第Ⅳ类时滞捕食系统的Hopf分支

研究了具有第Ⅳ类功能性反应的两种群时滞捕食系统正平衡点的稳定性，讨论了该系统的Hopf分支现象，并进行了数值模拟。     

具有随机扰动的SISV模型的解的渐近性态

研究一类具有两种随机扰动的SISV传染病模型．对于第一种随机SISV模型,证明对任给的非负初值,该随机模型一定存在唯一的全局正解,并讨论该随机模型的解围绕确定性模型的无病平衡点的渐近行为;对于第二种随机SISV模型,通过构造适当的Lyapunov泛函证明该随机模型的解是随机渐近稳定的．     

美国后备役部队的编成

后备役部队是美国武装力量的组成部分。近年来,美军经国会批准每年召募约二十五万人入后备役。除部分首次服役的人员外,大部分是新退出现役的官兵或服满第一期后备役后重新报名服后备役的老兵。美国后备役部队有两种编成:一种是按训练程度和调服现役的顺序分为三类,即第一类、第二类、第三类。第一类后备役又区分为编组和非编组两种。前者成建制,紧急动员时首先征召;后者不成建制,紧急动员时个别征召。第二类后备役人数很少,平时无组织,通常在全面动员的第二阶段个别征召,平时一般不参加训练。第三类后备役主要是在部队服役二十年以上的校级军官和高级军士,亦称退休后备队,战时只有当第一、第二类后备役中无合格人员时,才调服现役。     

一类具有时滞的捕食系统的稳定性与Hopf分支

研究一类具有时滞的两种群捕食系统,通过分析特征方程讨论了正平衡点的局部稳定性问题。通过构造适当的Lyapunov泛函,得到了保证系统正平衡点全局渐近稳定的充分条件,并讨论了在正平衡点附近Hopf分支的存在性问题。     

一类具有饱和发生率的SEIS传染病模型全局稳定性研究

研究一类易感者和潜伏者都有新增常数输入,疾病具有饱和发生率的SEIS传染病模型．经计算得到模型的基本再生数,证明当基本再生数〉1时,模型只存在惟一的地方病平衡点的结论,并利用特征方程和Hurwitz判据分析地方病平衡点的局部稳定性,通过采用第二加性复合矩阵理论证明地方病平衡点的全局渐近稳定性．     

第二类曲面积分计算方法新探

首先对有向曲面∑1:z=z(x,y),(x,y)∈Dxy上的第二类曲面积分的计算进行了探讨,主要根据第二类曲面积分与第一类曲面积分的关系,通过计算有向曲面的法向量, 把被积函数转化为两向量的点积。然后利用曲面面积元素与坐标面上的面积元素的关系, 再转化为二重积分,简化了第二类曲面积分的计算。最后对其它形式的光滑有向曲面也进行了类似研究,都可直接转化为二重积分。     

认真落实新修订《兵役法》 抓好士兵预备役工作落实

新修订的《兵役法》第二十五条规定,士兵预备役分为第一类和第二类,第一类包括三部分人员:一是预编到现役部队的预备役士兵,二是编入预备役部队的预备役士兵,三是经过预备役登记编入基干民兵组织的人员;第二类包括两部分人员:一是经过预备役登记编入普通民兵组织的人员,二是其他经过预备役登记确定服士兵预备役的人员。     

多目标密集环境下航迹处理问题及集合论描述法(续) 上

在文献中,我已给出了第一类系统在目标密集环境下航迹处理的集合论描述法。本文应用并发展前文的原理与方法于第二类系统的二维测向站,给出了多目标密集环境下航迹处理问题及集合论描述法。分析指出:第二类系统较之第一类系统的多目标航迹处理问题更复杂,更困难。并提出了一些值得研究的新问题。     

多目标密集环境下航迹处理问题及集合论描述法(续)下

在文献[4.1]中,我已给出了第一类系统在目标密集环境下航迹处理的集合论描述法。本文应用并发展前文的原理与方法于第二类系统的二维测向站,给出了多目标密集环境下航迹处理问题及集合论描述法。分析指出:第二类系统较之第一类系统的多目标航迹处理问题更复杂,更困难。并提出了一些值得研究的问题。     

一类生态捕食模型的局部稳定性

文献3讨论了系统(1)在两个平衡点时平衡点的豫定性,分界线环的存在性等性质,本文则讨论系统(1)在两个平衡点时的局部稳定性。     

Landmarks in defense literature

The Brain of an Army: a Popular Account of the German General Staff. By Spenser Wilkinson. Archibald Constable, London (1st edition 1890, 2nd edition 1895)     

On nash subsets and mobility chains in bimatrix games

This work is concerned with constructing, analyzing, and finding “mobility chains” for bimatrix games, sequences of equilibrium points along which it is possible for the two players to progress, one equilibrium point at a time, to an equilibrium point that is preferred by both players. The relationship between mobility chains and Nash subsets is established, and some properties of maximal Nash subsets are proved.     

超声速燃烧流的双时间步计算方法研究

发展了模拟非定常超声速燃烧流场的隐式双时间步方法。采用时间分裂法对流动和反应进行解耦处理,流动方程组由双时间步方法求解,内迭代过程采用LU-SGS方法;反应源项方程组通过隐式二阶梯形公式求解。分析了时间分裂格式和时间步长对计算结果的影响,结果显示:一阶时间精度的分裂格式会略微高估化学效率,应该采用二阶时间精度的分裂格式;时间步长的选取对计算结果影响显著,为了保证解耦算法的计算精度,时间步长应足够小以能够较准确捕捉到主导各种输运过程的大尺度涡团的非定常行为。     

军事虚拟仓库组织结构的博弈分析

简要介绍了军事虚拟仓库及其组织结构形式．以及博弈论的相关知识。结合军事后勤系统的特点,采用完全信息静态博弈纳什均衡的方法分析了军事虚拟仓库的组织结构模式,在假设的合理的条件下模拟3种组织形式的博弈过程。通过各个模型的最终纳什均衡,指出了3种组织结构形式运作的结果和其积极因素、消极因素、噪声构成．结合我军现有的后勤保障体制,提出现行保障体制的合理与不合理的地方,并给出了改进方案,对优化全军后方仓库布局及管理和战备物资储备及应急保障有着重要意义,可以为总部决策提供咨询建议。     

Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

A simultaneous non‐zero‐sum game is modeled to extend the classical network interdiction problem. In this model, an interdictor (e.g., an enforcement agent) decides how much of an inspection resource to spend along each arc in the network to capture a smuggler. The smuggler (randomly) selects a commodity to smuggle—a source and destination pair of nodes, and also a corresponding path for traveling between the given pair of nodes. This model is motivated by a terrorist organization that can mobilize its human, financial, or weapon resources to carry out an attack at one of several potential target destinations. The probability of evading each of the network arcs nonlinearly decreases in the amount of resource that the interdictor spends on its inspection. We show that under reasonable assumptions with respect to the evasion probability functions, (approximate) Nash equilibria of this game can be determined in polynomial time; depending on whether the evasion functions are exponential or general logarithmically‐convex functions, exact Nash equilibria or approximate Nash equilibria, respectively, are computed. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 139–153, 2017     

基于博弈论的装备科研、购置、维修经费比例关系优化分析

通过不同时期国家战略部署、科研发展情况及经济承受能力对装备经费分配的影响分析,采用博弈的方法,建立了装备科研、购置和维修费之间的比例关系优化模型,给出了寻求纳什均衡点的迭代算法,并进行了仿真计算.仿真结果证明了该方法的可行性与正确性.     

Noncooperative cost spanning tree games with budget restrictions

We extend the noncooperative game associated with the cost spanning tree problem introduced by Bergantiños and Lorenzo (Math Method Oper Res 59(2004), 393–403) to situations where agents have budget restrictions. We study the Nash equilibria, subgame perfect Nash equilibria, and strong Nash equilibria of this game. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

A search game with a protector

A classic problem in Search Theory is one in which a searcher allocates resources to the points of the integer interval [1, n] in an attempt to find an object which has been hidden in them using a known probability function. In this paper we consider a modification of this problem in which there is a protector who can also allocate resources to the points; allocating these resources makes it more difficult for the searcher to find an object. We model the situation as a two‐person non‐zero‐sum game so that we can take into account the fact that using resources can be costly. It is shown that this game has a unique Nash equilibrium when the searcher's probability of finding an object located at point i is of the form (1 − exp (−λ_ix_i)) exp (−μ_iy_i) when the searcher and protector allocate resources x_i and y_i respectively to point i. An algorithm to find this Nash equilibrium is given. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47:85–96, 2000     

Technical note: Find a hidden “treasure”

This paper deals with a two searchers game and it investigates the problem of how the possibility of finding a hidden object simultaneously by players influences their behavior. Namely, we consider the following two‐sided allocation non‐zero‐sum game on an integer interval [1,n]. Two teams (Player 1 and 2) want to find an immobile object (say, a treasure) hidden at one of n points. Each point i ∈ [1,n] is characterized by a detection parameter λ_i (μ_i) for Player 1 (Player 2) such that p_i(1 ? exp(?λ_ix_i)) (p_i(1 ? exp(?μ_iy_i))) is the probability that Player 1 (Player 2) discovers the hidden object with amount of search effort x_i (y_i) applied at point i where p_i ∈ (0,1) is the probability that the object is hidden at point i. Player 1 (Player 2) undertakes the search by allocating the total amount of effort X(Y). The payoff for Player 1 (Player 2) is 1 if he detects the object but his opponent does not. If both players detect the object they can share it proportionally and even can pay some share to an umpire who takes care that the players do not cheat each other, namely Player 1 gets q₁ and Player 2 gets q₂ where q₁ + q₂ ≤ 1. The Nash equilibrium of this game is found and numerical examples are given. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007