Exponential Convergence to Equilibrium for Kinetic Fokker-Planck Equations

A class of linear kinetic Fokker-Planck equations with a non-trivial diffusion matrix and with periodic boundary conditions in the spatial variable is considered. After formulating the problem in a geometric setting, the question of the rate of convergence to equilibrium is studied within the formalism of differential calculus on Riemannian manifolds. Under explicit geometric assumptions on the velocity field, the energy function and the diffusion matrix, it is shown that global regular solutions converge in time to equilibrium with exponential rate. The result is proved by estimating the time derivative of a modified entropy functional, as recently proposed by Villani. For spatially homogeneous solutions the assumptions of the main theorem reduce to the curvature bound condition for the validity of logarithmic Sobolev inequalities discovered by Bakry and Emery. The result applies to the relativistic Fokker-Planck equation in the low temperature regime, for which exponential trend to equilibrium was previously unknown.     

Improved Duality Estimates and Applications to Reaction-Diffusion Equations

We present a refined duality estimate for parabolic equations. This estimate entails new results for systems of reaction-diffusion equations, including smoothness and exponential convergence towards equilibrium for equations with quadratic right-hand sides in two dimensions. For general systems in any space dimension, we obtain smooth solutions of reaction-diffusion systems coming out of reversible chemistry under an assumption that the diffusion coefficients are sufficiently close one to another.     

Subgame-perfection in free transition games

We prove the existence of a subgame-perfect ε-equilibrium, for every ε > 0, in a class of multi-player games with perfect information, which we call free transition games. The novelty is that a non-trivial class of perfect information games is solved for subgame-perfection, with multiple non-terminating actions, in which the payoff structure is generally not (upper or lower) semi-continuous. Due to the lack of semi-continuity, there is no general rule of comparison between the payoffs that a player can obtain by deviating a large but finite number of times or, respectively, infinitely many times. We introduce new techniques to overcome this difficulty.     

Competition among non-life insurers under solvency constraints: A game-theoretic approach

We formulate a noncooperative game to model competition for policyholders among non-life insurance companies, taking into account market premium, solvency level, market share and underwriting results. We study Nash equilibria and Stackelberg equilibria for the premium levels, and give numerical illustrations.     

供应链计划建模中的博弈方法

基于供应链管理思想,针对供应链上下游的主要合作伙伴关系,建立一种基于协商的上下游合作计划模型·根据外界情况(如价格、库存等因素),确定企业与战略伙伴的合作关系·在合作计划模型的基础上,分别讨论了动态博弈的纳什均衡理论和协商对策理论在模型中的应用·指出供应链的上下游合作企业达到"双赢"目标的条件及可行性·结果表明,非合作博弈体现了一种个人理性,而协商对策满足个人和群体合理性·仿真验证了模型和算法的有效性·     

随机均值短期利率期限结构模型与均衡

介绍了Tice和Webber给出的一类多因子随机均值短期利率期限结构模型·通过引入仿射变换函数,把相应的期限结构模型推广为仿射的多因子期限结构模型,使期限结构模型的适用范围更加广泛·并证明了扩展到开放经济条件下的宏观经济均衡模型(IS LM BP)是一族仿射的三因子随机均值短期利率期限结构模型的特例·此结果不仅给出了随机均值短期利率期限结构模型的一种经济解释,而且也说明了通过随机均值短期利率期限结构模型可以解决一系列的宏观经济问题·     

一种前馈控制混沌的方法

提出一种前馈控制混沌的方法.通过选取合适的前馈时间或控制系数,可将混沌系统稳定到平衡态.该方法用于控制Chuas混沌电路和混沌的Lorenz系统,仿真结果验证了其有效性.     

环境资本与人力资本的纳什均衡动态机制

在纳入人力资本因素所建立的两种资本(物质资本和人力资本)的内生经济增长模型基础上,将环境的外部有效性引入模型,考察利用划分有限边界情况下,同一代人产生的环境矛盾和各代人之间产生的环境矛盾对人力资本形成产生的影响.采用一个世代交叠模型研究环境和人力资本的纳什动态机制,推出了均衡的一般形式及简化形式,并考察了均衡路径的特征及经济含义.结果表明,自由放任的经济是否停滞、增长或衰退,取决于环境资本和人力资本学习回报的情况,经济的最初状态,以及环境产品和消费品的价格.     

收费公路和公共交通之间的定价博弈分析

研究了收费公路和公共交通的定价博弈问题.运用博弈论的模型和方法,在自由竞争和充分合作的情况下分别建立了两者间的定价模型;探讨了在自由竞争的情况下公路收费和公交票价达到的均衡状态,以及在多种政府政策下均衡状态的变化,同时分析了运营者相互合作下的公路收费和公交票价.结论表明,在自由竞争的情况下,政府税收对最优均衡定价没有影响,在固定出行需求的情况下,政府对公交进行补贴会导致两者的定价上升.     

应用数学方法 深化化学认知——以高中阶段速率平衡的常见结论的证明为例

选取了在高中课堂教学中出现的关于速率平衡的几个常见的结论,以阿伦尼乌斯公式为模型讨论了温度对反应速率的影响;推导并梳理了反应物转化率随投料量的变化关系;基于浓度商的单调性证明了平衡状态的"殊途同归"结论在数学上的合理性.在加深对常见结论认识的同时,通过对证明过程中应用的数学方法的总结,实现对几个相似化学问题证明方法的统...