一类具有两阶段结构同类相食模型的动力学分析

本文在假定成年个体会对幼年个体进行同类捕食和考虑幼年个体自然死亡的基础上,建立了一类具有两阶段结构的同类相食模型.当种群不存在同类捕食时,通过构造Lyapunov函数分别得到了种群灭绝平衡点和种群存活平衡点的全局渐近稳定的条件.对于种群存在同类捕食的情形,发现模型会同时存在两个种群存活平衡点和发生鞍结点分支,并通过构造...     

一类具有阶段结构的传染病模型的全局分析

考虑疾病仅在成年个体间传播,并且成年个体的增长受到密度制约,本文建立了一类具有双线性发生率和阶段结构的传染病模型．文中得到了种群增长的基本再生数和疾病传播的基本再生数,通过构造Lyapunov函数证明了平衡点的全局稳定性,通过数值模拟验证了所获得的结果．结果显示,两类基本再生数完全确定了模型的动力学性态,通过降低传染率和增大染病者移除率可以降低疾病基本再生数．     

一类具有Beverton-Holt出生函数的阶段结构传染病模型的全局分析

针对一些疾病仅在成年个体间传播和成年个体的成长受到密度制约等因素,建立了一类具有幼年和成年两个阶段且疾病仅在成年个体间传播的传染病模型,其中以具有饱和性质的Beverton-Holt函数作为幼年出生函数．通过构造恰当的Lyapunov函数和定性分析,得到了模型的全局动力学性态,并确定了决定模型动力学性态的种群存活的基本再生数和疾病传播的基本再生数．所得结果表明：当种群的基本再生数不大于 1 时,种群灭绝;当种群的基本再生数大于 1 而疾病传播的基本再生数不大于 1 时,种群持续生存而疾病灭绝;当疾病传播的基本再生数大于 1 时,种群持续存活且疾病会发展成地方病．     

一类具有交叉传染的流行病接种模型

通过对一类具有交叉传染的流行病接种模型进行分析，借助李雅普诺夫函数和Krasnoselakii技巧，得到结论：若该模型仅存在无病平衡点，则无病平衡点是全局渐近稳定的；若该模型有地方病平衡点存在，则无病平衡点是不稳定的，而正平衡点是渐近稳定的。     

一个捕食者染病、食饵具有阶段结构的生态 - 流行病模型的稳定性

研究了一个捕食者染病且食饵具有阶段结构的生态 - 流行病模型的稳定性,考虑了捕食者对食饵的 Holling-II 型功能性反应函数,并讨论了由捕食者的妊娠期引起的时滞对模型稳定性的影响。通过计算特征方程的特征值,运用 Hurwitz 判定定理,得到了该模型的在平凡平衡点、捕食者灭绝平衡点、无病平衡点和正平衡点的局部稳定性,得到了正平衡点处存在 Hopf 分支的充分条件。通过构造 Lyapunov 泛函,运用 LaSall 不变集原理得到了该模型的平凡平衡点、捕食者灭绝平衡点、无病平衡点和正平衡点全局稳定的充分条件。     

具有非线性传染率的两类传染病模型的全局分析

讨论了两类带有非线性传染率的SIS型和SIRS型传染病模型,得到了各类平衡点存在的阈值条件。借助构造Dulac函数和Liapunov函数,找到了各类平衡点全局渐近稳定的充要条件。     

一类带有毒素生产的恒化器模型的定性分析

讨论了一类带有毒素生产的恒化器模型,获得了模型各类平衡点存在及稳定的充要条件,通过构造Dulac函数和Lyapunov函数和运用极限系统理论,证明了该模型符合竞争排斥原理,并且得到了各类微生物绝灭的完整分析结果。     

一类具有非线性发生率的SEIR传染病模型的全局稳定性分析

本文对一类具有非线性发生率的SEIR传染病模型进行了研究.确定了决定疾病灭绝或持续存在的阈值-基本再生数,并分析了模型的平衡点的存在性;通过构造恰当的Lyapunov函数,运用La Salle不变性原理证明了当基本再生数小于或等于1时,无病平衡点是全局渐进稳定的;利用Lyapunov直接方法证明了当基本再生数大于1时,地方病平衡点是全局渐进稳定的.最后,将发生率具体化用数值模拟验证了所得理论分析结果的正确性.     

一类具有垂直传播的HIV模型的稳定性分析

根据艾滋病的传播规律,本文建立了一类传染病模型.在模型中,HIV携带者分为幼年和成年两类,HIV可垂直传染,艾滋病患者有额外死亡.我们用再生矩阵求出了模型的基本再生数,并得出当基本再生数小于1时,模型只有无病平衡点,而当基本再生数大于1时,模型还有地方病平衡点.最后,应用第二加性复合矩阵等理论,文中证明了各平衡点全局渐近稳定性.     

捕食者有病的生态-流行病SIS模型的分析

建立并分析了捕食者具有疾病的生态一流行病SIS模型,讨论了解的有界性。应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步,分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。     

一类含多时滞和扩散项的非标准离散模型

建立了一类以媒体效应作为主要预防传染病传播手段、并且含有多时滞和扩散项的传染病连续模型,并证明了该连续模型平衡点的全局稳定性。其次,利用非标准有限差分方法对该连续模型进行离散,离散后的模型具有和原连续模型一致的动力学性质。通过构造适当的李雅普诺夫函数,证明离散模型的平衡点在一定条件下也都是全局渐近稳定的。最后,数值模拟验证了理论结果。     

Modeling phase equilibria in polymer-solvent systems for process design

An excess Gibbs energy model is presented for calculating phase equilibria in multicomponent systems containing polymers and solvents. The model represents a combination of a physical contribution obtained from a lattice model and a chemical contribution that accounts for association and solvation effects. The lattice model is based on a revised version of Freed's latticc-field theory developed by Hu, Prausnitz, and co-workers. The model accurately represents solvent activities and liquid-liquid equilibria in binary and ternary polymer solutions over wide ranges of temperature and polymer molecular weight. It is capable of reproducing liquid-liquid equilibria with upper and lower critical solution temperatures as well as closed-loop and hourglass-shaped phase diagrams. Because of its numerical simplicity, a reasonably small number of binary parameters, and its applicability to multicomponent systems, the model cm be useful for modeling industrial processes involving polymers.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Sorption and desorption of lead (II) from wastewater by green algae Cladophora fascicularis

Biosorption is an effective method to remove heavy metals from wastewater. In this work, adsorption features of Cladophora fascicularis were investigated as a function of time, initial pH, initial Pb(II) concentrations, temperature and co-existing ions. Kinetics and equilibria were obtained from batch experiments. The biosorption kinetics followed the pseudo-second order model. Adsorption equilibria were well described by the Langmuir and Freundlich isotherm models. The maximum adsorption capacity was 198.5 mg/g at 298K and pH 5.0. The adsorption processes were endothermic and the biosorption heat was 29.6 kJ/mol. Desorption experiments indicated that 0.01 mol/L Na(2)EDTA was an efficient desorbent for the recovery of Pb(II) from biomass. IR spectrum analysis suggested amido or hydroxy, CO and C-O could combine intensively with Pb(II).     

具有一般传染率的 SIRS 年龄结构模型的分支研究

考虑到年龄在一些传染病流行过程中的重要影响,建立了一个具有一般传染率的 SIRS 年龄结构仓室模型。通过将模型改写为抽象柯西问题并利用 Hille-Yosida 算子相关定理,分析了模型的动力学性态,讨论了平衡点的稳定性以及平衡点失稳时产生 Hopf 分支的条件。结果表明,当基本再生数小于 1 时,免疫年龄不影响无病平衡点的全局稳定性;当基本再生数大于 1 时,免疫年龄扰动导致地方病平衡点的稳定性改变,从而产生 Hopf 分支。同时,数值模拟验证了理论结果并显示了免疫年龄对模型动力学性态的影响。     

Yield and control in a supplier-customer relationship

This paper considers the problem of yield production and the mutual sampling policies of a supplier and a customer. It is assumed that the parties do not cooperate and construct a random payoff game where, in addition to sampling, the supplier may choose a yield (a function of the production technology). Given binding contract parameters between the customer and the supplier, a solution of the game, which assumes risk neutrality, is shown to lead to two equilibria. These equilibria are discussed and contrasted with current approaches in the application of quality assurance inspection plans. Finally, yield optimization by the supplier in each of the equilibria will lead to the selection of a unique solution which will induce the customer not to sample at all or sample with a probability given in terms of the contract parameters of the problem.     

带有种群密度制约接触率的SIR流行病模型的全局分析

本文研究了两类具有种群密度制约接触率的SIR流行病模型,其生态学结构分别为常数输／Logistic出生。可以证明两模型均存在在强阈值现象,阈值参数即模型的基本再生数,它决定了疾病的绝灭和流行也决定了模型的全局性态。为了证明地方病平衡点的全局稳定性,对具有常数输入的SIR模型,引入了一个变量代换将三维模型转化为具有极限方程的二维渐近自治系统;对具有Logistic出生的SIR模型,构造了Lyapunov函数。     

Static buckling and actuation of free-standing mesoscale beams

We discuss the static buckling and actuation of free-standing mesoscopic beams. As the length-to-width aspect ratio of the beams is increased, the buckled shapes become more complex. Mechanical actuation confirms that the complex shapes are stable equilibria and that metastable equilibria also exist. This is consistent with a nonlinear elastic continuum model, which incorporates asymmetry in higher order buckling modes. Preliminary results indicate that, in addition to purely mechanical actuation, electromechanical mode-mode transitions can be induced by utilizing fabricated electrodes.