线性递归序列的矩阵表示

先给出k阶线性递归序列的矩阵表示,然后用矩阵方法得到2阶线性递归序列的通项及一些恒等式.     

局部广义高斯序列与广义线性过程

本文对局部广义高斯序列得到了ｒ阶绝对矩的上界不等式，进而对由其生成的广义线性过程｛Ｘｎ｝给出了ａ．ｓ．收敛的充分条件。     

递归序列与高阶项式

引　　言关于递归序列与Euler-Bernoulli数和多项式、递归序列与高阶Euler-Bernoulli数和多项式的关系问题的研究一直是国内外许多学者感兴趣的课题,并有了许多研究成果(见[1]～[7]).本文首先对Euler-Bernoulli数和多项式、高阶Euler-Bernoulli数和多项式进行推广,提出高阶多元Euler数和多项式、高阶多元Bernoulli数和多项式的定义,然后讨论它们与递归序列的关系,文中得出的结果是P.F.Byrd[1],R.P.Kelisky[2]和Zhangzhizheng[3]的相应结果的推广和深化.2　定义和引理定义2.1　k阶s元Euler数E(k)v1…vs和k阶s元Bernoulli数B(k)v1…v…     

渐近于Hermite多项式的双正交系统

本文利用渐近于Gauss函数的函数类?,给出渐近于Hermite正交多项式的一类Appell多项式的构造方法,使得该序列与?的n阶导数之间构成了一组双正交系统.利用此结果,本文得到多种正交多项式和组合多项式的渐近性质.特别地,由N阶B样条所生成的Appell多项式序列恰为N阶Bernoulli多项式.从而,Bernoulli多项式与B样条的导函数之间构成了一组双正交系统,且标准化之后的Bernoulli多项式的渐近形式为Hermite多项式.由二项分布所生成的Appell序列为Euler多项式,从而,Euler多项式与二项分布的导函数之间构成一组双正交系统,且标准化之后的Euler多项式渐近于Hermite多项式.本文给出Appell序列的生成函数满足的尺度方程的充要条件,给出渐近于Hermite多项式的函数列的判定定理.应用该定理,验证广义Buchholz多项式、广义Laguerre多项式和广义Ultraspherical(Gegenbauer)多项式渐近于Hermite多项式的性质,从而验证超几何多项式的Askey格式的成立.     

广义Riesz基的双正交特征刻画

本文利用广义双正交序列研究广义Riesz基的等价刻画,得到了算子序列是广义Riesz基当且仅当该算子列是广义完备的广义Bessel序列,且它存在广义双正交序列及这个双正交序列也是广义完备的广义Bessel序列.进一步证明了等价刻画中两个广义Bessel序列的广义完备性条件可以去掉一个(或者任一个),并举例说明了广义双正交,广义完备与广义Bessel条件之间的关系.     

局部广义高斯序列的若干新结果

给出了局部广义高斯序列部分和的一类绝对矩不等式及大偏差,并利用这些不等式证明了局部广义高斯序列的大数定律,同时建立了局部广义高斯序列的重对数收敛速度.     

关于素数阶循环群中短序列的等价类

考虑了素数阶循环群中的短序列的等价序列,并在某些情况下给出序列的Index值的上界．     

极大代数上多输入多输出线性系统的最小实现

研究了极大代数上无穷阵序列{Gi}0∞的实现问题.首先给出了周期阵序列的概念,得到了1-阶和2-阶周期阵序列{Gi}0∞元素之间的关系,并得到多输入多输出情况下线性系统存在1维和2维最小实现的充要条件.     

自回归序列的穿带率北大核心CSCD

穿零问题是时间序列分析中的一个重要研究内容,被广泛应用于语音识别、信号探测等科学研究领域．统计学者已经给出了二阶自回归序列AR（2）的渐进穿零率与一阶渐进相关函数的关系,以及均方渐近穿零率与自回归序列AR（P）的特征根的关系等一系列研究成果．在此基础上,本文引入了白回归序列AR（P）的渐近穿带率（BCR）的概念,建立了序列的2邻点渐近穿带率与一阶渐近相关函数之间的关系．当带宽足够窄时,用2邻点穿带率可以近似穿带率,从而建立了渐近穿带率和一阶渐近相关函数与方差的关系式．     

一个序列的组合解释及其应用

该文给出了一个序列的组合解释，讨论了这个序列在研究两类Chebyshev多项式，广义Fibonacci序列和广义Lucas序列中的一些应用.     

The generalized order-k Fibonacci–Pell sequence by matrix methods

In this paper, we consider the usual and generalized order-k Fibonacci and Pell recurrences, then we define a new recurrence, which we call generalized order-k F–P sequence. Also we present a systematic investigation of the generalized order-k F–P sequence. We give the generalized Binet formula, some identities and an explicit formula for sums of the generalized order-k F–P sequence by matrix methods. Further, we give the generating function and combinatorial representations of these numbers. Also we present an algorithm for computing the sums of the generalized order-k Pell numbers, as well as the Pell numbers themselves.     

On the Adjacency-Jacobsthal numbers

In this article, we define the adjacency-Jacobsthal sequence and then we obtain the combinatorial representations and the sums of adjacency-Jacobsthal numbers by the aid of generating function and generating matrix of the adjacency-Jacobsthal sequence. Also, we derive the determinantal and the permanental representations of adjacency-Jacobsthal numbers by using certain matrices which are obtained from generating matrix of adjacency-Jacobsthal numbers. Furthermore, using the roots of characteristic polynomial of the adjacency-Jacobsthal sequence, we produce the Binet formula for adjacency-Jacobsthal numbers. Finally, we give the relationships between adjacency-Jacobsthal numbers and Fibonacci, Pell, and Jacobsthal numbers.     

On the boundary sequence of an automatic sequence

In this paper, we prove a conjecture of Chen and Wen that the boundary sequence of an automatic sequence is also automatic. In particular, we study the boundary sequences of the generalized Cantor sequences, and give a complete characterization of the periodic boundary sequences. As an application, for a class of automatic sequences, we prove that their abelian complexities are also automatic.     

Golden proportions for the generalized Tribonacci numbers

It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the ‘golden proportion’ for the whole family of this generalized sequence.     

On powers of the Catalan number sequence

The Catalan number sequence is one of the most famous number sequences in combinatorics and is well studied in the literature. In this paper we further investigate its fundamental properties related to the moment problem and prove for the first time that it is an infinitely divisible Stieltjes moment sequence in the sense of S.-G.  Tyan. Besides, any positive real power of the sequence is still a Stieltjes determinate sequence. Some more cases including (a) the central binomial coefficient sequence (related to the Catalan sequence), (b) a double factorial number sequence and (c) the generalized Catalan (or Fuss–Catalan) sequence are also investigated. Finally, we pose two conjectures including the determinacy equivalence between powers of nonnegative random variables and powers of their moment sequences, which is supported by some existing results.     

Identities involving generalized Fibonacci-type polynomials

In this paper we consider a family of generalized Fibonacci-type polynomials. These polynomials have a lot of similar properties to the generalized Jacobsthal-type polynomials. As an extension of the work of Djordjevi? [G.B. Djordjevi?, Mixed convolutions of the Jacobsthal type, Appl. Math. Comput. 186 (2007) 646-651], we give some recurrence relations and identities involving the generalized Fibonacci-type polynomials.     

Generalized Fermat, double Fermat and Newton sequences

In this paper, we discuss the relationship among the generalized Fermat, double Fermat, and Newton sequences. In particular, we show that every double Fermat sequence is a generalized Fermat sequence, and the set of generalized Fermat sequences, as well as the set of double Fermat sequences, is closed under term-by-term multiplication. We also prove that every Newton sequence is a generalized Fermat sequence and vice versa. Finally, we show that double Fermat sequences are Newton sequences generated by certain sequences of integers. An approach of symbolic dynamical systems is used to obtain congruence identities.     

Generalized von Neumann–Kakutani transformation and random-start scrambled Halton sequences

It is a well-known fact that the Halton sequence exhibits poor uniformity in high dimensions. Starting with Braaten and Weller in 1979, several researchers introduced permutations to scramble the digits of the van der Corput sequences that make up the Halton sequence, in order to improve the uniformity of the Halton sequence. These sequences are called scrambled Halton, or generalized Halton sequences. Another significant result on the Halton sequence was the fact that it could be represented as the orbit of the von Neumann–Kakutani transformation, as observed by Lambert in 1982. In this paper, I will show that a scrambled Halton sequence can be represented as the orbit of an appropriately generalized von Neumann–Kakutani transformation. A practical implication of this result is that it gives a new family of randomized quasi-Monte Carlo sequences: random-start scrambled Halton sequences. This work generalizes random-start Halton sequences of Wang and Hickernell. Numerical results show that random-start scrambled Halton sequences can improve on the sample variance of random-start Halton sequences by factors as high as 7000.     

Riordan 矩阵的$(m,r,s)$-Halves

Riordan矩阵的垂直一半和水平一半已经被许多学者分别研究过.本文给出了Riordan矩阵的$(m,r,s)$-halves的定义.利用此定义能够统一的讨论Riordan矩阵的垂直一半和水平一半.作为应用,通过对Pascal和Delannoy矩阵的$(m,r,s)$-halves的研究,可以得到了一些与Fibonacci, Pell和Jacobsthal序列相关的等式.     

On improved asymptotic bounds for codes from global function fields

We analyse a binary cyclotomic sequence constructed via generalized cyclotomic classes by Bai et al. (IEEE Trans Inforem Theory 51: 1849–1853, 2005). First we determine the linear complexity of a natural generalization of this binary sequence to arbitrary prime fields. Secondly we consider k-error linear complexity and autocorrelation of these sequences and point out certain drawbacks of this construction. The results show that the parameters for the sequence construction must be carefully chosen in view of the respective application.