On Tue, Sep 2, 2008 at 12:43 AM, James G. Sack (jim) <[EMAIL PROTECTED]> wrote: > I've got a function of p (written in c) > f = pow(p, (log 0.5)/log m) > where m is a parametric constant 0<m<1 (not 0 or 1) > and p is in 0<=p<=1. > It /can be shown/ that f is also in the range [0,1]
Remember also that logB(A) (logarithm, base B, of argument A) = logK(A) / logK(B) where K is any constant. Therefore, your problem is really: f = p^(logm(0.5)) Also, take the expression logB(A) = E. This can also be expressed as B^E=A (the base, taken to the exponent, equals the argument of the logarithm). Therefore, logm(0.5) is whatever power takes m to 0.5, and you're then taking p to that result. Interestingly, when p=1, f=1 regardless of m. I plotted this in two dimensions, manually modifying the value of p to watch its effect on m and f. I could describe the shape, but it would make more sense if you plotted it yourself than if I tried to express it in English. -- Brad Beyenhof . . . . . . . . . . . . . . . . . http://augmentedfourth.com If the world were merely seductive, that would be easy. If it were merely challenging, that would be no problem. But I arise in the morning torn between a desire to improve the world and a desire to enjoy the world. This makes it hard to plan the day. ~ E.B. White, writer (1899-1985) -- [email protected] http://www.kernel-panic.org/cgi-bin/mailman/listinfo/kplug-list
