几乎弱加细空间

证明了如下结果:(1)空间X是几乎弱加细空间当且仅当X是几乎离散弱加细可膨胀的,并且X的每个开覆盖u={Uα:α∈Λ},都存在X的稠密子集D和u的开加细V=∪n∈ωVn,使得x∈D存在b∈ω和α∈Λ有x∈Uα,并且st(x,Vn)∪βα;(2)如果X=∏α∈λXα是|Λ|—仿紧空间,则X是几乎弱加     

赋Orlicz范数的Orlicz序列空间的接近一致凸性

本文给出了赋Ｏｒｌｉｃｚ序列空间的Ｈ点的充分必要条件,进而得至了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间具有（Ｈ）性质的判据．同时给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ序列空间的一致ＵＫＫ和接近一致凸性的等价条件。     

A NEW SEMI-ANALYTIC ALGORITHM OF NEARLY SINGULAR INTEGRALS IN HIGH ORDER BOUNDARY ELEMENT ANALYSIS OF 2D ELASTICITY

针对边界元法中高阶单元中几乎奇异积分计算难题,解剖了二维边界元法高阶单元的几何特征,定义源点相对高阶单元的接近度。将高阶单元上奇异积分核函数用近似奇异函数逼近,从而分离出积分核中主导的奇异函数部分,其奇异积分核分解为规则核函 数和奇异核函数两项积分之和。规则核函数用常规高斯数值积分,再对奇异核函数积分导出解析公式,从而建立了一种新的半解析法,用于高阶边界单元上几乎强奇异和超奇异积分计算。给出3个算例,采用边界元法高阶单元的半解析法计算了弹性力学薄体结构和近边界点位移/应力,并与线性边界元正则化算法结果作了比较,结果表明提出的二次元的半解析算法更加有效。特别是分析薄体结构,采用正则化算法的线性边界元分析比有限元有显著优势,而用提出的二次边界元半解析算法分析比其线性元的有效接近度又减小了4个量级。     

On Asymmetrically Decomposable Groups

Mathematical Notes -     

Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis

Summary In this paper we rigorously show the existence and smoothness inε of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameterε. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.     

近独立子系系统的统计规律（一）——二维系统统计规律的计算初席封以

利用刚球模型，根据力学规律，对二维近独立子系系统粒子的运动进行了计算机模拟；模拟中，在不同时刻对系统中各粒子的能量和速率进行多次测量，并对测量结果进行统计平均，得到了粒子数不同的力学系统中粒子按能量和速率的分布图；根据所得的分布图形曲线，给出了任意数目的粒子系统的统一的分布函数．从而完全证明了少量粒子构成的力学系统，其长时间行为也具有确定的统计规律．     

Computing a logarithm of a unitary matrix with general spectrum

We analyze an algorithm for computing a skew‐Hermitian logarithm of a unitary matrix and also skew‐Hermitian approximate logarithms for nearly unitary matrices. This algorithm is very easy to implement using standard software, and it works well even for unitary matrices with no spectral conditions assumed. Certain examples, with many eigenvalues near ? 1, lead to very non‐Hermitian output for other basic methods of calculating matrix logarithms. Altering the output of these algorithms to force skew‐Hermitian output creates accuracy issues, which are avoided by the considered algorithm. A modification is introduced to deal properly with the J‐skew‐symmetric unitary matrices. Applications to numerical studies of topological insulators in two symmetry classes are discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

NUMERICAL SOLUTIONS FOR A NEARLY CIRCULAR CRACK WITH DEVELOPING CUSPS UNDER SHEAR LOADING

In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then transformed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coeffcients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.     

刻划D-η-真预拟不变凸函数的新方法

The D-η-proper prequasi-invexity of vector-valued functions is characterized by means of (weak) nearly convexity and density of sets.Under weaker assumptions,some equivalent conditions for D-η-proper prequasi-invexity are derived.