一类线性errors－in－variables模型的参数强相合估计及其a．s．收敛速度

本文讨论了如下一类线性ｅｒｒｏｒｓ－ｉｎ－ｖａｒｉａｂｌｅｓ模型——多元线性结构关系模型β′ｘｋ＋α＝０，ξｋ＝ｘｋ＋εｋ．｛ｋ＝１，２，…，ｎ．其中，｛ｘｋ：ｋ＝１，２，…，ｎ｝为一组ｉ．ｉ．ｄ．的ｍ维随机向量，｛εｋ：ｋ＝１，２，…，ｎ｝是ｉ．ｉ．ｄ．的随机误差，Ｅ（ε１）＝０，Ｖａｒ（ε１）＝σ２Ｉｍ．且｛ｘｋ：ｋ＝１，２，…，ｎ｝与｛εｋ：ｋ＝１，２，…，ｎ｝相互独立．在一些条件下，我们证明了估计量β，α，σ２的强相合性、唯一性，并给出了估计量的收敛速度为ｏ（ｎ－１－１ｑ），这里ｑ∈［１，２）．对于Ｅ（ｘ１）ｕ１和Ｖａｒ（ｘ１）Ｖｘ的估计也得出了同样的结果     

一般限制线性方程组的迭代解法

本文研究带限制条件的线性方程组Ａｘ＝ｂ，Ｘ∈Ｔ的选代解法，这里Ａ∈Ｃｍ×ｎ，ｂ∈Ｃｍ，Ｔ是Ｃｎ的子空间．我们构造了迭代格式ｘｏ＝０，ｒｋ＝ｂ—Ａｘｋ，ｘｋ＋１＝ｘｋ＋βＹｒｋ，ｋ＝０，１，…其中β是非零实参数，Ｙ是参矩阵；在方程组有解时，给出了参数β与参阵Ｙ的选取方法，以保证选代序列｛ｘｋ｝收敛到它的一个解．     

局部广义高斯序列与广义线性过程

本文对局部广义高斯序列得到了ｒ阶绝对矩的上界不等式，进而对由其生成的广义线性过程｛Ｘｎ｝给出了ａ．ｓ．收敛的充分条件。     

泛函型重对数律的收敛速度

泛函型重对数律的收敛速度王启应（南京大学）设｛Ｘ＿ｎ，ｎ≥１｝为ｉ．ｉ．ｄ．随机变量序列为定义在［１，∞）上的实函数。近年来，级数的收敛性问题，引起了众多学者的兴趣。作为一个研究方向，１９６８年，Ｄａｖｌ５￣［１］指出：上述级数的收敛除需要一定矩条件...     

一致Banach空间中非扩张映象的弱收敛定理

设犈是一致凸Ｂａｎａｃｈ空间，满足Ｏｐｉａｌ条件或具有Ｆｒｅｃｈｅｔ可微范数，犆是犈的非空闭凸子集，且犜：犆→犆是非扩张映象．又设对任何初始数据狓１ ∈犆，序列｛狓狀｝由下列修改了的Ｉｓｈｉｋａｗａ迭代程序生成：狓狀＋１ ＝狋狀犜狀（狊狀犜狀狓狀＋ （１－狊狀）狓狀）＋ （１－狋狀）狓狀，　狀≥１， （Ｉ）其中，数列｛狋狀｝与｛狊狀｝满足下列条件（ｉ）和（ｉｉ）之一：（ｉ）狋狀∈ ［犪，犫］且狊狀∈ ［０，犫］；（ｉｉ）狋狀∈ ［犪，１］且狊狀∈ ［犪，犫］，这里，常数犪，犫满足０＜犪≤犫＜１．作者证明了，犜有不动点的充要条件是，｛狓狀｝ 弱收敛且｛‖狓狀－犜狓狀‖｝收敛到０．而且，由此即知，若犜有不动点，则｛狓狀｝弱收敛到犜的一个不动点．     

混合序列强大数定律的收敛速度

混合序列强大数定律的收敛速度薛留根（河南许昌师范高等专科学校数学系，许昌４６１０００）河南省自然科学基金资助项目．１９９０年１２月３日收到，１９９１年１１月１１日收到第一次修改稿．一、引言和引理关于独立同分布的随机变量序列｛Ｘｎ｝的强大数定律的收敛速...     

判别函数项级数不一致收敛的一种方法

本文利用一致收敛函数列的一个性质,给出了判别函数项级数（包括函数列）不一致收敛的一种方法;这种方法为教科书所忽视,然而它对于一类函数列与函数项级数来说,却十分有用;特别对于一类函数项级数,判别的方法和技巧都有它们的特点,有一定启发性;１　一致收敛函数列的一个性质一致收敛函数列有一个不为人注意的性质：命题１　设各项连续的函数列｛Ｓｎ（ｘ）｝在区间Ｉ上一致收敛于Ｓ（ｘ）,则对Ｉ中任何以ｘ０（ｘ０∈Ｉ）为极限的数列｛ｘｎ｝,都有ｌｉｍｎ→∞Ｓｎ（ｘｎ）＝Ｓ（ｘ０）．（１）这个性质仅在某些数学分析教科书…     

半参数回归估计的相合条件

设有半参数回归模型ｙｉ＝ｘ’，β＋ｆ（ｔｉ）＋ｅｉ，ｉ＝１，．．．ｎ，其中｛ｔｉ｝为常数列，本文对｛ｘｉ｝为设计点列的情形，给出了β、ｆ（ｔ）有相合估计的条件；在｛ｘｉ｝为随机的情形，建立了ｆ（ｔ）估计的相合性。     

分位点过程随机加权逼近的相合性

本文将随机加法应用于分位点过程，建立了ｎ＾１／２｛Ｆ＾－Ｄ１ｎ（ｇ）－Ｆ＾－１（Ｇ）｝的分布的随机加权逼近的相合性，并给出了其收敛速度。     

巴氏空间中独立随机元部分和的完全收敛性

设｛Ｘｎ，ｎ≥１｝是Ｂａｎａｃｈ空间Ｂ中的独立非同分布的随机元序列，本文给出了｛Ｘｎ，ｎ≥１｝分别为对称和非对称两种条件下的Ｈｓｕ－Ｒｉｂｂｉｎｓ型强大数定律。     

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     

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.     

(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).     

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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Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.