Thursday, August 24th, 2006

Time	Event
10:24p	Recurrence relations and the algebraic irrationality of Zeta(3). [math.NT/0608577] Recurrence relations and the algebraic irrationality of Zeta(3). [math.NT/0608577] Authors: Angelo B. Mingarelli We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, we show that there exists a four-term real linear recurrence relation whose solutions allow us to produce a tractable equivalent criterion for the quadratic irrationality of zeta(3), where zeta is the classic Zeta function of Riemann or, for that matter, the quadratic irrationality of any other irrational that arises either as a result of an Apery-like argument, or from a continued fraction expansion. The result is amplified to produce a criterion for the transcendence of such irrational numbers arising from three-term recurrence relations. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Penalized Partial Least Squares Based on B-Splines Transformations. [math.ST/0608576] Penalized Partial Least Squares Based on B-Splines Transformations. [math.ST/0608576] Authors: Nicole Kraemer, Anne-Laure Boulesteix, Gerhard Tutz We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in terms of a generous amount of B-Splines basis functions. In order to prevent overfitting and to obtain smooth functions, we estimate the regression model by applying a penalized version of PLS. Although our motivation for penalized PLS stems from its use for B-Splines transformed data, the proposed approach is very general and can be applied to other penalty terms or to other dimension reduction techniques. It turns out that penalized PLS can be computed virtually as fast as PLS. We prove a close connection of penalized PLS to the solutions of preconditioned linear systems. In the case of high-dimensional data, the new method is shown to be an attractive competitor to other techniques for estimating generalized additive models. If the number of predictor variables is high compared to the number of examples, traditional techniques often suffer from overfitting. We illustrate that penalized PLS performs well in these situations. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Some new algebras of functions on topological groups arising from $G$-spaces. [math.DS/0608575] Some new algebras of functions on topological groups arising from $G$-spaces. [math.DS/0608575] Authors: Eli Glasner, Michael Megrelishvili For a topological group G we introduce the algebra SUC(G) of \emph{strongly uniformly continuous} functions. We show that SUC(G) contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and Asplund functions respectively. For the Polish groups of order preserving homeomorphisms of the unit interval and of isometries of the Urysohn space of diameter 1, we show that SUC(G) is trivial. We introduce the notion of fixed point on a class P of flows (P-fpp) and study in particular groups with the SUC-fpp. We study the Roelcke algebra (= UC(G) = right and left uniformly continuous functions) and SUC compactifications of the groups S(N), of permutations of a countable set, and H(C), the group of homeomorphisms of the Cantor set. For the first group we show that WAP(G)=SUC(G)=UC(G) and also provide a concrete description of the corresponding metrizable (in fact Cantor) semitopological semigroup compactification. For the second group, in contrast, we show that SUC(G) is properly contained in UC(G). We then deduce that for this group UC(G) does not yield a right topological semigroup compactification. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Reconstructing projective schemes from Serre subcategories. [math.AG/0608574] Reconstructing projective schemes from Serre subcategories. [math.AG/0608574] Authors: Grigory Garkusha, Mike Prest Given a positively graded commutative coherent ring A which is finitely generated as an A_0-algebra, a bijection between the tensor Serre subcategories of qgr A and the set of all subsets Y\subseteq Proj A of the form Y=\bigcup_{i\in\Omega}Y_i with quasi-compact open complement Proj A\Y_i for all i\in\Omega is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective graded modules are used in an essential way. Also, there is constructed an isomorphism of ringed spaces (Proj A,O_{Proj A}) --> (Spec(qgr A),O_{qgr A}), where (Spec(qgr A),O_{qgr A}) is a ringed space associated to the lattice L_{serre}(qgr A) of tensor Serre subcategories of qgr A. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	On chaos of a cubic $p$-adic dynamical system. [math.DS/0608573] On chaos of a cubic $p$-adic dynamical system. [math.DS/0608573] Authors: Farrukh Mukhamedov, José F.F. Mendes In the paper we describe basin of attraction of the $p$-adic dynamical system $f(x)=x^3+ax^2$. Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the $p$-adic Siegel discs. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Morita equivalences induced by bimodules over Hopf-Galois extensions. [math.RA/0608572] Morita equivalences induced by bimodules over Hopf-Galois extensions. [math.RA/0608572] Authors: S. Caenepeel, S. Crivei, A. Marcus Let $H$ be a Hopf algebra, and $A,B$ be $H$-Galois extensions. We investigate the category ${}_A\mathcal{M}_B^H$ of relative Hopf bimodules, and the Morita equivalences between $A$ and $B$ induced by them. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Intensional Models for the Theory of Types. [math.LO/0608571] Intensional Models for the Theory of Types. [math.LO/0608571] Authors: Reinhard Muskens In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Integral representations of one dimensional projections for multivariate stable densities. [math.ST/ Integral representations of one dimensional projections for multivariate stable densities. [math.ST/0608570] Authors: Muneya Matsui, Akimichi Takemura We consider the numerical evaluation of one dimensional projections of general multivariate stable densities introduced by Abdul-Hamid and Nolan (1998). In their approach higher order derivatives of one dimensional densities are used, which seem to be cumbersome in practice. Furthermore there are some difficulties for even dimensions. In order to overcome these difficulties we obtain the explicit finite-interval integral representation of one dimensional projections for all dimensions. For this purpose we utilize the imaginary part of complex integration, whose real part corresponds to the derivative of the one dimensional inversion formula. We also give summaries on relations between various parameterizations of stable multivariate density and its one dimensional projection. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Stable principal bundles and reduction of structure group. [math.AG/0608569] Stable principal bundles and reduction of structure group. [math.AG/0608569] Authors: Indranil Biswas Let $E_G$ be a stable principal $G$--bundle over a compact connected Kaehler manifold, where $G$ is a connected reductive linear algebraic group defined over the complex numbers. Let $H\subset G$ be a complex reductive subgroup which is not necessarily connected, and let $E_H\subset E_G$ be a holomorphic reduction of structure group. We prove that $E_H$ is preserved by the Einstein-Hermitian connection on $E_G$. Using this we show that if $E_H$ is a minimal reductive reduction in the sense that there is no complex reductive proper subgroup of $H$ to which $E_H$ admits a holomorphic reduction of structure group, then $E_H$ is unique in the following sense: For any other minimal reductive reduction $(H', E_{H'})$ of $E_G$, there is some element $g$ of $G$ such that $H'= g^{-1}Hg$ and $E_{H'}= E_Hg$. As an application, we give an affirmative answer to a question of Balaji and Koll\'ar. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Analysis of a 3D chaotic system. [math.DS/0608568] Analysis of a 3D chaotic system. [math.DS/0608568] Authors: G. Tigan, D. Opris A 3D nonlinear chaotic system, called the T system, is analyzed in this paper. Horseshoe chaos is investigated via the heteroclinic Shilnikov method constructing a heteroclinic connections between the saddle equilibrium points of the system. Partially numerical computations are carried out to support the analytical results. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Well-Balanced Schemes for the Initial Boundary Value Problem for 1D Scaler Conservation Laws. [math. Well-Balanced Schemes for the Initial Boundary Value Problem for 1D Scaler Conservation Laws. [math.NA/0608567] Authors: M. Nolte, D. Kroener We consider well-balanced schemes for the following 1D scalar conservation law with source term: d_t u + d_x f(u) + z'(x) b(u) = 0. More precisely, we are interested in the numerical approximation of the initial boundary value problem for this equation. While our main concern is a convergence result, we also have to extend Otto's notion of entropy solutions to conservation laws with a source term. To obtain uniqueness, we show that a generalization, the so-called entropy process solution, is unique and coincides with the entropy solution. If the initial and boundary data are essentially bounded, we can establish convergence to the entropy solution. Showing that the numerical solutions are bounded we can extract a weak*-convergent subsequence. Identifying its limit as an entropy process solution requires some effort as we cannot use Kruzkov-type entropy pairs here. We restrict ourselves to the Engquist-Osher flux and identify the numerical entropy flux for an arbitrary entropy pair. By the uniqueness result, the scheme then approximates the entropy solution and a result by Vovelle then guarantees that the convergence is strong in L^p for finite p. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	A generalization of Wolstenholme's harmonic series congruence. [math.NT/0608566] A generalization of Wolstenholme's harmonic series congruence. [math.NT/0608566] Authors: Hao Pan We give a generalization of Wolstenholme's harmonic series congruence for the Lucas sequences. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Note on some congruences of Lehmer. [math.NT/0608565] Note on some congruences of Lehmer. [math.NT/0608565] Authors: Hui-Qin Cao, Hao Pan In the paper, we generalize some congruences of Lehmer for general composite numbers. read more at math updates on arXiv.org rss2lj (Comment on this)
10:24p	Congruences on Stirling numbers and Eulerian numbers. [math.NT/0608564] Congruences on Stirling numbers and Eulerian numbers. [math.NT/0608564] Authors: Hui-Qin Cao, Hao Pan In this paper, we establish some Fleck-Weisman type and Davis-Sun type congruences for the Stirling numbers and the Eulerian numbers. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	Polynomial-time word problems. [math.GR/0608563] Polynomial-time word problems. [math.GR/0608563] Authors: Saul Schleimer We find polynomial-time solutions to the word problem for free-by-cyclic groups, the word problem for automorphism groups of free groups, and the membership problem for the handlebody subgroup of the mapping class group. All of these results follow from observing that automorphisms of the free group strongly resemble straight line programs, which are widely studied in the theory of compressed data structures. In an effort to be self-contained we give a detailed exposition of the necessary results from computer science. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	On classification of resonance-free Anosov Z^k actions. [math.DS/0608562] On classification of resonance-free Anosov Z^k actions. [math.DS/0608562] Authors: Boris Kalinin, Victoria Sadovskaya We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are one-dimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a finite cover of such an action is smoothly conjugate to an action by toral automorphisms. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	Propagation Time in Stochastic Communication Networks. [math.PR/0608561] Propagation Time in Stochastic Communication Networks. [math.PR/0608561] Authors: Jonathan Rowe, Boris Mitavskiy Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including small world and scale free networks). They model a variety of phenomena, including the spread of information on the Internet; the outbreak of epidemics in a spatially structured population; and communication between randomly dispersed processors in an ad hoc wireless network. Typically, research has concentrated on the existence and size of a large connected component (representing, say, the size of the epidemic) in a percolation model, or uses differential equations to study the dynamics using a mean-field approximation in an infinite graph. Here we investigate the time taken for information to propagate from a single source through a finite network, as a function of the number of nodes and the network topology. We assume that time is discrete, and that nodes attempt to transmit to their neighbors in parallel, with a given probability of success. We solve this problem exactly for several specific topologies, and use a large-deviation theorem to derive general asymptotic bounds, which apply to any family of networks where the diameter grows at least logarithmically in the number of nodes. We use these bounds, for example, to show that a scale-free network has propagation time logarithmic in the number of nodes, and inversely proportional to the transmission probability. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	Extensions of Wilson's lemma and the Ax-Katz theorem. [math.NT/0608560] Extensions of Wilson's lemma and the Ax-Katz theorem. [math.NT/0608560] Authors: Zhi-Wei Sun A classical result of A. Fleck states that if p is a prime, and n>0 and r are integers, then $$\sum_{k=r(mod p)}\binom {n}{k}(-1)^k=0 (mod p^{[(n-1)/(p-1)]}).$$ Recently R. M. Wilson used Fleck's congruence and Weisman's extension to present a useful lemma on polynomials modulo prime powers, and applied this lemma to reprove the Ax-Katz theorem on solutions of congruences modulo p and deduce various results on codewords in p-ary linear codes with weights. In light of the recent generalizations of Fleck's congruence given by D. Wan, and D. M. Davis and Z. W. Sun, we obtain new extensions of Wilson's lemma and the Ax-Katz theorem. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	Quantum super spheres and their transformation groups, representations, and little $t$-Jacobi polyno Quantum super spheres and their transformation groups, representations, and little $t$-Jacobi polynomials. [math.QA/0608559] Authors: Yi Ming Zou Quantum super 2-shpheres and the corresponding quantum super transformation group are introduced in analogy to the well-known quantum 2-shpheres and quantum SL(2), connection between little $t$-Jacobi polynomials and the finite dimensional representations of the quantum super group is formulated, and the Peter-Weyl theorem is obtained. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	New inverse data for tridiagonal matrices. [math.SP/0608558] New inverse data for tridiagonal matrices. [math.SP/0608558] Authors: Ricardo S. Leite, Nicolau C. Saldanha, Carlos Tomei We introduce bidiagonal coordinates, a new set of spectral coordinates on open dense charts covering the space of real symmetric tridiagonal matrices of simple spectrum. In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, reduced tridiagonal matrices now lie in the interior of some chart. Bidiagonal coordinates yield therefore an explicit atlas for T_Lambda, the manifold of real tridiagonal matrices with given spectrum Lambda. These new coordinates are convenient for the study of asymptotics of isospectral dynamics, both for continuous and discrete time. read more at math updates on arXiv.org rss2lj (Comment on this)
10:25p	Equivariant isospectrality and isospectral deformations of metrics on spherical orbifolds. [math.DG/ Equivariant isospectrality and isospectral deformations of metrics on spherical orbifolds. [math.DG/0608557] Authors: Craig J. Sutton Most known examples of isospectral manifolds can be constructed through variations of Sunada's method or Gordon's torus method. In this paper we explore these two techniques in the framework of equivariant isospectrality. We begin by establishing an equivariant version of Sunada's technique and then we observe that many examples arising from the torus method are equivariantly isospectral. Using these observations we notice that many of the known torus method examples give rise to other (locally non-isometric) isospectral manifolds, and we also construct continuous families of isospectral metrics on orbifolds. In particular, for each finite subgroup $\Gamma$ of the 2-torus there exists a spherical orbifold (resp. orbifold with boundary) $\orb$ of dimension $n \geq 8$ (resp. $n \geq 9$) which has points with $\Gamma$-isotropy and admits a continuous family of locally non-isometric isospectral metrics (resp. Dirichlet and Neumann isospectral metrics). read more at math updates on arXiv.org rss2lj (Comment on this)

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