恒定电场边值问题中点源的处理

讨论了不同情况下恒定电场中点源函数的表达式;用两种方法对点源作不同的处理;通过一个实的求解验证和说明了本文的方法。     

导体表面电荷不均匀分布的数值计算

用积分法分析了被屏蔽导体表面的电荷分布,提出了一种具有特殊场域的求解电场 方法,为了求解在奇异点的积分,提出了一系列解析公式,可以避免复杂的数学处理,还分析了一个具体实例的临近效应,讨论了积分法的计算精度 。     

带Poisson跳随机微分方程终值与边值问题的适应解

Poisson跳的拟线性倒向随机微分方程x(t) ∫tf(s,x(s),,x(s)) y(s)]dMs =ξ,t∈[0,1],这里M = (W,Q)T,其中W为Wiener过程,Q为补偿Poisson过程.利用区间延拓和 Bihari 不等式证明了在某种弱于Lipschitz条件下方程存在唯一适应解,并给出了解的估计,从而将文章[1]的结论推广到带 Poission 跳的情形.另外,本文还讨论了以下形式的边值问题:dx(t) = f(t,x(t),y(t))dt y(t)dMt,Ax(0) Bx(1) =ξ*,t∈[0,1],并证明了在Lipschitz条件下适应解的存在唯一性.     

Transport Coefficients in Some Stochastic Models of the Revised Enskog Equation

A stochastic model of the revised Enskog equation is considered. A choice of the smearing function suggested by the work of Leegwater is used to apply the model to the repulsive part of the Lennard-Jones potential and the inverse-power soft-sphere potential. The virial coefficients obtained from the equilibrium properties of the models are in excellent agreement with the known exact coefficients for these models. The transport coefficients for the repulsive Lennard-Jones (RLP) model are also computed and appear to be of comparable accuracy to the Enskog-theory coefficients applied directly to a hard-sphere system, although exact results for the RLP with which to make an extensive comparison are not yet available. The pressure and the transport coefficients obtained from the model (shear viscosity, thermal conductivity, and self-diffusion) are compared with the pressure and the corresponding transport coefficients predicted by the Enskog and square-well kinetic theories.     

基于LAGRANGE插值的高阶微分中值定理

本文基于LAGRANGE插值，将微积分中非常重要的中值定理推广到了高阶的情形。     

A pair of stream functions for three-dimensional vortex flows

Introducing a vector potential, that is based on a pair of stream functions, and a velocity potential, antisymmetric equations for the stream functions are derived with the help of a variational principle. It is found that the equations are in a suitable form to investigate flows with helical symmetry, and, for example, to connect upstream axisymmetric flows with downstream helical flows. The special case of a transition from an upstream solid-body vortex to a downstream helical flow is investigated in detail. Furthermore, the stream-function equations are particularly useful to investigate general small-amplitude inertia waves on vortex flows. Time-dependent helical flows that are time-independent in a suitably rotating frame of reference can also be discussed with the proposed method.     

The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample

Generalizing recent work of P. C. Matthews and A. L. Rukhin (Ann. Appl. Probab.3(1993), 454–466), we obtain the limit law of the largest interpoint Euclidean distance for a spherically symmetric multivariate sample of the Kotz distribution. While going through the proof, some errors in the reasoning given by Matthews and Rukhin are pointed out and corrected.     

车灯配光性能在线检测系统研究

本文介绍一种能够对车灯光度、色度性能同时进行在线测试的计量仪器。它操作方便，精度较高，符合国标对车灯配光性能检测的要求。     

Approximating dominant singular triplets of large sparse matrices via modified moments

A procedure for determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modified moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel implementations on a network of workstations. Although no obvious relationship between modified moments and the corresponding eigenvectors is known to exist, a scheme to approximate both eigenvalues and eigenvectors (and subsequently singular values and singular vectors) has been produced. This scheme exploits both modified moments in conjunction with the Chebyshev semi-iterative method and deflation techniques to produce approximate eigenpairs of the equivalent sparse eigensystems. The performance of an ANSI-C implementation of this scheme on a network of UNIX workstations and a 256-processor Cray T3D is presented.This research was supported in part by the National Science Foundation under grant numbers NSF-ASC-92-03004 and NSF-ASC-94-11394.     

涉及微分多项式的亚纯函数的唯一性

设ｆ（ｚ）是非常数的整函数，ｎ是正整数，Ｆ（ｚ）＝ｆ￣（ｎ）（ｚ）＋ａ＿１（ｚ）ｆ￣（ｎ－１）（ｚ）＋…＋ａ＿ｎ（ｚ）ｆ（ｘ），其中ａ＿１（ｚ），ａ＿２（ｚ），…，ａ＿ｎ（ｚ）均是ｆ（ｚ）的小函数，本文证明了：若ｆ（ｚ）和Ｆ（ｚ）几乎ＣＭ分担两个不同的有穷复数ａ和ｂ，则ｆ（ｚ）≡Ｆ（ｚ）．