Re: parameter restrictions

*To*: mathgroup at smc.vnet.net*Subject*: [mg32442] Re: [mg32428] parameter restrictions*From*: "soso lala" <sosolala at hotmail.com>*Date*: Mon, 21 Jan 2002 02:54:53 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi Thanks for your answer. Unfortunately, it does not work like this. Consider the following example: Clear[f,x,a,b] f[x_,a_,b_]:= -x^(a+b) The second derivation with respect to x is: D[f[x,a,b],{x,2}] -(-1+a+b)(a+b)x^(-2+a+b) Given that x>0,a>0,b>0 and (a+b)<1 this derivation is unambiguously positive. I have tried to show this with Mathematica in the manner proposed: Clear[f,x,a,b] f[x_?Positive,a_?Positive,b_?Positive]:= -x^(a+b) /; (a+b)<1 Now, if I write D[f[x,a,b],{x,2}]>0 I would expect the output TRUE but I receive f^(2,0,0)[x,a,b]>0 Can somebody tell me where the mistake is or how I must define parameter restrictions? Thanks for your efforts Jack >From: BobHanlon at aol.com To: mathgroup at smc.vnet.net >Subject: [mg32442] Re: [mg32428] parameter restrictions >Date: Sat, 19 Jan 2002 20:47:10 EST > > >In a message dated 1/19/02 8:05:36 PM, sosolala at hotmail.com writes: > > >I am using Mathematica 4.0 and have a question about parameter >restrictions. > > > >How can I define the range of values of a parameter, e.g. that alpha must > >be > >positive or that (alpha + beta) must be less than unity? > > > >Although it may be a very simple question (and/or answer) I would be > >delighted if I get an answer. > > > >f[x_, a_?Positive] := a*x; > >f[x_, a_?Positive, b_?NonNegative] := a^x*b /; (a+b) < 1; > > >Bob Hanlon >Chantilly, VA USA _________________________________________________________________ Downloaden Sie MSN Explorer kostenlos unter http://explorer.msn.de/intl.asp.