具有Bernoulli反馈且带有负顾客的PH/M/1排队系统

在PH/M/1排队模型中,引入了负顾客和Bernoulli反馈,并讨论了服务台容量为有限和无限两类模型,其中,模型一为服务台容量为无限的PH/M/1排队模型,利用拟生灭过程和矩阵几何解法得到了系统的转移速率矩阵,给出了系统正常返的充要条件,并得到了系统的稳态队长、忙期长度的拉普拉斯变换,以及系统的其它相关性能指标.模型二为服务台容量为有限的PH/M/1/N排队模型,同样使用拟生灭过程给出了马尔科夫过程的转移速率矩阵,并利用矩阵分析法进行求解,得到了该系统的稳态解和其它相关指标.     

一般形式的连续时间拟生灭过程各种遍历性判定准则

侯振挺、李晓花在 [1]已经讨论了具有某些特殊形式的拟生灭过程各种遍历性 ,我们将在此基础讨论一般形式连续时间拟生灭过程各种遍历性 ,并给出 [1]中连续时间拟生灭过程的指数遍历及多项式遍历的一个新证明 ,该证明给出了具有某些特殊条件下连续时间拟生灭过程遍历性与离散时间拟生灭过程遍历性之间关系 .     

一类休假排队平稳队长分布的无限位相表示

讨论休假时间服从T-SPH分布的M/M/1单重休假模型,其中T-SPH表示可数状态吸收生灭过程吸收时间的分布.该排队模型可以用可数位相拟生灭过程(QBD过程)和算子几何解的方法进行建模分析.首先得到了QBD过程算子几何解的具体形式;其次在所得结果的基础上,进一步给出了排队模型平稳队长的随机分解结果,并说明附加队长服从离散时间无限位相分布.     

制造系统的单位时间费用的一个精确表达

讨论了由一个加工车间(workshop)和一个库房(warehouse)组成的按订单生产的制造系统,加工车间有有限等待场所,采用(s,S)订货策略.用二维随机过程刻划了该制造系统,该二维随机过程是一个拟生灭过程.利用矩阵几何解法,给出了随机过程的稳态分布.并以此为依据给出该系统的单位时间平均运作费用.     

对M/T-SPH/1排队平稳队长的分析

研究了M/T-SPH/l排队模型,利用拟生灭过程和算子几何解的方法给出了平稳队长分布的概率母函数.在此基础上,指出该分布不是一个离散PH分布,但在一定条件下却是一个几何尾部分布.     

对一类等待空间有限的抢占优先权排队的分析

讨论M/M/1抢占优先权排队模型, 且假设低优先权顾客的等待空间有限. 该模型可以用有限位相拟生灭过程来描述. 由矩阵解析方法, 对该拟生灭过程进行了分析, 并得到排队模型平稳队长的计算公式, 最后还用数值 结果说明了方法的有效性.     

生灭Q－矩阵

对于一般（不必全稳定）单边、双边拟生灭矩阵，本文分别给出了它们成为Ｑ－矩阵和诚实Ｑ－矩阵的充分必要条件；而且还分别得到了Ｑ过程和诚实Ｑ过程的唯一性准则．即，彻底解决了一般单边、双边生灭过程和诚实生灭过程的存在唯一性问题。     

生灭Q－矩阵

对于一般（不必全稳定）单边、双边拟生灭矩阵，本文分别给出了它们成为Ｑ－矩阵和诚实Ｑ－矩阵的充分必要条件；而且还分别得到了Ｑ过程和诚实Ｑ过程的唯一性准则．即，彻底解决了一般单边、双边生灭过程和诚实生灭过程的存在唯一性问题。     

带启动时间的Geom/Geom/1多重工作休假排队

本文中研究了一个带有启动时间的Geom/Geom/1多重工作休假排队模型。服务台在休假期间,不停止服务,而是以较低的服务率为顾客提供服务。运用拟生灭过程和矩阵几何解的方法,给出了该模型的稳态队长分布,并求出了平均队长以及顾客的平均逗留时间。     

拟生灭过程几种遍历性的判别准则(Ⅱ)

本文是文[7]的继续,研究了连续时间拟生灭过程,给出了一类连续时间拟生灭过程l-遍历和几何遍历行之有效的判别准则,并证明其不可能是多项式一致遍历和强遍历的.     

Sequential Linear-Quadratic Method for Differential Games with Air Combat Applications

We present a numerical method for computing a local Nash (saddle-point) solution to a zero-sum differential game for a nonlinear system. Given a solution estimate to the game, we define a subproblem, which is obtained from the original problem by linearizing its system dynamics around the solution estimate and expanding its payoff function to quadratic terms around the same solution estimate. We then apply the standard Riccati equation method to the linear-quadratic subproblem and compute its saddle solution. We then update the current solution estimate by adding the computed saddle solution of the subproblem multiplied by a small positive constant (a step size) to the current solution estimate for the original game. We repeat this process and successively generate better solution estimates. Our applications of this sequential method to air combat simulations demonstrate experimentally that the solution estimates converge to a local Nash (saddle) solution of the original game.     

一类带非线性边界条件的拟线性抛物方程的第二初边值问题

利用先验估计的方法讨论具非线性第二边界条件的快扩散方程解的存在性、唯一性、稳定性和渐近性.主要结果是:1)存在唯的整体广义解,解连续依赖于初值;2)存在T₀,t<T₀时解是无穷次可微的正则解;3)当t充分大时,解一致收敛到零.     

非光滑非凸向量极值问题的真有效解

本文考虑非光滑非凸向量极值问题的真有效解,其主要结果如下:(1)Borwein真有效解与Benson真有效解的等价性;(2)向量极值问题的真有效解与标量极值问题的最优解的等价性;(3)广义鞍点定理;(4)真有效解的必要和充分条件。     

SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS

This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations(for example, stochastic heat equations)driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical(square integrable) solution(mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution; Feynman-Kac formula for the moments of the solution; and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.     

准晶弹性理论边值问题的可解性

通过给出准晶弹性偏微分方程组边值问题的矩阵表示去定义弱解,利用Korn不等式和函数空间理论证明了这种弱解的存在性与唯一性,从而把经典弹性理论边值问题解的存在性定理推广到准晶弹性理论上,这种理论为发展极其复杂与困难的准晶弹性的偏微分方程的边值问题的数值解提供了一个基础．     

The solution sets of infinite fuzzy relational equations with sup-conjunctor composition on complete distributive lattices

This paper deals with sup-conjunctor composition fuzzy relational equations in infinite domains and on complete distributive lattices. When its right-hand side is a continuous join-irreducible element or has an irredundant continuous join-decomposition, a necessary and sufficient condition describing an attainable solution (resp. an unattainable solution) is formulated and some properties of the attainable solution (resp. the unattainable solution) are shown. Further, the structure of solution sets is investigated.     

Comment on a paper by M.C. Cheng

In a recent paper M.C. Cheng proposed new criteria for the simplex algorithm which guarantee that (i) a nonbasic variable of a basic feasible solution will remain nonbasic in an optimal basic solution, (ii) a basic variable of a basic solution will remain basic in an optimal basic solution. This comment gives (i) a slight generalization of the first result and (ii) a counterexample to the second proposition.     

Logistic型方程周期解和概周期解的存在性

In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.     

(2+1)维AKNS方程的行波解研究(英文)

Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.     

THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS

In this article, the authors show the existence of global solution of two-dimensional viscous Camassa-Holm (Navier-Stokes-alpha) (NS-α) equations. The authors also prove that the solution of the NS-α equations converges to the solution of the 2D NS equations in the inviscid limit and give the convergence rate of the difference of the solution.