Wednesday, July 1st, 2009

Time	Event
8:02a	Explicit probabilistic models for databases and networks. (arXiv:0906.5148v1 [cs.AI]) Explicit probabilistic models for databases and networks. (arXiv:0906.5148v1 [cs.AI]) Authors: Tijl De Bie Recent work in data mining and related areas has highlighted the importance of the statistical assessment of data mining results. Crucial to this endeavour is the choice of a non-trivial null model for the data, to which the found patterns can be contrasted. The most influential null models proposed so far are defined in terms of invariants of the null distribution. Such null models can be used by computation intensive randomization approaches in estimating the statistical significance of data mining results. Here, we introduce a methodology to construct non-trivial probabilistic models based on the maximum entropy (MaxEnt) principle. We show how MaxEnt models allow for the natural incorporation of prior information. Furthermore, they satisfy a number of desirable properties of previously introduced randomization approaches. Lastly, they also have the benefit that they can be represented explicitly. We argue that our approach can be used for a variety of data types. However, for concreteness, we have chosen to demonstrate it in particular for databases and networks. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Congruences involving the reciprocals of central binomial coefficients. (arXiv:0906.5150v1 [math.NT] Congruences involving the reciprocals of central binomial coefficients. (arXiv:0906.5150v1 [math.NT]) Authors: Roberto Tauraso We present several congruences modulo a power of prime $p$ concerning sums of the following type $\sum_{k=1}^{p-1}{m^k\over k^r}{2k\choose k}^{-1}$ which reveal some interesting connections with the analogous infinite series. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	An Asymptotic Version of a Theorem of Knuth. (arXiv:0906.5167v1 [math.CO]) An Asymptotic Version of a Theorem of Knuth. (arXiv:0906.5167v1 [math.CO]) Authors: Jonathan Novak If $u_d(N)$ is the number of permutations in the symmetric group S(N) with no decreasing subsequence of length $d+1,$ then $$u_d(N) \sim (2\pi)^{\frac{1-d}{2}} \bigg{(} \prod_{i=0}^{d-1} i! \bigg{)} d^{2N + \frac{d^2}{2}} (2N)^{\frac{1-d^2}{2}}$$ as $N \to \infty.$ We give a new proof of this result, which is originally due to Regev, by developing it as the asymptotic analogue of a well-known exact formula of Knuth. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Nonlinear Integer Programming. (arXiv:0906.5171v1 [math.OC]) Nonlinear Integer Programming. (arXiv:0906.5171v1 [math.OC]) Authors: Raymond Hemmecke, Matthias Köppe, Jon Lee, Robert Weismantel Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject to integrality requirements for the variables. This chapter is dedicated to this topic. The primary goal is a study of a simple version of general nonlinear integer problems, where all constraints are still linear. Our focus is on the computational complexity of the problem, which varies significantly with the type of nonlinear objective function in combination with the underlying combinatorial structure. Numerous boundary cases of complexity emerge, which sometimes surprisingly lead even to polynomial time algorithms. We also cover recent successful approaches for more general classes of problems. Though no positive theoretical efficiency results are available, nor are they likely to ever be available, these seem to be the currently most successful and interesting approaches for solving practical problems. It is our belief that the study of algorithms motivated by theoretical considerations and those motivated by our desire to solve practical instances should and do inform one another. So it is with this viewpoint that we present the subject, and it is in this direction that we hope to spark further research. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	The pressure, densities and first order phase transitions associated with multidimensional SOFT. (ar The pressure, densities and first order phase transitions associated with multidimensional SOFT. (arXiv:0906.5176v1 [math-ph]) Authors: Shmuel Friedland, Uri N. Peled We study theoretical and computational properties of the pressure function for subshifts of finite type on the integer lattice $\Z^d$, multidimensional SOFT, which are called Potts models in mathematical physics. We show that the pressure is Lipschitz and convex. We use the properties of convex functions to show rigorously that the phase transition of the first order correspond exactly to the points where the pressure is not differentiable. We give computable upper and lower bounds for the pressure, which can be arbitrary close the values of the pressure given a sufficient computational power. We apply our numerical methods to confirm Baxter's heuristic computations for two dimensional monomer-dimer model, and to compute the pressure and the density entropy as functions of two variables for the two dimensional monomer-dimer model. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Man and machine thinking about the smooth 4-dimensional Poincar\'e conjecture. (arXiv:0906.5177v1 [m Man and machine thinking about the smooth 4-dimensional Poincar\'e conjecture. (arXiv:0906.5177v1 [math.GT]) Authors: Michael Freedman, Robert Gompf, Scott Morrison, Kevin Walker While topologists have had possession of possible counterexamples to the smooth 4-dimensional Poincar\'e conjecture (SPC4) for over 30 years, until recently no invariant has existed which could potentially distinguish these examples from the standard 4-sphere. Rassumsen's s-invariant, a slice obstruction within the general framework of Khovanov homology, changes this state of affairs. We describe knots K so that s(K) nonzero implies a counterexample to SPC4. Computations are extremely costly and so far we have only completed a single test. Unfortunately for that K the computation showed that s was 0. Only a few of the relevant knots will be computationally tractable and the effort to compute s for them is ongoing. Our perspective is neutral, however, and in another section of this paper we explain that SPC4 is equivalent to an appropriate generalization of Property R ("in S^3, only an unknot can yield S^1 x S^2 under surgery"). We hope that this observation, and the rich relations between Property R and ideas such as taut foliations, contact geometry, and Heegaard Floer homology, will encourage three manifold topologists to look at SPC4. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Diffusion of a massive quantum particle coupled to a quasi-free thermal reservoir in dimension $d\ge Diffusion of a massive quantum particle coupled to a quasi-free thermal reservoir in dimension $d\geq 4$. (arXiv:0906.5178v1 [math-ph]) Authors: W. De Roeck, J. Froehlich We consider a heavy quantum particle with an internal degree of freedom moving on the $d$-dimensional lattice $\bbZ^d$ (e.g., a heavy atom with finitely many excited states). The particle is coupled to a thermal bath consisting of free relativistic bosons through an interaction of strength $\la$ linear in creation and annihilation operators. The mass of the quantum particle is assumed to be of order $\la^{-2}$, and we assume that the internal degree of freedom is coupled "effectively" to the thermal bath. We prove that the motion of the quantum particle is diffusive in $d\geq 4$ and for $\la$ small enough. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Superbimatrices and their generalizations. (arXiv:0906.5143v1 [math.GM]) Superbimatrices and their generalizations. (arXiv:0906.5143v1 [math.GM]) Authors: W.B.Vasantha Kandasamy, Florentin Smarandache In this book, the authors introduce the new notion of superbimatrices and generalize it to supertrimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerize world. The main difference between simple bimatrices and super bimatrices is that in case of simple bimatrices we have only one type of product defined on them, whereas in case of superbimatrices we have different types of products called minor and major defined using them. This book has four chapters. Chapter one describes the basic concepts to make this book a selfcontained one. Superbimatrices, semi superbimatrices, symmetric superbimatrices are introduced in chapter two. Chapter three introduces the notion of super trimatrices and the products defined using them. Chapter four gives the most generalized form of the superbimatrix, viz. super n-matrix read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications. (arXiv:0906.5141v1 [math-ph]) Authors: I.A. Taimanov, S.P. Tsarev We consider the Moutard transformation which is a two-dimensional version of the well-known Darboux transformation. We give an algebraic interpretation of the Moutard transformation as a conjugation in an appropriate ring and the corresponding version of the algebro-geometric formalism for two-dimensional Schroedinger operators. An application to some problems of the spectral theory of two-dimensional Schroedinger operators and to the $(2+1)$-dimensional Novikov--Veselov equation is sketched. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Well-posedness for fractional Navier-Stokes equations in critical spaces close to $\dot{B}^{-(2\beta Well-posedness for fractional Navier-Stokes equations in critical spaces close to $\dot{B}^{-(2\beta-1)}_{\infty,\infty}(\mathbb{R}^{n})$. (arXiv:0906.5140v1 [math.AP]) Authors: Zhichun Zhai In this paper, we prove the well-posedness for the fractional Navier-Stokes equations in critical spaces $G^{-(2\beta-1)}_{n}(\mathbb{R}^{n})$ and $BMO^{-(2\beta-1)}(\mathbb{R}^{n}).$ Both of them are close to the largest critical space $\dot{B}^{-(2\beta-1)}_{\infty,\infty}(\mathbb{R}^{n}).$ In $G^{-(2\beta-1)}_{n}(\mathbb{R}^{n}),$ we establish the well-posedness based on a priori estimates for the fractional Navier-Stokes equations in Besov spaces. To obtain the well-posedness in $BMO^{-(2\beta-1)}(\mathbb{R}^{n}),$ we find a relationship between $Q_{\alpha;\infty}^{\beta,-1}(\mathbb{R}^{n})$ and $BMO(\mathbb{R}^{n})$ by giving an equivalent characterization of $BMO^{-\zeta}(\mathbb{R}^{n}).$ read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Multicommodity Flow in Polynomial Time. (arXiv:0906.5106v1 [math.CO]) Multicommodity Flow in Polynomial Time. (arXiv:0906.5106v1 [math.CO]) Authors: Raymond Hemmecke, Shmuel Onn, Robert Weismantel The multicommodity flow problem is NP-hard already for two commodities on bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising polynomial time solvability of the problem in two broad situations. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Module homomorphisms and multipliers on locally compact quantum groups. (arXiv:0906.5107v1 [math.OA] Module homomorphisms and multipliers on locally compact quantum groups. (arXiv:0906.5107v1 [math.OA]) Authors: M. Ramezanpour, H. R. E. Vishki For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an ideal of $A^{**}$. We obtain some characterizations of compactness and discreteness for a locally compact quantum group $\G$. Furthermore, in the co-amenable case we prove that the multiplier algebra of $\LL$ can be identified with $\MG.$ As a consequence, we prove that $\G$ is compact if and only if $\LUC={\rm WAP}(\G)$ and $\MG\cong\mathcal{Z}({\rm LUC}(\G)^*)$; which partially answer a problem raised by Volker Runde. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Brou\'e's abelian defect group conjecture holds for the Harada-Norton sporadic simple group $HN$. (a Brou\'e's abelian defect group conjecture holds for the Harada-Norton sporadic simple group $HN$. (arXiv:0906.5124v1 [math.RT]) Authors: Shigeo Koshitani, Jürgen Müller In representation theory of finite groups, there is a well-known and important conjecture due to M. Brou\'e. He conjectures that, for any prime $p$, if a $p$-block $A$ of a finite group $G$ has an abelian defect group $P$, then $A$ and its Brauer corresponding block $B$ of the normaliser $N_G(P)$ of $P$ in $G$ are derived equivalent (Rickard equivalent). This conjecture is called Brou\'e's abelian defect group conjecture. We prove in this paper that Brou\'e's abelian defect group conjecture is true for a non-principal 3-block $A$ with an elementary abelian defect group $P$ of order 9 of the Harada-Norton simple group $HN$. It then turns out that Brou\'e's abelian defect group conjecture holds for all primes $p$ and for all $p$-blocks of the Harada-Norton simple group $HN$. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Existence of parabolic boundary points of certain domains in $\mathbb C^2$. (arXiv:0906.5125v1 [math Existence of parabolic boundary points of certain domains in $\mathbb C^2$. (arXiv:0906.5125v1 [math.CV]) Authors: François Berteloot, Ninh Van Thu In this paper, the existence of parabolic boundary points of certain convex domains in $\mathbb C^2$ is given. On the other hand, the nonexistence of parabolic boundary points of infinite type of certain domains in $\mathbb C^2$ is also shown. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Representing multipliers of the Fourier algebra on non-commutative $L^p$ spaces. (arXiv:0906.5128v1 Representing multipliers of the Fourier algebra on non-commutative $L^p$ spaces. (arXiv:0906.5128v1 [math.FA]) Authors: Matthew Daws We show that the multiplier algebra of the Fourier algebra on a locally compact group $G$ can be isometrically represented on a direct sum on non-commutative $L^p$ spaces associated to the right von Neumann algebra of $G$. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative $L^p$ spaces we construct, and show that they are completely isometric to those considered recently by Forrest, Lee and Samei; we improve a result about module homomorphisms. We suggest a definition of a Figa-Talamanca--Herz algebra built out of these non-commutative $L^p$ spaces, say $A_p(\hat G)$. It is shown that $A_2(\hat G)$ is isometric to $L^1(G)$, generalising the abelian situation. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Toric ideals for high Veronese subrings of toric algebras. (arXiv:0906.5129v1 [math.AC]) Toric ideals for high Veronese subrings of toric algebras. (arXiv:0906.5129v1 [math.AC]) Authors: Takafumi Shibuta We prove that the defining ideal of a sufficiently high Veronese subring of a toric algebra admits a quadratic Gr\"obner basis consisting of binomials. More generally, we prove that the defining ideal of a sufficiently high Veronese subring of a standard graded ring admits a quadratic Gr\"obner basis. This was proved by Eisenbud--Reeves--Totaro in the case where coordinates are generic. Our proof does not need coordinate transformations. Note that a change of coordinates does not preserve the property that an ideal is generated by binomials in general. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	A Comment on Nonextensive Statistical Mechanics. (arXiv:0906.5131v2 [cs.IT]) A Comment on Nonextensive Statistical Mechanics. (arXiv:0906.5131v2 [cs.IT]) Authors: Oded Kafri There is a conception that Boltzmann-Gibbs statistics cannot yield the long tail distribution. This is the justification for the intensive research of nonextensive entropies (i.e. Tsallis entropy and others). Here the error that caused this misconception is explained and it is shown that a long tail distribution exists in equilibrium thermodynamics for more than a century. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Characterization of domains in $\mathbb C^n$ by their noncompact automorphism groups. (arXiv:0906.51 Characterization of domains in $\mathbb C^n$ by their noncompact automorphism groups. (arXiv:0906.5133v1 [math.CV]) Authors: Do Duc Thai, Ninh Van Thu In this paper, the characterization of domains in $\mathbb C^n$ by their noncompact automorphism groups are given. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Linear $\sigma$-additivity and some applications. (arXiv:0906.5136v1 [math.GN]) Linear $\sigma$-additivity and some applications. (arXiv:0906.5136v1 [math.GN]) Authors: Tal Orenshtein, Boaz Tsaban We show that a large family of well-studied covering properties, which are not necessarily $\sigma$-additive, are preserved by countable \emph{increasing} unions. Using this and simple forcing theoretic methods, we explain several phenomena, settle some problems, and construct topological groups with very strong combinatorial properties. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Quaternion algebras with the same subfields. (arXiv:0906.5137v1 [math.RA]) Quaternion algebras with the same subfields. (arXiv:0906.5137v1 [math.RA]) Authors: Skip Garibaldi, David J. Saltman G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an extension of a global field K so that F /K is unirational and has zero unramified Brauer group. We also prove a similar result for Pfister forms and give an application to tractable fields. read more at math updates on arXiv.org rss2lj (Comment on this)
8:02a	Testing for white noise under unknown dependence and its applications to goodness-of-fit for time se Testing for white noise under unknown dependence and its applications to goodness-of-fit for time series models. (arXiv:0906.5179v1 [math.ST]) Authors: Xiaofeng Shao Testing for white noise has been well studied in the literature of econometrics and statistics. For most of the proposed test statistics, such as the well-known Box-Pierce's test statistic with fixed lag truncation number, the asymptotic null distributions are obtained under independent and identically distributed assumptions and may not be valid for the dependent white noise. Due to recent popularity of conditional heteroscedastic models (e.g., GARCH models), which imply nonlinear dependence with zero autocorrelation, there is a need to understand the asymptotic properties of the existing test statistics under unknown dependence. In this paper, we showed that the asymptotic null distribution of Box-Pierce's test statistic with general weights still holds under unknown weak dependence so long as the lag truncation number grows at an appropriate rate with increasing sample size. Further applications to diagnostic checking of the ARMA and FARIMA models with dependent white noise errors are also addressed. Our results go beyond earlier ones by allowing non-Gaussian and conditional heteroscedastic errors in the ARMA and FARIMA models and provide theoretical support for some empirical findings reported in the literature. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	How to obtain division algebras from a generalized Cayley-Dickson doubling process. (arXiv:0906.5374 How to obtain division algebras from a generalized Cayley-Dickson doubling process. (arXiv:0906.5374v1 [math.RA]) Authors: Susanne Pumpluen We generalize the classical Cayley-Dickson doubling process starting with a quaternion algebra over a field F by allowing the scalar in the doubling to be an invertible element in the algebra. We investigate the resulting eight-dimensional algebras over F and show that they are division algebras for all scalars chosen in D^\times outside of the base field F, if D is a division algebra. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Quasi-Invariant measures, escape rates and the effect of the hole. (arXiv:0906.5375v1 [math.DS]) Quasi-Invariant measures, escape rates and the effect of the hole. (arXiv:0906.5375v1 [math.DS]) Authors: Wael Bahsoun, Christopher Bose Let $T$ be a piecewise expanding interval map and $T_H$ be an abstract perturbation of $T$ into an interval map with a hole. Given a number $\ell$, $0<\ell<1$, we compute an upper-bound on the size of a hole needed for the existence of an absolutely continuous conditionally invariant measure (accim) with escape rate not greater than $-\ln(1-\ell)$. The two main ingredients of our approach are Ulam's method and an abstract perturbation result of Keller and Liverani. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion. (a Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion. (arXiv:0906.5379v1 [math.AP]) Authors: José A. Cañizo, Laurent Desvillettes, Klemens Fellner We present a new a-priori estimate for discrete coagulation-fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global $L^2$ bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equ Stochastic Calculus for a Time-changed Semimartingale and the Associated Stochastic Differential Equations. (arXiv:0906.5385v1 [math.PR]) Authors: Kei Kobayashi It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct consequence, a specialized form of the Ito formula is derived. When a standard Brownian motion is the original semimartingale, classical Ito stochastic differential equations driven by the Brownian motion with drift extend to a larger class of stochastic differential equations involving a time-change with continuous paths. A form of the general solution of linear equations in this new class is established, followed by consideration of some examples analogous to the classical equations. Through these examples, each coefficient of the stochastic differential equations in the new class is given meaning. The new feature is the coexistence of a usual drift term along with a term related to the time-change. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Thin film limits for Ginzburg--Landau with strong applied magnetic fields. (arXiv:0906.5403v1 [math. Thin film limits for Ginzburg--Landau with strong applied magnetic fields. (arXiv:0906.5403v1 [math.AP]) Authors: Stan Alama, Lia Bronsard, Bernardo Galvão-Sousa In this work, we study thin-film limits of the full three-dimensional Ginzburg-Landau model for a superconductor in an applied magnetic field oriented obliquely to the film surface. We obtain Gamma-convergence results in several regimes, determined by the asymptotic ratio between the magnitude of the parallel applied magnetic field and the thickness of the film. Depending on the regime, we show that there may be a decrease in the density of Cooper pairs. We also show that in the case of variable thickness of the film, its geometry will affect the effective applied magnetic field, thus influencing the position of vortices. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Compressive Inverse Scattering I. High Frequency SIMO Measurements. (arXiv:0906.5405v1 [math-ph]) Compressive Inverse Scattering I. High Frequency SIMO Measurements. (arXiv:0906.5405v1 [math-ph]) Authors: Albert C. Fannjiang The inverse scattering problem with point scatterers and the single-input-multiple-output (SIMO) measurements is analyzed by the compressed sensing techniques with and without the Born approximation. Three main results about (probabilistic) recoverability of sparse target by the $L^1$-optimization technique called Basis Pursuit (BP) are obtained in the high frequency limit. In the absence of noise, it is shown that BP can recover exactly the target of sparsity up to the dimension of the measurement either with the multi-shot SIMO measurement for the Born scattering or with the single-shot SIMO measurement for the exact scattering. The stability with respect to noisy data is proved for weak or widely separated scatterers under a stronger sparsity constraint. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Componentwise and Cartesian decompositions of linear relations. (arXiv:0906.5406v1 [math.FA]) Componentwise and Cartesian decompositions of linear relations. (arXiv:0906.5406v1 [math.FA]) Authors: S. Hassi, H.S.V. de Snoo, F.H. Szafraniec Let $A$ be a, not necessarily closed, linear relation in a Hilbert space $\sH$ with a multivalued part $\mul A$. An operator $B$ in $\sH$ with $\ran B\perp\mul A^{**}$ is said to be an operator part of $A$ when $A=B \hplus (\{0\}\times \mul A)$, where the sum is componentwise (i.e. span of the graphs). This decomposition provides a counterpart and an extension for the notion of closability of (unbounded) operators to the setting of linear relations. Existence and uniqueness criteria for the existence of an operator part are established via the so-called canonical decomposition of $A$. In addition, conditions are developed for the decomposition to be orthogonal (components defined in orthogonal subspaces of the underlying space). Such orthogonal decompositions are shown to be valid for several classes of relations. The relation $A$ is said to have a Cartesian decomposition if $A=U+\I V$, where $U$ and $V$ are symmetric relations and the sum is operatorwise. The connection between a Cartesian decomposition of $A$ and the real and imaginary parts of $A$ is investigated. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	The optimal strategy for symmetric rendezvous search on K3. (arXiv:0906.5447v1 [math.OC]) The optimal strategy for symmetric rendezvous search on K3. (arXiv:0906.5447v1 [math.OC]) Authors: Richard Weber In the symmetric rendezvous search game played on Kn (the completely connected graph on n vertices) two players are initially placed at two distinct vertices (called locations). The game is played in discrete steps and at each step each player can either stay where he is or move to a different location. The players share no common labelling of the locations. They wish to minimize the expected number of steps until they first meet. Rendezvous search games of this type were first proposed by Steve Alpern in 1976. They are simple to describe, and have received considerable attention in the popular press as they model problems that are familiar in real life. They are notoriously difficult to analyse. Our solution of the symmetric rendezvous game on K3 makes this the first interesting game of its type to be solved, and establishes a 20 year old conjecture that the Anderson-Weber strategy is optimal. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	On geometric problems related to Brown-York and Liu-Yau quasilocal mass. (arXiv:0906.5451v1 [math.DG On geometric problems related to Brown-York and Liu-Yau quasilocal mass. (arXiv:0906.5451v1 [math.DG]) Authors: Pengzi Miao, Yuguang Shi, Luen-Fai Tam We discuss some geometric problems related to the definitions of quasilocal mass proposed by Brown-York \cite{BYmass1} \cite{BYmass2} and Liu-Yau \cite{LY1} \cite{LY2}. Our discussion consists of three parts. In the first part, we propose a new variational problem on compact manifolds with boundary, which is motivated by the study of Brown-York mass. We prove that critical points of this variation problem are exactly static metrics. In the second part, we derive a derivative formula for the Brown-York mass of a smooth family of closed 2 dimensional surfaces evolving in an ambient three dimensional manifold. As an interesting by-product, we are able to write the ADM mass \cite{ADM61} of an asymptotically flat 3-manifold as the sum of the Brown-York mass of a coordinate sphere $S_r$ and an integral of the scalar curvature plus a geometrically constructed function $\Phi(x)$ in the asymptotic region outside $S_r $. In the third part, we prove that for any closed, spacelike, 2-surface $\Sigma$ in the Minkowski space $\R^{3,1}$ for which the Liu-Yau mass is defined, if $\Sigma$ bounds a compact spacelike hypersurface in $\R^{3,1}$, then the Liu-Yau mass of $\Sigma$ is strictly positive unless $\Sigma$ lies on a hyperplane. We also show that the examples given by \'{O} Murchadha, Szabados and Tod \cite{MST} are special cases of this result. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Longest convex chains. (arXiv:0906.5452v1 [math.PR]) Longest convex chains. (arXiv:0906.5452v1 [math.PR]) Authors: Gergely Ambrus, Imre Barany Assume $X_n$ is a random sample of $n$ uniform, independent points from a triangle $T$. The longest convex chain, $Y$, of $X_n$ is defined naturally. The length $|Y|$ of $Y$ is a random variable, denoted by $L_n$. In this article, we determine the order of magnitude of the expectation of $L_n$. We show further that $L_n$ is highly concentrated around its mean, and that the longest convex chains have a limit shape. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Large Spaces Between the Zeros of the Riemann Zeta-Function. (arXiv:0906.5458v1 [math.NT]) Large Spaces Between the Zeros of the Riemann Zeta-Function. (arXiv:0906.5458v1 [math.NT]) Authors: S. H. Saker On the hypothesis that the mixed moments of Hardy's function and its derivative are correctly predicted by random matrix theory we derive new large spaces between the zeros of the Riemann zeta-function. Our proof depends on new Wirtinger-type inequalities and numerical solutions of algebraic equations. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Support Sets in Exponential Families and Oriented Matroid Theory. (arXiv:0906.5462v1 [math.ST]) Support Sets in Exponential Families and Oriented Matroid Theory. (arXiv:0906.5462v1 [math.ST]) Authors: Johannes Rauh, Thomas Kahle, Nihat Ay We discuss how to obtain an implicit description of the closure of a discrete exponential family with a finite set of equations derived from an underlying oriented matroid. These equations are similar to the equations used in algebraic statistics, although they need not be polynomial in the general case. This framework allows us to study the possible support sets of an exponential families with the help of oriented matroid theory. In particular, if two exponential families induce the same oriented matroid, then they have the same support sets. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Orthogonal series and limit theorems for canonical U- and V-statistics of stationary connected obser Orthogonal series and limit theorems for canonical U- and V-statistics of stationary connected observations. (arXiv:0906.5465v1 [math.PR]) Authors: I.S.Borisov, N.Volodko The limit behavior is studied for the distributions of normalized U- and V-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying classical mixing conditions. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	One-Parameter Generalizations of Rogers-Ramanujan Type Identities. (arXiv:0906.5438v1 [math.CO]) One-Parameter Generalizations of Rogers-Ramanujan Type Identities. (arXiv:0906.5438v1 [math.CO]) Authors: N.S.S. Gu, H. Prodinger Resorting to the recursions satisfied by the polynomials which converge to the right hand sides of the Rogers-Ramanujan type identities given by Sills and a determinant method presented in a paper by Ismail-Prodinger-Stanton, we obtain many new one-parameter generalizations of the Rogers-Ramanujan type identities, such as a generalization of the analytic versions of the first and second G\"{o}llnitz-Gordon partition identities, and generalizations of the first, second, and third Rogers-Selberg identities. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Murphy's {\em Positive definite kernels and Hilbert C${}^*$--modules} reorganized. (arXiv:0906.5408v Murphy's {\em Positive definite kernels and Hilbert C${}^*$--modules} reorganized. (arXiv:0906.5408v1 [math.OA]) Authors: F.H. Szafraniec The paper the title refers to is that in {\em Proceedings of the Edinburgh Mathematical Society}, {\bf 40} (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: to atomize that important result showing by the way connections which are out of favour and to rectify a tiny piece of history. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Extending positive definiteness. (arXiv:0906.5410v1 [math.FA]) Extending positive definiteness. (arXiv:0906.5410v1 [math.FA]) Authors: D. Cichoń, J. Stochel, F.H. Szafraniec The main result of the paper gives criteria for extendibility of sesquilinear form-valued mappings defined on symmetric subsets of *-semigroups to positive definite ones. By specifying this we obtain new solutions of: * the truncated complex moment problem, * the truncated multidimensional trigonometric moment problem, * the truncated two-sided complex moment problem, as well as characterizations of unbounded subnormality and criteria for the existence of unitary power dilation. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Normals, subnormals and an open question. (arXiv:0906.5412v1 [math.FA]) Normals, subnormals and an open question. (arXiv:0906.5412v1 [math.FA]) Authors: F.H.Szafraniec An acute look at \underbar{basic} facts concerning \underbar{unbounded} subnormal operators is taken here. These operators have the richest structure and are the most exciting among the whole family of beneficiaries of the normal ones. Therefore, the latter must necessarily be taken into account as the reference point for any exposition of subnormality. So as to make the presentation more appealing a kind of comparative survey of the bounded and unbounded case has been set forth. \noindent This piece of writing serves rather as a practical guide to this largely impenetrable territory than an exhausting report. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Martingale differences and the metric theory of continued fractions. (arXiv:0906.5428v1 [math.NT]) Martingale differences and the metric theory of continued fractions. (arXiv:0906.5428v1 [math.NT]) Authors: Alan K. Haynes, Jeffrey D. Vaaler We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by R. F. Gundy. By applying known results for martingales we obtain corresponding metric theorems for the continued fraction expansion of almost all real numbers. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Families of curves over any finite field with a class number greater than the Lachaud - Martin-Desch Families of curves over any finite field with a class number greater than the Lachaud - Martin-Deschamps bounds. (arXiv:0906.5432v1 [math.NT]) Authors: Stéphane Ballet, Robert Rolland We study and explicitly construct some families of asymptotically exact sequences of algebraic function fields. It turns out that these families have an asymptotical class number widely greater than the general Lachaud - Martin-Deschamps bounds. We emphasize that we obtain asymptotically exact sequences of algebraic function fields over any finite field $\F_q$, in particular when $q$ is not a square and that these sequences are dense towers. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segr Relative Density of the Random r-Factor Proximity Catch Digraph for Testing Spatial Patterns of Segregation and Association (Technical Report). (arXiv:0906.5436v1 [math.ST]) Authors: Elvan Ceyhan, Carey E. Priebe, John C. Wierman Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes. Different random graphs result from different definitions of the proximity region associated with each data point and different graph statistics can be employed for data reduction. The approach used in this article is based on a parameterized family of proximity maps determining an associated family of data-random digraphs. The relative arc density of the digraph is used as the summary statistic, providing an alternative to the domination number employed previously. An important advantage of the relative arc density is that, properly re-scaled, it is a U-statistic, facilitating analytic study of its asymptotic distribution using standard U-statistic central limit theory. The approach is illustrated with an application to the testing of spatial patterns of segregation and association. Knowledge of the asymptotic distribution allows evaluation of the Pitman and Hodges-Lehmann asymptotic efficacy, and selection of the proximity map parameter to optimize efficacy. Notice that the approach presented here also has the advantage of validity for data in any dimension. read more at math updates on arXiv.org rss2lj (Comment on this)
8:21p	Construction of operator product expansion coefficients via consistency conditions. (arXiv:0906.5468 Construction of operator product expansion coefficients via consistency conditions. (arXiv:0906.5468v1 [math-ph]) Authors: Jan Holland In this thesis an iterative scheme for the construction of operator product expansion (OPE) coefficients is applied to determine low order coefficients in perturbation theory for a specific toy model. We use the approach to quantum field theory proposed by S. Hollands [arXiv:0802.2198], which is centered around the OPE and a number of axioms on the corresponding OPE coefficients. This framework is reviewed in the first part of the thesis. In the second part we apply an algorithm for the perturbative construction of OPE coefficients to a toy model: Euclidean $\varphi^6$-theory in 3-dimensions. Using a recently found formulation in terms of vertex operators and a diagrammatic notation in terms of trees [arXiv:0906.5313v1], coefficients up to second order are constructed, some general features of coefficients at arbitrary order are presented and an exemplary comparison to the corresponding customary method of computation is given. read more at math updates on arXiv.org rss2lj (Comment on this)

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