ARMA(1,1)需求条件下供应链需求提前承诺的影响效果分析

为了分析供应链需求提前承诺的影响效果,考虑供应链所面临的顾客需求满足ARMA（1,1）过程。首先从理论上建立正常顾客需求与顾客需求提前承诺时零售商订单量波动程度和平均库存的定量描述模型,通过两种情形下的比较分析,得出在顾客需求自回归系数大于零时,顾客需求提前承诺将减小牛鞭效应和平均库存水平;同时得出在顾客需求提前承诺时,如果顾客需求自回归系数大于零,顾客提前承诺的需求比例越高,则牛鞭效应和平均库存水平越低;顾客需求提前承诺的时间跨度越长,则牛鞭效应和平均库存水平也越低。反之亦然。其次运用仿真方法分析了顾客需求提前承诺对零售商平均库存成本的影响,得出在顾客需求自回归系数大于零时,顾客需求提前承诺将有效降低零售商的平均库存成本。     

Comparison of Three Web Search Algorithms

In this paper we discuss three important kinds of Markov chains used in Web search algorithms-the maximal irreducible Markov chain, the miuimal irreducible Markov chain and the middle irreducible Markov chain, We discuss the stationary distributions, the convergence rates and the Maclaurin series of the stationary distributions of the three kinds of Markov chains. Among other things, our results show that the maximal and minimal Markov chains have the same stationary distribution and that the stationary distribution of the middle Markov chain reflects the real Web structure more objectively. Our results also prove that the maximal and middle Markov chains have the same convergence rate and that the maximal Markov chain converges faster than the minimal Markov chain when the damping factor α 〉1/√2.     

CTH算法,嵌入马氏链和RG-分解

本文是一篇关于GTH算法的综述.GTH算法是一种稳定的数值算法,常被用于计算马氏链的平稳概率.GTH算法是高斯消元法的一种重排,因此它们在数学上具有等价的意义.GTH算法的所有步骤都可以用嵌入的概念来进行概率解释,并且算法的每一次消元都会产生一个嵌入马氏链.在这种情况下,RG-分解与高斯消元法中的LU-分解相对应.此外,在处理一个由无限多个线性方程组成的系统时,嵌入马氏链能被视为GTH算法的一种扩展,同时,它在被用于近似估算原始马氏链时,会产生在l1范数意义下的最小误差.     

有限个互素因子链上幂GCD矩阵与幂LCM矩阵的行列式的整除性

设S={x1,x2,...,xn}是由n个不同的正整数组成的集合,并设a为正整数.如果一个n阶矩阵的第i行j列元素是S中元素xi和xj的最大公因子的a次幂(xi,xj)a,则称该矩阵为定义在S上的a次幂最大公因子(GCD)矩阵,用(Sa)表示;类似定义a次幂LCM矩阵[Sa].如果存在{1,2,...,n}上的一个置换σ使得xσ(1)|xσ(2)|···|xσ(n),则称S为一个因子链.如果存在正整数k,使得S=S1∪S2∪···∪Sk,其中每一个Si(1ik)均为一个因子链,并且对所有的1i=jk,Si中的每个元素与Sj中的每个元素互素,则称S由有限个互素因子链构成.本文中,设S由有限个互素的因子链构成,并且1∈S.我们首先给出幂GCD矩阵与幂LCM矩阵的行列式的公式,然后证明:如果a|b,则det(Sa)|det(Sb),det[Sa]|det[Sb],det(Sa)|det[Sb].最后我们指出:如果构成S的有限个因子链不互素,则此结论一般不成立.     

Ergodicity of a class of nonlinear time series models in random environment domain

In this paper, we study the problem of a variety of p, onlinear time series model Xn＋ 1= TZn＋1（X（n）, … ,X（n - Zn＋l）, en＋1（Zn＋1）） in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {en（i）} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.     

Coordinating pricing and inventory control in a fluctuating environment

This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.     

数学中的对立统一

2/1/a＋1/b〈√ab〈a＋b/2〈√a^2＋b^2/2     

万有Teichmüller空间与Loewner链

通过采用构造Loewner链的方法,得到了单叶函数的充分条件,同时,结合万有Teichmüller空间理论,利用Loewner链构造了单叶函数的拟共形扩张表达式,并且得到了一些拟圆区域的单叶性内径的下界估计不等式.     

单可变资源最小化加权完工时间和排序问题的强NP-困难性

Baker和Nuttle提出了下述单可变资源排序问题：扎个工件利用某个单资源进行加工使得工件的完工时间的某个函数达到最小,而资源的可利用率是随着时间而变化的．当最小化的目标函数是工件的加权完工时间和时,Baker和Nuttle猜测该问题是NP-困难的．最近,Yuan、Cheng和Ng证明该问题在一般意义下是NP-困难的,但是问题的精确复杂性仍然是悬而未决的．本文我们证明了该问题是强NP-困难的．     

模糊需求下的库存风险及最优库存决策

分析了在模糊需求下,按经典库存模型中的经济订货批量和订货周期所导致的库存风险损失。推导了模糊需求下的经济风险函数。给出了风险函数在模糊需求分布下的重心决策方法,在此基础上得到了模糊需求下经济批量的修正公式,为模糊库存风险分析的研究提供了一种方法。