Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

I would like to pay attention to a series of applications by Samir Khan
http://www.maplesoft.com/applications/view.aspx?SID=153600
http://www.maplesoft.com/applications/view.aspx?SID=153599
http://www.maplesoft.com/applications/view.aspx?SID=153596
http://www.maplesoft.com/applications/view.aspx?SID=153598
My congratulations to the author on his work well done. New capacities of Global Optimization Toolbox are spectacular. For example, in the first application  an optimization
problem in 101 variables under 5050 nonlinear  constraints
(other than 202 bounds) is solved.
I think it requires a very powerful comp and much time.
I tried that  problem for n=20 with the good old DirectSearch
on my comp (4 GB RAM, Pentium Dual-Core CPU E5700@3GHz) by

soln2 := DirectSearch:-GlobalSearch(rc, {cons1, cons2, rc >= 0,
seq(`and`(vars[i] >= -70, vars[i] <= 70), i = 1 .. 2*n), rc <= 70},
variables = vars, method = quadratic, number = 140, solutions = 1,
evaluationlimit = 20000)

and obtained not so bad rc=69.9609360106765 (whereas www.packomania.com gives rc=58.4005674790451137175957) in about one hour.

Packing_by_DS.mw
For n=50 the memory of my comp cannot allocate calculations or the obtained result by the Search command is far away from the one in packomania.

 

Hi i have trouble with this equation to solve with maple please help me

with boundary condition :

 

how i solve above equation with maple?( there is function to solve this equation in maple ?

email :

sattar.dogonchi@yahoo.com

Hi There

I'm getting started with maple and facing a doubt about using subs, somehow it does not seem to work, this is my expression:

 

> restart;
> theta := omega*t-k*x;
                                omega t - k x
> phi[1] := -(1/2)*H*c*cosh(k*(z+h))*sin(theta)/sinh(k*h);
                   H c cosh(k (z + h)) sin(-omega t + k x)
                   ---------------------------------------
                                 2 sinh(k h)              
> diff(phi[1], t, t);
                                                             2
                H c cosh(k (z + h)) sin(-omega t + k x) omega
              - ----------------------------------------------
                                 2 sinh(k h)                  
> td := simplify(subs(z = 0, %));
                                                          2
                   H c cosh(k h) sin(-omega t + k x) omega
                 - ----------------------------------------
                                 2 sinh(k h)               
> simplify(subs(cosh(k*h)/sinh(k*h) = 1/tanh(k*h), %));
                                                          2
                   H c cosh(k h) sin(-omega t + k x) omega
                 - ----------------------------------------
                                 2 sinh(k h)               
I cannot subs cosh/sinh = tanh. I would like to know why.

Any tips? Thank you

Dear friends:

I have a long expression having a/some RootOf(something..) inside it. 

Any way to get just that "something..", i.e., the argument of RootOf() from that expression?

 

Thank you very much.

César Lozada

 

 

Hi all,

 

Sorry if the question of the title wasn't very clear. I am not sure how to express it correctly.

But here is what I do for linux,

and I get

 

So when I submitted a lot of jobs, I can see the arguments that was passed to it. I can easily kill a process.

 

How do I do that in windows if anyone knows?

Here is a screenshot from windows task manager:

 

That does not give informative details, just like the 'top' command in linux.

 

Thanks,

Maplesoft regularly hosts live webinars on a variety of topics. Below you will find details on an upcoming webinar we think may be of interest to the MaplePrimes community.  For the complete list of upcoming webinars, visit our website.

Hollywood Math 2

In this second installment of the Hollywood Math webinar series, we will present some more examples of mathematics being used in Hollywood films and popular hit TV series. For instance, have you wondered how Ben Campbell solved his professor’s challenge so easily in the movie “21”? Or about the details of the Nash equilibrium that John Nash first developed in a “A Beautiful Mind”? We’ve got the answers! These relevant, and exciting examples can be used as material to engage your students with examples familiar to them, or you can just attend the webinar for its entertainment value.

Anyone with an interest in mathematics, especially high school and early college math educators, will be both entertained and informed by attending this webinar. At the end of the webinar you’ll be given an opportunity to download an application containing all of the examples that we demonstrate.

To join us for the live presentation, please click here to register.

If you missed the first webinar in this two part series, you can view the 'Hollywood Math' recording on our website.

How to make Decimal number in maple by default? 

How to make radian to degrees? Think It is like this "degcos" but I cant see the correct result, because it is not showed in decimals

Why do I have to active all my varibles when I open the document after I have saved it?

 

Regards

Østerbro

Does anyone have JavaViewLib running on Maple 18?  Could you help me out?  I can't get it running and I really need a way to export some 3d plots to a web page where a colleague can view them (rotate and such).

Thanks, Chad.

Hello everyone,

I'm trying to do some fitting using NonlinearFit, for the coefficients I know in advance, that they have to fulfill a condition (a+b>c+1). I couldn't find a way to make Maple take this condition into consideration while fitting my data. I tried to use Parameterrange to make the difference a+b-c+1 positive, this works for linear conditions like mine but leads to computational difficulties and errors like "no improved point could be found".

Thanks in advance,

Sören

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 ? 


Dear users,

In my attached file I have two PDES, (PDE1 and PDE2). PDE1 is a function of v(t) and w(x,t) and PDE2 is also a function of v(t) and w(x,t). I can solve PDE2 if I say v(t) is 1 for example and you can see the plot. But what if I put v(t) back in PDE2 and want to find v(t) and w(x,t) from PDE1 and PDE2 together? 

Many Thanks,

Baharm31

 

Define PDE Euler-Bernoulli Beam

 

NULL

restart:

Parametrs of piezoelectric and cantilever beam

 

``

Ys := 70*10^9: # Young's Modulus structure

Yp := 11.1*10^10: # Young's Modulus pieazo

ha := -0.00125: # Position

hb := 0.001: # Position

hc := 0.0015: # Position

d31 := -180*10^(-12): # Piezoelectric constant

b := 0.01: #Width of the beam

tb := 0.002:

epsilon33 := 15.92*10^(-9):

hp :=0.00025: # Position

hpc := 0.00125: # Position

YI := b*(Ys*(hb^3- ha^3)+Yp*(hc^3-hb^3))/3: # Bending stiffness of the composit cross section

cs := 0.564: # The equivqlent coefficient of strain rate damping

ca := 0: # Viscous air damping coefficient

Ibeam := (b * tb^3 )/12: # The equivalent moment of inertia

m := 0.101: # Mass of the structure

upsilon := - Yp*d31*b*(hc^2-hb^2)/(2*hp): # Coupling term

lb := 0.57:# Length of the structure (Cantilever Beam)

lp := 0.05:# Length of the Piezoelectric

R:= 10000: # Shunted resistor

Electrical circuit equation

 

PDE1:=(epsilon33 * b*lp / hp) * diff(v(t), t) + (v(t)/R)+ int(d31*Yp*hpc*b* diff(w(x, t),$(x, 2))*diff(w(x, t), t),x = 0..lp)=0;

0.3184000000e-7*(diff(v(t), t))+(1/10000)*v(t)+int(-0.2497500000e-3*(diff(diff(w(x, t), x), x))*(diff(w(x, t), t)), x = 0 .. 0.5e-1) = 0

(1.1.1.1)

``

 

PDE Equation

 

fn := 3.8:# Direct Excitation frequency;

wb(x,t) := 0.01*sin(fn*2*Pi*t):#Direct Excitation;

plot(wb(x,t),t = 0 .. 0.25*Pi,labels = [t,wb], labeldirections = ["horizontal", "vertical"], labelfont = ["HELVETICA", 15], linestyle = [longdash], axesfont = ["HELVETICA", "ROMAN", 10], legendstyle = [font = ["HELVETICA", 10], location = right],color = black);

 

 

FunctionAdvisor(definition, Dirac(n,x));

[Dirac(n, x) = (1/2)*(Int((I*_k1)^n*exp(I*_k1*x), _k1 = -infinity .. infinity))/Pi, `with no restrictions on `(n, x)]

(1.2.1)

 

PDE2 := YI*diff(w(x, t),$(x, 4))+ cs*Ibeam*diff(w(x, t),$(x, 4))*diff(w(x, t), t)+ ca* diff(w(x, t), t) + m * diff(w(x, t),$(t, 2))+ upsilon*v(t)*(Dirac(1,x) -Dirac(1,x-lp) ) =-m*diff(wb(x, t),$(t, 2))-ca*diff(wb(x, t), t);#PDE

1.567812500*(diff(diff(diff(diff(w(x, t), x), x), x), x))+0.3760000000e-11*(diff(diff(diff(diff(w(x, t), x), x), x), x))*(diff(w(x, t), t))+.101*(diff(diff(w(x, t), t), t))+0.4995000000e-3*Dirac(1, x)-0.4995000000e-3*Dirac(1, x-0.5e-1) = 0.583376e-1*sin(7.6*Pi*t)*Pi^2

(1.2.2)

tmax := 0.3:

xmin := 0:

xmax := lb:

N := 20:#NUMBER OF NODE POINT

bc1 := dw(xmin, t) = 0:

bc2 := dw(xmax, t) = 0:

bc3 := w(xmin, t) = 0:

ic1 := wl(x, 0) = 0:

Maple's pdsolve command

 

 

 

bcs := { w(x,0)=0 , D[2](w)(x,0)=0 , w(0, t) = rhs(bc1), D[1](w)(0, t)= rhs(bc1), D[1,1](w)(lb,t) = rhs(bc2), D[1,1,1](w)(lb,t) = rhs(bc2)}; # Boundary conditions for PDE2.

{w(0, t) = 0, w(x, 0) = 0, (D[1](w))(0, t) = 0, (D[2](w))(x, 0) = 0, (D[1, 1](w))(.57, t) = 0, (D[1, 1, 1](w))(.57, t) = 0}

(2.1)

PDES := pdsolve(PDE2, bcs, numeric, time = t, range = 0 .. xmax, indepvars = [x, t], spacestep = (1/1000)*xmax, timestep = (1/1000)*tmax);

 

module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module

(2.2)

PDES:-plot3d(t = 0 .. tmax, x = 0 .. xmax, axes = boxed, orientation = [-120, 40], shading = zhue, transparency = 0.3);

 

 

NULL


Download Euler-Bernoulli_Beam-last_version.mw

 

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?

 

 

 

 

Dear Maple users

 

I have a question about applying pdsolve MAPLE for solving two dimensional heat equations:

My codes have been provided but it shows to me this error:

Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}

If kindly is possible, please help me in this case.

 

With kind regards,

Emran Tohidi.

 

> restart;
> with(plots);
print(??); # input placeholder
> with(PDEtools);
print(??); # input placeholder
> declare(u(x, y, t));
print(`output redirected...`); # input placeholder
                    u(x, y, t) will now be displayed as u
> S := 1/100; tR := 0 .. 1; xR := 0 .. 1; yR := 0 .. 1; NF := 30; NP := 100;
print(??); # input placeholder
> N := 3; L1 := [red, blue, green]; L2 := [0, 1/2, 1]; Ops := spacestep = S, timestep = S;
print(??); # input placeholder
> Op1 := frames = NF, numpoints = NP;
print(??); # input placeholder
> PDE1 := diff(u(x, y, t), t)-(diff(u(x, y, t), `$`(x, 2)))-(diff(u(x, y, t), `$`(y, 2))) = 0;
print(??); # input placeholder
> IC := {u(x, y, 0) = exp(x+y)}; BC := {u(0, y, t) = exp(2*t+y), u(1, y, t) = exp(2*t+y+1), u(x, 0, t) = exp(2*t+x), u(x, 1, t) = exp(2*t+x+1)};
print(??); # input placeholder
> Sol := pdsolve(PDE1, `union`(IC, BC), numeric, u(x, t), Ops);
Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {t, x, y}


I am having problems with the curly brackets in math mode. I am using a Danish keyboard, and since changing to Maple 17, the inline evaluation (usually [CTRL]+=) has been placed as [CTRL]+[ALT]+0 which - by Maple - is interpreted the same way as [ALT-GR]+0. Unfortunately [ALT-GR]+0 is the way to get the end-bracket for curly brackets, i.e. }

Therefore, I am not able to write } in math mode. Maple interprets my keystrokes as a wish to do inline evaluation when trying to write }.

Has anyone experienced this issue - and if so: Is there a way to fix it?

Is there a way to change the shortcut keys in Maple (e.g. make an alternative shortcut for inline evaluations)?

 

Hi.

I am new in Maple and I'm trying to get functions from system of equations.

Constants are defined in line 4 and equations are:

eq1 := E2 = fE2(1+(KaE2+Ca)/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsE2*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

eq2 := T = fT(1+KaT*Ca/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsT*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

eq3 := DHT = fDHT(1+KaDHT*Ca/(1+KaE2*fE2+KaT*fT+KaDHT*fDHT)+KsDHT*Cshbg/(1+KsE2*fE2+KsT*fT+KsDHT*fDHT))

KsT = 0.10e11; KaT = 4.6*0.10e6; KsE2 = 3.14*0.10e10; KaE2 = 4.21*0.10e6; KsDHT = 3*0.10e6; KaDHT = 3.5*0.10e6;

fT, fE2 and fDHT are variables, not functions (i.e. fT is not f(T) ) and I am trying to get fT=f(E2,T,DHT,Ca,Cshbg), fE2=f(E2,T,DHT,Ca,Cshbg) and fDHT=f(E2,T,DHT,Ca,Cshbg).

When I type:

eliminate({eq1, eq2, eq3}, {fE2, fT, fDHT})

Maple gives me a blank field. No error, no other comment.

I have no idea where I'm making mistakes.

Any suggestion is appreciated.

 

Thanks in advance.

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