奇数阶中立型时滞微分方程的线性化振动性

考虑奇数阶中立型非线性微分方程ｄ＾ｎ／ｄｔ＾ｎ（ｘ（ｔ）－Ｐ（ｔ）ｇ（ｘ（ｔ－τ）））＋Ｑ（ｔ）ｈ（ｘ（ｔ－σ））＝０。本文在允许Ｐ（ｔ）－１振动的条件下给出了该方程的几个线性化振动结果。     

具周期系数的奇阶中立型微分方程的振动与非振动结果

对于奇阶中立型方程［ｘ（ｔ） － ｐｘ（ｔ－ τ）］（ｎ） ＋ ｑ（ｔ）ｘ（ｔ－ σ） ＝ ０,其中ｑ（ｔ） 为τ－周期函数,分别得出了振动与非振动结果,并将所得结果用到方程［ｘ（ｔ） － Ｐ（ｔ）ｘ（ｔ－ τ）］（ｎ） ＋Ｑ（ｔ）ｘ（ｔ－ σ） ＝ ０,其中Ｑ（ｔ） 为渐近周期函数．     

高阶非线性差分方程的振动性

本文研究了差分方程△ｄｘ（ｎ）＋ｐ（ｎ）△（ｄ－１）ｘ（ｎ）＋Ｈ（ｎ，ｘ（ｎ））＝０，（１．１）△ｄｘ（ｎ）＋ｐ（ｎ）△（ｄ－１）ｘ（ｎ，ｘ（ｎ））＝Ｑ（ｎ）．（１．２）在一定的条件下，证明了方程（１．１）与（１．２）在振动性方面的等价问题．对于方程（１．１）或（１．２），在ｎ是偶数时的每一个有界解是振动的，在ｎ是奇数时，每一个有界解是振动的或当→∞时单调趋于零的充要性定理也建立了．     

具正负系数中立型时滞差分方程解的振动性

本文讨论一阶具正负系数中立型时滞差分方程 △（ｘ（ｎ）－ｃ（ｎ）ｘ（ｎ－ｋ））＋ｐ（ｎ）ｘ（ｎ－ｍ）－Ｑ（ｎ）ｘ（ｎ－１）－０,ｎ＝０,１,２,…我们获得了使方程所有解振动的“ｓｈａｒｐ”条件,即在系数ｐ（ｎ）,Ｑ（ｎ）,Ｃ（ｎ）为常数时是充分必要条件,本文的结果推广并改进了已有的结果．     

二阶中立型差分方程的振动性与渐近性

考虑二阶中立型差分方程 △~２（ｘ_ｎ－ｃｘ_（ｎ－ｒ）＋∑ｑ_（ｉ,ｎ）ｘ_（ｎ－σ_ｉ）＝０（ｎ＝０,１,２,…） （１）当 Ｃ＞０时我们得到了方程的所有解振动或非振动解趋于零的若干充分条件,本文的结果推广了文［２］中的结果．     

脉冲时滞差分方程的振动性

讨论脉冲时滞差分方程｛ｘπ＋１－ｘπ＋ｐπｘπ－１＝０,ｎ≥０,ｎ≠ｎｋ;ｘπｋ＋１－ｘπｋ＝ｂｋｘπｋ,ｋ＝１,２,３…给出了方程所有解振动的充分条件。     

一类中立型泛函微分方程的振动性

本文给出较为一般的含有多个滞量的中立型泛函数微分方程ｅ／ｅｔ（α（ｔ）ｘ（ｔ）『Σ＾ｍｉ＝１ｂｉ（ｔ）ｘ（ｔ－ｒｉ）」＝Σ＾ｎｊ＝１ｆｊ（ｔ，ｘ（ｔ），ｘ（ｔ－τｊ（ｔ）））振动的一个充要条件，同时又给出该方程振动的几个判定准则。     

临界状态下一阶时滞微分方程的线性化振动性

本文首先在临界状态下建立了一阶非线性非自治时滞微分方程ｘ＇（ｔ）＋＝１ｐｉｘ（ｔ－Ｔｉ）＋ｆ（ｔ,ｘ（ｔ－σ１（ｔ））…,ｘ（ｔ－σｎ（ｔ））＝０与一个相关的二阶常微分方程振动性等价定理,进而给出了一阶非线性自治微分方程与相应的线性方程振动性等价的充分条件,从而较好地回答了张炳根在文［２］中提出的一个公开问题．     

高阶具“积分小”系数中立型微分方程的振动性

本文提出了一种研究高阶中立型方程「ｘ（ｔ）－Ｐ（ｔ）ｘ（Ｔ－τ）」＾（ｎ）＋Ｑ（ｔ）ｘ（ｔ－δ）＝０,ｔ≥ｔ振动性的新技巧,其中不需要通常的积分发散条件∫＾∞Ｑ（ｓ）ｄｓ＝∞。     

一类非线性中立型差分方程的振动性

本首先建立下列两类差分方程△（ｘｎ－ｒｎｒｎ－ｒｘｎ＋ｒ）＾ａ＋ｑｎｆ（ｎ－σ）＝０（＊）和△（ｒｎ△ｙ）＾ｎ＋τ＾－ａｑｎｆ（ｒｎ－σｙｎ）＝０（＊＊）振动性的等价性,然后给出方程（＊）振动性的一些判则。     

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     

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.     

(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

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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].