一些蕴含Furuta不等式的算子单调函数的算子不等式

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

一些蕴含Furuta不等式的算子单调函数的算子不等式（英文）

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

正线性算子的Young型逆不等式的一个改进（英文）

本文研究了正线性算子的Young型逆不等式的问题.利用算子单调函数以及凸函数的性质,获得了若干带有Kantorovich常数的Young型逆不等式标量形式及相对应的正线性算子的Young型逆不等式的改进形式,推广了现有文献中的结论.     

正线性算子的Young型逆不等式的一个改进

本文研究了正线性算子的Young型逆不等式的问题.利用算子单调函数以及凸函数的性质,获得了若干带有Kantorovich常数的Young型逆不等式标量形式及相对应的正线性算子的Young型逆不等式的改进形式,推广了现有文献中的结论.     

关于矩阵和算子迹的一组不等式

给出关于半正定矩阵迹和正算子迹的一组不等式,得到与邱贤忠关于实数的不等式的类似结果.     

算子Dunkl-Williams型不等式

在于讨论和经典Dunkl-Williams型不等式相类似的算子不等式,得到了几个算子Dunkl-Williams型不等式,并将其与现有的不等式进行了比较,结果表明,所得的结果是前期结果的推广和改进.     

球面卷积算子逼近

研究d维欧氏空间R~d中单位球面上卷积算子的逼近问题.利用球面乘子理论以及K-泛函与光滑模等价关系,建立一类球面卷积算子逼近的正、逆定理.特别地,给出了逼近的强型逆向不等式,从而揭示了该类球面卷积算子的本质逼近阶.此外,作为应用,给出了球面Jackson-Matsuoka卷积算子与Abel-Poisson卷积算子逼近上、下界的相同阶估计.     

两个正交射影差的范数不等式

设H是一个希尔伯特空间,B(H)表示H上有界线性算子全体构成的集合.P,Q∈B(H)是两个正交射影.运用算子分块技巧给出了||PX-XQ||的一个刻画,在此基础上证明了不等式||P-Q||≤1.进一步运用算子分块技巧与算子谱理论,给出||P-Q||=1以及严格不等式成立的充分条件.最后给出P-Q可逆的一个等价刻画.     

Riesz位势算子范数不等式及其推广

如何求出Riesz位势算子不等式中的最佳常数,一直是还没有完全解决的难题.本文通过将求最佳常数问题转化为求相应的算子范数等新的分析技巧,得到了Riesz位势算子的范数不等式.作为它的推广,得到了n维向量空间上具有径向核的新的积分算子范数不等式.     

一类算子迹的不等式

将一个算子迹的不等式进行加细,并获得了一个新的算子迹不等式.     

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].