关于随机勒襄特级数的一些性质

本文研究随机勒襄特级数的 a.s.收敛性,a.s.增长性,自然边界及随机勒襄特-高斯级数在收敛椭圆附近的本性发散性质.     

简化原理在Hilbert空间与可分Banach空间的一些应用

本文研究了简化原理在Hilbert空间与可分Banach空间中的一些应用,利用简化原理和独立随机元收敛准则获得了中分Banach空间随机级数的收缩原理和B-值随机Dirichlet级数简单收敛横坐标及一般随机整函数的增长性和值分布,将许多以Rademacher序列为系数的随机Tayor级数和随机Dirichlet级数的相关结果,推广到一般的具有独立对称分布系数的随机级数上去。     

缺项及随机Legendre级数的边界性质

本文沿用「１」中的方法及Ｌｅｇｅｎｄｒｅ多项式的性质，证明了一类缺项Ｌｅｇｅｎｄｒｅ级数在其收敛椭圆上任意一段弧的像都是不可求长曲线，从而可知它的收敛椭圆为其自然边界，并证明了一类随机Ｌｅｇｅｎｄｒｅ级数几乎必然具有上述性质。     

指数型随机三角级数的一些性质

Paley,Zygmund和Kahane等人研究过系数是Gauss随机变量序列,Steinhaus序列、Rademacher序列或更一般的独立对称随机变量的随机三角级数的a.s.收敛性、可积性、连续性.Kahane还给出了次Gauss随机三角级数a.s.表示的连续函数的连续模及轨道性质。但至今,对于系数是其它独立对称随机变量的三角级数还没有一般的结果,本文研究系数是指数型随机变量的随机三角级数的连续模、象集和水平集的性质。     

交错级数敛散性判别法

给出了交错级数的一个判别法,应用此判别法可直接判别交错级数是否收敛,以及收敛时是绝对收敛还是条件收敛.     

交错级数收敛性的几个结果及其应用

莱布尼兹判别法只是一个充分条件。有大量交错级数虽然不满足其条件,但却是收敛的．对于无法用莱布尼兹判别法判定的三类交错级数,利用常数项级数收敛的定义及相关结果,可以证明在一定条件下它们都是收敛的．并通过实例说明所得结果的应用价值．     

交错级数敛散性的微分形式判别法

给出交错级数敛散性微分形式的判别法,应用此判别法可直接判别交错级数是否收敛,以及收敛时是绝对收敛还是条件收敛.     

随机狄里克莱级数的一些性质

本文研究随机狄里克莱级数的a.s.(几乎必然)收敛性和在a.s.收敛半平面内的a.s.增长性;为此,还研究了狄里克莱级数在收敛半平面内的增长性.这里推进了Valiron G.和Arnold L.的有关结果.文中还证明了在一定条件下,两类随机狄里克莱级数a.s.以其收敛轴上每一点为其Picard点或Borel(R)点.     

基于p-级数的交错级数敛散性判别法

选择p-级数作为参照级数,由比较判别法可得关于交错级数敛散性判别的一种新方法.新方法可直接判别交错级数的敛散性,并在收敛时,给出级数是条件收敛还是绝对收敛.实例说明其应用.     

关于调和级数的一些探讨

通过对调和级数的探讨．发现调和级数中分母含9的所有项构成的级数发散,从而解决了有人关于调和级数既发散又收敛的疑问．此外还对调和级数去掉分母含某类数字的项后所得级数收敛这个奇妙特性给出注释．     

An approach to solving axially symmetric problems for spherical orthotropic bodies

A series expansion method is developed in which the small parameter is the deviation of the spherically orthotropic properties of deformable bodies from their transversally isotropic properties. The problem is reduced to a rigorous analytic solution of inhomogeneous boundary value problems. The efficiency of the approximation technique developed here and its practical convergence are examined in a centrally symmetric problem for an orthotropic sphere which permits an exact analytic solution. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 17–24, 1999.     

Liouville property for groups and manifolds

We introduce a method to estimate the entropy of random walks on groups. We apply this method to exhibit the existence of compact manifolds with amenable fundamental groups such that the universal cover is not Liouville. We also use the criterion to prove that a finitely generated solvable group admits a symmetric measure with non-trivial Poisson boundary if and only if this group is not virtually nilpotent. This, in particular, shows that any polycyclic group admits a symmetric measure such that its boundary does not readily interprete in terms of the ambient Lie group. As another application we get a series of examples of amenable groups such that any finite entropy non-degenerate measure on them has non-trivial Poisson boundary. Since the groups in question are amenable, they do admit measures such that the corresponding random walks have trivial boundary; the above shows that such measures on these groups have infinite entropy. Mathematics Subject Classification (1991) 60B15, 60J50, 28D20, 20P05, 43A07, 60J65, 43A85, 20f16     

关于任意边界缺口或裂纹群问题的一类解法(Ⅰ)解析方法

在工程断裂分析中任意边界缺陷如缺口或裂纹群是常见和重要的情况.本文推广穆斯赫利施维利方法作出了任意二维边界缺口或裂纹群问题的一类解法,通过相继应用解析延拓、劳朗级数展开和共形映照.我们最终获得支配问题的一组线性代数方程,然后应用标准的线代数方程组求解程序对问题就作出了解答.值得注意的是.本文方法可用于作出缺陷表面具有任意的光滑载荷分布情况的解答.     

一般随机富里叶级数

人们通常是在随机系数对称条件下，研究随机富里叶级数的，例文南[1]。本文不要对称性假设，研究一般随机富里叶级数一些性质，并得到一些重要成果。     

An analytic series method for Laplacian problems with mixed boundary conditions

Mixed boundary value problems are characterised by a combination of Dirichlet and Neumann conditions along at least one boundary. Historically, only a very small subset of these problems could be solved using analytic series methods (“analytic” is taken here to mean a series whose terms are analytic in the complex plane). In the past, series solutions were obtained by using an appropriate choice of axes, or a co-ordinate transformation to suitable axes where the boundaries are parallel to the abscissa and the boundary conditions are separated into pure Dirichlet or Neumann form. In this paper, I will consider the more general problem where the mixed boundary conditions cannot be resolved by a co-ordinate transformation. That is, a Dirichlet condition applies on part of the boundary and a Neumann condition applies along the remaining section. I will present a general method for obtaining analytic series solutions for the classic problem where the boundary is parallel to the abscissa. In addition, I will extend this technique to the general mixed boundary value problem, defined on an arbitrary boundary, where the boundary is not parallel to the abscissa. I will demonstrate the efficacy of the method on a well known seepage problem.     

ANALYTIC BOUNDARY VALUE PROBLEMS ON CLASSICAL DOMAINS

In this paper analytic boundary value problems for some classical domains in Cn are developed by using the harmonic analysis due to L.K. Hua. First it is discussed for the version of one variable in order to induce the relation between the analytic boundary value problem and the decomposition of function spaceL2 on the boundary manifold. Then an easy example of several variables, the version of torus in C2, is stated. For the noncommutative classical groupLI, the characteristic boundary of a kind of bounded symmetric domain in C4, the boundary behaviors of the Cauchy integral are obtained by using both the harmonic expansion and polar coordinate transformation. At last we obtain the conditions of solvability of Schwarz problem onLI, if so, the solution is given explicitly.     

一类亚解析函数的复合边值问题

本文研究了一类亚解析函数的复合边值问题.利用经典的消去法和对称扩张,得到了边值问题的可解条件和解的表达式.推广了解析函数的相应理论.     

Hypergeometric Functions of Second Kind and Spherical Functions on an Ordered Symmetric Space

We define new solutions of the hypergeometric system that are invariant with respect to a parabolic Weyl subgroup. They generalize the spherical functions of an ordered symmetric space. We study their properties with respect to monodromy, their analytic extensions and their boundary value on the imaginary axis.     

再生核空间偏微分方程解析数值解

１．引言 偏微分方程的近似解法一直是数值计算的重要内容之一。随着计算机的发展,各种实用的新方法也不断涌现．本文在再生核空间Ｈ　（Ｄ）中给出二阶偏微分方程边值问题解析形式的级数解,该级数解具有如下特点：１．级数截断就可直接得到解析数值解;２．解析数值解的误差在空间范数意义下单调下降． 设 Ｄ＝［ａ, ｂ］ ｘ ［ｃ, ｄ］是 Ｒ２中的任一矩形域, Г为边界,０,ｕ（ｘ,ｙ）∈Ｌ２（Ｄ）且是实的绝对连续函数,中规定内积如下： 范数定义为： 山中已证明码（利是一个再生核函数空间,其再生校函数研Ｘ,认（,…表达式…