由吴方法计算零维系统的有理单元表示

本文提出一个计算零维系统的有理单元表示的新算法.无需进行Grbner基运算,我们的算法仅运用了著名的吴方法.基于吴方法,我们的算法在Maple平台上被编制成一个通用程序RUR-Wu,可快速地计算出零维系统的有理单元表示.作为一个应用,本文提出了一个有效方法,用来计算某些多项式的整体最小值.此外,本文给出了几个实例,用来表明算法的效率.     

部分线性函数多项式模型的联合探测

本文提出了一个新的部分线性函数多项式回归模型,该模型中响应变量依赖于一个p阶函数多项式和一些非函数型数据的协变量.函数多项式模型、函数线性模型和部分函数线性模型是该模型的特殊情形.本文提出了一个模型探测方法,它能同时探测部分线性函数多项式回归模型中哪些阶是重要的以及哪些非函数型变量是重要的.提出的方法能相合地识别真实的模型并有好的预测表现.数值模拟能清晰地证实我们的理论结果.     

Krattenthaler反演公式的简短证明

为了提出研究Lagrange反演关系的统一方法,Krattenthaler建立了算子方法,并由此得到一个广泛的反演关系:Gould-Hsu-Carliz-Krattenthaler反演公式.本文利用Lagrange插值公式给出它的一个简短证明,进一步地证明在Lagrange插值的意义下,该反演关系是唯一性的.     

一个求解特殊加权线性互补问题的预估校正光滑牛顿法

本文研究特殊加权线性互补问题的求解方法.我们利用一个带有权重的光滑函数将问题转化成一个光滑方程组,然后提出一个预估校正光滑牛顿法去求解它.在适当条件下,我们证明提出的算法具有全局和局部二次收敛性质.特别地,在解集非空的条件下,我们证明价值函数点列收敛到零.数值试验表明算法是有效的.     

带有长期趋势的近似周期时间序列的刻度变换估计

近似周期时间序列具有近似的周期趋势,即近似周期性.所谓近似周期性是指它看起来有周期性,但是每个周期的长度不是常数,比如太阳黑子数序列.近似周期时间序列在社会经济现象建模中有着广泛的应用前景.对于近似周期时间序列,关键在于刻画它的近似周期趋势,因为一旦近似周期趋势被刻画出来它就可以作为一个普通的时间序列来处理.然而,关于近似周期趋势刻画的研究却很少. 本文首先建立一些必要的理论,特别地,提出了带长度压缩的保形变换概念,并且得到了带长度压缩的线性保形变换的充分必要,然后基于此理论作者提出了一种估计尺度变换的方法,该方法可以很好地估计出近似周期趋势.最后,对一个仿真实例进行了分析.结果表明,本文所提出的方法强力有效.     

基于降维思想的客观组合评价模型

为了解决多方法评价结论的非一致性问题,产生了组合评价方法.最大限度地利用多评价结论的信息是组合评价的关键.为此提出了一个基于降维思想的客观组合评价模型,它能够最大程度地保留多评价结论所包含的评价信息,充分地整合多评价结论中的共性信息.鉴于该模型求解属复杂非线性优化问题,常规方法难以直接处理,建立了微粒群改进算法,进行全局寻优.最后,通过实例说明了模型的可操作性和实用性.     

矿藏分布型函数描述的特殊性及其插值模型

矿藏描述所提出的插值问题有二个特点,一是数据分布通常是不规则的;二是数据可能只是被讨论函数的一个泛函,所以一般的插值方法都有所不足.本文提出的插值模型能较好地处理这个问题.     

薛定谔方程的整体几何光学近似

整体几何光学方法是一种新的求解高频线性波动方程初值问题的渐进近似理论.该理论最初是对WKB初值数据问题提出来的.在本文中,我们将采用不同的方法,对这一方法予以重新推导,使得该理论同样适用于初值为扩展WKB函数的情形.特别地,我们将建立的理论用于薛定谔方程传播子的半经典近似上来.结果表明,整体几何光学方法提供的波场近似恰好是Kay提出的半相空间公式的一个实例.作为副产品,我们指出Van Vleck近似中起到关键作用的Maslov指标可以通过一个简单的代数关系式来确定.     

一个新非协调单元对扩散对流反应方程的应用

利用最近提出的一个新型非协调双参数单元,将流线扩散有限元方法成功地应用于对流占优的扩散对流反应方程,并且得到流线扩散模意义下的误差估计结果.     

关于开紧映射与Arhangel''''skiǐ的问题

首先构造一T2的亚紧空间使其不是任一仿紧T2空间的开紧映象,否定了A.Arhangel'skiǐ1962年提出的一个问题;其次利用构造开紧映射的方法指出存在具有Gδ对角线的T2的次亚紧空间使其不具有G*δ对角线,肯定地回答了1999年R Hodel提出的一个猜测.     

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.     

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].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].