Asymptotics of derivatives of orthogonal polynomials on the real line

We show that uniform asymptotics of orthogonal polynomials on the real line imply uniform asymptotics for all their derivatives. This is more technically challenging than the corresponding problem on the unit circle. We also examine asymptotics in the L ₂ norm. Research supported by NSF grant DMS0400446 and US-Israel BSF grant 2004353.     

双光子技术在三维成像和三维存储技术中的应用

对双光子过程的空间分辨能力进行了理论分析。阐明了双光子技术在三维成像和三维存储中的独特优势。着重介绍了双光子技术与扫描共焦显微术、近场显微术相结合进行三维成像 ,以及一种多焦点多光子显微术和用连续光源激发的双光子三维成像技术的研究和进展情况。对建立在共焦显微镜基础之上的双光子三维光存储和微细加工方面的研究也作了回顾与展望     

A multi‐energy‐level lattice Boltzmann model for the compressible Navier–Stokes equations

In this paper, we propose a new lattice Boltzmann model for the compressible Navier–Stokes equations. The new model is based on a three‐energy‐level and three‐speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. As the 25‐bit model, we obtained the equilibrium distribution functions and the compressible Navier–Stokes equations with the second accuracy of the truncation errors. The numerical examples show that the model can be used to simulate the shock waves, contact discontinuities and supersonic flows around circular cylinder. The numerical results are compared with those obtained by traditional method. Copyright © 2007 John Wiley & Sons, Ltd.     

Well-posedness of the free-surface incompressible Euler equations with or without surface tension

We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.

     

On the efficiency of linearization schemes and coupled multigrid methods in the simulation of a 3D flow around a cylinder

This paper studies the efficiency of two ways to treat the non‐linear convective term in the time‐dependent incompressible Navier–Stokes equations and of two multigrid approaches for solving the arising linear algebraic saddle point problems. The Navier–Stokes equations are discretized by a second‐order implicit time stepping scheme and by inf–sup stable, higher order finite elements in space. The numerical studies are performed at a 3D flow around a cylinder. Copyright © 2005 John Wiley & Sons, Ltd.     

Novel family of triphenylamine‐containing,hole‐transporting,amorphous, aromatic polyamides with stable electrochromic properties

We report the preparation and characterization of a series of novel electrochromic, aromatic poly(amine amide)s with pendent triphenylamine units. The synthesis proceeded via direct phosphorylation polycondensation between a novel diamine, N,N‐bis(4‐aminophenyl)‐N′,N′‐diphenyl‐1,4‐phenylenediamine, and various aromatic dicarboxylic acids. All the poly(amine amide)s were amorphous and readily soluble in many common organic solvents and could be solution‐cast into transparent, tough, and flexible films with good mechanical properties. They exhibited good thermal stability and 10% weight‐loss temperatures above 540 °C. Their glass‐transition temperatures were 263–290 °C. These polymers in N‐methyl‐2‐pyrrolidinone solutions exhibited strong ultraviolet–visible absorption peaks at 307–358 nm and photoluminescence peaks around 532–590 nm in the green region. The hole‐transporting and electrochromic properties were studied with electrochemical and spectroelectrochemical methods. Cyclic voltammograms of poly(amine amide) films prepared by the casting of polymer solutions onto an indium tin oxide coated glass substrate exhibited two reversible oxidation redox couples at 0.65 and 1.03 V versus Ag/AgCl in an acetonitrile solution. All the poly(amine amide)s showed excellent stability with respect to their electrochromic characteristics; the color of the films changed from pale yellow to green and then blue at 0.85 and 1.25 V, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2085–2098, 2005     

Perturbed kernel approximation on homogeneous manifolds

Current methods for interpolation and approximation within a native space rely heavily on the strict positive-definiteness of the underlying kernels. If the domains of approximation are the unit spheres in euclidean spaces, then zonal kernels (kernels that are invariant under the orthogonal group action) are strongly favored. In the implementation of these methods to handle real world problems, however, some or all of the symmetries and positive-definiteness may be lost in digitalization due to small random errors that occur unpredictably during various stages of the execution. Perturbation analysis is therefore needed to address the stability problem encountered. In this paper we study two kinds of perturbations of positive-definite kernels: small random perturbations and perturbations by Dunkl's intertwining operators [C. Dunkl, Y. Xu, Orthogonal polynomials of several variables, Encyclopedia of Mathematics and Its Applications, vol. 81, Cambridge University Press, Cambridge, 2001]. We show that with some reasonable assumptions, a small random perturbation of a strictly positive-definite kernel can still provide vehicles for interpolation and enjoy the same error estimates. We examine the actions of the Dunkl intertwining operators on zonal (strictly) positive-definite kernels on spheres. We show that the resulted kernels are (strictly) positive-definite on spheres of lower dimensions.     

关于Yang Bicheng不等式的另一个最佳常数

对Yang Bicheng不等式进行了再加强,获得了如下不等式:e 1-2n+(4-1 e)/(e-2)1+n1n相似文献   

Random Flights in Higher Spaces

We consider in this paper random flights in ℝ ^d performed by a particle changing direction of motion at Poisson times. Directions are uniformly distributed on hyperspheres S ₁ ^d . We obtain the conditional characteristic function of the position of the particle after n changes of direction. From this characteristic function we extract the conditional distributions in terms of (n+1)−fold integrals of products of Bessel functions. These integrals can be worked out in simple terms for spaces of dimension d=2 and d=4. In these two cases also the unconditional distribution is determined in explicit form. Some distributions connected with random flights in ℝ³ are discussed and in some special cases are analyzed in full detail. We point out that a strict connection between these types of motions with infinite directions and the equation of damped waves holds only for d=2. Related motions with random velocity in spaces of lower dimension are analyzed and their distributions derived.     

On the Maximum Number of Cliques in a Graph

A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m edges; (2) graphs with n vertices, m edges, and maximum degree Δ; (3) d-degenerate graphs with n vertices and m edges; (4) planar graphs with n vertices and m edges; and (5) graphs with n vertices and no K₅-minor or no K_3,3-minor. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2). Research supported by a Marie Curie Fellowship of the European Community under contract 023865, and by the projects MCYT-FEDER BFM2003-00368 and Gen. Cat 2001SGR00224.