On the nonvanishing of the central value of the Rankin-Selberg -functions

We characterize the nonvanishing of the central value of the Rankin-Selberg -functions in terms of periods of Fourier-Jacobi type. This characterization is based on the Langlands philosophy on functoriality and on applications of invariant theory to automorphic representations. The result is the symplectic analog of the Gross-Prasad conjecture.

     

图像处理的结构层次建模

图像处理是应用广泛的现代工程技术 ,但直到现在尚无完备的数学模型体系 .依结构层次观点对其数学模型化进行探索 ,给出了图像处理的结构层次模型 ,将图像处理与数学科学中的常见数学理论联系起来 .同时 ,对目前常见图像处理器进行数学模型描述 .     

Stickelberger elements for -extensions of function fields

We study Stickelberger elements associated to -extensions over global function fields of characteristic p>0 and show that they are in some sense generically irreducible in the Iwasawa algebras.     

Exploiting structure in piecewise-linear homotopy algorithms for solving equations

We consider the recent algorithms for computing fixed points or zeros of continuous functions fromR ⁿ to itself that are based on tracing piecewise-linear paths in triangulations. We investigate the possible savings that arise when these fixed-point algorithms with their usual triangulations are applied to computing zeros of functionsf with special structure:f is either piecewise-linear in certain variables, separable, or has Jacobian with small bandwidth. Each of these structures leads to a property we call modularity; the algorithmic path within a simplex can be continued into an adjacent simplex without a function evaluation or linear programming pivot. Modularity also arises without any special structure onf from the linearity of the function that is deformed tof. In the case thatf is separable we show that the path generated by Kojima's algorithm with the homotopyH ² coincides with the path generated by the standard restart algorithm of Merrill when the usual triangulations are employed. The extra function evaluations and linear programming steps required by the standard algorithm can be avoided by exploiting modularity.This research was performed while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, and was sponsored by the United States Army under Contract No. DAAG-29-75-C-0024 and by the National Science Foundation under Grant No. ENG76-08749.     

State space collapse with application to heavy traffic limits for multiclass queueing networks

Heavy traffic limits for multiclass queueing networks are a topic of continuing interest. Presently, the class of networks for which these limits have been rigorously derived is restricted. An important ingredient in such work is the demonstration of state space collapse. Here, we demonstrate state space collapse for two families of networks, first-in first-out (FIFO) queueing networks of Kelly type and head-of-the-line proportional processor sharing (HLPPS) queueing networks. We then apply our techniques to more general networks. To demonstrate state space collapse for FIFO networks of Kelly type and HLPPS networks, we employ law of large number estimates to show a form of compactness for appropriately scaled solutions. The limits of these solutions are next shown to satisfy fluid model equations corresponding to the above queueing networks. Results from Bramson [4,5] on the asymptotic behavior of these limits then imply state space collapse. The desired heavy traffic limits for FIFO networks of Kelly type and HLPPS networks follow from this and the general criteria set forth in the companion paper Williams [41]. State space collapse and the ensuing heavy traffic limits also hold for more general queueing networks, provided the solutions of their fluid model equations converge. Partial results are given for such networks, which include the static priority disciplines. This revised version was published online in June 2006 with corrections to the Cover Date.     

NONCONFORMING FINITE ELEMENT PENALTY METHOD FOR STOKES EQUATION

a special penalty method is presented to improve the accuracy of the standard penaltymethod (or solving Stokes equation with nonconforming finite element, It is shown that thismethod with a larger penalty parameter can achieve the same accuracy as the staodaxd methodwith a smaller penalty parameter. The convergence rate of the standard method is just hall order of this penalty method when using the same penalty parameter, while the extrapolationmethod proposed by Faik et al can not yield so high accuracy of convergence. At last, we alsoget the super-convergence estimates for total flux.     

A Skorokhod Problem formulation and large deviation analysis of a processor sharing model

Generalized processor sharing has been proposed as a policy for distributing processing in a fair manner between different data classes in high-speed networks. In this paper we show how recent results on the Skorokhod Problem can be used to construct and analyze the mapping that takes the input processes into the buffer content. More precisely, we show how to represent the map in terms of a Skorokhod Problem, and from this infer that the mapping is well defined (existence and uniqueness) and well behaved (Lipschitz continuity). As an elementary application we present some large deviation estimates for a many data source model. This revised version was published online in June 2006 with corrections to the Cover Date.     

The plane wave expansion, infinite integrals and identities involving spherical Bessel functions

This paper shows that the plane wave expansion can be a useful tool in obtaining analytical solutions to infinite integrals over spherical Bessel functions and the derivation of identities for these functions. The integrals are often used in nuclear scattering calculations, where an analytical result can provide an insight into the reaction mechanism. A technique is developed whereby an integral over several special functions which cannot be found in any standard integral table can be broken down into integrals that have existing analytical solutions.     

Left invariant special Kähler structures

We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples.