Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

Hello everyone, my computer installed Maple 2016, 2020 and set Maple 2016 as default opening files .mw, .mws. How to change default to Maple 2020 . I tried searching on Google but not found.

Thank you very much.

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see 

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

Determine how many transitive relations there are on a set with n elements for all positive integers n with n<=7.

Custom Palettes and Palette Entries on windows Pro 7 
Read a tutorial from a user @les 185

https://www.mapleprimes.com/posts/207781-Custom-Palettes-And-Palette-Entries

Is this still valid this tutorial from 2015  in the current version of Maple ?
This seems to be userunfriendly.

 

This is strange.  It is true that this function (a modular form) goes to infinity as t -> 0 from the right.
But should plotting it it do this?


    |\^/|     Maple 2019 (APPLE UNIVERSAL OSX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> version();
 User Interface: 1435526
         Kernel: 1435526
        Library: 1435526
                                    1435526

> exp(-Pi*t/3)^8*JacobiTheta3(Pi*(4*I*t+1)/2,
> exp(-12*Pi*t))^8/(exp(-Pi*t/6)^4*
> JacobiTheta3(Pi*(2*I*t + 1)/2, exp(-6*Pi*t))^4);
                 Pi t 8              Pi (4 I t + 1)                8
           exp(- ----)  JacobiTheta3(--------------, exp(-12 Pi t))
                  3                        2
           ---------------------------------------------------------
                 Pi t 4              Pi (2 I t + 1)               4
           exp(- ----)  JacobiTheta3(--------------, exp(-6 Pi t))
                  6                        2

> plot(%,t=0..4);
memory used=48.4MB, alloc=45.3MB, time=0.45
Execution stopped: Stack limit reached.

 

Hi,

Thank you all for participating to my questions before.

I was wondering if we can change an equation into quartic form or quadratic form in maple.

I have succesfully got an equation like the following:

`S__2 ` = sin(alpha - phi)*sin(-beta + alpha)*(gamma*H^2*sin(beta - varepsilon)*sin(alpha) - h^2*sin(beta)*sin(alpha - varepsilon)*gamma + h^2*sin(beta)*sin(alpha - varepsilon)*psi)/(2*sin(-beta - delta - phi + alpha)*sin(beta)^2*sin(alpha - varepsilon)*sin(alpha)) - S__1

From the paper I studied, they change it to form an equation like this

 

`S__2 ` = 1/2*gamma*H^2*sin(beta - alpha)*(M__3(X)^3 + M__2(X)^2 + M__1*X)/(sin(beta)^2*(D__3(X)^3 + D__2(X)^2 + D__1*X + D__0)) - S__1

 

Where value of M, D and X is sets of long equation. Can someone teach me how to assign maple to change this kind of equation to another form of equation. It's good enough if I can learn how to learn the basic.

 

Thank you.

 

Regards

Faiz Farhan

 

Dear All,

I want to apply the ‘simplify’ command, in parallel, for the simplification of some parameters. Both Grid:-Map and Grid:-Run commands are tested. There is no error in both, whereas no simplification is implemented. It seems that the ‘simplify’ command correctly works on only ‘Master’ node, namely anywhere we are typing.

Can anyone help me to simplify in parallel. I examined two following codes.

1)

with (Grid);

for i from 1 to nops(dummy_UU1) do

freenode:=WaitForFirst():

Run(freenode,simplify,[dummy_UU1[i]],assignto='dummy_UU2'[i]):

end do:

Wait();

2)

dummy_UU2:=Map[tasksize=1](simplify,[seq(dummy_UU1[i],i=1..nops(dummy_UU1))]):

 

 

The following code is correctly executed and resulted in the simplification of dummy_UU1 components in serial.

for i from 1 to nops(dummy_UU1) do

dummy_UU2[i]:=simplify(dummy_UU1[i]):

end do:

 

Could anyone help me out to convert the equation into differential transform method

 

Hello Everyone, can anyone explain how to import a mathematical equation from maple to word directly?

Just wonder about the status of the public folder in Maple Cloud.

I've tried to upload a file there, but got the reply that the uploaded file is going to be reviewed first. That was end of july.

Sorting files after date shows that the last upload was done in october 2019. Content unknown as it that was in chinese (probably).

It's not really important to me, as I can always find another site to upload stuff, just wondering.

I want to to solve the system of partial differential equation using maple. I tried it but I am not able to solve it ... please help.

the equations are as follows

 


 

``

Finding transformation eqn between zero and harmonic with conformal1

``

 

restart

``

with(PDEtools)

sys := {(diff(Phi(r1, r2, r4), r1))^2-(diff(R(r1, r2, r4), r1))^2 = cos(T(r1, r2, r4))^2, (diff(Phi(r1, r2, r4), r2))^2-(diff(R(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, -(diff(R(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r1))+(diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))+(diff(Theta(r1, r2, r4), r1))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2))+(diff(Theta(r1, r2, r4), r2))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2)) = 0, (R(r1, r2, r4)^2-Phi(r1, r2, r4)^2)*(diff(T(r1, r2, r4), r4))^2+2*(diff(Theta(r1, r2, r4), r4))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))^2-(diff(R(r1, r2, r4), r4))^2 = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2}

{(diff(Phi(r1, r2, r4), r1))^2-(diff(R(r1, r2, r4), r1))^2 = cos(T(r1, r2, r4))^2, (diff(Phi(r1, r2, r4), r2))^2-(diff(R(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, -(diff(R(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r1))+(diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))+(diff(Theta(r1, r2, r4), r1))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2))+(diff(Theta(r1, r2, r4), r2))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2)) = 0, (R(r1, r2, r4)^2-Phi(r1, r2, r4)^2)*(diff(T(r1, r2, r4), r4))^2+2*(diff(Theta(r1, r2, r4), r4))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))^2-(diff(R(r1, r2, r4), r4))^2 = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2}

(1)

``

declare(Phi(r1, r2, r4), R(r1, r2, r4), T(r1, r2, r4), Theta(r1, r2, r4))

` Phi`(r1, r2, r4)*`will now be displayed as`*Phi

 

` R`(r1, r2, r4)*`will now be displayed as`*R

 

` T`(r1, r2, r4)*`will now be displayed as`*T

 

` Theta`(r1, r2, r4)*`will now be displayed as`*Theta

(2)

``

cases := [PDEtools:-casesplit({(diff(Phi(r1, r2, r4), r1))^2-(diff(R(r1, r2, r4), r1))^2 = cos(T(r1, r2, r4))^2, (diff(Phi(r1, r2, r4), r2))^2-(diff(R(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, -(diff(R(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r1))+(diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))+(diff(Theta(r1, r2, r4), r1))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1)) = 0, -(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2))+(diff(Theta(r1, r2, r4), r2))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2)) = 0, (R(r1, r2, r4)^2-Phi(r1, r2, r4)^2)*(diff(T(r1, r2, r4), r4))^2+2*(diff(Theta(r1, r2, r4), r4))*(diff(T(r1, r2, r4), r4))+(diff(Phi(r1, r2, r4), r4))^2-(diff(R(r1, r2, r4), r4))^2 = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2}, caseplot)]

`========= Pivots Legend =========`

 

p1 = diff(R(r1, r2, r4), r2)

 

p2 = diff(Phi(r1, r2, r4), r1)

 

p3 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2

 

p4 = diff(Phi(r1, r2, r4), r2)

 

p5 = diff(R(r1, r2, r4), r1)

 

 

[`casesplit/ans`([diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))^2-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*cos(T(r1, r2, r4))^2+(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/(cos(T(r1, r2, r4))^2*(diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^4), diff(Theta(r1, r2, r4), r2) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))+(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r1) = (diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1))/(diff(R(r1, r2, r4), r2)), (diff(R(r1, r2, r4), r2))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r4) = -(diff(Phi(r1, r2, r4), r2))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r2) = 0, (diff(Phi(r1, r2, r4), r1))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0], [diff(R(r1, r2, r4), r2) <> 0, diff(Phi(r1, r2, r4), r1) <> 0]), `casesplit/ans`([diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r2) = 0, (diff(R(r1, r2, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(Phi(r1, r2, r4), r1) = 0, (diff(Phi(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0], [diff(R(r1, r2, r4), r1) <> 0, diff(Phi(r1, r2, r4), r2) <> 0])]

(3)

``

map(length, cases)

[2101, 1405]

(4)

sys1 := op(1, cases[2])

[diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r2) = 0, (diff(R(r1, r2, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(Phi(r1, r2, r4), r1) = 0, (diff(Phi(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(5)

``

sys2 := op(1, cases[1])

[diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))^2-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r1))*cos(T(r1, r2, r4))^2+(diff(Phi(r1, r2, r4), r1))*(diff(Phi(r1, r2, r4), r2))*(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/(cos(T(r1, r2, r4))^2*(diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^4), diff(Theta(r1, r2, r4), r2) = (-(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))+(diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r2)))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), diff(R(r1, r2, r4), r1) = (diff(Phi(r1, r2, r4), r2))*(diff(Phi(r1, r2, r4), r1))/(diff(R(r1, r2, r4), r2)), (diff(R(r1, r2, r4), r2))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r4) = -(diff(Phi(r1, r2, r4), r2))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), diff(diff(Phi(r1, r2, r4), r2), r2) = 0, (diff(Phi(r1, r2, r4), r1))^2 = (diff(Phi(r1, r2, r4), r2))^2+cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(6)

``

sys3 := op(2, cases[1])

[diff(R(r1, r2, r4), r2) <> 0, diff(Phi(r1, r2, r4), r1) <> 0]

(7)

``

sys4 := op(2, cases[2])

[diff(R(r1, r2, r4), r1) <> 0, diff(Phi(r1, r2, r4), r2) <> 0]

(8)

``

sol1 := dsolve(sys1, explicit)

(9)

``

constraint, subsystem := selectremove(has, sys1, T)

[diff(Theta(r1, r2, r4), r4) = (1/2)*(Phi(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-R(r1, r2, r4)^2*cos(T(r1, r2, r4))^4-(diff(Phi(r1, r2, r4), r4))^2+(diff(R(r1, r2, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(R(r1, r2, r4), r4))*(diff(R(r1, r2, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(Phi(r1, r2, r4), r4))*(diff(Phi(r1, r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(R(r1, r2, r4), r4), r4) = -R(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(R(r1, r2, r4), r4)), (diff(R(r1, r2, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(Phi(r1, r2, r4), r4), r4) = -Phi(r1, r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(Phi(r1, r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(Phi(r1, r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0], [diff(R(r1, r2, r4), r2) = 0, diff(Phi(r1, r2, r4), r1) = 0]

(10)

``

sol__subsystem := dsolve(subsystem)

{Phi(r1, r2, r4) = _F1(r2, r4), R(r1, r2, r4) = _F2(r1, r4)}

(11)

``

eval(constraint, sol__subsystem)

[diff(Theta(r1, r2, r4), r4) = (1/2)*(_F1(r2, r4)^2*cos(T(r1, r2, r4))^4-_F2(r1, r4)^2*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -_F2(r1, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(_F2(r1, r4), r4)), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -_F1(r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(_F1(r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(12)

map(simplify, [diff(Theta(r1, r2, r4), r4) = (1/2)*(_F1(r2, r4)^2*cos(T(r1, r2, r4))^4-_F2(r1, r4)^2*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -_F2(r1, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(_F2(r1, r4), r4)), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -_F1(r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(_F1(r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0])

[diff(Theta(r1, r2, r4), r4) = (1/2)*((_F1(r2, r4)^2-_F2(r1, r4)^2)*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -cos(T(r1, r2, r4))*(_F2(r1, r4)*cos(T(r1, r2, r4))^3+2*(diff(_F2(r1, r4), r4))*sin(T(r1, r2, r4))), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -cos(T(r1, r2, r4))*(_F1(r2, r4)*cos(T(r1, r2, r4))^3+2*(diff(_F1(r2, r4), r4))*sin(T(r1, r2, r4))), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = sin(T(r1, r2, r4))^2, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(13)

``

eval(constraint, sol__subsystem)

[diff(Theta(r1, r2, r4), r4) = (1/2)*(_F1(r2, r4)^2*cos(T(r1, r2, r4))^4-_F2(r1, r4)^2*cos(T(r1, r2, r4))^4-(diff(_F1(r2, r4), r4))^2+(diff(_F2(r1, r4), r4))^2)/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r1) = (diff(_F2(r1, r4), r4))*(diff(_F2(r1, r4), r1))/cos(T(r1, r2, r4))^2, diff(Theta(r1, r2, r4), r2) = -(diff(_F1(r2, r4), r4))*(diff(_F1(r2, r4), r2))/cos(T(r1, r2, r4))^2, diff(diff(_F2(r1, r4), r4), r4) = -_F2(r1, r4)*cos(T(r1, r2, r4))^4-2*cos(T(r1, r2, r4))*sin(T(r1, r2, r4))*(diff(_F2(r1, r4), r4)), (diff(_F2(r1, r4), r1))^2 = -cos(T(r1, r2, r4))^2, diff(diff(_F1(r2, r4), r4), r4) = -_F1(r2, r4)*cos(T(r1, r2, r4))^4-2*(diff(_F1(r2, r4), r4))*cos(T(r1, r2, r4))*sin(T(r1, r2, r4)), (diff(_F1(r2, r4), r2))^2 = -cos(T(r1, r2, r4))^2, sin(T(r1, r2, r4))^2 = -cos(T(r1, r2, r4))^2+1, diff(T(r1, r2, r4), r4) = cos(T(r1, r2, r4))^2, (diff(T(r1, r2, r4), r1))*sin(T(r1, r2, r4)) = 0, (diff(T(r1, r2, r4), r2))*sin(T(r1, r2, r4)) = 0, diff(T(r1, r2, r4), r1) = 0, diff(T(r1, r2, r4), r2) = 0]

(14)

``

``


 

Download Finding_transformation_eqn_between_zero_and_harmonic_with_conformal1.mw

Hi,

I am trying to solve a differentiation but I think I am stuck since the solution is not what it should be.

So, I got the equation below

eq4 := `S__2 ` = sin(alpha - phi)*sin(-beta + alpha)*H^2*M/(2*sin(-beta - delta - phi + alpha)*sin(beta)*sin(alpha)) - S__1

And according to the paper I read, to get the maximum value of alpha for maximum value of S_2, I need to make differentiation to first derivative where dS_2/d(alpha) = 0

Then I should substitute back value of alpha to equation above and the paper shows that i should get equation below.

`S__2 ` = 1/2*M*K__a*H^2 - `S__2 `

where K_a is

`K__a`= [(sin(beta+phi))/((sin(beta))/(sqrt(sin(beta+delta))+(sqrt(sin(phi+delta)*(sin(phi-varepsilon)))/(sin(beta-varepsilon))))]

 

I know its really hard but hope someone can give some idea how to do it.

 

Thank you very much.

 

Kind regards

Faiz Farhan

Got a lot of worksheets who are not complete anymore once opened in maple 2020

It can be only opened with a old version of Maple
Can it be imported in Maple 2020?

example 

Dynmod03.mws

Please can you help me in resolving this error?

Here is the codeOptimal_control_model_of_DF_and_LP_2.mw

First 96 97 98 99 100 101 102 Last Page 98 of 365