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.     

一些组合地图新算法的实现

本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.     

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.……     

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     

树的稳定子集和稳定指标

一个实矩阵的符号稳定性问题在经济学、生态学等诸多领域中都有应用背景．本文利用[1]中给出的不可约矩阵的符号稳定性的有关结论，将一个实矩阵的符号稳定性判定问题转化为一个等价的图论问题，即判定无向树中一个点子集的稳定性问题．本文引入了树的稳定子集的概念并给出了稳定子集的递归判别方法．本文还提出井研究了树的稳定指标，即树中所有稳定子集的最小基数，证明了关于稳定指标的一个min—max型定理，井给出了n阶树的稳定指标的最好上界及达到上界的极树的完全刻划。     

Implicit construction of multiple eigenvalues for trees

We are generally concerned with the possible lists of multiplicities for the eigenvalues of a real symmetric matrix with a given graph. Many restrictions are known, but it is often problematic to construct a matrix with desired multiplicities, even if a matrix with such multiplicities exists. Here, we develop a technique for construction using the implicit function theorem in a certain way. We show that the technique works for a large variety of trees, give examples and determine all possible multiplicities for a large class of trees for which this was not previously known.     

Diffusion in poro‐plastic media

A model is developed for the flow of a slightly compressible fluid through a saturated inelastic porous medium. The initial‐boundary‐value problem is a system that consists of the diffusion equation for the fluid coupled to the momentum equation for the porous solid together with a constitutive law which includes a possibly hysteretic relation of elasto‐visco‐plastic type. The variational form of this problem in Hilbert space is a non‐linear evolution equation for which the existence and uniqueness of a global strong solution is proved by means of monotonicity methods. Various degenerate situations are permitted, such as incompressible fluid, negligible porosity, or a quasi‐static momentum equation. The essential sufficient conditions for the well‐posedness of the system consist of an ellipticity condition on the term for diffusion of fluid and either a viscous or a hardening assumption in the constitutive relation for the porous solid. Copyright © 2004 John Wiley & Sons, Ltd.     

Stackelberg–Nash exact controllability for the Kuramoto–Sivashinsky equation

This paper deals with a hierarchical control problem for the Kuramoto–Sivashinsky equation following a Stackelberg–Nash strategy. We assume that there is a main control, called the leader, and two secondary controls, called the followers. The leader tries to drive the solution to a prescribed target and the followers intend to be a Nash equilibrium for given functionals. It is known that this problem is equivalent to a null controllability result for an optimality system consisting of three non-linear equations. One of the novelties is a new Carleman estimate for a fourth-order equation with right-hand sides in Sobolev spaces of negative order, which allows to relax some geometric conditions for the observation sets for the followers.     

Competence-driven project portfolio selection,scheduling and staff assignment

This paper presents a new model for project portfolio selection, paying specific attention to competence development. The model seeks to maximize a weighted average of economic gains from projects and strategic gains from the increment of desirable competencies. As a sub-problem, scheduling and staff assignment for a candidate set of selected projects must also be optimized. We provide a nonlinear mixed-integer program formulation for the overall problem, and then propose heuristic solution techniques composed of (1) a greedy heuristic for the scheduling and staff assignment part, and (2) two (alternative) metaheuristics for the project selection part. The paper outlines experimental results on a real-world application provided by the E-Commerce Competence Center Austria and, for a slightly simplified instance, presents comparisons with the exact solution computed by CPLEX.     

Exceptional Family of Elements for a Variational Inequality Problem and its Applications

This paper introduces a new concept of exceptional family of elements (abbreviated, exceptional family) for a finite-dimensional nonlinear variational inequality problem. By using this new concept, we establish a general sufficient condition for the existence of a solution to the problem. Such a condition is used to develop several new existence theorems. Among other things, a sufficient and necessary condition for the solvability of pseudo-monotone variational inequality problem is proved. The notion of coercivity of a function and related classical existence theorems for variational inequality are also generalized. Finally, a solution condition for a class of nonlinear complementarity problems with so-called P _* -mappings is also obtained.     

Carleman estimate for a strongly damped wave equation and applications to an inverse problem

In this paper, we establish a Carleman estimate for a strongly damped wave equation in order to solve a coefficient inverse problems of retrieving a stationary potential from a single time‐dependent Neumann boundary measurement on a suitable part of the boundary. This coefficient inverse problem is for a strongly damped wave equation. We prove the uniqueness and the local stability results for this inverse problem. The proof of the results relies on Carleman estimate and a certain energy estimates for hyperbolic equation with strongly damped term. Moreover, this method could be used for a similar inverse problem for an integro‐differential equation with hyperbolic memory kernel. Copyright © 2012 John Wiley & Sons, Ltd.     

Testing for elliptical symmetry in covariance-matrix-based analyses

Many normal-theory test procedures for covariance matrices remain valid outside the family of normal distributions if the matrix of fourth-order moments has structure similar to that of a normal distribution. In particular, for elliptical distributions this matrix of fourth-order moments is a scalar multiple of that for the normal, and for this reason many normal-theory statistics can be adjusted by a scalar multiple so as to retain their asymptotic distributional properties across elliptical distributions. For these analyses, a test for the validity of these scalar-adjusted normal-theory procedures can be viewed as a test on the structure of the matrix of fourth-order moments. In this paper, we develop a Wald statistic for conducting such a test.     

Contractibility and Connectedness of Efficient Point Sets

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.