## Transition Matrix irreductible aperiodic ...

Hi

I have the transition matrix used in Markov chain

A := Matrix([[alpha, beta, gamma], [delta, epsilon, zeta], [eta, theta, mu]])

I would like to write a system of equations that can be solved  to get a Markov chain  irreducible and aperiodic

All the entries of the transition matrix are in the interval [0,1)

Many tanks for any help

## why simplify command doesn't work for Ei function?...

if I use the command below, I will get the right answer.

`assuming`([simplify((2*I)*deltas*Pi*BW*Ei(1, (2*I)*deltas*Pi*BW)-(2*I)*deltas*Pi*BW*Ei(1, -(2*I)*deltas*Pi*BW))], [real, BW > 0, deltas > 0, ts > 0, deltas <= ts, 2*BW*ts >= 1])

2*BW*Pi*deltas*(Pi-2*Si(2*BW*Pi*deltas))

while I use the same command for the compliacated Ei function, it doesn't work any more, I don't know the reason.

`assuming`([simplify(Ei(1, I*BW*Pi*deltas-(5*I)*BW*Pi*ts)-Ei(1, -I*BW*Pi*deltas+(5*I)*BW*Pi*ts), Ei)], [real, BW > 0, deltas > 0, ts > 0, deltas <= ts, 2*BW*ts >= 1])

and it's reault is :

Ei(1,I*BW*Pi*deltas-5*I*BW*Pi*ts)-Ei(1,-I*BW*Pi*deltas+5*I*BW*Pi*ts)

## Algebraic combinations of polynomials...

I am looking for a nice algorithm to determine if a polynomial is expressible as an ALGEBRAIC combination of a list of other polynomials. I have written my own for LINEAR combinations, but cannot quite generalize this method.

Any help would be greatly appreciated.

## Plotting an expression with unknown function Gener...

Hello, I am trying to plot an expression for my General Relativity class, this expression is one of the expanding universe FLRW solutions to the Einstein field equations and contains an unknown functions.

My question is how do I get maple to plot this?

Thank you

## how to calculate implication logic result directly...

i use

A -> B

B -> C

would like to find A -> C directly from A -> B and B -> C

but logic table show that AND(A->B, B->C) is not equal to A -> C

and (A->B) -> (B->C) is not equal to A -> C too

which logic operations can do this?

because do not want to use result to verify and because i do not know the result in the beginning

## How do I generate all non-isomorphic trees of orde...

I could keep on using the commands

with(GraphTheory):

with(RandomGraphs):

DrawGraph(RandomTree(7))

but then this is not helpful because I do not get non-isomorphic graph each time and there are repetitions. So any other suggestions would be very helpful.

## How can I assign pi to a value on Maple?...

I assigned the greek alphabet  in Maple but it displayed an error message since it is already a known constant 3.142. Please how can I assign pi to 0.45 in Maple ?

## how to write better for passing parameter which is...

for example

func1 := proc(system1)

for i from 1 to 100 do

solve([system1[1], system1[2]],[x,y]);

od:

end proc:

func1([diff(y,t) = data[i+t+1], diff(x,t) = data[i+t+1]])

i is depend on the for loop inside a function, but woud like to pass this system into a function with i

this will cause error

how to write better for passing a system as parameter using variable inside a function?

## indets is different in this case, how to do?...

indets(AA(MM(AA(X1,X2),B2),MM(AA(B2,X3),X5)));
this can get a list of X1,X2,B2,X3,X5

propositionsentence := MM(AA("it", "run"), "maple"):
indets(propositionsentence);

but this can not get "it", "run", "maple"

how to do this in case this in maple 12?

## Using the Explore command to produce more advanced...

Dear Maple users

I was using the animation command to create an animation consisting of a running sine curve with a ball following the curve, as shown below. I wonder if it is possible to create it with the Explore command too? Or is this command more limited? I need to be able to add more animations, like I can with the display command ...

Regards, Erik.

## How do I get an analytic solution to this integral...

Hello all,

So far I have been unable to find this question anywhere, but I apologize if it is a duplicate. I'm trying to evaluate the integral of sechq(x), where q is a positive integer. Mathematica is able to tell me the result (a hypergeometric function), but for some reason, Maple seems not to be able to compute this integral, it just gives me back the integral. A higher info-level on the 'int' function reveals a line that says 'Risch d.e. has no solution', but I'm not sure if that has anything to do with my problem. Any suggestions or tips on how to get an answer out of Maple would be greatly appreciated!

## First order frequency response, no plot possible....

Hi guys,

I've had only a little experience with Maple, but I decided to use it for preliminary frequecy response calculations. The funny thing is, I have already the solution in some way, but I'm too stupid to get it working. I can't see the mistake, however, it should have something to do with the H_n(f) function and the other normalized functions.

NASA has published a nice paper which explains the calculations, however, they have used MathCAD. Anyway, I don't think this should be a problem. Here is the documentation: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070016024.pdf

The error message is for example for the H_n(f) function:

Warning, expecting only range variable f in expression H__n(f) to be plotted but found name H__n

Maple file: calculations.mw

## Can I solve an inequality with an assumption?...

Hello people in mapleprimes,

I want to modify the inequality of e assuming d.
But, e/(1-a) assuming(d) does not work well.
How can I do for this?

```d:=(a>0,a<1,b>0,c>0);
0 < a, a < 1, 0 < b, 0 < c
e:=(1-a)*b>c;
c < (1 - a) b
e/(1-a)assuming(d);
`*`(c<(1-a)b,1/(1-a))
```

inequality.mw

## interaktive Functions-analysis program in Maple ?...

Hi I teach math,

And I seek help to make the following.

Lets say you have a function f(x)=x^3-x^2-4*x+12 and you want make a Maple demonstration which shows the students first how they find the extreme-points of this function by first solving f'(x) = 0 -> 3x^2 - 2*x - 4=0 and then taking the two extreme points and calculating the slope the tangent on their respective left and right side of the point x =. And then outputting.

Since the slope of the tangent on the left side x = .... is positive and the slope of the right to the right of the point is negative, then  x = ..... is a local max.

Since the slope of the tangent on the left side x = .... is negative and the slope of the right to the right of the point is positive, then  x = ..... is a local minimum.

I know that this can be done using FunctionAnalysisTutor from the StudentCalculus1, but since I teach student whos first language is english, I would to be able to do a worksheet/document which shows the above mentioned textoutput. It is possible? If yes if anyone has ideer howto do this? I would very much appriciate some input.

best regards

Fred

## Bug in MapleTA?...

When I execute the following code in Maplesoft on my computer, there are no problems.  However when I execute the same code in mapleTA occasionally Maple only finds a single input value corresponding with h_given.  Anybody have any idea what is going on?

Basically I have a function, f,  that I am only interested in plotting and analyzing real-valued inputs, t, from =0 to 100 (or so).  At some point I assign an output value, h_given, and I wish to find the correlated real-valued inputs.  From the graph you can clearly see that there are 2 inputs, however the script occassionally only produces 1 output. (when running on mapleTA).

with(Optimization):
with(plots):
restart:
randomize():
a := MapleTA:-Builtin:-range(1800, 2300, 100):
b := (1/10)*MapleTA:-Builtin:-range(4, 8, 1):
timeT := MapleTA:-Builtin:-range(70, 100, 10):
f := -t*(b*t-b*timeT)^2*(cos(.15*t+4)^2-3)/a:
maxs := NLPSolve(f, t = 0 .. timeT, maximize):
maxim := maxs[1]:
graph := plot(f, t = 0 .. timeT, gridlines = true, 0 .. maxim+10, labels = [t, h(t)], labeldirections = [horizontal, vertical]);
h_given := 10;
expr := h_given-f:
answer_t := Student:-Calculus1:-Roots(expr, t = 0 .. timeT+5);