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Hi all 

I have the following segment of maple program which belongs to time delay systems dynamic. here C=X-X0-G.Z-X.Dtau.P+X.Dtau.Z-U.P, is a matrix(vector) which comes from reordering the system terms and my goal is to minimizing J:=X.E.Transpose(X)+U.E.Transpose(U), subject to constraint C=0, but i don't know how to do so.

I will be so grateful if anyone can guide me

best wishes

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department


restart:
with(Optimization):
with(LinearAlgebra):
macro(LA= LinearAlgebra):
L:=1:  r:=2:  tau:= 1:
interface(rtablesize= 2*r+1):

Z:= Matrix(
     2*r+1, 2*r+1,
     [tau,
      seq(evalf((L/(2*(iz-1)*Pi))*sin(2*(iz-1)*Pi*tau/L)), iz= 2..r+1),
      seq(evalf((L/(2*(iz-1-r)*Pi))*(1-cos(2*(iz-1-r)*Pi*tau/L))), iz= r+2..2*r+1)
      ],
     scan= columns,
     datatype= float[8]
);
                        
Dtau00:= < 1 >:
Dtau01:= Vector[row](r):
Dtau02:= Vector[row](r):
Dtau10:= Vector(r):
Dtau20:= Vector(r):

Dtau1:= LA:-DiagonalMatrix([seq(evalf(cos(2*i*Pi*tau/L)), i= 1..r)]):
Dtau2:= LA:-DiagonalMatrix([seq(evalf(sin(2*i*Pi*tau/L)), i= 1..r)]):
Dtau3:= -Dtau2:
Dtau4:= copy(Dtau1):

Dtau:= < < Dtau00 | Dtau01 | Dtau02 >,
         < Dtau10 | Dtau1  | Dtau2  >,
         < Dtau20 | Dtau3  | Dtau4  > >;
 
P00:= < L/2 >:
P01:= Vector[row](r):
P02:= Vector[row](r, j-> evalf(-L/j/Pi), datatype= float[8]):
P10:= Vector(r):
P20:= Vector(r, i-> evalf(L/2/i/Pi)):
P1:= Matrix(r,r):
P2:= LA:-DiagonalMatrix(P20):
P3:= LA:-DiagonalMatrix(-P20):
P4:= Matrix(r,r):

P:= < < P00 | P01 | P02 >,
      < P10 | P1  | P2  >,
      < P20 | P3  | P4  > >;

interface(rtablesize=2*r+1):    # optionally
J:=Vector([L, L/2 $ 2*r]):      # Matrix([[...]]) would also work here

E:=DiagonalMatrix(J);

X:=  Vector[row](2*r+1,symbol=a);
U:=Vector[row](2*r+1,symbol=b);

X0:= Vector[row](2*r+1,[1]);
G:=Vector[row](2*r+1,[1]);
C:=simplify(X-X0-G.Z-X.Dtau.P+X.Dtau.Z-U.P);

Z := Matrix(5, 5, {(1, 1) = 1., (1, 2) = 0., (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (2, 1) = 0., (2, 2) = 0., (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0., (3, 4) = 0., (3, 5) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0., (4, 5) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 0.})

Dtau := Matrix(5, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 1., (2, 3) = 0, (2, 4) = 0., (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1., (3, 4) = 0, (3, 5) = 0., (4, 1) = 0, (4, 2) = -0., (4, 3) = -0., (4, 4) = 1., (4, 5) = 0, (5, 1) = 0, (5, 2) = -0., (5, 3) = -0., (5, 4) = 0, (5, 5) = 1.})

P := Matrix(5, 5, {(1, 1) = 1/2, (1, 2) = 0, (1, 3) = 0, (1, 4) = -.318309886100000, (1, 5) = -.159154943000000, (2, 1) = 0, (2, 2) = 0, (2, 3) = 0, (2, 4) = .1591549430, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 0, (3, 4) = 0, (3, 5) = 0.7957747152e-1, (4, 1) = .1591549430, (4, 2) = -.159154943000000, (4, 3) = 0, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0.7957747152e-1, (5, 2) = 0, (5, 3) = -0.795774715200000e-1, (5, 4) = 0, (5, 5) = 0})

E := Matrix(5, 5, {(1, 1) = 1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (1, 5) = 0, (2, 1) = 0, (2, 2) = 1/2, (2, 3) = 0, (2, 4) = 0, (2, 5) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 1/2, (3, 4) = 0, (3, 5) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 1/2, (4, 5) = 0, (5, 1) = 0, (5, 2) = 0, (5, 3) = 0, (5, 4) = 0, (5, 5) = 1/2})

X := Vector[row](5, {(1) = a[1], (2) = a[2], (3) = a[3], (4) = a[4], (5) = a[5]})

U := Vector[row](5, {(1) = b[1], (2) = b[2], (3) = b[3], (4) = b[4], (5) = b[5]})

X0 := Vector[row](5, {(1) = 1, (2) = 0, (3) = 0, (4) = 0, (5) = 0})

G := Vector[row](5, {(1) = 1, (2) = 0, (3) = 0, (4) = 0, (5) = 0})

C := Vector[row](5, {(1) = 1.500000000*a[1]-2.-.1591549430*a[4]-0.7957747152e-1*a[5]-.5000000000*b[1]-.1591549430*b[4]-0.7957747152e-1*b[5], (2) = a[2]+.1591549430*a[4]+.1591549430*b[4], (3) = a[3]+0.7957747152e-1*a[5]+0.7957747152e-1*b[5], (4) = a[4]+.3183098861*a[1]-.1591549430*a[2]+.3183098861*b[1]-.1591549430*b[2], (5) = a[5]+.1591549430*a[1]-0.7957747152e-1*a[3]+.1591549430*b[1]-0.7957747152e-1*b[3]})

(1)

J:=X.E.Transpose(X)+U.E.Transpose(U);

J := a[1]^2+(1/2)*(a[2]^2)+(1/2)*(a[3]^2)+(1/2)*(a[4]^2)+(1/2)*(a[5]^2)+b[1]^2+(1/2)*(b[2]^2)+(1/2)*(b[3]^2)+(1/2)*(b[4]^2)+(1/2)*(b[5]^2)

(2)

Minimize(J,{C=0});






Error, (in Optimization:-NLPSolve) invalid arguments

 

#XP:=-.015+X[1]+add(X[l+1]*f1(l)+X[r+l+1]*f2(l), l= 1..r):
#plot([XP,T1], t= 0..1);#,legend= "Solution Of x(t) with r=50"):

 

 

 

 

 

 

Download work1.mwswork1.mws

I am new user of Maple. I have an expression like f(x,y)/g(x,y) and I want to have Maple name f(x,y) as something simple like "h" so that later equations write h/g(x,y) instead of the complete f(x,y)/g(x,y), and also to be able to simplify other equations in terms of h.

For example, a=(x+1)(y-5)^2/(x+y-3). Can I get Maple to let h=(x+1)(y-5)^2, so that I get h/(x+y-3) when I ask for a?

Sorry if this question is basic (and my math terminology incorrect), but I have been trying for a while.

Does anyone has any maple worksheet that generate surface using the PDE method described in this article?  I am trying to learn this method but I am not familiar with the mathematics to do it although the paper gives some description of it.  I hope someone can demonstrate the procedure in Maple.  Thanks

http://www.researchgate.net/publication/259095177_Automatic_shape_optimisation_of_pharmaceutical_tablets_using_Partial_Differential_Equations/file/72e7e52a87ed129d4a.pdf

EDIT:EDIT: I found what I was looking for. Thanks!

 

eq:=(V^(1-r/(r-s))*V*k/(r-2*s)+_C1)*V^(r/(r-s))=0;

 

equation 1

 

solve(eq,C1);

 

Can anyone tell me why nothing happens when I solve the above equation for C1.

I've been coming across this problem a few times lately, but sometimes when the equations are less complicated it does work from time to time. 

Any help would be greatly appreciated.

 

EDIT:  Thanks Markiyan Hirnyk

But I'm still having some trouble.

 

f:=t->(-r*t+s*t+V)^(r/(r-s));

eq2:=diff(C*f(t),t)+C*f(t)*r/(V+s*t-r*t)=s*k*t;

solve(eq2,C);

 


When I try solving eq2 nothing happens. 


This time C is just a variable I used and not one Maple generated.

So why doesn't it work with this particular equation?

 

 

Hi. I'd like to find the solution closest to zero for sum(abs(f(k, m, n)+g(k, m, n)), n = i .. j) , when a < m, n < b . 

Have trouble wrapping my head around how to do that and would appreciate any help.

Even better would be to find a solution where the maximum absolute value of f(k, m, n) + g(k, m, n) is minimized for n = i .. j) and when a < m, n < b , but I'm guessing the sum would be easier, and close enough.

Maybe I'm barking up the wrong tree getting this done with Maple, but I'm hopeful.

Thank you for looking

This is just a question on terminology. The name "combine" implies pulling terms together. Yet, when applied to something like sin(x)^2 it has the effect of expanding it:

r:=sin(x)^2;
combine(r);

 

Which seems counter-intutive to me. I tried first expand(r) but that did not expand it.

Fyi, in Mathematica the function to do the above is called

Sin[x]^2;
TrigReduce[%]

    1/2 (1 - Cos[2 x])

As Mathematica does not have a Combine[] function.

So, I am just wondering about the naming, that is all. I would never have thought first that a command called combine() will expand sin(x)^2.

 

 

Hi, all

I want to get some formular by the maple. I have some S domain transfer function, want to transform to the Z domain, but I don't know the way to realize it, is there any library function like "c2d" as in the Matlab? but "c2d" can not deal with the expression.

Thanks for replay to me!!!

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Hi,

I'm preparing for GRE and i came across this question from 800score.com while reviewing concepts for probability.

In a deck of 52 standard playing cards, what is the probability that pulling a single card from the deck 
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http://www.800score.com/content/gre/guidec7dview1a.html

Please...

I have bracket matching turned on but donot get the rectangular yellow box around matching brackets as shown in the attached picture. Can anyone help me how to turn this feature on for both input and output?

I have the following equation, I want to solve it for b keeping a and c fixed.

5*b^5+(60-5a)*b^4+(125+50c-80a)*b^3+(594c-445a-775)*b^2+(2324c-1005a-3270)*b+3000c-750a-3000=0.

How to solve it in maple?

 

 

 

Hello,

I've been trying to force maple to find a solution of this differential equation:

ode := -((D@@2)(y))(r)-2*y(r)/r+y(r) = (2-V(r))*u[0](r)

dsolve(ode, y(r));

gives

y(r) = r exp(-r) _C2 + (exp(r) + 2 exp(-r) Ei(1, -2 r) r) _C1 - 4 

/ / /
|1 | |
exp(-3 r) |- | |
|2 | |
\ \/

/ 2 \ \

For a math class, we have to create a roller coaster. Part of the coaster consists of two banked curves. I've tried looking it up but Maple isn't very clear on how to create the. So, how do you create banked curves in Maple?

Hi,

 

I have two differential equations describing a solar sail in 2D.

One is my radial direction and one is the tangential direction.

I have plotted r(t) and theta(t) but I want r(theta) so I have assigned my two differential equations and initial conditions, have my two plots for r and theta in terms of t and then I have used the following command to plot in polar coordinates:

 

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I just realised Maple is allowed for my upcoming exam after New Year.

My plan is to have templates of the most common math problems, I might encounter for quick solutions.

Anyway, I have run into a problem with Laplace shifted data, particularly initial value problems. I have been searching for HOURS, and feel like I have look up everything on google, maplesoft and other sites without succes.

I hope some of you are able to help me. The exercise is:

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