Clifford分析中无界域上正则函数的边值问题

在引入修正Cauchy核的基础上,讨论了无界域上正则函数的带共轭值的边值问题：a(t)Φ (t) b(t)Φ (t) c(t)Φ-(t) d(t)Φ=g(t)．首先给出了无界域上正则函数的Plemelj公式,然后利用积分方程方法和压缩不动点原理证明了问题解的存在唯一性．     

Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations

It is well-known that the classical Chapman-Enskog procedure does not work at the level of Burnett equations (the next step after the Navier-Stokes equations). Roughly speaking, the reason is that the solutions of higher equations of hydrodynamics (Burnett's, etc.) become unstable with respect to short-wave perturbations. This problem was recently attacked by several authors who proposed different ways to deal with it. We present in this paper one of possible alternatives. First we deduce a criterion for hyperbolicity of Burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases. Then we discuss in more detail the problem of truncation of the Chapman-Enskog expansion and show that the way of truncation is not unique. The general idea of changes of coordinates (based on analogy with the theory of dynamical systems) leads finally to nonlinear Hyperbolic Burnett Equations (HBEs) without using any information beyond the classical Burnett equations. It is proved that HBEs satisfy the linearized H-theorem. The linear version of the problem is studied in more detail, the complete Chapman-Enskog expansion is given for the linear case. A simplified proof of the Slemrod identity for Burnett coefficients is also given.     

鞅差序列的Bernstein型不等式及其应用

本文将独立随机变量序列的Bernstein型不等式推广到鞅差序列情形,给出该不等式的一个应用,并在一定条件下证明了非参数回归中函数估计的强相合性.     

TWO-POINT BOUNDARY VALUE PROBLEM FOR A CLASS OF SECOND-ORDER DIFFERENCE EQUATIONS

In this paper, we apply a critical point theorem and obtain the condition for the existence of three solutions to two-point boundary value problem of a second order nonlinear difference equation.     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

ON A LINEAR DELAY DIFFERENCE EQUATION WITH IMPULSES

IIntroductlonLet N denote the set of all Integers．FOr any a;b E N,define N(a)＝{a,a＋1,…},N(a,b)二{a,a＋1,…,b}when a＜b．Consider the dlf卜巳renceequationl 凸x。＋P。x。－。＝0;nEN(0)andN4n。;2—“－””’”门二l0 凸X。,＝~X。,,JENO);where A denotes the forward difference operator八。。＝x。＋l一 x。,{P。} Isa sequence ofnon－negative real numbers,{nj}Is a sequence ofnon－negativeIntegers with nj＜nj＋lfor j E N(1)and nj一 co as ;一 co,{4}Is a sequence。I优。且皿mb ers,…     

Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations

Abstract In this paper, a dissipative Zakharov equations are discretized by difference method.We make priorestimates for the algebric system of equations. It is proved that for each mesh size,there exist attractors forthe discretized system.The bounds of the Hausdorff dimensions of the discrete attractors are obtained,and thevarious bounds are dependent of the mesh sizes.     

The mapping properties of the radiosity operator along an edge

In this article we study the radiosity operator along an edge between two adjacent half‐planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half‐planes, the reflectivity coefficients and the right‐hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22 : 217–241). Copyright © 2002 John Wiley & Sons, Ltd.     

Global Phase Time and Wave Function for the Kantowski-Sachs Anisotropic Universe

A consistent quantization with a clear notion of time and evolution is given for the anisotropic Kantowski–Sachs cosmological model. It is shown that a suitable coordinate choice allows to obtain a solution of the Wheeler–DeWitt equation in the form of definite energy states, and that the results can be associated to two disjoint equivalent theories, one for each sheet of the constraint surface.     

曲面平滑的自适应几何扩散

1.引 言 本文的目的是用求解偏微分方程（PDE）的方法来消除离散三角形曲面的噪声,所使用的方程是热传导方程到曲面的推广.热传导方程应用于图像处理已有二十余年的历史,有关参考文献相当丰富（见[1,11,12,19]）.众所周知,对于给定的初始图像ρ0,热传导方程　　在τ时刻的解与用Gauss滤波器Gσ（x）=　（当标准差σ=2τ,时）和ρ0作卷积的结果相同.容易看出Gρ和ρ0的卷积运算相当于对ρ0做加权平均,当标准离差σ变大时,该加权平均在一个较大的范围实现,这解释了热传导方程的滤波作用.近来热传导方程已推广到空间曲面[4,5]以及高维空间中的二维流形（见[3]）,对