Recent content by thrillhouse86

Sorry I mean to evaulate: \lim_{x\to 0^{+}} \frac{\delta'(x)}{\delta''(x)}

Hey All, I am trying to evaluate the limit: \lim_{x\to 0^{+}} \frac{\delta''(x)}{\delta''(x)} Where \delta'(x) is the first derivative of the dirac distribution and \delta''(x) is the second derivative of the dirac distribution. I thought about the fact that this expression...

Thanks Mathman

Thanks mathman, I think I expressed the question wrong. I don't really care (for the purposes of this post) about when the expression will be zero, I am more interested in understanding what the mathematician was talking about with the theorem of dominated convergence. Lets say the function...

Hey All, I have the following integral expression: y = lim_{h\to0^{+}} \frac{1}{2\pi} \left\{\int^{\infty}_{-\infty} P(\omega)\left[e^{i\omega h} - 1 \right] \right\} \Bigg/ h And I am trying to understand when this expression will be zero. I was talking to a mathematician who said...

Hey All - I am trying to solve a problem that should be really easy (at least every paper I read says the step is!) I'm trying to understand where the Vasicek entropy estimator comes from: I can write the differential entropy of a system as: H(f) = -\int^{\infty}_{-\infty} f(x)log(f(x))dx...

Thanks for the help guys - can you briefly explain (or point me towards) why real roots are a problem ? is it something to do with branch points in the complex plane ?

Hi I was wondering if anyone has seen this integral in a table, or indeed knows if it is possible to solve: \int^{\infty}_{-\infty} \frac{x^{2}}{ax^{4} + bx^{2} + c} every table I look at seems to only go up to the first power of x in the numerator Thanks, Thrillhouse

In the case of autocorrelation functions - have a look at any material you can on Gauss-markov processes - a book with a little bit on them is "Introduction to Random Signals and Applied Kalman Filtering" by Brown & Hwang

Thanks AlpehZero - I guess it always helps to go back to the fundamental definitions ...

Hi - I'm trying to work out the following convolution problem: I have the following integral: \int^{\infty}_{-\infty}p(x)U(x)e^{-i \omega x}dx Where p(x) is any real function which is always positive and U(x) is the step function Obviously this can easily be solved using the...

Hey Ray, yeah I've noticed that Laplace transform one, but I really need the Fourier transform of this one sided one. I was hoping that the heaviside function would kill the -ve bounds of my Fourier Transform so that it would look like a Laplace transform, but in order to do that I need to...

Hi, Can anyone tell me if there is a convolution theorem for the Fourier transform of: \int^{t}_{0}f(t-\tau)g(\tau)d\tau I know the convolution theorem for the Fourier Transform of: \int^{\infty}_{-\infty}f(t-\tau)g(\tau)d\tau But I can't seem to find (or proove!) anything...

Hey: I have an integral of the form: \int^{\infty}_{-\infty}\frac{x(\omega)}{\sigma^{2} + \omega^{2}}d\omega I'm wondering if this integral is a candidate for asymptotic analysis. My rationale is that as omega increases to either positive infinity or negative infinity, the function being...

Hi, I am going through Non Equilibrium Statistical Mechanics by Zwanzig and I can't follow, the step below: I have the equation: <x^{2}> = \int^{t}_{0}ds_{1}\int^{t}_{0}ds_{2}<v(s_{1})v(s_{2})> I can't show that: \frac{\partial <x^{2}>}{\partial t} = 2 \int^{t}_{0}ds<v(s)v(t)>...