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MathGroup Archive 2004

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Re: System of NonLinear Inequalities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48564] Re: [mg48511] System of NonLinear Inequalities
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sat, 5 Jun 2004 07:19:07 -0400 (EDT)
  • References: <200406040849.EAA23604@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

First of all, your inequalities are not written using Mathematica 
syntax (you can't use square brackets in this way). But looking at them 
I see it does not matter whether you use proper syntax or not: no 
computer program will ever solve a system of inequalites involving 
someting like x^(2/(2 - x)). Your only chance is a human brain and some 
fantastic stroke of luck.
Sorry for being so unhelpful.

Andrzej

On 4 Jun 2004, at 17:49, maurizio lisciandra wrote:

> Dear Friends,
>
> I tried to solve the following system of nonlinear inequalities with
> Mathematica 5.0:
>
> F < (1/2)*[a^(x/(2 - x))]*[x^(2/(2 - x))] &&
> (2*a*B)^(x/2) + F - B > (2*a*F)^(x/2) &&
> F > B > 0 &&
> 0 <= a <= 1 &&
> 0 < x < 2.
>
> I tried with Reduce, SolveInequality, SemiAlgebraicComponent, 
> FindInstance,
> but all these function do not solve it. I tried to substitute x for 
> some
> fixed value, but again I cannot solve it. The only value that I can
> substitute for x is 1, and in this case the solution is an empty 
> space. I
> may be happy if I find a value that solves the system, although I 
> really
> need for which inetervals in the variable this system is not an empty 
> space.
>
> Hope some nice Mathematica expert can help me.
>
> Cheers,
>
> Maurizio Lisciandra
> Trinity College
> Cambridge (UK)
>
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>


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