## how do I simulate optimal control in maple (direct...

How do we write code for optimal problem using Pontryagin's maximum principle for simulation.

## Population balance up to Luo and Svendsen model...

Hi,

I am working on making a population balance model for gas bubbles is a stirred reactor. I have data in excel about the bubble size and need to make a population model to compare the experiment with theoretical findings.

But I have not much experience in population balance modeling. Is there anyone who has an example of a solved population balance model in maple? This would help me greatly in understanding the subject. I would want to use the Luo and Svendsen model as I found it most matching with the result.

Kind regards, Hasselhof

## best approximation of six multivariate normally di...

Dear Maple experts,

I would like to generate population data that is the best possible approximation of a multivariate normal distribution with a specified covariance matrix and vector of means. I do not want to draw a sample from a multivariate distribution, but I want the population values itself which are approximately multivariate normal distributed. The size of the datamatrix should be limited, otherwise I could draw a huge sample from a multivariate normal distribution. For instance, I would like to generate a 200 by 6 data matrix that is the best (or at least good enough) approximation of a MVN distribution. For a bivariate normal distribution one could calculate the probalities of a grid by integrating the density, but for six variables that seems undoable.

Before trying the invent the wheel again, I think I will ask this question to experts, because it is unlikely that there is no already existing algorithm that does the job pretty well.

Harry Garst

## Assigning characteristics to each member of an arr...

I know how to create arrays, but I want to assign characteristics to each position in the array; the array being a population with each member having a set of characteistics like height, weight etc. I want to be able to have some of the characteristics able to change with time, and some remain constant (those that change with time will be defined by generic equations)

I have tried looking on maplesoft for answers, and the help within maple 16, but have been unable to make any progress.

Sorry if the question is not specific enough.

## Graphing Logistic Population Models...

Hi, I need help with graphing a certain logistics population model for an initial population size that is equal to 1.

dy/dt = k(1 - y/M)y  k=2 M(t)=10e^-t/5 +3(1-e^-t/5)

So far I've worked out the values to input, but I don't know how to write it in Maple.

I know all I have to replace is the M in the dy/dt equation with these 2 values.

M(0) = 10

M(t goes to infinity) = 3

## How to use Maple to solve a war-related math probl...

by: Maple 15
 > restart;

## Linear Population Models...

I am trying to plot a Linear Population Model using Maple, could anybody tell me what I am doing wrong. My plot is just registering as a straight line at 1.0 and I know this is incorrect.

>

## Brownian Motion_Mean not zero...

Hello everyone,

I have a problem with the Brownian Motion (I'm using Maple 15).

Here is the code:

X:=BrownianMotion(0,0,1,t);

X1:=SamplePath(X(t),t=0..T,timesteps =T/d):

Mean(X1);

The last line give me a number different from zero, which is not true for a Brownian Motion as defined.

Could you please tell me where is the problem?

PS: I have the same problem with WienerProcess(sigma).

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