## How can I attach labels to LP solution matrices an...

Good day.

I am working on a network flow problem that uses a linear programming (simplex) technique.The flow is directed across 3 regions (a, b, and c) and there are 2 nodes within region a, 4 nodes in region b, and 5 nodes in region c.

I wish to determine the minimum cost from regions a to c and from regions b to c that satisfies the requirement of each of the 5 nodes in region c. The objective and constraints are constructed and Maple produces the minimum solution (see attached). While the output is useful when the number of nodes is small, I would like to extend this to a larger-scale case and so the output would need to be more user-friendly / graphic.

I have 2 questions -

1. Does anyone know a way to attach labels for each region and each node to these solution matrices?
For instance -  the first matrix, x, specifies a quantity of 2,000 that flows from node #1 in region a to node #2 in region b
2. Is it possible to produce a network graph showing the directed flow from each region and from node to node?

Thanks to all for reading this!

MaplePrimes_Network.mw

## How can I write a sum over even numbers, of a term...

Hello

I have the following summation to do,

d(l,m')=\sum_{N=-l'}^{l'}d(l',N,m')=d^{l'}_{00}(\dfrac{\pi}{2})d^{l'}_{0m'}(\dfrac{\pi}{2})f_{m'0}+\sum_{N=1}^{l'}((-1)^{l'}+1)d^{l'}_{0N}(\dfrac{\pi}{2})d^{l'}_{Nm'}(\dfrac{\pi}{2})f_{m'N}

where  d^{l'}_{0N} are the rotation matrix functions and  f_{m'N} is a piecewise function which takes a certain value at N=0, another value for N even and it takes 0 as a value for N odd.

The prblem is that I don't know how to write a summation for N even only so that in that case i can replace f_{m'N} by its expression for N even. The other way is to write f_{m'N} as a piecewise function but in that case, i don't know how to do it (I tried to use assuming N even ..) but got wrong answer.

Thank you for helping me solving my proble.

Best regards.

## How to plot this equation?...

where p, q, r, a are positive constants and phi(0) be a initial condition

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## I have a problem with the "Diff" command....

Hi !

Looks like there is a bug in the inert "Diff" command.

I have Maple 2018 on Windows 10 ,64 bits.

Does Maple consider Diff(f(x),x) to be equal to Diff(f(x),[x]) ?

It should be the same.

Maple displays  that it is equal but keeps in memory something else.

In the attached file, I give a very simple example.

I don't like to say this but my old version of Maple V Release V (1997) is more consistent i.e.

this version shows it's different and  keeps in memory that difference.

diff-problem.mw

I wonder if newer versions have this problem ?

Best regards !

## DirectSearch finds nonexisting roots...

DirectSearch finds nonexisting roots....     DirectSearch_finds_nonexisting_roots.mw

 >
 > restart
 > plot([cos(x), 0.001*x*x],x=-40..40,y=0..2)     ### test function plot
 > eq:= cos(x)= 0.001*x*x;     ###   float
 (1)
 > use RealDomain in solve(eq,x,explicit) end use   ## lacking some of the roots
 (2)
 > use RealDomain in solve(eq,x) end use
 (3)
 > fsolve(eq,x=-30)
 (4)
 > plot([cos(x), 0.001*x*x],x=-32..-31,y=0.9..1)
 > fsolve(eq,x=-32..-30);  fsolve(eq,x=-31.7..-31.4)
 (5)
 > with(DirectSearch)
 (6)
 > eq; SolveEquations(eq,AllSolutions):
 (7)
 > interface(rtablesize=90); SolveEquations(eq, AllSolutions)
 (8)

DirectSearch finds nonexisting roots!!!

Dr. Ali GÜZEL

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## How do i solve State Space system in Maple??...

Hii!!

I need your help in state space system.... kindly guide me how to solve State Space system in maplesoft.....i excecute the command but i didn't find the answer....can you plz help me?I have been trying for two weeks now but it is not working.Thank you!!

## How to solve ode system with equilibrium points...

eq1 := diff(x(t), t) = x(K[1]-x(t))-p*x(t-tau[1])*y(t); eq2 := diff(y(t), t) = y(K[2]-x(t))-q*y(t-tau[2])*x(t);
(x*, y*):= (p*K[2]-k[1])/(p*q-1), (q*K[1]-k[2])/(p*q-1);

where, k_1, k_2, p, q, tau_1, tau_2 are positive constants

## Plot with explore...

How to plot this equation with explore or animation

E[1]:=Sum((GAMMA(((beta+1)n-gamma(nu-1))+k))/(GAMMA(((beta+1)n-gamma(nu-1)))*GAMMA(rho*k + (nu(1-mu)+mu(2 n+1))))*((omega*t^(p))^(k))/(k!),k=0..5);  E[2] :=Sum((GAMMA((gamma(n+1)-beta *n)+k))/(GAMMA((gamma(n+1)-beta *n))*GAMMA(rho*k + (mu(2 n+1))))*((omega*t^(p))^(k))/(k!),k=0..5);    y(p):=Sum(c*gamma^(n)*t^(nu*(1-mu)+mu+2*mu*n-1)*E[1]+gamma^(n)t^(mu(2 n+1)-1)*E[2]*g, n=0..5);

with the conditions

mu, nu \in (0, 1); omega \in R; rho > 0; gamma, beta > or = 0; c & g are constant

## How to solve a differential equation in Maple?...

Hi,

I want to solve a differential equation and plot the particle densities versus the distance.

How can I do this in Maple?

DE.mw

Sincerely

## Changing the value of variable 'S' from 1 to 1.0 a...

I wrote a small code to solve the equations. The problem is whenever i change the value of variable 'S' from 1 to 1.0 maple produces different solution. It means that i am only right solution for S=1. I can't get right solution other than S=1. I haven't faced this kind of problem before. Can anybody take a look? Is there something wrong with the code? Thanks!

restart:with(PDEtools):declare(f(eta),theta(eta),quiet):S:=1:
f(eta):=sum((q^i)*f[i](eta),i=0..16):
eqa:=simplify(diff(f(eta),eta,eta,eta)+(q*g*((f(eta)*diff(f(eta),eta,eta))-((diff(f(eta),eta))*(diff(f(eta),eta)))-(S*diff(f(eta),eta))-(((S*eta)/2)*diff(f(eta),eta,eta))))):
f[0](eta):=(alpha/2)*eta^2+eta:
for m from 1 to 8 do eq[m]:=coeff(eqa,q^m) end do:
for m from 1 to 8 do (simplify(int(int(int(((-1)*eq[m]),eta),eta),eta)+f[m](eta))):f[m](eta):=simplify(%) end do:
a1:=simplify(sum(f[n](eta),n=0..8)):
b1:=simplify(subs(eta=1,a1))=(S/2):b2:=simplify(subs(eta=1,diff(a1,eta,eta)))=0:
sys:={b1,b2}:solution:=fsolve(sys):s1:=solution[1]:s2:=solution[2]:
alpha:=rhs(s1);g:=rhs(s2);beta:=g^(1/2);
c1:=simplify(a1):c2:=diff(c1,eta,eta):c3:=subs(eta=0,c2)


## add and add with different results...

Hello,

I noted that add and 'add' can give different result, can somebody help me understand it?  Consider the code below:

>phi1 := GAMMA(-(1/2)*vst-8.333500000-(1/2)*r)*GAMMA((1/2)*vst+21/2+(1/2)*r); phi2 := GAMMA(16.66700000+r-2*vst)*GAMMA(2.166500000+vst); xi1 := -vst; xi2 := 16.66700000+r-2*vst; z := 37.52950222; K := 9.846618489*10^(-38)*33.330^(.5000000000*r+10.)

### Then I have the following sums (they were supposed to give the same results):

>f := unapply(K*add(phi1*(-1)^vst*z^(-xi1)/factorial(vst)+phi2*(-1)^vst*z^(-xi2)/(.5*factorial(vst)), vst = 0 .. 10000), r):

>g := unapply(K*'add'(phi1*(-1)^vst*z^(-xi1)/factorial(vst)+phi2*(-1)^vst*z^(-xi2)/(.5*factorial(vst)), vst = 0 .. upto), [r, upto]);

# I am interested in the following quantities:

>evalf(f(1)/f(0));

-6.265883733

>evalf(g(1,10000)/g(0,10000))

25.80438437

That seems very strange to me, why maple gives different results?

## How to solve this summation ?...

Hi !

I want to solve several summations which at first glance seems very easy to me.

But I definitely hit a wall. I have Maple 2018 on Windows 10.

I'm not very familiar with the sumtools or Sumtools packages.

I have attached a file that gives you an example summation and the

solution I found and especially I show you the way that I obtained this solution.

The big question is:

Is there a way to transform this summation to arrive at my solution?

Or . Can the result I obtained be demonstrated?

Maple seems unable to solve this summation. Mathematica did no better.

I know very well that this is more a question for mathematicians than for

Maple users. But when I look at the questions in Mapleprimes I see

although there are good mathematicians behind most of these questions.

sum1.mw

## Annoying little thing with Greeks letters . Known ...

Hi !

I just noticed a strange behavior of Maple with Greek letters.
I have Maple 2017 and 2018 on Windows 10 .

Suppose you write a procedure that contains Greek letters.

If you run the procedure definition, the Greek letters are not displayed correctly.
They will be displayed in words: alpha, beta, gamma,...
The procedure will still work.

Now close the file. Then open this file. Maple now shows you the procedure with the Greek letters correctly displayed.

I added a file as an example.
Maybe it's an annoying little problem known for a long time ? I don't know .
I have an old version of Maple V Release V (1997) which does not have this problem.

Best regards !

alphabeta.mw

## How to act with a differential operator on a funct...

This might be a trivial question, but I have not been able to find the answer. I am using Maple 2018.

I am working with differential operators acting on real valued functions of a real variable. On the first hand, I want to be able to do simple algebra with these operators. For example, I might want to compute the commutator of two such operators. I have been using the DEtools package, toghether with the 'mult' command to perform such calculations. See the atached file containing a simplified version of what I am doing.

Now, I also want to be able to act with my differential operators on a function, and get the resulting function.

(a) What command allows me to do that within my framework? (i.e. that of DEtools with the way I have defined and used my operators)

(b) I there a better way to proceed? (i.e. is there a better way to do both algebra with differential operators and to act with them on functions to get the resulting function)

Many thanks

Example.mw

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