STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

CONFLICT AND COOPERATION IN UTILIZING A COMMON PROPERTY RESOURCE

Noncooperative games are used to demonstrate that, while free riding is always an option, the “tragedy of the commons” is not inevitable. When the decision to cooperate or free ride is considered in a dynamic setting, there is no intermediate case where some cooperate and others free ride. The game is only stabilized in either full cooperation or full defection. The important factor in obtaining a cooperative outcome is the critical number of players that decide to cooperate. The concept of commitment is used to demonstrate the necessary and sufficient conditions for full cooperation. Although the analysis is based on a shared water resource, it can be extended to other natural resources with common costs and private benefits, especially in the cases where there are no international authorities or treaties that internalize the externalities involved in privatizing the resource.     

双甲基丙烯酰氧苯基丙烷与苯乙烯共聚物的光学性能

标题共聚物的耐冲击性与丙烯酸酯均聚物相比有明显改善,但随着双烯单体含量的降低,共聚物的耐热性和表面硬度有所下降。丙烯酸酯含量为70%的共聚物的吸收紫外光能力最强(<370nm全吸收),含量为5%～10%的共聚物耐吸水性、耐酸耐碱性及耐冲击性最好。     

纳米Sb2O3的制备与性能研究

由于Sb2O3是一种性能优良的无机阻燃剂,并与卤素阻燃剂有很好的协效作用[1],1998年,全球用于阻燃的Sb2O3达80kt以上,占阻燃剂总耗量的7%[2]。但由于其本身的极性特点,加入到纤维、塑料等高分子材料中,材料的力学性能受到很大损失[3],因此对传统的微米级的Sb2O3进行超细、表面处     

水相湿法改性纳米碳酸钙表面性质的研究

用特定的表面改性剂在水相中对纳米碳酸钙的悬浮液进行了湿法改性。红外光谱和热失重分析证明,改性剂与碳酸钙之间以化学键结合;沉降体积和接触角的测定结果说明改性粒子在液体石蜡中的润湿性和疏水性得到了提高;透射电子显微镜照片显示改性粒子在液体石蜡中有更好的分散性;体系粘度实验表明改性粒子与液体石蜡之间有较好的相容性。     

含吩噻嗪金属配合物的合成及非线性光学性质研究

本文报道了一种新的配体:10-乙基-3-甲酰吩噻嗪缩肼基二硫代甲酸甲酯(HL)及其金属配合物的合成。采用了元素分析、质谱、核磁共振、红外光谱对配体及其金属配合物进行了表征。此外,并应用紫外、荧光和Z-扫描技术,测定了配体及其金属配合物的荧光最佳发射波长(λ_max^em)、荧光量子产率(Φ_f)、寿命(τ)和非线性光学性质。结果表明它们在DMF溶液中都能发射出较强的橄榄色荧光,配体及其金属配合物都有双光子吸收,并且金属配合物的非线性光学效应比配体明显增强。用半经验量子化学方法(RHF/PM3)计算结果与实验值较为吻合。     

拓扑指数法研究显色剂结构与反应性能关系

本文讨论了２９个不对称色酸双偶氮膦酸型显色剂的分子联接性指数，并将其与结构选择性因子相结合，用于偶氮类剂结构与铈显色反应灵敏度的相关性研究，讨论了显色剂结构对显色反应灵敏度的影响。     

SA耐火材料多晶结构与性能的研究

本实验采用磨具废砂和炉皮SiC废砂生产SA耐火材料，通过XRD分析和计算机处理确定各试样中的晶相（4H－SiC，33R－SiC，3C－SiC，α－Al2O3，β-石英和Al6Si2O13）及其各相的含量。通过材料性能与结构综合分析，确定较好的配方，其含量：磨具废砂50％，炉皮砂45％，结合剂5％，外加矿化剂2％。     

Networks and chain coverings in partial orders and their products

For an arbitrary poset P, subposets {P _i : 1ik} form a transitive basis of P if P is the transitive closure of their union. Let u be the minimum size of a covering of P by chains within posets of the basis, s the maximum size of a family of elements with no pair comparable in any basis poset, and a the maximum size of an antichain in P. Define a dense covering to be a collection D of chains within basis posets such that each element belongs to a chain in D within each basis poset and is the top of at least k-1 chains and the bottom of at least k-1 chains in D. Dense coverings generalize ordinary chain coverings of poset. Let d=min {|D|–(k–1)|P|}. For an arbitrary poset and transitive basis, a convenient network model for dense coverings yields the following: Theorem 1: da, with equality iff P has a minimum chain decomposition in which every pair of consecutive elements on each chain are comparable in some basis poset. Theorem 2: usda. Theorem 3: s=d iff s=a. The most interesting special case is where the transitive basis expresses P as the product of two posets, in which case u and s measure the minimum and maximum sizes of unichain coverings and semiantichains.