一类具有小周期系数的椭圆型边值问题的双尺度渐近分析方法

1．引言在大型水坝和海港等大体积混凝土结构的施工及运行中,为防止结构开裂,必须采取水管冷却等控制温度技术;在大型仓储和化学反应器中,为了控制温度,必须采用有规律的供暖或冷却技术;刚性夹杂复合材料结构的稳态问题以及具有周期性约束的是网结构的平衡问题等．这些工程实际问题,在稳定状态或某个瞬时状态,都可以归结为一类具有周期性的复杂构造的椭圆型方程边值问题：其中路（x）二a。柞）,河为结构所占据的区域,其。维模型如图1．l所示．图1．1具有周期性特征的二维结构这类问题的特点是材料系数a勺（x）呈现高度振荡的以。…     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

整周期复合材料弹性结构的有限元计算

1．引言周期性复合材料与周期结构的弹性力学问题，由于其材料特征剧烈振荡，且周期很小，问题相当复杂，除了一些特殊的和简单的问题可以用解析法求解外，多数问题很难或不可能用解析法求解，需要采用数值方法计算，有限元法无疑是最有效的方法之一．用细观力学方法研究复合材料的力学问题时，需要涉及纤维的排列情况，纤维和基体的性能，界面的分布情况，以及细观的几何参数和物理参数等．由于复合材料细观构造的不均匀性和不规则性，损伤和缺陷的存在，以及许多难以精确测定的因素，使得复合材料的细观力学问题十分复杂，不作出一些简化…     

高校应用数学学报 第17卷(2002年)B辑(英文版)第2期目次和提要

图的割宽问题的度序列方法林诒勋　李湘露　杨爱峰 (郑州大学数学系 )一个图 G的割宽问题是把 G嵌入一条路 ,使得重叠边的最大数目为最小 .文中提出一种基于度序列的方法 ,以便确定一些典型图类 (如 n维立方体、毛虫树等 )的割宽精确值 .同时研究割宽与其它图论参数的关系 .一类二阶微分方程边值问题三解的存在性刘　斌 (武汉大学数学与统计学院 )利用重合度理论讨论了一类二阶微分方程边值问题三解的存在性 ,获得了三解存在的充分条件 .变系数三阶泛函微分方程的周期解张正球　王志成 (湖南大学应用数学系 )建立了下列具有变系数的三阶泛…     

n阶非线性常微分方程两点及三点边值问题解的存在性的进一步结果

本文利用上、下解方法讨论了n阶非线性常微分方程y^(n)=f(t,y,y‘…,y^(n-1))满足下列非线性边界条件的边值问题解的存在性。     

两个各向同性半平面焊接的界面共线裂纹问题

复合材料焊接的界面裂纹问题是工程中碰到的实际问题,这方面已有不少有意义的研究工作（如献[3]-[6]等等）。本讨论两个各同性半平面焊接的界面共线裂纹问题,利用复变方法和解析函数边值问题题的基本理论,给出了弹性体应力分布封闭形式的解。     

一类Navier-Stokes方程组的弱解

本文讨论了一类Ｎａｖｉｅｒ Ｓｔｏｋｅｓ型方程组初边值问题的可解性及解的性质，在解的存在性，正则性，渐进性，周期性等方面得到了某些新结果，进而将这些结果作了适当的应用．     

复合材料稳态热传导问题多尺度计算的一个数学模型

本文给出小周期复合材料稳态热传导问题的一种多尺度渐近展开方法，区别于传统方法中一次项和二次项系数都用解Hper^1（Q）周期边值问题得到，新展式构造时一次项系数仍通过解关于单胞Hper^1（Q）周期边值问题求得，而二次项系数用齐次边值问题求得，所构造渐近解属于H^1（n）．对光滑凸区域Ω，渐近解在H^1（Ω）空间仍具有较好的收敛性．优点为数值方法求解时，解一个齐次边界问题要比解一个Hper^1（Q）周期边值问题简单．     

具有两参数的非线性椭圆型方程边值问题解的渐近性态

讨论一类具有双参数的非线性椭圆型方程边值问题. 引入多重尺度变量, 构造问题的形式渐近解. 利用微分不等式理论, 证明边值问题渐近解的存在性和一致有效性. 由解的结构指出, 在两参数一定的情况下,相应问题的解只具有一个边界层.     

一元函数图形的周期性

本文讨论了一元函数图形呈现周期性的问题——周期图形函数概念,其函数结构、性质、导数与原函数的特点等,进而指出双中心对称函数是周期图形函数.     

On bounds for the mode and median of the generalized hyperbolic and related distributions

Except for certain parameter values, a closed form formula for the mode of the generalized hyperbolic (GH) distribution is not available. In this paper, we exploit results from the literature on modified Bessel functions and their ratios to obtain simple but tight two-sided inequalities for the mode of the GH distribution for general parameter values. As a special case, we deduce tight two-sided inequalities for the mode of the variance-gamma (VG) distribution, and through a similar approach we also obtain tight two-sided inequalities for the mode of the McKay Type I distribution. The analogous problem for the median is more challenging, but we conjecture some monotonicity results for the median of the VG and McKay Type I distributions, from we which we conjecture some tight two-sided inequalities for their medians. Numerical experiments support these conjectures and also lead us to a conjectured tight lower bound for the median of the GH distribution.     

Fast Algorithms for Identification and Comparison of Braids

A method for constructing algorithms solving the word and comparison problems for mapping class groups (in particular, for the braid group) is presented, and a family of one-side invariant orderings on the mapping class group of a surface with boundary is described. A method for constructing comparison algorithms for all finite orderings on the mapping class group of any surface with boundary is described, a fast and simple comparison algorithm for the Dehornoy order on the braid group is presented, examples of normal forms for braid groups are given, and algorithms for finding the forms are indicated. Bibliography: 15 titles.     

Sequence of operations analysis for dynamic data structures

This paper introduces a rather general technique for computing the average-case performance of dynamic data structures, subjected to arbitrary sequences of insert, delete, and search operations. The method allows us effectively to evaluate the integrated cost of various interesting data structure implementations, for stacks, dictionaries, symbol tables, priority queues, and linear lists; it can thus be used as a basis for measuring the efficiency of each proposed implementation. For each data type, a specific continued fraction and a family of orthogonal polynomials are associated with sequences of operations: Tchebycheff for stacks, Laguerre for dictionaries, Charlier for symbol tables, Hermite for priority queues, and Meixner for linear lists. Our main result is an explicit expression, for each of the above data types, of the generating function for integrated costs, as a linear integral transform of the generating functions for individual operation costs. We use the result to compute explicitly integrated costs of various implementations of dictionaries and priority queues.     

The Axiom of Choice in Second-Order Predicate Logic

The present article deals with the power of the axiom of choice (AC) within the second-order predicate logic. We investigate the relationship between several variants of AC and some other statements, known as equivalent to AC within the set theory of Zermelo and Fraenkel with atoms, in Henkin models of the one-sorted second-order predicate logic with identity without operation variables. The construction of models follows the ideas of Fraenkel and Mostowski. It is e. g. shown that the well-ordering theorem for unary predicates is independent from AC for binary predicates and from the trichotomy law for unary predicates. Moreover, we show that the AC for binary predicates follows neither from the trichotomy law for unary predicates nor from Zorn's lemma for unary predicates nor from the formalization of the axiom of choice for disjoint families of sets for binary predicates, and that the trichotomy law for unary predicates does not follow from AC for binary predicates. Mathematics Subject Classification: 03B15, 03E25, 04A25.     

Stokes方程的压力梯度局部投影间断有限元法

本文对定常的Stokes方程提出了一种新的间断有限元法,通过将通常的间断Galerkin有限元法与压力梯度局部投影相结合,建立了一个稳定的间断有限元格式,对速度和压力的任意分片多项式空间P_l(K),P_m(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L~2范数的最优误差估计.     

Differential inequalities for entire functions of finite degree and rational functions with prescribed poles

We establish new differential inequalities for the entire functions of finite degree with a majorant an entire function without zeros in the lower half-plane, for the entire functions with constraints on zeros and, as a consequence, for the rational functions with prescribed poles. All cases of equality in the main results are found. The estimates obtained generalize and strengthen some inequalities by Bernstein, Gardner, and Govil for entire functions of finite degree; by Smirnov, Aziz, and Shah for algebraic polynomials; and by Borwein and Erdelyi, Aziz and Shah, and the others for rational functions.     

Pricing strategies for perishable products: the case of Vienna and the hotel reservation system hrs.com

Consider a retailer who sells perishable products for which there is uncertain demand. Yield management with dynamic pricing is a standard practice that firms use for revenue management. For perishable products, recent analysis has focused on the distribution of flight capacity, referred to as ticket sales. Other non- storable, non-transportable, immaterial hospitality products include hotel capacity. The article discusses the extent to which hotel pricing strategies vary within the internet distribution system hrs.com. This study focuses on the distribution of hotel rooms available for booking on the internet for Vienna and gives an outlook to Euroland capitals. The main research interests are the underlying pricing models and the setting of the end price. Data was taken from hrs.com, which is the most important specialist for hotel room internet distribution in Germany according to recent studies by KMPG and others. The results include the identification of different pricing strategy clusters with regard to hotel category and hotel availability over a 22-day period for Vienna and one city from all Euroland countries (the capitals were studied for all cases except for the Netherlands, for which data was collected for Amsterdam). The study took the arrival days Mondays, Tuesdays, Wednesdays and Thursdays into account, and used data for all these days from the 11th of July, 2005, to the 10th of October, 2005, for Vienna, and the first and the last of these dates as a comparison base for the other Euroland cities.     

Half Space and Quarter Space Dirichlet Problems for the Partial Differential Equation

A customary, heuristic, method, by which the Poisson integral formula for the Dirichlet problem, for the half space, for Laplace's equation is obtained, involves Green's function, and Kelvin's method of images. Although this heuristic method leads one to guess the correct result, this Poisson formula still has to be verified directly, independently of the method by which it was arrived at, in order to be absolutely certain that a solution of the Dirichlet problem for the half space, for Laplace's equation, has been actually obtained. A similar heuristic method, as seems to be generally known, could be followed in solving the Dirichlet problem, for the half space, for the equation where is a real constant. However, in Part 1, a different, labor-saving, method is used to study Dirichlet problems for the equation. This method is essentially based on what Hadamard called the method of descent. Indeed, it is shown that he who has solved the half space Dirichlet problem for Laplace's equation has already solved the half space Dirichlet problem for the equation In Part 2, the solution formula for the quarter space Dirichlet problem for Laplace's equation is obtained from the Poisson integral formula for the half space Dirichlet problem for Laplace's equation. A representation theorem for harmonic functions in the quarter space is deduced. The method of descent is used, in Part 3, to obtain the solution formula for the quarter space Dirichlet problem for the equation by means of the solution formula for the quarter space Dirichlet problem for Laplace's equation. So that, indeed, it is also shown that he who has solved the quarter space Dirichlet problem for Laplace's equation has already solved the quarter space Dirichlet problem for the " equation" For the sake of completeness and clarity, and for the convenience of the reader, the appendix, at the end of Part 3, contains a detailed proof that the Poisson integral formula solves the half space Dirichlet problem for Laplace's equation. The Bibliography for Parts 1,2, 3 is to be found at the end of Part 1.     

英国运筹五十年：成就、困境和出路

英国是运筹学的发源地,五十年来对运筹学的创立,发展和推广起了重要作用,但到九十年代,情况起到了很大变化;运筹工作小组大量关闭;运筹学系基本消失,运筹工作另谋出路,为此,英国运筹学会拨出专款进行调研,组织专家讨论,在国际期刊上发表调研报告和讨论专辑,分析当前运筹学的困境和未来的路向,本对此进行介绍和探讨,希望对社会-经济转型时期的中国运筹学界和运筹工作有借鉴作用。