一类具有标准发生率的SIS传染病模型的全局稳定性

研究一类具有标准发生率的SIS传染病模型.应用微分方程定性理论,分别给出了保证该系统地方病平衡点、无病平衡点和总人口消亡平衡点全局渐近稳定的充分条件.     

一类具有非线性发生率的SIR传染病模型的全局稳定性

研究一类具有非线性发生率的SIR传染病模型.应用微分方程定性理论分别得到了该系统无病平衡点、地方病平衡点全局渐近稳定的充分条件,并进行了数值模拟.     

一类具有非线性发生率的SI传染病模型的定性分析

研究一类具有非线性发生率的SI传染病模型.应用微分方程定性理论,给出了该系统极限环的存在性、唯一性以及无病平衡点和地方病平衡点的全局渐近稳定性的充分条件.     

一类具有媒体影响的媒介传染病模型的分析北大核心CSCD

建立了一类媒体报道对媒介传染病传播影响的数学模型,研究了该传染病模型的动力学性态.通过求再生矩阵谱半径的方法得到基本再生数,并给出了地方病平衡点的存在性和局部稳定性.理论分析的结果表明,系统可能存在Hopf分支.进一步,由全局Lyapunov函数的方法得到了无病平衡点和地方病平衡点全局稳定的充分条件.     

具有阶段结构的Lotka-Volterra合作系统的稳定性和行波解

文建立并研究了一个两物种成年个体相互合作的时滞反应扩散模型.利用线性化稳定性方法和Redlinger上、下解方法证明了该模型具有简单的动力学行为,即零平衡点和边界平衡点是不稳定的,而唯一的正平衡点是全局渐近稳定的.同时, 利用Wang, Li 和Ruan建立的具有非局部时滞的反应扩散系统的波前解的存在性,证明了该模型连接零平衡点与唯一正平衡点的波前解的存在性.     

具有分布时滞和非局部空间效应的Gilpin-Ayala竞争模型的稳定性

本文构造并研究了一类具有分布时滞和非局部空间效应影响的Gilpin-Ayala竞争系统的反应扩散模型.利用线性稳定化方法和Redlinger上下解方法得到了该竞争模型的动力学性态,并证明了模型在边界平衡点和共存平衡点是全局渐近稳定的.     

一类抗体免疫下具有治愈率的HIV-1感染模型[英文]

本文主要研究一类抗体免疫下具有治愈率的HIV感染模型的动力学行为. 该模型不仅考虑潜伏阶段的感染细胞而且潜伏期的感染细胞可以治愈转化为健康的易感细胞. 通过构造Lyapunov函数, 证明了在一定条件下, 系统的无感染平衡点,无免疫平衡点以及感染平衡点的全局渐近稳定性.     

一类具有Beddington-Deangelis功能反应捕食系统的收获模型

研究了一类具有Beddington-Deangelis功能反应捕食系统的收获模型,讨论该系统生物经济平衡点的性态,得到了系统正平衡点全局渐进稳定的充分条件;然后利用Pontryagin最大值原理得到了最优收获策略,讨论了贴现率能影响收获种群的利润水平.     

一类具有媒体影响的媒介传染病模型的分析

建立了一类媒体报道对媒介传染病传播影响的数学模型,研究了该传染病模型的动力学性态.通过求再生矩阵谱半径的方法得到基本再生数,并给出了地方病平衡点的存在性和局部稳定性.理论分析的结果表明,系统可能存在Hopf分支.进一步,由全局Lyapunov函数的方法得到了无病平衡点和地方病平衡点全局稳定的充分条件.     

带有标准发生率和信息干预的随机时滞SIRS传染病模型的动力学行为

考虑了一类具有标准发生率和信息干预的随机时滞SIRS传染病模型.定义了一个停时,通过构造适当的Lyapunov函数证明了停时为无穷大,从而证明了该模型正解的全局存在性和唯一性.通过构造适当的 Lyapunov函数,研究了该模型的解在确定性模型无病平衡点和地方病平衡点附近的渐近行为,得到了在一定条件下随机系统的解分别围绕两个平衡点做随机振动.     

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.     

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 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.     

(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).     

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].