The Richardson scheme for the singularly perturbed parabolic reaction-diffusion equation in the case of a discontinuous initial condition

The Dirichlet problem for a singularly perturbed parabolic reaction-diffusion equation with a piecewise continuous initial condition in a rectangular domain is considered. The higher order derivative in the equation is multiplied by a parameter ?², where ? ∈ (0, 1]. When ? is small, a boundary and an interior layer (with the characteristic width ?) appear, respectively, in a neighborhood of the lateral part of the boundary and in a neighborhood of the characteristic of the reduced equation passing through the discontinuity point of the initial function; for fixed ?, these layers have limited smoothness. Using the method of additive splitting of singularities (induced by the discontinuities of the initial function and its low-order derivatives) and the condensing grid method (piecewise uniform grids that condense in a neighborhood of the boundary layers), a finite difference scheme is constructed that converges ?-uniformly at a rate of O(N ^?2ln² N + n ₀ ^?1 ), where N + 1 and N ₀ + 1 are the numbers of the mesh points in x and t, respectively. Based on the Richardson technique, a scheme that converges ?-uniformly at a rate of O(N ^?3 + N ₀ ^?2 ) is constructed. It is proved that the Richardson technique cannot construct a scheme that converges in ?-uniformly in x with an order greater than three.     

Stampacchia 广义向量拟均衡问题II

通过引进锥对角拟凸概念, 讨论了Stampacchia 广义向量拟均衡问题解的存在性.由于该问题包含了许多形式的变分不等式与均衡问题作为特例,所得解的存在性结果推广和发展了近期的一些研究结果,主要有以下两个方面: 1)放宽了对连续性的要求; 2)由数值型推广到了向量型.     

常见连续型统计分布的一点注记

正态分布是概率论与数理统计中最重要的一个分布,本文讨论了常见的连续型统计分布与标准正态分布间的关系,结果表明:几乎所有的常见连续型统计分布都是标准正态分布的函数.     

Possible Spectrums of 3×3 Upper Triangular Operator Matrices

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,E,F) a 3×3 upper triangular operator matrix acting on H1⊕H2⊕H3 of the form M(D,E,F)=(A D E 0 B F 0 0 C). For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets UD,E,F σp(M(D,E,F)), ∪D,E,F σr(M(D,E,F)), ∪D,E,F σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈ B(H3, H1), F ∈ B(H3, H2) and σ(·), σp(·), σr(·),σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

(D)族负象限相依随机变量和的精致大偏差

在负象限相依结构下,得到了支撵在(-∞,∞)上的(D)族随机变量非中心化以及中心化部分和的精致大偏差.同时,还在较弱的条件下,得到了相应的中心化随机和的精致大偏差.     

无穷维Hamilton算子的二次数值域

研究了一类无界无穷维Hamilton算子的二次数值域的性质,进而,应用二次数值域来刻画了无穷维Hamilton算子谱的分布范围,并给出了二次数值域的闭包包含谱集的结论.     

一类连续变量脉冲中立型差分方程

研究具连续变量脉冲中立型时滞差分方程△[y(t)-p(t)y(t-τ)]+q(t)y(t-σ)=0,t≠tky(tk+)-y(tk)=bky(tk),k=1,2,…利用辅助方程,建立等价定理,得到了方程解振动的显式充分性条件.     

正交饱和效应模型及其统计分析

文\cite{14}讨论了2水平正交饱和设计的一种统计分析方法---零效应搜索法, 本文将此方法推广到一般的饱和模型---正交饱和效应模型. 首先给出正交饱和效应模型的定义及其相关的参数估计和平方和分解, 然后用零效应搜索法对显著效应的检验问题进行分析, 模拟结果显示效果很好.     

组织性别构成多样性对员工组织承诺影响的实证分析

本文采用组织承诺的三维度概念模型探讨组织性别多样性对组织承诺的影响,研究认为员工工作级别中的性别多样性对其组织承诺(情感承诺、连续承诺)有显著的负影响,而上一级性别多样性只对其情感承诺有显著的正影响,并对此结果进行了深入讨论。     

关于弱压缩算子的变分不等式解的粘滞逼近算法

在严格凸且具有一致Gâteaux可微范数的Banach空间$E$框架内, 该文借助于两种粘滞逼近算法去近似逼近关于弱压缩算子的变分不等式解并且也获得了相应的收敛率估计.