Recent content by brahman

oh, the formula doesn't look familiar with me, it was more complicated than what we typed. Because i have no background of Stochastics prossess, so hope that some one else will help you with the general formula ^-^ . Anyway, the book you sent is worthy of note. Cheers! PS: edit what I typed...

okay, now i understand what you mean. You can do that in some special cases. If the function f in C^\infty ( \mathbb{R}) , ie, the n th derivative \frac{d^n f}{ dx^n} always exists and it is a continuos function on \mathbb{R}, for all n \in \mathbb{N} . Then you have f(u) = f(v) +...

Okay, I may be missing something that you typed ... which functional space are everything occurring to ? For example, when you said that f = g in C(a,b) then f (t) = g (t) for all t \in [a,b], or, when you said that f = g in L^1(a,b) then \int_{a}^b |f(t) - g(t)| dt = 0 etc ...

i think the problem (must) needs the boundary condition, if not it's ill-posed. The Green function of \nabla ^2 p = f \; , \; \text{ in } \mathbb{R} ^3 is G(x,y,z; \xi , \eta , \theta)= \frac{-1}{4\pi} \frac{1}{ \sqrt{(x-\xi )^2 +(y-\eta )^2+(z-\theta )^2}} and the Green function of...

Could you set the problem more completely ? domain, initial condition , ... where are they ?

What is \hat{x} ? If f,x \in C^{\infty} ( \mathbb{R}) then f[x(t)] = f[ x( t_0 )] + \left( f[x(t)] - f[x(t_0)] \right) \frac{\delta f}{\delta x(t)}|_{ t = t_0 } + \frac{ \left( f[x(t)] - f[x(t_0 )] \right) ^2}{2!}\frac{\delta ^2f}{\delta ^2x(t)}|_{t = t_0} } + \ldots forall t \in (...

L^2(0,1) is a Hilbert separable space with inner product <u,v> = \int_0^1 uv dx and the set of Legendre polynomials is a Hilbert base of L^2(0,1) P_n (x) = \frac{\sqrt{2n+1}}{ 2^{n+1/2} n!} \frac{d^n}{dx^n} \left[ (x^2 - 1)^n \right] \; \; , \; n = 1,2,3,... It mean \forall v \in L^2(0,1)...

You just try to apply the Cauchy theorem. It's not so hard. For example, the function f(z) = \left( \frac{1}{z^2 + a^2}\right) ^2 has two singular point z_{1,2} = \pm \, a i , where i^2 = -1. As the definition of residue, we have Res \left[ f , z = ai \right] = \frac{1}{ 2 \pi i } \oint...

Okay, God can tell you how it work. Human just try to compute and believe in conformation.