Recent content by jfitz

Nevermind, it's (D-1)/r.

Does anybody know, or know where to find, the expressions for the gradient and/or divergence in hyperspherical coordinates. Specifically, I'd like to know \nabla \cdot \hat{r} in dimensions higher than 3.

Nevermind, I figured it out.

Simulated annealing is a method which is designed to overcome being trapped in local minima. Section 10.9 of this book describes the method: http://www.fizyka.umk.pl/nrbook/bookcpdf.html

Can the method of steepest descent (saddle point method) be used if an integral has the following form: \int exp\left[M f(x) + g(x)\right]dx where M goes to infinity? I ask because all the examples I've seen of this method involve a function which is multiplied by a very large number...

Thanks

If so, then is \frac{\delta}{\delta h(s')} \textrm{ln}(F) = \frac{1}{F[h(s')]}\frac{\delta F}{\delta h(s')} ?Basically I'm not sure if the same kind of chain rule applies to functional derivatives as to regular ones. I haven't been able to find an example of a derivative of a function...

Given that F = \int{f[h(s),s]ds} does \frac{\partial}{\partial h}ln(F)=\frac{1}{F}\frac{\delta F}{\delta h}=\frac{1}{F}\frac{\partial f}{\partial h} ?

In case the question wasn't clear, here it is in a different way: Does the calculus of variations apply to situations where you're looking for some function, y(x), that extremizes (in my particular case) \int{ f(y,x) \ln{ \left[ \int{ f(y,x) dx } \right] } dx } ?

Is it possible to find the extrema of an integral equation if the integral depends on a variable and an integral of that variable, i.e. the integrand is f(x) * g(integral(x)). I'm not sure if this is a "nonlocal" functional, or not a functional at all, but I can't find any references that...