一类非线性非自治系统周期解的存在性

本文给出了系统ｄｘ／ｄｔ＝Ａ（ｔ）ｘ＋ｇ（ｔ，ｘ），ｇ∈Ｒ‘，ｘ∈Ｒ＾Ｎ，ω周期解存在的充分条件，推广了文「１」中的Ｋｒａｓｎｏｓｅｌｓｋｉｉ的结果。     

模糊值函数与模糊数积分区间[A,B]上的N—L公式

文「１」给出模糊值函数在普通区间「ａ,ｂ」上的Ｎ－Ｌ公式。本文在文「１」的基础上进一步给出模糊值函数区间「Ａ,Ｂ」上的积分。这个积分是Ⅱ型糊集。文「３」已经指出（Ｆ２「１,１」,∪,∩,ｃ）不是软代数,但这个积分是一个特殊Ⅱ型模糊集具有许多良好的代数性质,并存在着Ｎ－Ｌ公式。     

格上Ising模型的临界失真估计

本文是我们先前工作「１」，「２」的继续，对格上Ｉｓｉｎｇ模型的临界失真ｄｃ的估计，Ｎｅｗｍａｎ和Ｂａｋｅｒ「６」证明了ｄｃ和Ｉｓｉｎｇ模型的Ｍａｙｅｒ级数之收敛半径Ｒ有以下关系：ｄｃ＝Ｒ／（１＋Ｒ），在「１」中匀提出了估计Ｒ及ｄｃ的新方法，并它计算了二维矩形格Ｚ＾２上Ｉｓｉｎｇ模型的临界失真ｄｃ，此文中我们继续应用此方法首次计算了定义在其它二维和三维格上Ｉｓｉｎｇ模型的临界失真ｄｃ，数值计算的结果     

希尔伯特空间中半线性随机发展方程适度解的存在性

本文讨论如下形式的希尔伯特空间中半线性随机发展方程Ｃａｕｃｈｙ问题｛ｄｙ（ｔ）「Ａｙ（ｔ）＝ｆ（ｔ，ｙ（ｔ））」ｄｔ＋Ｇ（ｔ，ｙ（ｔ））ｄｗ（ｔ）ｙ（０）＝ｙ０适度解的存在性。在一组条件下得到了解的整体存在性，推广了文「１」的存在性定理。     

关于图的（g,f）—因子分解的一些新结果

本文讨论图的（ｇ，ｆ）－因子分解问题，推广了文「１」关于图的因子分解的理论，改进了文「２」的一些结果，给出了一个图Ｇ是（ｇ，ｆ）－可因子化的若干充分条件。     

广义Lienard方程非平凡周期解的存在性

本文给出了广义Ｌｉｅｎａｒｄ方程ｘ＋ｆ（ｘ）（ｘ）ｘ＋ｇ（ｘ）＝０存在非平凡周期解的两个充分条件,推广了文「４,５」中的结果,并且指出文「１」中的一个疏漏。     

平面定常系统的奇点指标问题

本文引进Ｓ－交点的概念，用新的方法研究了平面定常系统一支上两相邻初等奇点的指标问题，把文「１」的有关结果推广到一般的平面定常系统，作为作用，证明了文「２」猜测（Ⅱ）对ｎ次系统是正确的。     

GAOR迭代法和Jacobi迭代法的敛散关系

本文将文［１］中ＡＯＲ法和Ｊａｃｏｂｉ法同时敛散的结论推广到ＧＡＯＲ法．证明了当Ｊａｃｏｂｉ矩阵Ｂ非负时，解线性方程组Ａｘ＝ｂ（Ａ为不可约矩阵）的ＧＡＯＲ法（０≤γ_ｉ＜ω_ｉ≤１，ｉ＝１，２，…，ｎ）和Ｊａｃｏｂｉ法同时敛散，给出了其谱半径ρ（Ｌ_Ｒ，Ω）和ρ（Ｂ）之间的关系．     

两类求解y“=f（x,y）具有极小相位延迟的显式方法

本文提出了两类数值积分二阶周期性初值问题ｙ〃＝ｆ（ｘ，ｙ），ｙ（ｘ０）＝ｙ０，ｙ（ｘ０）＝ｙ０具有检小相位延迟的显式两步法。这些方法推广和改进了文献「１」１－「７」中的某些方法。数值试验表明本文中的某些方法优于「１」－「７」中的某些方法。     

L-统计量的Edgeworth展开和Bootstrap逼近

文「１」讨论了Ｌ－统计量的一种能达到０（１／√ｎ）精确性的Ｂｏｏｔｓｔｒａｐ逼近,本文则在适当条件下,证明了上述Ｂｏｏｔｓｔｒａｐ逼近能达到精确性０（１／√ｎ）,并给出了Ｌ－统计量的一阶Ｅｄｇｅｗｏｒｔｈ展开的估计。     

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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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.     

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.