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.     

二项式型自反多项式

In this paper, we define the self-inverse sequences related to sequences of polynomials of binomial type, and give some interesting results of these sequences. Moreover, we study the self-inverse sequences related to the Laguerre polynomials.     

Catalan-like number sequences and Hausdorff moment sequences

Many well-known Catalan-like sequences turn out to be Stieltjes moment sequences (Liang et al. (2016)). However, a Stieltjes moment sequence is in general not determinate; Liang et al. suggested a further analysis about whether these moment sequences are determinate and how to obtain the associated measures. In this paper we find necessary conditions for a Catalan-like sequence to be a Hausdorff moment sequence. As a consequence, we will see that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers, are Hausdorff moment sequences. We can also identify the smallest interval including the support of the unique representing measure. Since Hausdorff moment sequences are determinate and a representing measure for above mentioned sequences are already known, we could almost complete the analysis raised by Liang et al. In addition, subsequences of Catalan-like number sequences are also considered; we will see a necessary and sufficient condition for subsequences of Stieltjes Catalan-like number sequences to be Stieltjes Catalan-like number sequences. We will also study a representing measure for a linear combination of consecutive terms in Catalan-like number sequences.     

Identities on Bell polynomials and Sheffer sequences

In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.     

A Hadamard matrix of order 428

Four Turyn type sequences of lengths 36, 36, 36, 35 are found by a computer search. These sequences give new base sequences of lengths 71, 71, 36, 36 and are used to generate a number of new T‐sequences. The first order of many new Hadamard matrices constructible using these new T‐sequences is 428. © 2004 Wiley Periodicals, Inc.     

ND序列部分和的大偏差和强收敛性

利用ND随机变量序列的矩不等式、极大值不等式以及随机变量的截尾方法,重点研究了ND随机变量序列部分和的大偏差结果和强收敛性,推广了文献中一些相依随机变量序列的若干相应结果.     

任意随机变量序列级数的强收敛性

利用鞅差序列级数的收敛定理和条件三级数定理研究了任意随机变量序列级数的强收敛性,推广了某些经典的鞅差序列和独立随机变量序列及两两NQD序列的强极限定理.     

二阶矩限制下的Hajek-Renyi型不等式及其应用

在二阶矩限制下,获得了Hajek-Renyi型不等式,并给出了结果在PA,NA,Lr-混合序列场合下的应用.推广了Prakasa Rao关于PA序列的结果.     

一类非平稳时间序列的周期性

本文研究了一类非平稳时间序列的稳定性及周期性，得到了它为周期相关序列的充分必要条件，推广了文献[3]的结论．     

Parity Encoding of Binary Sequences

The parity encoding of binary sequences, which is essentially the inverse operation to the differentiationof binary sequences, partitions the sequences into cycles of sequences. The spectrum of these cycles is shown tobe a fractal-like semi-infinite sequence of powers of 2, with the property that truncating it at the(n + 1)st term yields the cycle spectrum for the parity encoding of the n-bitbinary sequences. A simple and complete characterization of both the cycles and of the cycle spectrum isgiven.