二阶线性时滞微分方程的广义振动性

本文主要研究了二阶线性时滞微分方程的广义振动性和广义非振动性,给出了方程广义振动和广义非振动的一些判定定理,同时给出了一类方程广义非振动的充要条件.     

高阶线性时滞微分方程的广义振动性

该文考虑了一类高阶线性常系数时滞微分方程 y( n) (t) py′(t) qy(t-τ) =0的广义振动性和广义非振动性 ,给出了一些该类方程广义振动和广义非振动的判定定理 .文中的定理 4还给出了一类非振动但广义振动的方程的判别法则     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

三阶非线性泛函微分方程振动的比较准则

本文利用比较法,与一阶时滞微分方程的振动性相比较,研究一类三阶非线性泛函微分方程的振动性,建立该类方程振动的新比较振动准则.本文结果推广和改进了最近文献中的一些新结果.     

n阶线性脉冲微分方程解的振动性

脉冲微分方程解的振动性由于在物理、生态、工程等领域有其应用背景,引起了人们的广泛兴趣,正在成为研究的热点．本文讨论了一类n阶线性脉冲微分方程解的振动性和非振动性,分别给出了n为奇数和偶数时该方程振动和非振动的充分条件,并通过3个例题说明了文中定理的应用,所得结论改进并推广了部分文献的相关结果．     

函数的振动熵

本文定义了振动函数与函数的振动熵。对函数的振动性质进行了初步的讨论。振动熵是对函数振动程度的度量(振动愈剧烈振动熵的值愈大)。导数是振动熵的特例。     

一类具连续分布滞量的高阶偏微分方程的振动性

研究一类具有连续分布滞量中立项的非线性偏微分方程解的振动性,得到该方程在给定边值条件下振动和非振动的一些充分条件.     

车桥系统的耦合振动

通过用正弦波形模拟桥面的不平和考虑移动车辆-桥梁间的相互作用,在Euler-Bernoulli梁理论的基础上建立了一种车桥系统的耦合振动模型．利用模态分析法和Runge-Kutta法对模型进行数值求解,获得了车桥系统耦合振动的动态响应和共振曲线．发现车桥耦合振动的共振曲线中存在两个共振区域,一个反映主共振而另一个反映次共振．讨论了桥面不平、桥梁振型和车辆间的相互作用对系统振动的影响．数值结果表明,这些参数对系统振动的影响很大,桥面不平和振型对车桥系统耦合振动的影响不能忽略,设计车速应该远离临界车速．     

时滞抛物方程组振动的充要条件

本文研究了一类时滞抛物微分方程组在齐次Neumann边界条件下解的振动性,用平均值技巧和Green公式把时滞抛物方程组的振动问题转化为泛函微分方程组的振动问题,获得了判别其所有解振动的一个易于验证的充要条件,并举出实例对主要结果进行阐明.     

二阶非线性泛函微分方程解的振动性质

研究了一类二阶非线性泛函微分方程解的振动性以及非振动解的有界性.在一定条件下,建立了几个新的振动性和有界性定理,其结果推广和改进了已有的一些结果.     

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.     

CONTENTS OF VOLUME 30

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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].     

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.