Description:
Discussion of current mathematical research. (Moderated)
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Jacobi polynomials
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I'm looking for the asymptotic behavior, just one term, of the nth Jacobi polynomial with (1,-1) superscript and argument x which is less than -1. Like, x= -3/2 would be typical. I need this behavior for fixed x and n large. I have looked at several papers on the subject but they seem to give varying results that are not purely real... more »
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Outer Actions Giving Rise to Distinct Group Extensions
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Hello, all! My dissertation involves taking a closed smooth manifold with finitely presented fundamental group Q and creating a cobordant manifold having fundamental group isomorphic to Q |x S ("Q semi-direct product S"), where S is a given finitely presented superperfect group. I have created a procedure for doing this, and am now at the point where I want to make... more »
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Sequence f_(n+1) = sin^2(pi/2*f_n) on [0,1]
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Have you seen this sequence before? Does this sequence have a name? I stumbled across this piece of mathematics by accident this morning. It's something I've been looking for for about thirty years. Consider the sequence: f_0 = x f_1 = sin^2(pi/2*x) f_2 = sin^2(pi/2*sin^2(pi/2*x)) f_3 = sin^2(pi/2*sin^2(pi/2*sin^2(pi /2*x)))... more »
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hyperbolic distance between two random points
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Hello! Let D denote the disk of radius R, centered at the origin, in the hyperbolic plane. Let P be a uniformly distributed random point in D. It is known that the hyperbolic distance between P and the origin has probability density [1] (1/(cosh(R)-1))*sinh(x), where 0 <= x <= R. Now let P, Q be independent uniformly distributed... more »
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the hyperarithmetical vs. lightface Borel hierarchies
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Hi. I'm very confused as to the relation between the [Kleene] hyperarithmetical hierarchy and [Addison] lightface Borel (aka, effective Borel) hierarchy. (Very briefly, a subset S of the integers--or perhaps even of the Baire space--is said to be Sigma_alpha in the hyperarithmetical hierarchy, where alpha is some recursive ordinal, when S is... more »
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naming "connection"
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According to the usual suspects, the name "connection" is differential geometry is due to Levi-Civita. However, no mention I've seen so far gives the precise reference to where this historic event occurred. His 1917 paper is mentioned in connection with the naming, but I can't find where therein he actually does so. Neither does it seem to be in... more »
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Statistical hypothesis testing
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Hi, I've a question about on statistical hypothesis testing. Let's say I've two approaches A and B and I would like to see if one approach is better than the other. These are my results (p-values) for the statistical testing: A B A - 0.002 B 0.998 - using the alternative hypothesis that the approaches in the first column... more »
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