一般交叉规划与经济均衡模型

本文首先给出了有多个子规划的一般交叉规划模型,然后把它转化为抽象经济模型,并给出其均衡解存在的条件.最后利用一般交叉规划建立了一类非合作型寡头垄断市场的均衡模型.     

效用函数与纳什均衡

本文引入效用函数将博弈问题描述为收入形式和效用形式两种模型,使得纳什均衡与参与人效用函数联系起来,并得到结论(1)效用函数的变化对纯策略纳什均衡不产生影响,却改变真混合策略纳什均衡;(2)效用函数严格拟凹时,真混合策略蚋什均衡是稳定的;(3)效用函数严格拟凸时,真混合策略纳什均衡不存在.     

On a game in manufacturing

We analyse a non-zero sum two-person game introduced by Teraoka and Yamada to model the strategic aspects of production development in manufacturing. In particular we investigate how sensitive their solution concept (Nash equilibrium) is to small variations in their assumptions. It is proved that a Nash equilibrium is unique if it exists and that a Nash equilibrium exists when the capital costs of the players are zero or when the players are equal in every respect. However, when the capital costs differ, in general a Nash equilibrium exists only when the players' capital costs are high compared to their profit rates.     

Two New Solutions of Non-constant-α Force-Free Magnetic Field

Two new solutions for non-constant-α force-free magnetic field are found analytically. Implications of the results to astrophysical solar plasmas as well tokamak plasmas are discussed.     

Evolution analysis of the states of the EZ model

Based on suitable choice of states, this paper studies the stability of the equilibrium state of the EZ model by regarding the evolution of the EZ model as a Markov chain and by showing that the Markov chain is ergodic. The Markov analysis is applied to the EZ model with small number of agents, the exact equilibrium state for N = 5 and numerical results for N=18 are obtained.     

Temperature Dependence of the Back-Stress in Shear for Glassy Polycarbonate

Summary: Back-stress is the equilibrium stress and represents conditions under which relaxation events in the material stop and the material can carry an applied load indefinitely without a change in strain. In most models for glassy polymers, back-stress plays a central role since relaxation in materials is closely related to the distance of the current conditions from equilibrium. A number of these models that are commonly used for modeling glassy polymers use a modeling structure similar to large deformation plasticity. The flow rule for the plastic strain in these models are directly connected to the “over-stress,” a properly invariant difference between the stress and the back-stress. The importance of correctly evaluating the back-stress to use in these models is clear. For this class of models, the authors have recently developed a method for directly calculating the back-stress under shear deformations. This method is based on evaluating the slope of the stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since plastic flow goes to zero at equilibrium, the back-stress can be found by locating points of zero plastic strain rate. Using the proposed method, the back-stress in glassy polycarbonate has been evaluated under shear in isothermal tests going from room temperature to 120 °C, just below the glass transition temperature for polycarbonate. The proposed method provided a full map of the back-stress for polycarbonate over a large range of shear strain and temperature.     

具有扩散影响的Hopfield型神经网络的全局渐近稳定性

对具有扩散影响的Hopfield型神经网络平衡点的存在唯一性和全局渐近稳定性进行了研究．在激活函数单调非减、可微且关联矩阵和Liapunov对角稳定矩阵有关时,利用拓扑度理论得到了系统平衡点存在的充分条件．通过构造适当的平均Liapunov函数,分析了系统平衡点的全局渐近稳定性．所得结论表明系统的平衡点(如果存在)是全局渐近稳定的而且也蕴含着系统的平衡点的唯一性．     

Yukawa流体的相平衡和界面张力研究

应用二阶微扰理论, Duh-Mier-Y-Teran状态方程和在平均球近似(mean spherical approximation, MSA)的基础上获得的直接相关函数, 建立了适用于均匀流体和非均匀流体的状态方程. 结合此状态方程, 重整化群理论(renormalization group theory, RG)和密度泛函理论(density functional theory, DFT), 分别研究了Yukawa流体的相平衡和界面张力. 结果与分子模拟数据吻合良好.     

局部G-凸空间内的广义矢量拟平衡问题

在局部G-凸空间内引入和研究了几类广义矢量拟平衡问题(GVQEP)．包含了大多数广义矢量平衡问题,广义矢量变分不等式问题,拟平衡问题和拟变分不等式问题作为特殊情形．首先在局部G-凸空间内对一人对策证明了一个平衡存在性定理．作为应用,在非紧局部G-凸空间内对GVQEP的解建立了某些新的存在定理．这些结果和论证方法与最近文献中的结果和论证方法相比较是新的和完全不同的．     

烷烃加和型性质的拓扑同系递变规律研究

用分子中原子的平衡电负性对分子图进行着色, 在距离矩阵的基础上结合分子中各原子的支化度构建一组拓扑指数ND, 它对分子结构实现唯一性表征, 具有优良的结构选择性, 用ND指数对链烷烃的加和型性质及同系递变规律进行研究, 结果表明烷烃加和型性质P可用下式来定量描述: P＝aND₁＋bND₂＋cND₃＋d, 其中a, b, c, d为常数. 用该式对85种链烷烃的标准生成焓Δ_fH^ө_m, 标准熵Δ_fS^ө_m, 标准生成吉布斯自由能Δ_fG^ө_m及67种链烷烃的摩尔体积V_m, 摩尔折射度R_m进行预测, 预测值与实验值吻合良好.