Below are the 20 most recent journal entries recorded in arxivmath's LiveJournal:

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Friday, July 17th, 2009
11:22 am	Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric va Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties. (arXiv:0907.2701v1 [math.CO]) Authors: Charles F. Doran, Andrey Y. Novoseltsev We use Batyrev-Borisov's formula for the generating function of stringy Hodge numbers of Calabi-Yau varieties realized as complete intersections in toric varieties in order to get closed form expressions for Hodge numbers of Calabi-Yau threefolds in five-dimensional ambient spaces. These expressions involve counts of lattice points on faces of associated Cayley polytopes. Using the same techniques, similar expressions may be obtained for higher dimensional varieties realized as complete intersections of two hypersurfaces. read more at math updates on arXiv.org rss2lj (4 Comments |Comment on this)
11:22 am	Invariant function algebras on compact commutative homogeneous spaces. (arXiv:0907.2744v1 [math.FA]) Invariant function algebras on compact commutative homogeneous spaces. (arXiv:0907.2744v1 [math.FA]) Authors: V.M. Gichev Let $M$ be a commutative homogeneous space of a compact Lie group $G$ and $A$ be a closed $G$-invariant subalgebra of the Banach algebra $C(M)$. A function algebra is called antisymmetric if it does not contain nonconstant real functions. By the main result of this paper, $A$ is antisymmetric if and only if the invariant probability measure on $M$ is multiplicative on $A$. This implies, for example, the following theorem: if $G^{\mathbb C}$ acts transitively on a Stein manifold $\cal M$, $v\in{\cal M}$, and the compact orbit $M=Gv$ is a commutative homogeneous space, then $M$ is a real form of $\cal M$. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	Remarks on the Blowup Criteria for Oldroyd Models. (arXiv:0907.2745v1 [math.AP]) Remarks on the Blowup Criteria for Oldroyd Models. (arXiv:0907.2745v1 [math.AP]) Authors: Zhen Lei, Nader Masmoudi, Yi Zhou We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in \cite{CM} in two space dimensions. Our method is much easier than the one based on the well-known \textit{losing a priori estimate} and is expected to be easily adopted to other problems involving the losing \textit{a priori} estimate. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion. (arXi Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion. (arXiv:0907.2748v1 [math.PR]) Authors: Mingshang Hu We obtain the viscosity solution of G-heat equation with the initial condition $\phi(x)=x^{n}$ for each integer $n\geq1$ using the method of G-Brownian motion. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem. (a Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem. (arXiv:0907.2758v1 [math.AP]) Authors: Claude-Michel Brauner (IMB), Josephus Hulshof, Luca Lorenzi In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter $\varepsilon$ and define rescaled variables accordingly. At fixed $\varepsilon$, our method is based on: definition of a suitable linear 1D operator, projection with respect to the longitudinal coordinate only, Lyapunov-Schmidt method. As a solvability condition, we derive a self-consistent parabolic equation for the front. We prove that, starting from the same configuration, the latter remains close to the solution of K--S on a fixed time interval, uniformly in $\varepsilon$ sufficiently small. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	Elementary divisor theory for the modular group over hermitian fields and definite quaternion algebr Elementary divisor theory for the modular group over hermitian fields and definite quaternion algebras. (arXiv:0907.2762v1 [math.NT]) Authors: Martin Raum We develop an elementary divisor theory for the unimodular and modular group over any hermitian field and any definite quaternion algebra. Moreover we deduce a necessary and sufficient condition on the occurring sets of elementary divisors. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	On semidefinite representations of sets. (arXiv:0907.2764v1 [math.OC]) On semidefinite representations of sets. (arXiv:0907.2764v1 [math.OC]) Authors: Tim Netzer Spectrahedra are sets defined by linear matrix inequalities. Projections of spectrahedra are called semidefinite representable sets. Both kinds of sets are of practical use in polynomial optimization, since they allow to apply semidefinite programming. In this work we develop some new methods to prove semidefinite representability of sets. We examine partial linear matrix inequalities, i.e. conditions stating that a linear matrix polynomial is conditional semidefinite (instead of positive semidefinite, as in the definition of a spectrahedron). For certain classes we prove that those conditions produce semidefinite representable sets. We then examine non-closed sets, which seem to have gained no attention at all so far. The interior of a semidefinite representable set is shown to be semidefinite representable. More general, one can remove faces of a semidefinite representable set and preserve semidefinite representability, as long as the faces are parametrized in a suitable way. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	Hecke algebras related to the unimodular and modular groups over hermitian fields and definite quate Hecke algebras related to the unimodular and modular groups over hermitian fields and definite quaternion algebras. (arXiv:0907.2766v1 [math.NT]) Authors: Martin Raum We investigate the structure of the Hecke algebras related to the unimodular and modular group over hermitian fields and definite quaternion algebras. In particular we show that in general there is no decomposition into primary components. We can give a set of generators and in some special cases we deduce the law of interchange of the Siegel $\Phi$-operator. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	The functional equation for the twisted spinor-L-function of genus 2. (arXiv:0907.2767v1 [math.NT]) The functional equation for the twisted spinor-L-function of genus 2. (arXiv:0907.2767v1 [math.NT]) Authors: Aloys Krieg, Martin Raum We prove a functional equation of the convolution of two paramodular forms of genus 2. An important application is the functional equation for the twist spinor L-function of arbitrary Siegel cusp eigenforms of genus 2 with a primitive Dirichlet character. read more at math updates on arXiv.org rss2lj (Comment on this)
11:22 am	Fano manifolds of degree ten and EPW sextics. (arXiv:0907.2781v1 [math.AG]) Fano manifolds of degree ten and EPW sextics. (arXiv:0907.2781v1 [math.AG]) Authors: Atanas Iliev, Laurent Manivel (IF) O'Grady showed that certain special sextics in $\mathbb{P}^5$ called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	On the derived category of the Cayley plane. (arXiv:0907.2784v1 [math.AG]) On the derived category of the Cayley plane. (arXiv:0907.2784v1 [math.AG]) Authors: Laurent Manivel (IF) We describe a maximal exceptional collection on the Cayley plane, the minimal homogeneous projective variety of $E_6$. This collection consists in a sequence of 27 irreducible homogeneous bundles. read more at math updates on arXiv.org rss2lj (1 Comment |Comment on this)
11:21 am	Generalized backward doubly stochastic differential equations driven by L\'evy processes with non-Li Generalized backward doubly stochastic differential equations driven by L\'evy processes with non-Lipschitz coefficients. (arXiv:0907.2785v1 [math.PR]) Authors: Auguste Aman (LMAI), Jean Marc Owo (LMAI) We prove an existence and uniqueness result for generalized backward doubly stochastic differential equations driven by L\'evy processes with non-Lipschitz assumptions. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Computation of an Integral Basis of Quartic Number Fields. (arXiv:0907.2786v1 [math.NT]) Computation of an Integral Basis of Quartic Number Fields. (arXiv:0907.2786v1 [math.NT]) Authors: Lhoussain El Fadil In this paper, based on techniques of Newton polygons, a result which allows the computation of a p integral basis of every quartic number field is given. For each prime integer p, this result allows to compute a p-integral basis of a quartic number field K defined by an irreducible polynomial $P(X) = X4 + aX + b \in\z[X]$ in methodical and complete generality. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Free involutions on $S^2 \times S^3$. (arXiv:0907.2800v1 [math.GT]) Free involutions on $S^2 \times S^3$. (arXiv:0907.2800v1 [math.GT]) Authors: Yang Su In this paper, an explicit classification of smooth free involutions on $S^2 \times S^3$ up to conjugation is obtained. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Tropical linear mappings on the plane. (arXiv:0907.2811v1 [math.AG]) Tropical linear mappings on the plane. (arXiv:0907.2811v1 [math.AG]) Authors: M.J. de la Puente In this paper we fully describe all tropical linear mappings in the tropical projective plane, that is, maps from the tropical plane to itself given by tropical multiplication by an order 3 matrix. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Fekete points and convergence towards equilibrium measures on complex manifolds. (arXiv:0907.2820v1 Fekete points and convergence towards equilibrium measures on complex manifolds. (arXiv:0907.2820v1 [math.CV]) Authors: Robert J.Berman, Sebastien Boucksom, David Witt Nystrom Building on the first two authors' previous results, we prove a general criterion for convergence of (possibly singular) Bergman measures towards equilibrium measures on complex manifolds. The criterion may be formulated in terms of growth properties of balls of holomorphic sections, or equivalently as an asymptotic minimization of generalized Donaldson L-functionals. Our result yields in particular the proof of a well-known conjecture in pluripotential theory concerning the equidistribution of Fekete points, and it also gives the convergence of Bergman measures towards equilibrium for Bernstein-Markov measures. Applications to interpolation of holomorphic sections are also discussed. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Optimal Control of Infinite Horizon Partially Observable Decision Processes Modeled As Generators of Optimal Control of Infinite Horizon Partially Observable Decision Processes Modeled As Generators of Probabilistic Regular Languages. (arXiv:0907.2738v1 [math.OC]) Authors: Ishanu Chattopadhyay, Asok Ray Decision processes with incomplete state feedback have been traditionally modeled as Partially Observable Markov Decision Processes. In this paper, we present an alternative formulation based on probabilistic regular languages. The proposed approach generalizes the recently reported work on language measure theoretic optimal control for perfectly observable situations and shows that such a framework is far more computationally tractable to the classical alternative. In particular, we show that the infinite horizon decision problem under partial observation, modeled in the proposed framework, is $\epsilon$-approximable and, in general, is no harder to solve compared to the fully observable case. The approach is illustrated via two simple examples. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Presentations of Graph Braid Groups. (arXiv:0907.2730v1 [math.GR]) Presentations of Graph Braid Groups. (arXiv:0907.2730v1 [math.GR]) Authors: Daniel Farley, Lucas Sabalka Let G be a graph. The (unlabeled) configuration space of n points on G is the space of all n-element subsets of G. The fundamental group of such a configuration space is called a graph braid group. We use a version of discrete Morse theory to compute presentations of all graph braid groups, for all finite connected graphs G and all natural numbers n. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	Interference Channels with Destination Cooperation. (arXiv:0907.2702v1 [cs.IT]) Interference Channels with Destination Cooperation. (arXiv:0907.2702v1 [cs.IT]) Authors: Vinod Prabhakaran, Pramod Viswanath Interference is a fundamental feature of the wireless channel. The two-user Gaussian interference channel where the destination nodes can both talk and listen is studied. Using novel inner and outer bounds the sum-capacity of this channel is characterized up to a constant number of bits. read more at math updates on arXiv.org rss2lj (Comment on this)
11:21 am	On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate. (arXiv On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate. (arXiv:0907.2708v1 [math.CV]) Authors: Jan-Fredrik Olsen, Eero Saksman A range of Hardy-like spaces of ordinary Dirichlet series, called the Dirichlet-Hardy spaces $\Hp^p$, $p \geq 1$, have been the focus of increasing interest among researchers following a paper of Hedenmalm, Lindqvist and Seip in Duke Math. J 86 (1997), 1-37. The Dirichlet series in these spaces converge on a certain half-plane, where one may also define the classical Hardy spaces $H^p$. In this paper, we compare the boundary behaviour of elements in $\Hp^p$ and $H^p$. Moreover, Carleson measures of the spaces $\Hp^p$ are studied. Our main result shows that for certain cases the following statement holds true. Given an interval on the boundary of the half-plane of definition and a function in the classical Hardy space, it possible to find a function in the corresponding Dirichlet-Hardy space such that their difference has an analytic continuation across this interval. read more at math updates on arXiv.org rss2lj (Comment on this)