带形区域上SLE壳的性质

利用带形区域上SLE的性质与Schwarz反射原理,讨论了带形区域上SLE壳的性质.给出了R-对称共形映射与带形区域内壳的关系;得到了带形区域内由一对不相交的壳组成集合与Loewner共形映射之间的关系;导出了R-对称共形映射的提升在带形区域的壳空间内以及带形区域的壳对空间上的相关映射是连续.这就将上半平面上SLE壳的有关性质推广到了带形区域的情形.     

非凸区域上的一些Hardy型不等式

研究非凸区域上的Hardy型不等式.通过选取特殊的向量值函数以及仔细的分析与计算,得到了各向异性Heisenberg群上一类非凸区域上的Hardy不等式,更进一步得到了非凸区域上与Greiner型向量场相关的几类Hardy型不等式.     

随机表示和次序约束下的混量与混料均匀设计

考虑 3种区域 :A型区域 ,V型区域和T型区域 ,其中A型区域同可靠性增长分析、次序约束的统计推断及保序回归理论紧密相联 ;V型区域同混量均匀设计相联 ;T型区域同混料均匀设计相联 .利用 [0 ,1 ]区间上的均匀分布、指数分布和Beta分布的次序统计量 ,对这 3种区域上的均匀分布获得了它们的随机表示 .用这些随机表示 ,可以产生相应区域上的数论网和均匀设计 .该方法称为次序统计量方法 .用两个关于可靠性增长分析和均匀设计的例子对这一方法作了说明 .     

无界区域R1上的吊桥方程的全局吸引子

本文研究了无界区域R^1上的吊桥方程，运用算子分解和带权空间上构造紧算子的方法，得到了该方程在无界区域R^1上存在全局吸引子．     

增长区域上Lengyel-Epstein系统的Turing不稳定性

建立了一般增长区域上的反应扩散模型,并给出了定义在一种特殊的一维增长区域上的Lengyel-Epstein系统发生Truing不稳定的条件,结论表明如果区域增长速度的散度为零,那么这种变化对系统的稳定性没有影响.     

Laplace方程有孔椭圆区域边值问题的解析解

本文利用相似流动替换方法 ,解决了中心有圆孔的椭园形区域上 Laplace方程第一类边值问题 ;采用分区域解法 ,给出了中心有椭园孔的椭园形区域上 Laplace方程第一类边值问题的解析通解 .这一结果在许多工程领域有重要应用 ,本文给出了油藏工程实例     

热传导方程的一类新型重叠型并行区域分解有限差分算法

0引言随着大规模科学工程计算的发展和计算精度要求的提高,区域分解和并行计算的发展越来越受到人们的重视.区域分解方法把复杂或大型的问题分解成若干重叠或非重叠子区域上的子问题,再在子区域上利用各种算法求解子问题.借助于区域分解,各子区域之间的计算可以并行,这引起了人们的研究兴趣和极大的应用前景.重叠型区域分解法的原始思想来源于Schwarz交替法.近年来建立在Schwarz交替法基础上的区域分解法在理论分析和实际应用中取得令人注目的发展,已成为一种有效的迭代方法.经典的Schwarz交替法本质上是串行的.随着并行计算的发展,出现了多种可完全并行化的Schwarz算法     

多边形区域上热传导方程的Legendre-Chebyshev谱元法

建立了多边形区域上热传导方程的Legendre-Chebyshev谱元法,通过把多边形区域剖分成一些互不相交的凸四边形子区域,在各个子区域上采用Legendre-Galerkin方法,右端项采用Chebyshev插值逼近,计算可并行实现,给出了方法的稳定性和收敛性分析.数值算例显示了方法的有效性.     

区域上Triebel-Lizorkin空间的原子分解与限制定理

本文在区域Ω( Rn,n≥1)上定义了某类在边界上消失的Triebel-Lizorkin空间 ,并给出了它的原子分解定理,对偶定理.同时证明了当区域 时,得到了限制和扩张定理     

无界区域R~1上的KDV型方程的指数吸引子

本文研究了无界区域R~1上的KDV型方程,运用带权空间构造一类紧算子和算子分解的方法,得到了该方程在无界区域R~1上拥有一个指数吸引子。     

L-Fuzzy Domain上的广义Scott拓扑

本文研究了L-fuzzy domain上的广义Scott拓扑,利用[1]中引入的L-fuzzy domain.获得了其上的广义Scott拓扑,它是Domain上Scott拓扑的推广,证明了一个L-fuzzy单调映射是L-fuzzy Scott连续映射当且仅当它关于L-fuzzy domain上的广义Scott拓扑连续.     

Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions

An essential part of any boundary value problem is the domain on which the problem is defined. The domain is often given by scanning or another digital image technique with limited resolution. This leads to significant uncertainty in the domain definition. The paper focuses on the impact of the uncertainty in the domain on the Neumann boundary value problem (NBVP). It studies a scalar NBVP defined on a sequence of domains. The sequence is supposed to converge in the set sense to a limit domain. Then the respective sequence of NBVP solutions is examined. First, it is shown that the classical variational formulation is not suitable for this type of problem as even a simple NBVP on a disk approximated by a pixel domain differs much from the solution on the original disk with smooth boundary. A new definition of the NBVP is introduced to avoid this difficulty by means of reformulated natural boundary conditions. Then the convergence of solutions of the NBVP is demonstrated. The uniqueness of the limit solution, however, depends on the stability property of the limit domain. Finally, estimates of the difference between two NBVP solutions on two different but close domains are given.

     

Dynamics of stochastic partly dissipative systems on time-varying domain

This article is devoted to stochastic partly dissipative systems (SPDS) defined on time-varying domain expending in time. The definition of a space–time trace class Wiener process on time-varying domain is presented by combining a time trace class Wiener process with a spatial intensity defined on time-varying domain. Some nice properties for Wiener process on time-varying domain are also presented. We develop a new penalty method to establish the existence and uniqueness of variational solution of SPDS with additive noise on time-varying domain. The existence of global attractor for the process generated by variational solution is also obtained.     

Hyperbolic metric,curvature of geodesics and hyperbolic discs in hyperbolic plane domains

The purpose of this paper is to investigate the relations among some geometric quantities defined for every hyperbolic plane domain of any connectivity, each of which measures, in some sense, how much the domain deviates either from a disc, convex domain, or simply connected domain on one hand, or a punctured domain on the other hand. Supported by the Landau Center for Mathematical Research in Analysis.     

An approximate solution of the MHD Falkner–Skan flow by Hermite functions pseudospectral method

Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner–Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. We also present the comparison of this work with numerical results and show that the present method is applicable.     

论域的模糊划分与仿真数据采集

给出一类MIMO模糊系统对紧集上连续函数的万能逼近定理的证明。在此证明基础上分析造成“规则灾难”的原因,提出基于覆盖重叠数的模糊划分方法和基于“线性”划分论域的方法,以及相应仿真数据的采集方法,对实际数据的处理提出不同的聚类处理方法。     

Classical solutions for the pressure-gradient equations in non-smooth and non-convex domains

We establish the existence of the classical solution for the pressure-gradient equation in a non-smooth and non-convex domain. The equation is elliptic inside the domain, becomes degenerate on the boundary, and is singular at the origin when the origin lies on the boundary. We show the solution is smooth inside the domain and continuous up to the boundary.     

一类Reinhardt陆启铿域

由陆启铿猜想在一类Reinhardt域上的解决,得到了一类Reinhardt陆启铿域,同时又给出了此域是非齐性域,从而得到一类非齐性的陆启铿域.     

Factorization in Integral Domains,IV

Let D be an integral domain such that every nonzero nonunit of D is a finite product of irreducible elements. In this article, we introduce and study several unifying concepts for the theory of nonunique factorization in D. They give a new way to measure, in some sense, how far an half-factorial domain (resp., bounded factorization domain, atomic domain) D is from being a UFD (resp., finite factorization domain, Cohen–Kaplansky domain) based on equivalence relations on the set of irreducible elements of D.