math updates on arXiv.orgMathematics (math) updates on the arXiv.org e-print archive$C$-algebras arising from substitutions. (arXiv:0801.3354v2 math.OA CROSS LISTED)- (Found June 29, 2008 ) In this paper, we introduce a $Cast$-algebra associated with a proper primitive substitution. We show that the $Cast$-algebra is simple and purely infinite and contains the associated Cuntz-Krieger algebra and the crossed product $Cast$-algebra of the corresponding Cantor minimal system. We calculate the $K$-groups.http://arxiv.org/abs/0801.3354 Corks, plugs and exotic structures. (arXiv:0806.3010v2 math.GT UPDATED)- (Found June 29, 2008 ) We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational blow-downs. We show how to detect corks and plugs inside of some exotic manifolds.http://arxiv.org/abs/0806.3010 On the zeroes of the Riemann zeta function. (arXiv:0806.2361v5 math.GM UPDATED)- (Found June 29, 2008 ) The paper gives another characterization to the Riemann hypothesis as convergence of a certain sequence of functions.http://arxiv.org/abs/0806.2361 Sharp asymptotics for the Neumann Laplacian with variable magnetic field : case of dimension 2. (arXiv:0806.1309v2 math-ph UPDATED)- (Found June 29, 2008 ) The aim of this paper is to establish estimates of the lowest eigenvalue of the Neumann realization of $(inabla+BtextbfA)2$ on an open bounded subset of $mathbbR2$ $Omega$ with smooth boundary as $B$ tends to infinity. We introduce a "magnetic" curvature mixing the curvature of $partialOmega$ and the normal derivative of the magnetic field and obtain an estimate analogous with the one of constant case. Actually, we give a precise estimate of the lowest eigenvalue in the case where the...http://arxiv.org/abs/0806.1309 P-values for classification. (arXiv:0801.2934v3 math.ST UPDATED)- (Found June 29, 2008 ) Let $(X,Y)$ be a random variable consisting of an observed feature vector $Xin mathcalX$ and an unobserved class label $Yin 1,2,...,L$ with unknown joint distribution. In addition, let $mathcalD$ be a training data set consisting of $n$ completely observed independent copies of $(X,Y)$. Usual classification procedures provide point predictors (classifiers) $widehatY(X,mathcalD)$ of $Y$ or estimate the conditional distribution of $Y$ given $X$. In order to quantify the certainty of classifying...http://arxiv.org/abs/0801.2934 Lectures on random matrix models. The Riemann-Hilbert approach. (arXiv:0801.1858v2 math-ph UPDATED)- (Found June 29, 2008 ) This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large $N$ asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the large $N$ asymptotics of the partition function, and random matrix models with external source.http://arxiv.org/abs/0801.1858 On the classification of gradient Ricci solitons. (arXiv:0712.1298v4 math.DG UPDATED)- (Found June 29, 2008 ) We show that the only complete shrinking gradient Ricci solitons with vanishing Weyl tensor are quotients of the standard ones. This gives a new proof of the Hamilton-Ivey-Perel'man classification of 3-dimensional shrinking gradient solitons. We also prove a classification for expanding gradient Ricci solitons with constant scalar curvature and suitably decaying Weyl tensor.http://arxiv.org/abs/0712.1298 Structural and Dynamical Aspects of the AdSCFT Correspondence: a Rigorous Approach. (arXiv:0712.0401v3 math-ph UPDATED)- (Found June 29, 2008 ) We elaborate a detailed study of certain aspects of (a version of) the AdSCFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's conformal infinity (in the sense of Penrose), aspects such that: (a) are independent from (the pair of) specific models in Quantum Field Theory, and (b) susceptible to a recast in a..http://arxiv.org/abs/0712.0401 Spotlight Tiling. (arXiv:0711.1819v3 math.CO UPDATED)- (Found June 29, 2008 ) This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the "tiles" have elastic size, and that the order of placement is significant. Spotlight tilings are decompositions, or coverings, and can be considered dynamic as compared to typical static tiling methods. A thorough examination of spotlight tilings of rectangles is presented, including the distribution of such tilings according to size, and how the...http://arxiv.org/abs/0711.1819 A Note on the Use of the Woodbury Formula To Solve Cyclic Block Tri-Diagonal and Cyclic Block Penta-diagonal Linear Systems of Equations. (arXiv:0806.- (Found June 29, 2008 ) The article presents the theoretical background of the algorithms for solving cyclic block tridiagonal and cyclic block penta-diagonal systems of linear algebraic equations present in ref 1 and 2. The theory is based on the Woodbury formula.http://arxiv.org/abs/0806.3639 |