n阶本原双随机矩阵遍历指数的上确界

本文给出了ｎ阶本原双随机矩阵遍历指数的上确界：     

关于带权的Hardy-Hilbert不等式中的一个上确界

本文引入了一个形如π/sin-Or（n）/n的权系数，其中Or（n）＞0（r＞1）．建立了带权的Hardy-Hilbert不等式，给出了Or（n）的下确界与上确界．特别当r=2时，证明了λ=1．4603545…是O2（n）的上确界，解决了文[2][6]中所提出的几个问题．     

一个求三对角矩阵的逆的并行算法

三对角矩阵的求逆问题是实际计算中经常遇到的。本文是以附加矩阵求逆法为基础,提出求这类矩阵的逆矩阵的一个并行计算格式。对于n阶矩阵,这个格式的时间界是0(log_2n),所需的处理机台数是0(n~2)为界。而以高斯法为基础的求逆并行计算法,运算的时间界是0(n),所需的处理机台数是以0(n)为界。     

体上矩阵广义逆的共变条件

设K为任意除环,F记其中心,K_r~m×n记K上秩r的m×n矩阵的集合.若A∈K_r~m×n则A’记A的转置,又设σ为K的对合反自同构则A→A’~σ为一个对合函数,记A’~σ=A,由此可定义A的M—P广义逆A~ 本文中I_n记n阶单位阵,GL_n(K)记K上n阶一般线性群,(E_ij)_mn记K上m×n矩阵且(i,j)位置为1,其余位置为0,本文研究广义逆的共变条件,推广了[2]的有关结果.     

p-除环上矩阵的广义逆

<正> 广义逆矩阵理论最近分别被推广到域上与有限域上.本文将讨论p-除环上矩阵的广义逆.我们要用到下面的 引理1 设A是除环△上矩阵的r×r可逆子阵,则     

（m，n）型二重（r1,r2）-循环矩阵的逆和广义逆

利用矩阵的Kronecker积给出了非奇异的（m,n）型二重（r1,r2）－循环矩阵求逆矩阵的一个计算公式,同时该方法还可以推广到求奇异的（m,n）型二重（r1,r2）－循环矩阵的反射g逆。     

二重(r1,r2)-循环矩阵求逆的一种新算法

本文给出了判定任意数域上二重（r1,r2)－循环矩阵非异性的一个充要条件，并提供了求这类矩阵逆的一种新方法。     

分块矩阵加权Moore-Penrose逆的块独立性

本文研究了分块矩阵关于加权Moore-Penrose逆的块独立性问题.利用加权Moore-Penrose逆的定义和性质,获得了2×2、1×2和2×1分块矩阵关于加权Moore-Penrose逆块独立的一些充分必要条件.     

基于广义逆矩阵的Ball曲线的降多阶逼近

给出了Ball曲线的一种降多阶逼近方法.将曲线的降多阶过程视为升阶的逆过程,利用广义逆矩阵的理论从而得到降阶曲线控制顶点的显式表示式.这种方法还考虑了原曲线与降阶曲线在两端点处分别达到(r,s)阶连续的情形(r≥0,s≥0).其次,给出了降阶误差界的估计.最后,给出数值例子.     

一类可逆矩阵逆矩阵的图论解法

设 M( G)是简单无向图 G的关联矩阵 ,A是 M( G)的可逆子矩阵 ,γ( A)是逆矩阵 A- 1中非零元素的个数 .获得了求逆矩阵 A- 1的一种图论方法 ,并且得到了γ( A)的精确上下界以及达到上下界时子矩阵 A的图论刻划     

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

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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].