随机环境下的对称零程过程的大偏差原理

利用相对熵方法及鞅方法给出了随机环境下的对称零程过程的经验测度的收敛速度函数.     

Fuzzy HX环的推广

为改进Fuzzy HX环的结果,使之包含Fuzzy商环,提出了弱Fuzzy HX环的概念,研究了它的性质与结构,并重新讨论了拟Fuzzy商环,证明了在正则条件下拟Fuzzy商环与弱Fuzzy HX环的统一性：同时也得到了一致弱Fuzzy HX环与普通Fuzzy商环的关系。     

On Extracting Maximum Stable Sets in Perfect Graphs Using Lovász's Theta Function

We study the maximum stable set problem. For a given graph, we establish several transformations among feasible solutions of different formulations of Lovász's theta function. We propose reductions from feasible solutions corresponding to a graph to those corresponding to its induced subgraphs. We develop an efficient, polynomial-time algorithm to extract a maximum stable set in a perfect graph using the theta function. Our algorithm iteratively transforms an approximate solution of the semidefinite formulation of the theta function into an approximate solution of another formulation, which is then used to identify a vertex that belongs to a maximum stable set. The subgraph induced by that vertex and its neighbors is removed and the same procedure is repeated on successively smaller graphs. We establish that solving the theta problem up to an adaptively chosen, fairly rough accuracy suffices in order for the algorithm to work properly. Furthermore, our algorithm successfully employs a warm-start strategy to recompute the theta function on smaller subgraphs. Computational results demonstrate that our algorithm can efficiently extract maximum stable sets in comparable time it takes to solve the theta problem on the original graph to optimality. This work was supported in part by NSF through CAREER Grant DMI-0237415. Part of this work was performed while the first author was at the Department of Applied Mathematics and Statisticsat Stony Brook University, Stony Brook, NY, USA.     

有Edgeworth展式的分布的随机加权逼近的重对数律

本文研究了未知分布的逼近问题，利用随机加权法，给出了有Edgeworth展式的一类（未知）分布的模拟分布，证明了在一定条件下，模拟分布与未知分布的逼近精度达到O(n^-1√lnlnn），称之为随机加权逼近的重对数律。     

用随机模糊方法研究合理确定工程项目工期

站在兼顾业主与建造商的公正立场,基于网络优化技术基础上并以系统的观点,采用随机模糊数学方法研究合理确定项目工期,进而用实际项目进行分析验证,是一种科学合理确定工期的方法.     

响应变量随机缺失下的半参变系数模型的均值估计

在响应变量随机缺失时,研究了半参数变系数模型响应变量均值的借补估计.首先利用完整个体估计模型中的参数与非参数部分,然后再用借补方法与加权借补方法估计响应变量的均值.最后求出了估计的渐近偏差与渐近方差,研究了所得到的估计的渐近性质,并进行模拟比较.     

Restorations of punctured languages and similarity of languages

Punctured languages are languages whose words are partial words in the sense that the letters at some positions are unknown. We investigate to which extent restoration of punctured languages is possible if the number of unknown positions or the proportion of unknown positions per word, respectively, is bounded, and we study their relationships for different boundings. The considered restoration classes coincide with similarity classes according to some kind of similarity for languages. Thus all results we can also formulate in the language of similarity. We show some hierarchies of similarity classes for each class from the Chomsky hierarchy and prove the existence of linear languages which are not δ ‐similar to any regular language for any δ < ½. For δ ≥ ½ this is unknown but it could only be possible in the case of non‐slender linear languages. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

带有无限到达源的Re-entrant Line的稳定性

用Foster判别准则,Weiss[13]给出了带有无限到达源的两站三步re-entrant line的稳定性的充分条件．本文用两种不同的方法得到了其稳定性的充分必要条件,即: 二维随机游动方法和Foster判别准则．同时,我们又用流体模型方法得到了系统稳定的充分条件,大大地简化了Weiss[13]的证明．     

正则带的半格结构

Petrich解决了一般带的构造定理（见[1]或[2]），在此基础上，我们将证明正则带（满足等式axya=axaya的带）的一些特征，并给出一个带为正则带或右似正规带（满足等式xya=xaya的带）的充分必要条件，这些结果是Yamada和Kimura的关于正规带（满足等式axya=ayxa的带）的结果的推广，正规带被他们描述为矩形带的强半格（见[1]或[3]）。     

Concentration for self‐bounding functions and an inequality of Talagrand

We see that the entropy method yields strong concentration results for general self‐bounding functions of independent random variables. These give an improvement of a concentration result of Talagrand much used in discrete mathematics. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006