Matrix geometric approach for random walks: Stability condition and equilibrium distribution

ABSTRACT

In this paper, we analyze a sub-class of two-dimensional homogeneous nearest neighbor (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the calculation of the stability condition, extending the result of Neuts drift conditions^[30 Neuts, M.F., Matrix-geometric Solutions in Stochastic Models: An Algorithmic Approach; The Johns Hopkins University Press: Baltimore, 1981. [Google Scholar]^] and connecting it with the result of Fayolle et al. which is based on Lyapunov functions.^[13 Fayolle, G.; Iasnogorodski, R.; Malyshev, V., Random Walks in the Quarter Plane; Springer-Verlag: New York, 1999. [Google Scholar]^] Furthermore, we consider the sub-class of random walks with equilibrium distributions given as series of product forms and, for this class of random walks, we calculate the eigenvalues and the corresponding eigenvectors of the infinite matrix R appearing in the matrix geometric approach. This result is obtained by connecting and extending three existing approaches available for such an analysis: the matrix geometric approach, the compensation approach and the boundary value problem method. In this paper, we also present the spectral properties of the infinite matrix R.     

Optimum reliability acceptance sampling plans under progressive type-I interval censoring with random removal using a cost model

A reliability acceptance sampling plan (RASP) is a variable sampling plan, which is used for lot sentencing based on the lifetime of the product under consideration. If a good lot is rejected then there is a loss of sales, whereas if a bad lot is accepted then the post sale cost increases and the brand image of the product is affected. Since cost is an important decision-making factor, adopting an economically optimal RASP is indispensable. This work considers the determination of an asymptotically optimum RASP under progressive type-I interval censoring scheme with random removal (PICR-I). We formulate a decision model for lot sentencing and a cost function is proposed that quantifies the losses. The cost function includes the cost of conducting the life test and warranty cost when the lot is accepted, and the cost of batch disposition when it is rejected. The asymptotically optimal RASP is obtained by minimizing the Bayes risk in a set of decision rules based on the maximum likelihood estimator of the mean lifetime of the items in the lot. For numerical illustration, we consider that lifetimes follow exponential or Weibull distributions.     

浚县方言的人称代词

浚县方言的人称代词跟普通话相比有相同之处,也有不同之处.单数形式与普通话相同,但句法功能较受限制.复数形式都来自合音,且复数单用逐渐向基本意义渗透,其中第一人称的复数单用已经进入基本意义.人称代词的基本意义在语用中常常发生变化,应该看作是语用中的转义,与基本意义分开讨论.     

产品级再使用的绩效测度

产品级再使用绩效测度有助于总结再使用的经验,加强停用产品的资源化管理,实现产品的最大再利用价值,提出了从技术先进性、绿色性、经济性和心理因素4个方面测度产品级再使用全过程绩效,建立了产品级再使用子系统和特征矩阵,提出了基于谱范数的测度方法,该方法充分利用了产品级再使用全过程的指标信息,并在不同阶段给予指标不同的权重。针对绩效测度指标过多的问题,提出了两阶段的层次分析法,在多指标权重确定中具有应用价值,另一方面也解决了专家的权威与共识问题。以电视再使用为案例,验证了提出的理论和方法能有效测度再使用绩效,并进行了结果分析,给出了再使用建议。     

合成孔径雷达图像目标分类研究

基于灰度共生矩阵技术,研究了可用于合成孔径雷达图像分类的灰度共生矩阵中差方差、差熵、对比度、能量、方差等纹理特征量,分析了其特征提取和分类特性。运用类内类间距准则,通过计算图像特征值的类内类间距,得到对合成孔径雷达图像分辨效果较好的纹理特征量,并利用三层BP神经网络进行图像分类,获得了满意的分类结果。     

用级数法导出各向同性谐振子径向矩阵元的通项

利用广义拉盖尔多项式的级数表达式和分步积分法,给出了各向同性谐振子径向矩阵元的另一种表达式.     

综合性物流企业信息系统集成度研究

本文从综合物流企业信息系统集成的角度出发，将集成部的定义引入，利用矩阵原理将复杂物流系统整体结构分解为多级递阶的等级结构，分析了各个信息系统之间的集成程度。仓储、海运、陆运、空运、快递业务管理信息系统之间是有循环存在的强联结关系，安全和客户管理信息系统是物流管理信息系统的最高级，外部资源辅助管理系统和呼叫中心处在同一级，财务管理信息系统位于第2级，人力资源管理信息系统位于最低一级。     

雷达极化理论中常见极化散射矩阵特性分析

介绍了雷达极化理论中常见的辛克莱(Sinclair)散射矩阵、米勒(Mueller)散射矩阵、格雷伍斯(Graves)功率散射矩阵等极化散射矩阵,并对其特性进行了较详尽的分析。导出了上述各种极化散射矩阵间的相互变换关系式,从而为其在雷达目标检测和识别领域中的应用提供了相应的理论依据.     

基于林业部门的中国宏观社会核算矩阵构建

森林碳汇在应对气候变化中的重要作用越来越突显。用可计算一般均衡模型(CGE)分析碳汇政策能够为政策的制订提供强有力的依据,构建CGE模型的前提需要构建基于林业部门的社会核算矩阵(SAM)。SAM中的林业产出和投入各账户、林产品供给和需求各账户,以及隐含的相对价格可以用来模拟碳汇政策对林业的影响。基于《2007年中国投入产出表》并结合其他统计数据,编制了基于林业部门的2007年中国社会核算矩阵。该表的特点是对涉及林业的账户进行了核算,对统计年鉴中没有的数据进行了合理的估算。编制的SAM为CGE模型的构建与应用提供了数据基础。     

Optimal block designs for three treatments when observations are correlated

E$E$-optimal designs for comparing three treatments in blocks of size three are identified, where intrablock observations are correlated according to a first order autoregressive error process with parameter ρ∈(0,1)$\rho \in (0,1)$. For number of blocks b   of the form b=3n+1$b=3n+1$, there are two distinct optimal designs depending on the value of ρ$\rho$, with the best design being unequally replicated for large ρ$\rho$. For other values of b$b$, binary, equireplicate designs with specified within-block assignment patterns are best. In many cases, the stronger majorization optimality is established.