Description:
Discussion of current mathematical research. (Moderated)
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This Week's Finds in Mathematical Physics (Week 284)
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Also available at [link] November 24, 2009 This Week's Finds in Mathematical Physics (Week 284) John Baez A couple of weeks ago there was a meeting of the American Mathematical Society here at UC Riverside. Mathematicians flooded in from across the western US and even further. They gave hundreds of 20-minute... more »
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Gauss-Bonnet for complex valued edge lengths[repost]
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I was trying to understand triangulated surfaces embedded in (2+1) dimensions. If we think of an "ordinary" triangulated surfaces, (ie embedded in 3D Euclidean space) we would take the edge lengths of all triangles, calculate all angles at the vertices, and find that the sum of deficits equals 2 pi times the Euler characteristic. (Gauss Bonnet theorem.)... more »
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Product of unique prime factors
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Is there a name for product of the unique prime factors of a number? For example, for 12, it would be 3x2=6. Does not sound like a research question. I could not find an answer elsewhere. Thanks.
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manifolds with no plane fields
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I'm looking for examples of compact manifolds M (without boundary) whose tangent bundle admits no non-trivial invariant sub-bundles. That is, M has no continuous field of k-planes, for all k with 0<k<dim(M). (In dim.2, that is easy: M is any surface with non-zero Euler characteristic.) Are there other simple examples?... more »
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Dense Linear Order
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Let S = { s0, s1, ... } be a countable linear order with s0 = bottom, s1 = top. Let D = Z[1/2] /\ [0,1] Define f:S -> D by induction: f(s0) = 0, f(s1) = 1 and for k > 1, let bk = max { sj | j < k, sj < sk } tk = min { sj | j < k, sk < sj } f(sk) = (f(bk) + f(tk))/2 It can be show that f is an increasing injection.... more »
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Question about the convergence of a stationary iteration procedure
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Let A be an n x n matrix such that - 0 <= (A)ij <= 1 - the sum over the values at a given column i is at most 1. (for all columns i=1,...,n) Let v be a n-dimension vector. Consider the following stationary iteration procedure: v_0 = v v_k+1 = A*v_k. Question: When does the limit when k->infinite of v_k converge? Does... more »
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Asymptotic behavior of Alternating Ordinary Dirichlet Series remainder 2nd
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Reposting in plain text format. Hi, I am posting this New Topic in an effort to verify whether it is an already known result that the n^th remainder, R_n(s) of an Alternating Ordinary Dirichelet Series (meaning: 1 - 2^-s + 3^-s - ..., s being a complex number) is Big Theta(n^(-Re(s))), as n->oo. Now, by means of standard analysis it is relatively easy to show that R_n(s)... more »
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Asymptotic behavior of Alternating Ordinary Dirichlet Series remainder
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This is a multi-part message in MIME format. ------=_NextPart_000_001E_01CA 6863.AA37B8F0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Hi, I am posting this New Topic in an effort to verify whether it is an = already known result that the n^th remainder, R_n(s) of an Alternating =... more »
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Choudhry's Theorems on Waring-like Problems for Rationals
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Hello all, Some results for a "Waring-like Problem". ANY rational N is, in an infinite number of _non-trivial_ ways: 1) the sum of 3 rational 3rd powers. (Ryley's Theorem) 2) the sum of 6 rational 5th powers. (Choudhry) 3) the sum of 8 rational 7th powers. (Choudhry) All results are dependent on certain algebraic identities, but whether... more »
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Perfect Square
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Let P(m) = (4m)^(4m-1) + 4m^2 + 1, where m is a positive integer. Is it true that this expression is not a perfect square for any value of m?
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