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System of NonLinear Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg48511] System of NonLinear Inequalities
• From: "maurizio lisciandra" <lisciandra at hotmail.com>
• Date: Fri, 4 Jun 2004 04:49:25 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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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• Follow-Ups:
  • Re: System of NonLinear Inequalities
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>