一族耦合Kaup-Newell方程及其相伴可积分解

通过介绍一个含四个位势的4×4矩阵谱问题,得到一个新的非线性发展方程族,其中较有意义的一个方程是耦合Kaup-Newell方程.利用迹恒等式,得到了它的双哈密顿结构.在某个约束条件下,通过特征值问题的非线性化方法,得到了Liouville意义下耦合Kaup-Newell方程新的可积分解.     

一个从多重特征值出发的分歧定理

讨论非线性方程F(λ,u)=0的分歧问题,这里F:R×X→Y为非线性微分映射,X,Y为Banach空间,利用Lyapunov-Schmidt约化过程和隐函数定理证得一个从多重特征值出发的分歧定理.推广了Crandall M G与Rabinowitz P H的经典分歧定理.     

非线性特征值问题的二次近似方法

本文研究求解非线性特征值问题的数值方法.基于矩阵值函数的二次近似,将非线性特征值问题转化为二次特征值问题,提出了求解非线性特征值问题的逐次二次近似方法,分析了该方法的收敛性.结合求解二次特征值问题的Arnoldi方法和Jacobi-Davidson方法,给出求解非线性特征值问题的一些二次近似方法.数值结果表明本文所给算法是有效的.     

一个Bargmann系统与TD族解的对合表示

§1.引言 孤子方程的Lax系统的非线性化方法已成功的用于寻找新的有限维完全可积的系统。本文基于以前的讨论研究与TD特征值问题相联系的非线性保谱演化方程族(TD族)。 TD特征值问题可写为下面等价的形式:     

由特征值唯一确定的实3×3Hankel矩阵(英文)

本文研究了由特征值唯一确定的3×3实Hankel矩阵.借助于M.Fielder[1]的结论并经过细致的讨论,得到3×3实Hankel矩阵由其特征值唯一确定的充分必要条件,刻画了3×3实Hankel矩阵的一种特征值性质.     

与三阶特征值问题相联系的Hamiltonian系统

利用特征值问题的非线性化方法,讨论了与三阶特征值问题相联系的Hamiltonian系统,并根据Arnold定理与生成函数方法,证明其在Liouville意义下是完全可积的.然后,借助位势函数与特征函数之间的关系,给出发展方程族的对合解.     

一个Bargmann系统及一类演化方程解的对合表示

本文通过一个特征值问题的非线性化,得到了一个Bargmann系统并证明了它是Liouville意义下的完全可积系统,并给出了与这个特征值问题相联系的演化方程解的对合表示。     

非单特征值引出的非线性方程分歧问题

本文讨论非线性方程f(x,λ)=θ的分歧问题,这里f:x×R→Y为非线性可微映射, x,Y为Banaclh空间.利用偏导算子A=fx(x0,λ0)的广义逆A ,研究了一类由非单特征值引出的分歧问题,给出了刻划分歧性的定理,推广了Crandall M G与Robinowitz P H的由单特征值引出的分歧性定理.     

一个新的Liouville可积系统及其Lax表示，Bi—Hamilton结构

从一个特征值问题出发,首先推导一族非线性发展方程,其中包括著名MKdV方程做为特殊约化,进一步证明这族方程在Liounille意义下可积并具有Bi-Hamilton结构,而在位执函数和特征函数之间的一定约束下,特征值问题被非线性化为一完全可积的有限维Hamilton系统。     

耦合KdV方程及无穷守恒律

通过一个带有4个位势的3×3矩阵谱问题,借助于零曲率方程,得到一族非线性演化方程.通过适当的约化,构造出了耦合KdV方程,并且给出了它的无穷守恒律.     

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].