On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

On the Bavrin Integro-Differential Operators and Their Applications to Solution of Functional Equations

We construct a multiplicative group structure in the class of integro-differential operators specific for a polydisk which was introduced by I. I. Bavrin. We indicate two applications of these operators to solution of functional equations.     

拟次酉阵与拟次Hermite阵

提出了拟次酉阵、拟(反)次Hermite阵概念，研究了它们的性质及其相互间的关系，将正交矩阵广义Gayley分解推广到拟次酉阵上。     

On the Differential Properties of Temlyakov-Type and Temlyakov-Bavrin-Type Integrals

We establish a formula that expresses the value of the density of the Temlyakov-type integral with defining domain of type A in terms of the integral itself by means of a differential operator. We extend this operator connection to the Temlyakov–Bavrin-type integral of order k. Our study bases on the method of linear differential operators with variable coefficients which is developed by A. V. Nelaev.     

Representability of Analytic Functions in Terms of Their Boundary Values

Suppose that is an arbitrary finite complex Borel measure on the interval is its Poisson integral, and are the conjugate harmonics of , and is the nontangential limiting value of the analytic function as . In this paper, we consider the problem of representing the analytic function in terms of its boundary values .     

Zeroes of complete polynomial vector fields

We prove that a complete polynomial vector field on has at most one zero, and analyze the possible cases of those with exactly one which is not of Poincaré-Dulac type. We also obtain the possible nonzero first jet singularities of the foliation at infinity and the nongenericity of completeness. Connections with the Jacobian Conjecture are established.

     

烃类烟粒红外复折射率的测定与应用

测定了室温下烃类(乙炔、乙烷)烟粒的红外复折射率,并讨论了所获数据在测量烟浓度与烟粒大小分类、计算光谱吸收系数及在特定浓度与温度下评估烟雾辐射率方面的应用。     

AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX

In this paper, we first introduce a concept of companion vector, and study the Jordan canonical forms of quaternion matrices by using the methods of complex rep resentation and companion vector, not only give out a practical algorithm for Jordan canonical form J of a quaternion matrix A, but also provide a practical algorithm for corresponding nonsingular matrix P with P-1AP = J.     

复调和函数及其在无穷远点的性质

本文讨论了复调和函数在无穷远点的性质,揭示出有界区域上复调和函数的两类表示式之间的关系.