离散的SI和SIS传染病模型的研究

为了描述个体的死亡、染病者的恢复以及疾病的传染,引入了相应的概率.基于总种群中个体数量为常数的假设,根据染病者能否恢复分别建立了具有生命动力学的离散SI和SIS传染病模型.所得到的结果显示:它们具有与相应连续模型相同的动力学性态,并确定了各自的阈值.在它们的阈值之下,传染病最终将灭绝;在它们的阈值之上,传染病将会发展成为地方病,染病者的数量将趋向于一确定的正常数.     

高中数学专题研究的一个案例──关于沪闵路─春申路口红绿灯时间设置合理性的研究

一、专题的背景与分析 　　1. 背景 　　闵行区的沪闵路─春申路口是交通特别拥挤的交叉路口之一.家住莘庄地区的同学有一个共同的感受,在他们到校或回家路上必经的沪闵路─春申路口时常遇到塞车现象.……     

报童模型及ARMA预测在航空配餐问题中的应用

航班承载人数的不确定性,造成航空公司在配餐中利润的流失,现存的配餐模式存在较多的浪费.本文利用基于损失厌恶的报童模型和ARMA时间序列分析模型对深圳航空公司某航班的配餐份数进行了建模分析和预测,并通过对两种模型输出的比较,得出了长期预测与短期预测的模型应用理论.将实际的历史数据代人到模型中验证,其结果优于经验模式下的配餐盈利情况.本文所采用的研究方法和研究结果对航空公司的精益发展有建设性的意义.     

巧解一道"牛吃草"问题

"牛吃草"问题又称为消长问题,是17世纪英国伟大的科学家牛顿提出来的.典型牛吃草问题的条件是假设草的生长速度固定不变,不同头数的牛吃光同一片草地所需的天数各不相同,求若干头牛吃这片草地可以吃多少天.由于吃的天数不同,草又是天天在生长的,所以草的存量随吃的天数不断地变化.……     

大钟与六位密码

福尔摩西接到电话的时候正在翻看一本关于城中富翁艾伦王的传奇故事。艾伦王年少时靠贩卖廉价的小闹钟起家,经过几十年的辛勤努力,把自己的事业拓展成了最有名的钟表公司,是本市最有名的富翁。艾伦王年纪已经很大了,身体也不好。他的儿女众多,但是他们和艾伦王的关系并不融洽。大家都猜测他们对艾伦王的财富虎视眈眈。"喂,福尔摩西吗?"约翰焦急的声音从电话那头传过来。"是我。"福尔摩西回应道。     

Drucker-Prager准则可靠度解析

视岩体强度参数为正态分布随机变量,以可靠度理论为基础,推导了Drucker-Prager准则可靠度判别的解析表达式,并通过Monte-Carlo法和一次可靠度方法验证了其正确性.应用所得到的公式分析了岩体强度参数的变异性对屈服准则判别结果的影响.结果表明,强度参数的变异性对Drucker-Prager准则可靠概率的影响程度不尽相同,在变异系数较大的情况下,它们对可靠概率的影响显著,不可忽略.为岩体屈服的可靠度判别提供了一条新思路.     

导数在高考命题中的"五大"热点

导数作为大学的重要内容,进入中学数学教材后,给传统的内容注入了生机与活力,为中学数学命题的研究提供了新视角,新方法.由于导数是研究函数性质的一个很好的工具,它的用途十分广泛,它在解决函数、不等式、解析几何等问题有独到的功能.因此,近几年的高考正逐年加大对导数问题的考查力度,本文通过对07年全国各地高考题的整理和分析寻找命题规律,希望能对今后的教学提供一点复习思路.……     

也谈立体几何中的轨迹问题——从一道调考试题说起

2010-2011学年度武汉市部分学校新高三起点调研测试的一道试题引起了我的注意.原题如下: 在正四面体P-ABC中,M为△ABC内(含边界)一动点,且点M到三个侧面PAB,PBC,PCA的距离成等差数列,则点M的轨迹是 A.一条线段 B.椭圆的一部分 C.双曲线的一部分 D.抛物线的一部分     

股票收益率和新息的尾部估计

利用极值理论来考虑上证综指收益率的尾部.为了选择合理的超越门限,采用平均剩余函数和De-Haan矩估计相结合的方法.在学生t分布和广义误差分布的新患假设下,用GARCH和EGARCH新息的ARMA模型拟合指数收益率,并且使用极值理论的极大似然方法估计模型残差的尾指,估计结果表明收益率的尾指和模型的残差尾指基本一致.     

神奇的骰子

骰子在许多游戏中出现,特别是赌博游戏,当中蕴含了丰富的数学知识,引起了许多数学爱好者们的关注和研究.一个普通的骰子是正六面体,它的六个面分别为数字1,2,3,4,5,6,还有许多不同的骰子、不同的玩法,充满了神奇,但神奇的骰子背后离不开数学知识的支撑.本文将介绍三     

Formulation of linear problems and solution by a universal machine

Using the predicate language for ordered fields a class of problems referred to aslinear problems is defined. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the testing of whether sets that are defined by linear inequalities are semilattices, all satisfiability problems in sentenial logic, the rank-computation of matrices, the computation of row-reduced echelon forms of matrices, and all quadratic programming problems with bounded variables. A single, one, algorithm, to which we refer as theUniversal Linear Machine, is described. It solves any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates alinear algorithm for the problem. Then, given an instance of the linear problem, in the second phase the linear algorithm solves the particular instance of the linear problem. The linear algorithm is finite, deterministic, loopless and executes only the five ordered field operations — additions, multiplications, subtractions, divisions and comparisons. Conversely, we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely. Finally, it is shown that with a linear algorithm for a linear problem, one can solve certain parametric instances of the linear problem.Research was supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 90-00434 and by ONR Grant N00014-92-J1142.Corresponding author.     

泛系分析:数学·方法论·相对论·辩证思维

基于对广义系统、泛导、泛对称、泛箱原理、泛系相对性提出了新的分析模式与新的相对数学化的简化强化的定义,发展了泛系方法论与泛系相对论的框架与理法,具体内容涉及:相对普适的数学化的泛系,200类对偶,对偶转化,泛对称转化,泛系辩证,八畴方法,泛系数学方法,广义量化,逼近转化原则,泛等价定理,供求分析,思维实验,广义灰色系统,等等.     

并行分批排序综述

并行分批排序起源于半导体芯片制造过程。在并行分批排序中,工件可成批加工,批加工机器最多可同时加工B个工件,批的加工时间为批中所有工件的最大工时。首先根据传统的机器环境和目标函数对并行分批排序已有成果进行分类介绍,主要为单机和平行机的机器环境,以及极小化最大完工时间、极小化总完工时间、极小化最大延迟、极小化误工工件数、极小化总延误和极小化最大延误的目标函数;然后梳理了由基本问题所衍生出来的具有新特点的16类新型并行分批排序,包括差异尺寸工件、多目标、工件加工时间或顺序存在限制、考虑费用和具有特殊机制等情况;最后展望未来的研究方向。     

A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

Transverse compression of PPTA fibers

Results of single transverse compression testing of PPTA and PIPD fibers, using a novel test device, are presented and discussed. In the tests, short lengths of single fibers are compressed between two parallel, stiff platens. The fiber elastic deformation is analyzed as a Hertzian contact problem. The inelastic deformation is analyzed by elastic-plastic FE simulation and by laser-scanning confocal microscopy of the compressed fibers ex post facto. The results obtained are compared to those in the literature and to the theoretical predictions of PPTA fiber transverse elasticity based on PPTA crystal elasticity.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).3TEX, Inc. 109, MacKenan Drive, Cary, North Carolina 27511, USA. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 533–544, March–April, 2000.     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

区组长为奇素数的自反MD设计

本文利用差方法对自反MD设计SCMD(4mp,p,1)的存在性给出了构造性证明,这里p为奇素数,m为正整数．     

On the weakening of the convergence of Newton’s method using recurrent functions

We use Newton’s method to approximate a locally unique solution of an equation in a Banach space setting. We introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton’s method than before [J. Appell, E. De Pascale, J.V. Lysenko, P.P. Zabrejko, New results on Newton–Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997) 1–17; I.K. Argyros, The theory and application of abstract polynomial equations, in: Mathematics Series, St. Lucie/CRC/Lewis Publ., Boca Raton, Florida, USA, 1998; I.K. Argyros, Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005) 179–194; I.K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer-Verlag Publ., New York, 2008; S. Chandrasekhar, Radiative Transfer, Dover Publ., New York, 1960; F. Cianciaruso, E. De Pascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003) 713–723; N.T. Demidovich, P.P. Zabrejko, Ju.V. Lysenko, Some remarks on the Newton–Kantorovich method for nonlinear equations with Hölder continuous linearizations, Izv. Akad. Nauk Belorus 3 (1993) 22–26. (in Russian); E. De Pascale, P.P. Zabrejko, Convergence of the Newton–Kantorovich method under Vertgeim conditions: A new improvement, Z. Anal. Anwendvugen 17 (1998) 271–280; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations, Dokl. Akad. Nauk BSSR 38 (1994) 20–24. (in Russian); B.A. Vertgeim, On conditions for the applicability of Newton’s method, (Russian), Dokl. Akad. Nauk., SSSR 110 (1956) 719–722; B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957) 166–169. (in Russian); English transl.:; Amer. Math. Soc. Transl. 16 (1960) 378–382] provided that the Fréchet-derivative of the operator involved is p$p$-Hölder continuous (p∈(0,1]$p\in (0,1]$).     

Holomorphic manifolds on locally convex spaces

Based on locally compact perturbations of the identity map similar to the Fredholm structures on real Banach manifolds, complex manifolds with inverse mapping theorem as part of the defintion are proposed. Standard topics including holomorphic maps, morphisms, derivatives, tangent bundles, product manifolds and submanifolds are presented. Although this framework is elementary, it lays the necessary foundation for all subsequent developments.