Description:
Discussion of current mathematical research. (Moderated)
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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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subgroups of ultrapowers
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Perhaps someone count direct me to some experts and/or references? Let *Z be an ultrapower of the integers Z, with respect to a nonprincipal ultrafilter on a countably infinite index set. For any real number r, one can associate a subgroup of *Z: S_r = { n in *Z: nr \in *Z + I } where I \subset *R consists of the infinitesimals in the... more »
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entropy question
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my data consists of a point on a grid which moves around through time. so, you can look at this as a trail through a plane, or a timeseries of (x,y) coordinates. imagine this as a bug moving around on a table. is there a way i could measure the "entropy" of this system? is there an information entropy measure that would be appropriate?... more »
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TMFCS-10 Call for papers
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TMFCS-10 Call for papers The 2010 International Conference on Theoretical and Mathematical Foundations of Computer Science (TMFCS-10) (website: [link]) will be held during 12-14 of July 2010 in Orlando, FL, USA. TMFCS is an important event in the theoretical, mathematical and logical areas... more »
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Can we speak about ill-conditioning when $\kappa(A)>\log(1)=0$ if elements of $A$ are known with an infinite precision?
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Hi, Here are two questions: 1) I am given a square matrix $A$. Its determinant does not equal $0$. Let's compute its condition number, according to the infinity norm, i.e. \[ \kappa(A)=||A||_{\infty}\cdot ||A^{-1}||_{\infty}. \] Elements of $A$, i.e. $A_{i,j}$, $1\leq i\leq n$, $1\leq j\leq n$, where $A$ is of dimension $n$, are known with an infinite precision,... more »
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minimal set
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Let (X,f) be a topological dynamical system, f a surjective map. R(f) is the set of recurrent points and AP(f) is the set of almost periodic points, There is a trivial inclusion AP(f)\subset R(f). Is it true that the closure of AP(f) contains R(f)? is there some reference about the second inclusion.... more »
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