三维调和问题的自然积分方程及其数值解

1．引言许多椭圆型偏微分方程边值问题可以通过不同途径归化为边界积分方程，由此发展出各种边界元方法．由我国学者冯康和余德浩首创并发展的自然边界元方法便是其中之一山．这一方法与经典边界元法相比有其独特的优点，它有着较高的数值稳定性，能与传统的有限元方法基于同一变分原理自然而直接地耦合［2］．近年来，无界区域问题倍受关注［2－71，其中，基于自然边界归化的耦合算法及区域分解算法是处理无界区域问题的一种有效手段．但是，迄今为止关于自然边界归化的研究仅仅局限于二维问题．而三维问题显然更需要发展相应方法且其结果…     

球型平移网络逼近周期函数

研究了球型平移网络对周期函数的逼近问题．文章首先将基函数eimx分别表示成为两种球型平移网络．进一步,将有关多重Fourier级数的Bochner-Riesz平均表示成为球型平移网络的形式．在此基础上构造出了两类球型平移网络序列,并借助于有关Bochner-Riesz平均对Lp空间中函数的逼近结果给出了这两类球型平移网络序列在Lp空间中的逼近阶．     

Isolated complex singularities and their CR links

In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information from its link. We also give some open problems to be further pursued. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

间接驱动的冲击波特性实验

报道在星光激光器上进行的X光辐射驱动(间接驱动)和激光直接驱动的冲击波实验。实验观察到了铝背冲击波发光信息。结果表明,间接驱动比直接驱动的冲击波平面性好。     

On Calculating a Translational Flow Through a System of Circular or Spherical Layers with Different Permeabilities

The problem of finding the potential of a translational flow through a system of circular or spherical layers in a porous medium obeying Darcy's law is considered. The permeability coefficients change stepwise across the interface. The method is based on deriving special recurrence relations which give a rational dependence of the potentials on the permeability coefficients suitable for specific calculations.     

腔靶转换区辐射温度测量及定标关系

对近年来的激光腔靶实验的辐射温度作了综合分析和研究。对多种不同类型的柱型腔靶,在波长1.06μm的各种激光条件(不同的能量和脉宽)下,测量了腔靶转换区的辐射温度,并研究了辐射温度作为入腔激光能量、脉宽及腔靶转换区内表面积函数的定标关系。     

Visible surgery, four-dimensionals-cobordisms and related questions in geometric topology

The visible surgery theory of M. Weiss is used to complete the topological classification of four-dimensionals-cobordisms between three-dimensional spherical spaceforms. Applications to various questions concerning pseudo-isotopies of 3-manifolds, computations of the simple Wall groups of finite periodic groups, and inductive detection of self-homeomorphisms of manifolds are also discussed.The first named author was partially supported by a grant from the Louisiana Board of Regents and National Science Foundation Grants DMS 89-01583 and 91-01575, and the second named author was partially supported by National Science Foundation Grants DMS 86-02543, 89-02622 and 91-02711.     

Finite-size scaling for the mean spherical model with inverse power law interaction

A new analytical technique based on integral transformations with Mittag-Leffler-type kernels is used to derive the finite-size scaling function for the free energy per particle of the mean spherical model with inverse power law asymptotics of the interaction potential. The asymptotic formation of the singularities in the specific heat and magnetic susceptibility at the bulk critical point is studied.     

Slow motions of a solid spherical particle close to a viscous interface

In order to investigate the hydrodynamic interaction between an interface and a spherical particle and its dependence on the type of interface, it is essential to compute the drag and torque exerted on the sphere in the vicinity of the interface. In this paper, the problem of all slow elementary motions (relative translation and rotation) and stationary movement of a spherical particle next to a solid, viscous or free interface is considered. For low capillary numbers and different values of surface dilatational and shear viscosities in a curvilinear co-ordinate system of revolution with bicylindrical co-ordinates in meridian planes, the problem reduces from three to two dimensions. The model equations and boundary conditions, which contain second-order derivatives of the velocities, transform to an equivalent well-defined system of second-order partial differential equations which is solved numerically for medium and small values of the dimensionless distance to the interface. Very good agreement with the asymptotic equation for a translating sphere close to a solid interface could be achieved. The numerical results reveal in all cases the strong influence of the surface viscosity on the motion of the solid sphere. For small distances from the interface, the drag and torque coefficients change significantly depending on the surface viscosity.