φ-混合随机变量序列加权和的完全收敛性

讨论了同分布下的φ-混合随机变量序列的完全收敛性,构建了1个定理和1个推论,它改进了前人的一些研究成果,获得了更一般的结论．     

同分布PA序列部分和之和的弱大数定律

本文主要研究了同分布PA序列{Xn}的部分和之和Tn的弱大数定律,与I.I.D序列以及NA序列部分和之和的弱大数定律形成对照,从而进一步完善了PA序列的大数定律理论.     

A Generalization of a Lower Bound Technique due to Fredman and Saks

{In a seminal paper of 1989, Fredman and Saks proved lower bounds for some important data-structure problems in the cell probe model. In particular, lower bounds were established on worst-case and amortized operation cost for the union-find problem and the prefix sum problem. The goal of this paper is to turn their proof technique into a general tool that can be applied to different problems and computational models. To this end we define two quantities: Output Variability depends only on the model of computation. It indicates how much variation can be found in the results of a program with certain resource bounds. This measures in some sense the power of a model. Problem Variability characterizes in a similar sense the difficulty of the problem. } Our Main Theorem shows that by comparing a model's output variability to a problem's problem variability, lower bounds on the complexity of solving the problem on the given model may be inferred. The theorem thus shows how to separate the analysis of the model of computation from that of the problem when proving lower bounds. We show how the results of Fredman and Saks fit our framework by computing the output variability of the cell probe model and the problem variability for problems considered in their paper. This allows us to reprove their lower bound results, and slightly extend them. The main purpose of this paper though is to present the generalized technique. Received January 25, 1999; revised July 30, 1999.     

An approach to evaluation of hierarchical systems performance

An approach to assessment of performance of hierarchical systems with simple subordination is developed with regard to moment characteristics of sequences of random sums. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 70–79, July–August, 2000.     

经验过程的一般加权和收敛的两个结果

研究了经验过程的一般加权和收敛问题,得到一般加权和收敛的两个结果.建立了实值情形下的结果在经验过程中的相应形式.     

Philippe Flajolet's Research in Analysis of Algorithms and Combinatorics

Philippe Flajolet's research in theoretical computer science spans over more than 20 years. He made lasting contributions to the analysis of algorithms and analytic combinatorics. Among many of his results we mention here some in such diversified topics as enumeration, number theory, formal languages, continued fractions, automatic analysis of algorithms, Mellin transform, digital sums, recurrences, trees, random generation of combinatorial objects, random graphs and mappings, polynomial factorization, communications, codes, graphics, etc. This gives only a small snapshot of his work, and we encourage the reader to visit Flajolet's homepage http://www-rocq.inria.fr/algo/flajolet/index.html for a fuller account. The bibliography was taken from his homepage and may not be totally complete, although we added a few items. Our paper was written without giving any prior notice to Philippe Flajolet. It reflects the view of the authors and any misunderstandings and shortcomings should be put on their account.     

Reversibility and Stochastic Networks

The experimental error variance in a response surface model with a block effect has traditionally been assumed to be constant. In some experimental situations, however, this variance may be different for the different blocks that compose the associated design. This article discusses the analysis of a response surface model with a random block effect and heterogeneous error variances among the blocks. The model includes interactions between the fixed polynomial effects and the block effect. Procedures for estimating and testing the fixed effects and the random effects in the model are described. In particular, ANOVA-based procedures for testing equality of the error variances and testing the random effects are introduced.     

关于模p的原根及逆的差的混合均值

研究模p的原根及其逆的差的渐近性质.利用广义Bernoulli数、Gauss和及Dirichlet L-函数的均值定理,得出Cochrane和与广义的Kloosterman和的一些混合均值公式.     

Minkowski和的一些性质

给出了混合面积A（t）和混合周长L（t）的表达式，并证明了√A（t）和A（t）／L（t）的凹凸性．这一性质建立了混合面积和混合周长与等周不等式之间的联系．