On the compactness method in general ergodic impulsive control of markov processes

In this paper the impulsive control of Feller Markov processes on compact state space with long run average cost criterion is studied. Under the assumption of compactness of the resolvent operator the optimal strategies corresponding to general cost for impulses are constructed. Also the case of purely jump Markov processes is considered     

Determining the optimal run time for EPQ model with scrap,rework, and stochastic breakdowns

This paper is concerned with determination of optimal run time for an economic production quantity (EPQ) model with scrap, rework, and stochastic machine breakdowns. In real life manufacturing systems, generation of defective items and random breakdown of production equipment are inevitable. In this study, a portion of the defective items is considered to be scrap, while the other is assumed to be repairable. Total production-inventory cost functions are derived respectively for both EPQ models with breakdown (no-resumption policy is adopted) and without breakdown taking place. These cost functions are integrated and the renewal reward theorem is used to cope with the variable cycle length. Theorems on conditional convexity of the integrated overall costs and bounds of the production run time are proposed and proved. We conclude that the optimal run time falls within the range of bounds and it can be pinpointed by the use of the bisection method based on the intermediate value theorem. Numerical example is provided to demonstrate its practical usages.     

Some results associated with the longest run in a strongly ergodic Markov chain

This paper discusses the asymptotic behaviors of the longest run on a countable state Markov chain.Let {Xa} a∈Z + be a stationary strongly ergodic reversible Markov chain on countablestate space S = {1,2,...}.Let TS be an arbitrary finite subset of S.Denote by Ln the length of the longest run of consecutive i's for i∈T,that occurs in the sequence X1,...,Xn.In this paper,we obtain a limit law and a week version of an Erds-Rényi type law for Ln.A large deviation result of Ln is also discussed.     

带警戒限的合格品链长控制图

研究了两种带警戒限的合格品链长控制图,一种是一个链长控制图,另一种是两个链长控制图.首先,给出了这两种控制图的制定方法;其次,利用概率流图方法得到了这两种控制图的平均链长(ARL)的计算公式;最后,推导了它们效率的度量指标ANI(发信号之前的平均检验的样品数)的计算公式.     

Evolutionary prisoner’s dilemma games with local interaction and best-response dynamics

This paper studies the long run behavior in evolutionary prisoner’s dilemma games. All players are assumed to sit around a circle and to interact only with their neighbors. It is known that full-defection is the unique long run equilibrium as the probability of players’ experimentation (or mutation) tends to zero in the best response dynamics. Here, it is shown that full-cooperation could emerge in the long run if one also cares for his neighbors in the bestresponse dynamics.     

基于SPEI及游程理论的云贵地区1960-2014年干旱时空变化特征

基于云贵地区49个气象站点1960-2014年的逐月气象数据,计算得到云贵地区季尺度及年尺度的标准化降水蒸散发指数序列,结合游程理论及经验正交（EOF）等方法,揭示云贵地区干旱的时空变化特征.研究结果表明：（1）云贵地区气候呈现逐渐变干的趋势,且年尺度和季尺度在21世纪初均出现由湿转干的迹象.（2）同一干旱历时条件下,不同等级干旱发生的频率不同,等级越小发生频率越高,反之亦然.同一等级的干旱发生频率随干旱历时长度的增加而减小.（3）在历时2~5个月的干旱事件中,云南省的干旱重现期均小于贵州省,即云南省发生干旱事件较贵州省频繁.27°N以北地区的干旱重现期较长,干旱事件发生频率较小.（4）对云贵地区近55 a的SPEI进行经验正交（EOF）分析知,EOF展开第1模态反映的是季风系统控制下的云贵地区旱涝一致性变化情况,21世纪后,云贵地区普遍处于干旱状态;EOF展开第2模态反映的是受乌蒙山阻隔,东西两侧干旱呈现反相位变化的空间分布特征.该研究对于认识和把握区域气候干旱趋势与规律,提高区域干旱预警能力,保证粮食安全和生态经济稳定有重要的现实意义.     

The analysis of evolutionary algorithms on sorting and shortest paths problems

The analysis of evolutionary algorithms is up to now limited to special classes of functions and fitness landscapes. E.g., it is not possible to characterize the set of TSP instances (or another NP-hard combinatorial optimization problem) which are solved by a generic evolutionary algorithm (EA) in an expected time bounded by some given polynomial. As a first step from artificial functions to typical problems from combinatorial optimization, we analyze simple EAs on well-known problems, namely sorting and shortest paths. Although it cannot be expected that EAs outperform the well-known problem specific algorithms on these simple problems, it is interesting to analyze how EAs work on these problems. The following results are obtained:– Sorting is the maximization of sortedness which is measured by one of several well-known measures of presortedness. The different measures of presortedness lead to fitness functions of quite different difficulty for EAs.– Shortest paths problems are hard for all types of EA, if they are considered as single-objective optimization problems, whereas they are easy as multi-objective optimization problems.     

Probability Distribution Functions of Succession Quotas in the Case of Markov Dependent Trials

The exact probability distribution functions (pdf's) of the sooner andlater waiting time random variables (rv's) for the succession quota problemare derived presently in the case of Markov dependent trials. This is doneby means of combinatorial arguments. The probability generating functions(pgf's) of these rv's are then obtained by means of enumerating generatingfunctions (enumerators). Obvious modifications of the proofs provideanalogous results for the occurrence of frequency quotas and such a resultis established regarding the pdf of a frequency and succession quotas rv.Longest success and failure runs are also considered and their jointcumulative distribution function (cdf) is obtained.     

递归树的若干枚举特征

递归树由Meir和Moon定义作非平面增长树的一种，且所有节点出度都是允许的．本文首先在n个节点的递归树集合和n-1个元素的排列之间建立一个新的──对应，这个对应能同时给出树叶子和排列中的路段之间的对应和树叶子数和排列中的路段数之间的密切关系．同时还研究递归树的各种枚举特征，诸如节点的分类枚举（内节点和叶子节点、偶节点和奇节点，具不同出度的节点）和通路长度枚举（接各种节点分类）．     

自相关过程的残差控制图

由于自相关过程违背了过程输出数据独立性的假定,使得传统休哈特图的有效性受到质疑。本文首先讨论控制图设计基本思想,然后分析了对自相关过程监控的残差控制图原理;进而以平均链长和各链点检出概率为准则,系统研究了AR(1)过程残差控制图的检测能力,并与休图进行了比较。最后,通过一个模拟验证了该方法的有效性。