Linear dependence of stationary distributions in ergodic Markov decision processes

In ergodic MDPs we consider stationary distributions of policies that coincide in all but n states, in which one of two possible actions is chosen. We give conditions and formulas for linear dependence of the stationary distributions of n+2 such policies, and show some results about combinations and mixtures of policies.     

Steady state analysis of an M/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.     

Towards Strong Duality in Integer Programming

We consider in this paper the Lagrangian dual method for solving general integer programming. New properties of Lagrangian duality are derived by a means of perturbation analysis. In particular, a necessary and sufficient condition for a primal optimal solution to be generated by the Lagrangian relaxation is obtained. The solution properties of Lagrangian relaxation problem are studied systematically. To overcome the difficulties caused by duality gap between the primal problem and the dual problem, we introduce an equivalent reformulation for the primal problem via applying a pth power to the constraints. We prove that this reformulation possesses an asymptotic strong duality property. Primal feasibility and primal optimality of the Lagrangian relaxation problems can be achieved in this reformulation when the parameter p is larger than a threshold value, thus ensuring the existence of an optimal primal-dual pair. We further show that duality gap for this partial pth power reformulation is a strictly decreasing function of p in the case of a single constraint. Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. Research supported by the Research Grants Council of Hong Kong under Grant CUHK 4214/01E, and the National Natural Science Foundation of China under Grants 79970107 and 10571116.     

The first <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-cohomology of some groups with one end

Let p be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first L ^p -cohomology space of some groups that have one end. We also make a connection between the first L ^p -cohomolgy space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show that there exists a real number p such that the first L ^p -cohomology space of a nonelementary hyperbolic group does not vanish. Received: 4 August 2006 Revised: 2 November 2006     

A topological aspect of Sobolev mappings

Let be a connected open set, . We give a sufficient condition for a mapping , , to have the property that sgn is almost everywhere of one sign. Following the work of Müller, Spector, and Tang [MST], we give an application of our results to the theory of non-linear elasticity. Received: 13 October 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

Enlarged symmetry groups of finite-size clusters with periodic noundary conditions

Any system that approximates an infinite lattice by a family of finite clusters (with periodic boundary conditions) passes through an intermediate region with enlarged (hidden) symmetry as the system size is increased. The hidden symmetry allows for extra degeneracies and level crossings and has application to exact-diagonalization studies, Monte Carlo simulations, lattice gauge theories, and renormalization group calculations.     

20世纪上半叶“扬黛抑钗”审美倾向浅探--钗黛形象接受史研究之三

“扬黛抑钗”的审美倾向贯穿于20世纪上半叶的四个历史阶段并各有特色，它鲜明地折射出每个时期的时代意识。     

新时期图书馆参考咨询服务的特征初探

对新世纪图书馆参考咨询服务工作的特征进行较为全面地阐述,认为新世纪图书馆参考咨询服务具有“新、广、快、精、信”的特点。     

20#管线钢在役焊接HAZ的组织与性能研究

在役焊接过程中，管内流动介质的快速冷却，易使接头出现氢致裂纹。对20^#管线钢在不同冷却条件和不同焊接线能量下的HAZ的组织性能进行了模拟研究。结果表明，在流动水冷却下，HAZ出现较多的贝氏体、马氏体和MA组元等不平衡组织，使得HAZ的硬度高达330HvN5，性能最差。采用大的线能量焊接，形成较多的上贝氏体和粒状贝氏体组织，对改善接头性能有利。因此，在避免烧穿的前提下增大焊接线能量或减小管内介质的冷却能力，减少高硬度不平衡相的形成，可以降低HAZ氢致开裂敏感性。