镓一镁二元相图研究

本文用两种差热分析方法即“一步法”和“二步法”以及多晶X-射线衍射法对镓-镁二元系相图进行了研究.修正了前人的工作. 为了考察该二元体系的金属间化合物是否以镓原子多面体簇状结构存在,作者对富镓部分相图(镓原子百分含量大于71.4％)进行了较为细致的研究.在三种不同比例下(含镓量分别为85at.％、90at.％、95at.％)合成,分离得到了颗粒状晶体.对这些晶体进行了差热分析和多晶X-射线研究.分析结果表明:从这三种不同比例的合金中分离得到的晶体为同一金属间化合物Mg_2Ga_5,也是该二元系镓含量最高的金属间化合物.考察Ga-Mg体系中存在的五种金属间化合物的结构,未能发现镓原子以多面体簇状结构存在的现象.     

加热模型及其最优控制

本文应用Pontryagin最大值原理研究加热过程,提出一个在加热过程中节能的最优控制方案。     

Regenerative queueing processes and their qualitative and quantitative analysis

Recently developed methods of qualitative analysis for regenerative processes arising in queueing are presented. These methods are essentially qualitative and use notions such as coupling, probability metrics, etc. They are developed for studying various properties of regenerative models, including convergence rate to a stationary regime, continuity of their characteristics with respect to some parameters and first-occurrence time of an event such as queue overflowing. In spite of their qualitative nature they lead to good quantitative estimates of underlying properties with computer methods available to calculate them.     

On the convergence of cross decomposition

Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence.In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.     

A central limit theorem for generalized multilinear forms

Let X₁, …, X_n be independent random variables and define for each finite subset I {1, …, n} the σ-algebra = σ{X_i : i ε I}. In this paper -measurable random variables W_I are considered, subject to the centering condition E(W_I ) = 0 a.s. unless I J. A central limit theorem is proven for d-homogeneous sums W(n) = Σ_{I = d}W_I, with var W(n) = 1, where the summation extends over all (_n^d) subsets I {1, …, n} of size I = d, under the condition that the normed fourth moment of W(n) tends to 3. Under some extra conditions the condition is also necessary.     

An optimal service rate in a Poisson arrival queue with two-stage service policy*

We consider a two-stage service policy for a Poisson arrival queueing system. The idle server starts to work with ordinary service rate when a customer arrives. If the number of customers in the system reaches N, the service rate gets faster and continues until the system becomes empty. Otherwise, the server finishes the busy period with ordinary service rate. After assigning various operating costs to the system, we show that there exists a unique fast service rate minimizing the long-run average cost per unit time.This work was supported by Korea Research Foundation Grant(KRF-2002-070-C00021).     

A queueing system with linear repeated attempts,bernoulli schedule and feedback

We analyse a single-server retrial queueing system with infinite buffer, Poisson arrivals, general distribution of service time and linear retrial policy. If an arriving customer finds the server occupied, he joins with probabilityp a retrial group (called orbit) and with complementary probabilityq a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority queue for another service with probability ϑ or to leave the system forever with probability =1−ϑ, where 0≤ϑ<1. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating function of system size distribution, which generalizes the well-knownPollaczek-Khinchin formula. Also we obtain a stochastic decomposition law for our queueing system and as an application we study the asymptotic behaviour under high rate of retrials. The results agree with known special cases. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.     

Shape-Memory Effect in Polymer Composites with a Compactible Filler

The shape-memory effect has been investigated in formed porous polymers and composites under heating. An epoxy polymer, ultrahigh-molecular polyethylene, and polypropylene were used as the polymeric matrix and carbon materials of different bulk density were taken for the filler. An unconventional shape-memory effect, which is accompanied by an increase in volume, was created. Processing schemes by which this effect can be achieved are proposed. They make it possible to obtain products of varying configuration.     

Stationary Distributions of GI/M/c Queue with PH Type Vacations

We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies.     

Analysis of Queueing Systems with Synchronous Single Vacation for Some Servers

We study a multi-server M/M/c type queue with a single vacation policy for some idle servers. In this queueing system, if at a service completion instant, any d (d c) servers become idle, these d servers will take one and only one vacation together. During the vacation of d servers, the other c–d servers do not take vacation even if they are idle. Using a quasi-birth-and-death process and the matrix analytic method, we obtain the stationary distribution of the system. Conditional stochastic decomposition properties have been established for the waiting time and the queue length given that all servers are busy.