一类解析多面体的奇异积分

本文利用Ｒ．Ｈａｒｖｅｙ和Ｊ．Ｐｏｒｋｉｎｇ的方法首先定义广义式的Ｃａｕｃｈｙ主值，利用同伦公式，借助积分变换技巧研究Ｗｅｉｌ型积分的边界性质，得到Ｐｌｅｍｅｌｊ公式．它有别于通常研究边界性质的方法．本文引入细复广义权和Ｃｈｏｑｕｅｔ型复广义权的概念，讨论了某些与复广义权相关的函数的拟连续性与细拟处处连续的关系．     

复广义权与拟连续性

本文引入复广义权的外权的概念，讨论了某些与复广义权相关的函数的拟连续性。     

复广义权的拟拓扑和可权集

本文讨论了Hausdorff空间中Borel集、细Borel集和拟开集之间的关系;引入复广义可权集的概念并讨论其性质.     

复广义权

本文引入复广义权的概念，讨论了具有右连续性或可数次可加性的复广义权的某些性质。     

在Radon测度给定下的一类退化椭圆型方程

此文研究一类在Ｒａｄｏｎ测度给定下二阶退化拟线性椭圆型方程．通过引入逼近子问题列并求解、先验估计和收敛性研究，证明了该方程广义解在带权Ｓｏｂｏｌｅｖ空间的存在性．     

广义复椭球上(-e)-方程的Lp估计

给出了Cn上一类耦合型弱拟凸域--广义复椭球的全纯支撑函数及其估计.使用此估计,证明了(-e)-方程的最佳Lp估计,同时给出广义复椭球上函数论的一些结果.     

数学研究 2005年总第38卷第1~4期 2005年12月 总目次

关于可加保幂零映射的一点注记(英文)…………………………………侯晋川崔建莲(1)守恒方程的Chebychev-Legendre拟谱粘性方法(英文)……………………………陈跃辉(10)复广义权的拟拓扑和可权集(英文)………………………………………张纪平邱曙熙(19)含各阶导数的非线性弹性梁方程的一个存在定理(英文)…………………………姚庆六(24)关于图是(g,f,n)-临界图的充分条件(英文)……………………………严秀坤李建湘(29)黎曼积分的几个等价定义(英文)…………………………………………麦结华曾素行(35)广义Baby-TKK李代数的一类顶点表示…………     

广义度量S-KKM映射的性质及其对鞍点问题的应用

引入了S为集盥映射情况下的广义度量S-KKM映射和超S-γ-广义拟凸（凹）函数，建立了广义度量S-KKM映射原理和广义度量S-KKM映射与超S-γ-广义拟凸（凹）函数的关系．作为应用，获得了超凸度量空间中的新的Ky Fan极大极小不等式和鞍点定理．     

求解广义混合隐拟平衡问题的预测修正算法

引入和研究了一类新的具有四元函数的广义混合隐拟平衡问题．这类平衡问题包含了很多已知的广义平衡问题和广义混合隐拟变分不等式问题作为很特殊的情形．利用辅助原理技巧建议和分析了求解广义混合隐拟平衡问题的预测修正迭代算法．所建议算法的收敛性仅需要映象的连续性和部分松弛强单调性．     

广义复椭球上∂-方程的Lp估计 *

给出了Cⁿ 上一类耦合型弱拟凸域———广义复椭球的全纯支撑函数及其估计 .使用此估计 ,证明了 方程的最佳L^p 估计 ,同时给出广义复椭球上函数论的一些结果 .     

带参数的C~3连续拟Catmull-Rom样条函数

为了使得Catmull-Rom型样条兼具形状可调性与高阶连续性,提出了一类带参数的拟CatmullRom样条函数.该样条函数不仅无需求解方程系统即可自动达到C~3连续,而且还可通过所带的2个参数对插值曲线的形状进行调整·通过确定所带参数的最优取值,可获得最佳拟Catmull-Rom样条插值函数.     

Fuzzy quasi C*-algebra

At the present paper, the new concepts of fuzzy quasi norm, fuzzy Banach space, fuzzy quasi continuity and fuzzy quasi boundedness is introduced. Furthermore, we define the fuzzy quasi operator norm and also it is shown that the set all of fuzzy quasi bounded operator from X to Y is fuzzy quasi Banach space. Finally, we have introduced and investigated some notions and some results on *-algebra theory.     

Brown运动增量拟必然局部Strassen重对数律

该文建立了Brown运动增量的拟必然局部Strassen重对数律.利用这一结果,得到了Brown运动拟必然泛函连续模.     

Compactification of the discrete state space of a Markov process

Summary The countable state space of a Markov chain whose stationary transition probabilities satisfy the continuity condition (1.5) is compactifled to get a state space on which the corresponding processes can be made right continuous with left limits, and strongly Markovian. There is a form of quasi left continuity, modified by the possible presence of branch points. Excessive functions are investigated.     

On the (in)stability of quasi‐static paths of smooth systems: definitions and sufficient conditions

A concept of stability of quasi‐static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi‐static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi‐static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi‐static paths of smooth systems are proved. Copyright © 2005 John Wiley & Sons, Ltd.     

Scattered data quasi‐interpolation on spheres

This paper studies the construction and approximation of quasi‐interpolation for spherical scattered data. First of all, a kind of quasi‐interpolation operator with Gaussian kernel is constructed to approximate the spherical function, and two Jackson type theorems are established. Second, the classical Shepard operator is extended from Euclidean space to the unit sphere, and the error of approximation by the spherical Shepard operator is estimated. Finally, the compact supported kernel is used to construct quasi‐interpolation operator for fitting spherical scattered data, where the spherical modulus of continuity and separation distance of scattered sampling points are employed as the measurements of approximation error. Copyright © 2014 John Wiley & Sons, Ltd.     

Absolute continuity and Radon-Nikodym type theorems for weights and traces on von Neumann algebras

A definition of absolute continuity for weights is introduced and Radon-Nikodym type results for weights and traces are proved which generalize Radon-Nikodym type theorems of R. Pallu de la Barrière and S. Sakai.     

Finely locally injective finely harmonic morphisms

We consider fine topology in the complex plane C and finely harmonic morphisms. We use oriented Jordan curves in the plane to prove that for a finely locally injective finely harmonic morphism f in a fine domain in C, either f or f is a finely holomorphic function. This partially extends result by Fuglede, who considered a kind of continuity for the fine derivatives of the finely harmonic morphism. As a consequence of this we obtain a both necessary and sufficient condition for a function f to be finely holomorphic or finely antiholomorphic. We do not know if the condition of finely local injectivity (q.e.) is automatically fulfilled by any non-constant finely harmonic morphism.