两极端值模型的比较和应用

极端值模型主要有分块样本极大值模型和阈顶点模型.从两模型极值分布的内在关系、尾部特征的角度作比较分析和证明.结果表明,它们的内在关系一致;随着形状参数的变化尾部各有不同特征,阈顶点模型更为具体和多样,更适合金融风险度量的应用.     

时间序列问题的建模方法和过程

时间序列分析是研究经济学和统计学的一种重要方法,通过分析实际的时间数据序列进行建立数学模型,用来预测序列的未来的发展情况。本文介绍了时间序列的发展概况和基本概念,论述了ARMA模型的自协方差函数、自相关系数、偏自相关函数的特征和Box-Jenkins建模。Box-Jenkins建模方法一般包括模型识别、参数估计、模型适用性检验和预测等步骤,该模型主要运用于单变量、同方差场合的线性模型。通过对模型的进一步研究,明确了模型的定阶与参数估计等问题。     

带有分段常数变量和避难所的天敌一害虫模型的稳定性和分支行为

研究一类带有分段常数变量和避难所的天敌-害虫模型的稳定性和分支行为.首先通过计算转化得到天敌-害虫模型对应的差分模型,利用线性稳定性理论讨论了正平衡态局部渐近稳定的充分条件.其次以害虫种群的内禀增长率或逃脱率为分支参数,利用分支理论研究了模型正平衡态处产生翻转分支周期解和Neimark-Sacker分支周期解的充分条件;并且使用正规形理论和中心流形定理构造了判断分支周期解稳定性的阈值.最后数值模拟验证了理论分析的正确性,并展示了该模型复杂的动力学行为.     

考虑投入和产出指标偏好的广义DEA模型

广义DEA是一种基于决策单元和非决策单元自由选择参考集的扩展DEA模型.传统DEA模型的最优解大多是由线性规划随机计算的,未能充分考虑投入和产出指标的重要程度.将投入和产出指标的决策者偏好引入到广义DEA模型约束条件中,首先定义投入和产出指标偏好矩阵,再将该矩阵纳入广义DEA模型的约束条件,构建了带投入和产出指标偏好的广义DEA模型(GDEA-IP).接下来给出决策单元GDEA-IP有效性与评价指标的量纲选择无关性的证明,以及决策单元为GDEA-IP弱有效和有效的理论证明.算例分析说明GDEA-IP模型的有效性,通过和其它经典模型的对比分析,进一步说明该模型比广义DEA模型具有更大的灵活性和通用性,拓展了DEA方法的理论研究.     

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.     

相关风险和模型的破产概率

本文研究了两险种理赔到达过程相关的正风险和模型与负风险和模型.利用Lundberg指数是相关因子的单调递减函数的性质,证明了破产概率是随着相关因子的增加而增大的,从而将相应的结果推广到了两险种理赔到达过程相关的风险和模型.     

钢管的订购和运输解答模型

首先通过最短路算法简化了供需距离网络 ,去掉了铁路、公路等边的性质 ,使供需距离网络简化为一个供需运输价格表 .在此基础上构造了三个模型 :线性费用的网络流模型、改进的线性费用的网络流模型和具有非线性费用的网络流模型 .通过改进传统的最小费用最大流算法 ,解决了本题的非线性费用网络流模型 ,并给出了算法的正确性证明与复杂度分析     

带有标准发生率和信息干预的随机SIRS传染病模型的灭绝性和平稳分布

本文考虑了一类具有标准发生率和信息干预的随机SIRS传染病模型.定义了一个停时,通过构造适当的Lyapunov函数证明了停时为无穷大,从而证明了该模型唯一正解的全局存在性.通过构造紧集和适当的Lyapunov函数,证明模型解的平稳分布的存在性及其遍历性.此外还证明了疾病的灭绝性.     

一类具有垂直传染和预防接种的SEIR传染病模型

建立并分析了一类具有垂直传染和预防接种的SEIR传染病模型,得到了该模型的基本再生数.通过对基本再生数的讨论和分析,得到了该模型的平衡点的稳定性和持续性.     

CML模型和湍流的非线性

本文在现有耦合映射格点（ＣＭＬ）动力系统模型的基础上，提出了能够同时模拟对流项和扩散项的强弱耦合系统的ＣＭＬ模型，分析了这类模型的特点和结构·数值试验表明，这类ＣＭＬ模型能够有效地研究时空复杂性，利用数值模拟的结果对湍流的物理机制作了初步的阐释·     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性

对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续（而非已有的大部分文献中假设是Sigmoid函数）的条件下,通过构造适当的泛函,给出了这类模型全避吸引和平衡点全局指数稳定的易于验证的充分条件。     

基于Agent与分解协调的综合生产计划研究

以作业单元为局部决策Agent,车间管理者为全局协调Agent,引入生产节点间的内部结算价格,基于多Agent系统,建立了综合生产计划的分布式决策模型.通过将局部Agent决策目标的总和与全局Agent决策目标进行对比,证明了所引入的内部结算价格就是全局Agent目标函数关于物流平衡约束的Lagrange乘子.基于Lagrange分解协调原理,设计了局部作业单元Agent和全局协调Agent的迭代协调算法.该迭代算法以上次计算的中间结果作为对其它作业单元生产需求的估计,从而能将各个生产单元Agent的决策模型分离,实现了分布建模与求解.在算例研究中使用启发式规则来确定Lagrange乘子迭代的步长系数,保证了较好的收敛性,证明模型和算法是有效的.     

Dynamical modeling and attitude analysis for the spacecraft with lateral solar arrays

The dynamics and attitude motion of the three-axis stabilized spacecraft installed with lateral solar arrays is investigated in terms of the rigid-flexible coupled global modes of the system. The spacecraft consists of a rigid platform with small moment of inertia and two groups of flexible solar arrays with relatively large moment of inertia installed on the rigid rotation shafts. The rigid-flexible coupled dynamic model of the spacecraft is established by using the Hamiltonian Principle. The global mode method is employed to work out the natural frequency and global modal shapes of the rigid-flexible coupled dynamic model combined with corresponding boundary conditions. To validate the effectiveness of the analytical results obtained by global mode method, the natural frequencies and mode shapes obtained from finite element model using MSC.Patran software are used as a reference. A numerical example is given to show that the results obtained from both methods are matched very well (the relative errors of the corresponding frequencies are small enough) and the rigid motion of the platform is coupled with the vibration mode of the flexible solar arrays. This implies that the global analytical modes can be used to accurately describe the rigid-flexible coupled motion of the spacecraft. By comparing with the finite element model, the reduced dynamical model derived in terms of the global modes of the system has a lower dimension. Numerical simulations for the system with variations of parameters and dynamic responses analysis for different applied forces are performed to illustrate that, the characteristics of the model are affected by inner and external factors.     

大气变暖对气候状况影响的分析及预测

以地球大气变暖海平面升高为背景,对近几十年CO2排放量上升引起气温升高,气温升高引起海平面上升分别建立了数学模型,同时针对美国佛罗里达州的气候状况进行分析,预测几十年后的海平面上升对大陆面积的影响.     

The persistence and global attractivity in general nonautonomous discrete single-species Kolmogorov model with delays

In this paper, general nonautonomous discrete-time single-species Kolmogorov model with delays is studied. Some sufficient conditions on the boundedness, persistence, permanence and global attractivity of solutions are established. As application, the discrete time nonautonomous delayed Allee-effect model is discussed. The sufficient conditions on the permanence and global attractivity are obtained.     

一类带有一般接触率和常数输入的流行病模型的全局分析

借助极限系统理论和构造适当的Liapunov函数，对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病输入时，地方病平衡点存在的阈值被找到．对相应的SIR模型，关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件；对相应的SIRS模型．得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病输入时，模型不存在无病平衡点．对相应的SIR模型，地方病平衡点是全局渐近稳定的；对相应的SIRS模型，得到地方病平衡点全局渐近稳定的充分条件．     

Coexistence and Asymptotic Periodicity in a Competition Model of Plankton Allelopathy

In this paper, the two species Lotka-Volterra competition model of plankton allelopathy from aquatic ecology is discussed. The authors study the existence of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions and consider the existence, stability and global attractivity of time-periodic solutions for a coupled parabolic equations in a bounded domain. Their results show that this model possesses at least one coexistence state if cross-diffusions and self-diffusions are weak. The existence of the positive T-periodic solutions and the global stability as well as the global attractivity for the parabolic system are also given.     

Partial hybrid finite elements for composite laminates

Three types of partial hybrid finite elements are presented in order to set up a global/local finite element model for analysis of composite laminates. In the global/local model, a composite laminate is divided into three different regions: global, local, and transition regions. These are modeled using three different elements. In the global region, a 4-node degenerated plate/shell element is used to model the overall response of the composite laminate. In the local region, a multilayer element is used to predict detailed stress distribution. In the transition region, a multilayer transition element is used to smoothly connect the two previous elements. The global/local finite element model satisfies the compatibility of displacement at the boundary between the global region and the local region. It also satisfies the continuity of transverse stresses at interlaminar surfaces and traction conditions on the top and bottom surfaces of composite laminates. The global/local finite element model has high accuracy and efficiency for stress analysis of composite laminates. A numerical example of analysis of a laminated strip with free edge is presented to illustrate the accuracy and efficiency of the model.     

Existence and stability of global solutions for a cross-diffusion predator-prey model with sex-structure

By means of the energy estimates and the bootstrap arguments, this thesis investigates the global existence of solutions for a cross-diffusion predator-prey model with sex-structure when the space dimension is less than ten. Furthermore, by constructing a Lyapunov function, the sufficient condition of global asymptotic stability of the positive equilibrium point for the model is given.