非线性守恒律高阶谱粘性法的收敛性

讨论守恒型方程周期边界问题的高阶谱粘性方法逼近解的收敛性.在逼近解一致有界的假设下,通过建立其高阶导数的上界估计,证明了高阶谱粘性方法逼近解具有同二阶谱粘性方法逼近解相类似的高频衰减性质.以此为基础,用补偿列紧法证明了高阶谱粘性方法逼近解收敛于守恒型方程的物理解.     

二维N－S方程的Fourier非线性Galerkin方法

本文对周期边界条件Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，证明了其Ｆｏｕｒｉｅｒ非线性Ｇａｌｅｒｋｉｎ逼近解的存在唯一性，同时给出了逼近解的误差估计．     

一类流固耦合系统强解的存在性问题

本文主要讨论一类多刚体与粘性系数依赖于密度的不可压缩流体耦合系统的强解存在性问题.首先,利用变量替换建立本文研究对象对应的非线性微分方程,然后,利用Garlerkin逼近方法获得线性化问题的光滑解,从而可以构造出原问题的逼近解.通过估计逼近解的一致有界性,最后证明了一类描述多刚体在不可压缩流体中运动的耦合系统强解的存在...     

带变系数的第二类奇异积分方程的Galerkin解法

基于对未知函数用适当的正交多项式进行逼近，本文讨论了带变系数的第二类奇异积分方程的Galerkin解法，证明了逼近解的存在唯一性，给出了逼近解在带权L^2模和一致模下的误差估计．     

Banach空间中含间断项Sturm—Liouville问题的解

利用拟上下解方法和混合单调迭代法,研究了Banach空间中含间断项的非线性Sturm-liouville问题解的存在唯一性,并给出逼近解迭代序列的误差估计．     

Banach空间微分方程初值问题

利用半序理论及单调迭代方法研究了Banach空间中非线性微分方程初值问题解的存在惟一性以及解的迭代逼近与误差估计。     

带Hilbert核奇异积分方程的Galerkin方法

该文讨论了以下形式的奇异积分方程其中ａ（ｘ），ｂ（ｘ），ｆ（ｘ），（ｘ）∈Ｈ（２π），ｋ（ｘ，ｔ）关于ｘ，ｔ也∈Ｈ（２π）的数值解法．在Ｌ２模下，得出了逼近解的存在性和收敛性；当ｆ（Ｘ），ｋ（ｘ，ｔ）∈Ｈμ２π，μ＞时，逼近解在最大模下一致收敛到精确解；当ｆ（ｐ）（Ｘ），ｋ（ｘ，ｔ）∈Ｈμ２π时，逼近解对精确解的逼近阶．     

带Poisson跳和Markovian调制的中立型随机延迟微分方程的数值解的收敛性

本文研究带Poisson跳和Markovian调制的中立型随机微分方程的数值解的收敛性质.用数值逼近方法求此微分方程的解,并证明了Euler近似解在此线性增长条件和全局Lipschitz条件更弱的条件下仍均方收敛于此方程的解析解.     

反对称偏对称矩阵反问题的最小二乘解

该文研究了反对称偏对称矩阵反问题的最小二乘解,得到了该问题解的表达式以及该问题有解的充分必要条件.证明了其最佳逼近解的存在性和唯一性,建立了其最佳逼近解的表达式,并给出了求最佳逼近解的数值算法和算例.     

二阶积分微分方程的广义拟线性化方法

运用广义拟线性化方法研究了正规锥上的二阶积分微分方程初值问题,获得了逼近解序列一致且平方收敛的结果.     

Fractal properties of number systems

In this paper we study properties of the fundamental domain F of number systems in the n-dimensional real vector space. In particular we investigate the fractal structure of its boundary F. In a first step we give upper and lower bounds for its box counting dimension. Under certain circumstances these bounds are identical and we get an exact value for the box counting dimension. Under additional assumptions we prove that the Hausdorf dimension of F is equal to its box counting dimension. Moreover, we show that the Hausdorf measure is positive and fnite. This is done by applying the theory of graphdirected self similar sets due to Falconer and Bandt. Finally, we discuss the connection to canonical number systems in number felds, and give some numerical examples.     

Weak Differentiability with Applications to Variational Analysis

In this paper we first review the theory of weak differentiability with some improvements and unifications of existing results; then we introduce an extended variant of this notion and establish its basic properties; finally we use the weak differentiability and its variant to develop new calculus results in variational analysis for the theory of generalized differentiation and the sequential normal compactness. In this way we demonstrate that the weak differentiability and its variant, in contrast to the usual differentiability, are in fact more suitable for Fréchet and limiting/Mordukhovich constructions in variational analysis.     

Periodic Solutions for Second Order Differential Inclusions with Nonconvex and Unbounded Multifunction

In this paper we consider a second order multivalued periodic boundary value problem with a nonconvex and unbounded orientor field (set-valued vector field). Using a directionally continuous selector, through its Filippov regularization we produce a convex-valued, bounded multifunction and with this as orientor field we introduce a new multivalued periodic problem. Using the Leray-Schauder principle, we solve the convex problem and then we show that its solutions also solve the original nonconvex problem.     

布朗运动的最大值和阶梯期权

在奇异期权定价中经常遇到的具有漂移的布朗运动的最大值问题,我们运用布朗运动的反射原理和G irsanov定理给出了在有限[0,T]区间上的具有漂移的布朗运动的最大值分布及其与终值的联合分布.然后把其应用到阶梯期权,得到了阶梯期权封闭形式的解.     

对角占优矩阵的推广及应用

研究了几类广义对角占优矩阵的可逆性，然后讨论它们的特征值的性质以及在M矩阵的应用．     

B-Fredholm Properties of Closed Invertible Operators

In this paper, we study B-Fredholm spectral properties of an invertible closed linear operator in relation with the B-Fredholm spectral properties of its bounded inverse. Precisely, for such operator, we characterize its B-Fredholm spectrum and other related spectra in terms of the corresponding spectra of its bounded inverse. As an application, we show that every normal operator with nonempty resolvent set, in particular self-adjoint Schrödinger operators, satisfies generalized Weyl’s theorem.

     

On the power graph and the reduced power graph of a finite group

In this paper, for a finite group, we investigate to what extent its directed (resp. undirected) reduced power graph determines its directed power graph (resp. reduced power graph). Moreover, we investigate the determination of the orders of the elements of a finite group from its directed (resp. undirected) reduced power graph. Consequently, we show that some classes of finite groups are recognizable from their undirected reduced power graphs. Also, we study the relationship between the isomorphism classes of groups corresponding to the equivalence relations induced by the isomorphism of each of these graphs on the set of all finite groups.     

有限点集的m级连心线及其性质(英文)

In this paper, we first give the concept of m-degree center-connecting line in n-dimensional Euclidean space Enand investigate its several properties, then we obtain the length of m-degree center-connecting line formula in finite points set. As its application,we extend the Leibniz formula and length of medians formula in n-dimensional simplex to polytope.     

关于一个Hilbert类积分不等式的推广及应用

本文引入单参数，对一个积分型Hilbert类不等式作具有最佳常数 推广。作为应用，建立它的等价形式。     

3阶齐次线性常微分方程的球面解曲线

首先给出3阶齐次线性常微分方程的球面解曲线的定义,然后讨论其球面解曲线与系数函数的关系,最后给出了球面解曲线的几何性质.