Description:
Mathematical discussions and pursuits.
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Finite, non-simple field extension: is this proof OK?
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Exercise 93 in Joseph Rotman's /Galois Theory/ (2nd ed. 1998): "Show that Z_p(x, y) is a finite extension of its subfield Z_p(x^p, y^p), but it is not a simple extension." My head still swims when I do abstract algebra (although I'm slowly becoming more confident and more able to check my own work). The following proof seems vaguely OK, but I'm not very... more »
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Combinatorics(?) notation question
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Hi folks, I came across a piece of notation that I haven't seen before, and I'm wondering if it has a name. It's a function denoted (a,n) where n is an integer and a is a real number, usually an integer or half- integer. (It appears in coefficients for expansions of Bessel functions.) A couple of equivalent definitions for it are:... more »
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orthogonal trajectories
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I'm showing that a given family of curves are orthogonal trajectories of each other. I have the two curves: x^2 + y^2 = ax x^2 + y^2 = by It is said that the two circles intersect at the origin. How is this evident other than by plugging in 0?
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Complex analysis
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(1) Does anyone have any recommendations for a good textbook on complex analysis? The background intention is to study the Riemann Zeta function and the distribution of primes, complex analytic proof of the prime number theorem, and related results - preferably no functional analysis, advanced topology, open covers etc.... more »
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simple probability question
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I found this result in a research paper. not sure how to derive it. any help?? suppose an n dimensional unit vector v=(v1,v2,...,vn) is chosen uniformly at random from an n dimensional unit sphere. clearly v1^2+v2^2+...+vn^2=1---------- -------(1) Then for any delta>0, with probability at least (1-delta) , we have... more »
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machine figure
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Say pieces on a board, make each a pair with another piece. like... ...so figure out how a piece can move. pick any piece, try to move it somewhere. when you move a piece you have to move it's pair at the same time. when you move to a piece it's pair has to move at the same time too. a piece always becomes a pair with the piece it moves to.... more »
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BBP - type to complex @ simon plouffe.
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Dear Simon Plouffe ( and others ) I request investigating BBP - type formula's of the following type : a = sum k = 0 .. oo [ ( b^k * p(k) * A(k) ) /q(k) ] Where b is a gaussian rational ( Q(i) ) < 1. p(k) and q(k) are polynomials with gaussian rational coefficients and A(k) is a vector of gaussian rationals.... more »
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expressing a working machine
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- Moving pairs Given something like a checkers board, moving pairs would be checker pieces paired together and arranged on the board so they each checker piece is said to be paired with another. The pairs don't have to be next to eachother, they can arrange on the board in any awy. Any way arranged is fair for how this works, but it matters for how... more »
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