关于扰动微分方程组零解部分变元的稳定性

本文讨论未被扰动运动关于部分变元的稳定性，一致稳定性和全局渐近稳定性，给出了一种判定，改进了文［１］中的相应定理。     

线性泛函数微分方程解的渐近表示

本文利用一类特殊方程的一致稳定性与收敛性定理研究Ｒ中线性泛函数分方程解的渐近表示，在较弱的条件下得到了与文「１」同样的渐近积分公式。文中还讨论了一些特殊解的存在性，零解的吸引性等等。     

Marachkov-Barbashin-Krasovskii型渐近稳定性定理

本文研究非自治系统的渐近稳定性.且得到了不要求Liapunov函数正定,也不要求其沿系统的解的导数负定的渐近稳定性定理.一致渐近稳定性定理及全局渐近稳定性定理.     

脉冲泛函微分方程的渐近稳定性

讨论了一类脉冲泛函微分方程的渐近稳定性.通过改进 Liapunov泛函的上界,利用Liapunov泛函第二方法和Jensen不等式,得到了一个一致稳定性定理和一个一致渐近稳定性定理,给出的例子说明了所得结果的优越性.     

时滞差分系统基于两种度量的稳定性分析

本文建立了一些关于时滞差分系统（h0,h）稳定性（一致稳定性，渐近稳定性，一致渐近稳定性）的判定准则。在所得到的定理中，去除了△V为常负的限制，特别地，△V甚至可以恒为正，从而大大改进了已有结果，并更加便于应用。     

非线性时变系统的Aeyels-Peuteman类型的Matrosov定理

主要讨论非线性时变系统的一致渐近稳定性,给出Aeyels-Peuteman类型的Matrosov定理定理.与一般的关于一致渐近稳定性的Matrosov定理不同,对Lyapunov函数的要求是不必可微的,并且Lyapunov函数的导数不必严格小于等于零.     

泛函微分方程的弱指数渐近稳定性

本文提出一种新的稳定性概念,即弱指数渐近稳定,并给出两个关于弱指数渐近稳定的判别定理和一个较广泛的指数渐近稳定判别结果.从而使得许多具有一致渐近稳定性的解的趋零速度,得到了一种估计.文中还深入地揭露了一致渐近稳定性和弱指数渐近稳定性之间的内在联系以及弱指数渐近稳定性和指数渐近稳定性的关系.     

关于扰动微分方程零解稳定性若干定理的改进

本文运用Ляиунов第二方法研究扰动微分方程零解稳定性，分别研讨了所给扰动微分方程的局部稳定性、全局渐近稳定性以及全局一致渐近稳定性问题，得到若干定理，这些结果在一定条件下改进了文[1]的相应结果，运用更加广泛．     

非线性微分方程组解的稳定性

本文研究以下两类非线性微分方程组零解的稳定性:■我们用定性方法,从分析轨线在原点邻域中的性态出发,得到了零解渐近稳定和不稳定的相应定理,可通过查表加以判定,简捷、实用。另外还可根据定理的条件具体构造渐近稳定和不稳定的系统。     

一类具有Beddington-DeAngelis响应函数的阶段结构捕食模型的稳定性

该文讨论一类具有Beddington-DeAngelis响应函数的阶段结构捕食模型.利用RouthHurwitz判别定理讨论了其正常数平衡解的局部渐近稳定性,通过构造Lyapunov函数方法得到了全局渐近稳定性.     

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.     

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.     

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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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.