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Hi all

I have a mathematical problem and I asked it in various sites but the answers till yet are not correct.

Assume that we have:

T[m]:=t->t^m:
b[n,m]:=unapply(piecewise(t>=(n-1)*tj/N and t<n*tj/N, T[m](N*t-(n-1)*tj), 0), t):

where n,N,tj are known constants. furthermore assume that we want to comute the following integral:

for following approximations:

I have written the following code but it seems to be incorrect:

V1:=Vector([seq(seq(b[n,m](t),m=0..1),n=1..3)]);
V:=evalf(V1.Transpose(V1));

the original program is :

taaylor.mws

I will be so grateful if any one can help me to solve it by maple

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Basically I have to find omega by solving determinant of the following matrix:

M := Matrix(4, 4, {(1, 1) = 0, (1, 2) = -1, (1, 3) = 0, (1, 4) = 1, (2, 1) = -EI*beta^3, (2, 2) = -m*omega^2, (2, 3) = EI*beta^3, (2, 4) = -m*omega^2, (3, 1) = EI*sin(147*beta)*beta+k_r*cos(147*beta)+I*c_r*omega*cos(147*beta), (3, 2) = EI*cos(147*beta)*beta-k_r*sin(147*beta)-I*c_r*omega*sin(147*beta), (3, 3) = -EI*sinh(147*beta)*beta+k_r*cosh(147*beta)+I*c_r*omega*cosh(147*beta), (3, 4) = -EI*cosh(147*beta)*beta+k_r*sinh(147*beta)+I*c_r*omega*sinh(147*beta), (4, 1) = -EI*cos(147*beta)*beta^3+sin(147*beta)*k_h, (4, 2) = EI*sin(147*beta)*beta^3+cos(147*beta)*k_h, (4, 3) = EI*cosh(147*beta)*beta^3+sinh(147*beta)*k_h, (4, 4) = EI*sinh(147*beta)*beta^3+cosh(147*beta)*k_h}):

The remaining values are:

beta=((5000/10^12)*(omega^2))^(1/4),k_r=3.33*10^10,k_h=1.62*10^9,c_r=3.14*10^9,m=350000,L=147,EI=10^12:

What is the proper way to deal with this problem numerically. Or maybe it is even possible to get a reasonable analytical expression?

hello, I put in the code:

> with(plots), with(ColorTools), with(LinearAlgebra), with(RandomTools), with(ExcelTools);
> A := `<|>`(`<,>`(1, 2, 0, 2, 3, 4, 3, 4, 7, 9, 5, 3, 4, 6, 7, 8, 3), `<,>`(0, 4, 7, 2, 2, 2, 4, 5, 6.5, 7, 5, 3, 2, 5, 9, 0, 1), `<,>`(1, 5, 2, 0, 4, 1, 2, 3, 4.3, 7, 8, 5, 3, 2, 9, 6, 4)); J := convert(Import("testB1.xlsx", "Cartesian", "E2:G18"), matrix);
Error, (in convert/matrix) expecting array, rtable or list
> B := matrix([[1], [.2], [.1], [.8], [.5], [.6], [.8], [.764], [.234], [0.4e-1], [.89], [.36], [.687], [.627], [.689], [.328], [.139]]); H := convert(Import("test.xlsx", "Cartesian", "D2:D18"), matrix);
Error, (in convert/matrix) expecting array, rtable or list
> C := [seq(Color([H[i, 1], 0, 0]), i = 1 .. RowDimension(A))];

 

And i get the error message everytime I try import m data list and I dont understand why. Any help would be appreciated. Thank you

 

Jennifer

Can someone please help me to find first 5 coplex valued roots of the followind expression:

Frequency_Equation := -(2.220315292*10^21*I)*csgn(omega)*omega^4*sin(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))-2.354665581*10^22*csgn(omega)*omega^3*sin(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))-2.354665581*10^22*sinh(1.236117731*(omega^2)^(1/4))*csgn(omega)*omega^3*cos(1.236117731*(omega^2)^(1/4))-6.415296703*10^25*(omega^2)^(3/4)*cos(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))-2.177438228*10^22*cosh(1.236117731*(omega^2)^(1/4))*(omega^2)^(3/4)*omega^2*cos(1.236117731*(omega^2)^(1/4))-5.946035576*10^21*omega^2*(omega^2)^(3/4)-6.415296702*10^25*(omega^2)^(3/4)-(3.560760000*10^24*I)*sinh(1.236117731*(omega^2)^(1/4))*omega^3*cos(1.236117731*(omega^2)^(1/4))+(3.560760000*10^24*I)*cosh(1.236117731*(omega^2)^(1/4))*omega^3*sin(1.236117731*(omega^2)^(1/4))-(2.613877239*10^21*I)*cosh(1.236117731*(omega^2)^(1/4))*(omega^2)^(3/4)*omega^3*cos(1.236117731*(omega^2)^(1/4))-(6.049258752*10^24*I)*(omega^2)^(3/4)*omega-1.907153069*10^25*sinh(1.236117731*(omega^2)^(1/4))*omega^2*sin(1.236117731*(omega^2)^(1/4))*(omega^2)^(1/4)-(2.220315292*10^21*I)*sinh(1.236117731*(omega^2)^(1/4))*csgn(omega)*omega^4*cos(1.236117731*(omega^2)^(1/4))-(6.049258753*10^24*I)*(omega^2)^(3/4)*cos(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))*omega-3.500000000*10^21*cosh(1.236117731*(omega^2)^(1/4))*omega^4*sin(1.236117731*(omega^2)^(1/4))+3.500000000*10^21*sinh(1.236117731*(omega^2)^(1/4))*omega^4*cos(1.236117731*(omega^2)^(1/4))-2.156220000*10^25*sinh(1.236117731*(omega^2)^(1/4))*omega^2*cos(1.236117731*(omega^2)^(1/4))+2.156220000*10^25*cosh(1.236117731*(omega^2)^(1/4))*omega^2*sin(1.236117731*(omega^2)^(1/4));

Hi all

Assume that we have construct new orthogonal Hybrid function of block pulse and bernstein poly nomials as follow:

and assume that we want to approximate a function as follows:

 

how can we do this with maple????Indeed we want to optimize using this hybrid functions

note that the degree of bernstein polynomials is fix or should be fixed...and

regards

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi,

I have the a code with some parameters including

Nr= 0, 50, 100

Ha=0, 5, 10

EPSILONE= 0, 0.5, 1

Phiavg= 0.02, 0.06, 0.1

0.1<NBT<10

I can give the solution for higher values of 5<NBT<10 and there is no problem. However, As I reduce the values of NBT, the convergence of the problem is hard. for some values of parameters I cannot find the solution. for example:

Nr=Ha=0

EPSILONE=1

Phiavg=0.06

NBT=0.3

 

I would be most grateful if you can tel me how change the algorithm to find the solution in the range of all parameters.

Many thanks for your attentions in advance

The code has been attached

code_7-8-2014_(1).mw

 

Amir

Here in this work and used as the main topic a short description of electrostatics and electrodynamics using the Explore to model the fundamental laws command.

 Corriente_Eléctrica.mw   (in spanish)

 

Atte.

L. Araujo C.

 

Hi All

Assume that we have:

and the hybrid function with block pulses with the following form:

if we want to introduce this form to maple so that we can do:

then how can we do this????

especially if we want to approximate t or t^2 or sin(3*t) by mentioned form, how maple can help us?

 

thanks a lot for coming answers 

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

Hi,

according to my previous question

http://www.mapleprimes.com/questions/201435-ODE-With-Constraint

I wrote the following code. at first, the code solve the equation for f and when it slves that, I want to solve Theta in such a way that use the values of f in previous calculation. I use the command 'known' but i couldnt find thesolution

I would be most grateful if you could help me in this problem

Thanks for your attentions in advance


restart; # Notice that Restart (capital R) has no effect (to catch that use semicolon, not colon)
a:=0.13:
b:=0.41:
reynolds:=1.125*10^7;  
Eq1:=diff(f(x),x$3)+diff(f(x),x$2)*f(x)+b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)^2*x^2,x$1);
Eq2:=diff(g(x),x$3)+diff(g(x),x$2)*g(x)+c*a^2*sqrt(2*reynolds)*diff(diff(g(x),x$2)^2*x,x$1);
eq1:=isolate(Eq1,diff(f(x),x,x,x));
eq2:=subs(g=f,isolate(Eq2,diff(g(x),x,x,x)));
EQ:=diff(f(x),x,x,x)=piecewise(x<c*0.1,rhs(eq1),rhs(eq2));


c:=75:
;
Q:=proc(pp2) local res,F0,F1,F2;
print(pp2);
if not type(pp2,numeric) then return 'procname(_passed)' end if:
res:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=pp2},numeric,output=listprocedure);
F0,F1,F2:=op(subs(subs(res),[f(x),diff(f(x),x),diff(f(x),x,x)])):
F1(c)-1;
end proc;


fsolve(Q(pp2)=0,pp2=(0..102));
se:=%;
res2:=dsolve({EQ,f(0)=0,D(f)(0)=0,(D@@2)(f)(0)=se},numeric,output=listprocedure);
G0,G1,G2:=op(subs(subs(res2),[f(x),diff(f(x),x),diff(f(x),x,x)])):

plots:-odeplot(res2,[seq([x,diff(f(x),[x$i])],i=0..2)],0..2); #This plots from and past 0.1*c
pr:=1;
prt:=0.89;

Eq11:=diff(theta(x),x$2)+pr*diff(theta(x),x$1)*f(x)+pr/prt*b^2*sqrt(2*reynolds)*diff(diff(f(x),x$2)*diff(theta(x),x$1)*x^2,x$1);
Eq22:=diff(g(x),x$2)+pr*diff(g(x),x$1)*f(x)+pr/prt*a^2*c*sqrt(2*reynolds)*diff(diff(f(x),x$2)*diff(g(x),x$1)*x^1,x$1);
eq11:=isolate(Eq11,diff(f(x),x,x));
eq22:=subs(g=theta,isolate(Eq22,diff(g(x),x,x)));
EQT:=diff(theta(x),x,x)=piecewise(x<c*0.1,rhs(eq11),rhs(eq22));


QT:=proc(pp3) local res3,theta0,theta1;
print(pp3);
if not type(pp3,numeric) then return 'procname(_passed)' end if:
res3:=dsolve({EQT,theta(0)=1,D(theta)(0)=pp3,known=f},numeric,output=listprocedure);
theta0,theta1:=op(subs(subs(res),[theta(x),diff(theta(x),x)])):
theta0(c);
end proc;

fsolve(QT(pp3)=0,pp3=(0..200));
res3(0);



Amir

We know that the set f:={(1,2),(2,a),(3,b)} can introduce a function from {1,2,3} to {2,a,b}. I want Maple to know f as a function. Is this job possible at Maple? I thought to find the Cartesian product of above latter sets and then try to select "f" as one of its subset but this did not help me to force Maple to take "f" as a function. Indeed, I want to work with this kind of function (like plotting and doing f+g, f-g, fog for two functions for example).

Thanks for your time and help.

 

hi maple-friends !

for my work i have to solve a system of differential equations numerically - no problem with maple :-)

my problem: how can i get the resulting data of the numeric solutions in a file ?

(for example to use them with gnuplot)

what i have to do exactly ? i know just about writedata and readdata commands...

can anyone send me an example with a few comments ?

greetings,  kreso

 

 

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

> restart;
> with(LinearAlgebra);
> q := a*mu^4+b*mu^3+d*mu^2+e*mu+f = 0;
> sol := solve(a*mu^4+b*mu^3+d*mu^2+e*mu+f = 0, mu);
> S[1] := allvalues(sol);
> PARAM := [a = -54/c^2-1269*A[1]/(8*c^2), b = 108/c^2+5013*A[1]/(8*c^2), d = 27-693/(2*c^2)+117*A[1]-7113*A[1]/(4*c^2), e = -27+585/(2*c^2)-111*A[1]+20439*A[1]/(16*c^2), f = 1-3*A[1]-18/c^2-8*A[1]/c^2];
> S2 := eval(S[1], PARAM);
Error, invalid input: eval received PARAM, which is not valid for its 2nd argument, eqns
> series(%, c = infinity, 3, A[1] = 0, 2]);
>
Please i mean by last statemene the solutions to be written i series as:

m1=.........+O(1/c^3)+O(A1^2)

m2=.......+O(1/c^3)+O(A1^2)

etf.

A1=0,2 means O(A1^2),therefore,i am not evaluating at .2 .

I am trying to design a question to test for divisibility

$n3=range(0,9,1); and students have to choose the next digit to make the number divisible by 4

if $n3 is even the students must input 0,4,8 to be true

if $n3 is odd the students must input 2 or 6 to be correct.

 

I am not sure how to us the if(a,b,c) in this case or if I should be using indexof....or both?  Any help would be appreciated. 

> restart;
> with(LinearAlgebra);
> q := a*mu^4+b*mu^3+d*mu^2+e*mu+f = 0;
> sol := solve(a*mu^4+b*mu^3+d*mu^2+e*mu+f = 0, mu);
> S[1] := allvalues(sol);
> PARAM := [a = -54/c^2-1269*A[1]/(8*c^2), b = 108/c^2+5013*A[1]/(8*c^2), d = 27-693/(2*c^2)+117*A[1]-7113*A[1]/(4*c^2), e = -27+585/(2*c^2)-111*A[1]+20439*A[1]/(16*c^2), f = 1-3*A[1]-18/c^2-8*A[1]/c^2];
> S2 := eval(S[1], PARAM);
> series(%, c = infinity, 3, A[1] = 0, 2);
> simplify(%)

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