超空间2x的局部覆盖性质

本文讨论了超空间２^x的某些局部覆盖性质，并给出下面二个结果：定理１设Ｘ是Ｔ₂空间，则２^x紧当且仅当２^x是局部ｍｅｔａ－Ｌｉｎｄｅｌｏｆ空间．定理２₁设Ｘ是Ｔ¹空间，则２^xｍ－紧当且仅当２^x是局部ｍ－紧。     

关于Lasnev空间的超空间

讨论了Ｌａｓｎｅｖ空间的超空间的某些性质．文中构造一反例，证明存在可数Ｌａｓｎｅｖ空间，其紧子集超空间不是层型空间．并指出文［６］中关于上述结果的证明中有一关键性失误，故［６］中的反例尚不能说明上述结论成立．本文还对具有σ－ＣＦ拟基的ｋ′空间给出一个刻画定理     

超序列紧fts,可数超紧fts和超列紧fts

文献[1]中定义了序列紧fts(每个不分明集序列有收敛的子序列)和可数紧fts(每个可数开覆盖存在有限子覆盖)。对于序列紧fts,得到“每个fts都是序列紧的”病态结果,由此可见这样定义的序列紧fts不是一般拓扑学中序列紧的良扩张。对于可数紧fts,[2]在评论F-紧性时,论证了凡T_1空间都不是F-紧空间,以上的论证也可得到凡T_1空间都不是可数紧fts的病态结果。我们还要指出,[1]定义的可数紧fts也不是一般拓扑学中可数紧的良扩张。     

关于某些拟一致空间的超空间拓扑

设(X,τ)是一个拓扑空间。在本文中,我们证明了在超空间2^X上局部有限拓扑e^τ与局部有限覆盖拟一致u_LF所导出的超拓扑|2^u_LF|是相同的。我们还证明了下面条件是等价的:(1)(X,τ)是仿紧的;(2)(X,τ)是orth紧的,且e^τ=|2^u_FT|;(3)存在一个Lebes-yue拟一致u_L,使e^τ<     

球覆盖性质不是同胚不变的

Banach空间$X$中的一个开球族$\ss$是$X$的球覆盖, 如果$B$中的任一元素不包含原点,且$B$中元素之并覆盖了$X$的单位球面$S_{X}$. Banach空间$X$称为具有球覆盖性质,如果$X$有一个由可数多个球组成的球覆盖. 通过在 $l^\infty$上构造等价范数证明了Banach空间$X$的球覆盖性质既不是线性同胚不变的, 也不是在商映射下不变的, 同时, 它也不具有子空间的可继承性.     

L-拓扑空间中的几乎超紧L-子集

在L-拓扑空间中定义了L-子集的几乎超紧性,讨论了几乎超紧L-子集的性质以及L-子集的几乎超紧性与超紧性、近似超紧性及几乎良紧性之间的关系,给出了几乎超紧L-子集的网式及滤子刻画并证明了L-拓扑空间的几乎超紧性是几乎紧性的“L-推广”.     

非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用

在非紧超凸度量空间中建立了一个新的极大元定理.作为应用，获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后，新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理.     

非紧超凸度量空间中的Browder不动点定理及其对重合问题的应用

在非紧超凸度量空间中的非紧允许集上，建立了一个新的Browder不动点定理．作为应用，在非紧超凸度量空间中，研究了Ky Fan截口问题和相交问题，并新建了两个Ky Fan重合定理．     

Ck（X）的扇密度和强Frechet性质

本文证明了如下两个定理：（１）Ｃ＿ｋ（Ｘ）为强Ｆｒｅｃｈｅｔ空间（或者Ｆｒｅｃｈｅｔ空间）的充分必要条件是Ｘ中的每一开Ｋ－覆盖序列｛ｕ＿ｎ：ｎ∈Ｎ｝，存在Ｕ＿ｎ∈ｕ＿ｎ，使｛Ｕ＿ｎ：ｎ∈Ｎ｝为Ｘ的Ｋ－序列，（２）Ｃ＿ｋ（Ｘ）有可数扇密度的充分必要条件是Ｘ中的每一开Ｋ－覆盖序列｛ｕ＿ｎ：ｎ∈Ｎ｝存在ｕ＿ｎ的有限于族ｕ＇＿ｎ，使｛ｕ＇＿ｎ：ｎ∈Ｎ｝是Ｘ的开Ｋ－覆盖．     

紧开覆盖的一个新的Ky Fan型匹配定理及其应用

建立了紧开覆盖的一个新的Ky Fan型匹配定理.作为应用,研究了Fan-Browder型重合定理、Ky Fan型最佳逼近定理、极大元定理及超凸空间中的定性对策和抽象经济的平衡存在定理.     

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.     

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.     

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.