Qualitative analysis on an SIRS reaction–diffusion epidemic model with saturation infection mechanism

In this paper, we deal with an SIRS reaction–diffusion epidemic model with saturation infection mechanism. Based on the uniform boundedness of the parabolic system, we investigate the extinction and persistence of the infectious disease in terms of the basic reproduction number. To better investigate the effects of infection mechanism and individual diffusion, we further analyze the asymptotic profiles of the endemic equilibrium for small or large motility rate and large saturation rate. In particular it is shown that large saturation may cause the elimination of disease. Our study may provide some significant useful insight on disease control and prevention.     

全内反射式衍射光栅近场光学特性

 利用傅里叶模式理论分析了具有高衍射效率的全内反射式衍射光栅在TE 和TM偏振态下的近场光分布特点,讨论了光栅结构参数以及入射角度对光栅内电场增强的影响。结果表明：全内反射光栅内部电场分布对偏振态较敏感,光栅槽深和占宽比对电场增强影响较小,光栅内的峰值电场随光栅周期增大而增大,并且峰值电场随着入射角度的增大而减小。在应用于高功率激光时,降低光栅内部的电场增强可以有效降低损伤风险。     

交货期差异下的双渠道订货与协调优化策略

由于顾客往往具有不同交货期的期望,从而导致线上与线下渠道冲突加剧,同时也为其进行合作提供了基础。因此针对该问题,以一个开辟线上渠道的制造商和一个线下零售商组成的双渠道供应链系统为研究对象,分别建立了考虑交货期差异下二者合作时的利润优化模型。在此基础上,首先采用不动点定理证明了制造商开辟的线上渠道与线下零售商订货纳什均衡的存在性与唯一性,并探讨了二者均衡订货量与交货期差异率的关系;其次,证明了仅仅采用批发价格与服务费用契约无法协调制造商与线下零售商组成的供应链系统,进一步优化设计了两部定价协调机制,并实现二者的双赢。最后通过算例证明了纳什均衡的存在性以及订货均衡与交货期差异率的关系。     

General construction of mean-field potential and its application to the multiphase equations of state of tin

The mean-field potential (MFP) approach is an efficient way to evaluate the free energy contribution of ion motions for both solid and liquid states. In this paper the MFP is generally constructed with a volume-dependent term and a shape function. The former is derived in accordance with quasi-harmonic approximation. The latter is given semi-empirically. Application to multiphase equations of state for β-, γ- and liquid-tin has been examined. The theoretical phase diagram and thermodynamic properties of isotherm, thermal expansion, heat capacity, Hugoniot states as well as phase transitions are all in excellent agreement with experiments.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

多重积分Nash平衡点的Lipschitz估计

设F（p，q）和G（p，q）在无穷远点的邻域内是分别关于p和q的近似凸函数，且具有二次增长．考虑由F和G构成的一对定义在Soblev空间中的泛函．本文利用blowup技巧，证明了这样一对泛函的Nash平衡点实际上是Lipschitz连续的．     

Generalized Equilibrium Problems and Generalized Complementarity Problems

From a general minimax inequality or an abstract lopsided saddle-point theorem, we deduce general Karamardian-type equilibrium theorems and generalized complementarity theorems. Our new results extend a number of well-known earlier works of many authors.     

Formulation,Stability, and Computation of Traffic Network Equilibria as Projected Dynamical Systems

In this paper, we present a unified treatment and analysis of a dynamic traffic network model with elastic demands formulated and studied as a projected dynamical system. We propose a travel route choice adjustment process that satisfies the projected dynamical system. Under certain conditions, stability and asymptotical stability of the equilibrium patterns are then derived. Finally, two discrete-time algorithms, the Euler method and the Heun method, are proposed for the computation of the solutions, and convergence results established. The convergence results depend crucially on stability analysis. The performance of the algorithms is then illustrated on several transportation networks.     

一类稀疏效应下捕食┐被捕食者系统极限环的存在性和唯一性

本文研究捕食者种群具有线性密度制约的一类稀疏效应下捕食－被捕食者系统ｘ＝ｘ（ａｘ－ｃｘ３－ｂｙ），ｙ＝ｙ（－α＋βｘ－γｙ）．（＊）得到：（１）当Ａ１＜Ａ１，Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在极限环；（２）当Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在唯一极限环