综合评判中的凸性

应用Ｆｕｚｚｙ综合评判模型进行决策时，我们发现综合评判中的凸性是必不可少的。如果不具备凸性，就会产生无法决策，甚至矛盾的情况。本文讨论了综合评判中的凸性及其它对综合评判结果的影响，给出了产生凸性的一些充分条件，从理论和应用上进一步完善了模糊综合评判的模型。     

基于模糊评价的管理数据库的知识挖掘

采用模糊数学中的综合评判方法对学生管理数据库中的成绩进行挖掘，得到学生个人综合素质的分类的相关知识，同时对模糊评判中评判标准，模糊关系矩阵的确定及模糊算法进行研究。得出比较满意的结论。     

Fuzzy-Grey综合评判模型与射击方案的优化

本考虑类别标准已确定的综合评判问题，将灰色理论中的关联分析用于Fuzzy综合评判模型，用灰色关联系数来替代隶属度，提出一种的综合评判的方法，运用于射击方案的优化．     

一种基于动态模糊综合评判的故障预测新方法

针对影响装备寿命的许多故障因素和故障关系具有复杂性、非确定性以及时变性的特点，指出了传统模糊综合评判方法的不足，提出了基于动态模糊综合评判的故障预测方法，给出了动态权重矩阵和动态隶属度的确定方法，以火炮反后坐装置为例对评判过程予以说明，证明了该方法的有效性和实用性。并将模糊综合评判与产生式规则相融合，利用复合推理机制提高预测结果的准确性。     

关联序分析在小麦品种(系)综合评判中的应用

本文应用关联序分析法对鲁西北棉区两熟的小麦配套品种（系）进行了综合评判，结果表明用关联序分析法综合评判小麦品种（系）其结果全面客观，整体量化，切合实际，克服了以往评判中只注重产量因素而忽视其它性状所造成的偏差。     

城市工业企业经济效益的综合评判

本文采用多元统计分析中的主成分分析方法改进型，对城市工业企业的经济效益给予综合评判，然后又对综合评判系数采用系统聚类分析方法对其作了分类，用以找出各类城市的优势和差距，便于针对性地制定提高经济效益的对策．     

一种改进的灰色多层次综合评判法

介绍了一种改进的灰色多层次综合评判法，并证明当评价中用各方案中的最优值作为参考数据列时，新方法与献[1]所述的灰色多层次综合评判法所得的评判矩阵是相等的。     

基于遗传算法的项目经理评价

本文根据自然进化规则，把项目经理视为评价系统，项目经理所要满足的要求视为系统环境，用遗传算法的方法评价项目经理，力求提出一种比较客观科学的、且可以定量分析的项目经理的评价方法。     

模糊数学在综合评判人口再生产类型中的应用

本文给出了用模糊数学对人口再生产类型进行综合评判的方法，并举例说明     

模糊数学在综合评判人口再生产类型中的应用

本给出了用模糊数学对人口再生产类型进行综合评判的方法，并举例说明     

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.     

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     

(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].