Dear All :

  I have a ODE equation system like this:

eqns := 1.00011000*10^(-7)*(diff(v[gs](t), t))-1.000*10^(-12)*(diff(v[ds](t), t))+v[gs](t)+1.000*10^(-18)*(diff(v[gs](t), t, t))+5.00*10^(-19)*(diff(v[ds](t), t, t)) = 12, 2.900*10^(-18)*(diff(v[ds](t), t, t))+5.00*10^(-7)*(diff(v[gs](t), t))+6.00*10^(-19)*(diff(v[gs](t), t, t))+v[ds](t) = 24
 

In honor of Pi Day, in this blog I would like to show that the MRB constant has some meaning in our day to day lives. The first two messages are lifted from a discussion group.

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.