Maple Questions and Posts

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Dear Users!

Hope you would be fine with everything. I want the simpliest for of the following expression in two step:

diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z))+u[delta]*lambda[1]*(diff(U(X, Y, Z, tau), tau, tau))/L[delta]+u[delta]*lambda[1]*(diff(U(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), X))/L[delta]+u[delta]*lambda[1]*U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, X))/L[delta]+u[delta]*lambda[1]*(diff(V(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), Y))/L[delta]+u[delta]*lambda[1]*V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, Y))/L[delta]+u[delta]*lambda[1]*(diff(W(X, Y, Z, tau), tau))*(diff(U(X, Y, Z, tau), Z))/L[delta]+u[delta]*lambda[1]*W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), tau, Z))/L[delta];
Step 1:
diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z))+u[delta]*lambda[1]*(diff(diff(U(X, Y, Z, tau), tau)+U(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), X))+V(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Y))+W(X, Y, Z, tau)*(diff(U(X, Y, Z, tau), Z)), tau))/L[delta];
Step 2: (final form I need)
(1+(u[delta] lambda[1])/(L[delta]) (∂)/(∂tau)) ((∂)/(∂tau) U(X,Y,Z,tau)+U(X,Y,Z,tau) ((∂)/(∂X) U(X,Y,Z,tau))+V(X,Y,Z,tau) ((∂)/(∂Y) U(X,Y,Z,tau))+W(X,Y,Z,tau) ((∂)/(∂Z) U(X,Y,Z,tau)));
I'm waiting for your response.
Special request:
@acer @Carl Love @Kitonum @Preben Alsholm


How do I remove these unwanted trailing zeros from my plot ? I have tried setting striptrailing=true from the Tyesetting package but no difference. Thanks

 

Hi

I would like to use  the Liebniz notation that someone from the technical support posted here
Writing Derivatives at a Point Using Leibniz Notation
to display a formula that is not just a partial derivative but a more complex expression invoking partial derivatives. 
Typically an expression like this one:

2*(Diff(f(mu__1, mu__2), mu__1))^2*lambda__1^2-(Diff(f(mu__1, mu__2), mu__1))^2*mu__1^2+2*(Diff(f(mu__1, mu__2), mu__2))^2*lambda__2^2-(Diff(f(mu__1, mu__2), mu__2))^2*mu__2^2+2*(Diff(f(mu__1, mu__2), mu__1))*(Diff(f(mu__1, mu__2), mu__2))*lambda__1*lambda__2-2*(Diff(f(mu__1, mu__2), mu__1))*mu__1*(Diff(f(mu__1, mu__2), mu__2))*mu__2

Could anyone help me to do this?
Thanks in advance

(PS: I'm still using Maple 2015.2)

Can I get to know how to interface maple with gnu plot. Thank you.

This must be so complicated process to describe the exact mechanism in human or animals ... and there are many reserchs on web for this subject ! Not expected Large answer !

By this way i am just curious to know by support of signal processing methods available in maple we can model a very basic vibrator as larynx and variable duct (what kind of filter we can call ?) or cavity that play the role of tongue or lips for changing of main stream to made various phonemes or frequencies

Here is a movie that show the section of human vocal system :

Anatomy

I found that while using maple gui cases of corruption, stuck while typing etc. Hope this problem will get solved in coming version

Need the code of the following:

 

h is the step size could be 0.1 or 0.01 etc

Dear experts

I am trying to study linear version of the Navier-Stokes (NS) equation. I define NS equations in a way suggested in this page

restart;

with(PDEtools): with(Student[VectorCalculus]):

SetCoordinates(cartesian[x,y,z]):

V:= VectorField(< v[1](x,z,t),0,v[3](x,z,t)>);

NavierStokes:= diff(V,t) - nu*Laplacian(V) +1/rho* Gradient(p(x,z,t)) - VectorField(< 0,0,-g>)=0;

the velocity components are intriduced as following

v[1]:=(x,z,t)->diff(f(z),z)*exp(I*k*x+(-1)*I*omega*t);

v[2]:=(x,z,t)->0;

v[3]:=(x,z,t)->(-1)*I*k*f(z)*exp(I*k*x+(-1)*I*omega*t);

So the problem is 2D model so that v[1] and v[3] satisfy incompresibility condition. It is clear that substituting velocity components into NS leads to differential equations for f(z). The general form of f(z) is

f(z) = a1*cosh(k*z)+a2*sinh(k*z)+a3*cosh(kappa*z)+a4*sinh(kappa*z).

my problems are

1) apply v[1], v[3] and find f(z) with Maple. then apply boundary conditions to find coeffs a[i] with Maple

2) In addition, Substituting the f(z) into BCs leads to a linear homogeneous system of equations for the coefficients. The vanishing of the determinant of this system which is the condition for the existence of a nontrivial solution is interested. How can I do that?

3) f(z) is for the case that the bottom is z=0 and surface is z=h. in my case bottom is z=-h and surface is z=0. how to do this in the solution. I dont know how to apply it.

4) calculate pressure

this file is what I did.

NSE.mw

 Mathematical model for the temperature profiles of steel pipes quenched by water cooling rings

Hi

 Can anyone solve the given equations along with the boundary conditions analytically with Maple and draw the graphs ???????????

maple save variables is greyed out  would anyone happen to know why this could be the case?

I have 4 ode equations. i just want to know can i use any option or simplification to have a analytical solution or NOT? Thanks in Advance

 

``

restart:

ode1 := -2*diff(lambda(t),t)*y1(t) - lambda(t)*diff((y1)(t),t)-0*diff(eta(t),t) - diff((y1)(t),t$3) + diff((y1)(t),t)*(y1(t)^2 + y2(t)^2) +4*y1(t)*sqrt(y1(t)^2 + y2(t)^2)*diff(sqrt(y1(t)^2 + y2(t)^2),t)+diff((y1)(t),t)/r^2
+ y1(t)^2*diff(y1(t),t) + y1(t)*y2(t)*diff(y2(t),t) - 2*diff(y1(t),t)/r^2 ;

 

-2*(diff(lambda(t), t))*y1(t)-lambda(t)*(diff(y1(t), t))-(diff(diff(diff(y1(t), t), t), t))+(diff(y1(t), t))*(y1(t)^2+y2(t)^2)+2*y1(t)*(2*y1(t)*(diff(y1(t), t))+2*y2(t)*(diff(y2(t), t)))-(diff(y1(t), t))/r^2+y1(t)^2*(diff(y1(t), t))+y1(t)*y2(t)*(diff(y2(t), t))

(1)

ode2 := diff((lambda)(t),t$2) + lambda(t)*(y1(t)^2 + y2(t)^2) - 2*y1(t)*diff((y1)(t),t$2) - y1(t)^2*(y1(t)^2 + y2(t)^2) - y1(t)^2/r^2 - diff((y1)(t),t)^2 - 2*diff(sqrt(y1(t)^2 + y2(t)^2),t)^2 - 2*sqrt(y1(t)^2 + y2(t)^2)*diff(sqrt(y1(t)^2 + y2(t)^2),t$2) - diff((y2)(t),t)^2 - 2*y2(t)*diff((y2)(t),t$2) - y2(t)^2*(y1(t)^2 + y2(t)^2)

diff(diff(lambda(t), t), t)+lambda(t)*(y1(t)^2+y2(t)^2)-2*y1(t)*(diff(diff(y1(t), t), t))-y1(t)^2*(y1(t)^2+y2(t)^2)-y1(t)^2/r^2-(diff(y1(t), t))^2-(1/2)*(2*y1(t)*(diff(y1(t), t))+2*y2(t)*(diff(y2(t), t)))^2/(y1(t)^2+y2(t)^2)-2*(y1(t)^2+y2(t)^2)^(1/2)*(-(1/4)*(2*y1(t)*(diff(y1(t), t))+2*y2(t)*(diff(y2(t), t)))^2/(y1(t)^2+y2(t)^2)^(3/2)+(1/2)*(2*(diff(y1(t), t))^2+2*y1(t)*(diff(diff(y1(t), t), t))+2*(diff(y2(t), t))^2+2*y2(t)*(diff(diff(y2(t), t), t)))/(y1(t)^2+y2(t)^2)^(1/2))-(diff(y2(t), t))^2-2*y2(t)*(diff(diff(y2(t), t), t))-y2(t)^2*(y1(t)^2+y2(t)^2)

(2)

ode3 := 2*diff((lambda)(t),t)*y2(t) + lambda(t)*diff((y2)(t),t) - y1(t)*y2(t)*diff((y1)(t),t) - 4*y2(t)*sqrt(y1(t)^2 + y2(t)^2)*diff((sqrt(y1(t)^2 + y2(t)^2)),t) - y2(t)^2*diff((y2)(t),t) - (y1(t)^2 + y2(t)^2)*diff((y2)(t),t) - diff((y2)(t),t$3) ;

2*(diff(lambda(t), t))*y2(t)+lambda(t)*(diff(y2(t), t))-y1(t)*y2(t)*(diff(y1(t), t))-2*y2(t)*(2*y1(t)*(diff(y1(t), t))+2*y2(t)*(diff(y2(t), t)))-y2(t)^2*(diff(y2(t), t))-(y1(t)^2+y2(t)^2)*(diff(y2(t), t))-(diff(diff(diff(y2(t), t), t), t))

(3)

ode4 := lambda(t)*y1(t)/r + mu(t)*r - diff((y1)(t),t$2)/r -1/r*y1(t)*(y1(t)^2 + y2(t)^2) - y1(t)/r^3-2/r*diff(y1(t),t$2)

lambda(t)*y1(t)/r+mu(t)*r-3*(diff(diff(y1(t), t), t))/r-y1(t)*(y1(t)^2+y2(t)^2)/r-y1(t)/r^3

(4)

sys := [ode1, ode2, ode3, ode4]:

dsolve(sys,[y1(t),y2(t),lambda(t),mu(t)],'implicit')

``

``


 

Download 1.1.mw

In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. I'd like to use maple to compute crossing number of some graphs (any graphs is ok,  for example: cr(K5)=1 ). Someone can help me ? thanks. 

I know the problem of computing the crossing number is NP, but I guess we have some good  ways to compute in some small graphs.

Sorry if this is stupid but How do I use the interactive debugger?   the button is greyed out for me and 
 

stopat(EAdd(x^3+2x+1,x, 13, 1, 2, 1, 2), 1);

Error, missing operator or `;`

 

stopat(EAdd, 1);

                             [EAdd]
 

debug button is still greyed out IDK what to do now


p.s. is there a way to set breakpoints in your code by clicking like in other programming?
 

I want to factor large numbers, for this purpose I want to utilize multi cores on my computer.

Anyone who can help me in solving this problem?

I am utilizing Lenovo Thinkpad T440s with specifications core i7-4600 CPU @ 2.19 GHz.

In addition I would like to ask if anyone can help me in integrating GPU's with Maplesoft 2019 for factorization.

 

I am having a cluster of 64 GPU's i.e. AMD RX-460.

 

Any help in this regard will be appreciated.

 

I am using a maple workbook to develop, test, and install a package I am developing.  Several days ago, I noticed that the workbook was not updating the package to reflect the most recent versions of my source code (.mpl). I initially assumed the problem caused by some unintentional change I made to the file, but in the end I found there is a general problem with the URIs in the maple workbook. Everything worked in 2019.1 and I hadn't made any changes after I updated to 2019.2.1.

To confirm the problem, I created a new directory(in fully updated Windows 10 ) and copied my source file into the directory. Then I created a worksheet in maple and saved it into the directory as xx.mw. Using the Navigator panel I then saved the worksheet as a workbook creating xx.maple in the directory.  I then tried to attach the mpl file to the workbook.  In the Navigator menu, the item "attach a file" is unavailable( greyed out).  This is also the case in any of the other earlier workbooks I have created.  I have confirmed the problem is not affecting worksheets because I was able to read my mpl file into a worksheet and load the module using a with(modulename) command.

Please advise.

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