分形Sierpinski Gasket上单点介质作用下的超过程

本文考虑分形ＳｉｅｒｐｉｎｓｋｉＧａｓｋｅｔ上的分枝粒子系统，当其受单点介质作用而导出了一类超过程．在理论上对过程的存在性给出了证明，同时研究了这类超过程作为随机测度值过程的轨道特征即证明了其轨道的连续性和联合连续的密度场的存在性．     

具有较一般分支特征的超布朗运动轨道性质

本文研究具有较一般分支特征的超布朗运动｛Ｘ（ｔ）｝ｔ０的轨道性质．首先给出了它的一个击中概率的表达式，其次找到了它的支集蔓延速度的估计式及证明了支撑过程的右连续性，从而验证了Ｄａｗｓｏｎ，Ｄ．Ａ．等人的猜想     

对偶条件下随机过程轨道的连续性

本文在强对偶条件下讨论transientHunt过程轨道的连续性，给出了轨道连续的充要条件为：过程末离任一相对紧开集的位置集中在其边界上．并讨论了轨道逆转的一些性质．     

局部凸代数L(E)的乘法连续性

本文讨论了(E,σ(E,E′))上连续自同态代数L(E)上在几种常见拓扑下的乘法连续性,得到相应的等价条件．     

非线性退缩抛物型方程弱解的梯度的Holder连续性

本文我们讨论如下的非线性退缩抛物型方程：设为上述方程的弱解．在一些结构性条件下，我们得到△ｕ的Ｈ　ｌｄｅｒ连续性．     

带误差项的下降算法的收敛性

本文考虑了Solodov和Svaiter提出的带误差项的下降算法的收敛性．其重要特征是在收敛性的证明过程中没有应用梯度函数的Hlder连续性．因此,我们在较弱的条件下得到了该算法的收敛性结果．     

带迁入超过程的轨道连续性

本文利用鞅测度的方法研究了一类带迁入超过程的轨道连续性问题。给出了这类测度值过程弱连续的一个充要条件，以及在τ－拓扑下连续的充分条件．     

一个椭圆特征问题解对参数的连续性

用变分方法证明了一个限制在球面上的椭圆特征问题解对参数（球面半径）的连续性，从而得到相应的不带限制的椭圆特征问题的解分枝。     

Kolmogorov定理的一个变形

本文研究了随机过程轨道连续性的Kolmogorov定理.通过将两点间的距离用矩形上的增量代替,得到了Kolmogorov定理在高维空间的一种推广.     

全局线性化及同胚函数的■连续性

本文证明了微分方程全局线性化中的同胚函数及其逆同胚函数都具有连续性，同时给出了具体的估计式．     

具有离散性的连续性模型映射

为了实现在连续性空间中的离散分段问题,采用解决离散性问题的方法虚拟构造连续性集合,将连续性问题映射为分段的离散问题,根据集合中元素的离散特性实现连续性模型的分段求解.通过数据结构的设计与压缩路径的算法证实,模型的映射能够解决实际问题的分段求解.     

Nonlocal Branching Superprocesses and Some Related Models

A new formulation of nonlocal branching superprocesses is given from which we derive as special cases the rebirth, the multitype, the mass-structured, the multilevel and the age-reproduction-structured superprocesses and the superprocess-controlled immigration process. This unified treatment simplifies considerably the proof of existence of the old classes of superprocesses and also gives rise to some new ones.     

The Boundary Regularity of Pseudo-holomorphic Disks

In this paper we will prove the continuity, the C^k-regularity after deforming suitably the domain, and the Hölder continuity, of the weakly pseudo-holomorphic disk with its boundary in a singular totally-real subvariety with only corners as its singularites.     

集值映射的伪(*)连续与弱(*)连续性

本文引入了集值映射的伪（＊）连续性与弱（＊）连续性概念的定义,研究了伪（＊）连续、（＊）连续及弱（＊）连续的等价关系,最后研究了乘积空间中的集值映射成为伪（＊）连续和弱（＊）连续的充要条件。     

Superprocesses arising from interactive stochastic flows

In this paper, we give a unified construction for superprocesses with dependent spatial motion constructed by Dawson, Li, Wang and superprocesses of stochastic flows constructed by Ma and Xiang. Furthermore, we also give some examples and rescaled limits of the new class of superprocesses.     

On States of Total Weighted Occupation Times of a Class of Infinitely Divisible Superprocesses on a Bounded Domain

In this paper, general conditions of state classification for the total weighted occupation times of a class of infinitely divisible superprocesses on a bounded domain D in ℝ ^d are given. As an application, some sufficient and necessary conditions are found for the total weighted occupation times of some special superprocesses on D to be absolutely continuous or singular with respect to the Lebesgue measure on D. The research of Yan-Xia Ren is supported by NNSF of China (Grant No. 10471003) and Foundation for Authors Awarded Excellent Ph.D. Dissertation.     

Parabolic Q-minima and Their Application

In this paper, the notion named parabolic Q-minima is endowed with rich meanings and its local behavior is investigated. As its direct application we obtain the local regularity, such as boundcdncss, continuity, llolder continuity of the weak solutions of the various filtration equations, e.g., the equation of Newtonian polytropic filtration, the general equation of Newtonian filtration, the equation of elastic filtration, the equation of non-Newtonian polytropic filtration. Therefore, a unifying approach to various regularity results for a great number of nonlinear degenerate parabolic equations is provided.     

随机流的超过程的状态分解

In this paper, we reconstruct the superprocesses of stochastic flows by martingale method, and prove that if and only if the infinitesimal particles never hit each other, then atomic part and diffuse part of this kind of superprocesses will be also superprocesses of stochastic flows. This result completely answers the open problem in [1].     

单子理论对拓扑等度连续与均匀连续的刻画及其应用

在扩大模型下,应用单子理论给出了拓扑等度连续和均匀连续的非标准刻画,并应用均匀连续的非标准特征证明了网收敛与均匀连续之间的关系,最后应用拓扑等度连续和均匀连续的非标准特征证明了拓扑等度连续和均匀连续之间的关系.     

Law of large numbers for supercritical superprocesses with non-local branching

In this paper we establish a weak and a strong law of large numbers for supercritical superprocesses with general non-local branching mechanisms. Our results complement earlier results obtained for superprocesses with only local branching. Several interesting examples are developed, including multitype continuous-state branching processes, multitype superdiffusions and superprocesses with discontinuous spatial motions and non-decomposable branching mechanisms.