On Almost Regular Convergence

Regular convergence of multiple sequences, introduced by G. H. Hardy and F. Móricz, can be generalized to almost convergent sequences in various ways. In the paper, classes of almost convergent double sequences with a kind of uniform regularity are studied, which make these classes similar to the class of regularly convergent sequences. Matrices, which convert sequences from these classes to bounded and convergent double sequences with limits equal to the generalized limits of the original sequences are characterized. The results extend results of F. Móricz and B. E. Rhoades on strongly regular matrices.     

Sequences of functions of binomial type

The theory of binomial enumeration leads to sequences of functions of binomial type which are not polynomials. The results of Mullin-Rota for these sequences are developed and a ring structure on the set of sequences is studied.     

Kronecker–Halton sequences in Fp((X−1))

In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences.     

两两NQD序列与随机Dirichlet级数

本文研究了一类两两NQD序列加权乘积和的Jamison型强稳定性.利用两两NQD序列的一些极限理论,获得了系数的模为两两NQD列的一类随机Difichlet级数的增长性和值分布的一些新的结果,推广和改进了两两独立序列的相关结论.     

New results on nonexistence of perfect p-ary sequences and almost p-ary sequences

Complex periodical sequences with lower autocorrelation values are used in CDMA communication systems and cryptography. In this paper we present new nonexistence results on perfect p-ary sequences and almost p-ary sequences and related difference sets by using some knowledge on cyclotomic fields and their subfields.     

Cross-Correlations of Quadratic Form Sequences in Odd Characteristic

Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in odd characteristic. These sequences are shown to have low cross-correlation values in certain cases. They also have significantly higher linear spans than previously studied geometric sequences. These results show that geometric sequences are candidates for use in spread-spectrum communications systems in which cryptographic security is a factor.     

加权和线性过程的渐近正态性

本文建立了α-混合序列情形的加权和平稳线性过程的渐近正态性.获得的结论基于最少的权条件.所得结论将Abadir等[Econometric Theory,2014,30(1):252-284]中的结论推广至α-混合序列情形.     

Cutting sequences on square-tiled surfaces

We characterize cutting sequences of infinite geodesics on square-tiled surfaces by considering interval exchanges on specially chosen intervals on the surface. These interval exchanges can be thought of as skew products over a rotation, and we convert cutting sequences to symbolic trajectories of these interval exchanges to show that special types of combinatorial lifts of Sturmian sequences completely describe all cutting sequences on a square-tiled surface. Our results extend the list of families of surfaces where cutting sequences are understood to a dense subset of the moduli space of all translation surfaces.     

On tightness and stopping times

This paper studies conditions of tightness for sequences of processes, which conditions are mostly based on the use of ‘dominating’ increasing processes. The results obtained follow in directions initiated by Aldous and Rebolledo and are particularly well-suited for studying sequences of semimartingales. Also obtained are results that extend sufficient conditions of Aldous's type to processes that are not quasi-left-continuous.     

(α,β)混合序列的强稳定性

研究一类被随机控制的(α,β)混合序列,并得到了关于其强稳定性的若干结论.     

Convergence of sequences of semi-continuous functions

In this paper we investigate how three well-known modes of convergence for (real-valued) functions are related to one another. In particular, we consider order convergence, pointwise convergence and continuous convergence of sequences of nearly finite normal lower semi-continuous functions. There is a natural comparison to be made between the results we obtain for convergence of sequences of semi-continuous functions, and classic results on the convergence of sequences of measurable functions.     

本刊英文版Vol.32(2016),No.1论文摘要（英文）

正New Results on Nonexistence of Perfect p-Ary Sequences and Almost p-Ary Sequences Hal Ying LIU Ke Qin FENG Abstract Complex periodical sequences with lower autocorrelation values are used in CDMA communication systems and cryptography.In this paper we present new nonexistence results on perfect p-ary sequences and almost p-ary sequences and related difference sets by using some knowledge on cyclotomic fields and their subfields.     

String patterns of leading digits

This paper reviews numerous theoretical results on properties of string sequences generated by leading digits of 2ⁿ and explores their practical implications. The result of Rajagopal et al. on statistical properties of string sequences is discussed. Several recent ideas on the graph-theoretic complexity of string sequences of leading digits are then explored. The application of McCabe's complexity measure to the directed graphs of strings of leading digits is given. In conclusion, uses of these string sequences in different areas of computer science are discussed.     

Cross-correlations of geometric sequences in characteristic two

Cross-correlation functions are determined for a large class of geometric sequences based on m-sequences in characteristic two. These sequences are shown to have low cross-correlation values in certain cases. They are also shown to have significantly higher linear complexities than previously studied geometric sequences. These results show that geometric sequences are candidates for use in spread-spectrum communications systems in which cryptographic security is a factor.Parts of this work were presented at the International Symposium on Information Theory, Honolulu, Hawaii, November, 1990.Project sponsored by the National Security Agency under Grant Number MDA904-91-H-0012. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation hereon.     

Strong convergence of pairwise NQD random sequences

Strong limit theory is one of the most important problems in probability theory. Some results on the convergence of pairwise NQD random sequences have been presented. This paper further analyzes the strong convergence of pairwise NQD sequences and generalizes partial results of Wu [Q.Y. Wu, Convergence properties of pairwise NQD random sequences, Acta Math. Sinica 45 (3) (2002) 617-624 (in Chinese)]. Since no general moment inequalities are given as so far, we avoid this problem and obtain a class of strong limit theorem for NQD sequences and some corresponding conclusions by use of truncation methods and generalized three series theorem, which are the supplements to the previous fruits.     

B值随机元和的完全收敛性

在B值随机元随机有界于一非负随机变量的情况下．讨论了B值独立随机元序列非随机足标和的完全收敛性，作为应用，得到了随机足标和完全收敛性的相应结果，将[5]中的一些结果推广到B值独立随机无情形，同时使[3]（d=1），[4]，[6]的相应结果成为特例．     

Ergodicity of Jackson-type queueing networks

This paper gives a pathwise construction of Jackson-type queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMPs. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which were studied in the past.The work of this author was supported in part by a grant from the European Commission DG XIII, under the BRA Qmips contract.The work of this author was supported by a sabbatical grant from INRIA Sophia Antipolis.     

Time series model based on global structure of complete genome

A time series model based on the global structure of the complete genome is proposed. Three kinds of length sequences of the complete genome are considered. The correlation dimensions and Hurst exponents of the length sequences are calculated. Using these two exponents, some interesting results related to the problem of classification and evolution relationship of bacteria are obtained.     

Perturbations of frames

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic.     

On the eigenvalue and Shannon's entropy of finite length random sequences

Pseudorandom binary sequences play a significant role in many fields, such as spread spectrum communications, stochastic computation, and cryptography. The complexity measures of sequences and their relationship still remain an interesting open problem. In this article, we study on the eigenvalue of random sequences, deduce its theoretical expectation and variance of random sequences with length N, and establish the relationship between eigenvalue and Shannon's entropy. The results show that these two measures are consistent. Furthermore, the eigenvalue of random n‐block sequences and its relation to Shannon's entropy are also been studied. © 2014 Wiley Periodicals, Inc. Complexity 21: 154–161, 2015