H-张量的新判定及其应用

<正>1引言实对称张量具有广泛的应用背景~([1-3]),众多学者对其进行研究~([4-8]).研究实对称张量的主要问题之一是其正定性的判定~([9]),其应用在于解决多元偶次齐次多项式f(x)≡Ax~m=sum from (i_1,...,i_m=1) to n(a_(i_1…i_m)x_(i_1)…x_i_m)(m为偶数,A为实对称张量)正定性的判定问题~([10]),即f(x)0,?x=(x_1,x_2,…,x_n)~T∈R~n,x≠0(1)是否成立?问题(1)不仅是一个重要的问题,而且在许多领域具有应用.如在自动控制系     

H-张量的判定及其应用

H-张量在科学和工程实际中具有重要应用,但在实际中要判定H-张量是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了一些比较实用的新条件.作为应用,给出判定偶数阶实对称张量正定性的条件,相应数值例子说明了结果的有效性.     

H-张量的迭代判定及其应用（英文）

H-张量在科学和工程实际中具有重要应用,但在实际中要判定H-张量是不容易的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出一些比较实用的H-张量新判别方法.作为应用,给出判定偶数阶实对称张量正定性的条件,相应数值例子说明了结果的有效性.     

$\mathcal{H}$-张量的迭代判定及其应用[英文]

H-张量在科学和工程实际中具有重要应用, 但在实际中要判定H-张量是不容易的. 通过构造不同的正对角阵,结合不等式的放缩技巧,给出一些比较实用的H-张量新判别方法.作 为应用,给出判定偶数阶实对称张量正定性的条件, 相应数值例子说明了结果的有效性.     

H-张量判定的新迭代准则及其应用

H-张量在科学和工程实际中具有重要应用,但在实际中要判定H-张量是比较困难的.通过构造不同的正对角阵,结合不等式的放缩技巧,给出了H-张量判定的几个新迭代准则.作为应用,给出了判定偶数阶实对称张量正定性的条件,相应的数值例子说明了结果的有效性.     

四阶不完全对称张量M-特征值的新包含域及应用

四阶不完全对称张量的M-特征值在非线性弹性材料分析中有着广泛的应用.本文的目的是给出四阶不完全对称张量M-特征值的新包含域,得到最大M-特征值上界更精确的估计,并将得到的上界估计值应用到计算最大M-特征值的WQZ算法中,数值例子验证了结果的有效性.最后,基于得到的包含域,给出了四阶不完全对称张量正定性判定的充分条件.     

初等变换的若干应用

讨论了初等变换在高等代数中的若干应用,介绍了求出多项式的最大公因式的方法,给出了矩阵的秩及实对称阵A正定定理的证明.     

实正定矩阵的复合矩阵的正定性

本文讨论了实正定矩阵的复合矩阵的正定性，并且给出了实正定矩阵的复合矩阵仍为正定矩阵的一个充要条件.     

广义实正定矩阵的几个不等式

推广了文献[3]中的广义实正定矩阵的行列式不等式,同时给出了广义实正定矩阵的凸性不等式.     

齐次对称多项式的半正定性

给出了某些齐次对称多项式半正定的充分必要条件,并举例说明其应用.     

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.     

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].