## The MRB Constant

Maple

The appearance of this thread has degraded over the years, but most all post about the MRB constant can be found by entering "MRB constant" into the search box.

Some links were updated on June 26, 2010.

## Complex typesetting...

I know that the purpose of Maple is not to be a typesetting worksheet. But the improved typesetting abilities (Ver 10) are useful for making demonstration worksheet. Specifically, I would like to make a demonstration worksheet of a mark-recapture model I am currently working on. The main purpose is show how how the likelihood is built, step by step, following the paper's notation. As well as showing estimable parameters (including sparse data scenarios). Since my work is used by biologists rather than mathematicians, I feel it is a worth pursuit. The only problem is that I cannot dupicate notation such as:

## using mouse to get data from plot...

I have still been using mostly release 8, but was wondering whether MAPLE 10 now can do things standard in MATLAB, JAVA: Is there a way in release 10 (maybe via maplets?) to use the mouse for extract the coordinates of a point from a maple-plot [[ e.g. want to use initialize a dsolve() by graphically selecting the initil data.]] going further, is there a way to "draw" a curve on a maple plot using the mouse -- and get the coordinates of points along the curve back into the worksheet )(e.g. as an array that can be further manipulated)?

## Polar representation of complex numbers?...

Greetings, I have done some searching and have been unable to find out how to use complex numbers in polar form in Maple 10. Is this possible? If so, what about degrees versus radians and can both polar and rectangular representations be used in the same document/worksheet? Thanks, Ken

## Brain teaser # 1

by: Maple
A few years ago I saw somewhere in a math forum a brain-teaser type problem which I'm about to present. I wasn't able to solve it at the time. I haven't been able to find the original forum, so I don't know whether or not my answer is right. I do know that I could never have attacked the problem without MAPLE. We have a cube of edge a and a drill bit of diameter b. We drill one hole from the center of the front face to the center of the back face, and another from the center of the right face to the center of the left. What is the total volume of material removed? I get (Pi*(b^2)*a)/2 - ((2/3)*b^3) Am I right?

## Problems with subs and collect...

I am having problems with subs and collect. Unfortunately, I still haven't figered out how to make the input part of a MAPLE equation visible in the post. I still have the problem that it just appears as "MAPLE equation" so anyone who is kind enough to want to help me will have to look at my file Thank you View 2292_SubstitutionAndCollect.mw on MapleNet or Download 2292_SubstitutionAndCollect.mw

## substitution of expressions involving functions...

I would like to apply a relation such as f(x,a)*f(x,b) = (f(x,a)+f(x,b))/c (where x,a,b are any real number say) to simplify an expression such as f(y1,a1)*f(y2,a2)*a3*f(y1,a4)*f(y2,a5) to a3*( f(y1,a1)+f(y1,a4) )*( f(y2,a2)+f(y2,a5) )/c/c The only way I can see to do this is to struggle to get the function in the `right' order with no constants between them, and then do a substitution for every variable triple (y1,a1,a2) that occurs. There must be a better way. I've looked around the forums but I don't even know what to look for really so any suggestions of where to look would be great.

## Rounding very small numbers to zero...

Hi - Is there a way to tell Maple to zero out terms in an expression that have a very small constant. For example I would like to round something like (1x + 2y - (1x10^-20)z) to (1x + 2y). Thanks. Bryan

## plot a function...

Hereby I'm telling you I'm new in using Maple, so please don't laugh after reading my problem. I want to plot the function x=6. In my brain this is a vertical line, through the x-axis with x=6. After several attempts, the only thing I get is a horizontal line through y=6. Where did I go wrong? > x:=6; > plot(x);

## Coupled diff eq using Rkf45...

(D@@2)(x)(t)=(-g/v)*sqrt(D(x)(t)^2+D(y)(t)^2)*D(x)(t)
(D@@2)(x)(t)=g-g/v*sqrt(D(x)(t)^2+D(y)(t)^2)*D(y)(t)
initial conditions
x(0)=0,y(0)=0,d(x)(0)=134,d(y)(0)=0
using rkf45
for time, 0-30
solve for x(t),y(t)
then i plan to plot the two and find the intersection
but i'm having trouble getting through the rkf45 to get my x(t) and y(t)

## Multiple Mapping...

I intended to post this msg in this forum but somehow put into the MAPLE TA forum. Here it is where it belongs. I know this is a really basic question & I'm kind of surprised I haven't run into this situation before, but here goes. Multiple assignments are possible, e. g. a,b,c = 1,2,3 What's the simplest MAPLE command(s) which will place into each of these 3 variables a value twice its previous value. I try stuff like a,b,c = map(x->2*x,(a,b,c)) and MAPLE says no way!

## coupled differential equations...

how do i solve a set of coupled differential equations like these for x(t) and y(t) eqn1 := (D,2)(x)(t) = -a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(x)(t), eqn2 := (D,2)(y)(t) = g-a*sqrt(D(x)(t)^2+D(y)(t)^2)*D(y)(t)

## Nice numerical trouble

by: Maple
Playing with numerics for the hypergeometric function 2F1 i stumbled into the following exactness stuff, where lots of digits are lost and one needs to increase working precision quite a lot to get a good answer: f1 and f2 result from evaluating ugly, but usual transcendent functions, f3 comes through high precision and f0 is the limiting case.
```  restart;

hypergeom([1,2+epsilon],[3],z):
'%' = simplify(convert(%,StandardFunctions));
theSol1:=rhs(%):

theSol1 = -2*(z*(1-z)^epsilon*epsilon-1+(1-z)^epsilon)/
z^2/((1-z)^epsilon)/epsilon/(1+epsilon);
is(%);
```