Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients

We prove extension theorems in the norms described by Stokes and Lamé operators for the three‐dimensional case with periodic boundary conditions. For the Lamé equations, we show that the extension theorem holds for nearly incompressible media, but may fail in the opposite limit, i.e. for case of absolutely compressible media. We study carefully the latter case and associate it with the Cosserat problem. Extension theorems serve as an important tool in many applications, e.g. in domain decomposition and fictitious domain methods, and in analysis of finite element methods. We consider an application of established extension theorems to an efficient iterative solution technique for the isotropic linear elasticity equations for nearly incompressible media and for the Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. Such preconditioner allows the use of well‐known fast algorithms for preconditioning. Under some natural assumptions on smoothness and topological properties of subdomains with small coefficients, we prove convergence of the simplest Richardson method uniform in the jump of coefficients. For the Lamé equations, the convergence is also uniform in the incompressible limit. Our preliminary numerical results for two‐dimensional diffusion problems show fast convergence uniform in the jump and in the mesh size parameter. Copyright © 2002 John Wiley & Sons, Ltd.     

A Nd: YAG laser with a flat-top beam profile and constant divergence

An active resonator designed especially for Nd: YAG lasers is proposed. The expected performance of this resonator is the generation of a laser beam with a flat-topped distribution and a divergence invariant under the thermal lensing effect, such that it could be applied to surface treatment without special optical or mechanical elements. The beam quality and efficiency of such a resonator are presented and discussed in comparison with a parallel-plane resonator as adopted by most industrial Nd: YAG lasers.     

两个多元t分布之间的Kullback Leibler距离

该文将文［1］的结果推广到多元t分布的情形.结果表明, 两个多元t分布之间的Kullback Leibler距离与分布中的刻度矩阵之比的最大特征根密切相关.作为应用, 文章建立了一种在估计未知正定阵时的熵损失函数.     

类Ne钛X射线激光输出特性实验

 在星光激光装置上, 使用X射线多层膜反射镜、铝滤片及X射线CCD探测器组成高灵敏度空间分辨探测系统, 对用预脉冲技术产生的类Ne钛单线 (J=0-1, 3p-3s跃迁)软X射线激光输出特性进行了测量。由实验得到了类Ne钛X 射线激光束近场与距靶端32mm处(准远场)强度的空间分布, 给出了该激光束在近场强度最大区域的空间尺度(FWHM)约为72μm×31μm, 以及在垂直靶面与平行靶面方向的束发散角分别约为4mrad与9mrad。     

Global statistical information in exponential experiments and selection of exponential models

The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion.     

A fast direct solver for elliptic problems with a divergence constraint

A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

板条固体激光器热稳特性的研究

本文报道板条激光器的热稳运行,在150W至10000W的泵浦功率下输出发散角基本保持不变,最大输出功率大于150W;并绘出了腔内插入柱面镜,以压缩输出激光发散角的初步结果.     

Necessary conditions for optimal controls for systems governed by parabolic partial delay-differential equations in divergence form with first boundary conditions

In this paper, we consider the question of necessary conditions for optimality for systems governed by second-order parabolic partial delay-differential equations with first boundary conditions. All the coefficients of the system are assumed bounded measurable and contain controls and delays in their arguments. The second-order parabolic partial delay-differential equation is in divergence form. In Theorem 4.1, we present results on the existence and uniqueness of weak solutions in the sense of Ladyzhenskaya-Solonnikov-Ural'ceva for this class of systems. An integral maximum principle and its point-wise version for the corresponding controlled system are established in Theorem 5.1 and Corollary 5.1, respectively.The authors wish to thank Dr. E. Noussair for his stimulating discussion and valuable comments in the preparation of this paper. Further, they also wish to acknowledge the referee of the paper for his valuable suggestions and comments. The discussion presented in Section 6 is in response to his suggestions.     

针板型电晕稳定开关的电晕稳定性

设计了一款可用于触发和自触发的针板型电晕稳定开关,其中针电极直径为2 mm,主间隙距离为10 mm,触发间隙为5 mm。通过静电场的模拟得知其场强的不均匀系数大于7,并且通过大量实验数据得出:开关起晕电压和击穿电压分别为6.8 kV和19.3 kV,由此得知电晕稳定开关的电晕稳定因子为0.55,这说明开关具有较好的电晕稳定性。     

Uniform and L-convergence of Logarithmic Means of Walsh-Fourier Series

The （NSrlund） logarithmic means of the Fourier series of the integrable function f is： 1/lnn-1∑k=1Sk（f）/n-k, where ln：=n-1∑k=11/k. In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L^1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Móricz concerning the convergence of logarithmic means in norm.