群测模型在多路存取信道中竞争消解方面的应用

非适应性组合群测(group testing)是组合数学的一个分支,它有着广泛的应用.在一个有限集[n]上构作了一个群测模型,并利用这个群测模型介绍了它在多路存取信道中竞争消解方面的应用.     

基于组合群验模型的大学生就业竞争力评价与分析

利用非适应性组合群验的相关理论与方法,构建了一个用以衡量大学生就业竞争力的数学模型,基于该数学模型可针对在校大学生的个人就业竞争力做出预估和评价,为在校学生的教育和提升提供参考.     

数控机床故障分析的组合群验方法研究

介绍了两个组合群验数学模型,然后根据这两个数学模型,利用组合群验的理论和方法诊断数控机床故障部件,给出了数控机床故障诊断的新方法.     

组合群试

概率群试的方法针对所提出的方案理论上是相当完美的 .当情况很不明确时 ,独立性的假设也是可以理解的 ,而且具有容易执行的优点 .但如果能够掌握更多的信息 ,例如能够确切知道带菌者的人数 ,组合群试的方法效果更佳 .例如确切知道万名应征者中 ,恰有一名带菌者 ,用概率群试方法 ,ｐ=0 0 0 0 1 ,最佳群试为 1 0 1 -试 ,大约要做2 0 0次化验才能查清谁是带菌者 ;而用组合群试方法只需要 1 4次就够了 .为什么会有这么大的差距呢 ?显然概率群试的方案本身就提得不尽合理 ,一旦群试的结果是阳性 ,就不论组里个人带菌的概率有多大 ,一律逐个进行…     

利用组合群验数学模型分析汽车故障

利用组合群验的理论和方法建立数学模型,依据汽车可靠度对汽车系统定量分析,为确定故障部位,汽车维修,故障分析提供方法.     

学生体质评价模型的构建与分析

利用组合群验的理论和方法构建了学生体质评价数学模型,在这一模型基础上介绍了该模型的应用方法,为评价学生体质提供了新方法.     

组合群验在数控机床可靠性方面的应用

对数控机床子系统或子系统单元定量分析,得到了数控机床串联系统可靠度;利用组合群验数学模型,依据数控机床串联系统模型可靠度评价子系统的可靠性,也可为子系统故障分析提供方法.     

基于组合群验的汽车故障分析法

基于汽车故障部件与汽车故障现象之间的关系建立了数学模型,根据这一模型,利用组合群验的理论和方法分析了汽车故障,给出了汽车故障诊断的一种新方法.     

排序问题

写些短文的动机是想用一个更浅显的例子(跟组合群试比较 )解释“优化问题”中的组合概率论方法 ,包括不确定性的数量刻画、信息下界等概念 ,顺便纠正组合群试一文中的打印错误 .问题的提法 :ｎ个重量互不相同的球 ,通过在天平上比较可以确定两个球谁轻谁重 ,问立足于最坏可能 ,把它们按从最轻到最重的次序排列出来 ,需要使用几次天平 ?一个完整的方案遇到不同的中间结果 ,所需要使用天平的次数可能是不同的 ,但我们只关注这个方案遇到最倒霉的情形所需要的使用天平的(最大 )次数 .两个不同的方案 ,当然是那个这一(最大 )次数小的方案好 .问…     

基于群验模型的运动员选材方法研究

竞技体育中,运动员选材问题是一个极其重要而又复杂的问题,就方法而言,目前尚无公认的最优选材方法.在此运用组合群验的理论和方法构建了运动员选材数学模型,并介绍了该模型的应用,为运动员科学选材提供了一种新方法.     

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.     

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.     

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     

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.     

(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).     

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].