tem*polylog(2, -exp(c+enph/(kb*tem)))+exp(c+d)*kb*tem*polylog(2, -exp(b-d+enph/(kb*tem))))*enph*(kb*tem)^2/((exp(b)-exp(c+d))*kb*tem)+(exp(b)*enph^2*ln(1+exp(c+enph/(kb*tem)))-exp(c+d)*enph^2*ln(1+exp(b-d+enph/(kb*tem)))+2*exp(b)*enph*kb*tem*polylog(2, -exp(c+enph/(kb*tem)))-2*exp(c+d)*enph*kb*tem*polylog(2, -exp(b-d+enph/(kb*tem)))+2*exp(b)*kb^2*tem^2*polylog(3, -exp(c))-2*exp(c+d)*kb^2*tem^2*polylog(3, -exp(b-d))-2*exp(b)*kb^2*tem^2*polylog(3, -exp(c+enph/(kb*tem)))+2*exp(c+d)*kb^2*tem^2*polylog(3, -exp(b-d+enph/(kb*tem))))*(kb*tem)^3/((exp(b)-exp(c+d))*kb^2*tem^2))*bb+u*(1/(1+exp(-l-c))-1/((1+exp(-l-c))*(1+exp(l-b))))-(((1*enph)*(enph-2*kb*tem*ln(1+exp(-b+enph/(kb*tem))))/(2*kb^2*tem^2)+2*kb^2*tem^2*(-polylog(2, -exp(-b+enph/(kb*tem)))+polylog(2, -cosh(b)+sinh(b))))*enph*(kb*tem)^2-(enph^2*(enph-3*kb*tem*ln(1+exp(-b+enph/(kb*tem))))-6*kb^2*tem^2*(enph*polylog(2, -exp(-b+enph/(kb*tem)))+kb*tem*(-polylog(3, -exp(-b+enph/(kb*tem)))+polylog(3, -cosh(b)+sinh(b)))))*(kb*tem)^3/(3*kb^3*tem^3)-(-exp(b)*enph^2+exp(c+d)*enph^2-2*exp(c+d)*enph*kb*tem*ln(1+exp(-b+enph/(kb*tem)))+2*exp(b)*enph*kb*tem*ln(1+exp(-c-d+enph/(kb*tem)))+2*exp(c+d)*kb^2*tem^2*polylog(2, -exp(-b))-2*exp(b)*kb^2*tem^2*polylog(2, -exp(-c-d))-2*exp(c+d)*kb^2*tem^2*polylog(2, -exp(-b+enph/(kb*tem)))+2*exp(b)*kb^2*tem^2*polylog(2, -exp(-c-d+enph/(kb*tem))))*enph*(kb*tem)^2/((2*(-exp(b)+exp(c+d)))*kb^2*tem^2)-(exp(b)*enph^3-exp(c+d)*enph^3+3*exp(c+d)*enph^2*kb*tem*ln(1+exp(-b+enph/(kb*tem)))-3*exp(b)*enph^2*kb*tem*ln(1+exp(-c-d+enph/(kb*tem)))+6*exp(c+d)*enph*kb^2*tem^2*polylog(2, -exp(-b+enph/(kb*tem)))-6*exp(b)*enph*kb^2*tem^2*polylog(2, -exp(-c-d+enph/(kb*tem)))+6*exp(c+d)*kb^3*tem^3*polylog(3, -exp(-b))-6*exp(b)*kb^3*tem^3*polylog(3, -exp(-c-d))-6*exp(c+d)*kb^3*tem^3*polylog(3, -exp(-b+enph/(kb*tem)))+6*exp(b)*kb^3*tem^3*polylog(3, -exp(-c-d+enph/(kb*tem))))*(kb*tem)^3/((3*(-exp(b)+exp(c+d)))*kb^3*tem^3))*aa-u*(1/(1+exp(l-b))-1/((1+exp(-l-c))*(1+exp(l-b)))) = 0, -cc*polylog(2, -exp(b))+cc*polylog(2, -exp(-c))-impurity = 0])], tolerances = 10^(-8), evaluationlimit = 20000)

Can someone please advise me how to solve the following for 'beta'. Solve function is not able to do that, or at least I dont know how.

-9999990000000000000000*cos(166*beta)*sinh(166*beta)*cosh(88*beta)^2-9999990000000000000000*cos(88*beta)^2*sin(166*beta)*cosh(166*beta)+9999990000000000000000*sinh(166*beta)*cos(88*beta)^2*cos(166*beta)+9999990000000000000000*cosh(88*beta)^2*cosh(166*beta)*sin(166*beta)+10000010000000000000000*cos(166*beta)*sinh(166*beta)+10000010000000000000000*sin(166*beta)*cosh(166*beta)+9999990000000000000000*sinh(88*beta)*cos(166*beta)*cosh(166*beta)*cosh(88*beta)-9999990000000000000000*sinh(88*beta)*sin(166*beta)*sinh(166*beta)*cosh(88*beta)+9999990000000000000000*sin(88*beta)*cos(88*beta)*sinh(166*beta)*sin(166*beta)+9999990000000000000000*cos(88*beta)*cos(166*beta)*sin(88*beta)*cosh(166*beta)-9980010000000000000000*cosh(88*beta)^2*sinh(166*beta)*cos(88*beta)^2*cos(166*beta)-9980010000000000000000*cosh(88*beta)^2*cosh(166*beta)*sin(166*beta)*cos(88*beta)^2+9980010000000000000000*sinh(88*beta)*cos(88*beta)^2*sin(166*beta)*sinh(166*beta)*cosh(88*beta)-9980010000000000000000*cos(88*beta)*cosh(88*beta)^2*sin(88*beta)*sin(166*beta)*sinh(166*beta)+9980010000000000000000*sinh(88*beta)*cosh(88*beta)*cosh(166*beta)*cos(88*beta)^2*cos(166*beta)+9980010000000000000000*cosh(88*beta)^2*cosh(166*beta)*cos(88*beta)*sin(88*beta)*cos(166*beta)-9980010000000000000000*cos(88*beta)*sinh(88*beta)*cos(166*beta)*sin(88*beta)*sinh(166*beta)*cosh(88*beta)+9980010000000000000000*cos(88*beta)*cosh(88*beta)*sin(88*beta)*sin(166*beta)*cosh(166*beta)*sinh(88*beta)=0

Is it within the Physics environment possible to specify two sets, A and B, say, of quantities for which the following holds?

1.) any two elements of A anticommute,

2.) any two elements of B anticommute (as well), but

3.) any quantity from A commutes (not anticommutes) with any quantity from B.

hi 

i want clear ss variable but i can not do it please help me.

my code:

restart;

a := Matrix([1, 2, 3, 4, 5]); S := {}; ss := {};

for k to 5 do

S := `union`(S, {op(DirectSearch:-SolveEquations([a(1, k)*x+2+y = 0, x+y = 0])[3])});

ss := map(proc (c) options operator, arrow; rhs(c) end proc, S);

aaa := op(ss[[1]]); bbb := op(ss[[2]]);

"i want clear ss and then make ss as ss:={} in loop"

"for example if clear command clear ss variable"

"clear(ss)"

"ss:={}"

end do

Does there exist a Frobenius Group which is not  neither a Dihedralgroup nor  Symm(3) ?

Best regards

Kurt Ewald

Hello those in Mapleprimes,

What I want to know is whether this is possible or not, and if possible, how should I write a code?

The following code works properly:

U:=(x,y)->(x^theta+y^theta+X)^(1/theta);

diff(U(x,y),x)/diff(U(x,y),y)=p/q;simplify(%);

But, what I want to ask is this. As for the part of simplify(%), I want to do it with a way which has me 

feel more being from the former to latter.

That is, if ,for example, "diff(U(x,y),x)/diff(U(x,y),y)=p/q;@simplify;" works, it is better to me, though this does not work.

As the second part, @simplify, receives the result of the first part"diff(U(x,y),x)/diff(U(x,y),y)", it seems more 

natural to me than to write simplify(%).

Can't I do this, in a meaning, reversal of operator to argument?

taro

Hello,
I have a system of first order diff. equations which I would like to solve symbolically. Unfortunately, Maple does not solve the system. Do anybody have suggestions how can I solve this system (please see below):

diff(S(t), t) = -eta*(C[max]*w*N-alpha*Q(t))*K(t)*S(t)/(w*N*(S(t)+K(t))),

diff(K(t), t) = S(t)*((z*eta*alpha*(C[max]*w*N-alpha*Q(t))*S(t)-upsilon*(eta*alpha^2*Q(t)^2-2*C[max]*w*N*eta*alpha*Q(t)+((-N*w+z)*alpha+N*C[max]^2*w*eta)*N*w))*K(t)^2+(2*((1/2)*z*eta*(C[max]*w*N-alpha*Q(t))*S(t)+N*w*upsilon*(N*w-z)))*S(t)*alpha*K(t)+N*S(t)^2*w*alpha*upsilon*(N*w-z))/((K(t)^2*alpha*z+3*S(t)*K(t)*alpha*z+S(t)*(2*S(t)*z*alpha+upsilon*(C[max]*w*N-alpha*Q(t))))*(S(t)+K(t))*N*w),

diff(Q(t), t) = (-alpha*z*(z*eta*(C[max]*w*N-alpha*Q(t))*K(t)+N*w*upsilon*(N*w-z))*S(t)^2+(-z^2*eta*alpha*(C[max]*w*N-alpha*Q(t))*K(t)^2-(eta*alpha^2*Q(t)^2-2*C[max]*w*N*eta*alpha*Q(t)+N*w*((2*N*w-2*z)*alpha+N*C[max]^2*w*eta))*z*upsilon*K(t)-N*w*upsilon^2*(N*w-z)*(C[max]*w*N-alpha*Q(t)))*S(t)-N*w*z*alpha*upsilon*K(t)^2*(N*w-z))/((2*S(t)^2*alpha*z+(3*z*alpha*K(t)+upsilon*(C[max]*w*N-alpha*Q(t)))*S(t)+K(t)^2*alpha*z)*N*w*upsilon)

where initials conditions are:

S(0) = S0, K(0) = K0, Q(0) = Q0

Thanks,

Dmitry

Hello those in Mapleprimes,

I want to know whether there is a good way to modify the first expression to the second one below.

first expression: 

> p+p^(-1/(theta-1))*sum(q[i]^(theta/(theta-1)), i = (1 .. n));

second expression:

> p^(-1/(theta-1))*(p^(theta/(theta-1))+sum(q[i]^(theta/(theta-1)),i=1..n));

First and Second are the same. But, I want to know how I can modify from the former to the latter.

Thank you in advance.

taro

Let us consider the expression

restart;
f := log[x](1+(x^a-1)*(x^b-1)/(x-1));
Does it define a convex function on the interval 0..1 and on the interval 1..infinity if the parameters a>0, a< 1, b >0, b <1?

My try is

and

.

At the same time I have got problems in the general case. For example,

Error, (in @) too many levels of recursion

and

That's all right if

convex.mw

very slow cause my computer have sound and overheat, still can not 

calculated result

%c := Old_Asso_eigenvector1, a := Old_Asso_eigenvector3,

%b := Old_Asso_eigenvector2

% b <= c, a <= c,

% a ^ c = a, a V c = c

% b ^ c = b, b V c = c

restart;
with(ExcelTools):
with(ListTools):
with(DynamicSystems):
filename := "1207.HK";
open3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "B2:B100");
high3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "C2:C100");
low3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "D2:D100");
close3 := Import(cat(cat("C://Temp//HK//Coal//",filename),".xls"), filename, "E2:E100");
with(CurveFitting):
n := 31;
f := Vector(n);
f2 := Vector(n);
open2 := Vector(n);high2 := Vector(n);gain2 := Vector(n);algebra2 := Vector(n);creative2 := Vector(n);creative3 := Vector(n);
upper2 := Vector(n);lower2 := Vector(n);upperloweratio := Vector(n);
deltaopen2 := Vector(n); deltahigh2 := Vector(n); deltalow2 := Vector(n); deltaclose2 := Vector(n);
logn := Vector(n);
for i from 0 to n-4 do
open2[i+1] := PolynomialInterpolation([[0,open3[n-i][1]],[1,open3[n-(i+1)][1]],[2,open3[n-(i+2)][1]],[4,open3[n-(i+3)][1]]],t):
high2[i+1] := PolynomialInterpolation([[0,high3[n-i][1]],[1,high3[n-(i+1)][1]],[2,high3[n-(i+2)][1]],[4,high3[n-(i+3)][1]]],t):
low2[i+1] := PolynomialInterpolation([[0,low3[n-i][1]],[1,low3[n-(i+1)][1]],[2,low3[n-(i+2)][1]],[4,low3[n-(i+3)][1]]],t):
if (close3[i+1][1]/close3[i+2][1]-1) < 0 then
gain2[i+1] := -1*round(100*abs(close3[i+1][1]/close3[i+2][1]-1)):
else
gain2[i+1] := round(abs(100*(close3[i+1][1]/close3[i+2][1]-1))):
end if;
deltaclose2[i+1] := close3[i+1][1] - close3[i+2][1];
deltahigh2[i+1] := high3[i+1][1] - high3[i+2][1];
deltaopen2[i+1] := open3[i+1][1] - open3[i+2][1];
logn[i+1] := ln(close3[i+1][1]/close3[i+2][1]);
f[i+1] := (high2[i+1] - open2[i+1])/4*1.8:
f2[i+1] := (open2[i+1] - low2[i+1])/4*1.8:
creative2[i+1] := simplify(((((close3[i+1][1]-close3[i+2][1]) + x)^2 -(close3[i+1][1]-close3[i+2][1])^2))/x)-x;
creative3[i+1] := simplify(((((close3[i+1][1]-close3[i+2][1]) + x)^3 -(close3[i+1][1]-close3[i+2][1])^3))/x);
upper2[i+1] := high3[i+1]-close3[i+1];
lower2[i+1] := close3[i+1]-low3[i+1];
upperloweratio[i+1] := round((lower2[i+1]/upper2[i+1])[1]);
od;
with(LinearAlgebra):
HilbertConj := proc(Px,Py)
return MatrixMatrixMultiply(Px,Py);
end proc:
HilbertDisj := proc(Px,Py)
return Px+Py- MatrixMatrixMultiply(Px,Py);
end proc:

t:=1;
i := 0;
InputMatrix3 := Matrix([[xxx, close3(t+1+i) , close3(t+2+i)],
[close3(t+1+i) , close3(t+2+i),0],
[close3(t+2+i),0 , 0]]):
InputMatrix3b := Matrix([[close3(t+1+i), close3(t+2+i) , close3(t+3+i)],
[close3(t+2+i) , close3(t+3+i),0],
[close3(t+3+i),0 , 0]]):
InputMatrix3c := Matrix([[close3(t+2+i), close3(t+3+i) , close3(t+4+i)],
[close3(t+3+i) , close3(t+4+i),0],
[close3(t+4+i),0 , 0]]):
m := MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3);
eigenvalues1 := Eigenvalues(m);
sys1 := MatrixMatrixMultiply(m-Matrix([[eigenvalues1[1],0,0],[0,eigenvalues1[1],0],[0,0,eigenvalues1[1]]]), Matrix([[x],[y],[z]]));
%solve([sys1[1][1],sys1[2][1],sys1[3][1]], [x,y,z]);
sol1 := solve([sys1[1][1],sys1[2][1]], [x,y,z]);

sys2 := MatrixMatrixMultiply(m-Matrix([[eigenvalues1[2],0,0],[0,eigenvalues1[2],0],[0,0,eigenvalues1[2]]]), Matrix([[x],[y],[z]]));
%solve([sys2[1][1],sys2[2][1],sys2[3][1]], [x,y,z]);
sol2 := solve([sys2[1][1],sys2[2][1]], [x,y,z]);

sys3 := MatrixMatrixMultiply(m-Matrix([[eigenvalues1[3],0,0],[0,eigenvalues1[3],0],[0,0,eigenvalues1[3]]]), Matrix([[x],[y],[z]]));
%solve([sys3[1][1],sys3[2][1],sys3[3][1]], [x,y,z]);
sol3 := solve([sys3[1][1],sys3[2][1]], [x,y,z]);

Old_Asso_eigenvector1 := Matrix([[rhs(sol1[1][1]),rhs(sol2[1][1]),rhs(sol3[1][1])],[rhs(sol1[1][2]),rhs(sol2[1][2]),rhs(sol3[1][2])],[rhs(sol1[1][3]),rhs(sol2[1][3]),rhs(sol3[1][3])]]);
Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)):
Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)):

% b <= c, a <= c, c := Old_Asso_eigenvector1, a := Old_Asso_eigenvector3, b := Old_Asso_eigenvector2
testa := HilbertConj(Old_Asso_eigenvector3[2], Old_Asso_eigenvector1);
testb := HilbertDisj(Old_Asso_eigenvector3[2], Old_Asso_eigenvector1);
testc := HilbertConj(Old_Asso_eigenvector2[2], Old_Asso_eigenvector1);
testd := HilbertDisj(Old_Asso_eigenvector2[2], Old_Asso_eigenvector1);

sysa := testa[1][1] = Old_Asso_eigenvector3[2][1][1];
sysb := testb[1][1] = Old_Asso_eigenvector1[2][1][1];
sysc := testc[1][1] = Old_Asso_eigenvector2[2][1][1];
sysd := testd[1][1] = Old_Asso_eigenvector1[2][1][1];

solve(sysa, xxx);