Complete Convergenceand Complete Moment Convergence for Weighted Sums of ANA Random Variables

In this paper,we investigate the complete convergence and complete moment conver-gence for weighted sums of arrays of rowwise asymptotically negatively associated(ANA)random variables,without assuming identical distribution.The obtained results not only extend those of An and Yuan[1]and Shen et al.[2]to the case of ANA random variables,but also partially improve them.

Several Classes of Two-weight or Three-weight Linear Codes and Their Applications

Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].

On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables

In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.

SOME LIMIT THEOREMS FOR WEIGHTED SUMS OF ARRAYS OF NOD RANDOM VARIABLES

In this paper the authors study the complete, weak and almost sure convergence for weighted sums of NOD random variables and obtain some new limit theorems for weighted sums of NOD random variables, which extend the corresponding theorems of Stout [1], Thrum [2] and Hu et al. [3].

Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

Almost Sure Convergence and Complete Convergence for the Weighted Sums of Martingale Differences

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums ?i = 1n ani D1\sum\limits_{i = 1}^n {a_{ni} D_1 } are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

On complete convergence for Stout's type weighted sums of NOD sequence

In this paper, the complete convergence for the weighted sums of independent and identically distributed random variables in Stout [9] is improved and extended under NOD setup.The more optimal moment condition is given. The main results also hold for END sequence.

Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables

By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.

Complete Convergence of Weighted Sums for Asymptotically Almost Negatively Associated Sequences

For weighted sums of asymptotically almost negatively associated (AANA) random variables sequences, we use the Rosenthal type moment inequalities and prove the Marcinkiewicz-Zygmund type complete convergence and obtain the complete convergence rates. Our results extend some known ones.

Complete Convergence of Weighted Sums for Arrays of Rowwise m-negatively Associated Random Variables

In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

Complete Convergence for Weighted Sums of WOD Random Variables

In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent random variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.

Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations

In this article,we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.We establish general strong law and complete convergence theorems for weighted sums of extended negatively dependent random variables under the sub-linear expectations.Our results of strong limit theorems are more general than some related results previously obtained by Thrum(1987),Li et al.(1995)and Wu(2010)in classical probability space.

Some Convergence Properties for Weighted Sums of Martingale Difference Random Vectors

Let{X_(ni),F_(ni);1≤i≤n,n≥1}be an array of R^(d)martingale difference random vectors and{A_(ni),1≤i≤n,n≥1}be an array of m×d matrices of real numbers.In this paper,the Marcinkiewicz-Zygmund type weak law of large numbers for maximal weighted sums of martingale difference random vectors is obtained with not necessarily finite p-th(1<p<2)moments.Moreover,the complete convergence and strong law of large numbers are established under some mild conditions.An application to multivariate simple linear regression model is also provided.

工件权重带限制的最小化最大加权完工时间的单机在线排序问题

本文考虑了最小化最大加权完工时间的单机在线排序问题,要求工件的权重在工件加工时间一定范围之内且工件的权重和工件加工时间具有一致性,即apj≤wj≤bpj(a≥(5√−1)/2b,b≥a)且若wi>wj则pi≥pj,如果wi=wj则pi=pj。工件以时间在线的方式到达,只有工件Jj在达到释放时间rj后,决策者才知晓工件的基本信息,如加工时间pj和权重wj。对于此问题,首先利用对手法证明了其下界为1+b/(b+a),随后给出了竞争比为1+b/(b+a)的最好可能的在线算法。特别地,当a=(5√−1)/2b时,该算法的竞争比为(5√+1)/2。

基于二次高斯和的增信码重量分布

循环码是一类具有高效编码和译码算法的重要线性码,在通信和数据存储系统等领域被广泛应用。重量分布是循环码的重要研究对象,如何构造具有较少重量的循环码是编码理论中的重要研究问题。借助于二次高斯和、有限域上特征标的性质等数论工具研究了一类循环码的增信码,给出了增信码的重量分布和参数。结果表明,这类增信码是射影循环码且具有较少的重量。该增信码与原码相比有更高的传输效率且其对偶码关于球填充界最优或几乎最优。此外,还给出了原码的完全重量分布。

考虑退化效应的钢箱梁小节段在线生产调度研究

钢箱梁小节段作为桥梁组装的基础构件,需求量非常大,其生产方案的优化对制造商有着很大的影响,针对钢箱梁小节段的在线生产调度研究就显得愈发迫切与重要。本文研究工件具有退化效应的钢箱梁小节段单机在线生产问题,建立了的两个不同的退化加工模型,以最小化最大加权完工时间为优化目标。首先,对所研究的两个问题,都证明了最优排序应具有的性质。然后,对加工时长模型为pj=αjt(t>0)的问题,给出了一个竞争比为1+αmax最好可能的在线算法,其中αj为工件Jj的退化因子;同样,对加工时长模型为pj=αj(A+Bt)(A>0)的问题,也给出了一个竞争比为2+Bαmax最好可能的在线算法。最后,对文中的两个在线模型都进行了数据模拟,验证了在线算法的有效性与正确性,也为制造商的生产管理提供了有效参考。

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent of each other. Then the applications to ruin probabilities in a discrete time risk model with dependent stochastic returns are considered.

MAXIMAL INEQUALITY AND COMPLETE CONVERGENCES OF NON-IDENTICALLY DISTRIBUTED NEGATIVELY ASSOCIATED SEQUENCES

A maximal inequality for the partial sum of NA sequence is constructed. By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed. The results obtained extend the results of Liang （1999, 2000）.

m-WOD序列随机加权和的完全收敛性

在一些宽泛条件下,研究m-宽象限相依序列(m-WOD)随机加权和的完全收敛性,该结果将现有文献中宽象限相依(WOD)序列的相关结论拓展到m-WOD序列的情形.