I am working on a problem in geometry where I have ended up with a system of nonlinear ODEs in F and G where F and G are functions of a coordinate y, and A and B are both real constants.  I have included the worksheet where I am working on the equations.

Ric_Equations.mw
 

 I would like to solve these in as explicit a way as possible by obtaining expressions for F and G and was wondering how best to do this with Maple (it doesn't really matter if the explicit solutions are messy, as I just need to know that they exist and can be written down in some form).  I have tried using the dsolve command directly but I receive the error message which you can see above.

Consider A is an nxn binary matrix where n>1000. Assume that there is an integer k<100 such that the entries of the kth power of A, denoted A^k, are all positive integer numbers.  

My problem is that the computation of A^k takes too times and I want to ask: Is there some techniques in Maple for obtaining the matrix A^k. 

One technique that I am used is based on the boolean semiring with 1+1=1. In fact, I evaluate A^k until I reach the full-1 matrix. But the mentioned technique dose not effect the time of computation. 

For example consider the 1024*1024 binary matrix which is given as an attachment. It takes 2278 seconds to find out the entries of the 20th power of this matrix are all positive integer numbers.

I am used the following version of Maple 15. 
Thanks for any suggestions.

 Matrix.txt

Edition(1): The following command maybe useful. From the next command you can upload the given matrix in your worksheet and test it for my claim.

input := FileTools:-Text:-ReadFile("C:/Users/Desktop/Matrix.txt")

Sam := Sample(('Uniform')(10, 20), 30)

My question has two steps:

STEP 1:  The multiplication  of is defined as follows

if n<>l, then

.

if n=l and m<=s,

Question 1: I wrote a code for calculating the multiplication  of. Is it right?

The code for Step 1  

restart;

multiply:=proc(n,m,l,s) local g,a: 
a:=unapply(doublefactorial(2*j-1)/factorial(j),j):
g:=unapply((a(m-j)*a(j)*a(s-j)/a(m+s-j))*(2*m+2*s-4*j+1)/(2*m+2*s-2*j+1),j):

if n<>l then 0 else
sqrt((2*m+1)*(2*s+1))*2^(K/2-1).add((g(j)/sqrt(m+s-2*j+1/2))*phi[n, m+s-2*j],j=0..m) 
end if
end proc:
 
n:=2:
l:=2:
m:=1:
s:=1:
multiply(n,m,l,s);

when I compared the results which I got and the results which is given in the book as follows, I think it is right.

Step 2:

We know that the outer product matrix is calculated as follows 

We found the elements of the outer product matrix in Step 1. 

Question 2 : I want to write the elements which are derived in step 1 to the outer product matrix in step 2. In here, the outer product matrix is NxN matrix. N=(M+1).2^(K-1) where K, M are any integers.

Hello,

How I can take variation from left-hand side of  5, and reach to right-hand side of  5. After by using integral by part obtained  7?

Thank you

I use Maple 2015, is it possible to animate a standing wave as shown below?

 A working animation can be found on https://oceanservice.noaa.gov/facts/seiche.html

Download dummy_1.mw

I want to write a procedure P such that the input of P is a positive integer number n and the output of P is a random permutation of the numbers {1,2,..,n}. 

I know that there is a command in Maple 2017 such that the command produces the mentioned request (random permutation in the combinatoric package), but I should work with Maple 15 and there is no the random permutation command in Maple 15. 

One of the solutions that I am used is based on the random number and check that if the produced numbers are pairwise distinct or not. The problem of this method  is that for n>128, it takes too time to generate a random permutation of the length n.

Thanks for any suggestions. 

I'm trying to better understand the Black and Scholes model; which is a scalar function on (positive reals)^5.
a maplesoft worksheet defines it as

BS_Price=exp(-r*T)*(-(1/2)*erf((1/4)*sqrt(2)*(sigma^2*T-2*r*T+2*ln(K)-2*ln(S[0]))/(sigma*sqrt(T)))+1/2)

I am trying to understand the parameter vectors (r ,T,K,S[0],sigma) that give the same values of BS_Price - and particularly whether these form curves, closed curves, surfaces or similar.

Right now, I am not sure how to procede.

EDIT
I've just put together  a procedure that evaluates BS at points in R^5 - and i think i can move forward by using the curry or rcurry functions to get a 5d tensor of the values of BS, that i can start to look for patterns within.

BS_Price := proc (InterestRate, StockPrice, StrikePrice, Duration, Volatility) evalf(subs([r = InterestRate, S[0] = StockPrice, K = StrikePrice, T = Duration, sigma = Volatility], exp(-r*T)*(-(1/2)*erf((1/4)*sqrt(2)*(sigma^2*T-2*r*T+2*ln(K)-2*ln(S[0]))/(sigma*sqrt(T)))+1/2))) end proc

could anyone give me advice on doing this?
 

The animation in this worksheet seems realistic but I wonder if the physics which is implemented is correct since there is no explicit mention of rotational energy.

ThrowBola.mw

Dear Community,

I have set up a simple 2D RC network with 1 lookup table current source, and a few probes. The model runs fine. Now I wanted to run it from Maple, and followed carefully a MapleSim tutorial which exlained how to establish the link between Maple and MapleSim. I added a worksheet called RCNetworkMaple.mw and run the A := MapleSim:-LinkModel(): command. Then I wanted to run the simulation with the A := Simulate() ; command, but nothing happened, Maple returned A := Simulate(). What did I wrong? In the tutorial it runs perfectly. (Files attached.)

Tx for the kind help in advance,

best regards

Andras

RCNetwork.msim  RC_Rate_Schedule.xlsx

Hellow, help required to remove the errors

 How to  obtain the pressure drop i am unable to get the output. I am uploading the file  and the equations

help_dp.mw

Hi, I’m new to maple and I’m not very good with these things, but could someone tell me if there’s a way to calculate a^b with large numbers?

I’ve tried to do it but it just says evaluating in the bottom left corner but doesn’t actually do anything. This is an example with two of the large numbers i have to use(if this helps):

815427339135043^5579408896058

Thank you in advance for any help.

Good day!

I wish to represent the flow across a network from a set of sources to a number of destinations or sinks.

In the simple example attached, there are 4 sources and 10 possible sinks. The flow from source to sink is given by the matrix, A, and each element is a binary entry; 1 for active and 0, otherwise. I would like to assign labels to each source (A,B,C,D) and sink (1,2,3,..., 9,10) and this feature will be most convenient for large matrices.The idea is to have these labels shown on the directed graph so that it is easy to see the flow configurations at a glance.

Does anyone know how this can be done?

Thanks in advance.

MaplePrimes_network_labels.mw