一类带有潜伏期和部分免疫的传染病模型的全局分析

通过假设被接种者具有部分免疫,建立了一类具有潜伏期和接种的SEIR传染病模型,借助再生矩阵得到了确定此接种模型动力学行为的基本再生数.当基本再生数小于1时,模型只有无病平衡点;当基本再生数大于1时,除无病平衡点外,模型还有唯一的地方病平衡点.借助Liapunov函数,证明了无病平衡点和地方病平衡点的全局稳定性.     

Advertising in a Differential Oligopoly Game

We illustrate a differential oligopoly game where firms compete à la Cournot in homogeneous goods in the market phase and invest in advertising activities aimed at increasing the consumers reservation price. Such investments produce external effects, characterizing the advertising activity as a public good. We derive the open-loop and closed-loop Nash equilibria, and show that the properties of the equilibria depend on the curvature of the market demand function. The comparative assessment of these equilibria shows that the firms advertising efforts are larger in the open-loop equilibrium than in the closed-loop equilibrium. We also show that a cartel involving all the firms, setting both output levels and advertising efforts, may produce a steady state where the social welfare level is higher than the social welfare levels associated with both open-loop and closed-loop noncooperative settings.     

不确定条件下可可耗竭资源与可再生资源的博弈分析

能源是经济可持续发展的重要的物质基础.在能源开发时间路径上,不可再生资源面临资源储量的约束,可再生资源面临技术水平的约束.R&D投资可以促进技术进步.但是不论是可耗竭资源的储量还是技术进步水平都具有很大的不确定性.就此情形构建了基于两类能源的生产者利润最大化为目标的随机动态微分博弈,研究不确定性对能源市场均衡的影响.     

农户生产合作博弈模型

合作是广大分散的小规模经营的农户进入市场、改善自身经济地位的有效途径。本文从农户之间相互作用、相互影响的角度出发，用博弈模型对农户之间合作的动机和制约因素进行了合理的解释。结果表明：一次性博弈和重复博弈无法使农户摆脱合作失败的困境，引入激励机制，成立农户自愿参加的合作组织是适合我国国情的农户合作之路。     

成本约束下不可再生资源开采微分对策问题研究

研究开采成本等重要因素对不可再生资源开采的影响.假定有N个厂商对不可再生资源进行开采,其面临的市场需求价格弹性为常数,开采成本是开采量的线性函数.利用微分对策理论,分析该寡头市场中各个厂商的均衡开采策略.研究表明,开采成本对是否开采、开采速度、结束时点等有重要影响.同时,本文还与某些经典论文进行了简要比较.     

促进技术成果转化长期合作的重复博弈分析

本通过对目前中国技术创新工程中。国内技术市场成果转化过程的分析，利用重复博弈的方法进行分析。提出了建立长期合作的成果转化机制，大大有利于提高技术成果的技术含量及其转化的程度，促进研制技术成果的科研院所与利用技术成果创造效益的企业的共同发展。     

网格状有向图上的部分合作对策

本文通过在有向图上每个状态结点处定义合作函数,运用Berge C的关于图匕对策中策略的概念,在网格状有向图上考察部分合作动态对策.局中人在对策进程中将采取部分合作而不是完全合作,部分合作的主要特征是每个局中人的行为是合作行动与单独行动的组合.本文合作函数的设定允许局中人加入某个联盟之后再脱离该联盟,同时给出了有向图上部分合作对策的值、最优路径的算法及示例.     

一类竞争——合作生态模型平衡点的渐近稳定性

研究一类竞争-合作生态数学模型平衡点的渐近稳定性,得到了一组保证平衡点渐近稳定的充分条件.     

On an Alternative Parameterization of the Solutions of the Partial Realization Problem

The solutions of the partial realization problem have to satisfy a finite number of interpolation conditions at . The minimal degree of an interpolating deterministic system is called the algebraic degree or McMillan degree of the partial covariance sequence and is easy to compute. The solutions of the partial stochastic realization problem have to satisfy the same interpolation conditions and have to fulfill a positive realness constraint. The minimal degree of a stochastic realization is called the positive degree. In the literature, solutions of the partial realization problem are parameterized by the Kimura–Georgiou parameterization. Solutions of the partial stochastic realization problem are then obtained by checking the positive realness constraint for the interpolating solutions of the corresponding partial realization problem. In this paper, an alternative parameterization is developed for the solutions of the partial realization problems. Both the solutions of the partial and partial stochastic realization problem are analyzed in this parameterization, while the main concerns are the minimality and the uniqueness of the solutions. Based on the structure of the parameterization, a lower bound for the positive degree is derived.     

Optimal Ordering Policy for Deteriorating Items with Partial Backlogging under Permissible Delay in Payments

In 1985, Goyal developed an Economic order quantity (EOQ) model under conditions of permissible delay in payments. Jamal et al. then generalized Goyal’s model for deteriorating items with completely backlogging. However, they only ran several simulations to indicate that the total relevant cost may be convex. Recently, Teng amended Goyal’s model by considering the difference between unit price and unit cost, and provided an alternative conclusion that it makes economic sense for some retailers to order less quantity and take the benefits of the permissible delay more frequently. However, he did not consider deteriorating items and partial backlogging. In this paper, we establish a general EOQ model for deteriorating items when the supplier offers a permissible delay in payments. For generality, our model allows not only the partial backlogging rate to be related to the waiting time but also the unit selling price to be larger than the unit purchase cost. Consequently, the proposed model includes numerous previous models as special cases. In addition, we mathematically prove that the total relevant cost is strictly pseudo-convex so that the optimal solution exists and is unique. Finally, our computational results reveal six managerial phenomena.     

不确定性环境下的经理人与股东合作博弈分析

针对不确定环境下的合作博弈问题，引入置信与丘奎特积分，给出了其均衡定义及求解方法。将上述方法应用到公司治理结构中，对经理人与股东在不确定性环境下的合作博弈进行求解，通过比较其均衡与非合作博弈均衡结果，说明该方法能够给双方带来更多的收益，从而实现帕累托改进。     

保持一个等价关系的部分变换半群

设X是一个集合,|X|≥3. Px为集合X上所有部分变换构成的半群.设E是集合X的一个等价关系.定义 PE(X)=｛f∈Px:(A)x,y∈domf,(x,y)∈E(→)f(x),f(y)∈E｝ 则PE(X)作成PX的一个子半群.本文讨论半群PE(X)的格林关系和正则性,并研究当等价关系E满足什么条件时,半群PE(X)是富足半群.     

Partial Ovoids in Classical Finite Polar Spaces

Ovoids in finite polar spaces are related to many other objects in finite geometries. In this article, we prove some new upper bounds for the size of partial ovoids in Q ^–(2n+1,q) and W(2n+ 1,q). Further, we give a combinatorial proof for the non-existence of ovoids of H(2n +1,q ²) for n>q ³.     

A scatter search algorithm for project scheduling under partially renewable resources

In this paper we develop a heuristic algorithm, based on Scatter Search, for project scheduling problems under partially renewable resources. This new type of resource can be viewed as a generalization of renewable and non-renewable resources, and is very helpful in modelling conditions that do no fit into classical models, but which appear in real timetabling and labor scheduling problems. The Scatter Search algorithm is tested on existing test instances and obtains the best results known so far.     

Stochastic differential game model of a common property fishery

The paper presents a stochastic differential game model of a common-property commercial fishery and determines a feedback Nash equilibrium of the game. Closed-form expressions for the value functions, the equilibrium harvesting strategies, and stationary distributions of the fish stock are derived. Sensitivity analyses with respect tot he model parameters are carried out. The paper also considers equilibrium outcomes under joint maximization and surplus maximization. In the latter case, an optimal market size (i.e., number of firms) is identified.The research of the first author was supported in part by Grant 5.20.31.02 from the Danish Research Council for the Social Sciences. The research of the second author was supported in part by the CRGC Fund of the University of Hong Kong. The authors would like to thank the editor for constructive comments.     

Coordination and Cooperation in Dyadic Relationships

A Markov model with a coordination parameter isdeveloped to depict coordination and cooperation decisionprocesses in 2 × 2 game relationships. The parameters ofthe model can be used to define and measure various forms ofinfluence. The model is applied to data collected using aprisoner's dilemma payoff structure to represent thesuperior-subordinate relationship. The results demonstrate theusefulness of the model and the measures of influence. Superiorsand subordinates are more likely to coordinate following mutualcooperation, achieving matching behaviors more frequently thanan independent-decisions model would predict. Subordinates showslightly more influence over leaders' behaviors than vice versa.     

GRASP and path relinking for project scheduling under partially renewable resources

Recently, in the field of project scheduling problems the concept of partially renewable resources has been introduced. Theoretically, it is a generalization of both renewable and non-renewable resources. From an applied point of view, partially renewable resources allow us to model a large variety of situations that do not fit into classical models, but can be found in real problems in timetabling and labor scheduling. In this paper, we develop some preprocessing techniques and several heuristic algorithms for the problem. Preprocessing significantly reduces the dimension of the problems, therefore improving the efficiency of solution procedures. Heuristic algorithms based on GRASP and Path relinking are then developed and tested on existing test instances, obtaining excellent results.     

不完全信息研发合作的形成及参与人行为选择因素

本通过囚徒困境重复博弈模型的思想研究合作研发中参与人合作策略形成的条件，考察了不完全信息研发合作中参与人合作行为的基础，并在此基础上讨论了研发合作中合作预期收益、不合作激励和合作机会成本对参与人研发合作行为选择的影响。     

Partial linearization methods in nonlinear programming

In this paper, we characterize a class of feasible direction methods in nonlinear programming through the concept of partial linearization of the objective function. Based on a feasible point, the objective is replaced by an arbitrary convex and continuously differentiable function, and the error is taken into account by a first-order approximation of it. A new feasible point is defined through a line search with respect to the original objective, toward the solution of the approximate problem. Global convergence results are given for exact and approximate line searches, and possible interpretations are made. We present some instances of the general algorithm and discuss extensions to nondifferentiable programming.The author wishes to thank Drs. K. Holmberg, T. Larsson, and A. Migdalas for their helpful comments.     

马尔可夫排队模型中的合作问题分析

结合合作博弈理论,建立了合作条件下的马尔可夫排队模型.模型以多个提供同质服务的M/M/1马尔可夫排队系统达成协议形成联盟,共用一台服务器为顾客服务为研究重点,以机构维护服务器的成本与顾客在系统中排队等待的时间成本之和作为成本函数,得出形成联盟共用服务器可以降低总成本.最后给出总成本在形成联盟的机构中的分配规则.