Weighted Discrepancy and High-Dimensional Numerical Integration

The concept of weighted discrepancy of sequences was introduced by Sloan and Woniakowski when they proved a general form of a Koksma–Hlawka inequality for the numerical integration of functions. This version takes imbalances in the importance of the projections of the integrand into account.In this paper we give estimates for the weighted discrepancy of several important point sets. Further we carry out various (high-dimensional) numerical integration experiments and we compare the results with the error bounds provided by the generalized Koksma–Hlawka inequality and by the estimates for the weighted discrepancy. Finally we discuss various consequences.     

A three‐dimensional coordination polymer based on the Zn4(μ3‐OH)2 unit: poly[[(μ4‐benzene‐1,4‐dicarboxylato)bis(μ3‐benzene‐1,4‐dicarboxylato)bis(μ3‐hydroxido)bis(1,10‐phenanthroline‐5,6‐dione)tetrazinc] dihydrate]

The title compound, {[Zn₄(C₈H₄O₄)₃(OH)₂(C₁₂H₆N₂O₂)₂]·2H₂O}_n, has been prepared hydrothermally by the reaction of Zn(NO₃)₂·6H₂O with benzene‐1,4‐dicarboxylic acid (H₂bdc) and 1,10‐phenanthroline‐5,6‐dione (pdon) in H₂O. In the crystal structure, a tetranuclear Zn₄(OH)₂ fragment is located on a crystallographic inversion centre which relates two subunits, each containing a [ZnN₂O₄] octahedron and a [ZnO₄] tetrahedron bridged by a μ₃‐OH group. The pdon ligand chelates to zinc through its two N atoms to form part of the [ZnN₂O₄] octahedron. The two crystallographically independent bdc²⁻ ligands are fully deprotonated and adopt μ₃‐κO:κO′:κO′′ and μ₄‐κO:κO′:κO′′:κO′′′ coordination modes, bridging three or four Zn^II cations, respectively, from two Zn₄(OH)₂ units. The Zn₄(OH)₂ fragment connects six neighbouring tetranuclear units through four μ₃‐bdc²⁻ and two μ₄‐bdc²⁻ ligands, forming a three‐dimensional framework with uninodal 6‐connected α‐Po topology, in which the tetranuclear Zn₄(OH)₂ units are considered as 6‐connected nodes and the bdc²⁻ ligands act as linkers. The uncoordinated water molecules are located on opposite sides of the Zn₄(OH)₂ unit and are connected to it through hydrogen‐bonding interactions involving hydroxide and carboxylate groups. The structure is further stabilized by extensive π–π interactions between the pdon and μ₄‐bdc²⁻ ligands.     

服务中断的M/M/1重试排队模型的稳态解

研究服务中断的M/M/1重试排队模型的稳态解,证明当α+μ>λ时0不足该模型主算子的特征值.由此推出该模型不存在稳态解.     

IPP+M/M／C排队的遍历性(英文)

The IP P＋M/M/c queueing system has been extensively used in the modern communication system.The existence and uniqueness of stationary distribution of the queue length L（t）for IP P＋M/M/1 queue has been proved in[10].In this paper,we shall give the su？cient and necessary conditions of l-ergodicity,geometric ergodicity,and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.     

A Simple proof for the stability of global FIFO queueing networks

We study the stability of multiclass queueing networks under the global FIFO （first in first out） service discipline, which was established by Bramson in 2001. For these networks, the service priority of a customer is determined by his entrance time. Using fluid models, we describe the entrance time of the most senior customer in the networks at time t, which is the key to simplify the proof for the stability of the global FIFO queueing networks.     

Product form in networks of queues with batch arrivals and batch services

A product form equilibrium distribution is derived for a class of queueing networks in either discrete or continuous time, in which multiple customers arrive simultaneously and batches of customers complete service simultaneously.     

CBR:一种支持工作流过程语义验证的组件级 化简方法

目前的工作流过程验证方法多数侧重控制流特性验证,与数据或资源信息相结合的验证尚未得到很好发展.然而,业务过程的目标实现依赖于控制流、数据流和资源三维基本观点的协作.保证过程的目标实现需要验证这三维观点协作的正确性,称为语义验证.该文侧重讨论大型、灵活的过程语义验证问题.首先,形式化定义过程模型,综合体现三维基本观点,表达完整的过程语义,并使用基于组件的思想,具有一定可扩展性和灵活性.然后,通过探讨组件间的协作逻辑,提出基于组件的化简方法(Component Based Reduction,CBR)和化简规则,为过程语义验证提供有力支持.     

AIS—NC多类型开放队列网络性能分析

本文研究了基于网络计算机会计信息系统性能分析方法，针对会计信息系统结构特点及硬件资源请求类型，抽象出三种系统响应模式．据此，构建了AIS-NC多类型开放队列网络性能模型，并且给出了性能分析的步骤和方法．举例说明了该方法的应用．该方法对其他多类型开放队列网络性能分析具有借鉴意义．     

On the asymmetric clocked buffered switch

A 2 × 2 clocked buffered switch is a device used in data-processing networks for routing messages from one node to another. The message handling process of this switch can be modelled as a two-server, time slotted, queueing process with state space the number of messages (x_n , y_n) present at the servers at the end of a time slot. The x_n , y_n-process is a two-dimensional nearest-neighbour random walk. In the present study the bivariate generating function Φ(p,q) of the stationary distribution of this random walk is determined, assuming that this distribution exists. Φ(p,q) is known, whenever Φ(p,0) and Φ(0,q) are known. The essential points of the present study are the construction of these two functions from the knowledge of their poles and zeros and the simple determination of these poles and zeros. This revised version was published online in June 2006 with corrections to the Cover Date.     

THE POINT PROCESS OF STATETRANSITIONS IN AREGULAR MARKOV CHAIN

1.IntroductionInreliabilitytheory,inordertocalculatethefailurefrequencyofarepairablesystem,Shily]firstintroducedandstudiedthetransitionfrequencybetweentwodisjointstatesetsforafiniteMarkovchainandavectorMarkovprocesswithfinitediscretestatespaceandobtainedageneralformulaoftransitionfrequency.Then,ontheconditionthatthegeneratormatrixofMarkovchainisuniformlybounded,Shi[8'9]againprovedthetransitionfrequencyformulaandobtainedthreeotherusefulformulas.Obviously,thepoint(orcalledcounting)processofsta…