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    Limit involving dirac delta distributions

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

    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...
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    I think this is a dominated convergence theorem question

    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...
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    I think this is a dominated convergence theorem question

    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...
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    Derivation of Vasicek Entropy Estimator

    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...
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    Is this integral possible to solve

    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 ?
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    Is this integral possible to solve

    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
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    Correlation functions

    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
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    Difference between Renewal Process and Poisson Processes

    Hey All, Can someone please explain to me the difference between a Poisson Process and a Renewal Process ? is it just that the Holding times for Poisson processes are exponential and Holding times for Renewal Processes are any kind of probability distribution (as the wiki page seems to imply)...
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    Conceptual Problem with Convolution Theorem

    Thanks AlpehZero - I guess it always helps to go back to the fundamental definitions ...
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    Conceptual Problem with Convolution Theorem

    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...
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    Fourier Transform of One-Sided Convolution

    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...
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    Fourier Transform of One-Sided Convolution

    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...
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    Asymptotic Form of an Integral

    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...
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    Constants of Motion in the Kuramoto Model

    Hey All, I realise this is a slightly peculiar question - but does anyone know if there is any conserved quantities in the Kuramoto Model. I've been thinking about it, and since the system is made up of coupled Limit Cycle Oscillators and there is no dissipation, wouldn't the total energy be...
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    Velocity correlation functions

    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)>...
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    Confused about phase difference

    do you mean why should the phase difference be small when the forcing frequency and natural frequency are the same ?
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    How can I teach myself more advanced math?

    I would start by grabbing a college calculus book and linear algebra book. Calculus by Stewart is a good start for calculus Linear Algebra by David C. Lay is a good start for Linear Algebra If you can understand these books then you can start to move onto more advanced topics like Real...
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    The Physics of Le Chatelier's Principle

    Thats a good question, Intuitively I would think the following: The equillibrium constant (and the law of mass action) is derived from minimisation of Gibbs free energy arguments. This means that the ammount of products and reactants that exist at equillibrium are determined by minimising...
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    Lagrangian: Inverted telescoping pendulum (robot leg)

    Sorry but the Latex code not coming out was really bugging me! L=T-V then L=\left[\frac{1}{2}m\omega^{2}+\frac{1}{2}m\dot{x}^{2}\right]-mgxcos(\theta) then L=\frac{1}{2}m(x^{2}\dot{\theta}^{2}+\dot{x}^{2})-mgxcos(\theta)\\ then \frac{d}{dt}\frac{\partial...
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    Anode break excitation

    thanks Kglocc, I also stumbled across this youtube video which gives an example (but not an explanation) of Anode Break Excitation.
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    Anode break excitation

    Hey, Can someone point me in the direction (or just explain to me!) the idea of Anode Break excitation in neuroscience ? Thanks
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    Difference between Power Sets and Sample Space

    Hey All, In my probability theory class we have just started learning about how a probability space is defined by a sample space (which contains all possible events), events and a measure. We briefly went over the idea of the Power Set, which seems to be the set of all subsets in your...
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    Surface integral with vector integrand

    But the surface is a vector because its an orientated surface right (surface + direction) ? I mean when you do your surface integrals, you don't just define the surface, you define direction of the normal vector of the differential elements of the surface surface Supposing you have some...
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    Second Shifting Theorem for Fourier Transforms ?

    Hi, I know from my the t shifting theorem that if I take the laplace transform of a function which is multiplied by a step function: \mathcal{L}\{f(t-a)U(t-a) \} = e^{as}F(s) Does this same rule apply for Fourier Transforms ? i.e. \mathcal{F}\{f(t-a)U(t-a) \} = e^{as}F(\omega)...
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    Why can t statistic deal with small numbers ?

    Hi, I've been trying to get my head around z and t statistics. and I almost have a matra in my head that "when the sample are small, use the t test, when the samples are big, use either the t or the z test". Now As I understand it, the z test requires a large number of samples, because it...
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    A convolution of a convolution

    thanks pbandjay
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    Help with understanding kalman filter

    I certainly agree with DH - that Kalman filters are far too complex for someone who has not taken a calculus course. Out of interest though - whats the real analysis needed for Kalman filters ?
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    A convolution of a convolution

    as in: f*g = \int^{\infty}_{-\infty} f(\tau)g(t-\tau) d\tau what would h*(f*g) look like ? -Thrillhouse