一个函数不等式的加强与延伸

从一个常见的不等式谈起,分析了多种证明方法,运用该不等式推导出了多个重要结论,对不等式进行了扩充和加强,解释了蕴含的意义,显示了该不等式的重要性和深刻性.     

基于粗糙集的患者满意度评价模型及其实证分析

在文献阅读及实地调研的基础上,本文提出了患者满意度的定义,建立了影响患者满意度的指标体系,介绍了粗糙集的相关概念及利用粗糙集进行评价的步骤,提出了新的约简方法,构建了基于粗糙集的患者满意度评价模型并进行了实证分析,得出了影响患者满意度的关键指标,并计算了关键指标权重,对江西省十个医院进行了综合评价值的计算.     

交通运输系统协调发展理论与模型研究

提出了交通运输系统协调度的评价分析模型.从系统论的观点出发,提出了交通运输系统协调理论的概念,探讨了交通运输系统随时间而不断演化变迁的规律,给出了交通运输系统协调发展基本步骤;并根据协调学原理,讨论了交通运输系统的协调性问题,提出了系统协调发展模型,对交通运输子系统内部及子系统之间及系统整体的协调发展问题进行了研究,探讨了交通运输可持续发展的系统协调管理过程,为进一步研究交通运输系统的可持续发展奠定了基础.     

关于举办2012年中学生数学奥林匹克夏令营活动的启事

从1996年至今,华中师范大学数学与统计学学院已成功举办多届全国中学生数学奥林匹克夏令营活动,培养了大批优秀的数学竞赛选手,他们经过权威名师的指点,既丰富了理论知识,更掌握了实践经验,为走上成功明确了航向,在国内、国际数学竞赛中取得了令人瞩目的成绩。我院已成为全国数学奥林匹克活动的重要培训基地,吸引了众多优秀中学生云集武汉参     

系统动力学在城市污水再生回用系统中的应用

用系统动力学方法研究了城市污水回用系统.首先分析了影响城市污水回用系统的诸多因素以及它们之间的相互关系,探讨了污水再生回用系统行为和结构的特点,确定了系统中因素之间的定量关系,建立了城市污水回用系统动力学(SD)模型,并介绍了模型的检验方法.同时给出了SD模型的具体应用实例,对西北地区的某一城市的污水回用进行了预测和分析,提出了符合该城市发展的污水回用方案.     

压板松动时大型发电机端部绕组的主共振与分岔

研究了大型汽轮发电机定子端部固定绕组的压板松动时,位于两侧压板间某段绕组的振动问题．首先,采用分离变量法,给出了发电机运行时定子端部绕组区域的磁感应强度表达式,并给出了绕组所受电磁力及与松动压板间摩擦力的计算式．其次,建立了研究绕组非线性振动问题的力学分析模型,采用多尺度法对主共振情形进行了解析求解,推得了稳态运动下的幅频响应方程,并对定常解的稳定性及分岔奇异性进行了研究,得到了稳定性的判定条件及分岔方程的转迁集．最后,针对工程实际问题进行了计算,给出了相应的幅频响应曲线图,并进行了分析讨论．     

求解资源受限项目调度问题的人工鱼群算法

提出了将人工鱼群算法应用于求解资源受限项目调度问题中的构想,建立了求解资源受限项目调度问题的人工鱼群算法模型,设计了一种标准随机键编码方式,构建了人工鱼的觅食行为、聚群行为、追尾行为和随机行为四种基本算子,采用了正向逆向局部改进技术和精英保留策略,并给出了算法流程。应用PSPLIB标准问题库对该算法进行了大量的测试,并与其他算法进行了比较,验证了该算法的有效性。     

红树林自然保护区湿地生态系统的数学模型及其应用

研究了红树林自然保护区自然环境和人类社会活动对于生态系统的影响,考虑了生物之间的相互关系,将生物量、生物生长的面积等作为主要指标,建立了常微分方程组模型,对生态系统的变化情况进行了描述,借助稳定性分析对方程进行了研究,并进行了数值模拟。根据理论分析和数值模拟的结果,对保护区的林木恢复工作提出了合理的建议。     

一个游戏难题的推广、建模及求解

推广了RPG游戏中的一个难题,建立了相应的数学模型,给出了完善的解决方案,深化了现行的相关结果.     

网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

我国省域人口的时序预测模型的选择——基于预测精度、偏差和不确定性的分析

人口预测作为区域规划和政策决策的依据对于区域经济社会可持续发展有重要理论价值和现实意义.目前已有不少学者使用时序模型进行了人口预测,但从预测精度、偏差和不确定性角度考虑时序模型选择的研究几乎没有.利用ARIMA模型对我国部分具有代表性的省域进行人口预测的基础上,探讨了不同基区间、临界年及预测区间等条件下人口最优时序预测模型选择的一般性规律.研究发现,一些ARIMA模型能提供相对精确的结果,另一些则不能;线性与非线性模型在预测精度上有较大差异;历史数据长短可能导致选择不同的模型;不同精度视角下的模型选择有较强一致性,但也有一定程度的不确定性.     

Modelling and stability analysis in human population genetics with selection and mutation

Population genetics is a scientific discipline that has extensively benefitted from mathematical modelling; since the Hardy‐Weinberg law (1908) to date, many mathematical models have been designed to describe the genotype frequencies evolution in a population. Existing models differ in adopted hypothesis on evolutionary forces (such as, for example, mutation, selection, and migration) acting in the population. Mathematical analysis of population genetics models help to understand if the genetic population admits an equilibrium, ie, genotype frequencies that will not change over time. Nevertheless, the existence of an equilibrium is only an aspect of a more complex issue concerning the conditions that would allow or prevent populations to reach the equilibrium. This latter matter, much more complex, has been only partially investigated in population genetics studies. We here propose a new mathematical model to analyse the genotype frequencies distribution in a population over time and under two major evolutionary forces, namely, mutation and selection; the model allows for both infinite and finite populations. In this paper, we present our model and we analyse its convergence properties to the equilibrium genotype frequency; we also derive conditions allowing convergence. Moreover, we show that our model is a generalisation of the Hardy‐Weinberg law and of subsequent models that allow for selection or mutation. Some examples of applications are reported at the end of the paper, and the code that simulates our model is available online at https://www.ding.unisannio.it/persone/docenti/del-vecchio for free use and testing.     

On the convergence of a factorized distribution algorithm with truncation selection

We investigate the global convergence of a factorized distribution algorithm (FDA) with truncation selection. Like conventional genetic algorithms, FDAs maintain and successively improve a population of solutions. In FDAs, a distribution model is built based on the statistical information extracted from a set of selected solutions in the current population, and then the model thus built is used to generate new solutions for the next generation. The variable‐dependence structure of the distribution model in FDAs is determined by the variable‐interaction structure of the objective function. We prove that the FDA with truncation selection converges globally for optimization of a class of additively decomposable functions (ADF). Our results imply that the utilization of appropriately selected dependence relationships is sufficient to guarantee the global convergence of estimation of distribution algorithms (EDAs) for optimization of ADFs. © 2004 Wiley Periodicals, Inc. Complexity 9: 17–23, 2004     

Numerical integration of fully nonlinear size-structured population models

Characteristics' schemes of second order are introduced for the numerical solution of size-structured population models. The models are fully nonlinear: all the vital functions (growth, mortality and fertility rates) depend on the total population. The schemes are completely analysed: consistency, stability, existence and convergence are established. Some numerical experiments are also reported in order to show numerically the results proved in our analysis and to study the efficiency of a selection nodes technique.     

EFFECTS OF INDIVIDUAL HETEROGENEITY IN ESTIMATING THE PERSISTENCE OF SMALL POPULATIONS

ABSTRACT. Population viability models are commonly used to estimate the probability of persistence of small, threatened, or endangered populations. Demographic, temporal, spatial, and individual heterogeneity are important factors affecting the probability of persistence of small populations. Because stochastic process are intractable analytically (Lud-wig [1996]), computer simulation models are often used for estimating population viability via numerical techniques. Although demographic, spatial, and temporal stochasticity have been incorporated into some population viability models, individual heterogeneity has not been included. In this paper we include individual heterogeneity in a simulation model and examine probabilities of population persistence at different levels of heterogeneity and population size. Individual heterogeneity may increase the probability of persistence of small populations. The mechanism for the extension in persistence may be explained by natural selection. Genotypes persisting through a decline may be those that survive better under the conditions causing the decline. These individuals that survive and reproduce in the face of adverse conditions may extend the probability that a small population persists.     

Mathematical Theory of Phenotypical Selection

A general concept of phenotypical structure over a genotypical structure is developed. The direct decompositions of multilocus phenotypical structures are considered. Some aspects of phenotypical heredity are described in terms of graph theory. The acyclic phenotypical structures are introduced and studied on this base. The evolutionary equations are adjusted to the phenotypical selection. It is proved that if a phenotypical structure is acyclic then the set of fixed points of the corresponding evolutionary operator is finite except for a proper algebraic subset of the operator space. Some applications of this theorem are given.     

A stochastic model for the HIV epidemic in homosexual populations involving age and race

In this paper, we derive a stochastic model for the HIV epidemic in homosexual populations involving age and race. To account for effects of different mixing patterns, a low risk selection rule is introduced. The model is then formulated in terms of chain multinomial distributions by means of which the means are derived. Some simulation studies by computer indicate clearly that age and race have a significant impact on the HIV epidemic.     

阶梯状黄土边坡稳定性分析的改进遗传算法及应用

阶梯状黄土边坡稳定性分析的关键是估算其稳定系数的最小值.稳定系数的求解涉及诸多因素且计算过程繁杂,传统优化算法往往不能有效地搜索到其全局最小解.为此,提出一种改进的自适应遗传算法.算法对基因变量空间进行网格状划分,采用迭代选优法建立均匀分布的初始种群,运用优质个体保留遗传策略,并按照特定的准则自适应地调整交叉概率和变异概率,提高算法的全局搜索能力和收敛速度.实例应用表明算法能够快速有效地收敛于土坡稳定系数的全局最小解,且计算结果与实际情况更加吻合.     

黄冈市人口增长模型的研究

分析了1978年以来黄冈市人口发展的现状,选择黄冈市1978~2004年的总人口统计数据来建立马尔萨斯人口模型和L og istic人口模型,运用2005~2006年的总人口数据来验证模型,并对黄冈市未来8年的总人口数进行了预测.     

基于变动人口的Solow模型

本文在Solow模型框架中引入随时间变动人口增长函数，并假定人口增长率最终趋于零，证明该模型的解是渐近稳定的，收敛于零人口增长率的经典Solow模型的解。通过引入变动人口增长率，讨论人口过渡时期和人口波动对经济增长的影响，并给出数值计算结果。