In this blog we will consider what happens when the formula for the MRB constant is iterated infinitely. This will invoke divergent series, but we will use an analytic extension of the formula to continue our iterating. We will also find a new use for MRB2=1-2*MRB constant.( Sloane's A173273 )

This is an update to my earlier post on the Rossler system, one of the simplest examples of a dynamical system in 3 dimensions that can exhibit deterministic chaos.

restart;

interface(displayprecision=10):

PDEtools:-declare(prime=t,quiet):

ross_x:=diff(x(t),t)=-y(t)-z(t):

ross_y:=diff(y(t),t)=x(t)+a*y(t):

ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t):

rossler_sys:=ross_x,ross_y,ross_z;

#Find fixed points:

 Consider the sequence of divergentt series in part evaluated by the following maple input.

f1 := seq((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 1/10 .. 9*(1/10), 1/10): evalf(f): where abs(a)<1

and

f2 := `$`((1-a)*(1/2)+sum((-1)^n*(n^(1/n)-a), n = 1 .. infinity), a = 2 .. 10): evalf(f2); where abs(a)>1 .

Here is the Rossler system, one of the simplest examples of 3 dimensional deterministic chaos (under certain conditions according to "params"). Thanks to Doug and Joe for various assists. Comments and critiques most welcome !

To judge results of functions coded in double precision against precise results (as they may be given by Maple) one has to respect decimal presentations on one side and IEEE on the other side.

For that one can use routines developed by Florent de Dinechin, which are worth to be better known.

Here is a Maple sheet showing how one can do it (looking at the complex valued power function using evalhf versus using MS VC2005 as an example).

Dear all:

     i want to useas a variable, but the maple show the following error message: " Error, illegal use of an object as a name" .
 

    So can anyone tell me how to solve this problem. tks very much

Andy

Dear all:

  we know the bode digaram produced by BodePlot function is arrangment horihorizontally? That is not suible for oberseve ,i want the bode diagram arrangment vitically (  amplitude & phase), Does anyone known how to do that ?

 tks very much!

Andy

Hi all .. is there a way in maple tht i can do matrix manupulations symbolically without defining its elements?
Eq:=

say if i give Transpose(MatrixMultiply(A,B)) should give BT * AT (where the 'T' represents Transpose_Superscript)

Thanks in advance.

Every year my extended family does a "secret santa" gift exchange. Each person draws another person at random and then gets a gift for them. At first, none of my siblings were married, and so the draw was completely random. Then, as people got married, we added the restriction that spouses should not draw each others names. This restriction meant that we moved from using slips of paper on a hat to using a simple computer program to choose names. Then people began to complain when they would get the same person two years in a row, so the program was modified to keep some history and avoid giving anyone a name in their recent history. This year, not everyone was participating, and so after removing names, and limiting the number of exclusions to four per person, I had data something like this:

Download 10597_asymp.mws
View file details

Hi
I am facing problem with maple. I try to get a asymptotic series of a transcendental equation but I get failed again and again. If You people could help me.

I am waiting for ur kind responce.

Thanks