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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

    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

    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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    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

    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

    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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    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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    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

    Hi, can someone please give me an example of what a convolution of a convolution would look like ? Thanks
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    Should I do measure theory ?

    Hi All, I am a new phd student in engineering, working in signals analysis in neuroscience who seems to be doing a lot of work in statistics and probability theory. My uni is offering a course in measure theory. The course profile says: "The course is an introduction to measure theory and...
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    What is Selective about SSRIs ?

    Hi, I have been reading up about SSRIS (Selective Serotonin Reuptake Inhibitors) - and as I understand it they basically bind to the monoamine transporter which tries to take the serotonin back from the post synaptic terminal to the pre synaptic terminal. By binding to the monoamine...
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    Random vs fixed effects in ANOVA

    I am having a lot of trouble conceptually understanding the idea of a random effect in ANOVA testing - more specifically identifying whether a factor is random or fixed Thanks, Thrillhouse86
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    Importance of homogenity of variance

    Hey all, When performing parametric statistical tests (especially t tests and ANOVA), why is the homogenity of variance important ? I mean why do these tests care if the samples have significantly different variance ? Is it because the methods used to determine the test statistics require...
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    P value from z statistic

    Hey All, Can someone please explain to me why the p value is obtained by taking the integral under the z curve from the z statistic you calculate to the end of the tail ? Thanks
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    Matlab xcorr function

    Hey All, does anyone know what algorithm matlab uses to determine the autocorrelation function when you use the 'xcorr' function. the matlab help page refers to a textbook: "Orfanidis, S.J., Optimum Signal Processing. An Introduction. 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ...
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    Biased and unbiased estimators

    Hey All, I am comfortable with the idea of biased and unbiased estimators, but what I don't understand is why you would ever want to use a biased estimator ? at the end of the day doesn't it mean that the sample statistic is different from the population statistic you are trying to estimate ?
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    Understanding Sodium Chloride Co Transporters

    Hey All, In my cellular & tissue biology class our lecturer was talking about neurons. Basically he was explaining that the concentrations are as follows: Pottasium: higher inside the cell then outside. Sodium: higher outside the cell then inside. Chloride: higher outside the cell then...
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    Unbiased estimator of variance

    Hey all, In Schaum's outline it claims that the sample variance of s^2 is a biased estimate of the population variance because its mean is given by: \mu_{s^{2}} = \frac{N-1}{N}\sigma^{2} which I am cool with. It then says that the modified variance given by: \hat{s} =...
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    Laplacian of 1/r is zero at orign

    Hey All, In my vector calculus class my lecturer was showing that the laplacian of 1/r is zero. He further said that since 1/r and its derivatives are not defined at the origin we state that the Laplacian of 1/r is zero for all values of r not equal to zero. He then says that this caveat is...
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    Greens Theorem for negatively orientated curve

    Hey All, in vector calculus we learned that greens theorem can be used to solve path integrals which have positive orientation. Can you use greens theorem if you have negative orientation by 'pretending' your path has positive orientated and then just negating your answer ? Regards...
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    Feedback changes topology

    Hi All, In my control systems lectures my professor talks about feedback changing the 'topology' of the system. Is he just talking about the structure of the block diagram changing, or is there some link to the topology which mathematicians refer to Regards, Thrillhouse86
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    Showing Integral form satisfies the Airy function

    Hey All, Can someone please give me the gist of how to show that the integral form of the Airy function for real inputs: Ai(x) = \frac{1}{\pi} \int_0^\infty \cos\left(\tfrac13t^3 + xt\right)\, dt, satisfies the Airy Differential Equation: y'' - xy = 0 I tried differentiating twice...
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    Where will engineers use vector spaces ?

    Hey All, I am tutoring a mixed class of (mostly) engineers and physicists and I am trying to get across how important the concept of a vector space is - that its not just some abstract problem that only pure mathematicians need to worry about. Its easy to highlight the need for linear...
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    Fluid Mechanics Internal Flow Question

    Hey all, I know that it is forbidden to post homework questions here, this is a question off a past exam, so I'm hope asking this is Kosher. A question says: "For a circular pipe of 6cm diameter, what is the expected pressure drop per unit length due to frictional losses, at a Reynolds...