Groups > comp.soft-sys.math.mathematica > #1602

Re: from Rumen, MEXICO, petition

From	"Stephen Luttrell" <steve@_removemefirst_stephenluttrell.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Re: from Rumen, MEXICO, petition
Date	2011-04-11 11:05 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<inun9a$2a9$1@smc.vnet.net> (permalink)
References	<inpeua$8ul$1@smc.vnet.net>

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The roots are complex-valued. Here is a way of finding them:

Define the function whose roots you want.

f[z_] := 11 Exp[-(z/135)] + 10.5` Exp[-(z/425)] + 4.899` Exp[-(z/1754)] + 
2.02912`;

Contour plot the absolute value over a large enough region to get a feel for 
what the function looks like.

ContourPlot[Abs[f[x + I y]], {x, -200, 300}, {y, -3000, 3000},  Contours -> 
50]

The zeros all lie at around Re(z) = -50, and they repeat periodically in 
Im(z) as you would expect from the exponential dependence of f(z) on z.

Use your mouse to grab the approximate position of one of the zeros (I got 
{-58.01, 478.8}), and find the minimum.

FindMinimum[Abs[f[x + I y]], {{x, -58.01}, {y, 478.8}}]

which gives

{2.04123*10^-7,{x->-55.0724,y->546.446}}

-- 
Stephen Luttrell
West Malvern, UK

"Rumen Ivanov" <rumen5252@yahoo.com.mx> wrote in message 
news:inpeua$8ul$1@smc.vnet.net...
> Hello,
>
> 11*Exp[-Es/135]+10.5*Exp[-Es/425]+
> 4.899*Exp[-Es/1754]+ 2.02912  = 0
> Please tell me how Mathematica can solve this equation
> for Es? With the derivatives of "Solve" it is impossible.
>
> Best
>
> Regards,
>
> Rumen
>
> Prof. Dr. Rumen Ivanov Tsonchev
> Facultad de F=EDsica
> Universidad Aut=F3noma de Zacatecas
> e-mail=B4s:
> rumen5252@yahoo.com.mx
> rumen@fisica.uaz.edu.mx

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from Rumen, MEXICO, petition Rumen Ivanov <rumen5252@yahoo.com.mx> - 2011-04-09 11:12 +0000
  Re: from Rumen, MEXICO, petition Peter <petsie@dordos.net> - 2011-04-11 11:07 +0000
  Re: from Rumen, MEXICO, petition Noqsi <noqsiaerospace@gmail.com> - 2011-04-11 11:07 +0000
  Re: from Rumen, MEXICO, petition "Stephen Luttrell" <steve@_removemefirst_stephenluttrell.com> - 2011-04-11 11:05 +0000

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