模糊群的模糊同态

引进模糊群的模糊同态概念，给出模糊同态下子模糊群(正规子模糊群)间的对应关系’建立模糊群的模糊同态基本定理，同时讨论模糊群的若干性质，得到一系列等价条件。     

模糊数序列的收敛性

探讨L-R型模糊数序列的S-和问题，定义关于模糊数的模糊小于的概念，在此基础上探讨模糊数的有序性，模糊数的截集函数的连续性，模糊数的格结构以及模糊数序列的收敛性等重要性质。     

群的模糊同态与模糊商群的同构定理

利用模糊映射，给出群的模糊同态的概念，并得到模糊同态基本定理，同时建立模糊商群的同构定理。     

完备格上模糊粗近似算子的代数结构

模糊粗集是粗集的模糊化。现有模糊粗集大多建立在t-范数、模糊（t-）相似关系以及对偶原理基础之上。本文将模糊知识（模糊数据）的属性值集[0，1]拓广到一般完备格，基于一般二元模糊关系、模糊合取算子以及模糊合取和模糊蕴涵间的“伴随”关系研究一类模糊粗近似算子。本文对一般模糊粗集的代数结构做了详尽的探讨，并研究了新的模糊粗集与经典粗集和模糊粗集之间的联系。结论表明：粗集的这种模糊化方法保持了Pawlak粗集的代数性质；所提出的模糊粗集是现有典型模糊粗集的一般化；而且，模糊粗近似的贴近度得以提高。     

模糊仿射集与模糊向量子空间的再定义

利用模糊直线定义模糊仿射集，研究其有关性质。在此基础上，定义模糊向量子空间，证明一个模糊集为模糊仿射集的充要条件是该模糊集是一个模糊子空间的平移。     

求最优模糊等价矩阵的一个算法

本文说明了模糊等价矩阵的结构，然后提出求模糊相似矩阵的最优模糊等价矩阵的一个算法，最后指出最优模糊等价矩阵一定存在，但不唯一。     

基于模糊统计的公司违约预测

针对KMV违约预测模糊中固定违约点的缺陷，将违约点模糊化，以模糊事件表示违约，从而修改确定公司股权价值的期权公式，进一步得到违约概率预测，重点讨论计算违约模糊事件的基本思路，详细给出模糊统计方法，通过案例分析说明本文提出的模糊方法的可行性与长处。     

由KM-模糊伪度量诱导的模糊化粗糙集及其性质

本文首先介绍了由KM-模糊伪度量诱导的模糊等价关系。基于此模糊等价关系，然后，得到了由KM-模糊伪度量诱导的模糊化粗糙集，并研究了其性质。最后，详细探究了KM-模糊伪度量及其诱导的模糊化粗糙集之间的关系，丰富和完善了模糊粗糙集理论的研究内容。     

模糊商群的推广

引入关于一个子群的正规模糊子集概念，研究正规模糊子集的一些性质，并在此基础上将模糊商群做了自然推广，最后建立群同态下正规模糊子集的对应定理。     

一种广义模糊补运算和相应的广义模糊熵

介绍广义模糊补的公理化定义，给出一种构造广义模糊补的方法，运用此方法构造出一种性质良好的广义模糊补；在此基础上提出一种广义模糊熵，这种广义模糊熵的最大值点可以在（0，1）开区间内自由移动。给出一类广义模糊熵的计算公式,便于实际应用。     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Journal of the Operations Research Society of China Special issue on Operations Research in Healthcare Management

正Guest Editors:Hong Chen,Shanghai Jiao Tong University,Shanghai,China Guohua Wan,Shanghai Jiao Tong University,Shanghai,China David Yao,Columbia University,New York,USA Scope:Healthcare delivery worldwide has been fraught with high cost,low efficiency and poor quality of patient care service.For the field of operations research(OR),healthcare offers some of the biggest challenges as well as best opportunities in     

ANALYSIS IN THEORY AND APPLICATIONS Vol. 30, 2014 CONTENTS

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On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

An alternative mathematical algorithm for the photo- and videokeratoscope

Due to the resolution of current laser technology, the accuracy of corneal topography as measured by the videokeratoscope is no longer adequate to provide precise enough data for refractive surgery or for the fitting of customized contact lenses. We present an algorithm for recovering corneal topography that makes use of modern differential geometric techniques and numerical descent in Sobolev spaces. We believe this algorithm may be used with the photo- and videokeratoscope to increase the accuracy of the recovered corneal topography.