概率密度函数核估计的Bootstrap逼近

主要研究了密度函数核估计逼近的速度,用Bootstrap方法对核密度进行估计,在适当的条件下,进一步提高了密度核估计Bootstrap逼近的速度,所得到的结果使得密度核估计Bootstrap逼近的速度与密度函数及其导数之间的关系更加的明确.     

条件中位数的核估计及其Bootstrap逼近的收敛速度

本文进一步讨论了条件中位数的核估计及其Bootstrap逼近的有关收敛速度.     

条件密度的近邻-核估计及其Bootstrap逼近

本文讨论了条件密度的近邻-核估计及其Bootstrap逼近的问题，证明了条件密度近邻-核估计的渐近正志性，Bootstrap逼近的相合性，讨论了有关的收敛速度．     

最近核邻型的光滑条件分位过程强逼近及其应用

文中证明了核邻型的光滑条件分位过程的强逼近，获得了其一致逼近速度．并由此结果推导出了光滑条件分位估计的渐近正态性、弱收敛和对数律等深刻结果．     

高维非均匀核N.N.估计的强一致收敛速度

本文讨论了高维空间中非均匀核Ｎ．Ｎ．Ｗ估计的一致强收敛强度。在密度数的条件与［１，２］相同时，得到了比［１，２］更好的收敛速度，就其收敛的主要部分而言已无可改进。由于均匀核Ｎ．Ｎ．估计是非均匀核Ｎ．Ｎ．估计的特例，从而大大拓广了Ｎ．Ｎ．估计的理论价值和应用范围。     

条件密度近邻－核估计的逼近速度

本文首先研究了条件密度函数近邻－核估计的误差分布的正态逼近精度,然后利用随机加权法构造了近邻－核估计的随机加权统计量,获得了随机加权逼近精度。     

条件密度近邻—核估计的逼近速度

本文首先了条件密度函数近邻一核估计的误差分布的正态逼近精度,然后利用随机加权法构造了近邻－核估计的随机加权统计量,获得了随机加权逼近精度。     

单隐层神经网络与最佳多项式逼近

研究单隐层神经网络逼近问题．以最佳多项式逼近为度量,用构造性方法估计单隐层神经网络逼近连续函数的速度．所获结果表明:对定义在紧集上的任何连续函数,均可以构造一个单隐层神经网络逼近该函数,并且其逼近速度不超过该函数的最佳多项式逼近的二倍．     

线性模型M估计分布的Bootstrap逼近的强收敛

本文讨论标准线性模型M估计分布的随机加权逼近，建立了随机加权M估计的线性表示及Bootstrap强逼近，同时还得到了逼近的一致强收敛速度，其主要部分的阶在Berry－Esseen意义下已达最优．     

单变量Sigmoidal型神经网络的逼近

引入了一种新的sigmoidal型神经网络,给出了其对连续函数逼近的点态和整体估计.结果表明这种新的神经网络算子具有多项式逼近所不能达到的很好的逼近速度.为了改进对光滑函数的逼近速度,我们进一步引入了一种新的神经网络的线性组合,并给出了这种组合逼近的点态估计和整体估计.最后给出了一个数值例子.     

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     

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 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.     

(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 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.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].