拟完美序列的性质和一种构造方法

利用代数组合论中的差集 ,研究了在流密码和 CDMA移动通信中有重要应用的拟完美序列的性质 ,给出了构造拟完美序列的一种方法     

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.     

广义差集与几乎完美序列

提出了广义差集的概念,并且给出了广义差集的一些初等性质.从应用的角度讲,广义差集就是使得其±1特征序列的自相关函数是(最多)三值的一种组合结构.因此,广义差集不仅仅是在概念(理论)上的推广,它还具有深层次的应用背景.事实上,给出了一些广义差集,它不是可分差集,也不是相对差集.同时也给出了一类广义差集存在的一些必要条件,使得这些广义差集对应的±1特征序列成为几乎完美序列.并举例说明本文中的方法是有效的.     

On Minimizing and Stationary Sequences of a New Class of Merit Functions for Nonlinear Complementarity Problems

Motivated by the work of Fukushima and Pang (Ref. 1), we study the equivalent relationship between minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems (NCP). These merit functions generalize that obtained via the squared Fischer–Burmeister NCP function, which was used in Ref. 1. We show that a stationary sequence {x^k} /Reⁿ is a minimizing sequence under the condition that the function value sequence {F(x ^k)} is bounded above or the Jacobian matrix sequence {F(x ^k)} is bounded, where F is the function involved in NCP. The latter condition is also assumed by Fukushima and Pang. The converse is true under the assumption of {F(x ^k)} bounded. As an example shows, even for a bounded function F, the boundedness of the sequence {F(x ^k)} is necessary for a minimizing sequence to be a stationary sequence.     

A Uniform Approach to Fundamental Sequences and Hierarchies

In this article we give a unifying approach to the theory of fundamental sequences and their related Hardy hierarchies of number-theoretic functions and we show the equivalence of the new approach with the classical one. Mathematics Subject Classification: 03D20, 03F15, 03E10.     

Exhaustive determination of (1023, 511, 255)-cyclic difference sets

An exhaustive search for (1023, 511, 255)-cyclic difference sets has been conducted. A total of 10 non-equivalent (1023, 511, 255)-cyclic difference sets have been found, all of which are members of previously known or conjectured infinite families. A fast and effective autocorrelation test method was utilized that can also facilitate the testing of longer sequences.

     

Short k‐radius sequences, k‐difference sequences and universal cycles

An $n$‐ary $k$‐radius sequence is a finite sequence of elements taken from an alphabet of size $n$ in which any two distinct elements occur within distance $k$ of each other somewhere in the sequence. The study of constructing short $k$‐radius sequences was motivated by some problems occurring in large data transfer. Let $f_k\left(n\right)$ be the shortest length of any $n$‐ary $k$‐radius sequence. We show that the conjecture $f_k\left(n\right)=\frac{n^2}{2k}+O\left(n\right)$ by Bondy et al is true for $k\le 4$, and determine the exact values of $f_2\left(n\right)$ for new infinitely many $n$. Further, we investigate new sequences which we call $k$‐difference, as they are related to $k$‐radius sequences and seem to be interesting in themselves. Finally, we answer a question about the optimal length of packing and covering analogs of universal cycles proposed by D?bski et al.     

The Dual Spaces of Sets of Difference Sequences of Order <Emphasis Type="Italic">m</Emphasis> and Matrix Transformations

Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.     

Large Deviation Principle for Exchangeable Sequences: Necessary and Sufficient Condition

For an exchangeable sequence of random variables valued in a Polish space, we obtain a necessary and sufficient condition for the large deviation principles of the occupation measure L _n :=(1/n) and of the process-level empirical measures.     

Classification of qt=P(x, t, q, qx, qxx)

The classification of q_t = P ( x ,  t ,  q ,  q_x ,  q_xx ) is given by using linearization. Two types of integrable equations which are generalizations of the integrable equations of Fokas and Svinolupov are given. Results are compared with Fokas's symmetry and the Mikhailov–Shabat–Sokolov formal symmetry approaches.     

New implementation of radial basis functions for solving Burgers‐Fisher equation

In this article, we consider the problem of solving Burgers‐Fisher equation. The approximate solution is found using the radial basis functions collocation method. Also for solving of the resulted nonlinear system of equations, we proposed a predictor corrector method based on the fixed point iterations. The numerical tests show that this method is accurate and efficient for finding a closed form approximation of the solution of nonlinear partial differential equations. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 248–262, 2012     

Enumeration, Construction and Random Generation of Block Codes

We discuss some methods for the enumeration, construction and random generation of isometry classes of block codes using methods from algebraic combinatorics.     

Enclosings of λ‐Fold 5‐Cycle Systems: Adding One Vertex

A k‐cycle system of a multigraph G is an ordered pair (V, C) where V is the vertex set of G and C is a set of k‐cycles, the edges of which partition the edges of G. A k‐cycle system of is known as a λ‐fold k‐cycle system of order V. A k‐cycle system of (V, C) is said to be enclosed in a k‐cycle system of if and . We settle the difficult enclosing problem for λ‐fold 5‐cycle systems with u = 1.     

The form factor program: A review and new results,the nested <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) off-shell Bethe ansatz and the 1/<Emphasis Type="Italic">N</Emphasis> expansion

The purpose of the “bootstrap program” for integrable quantum field theories in 1+1 dimensions is to construct a model explicitly in terms of its Wightman functions. We illustrate this program here mainly in terms of the SU(N) Gross-Neveu model. We construct the nested off-shell Bethe ansatz for an SU(N) factoring S-matrix and consider the problem of how to sum over intermediate states in the short-distance limit of the two-point Wightman function for the sinh-Gordon model. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 13–24, April, 2008.     

On the Enumeration of ‐Optimal and Minimax‐Optimal k‐Circulant Supersaturated Designs

In recent years, several methods have been proposed for constructing ‐optimal and minimax‐optimal supersaturated designs (SSDs). However, until now the enumeration problem of such designs has not been yet considered. In this paper, ‐optimal and minimax‐optimal k‐circulant SSDs with 6, 10, 14, 18, 22, and 26 runs, factors and are enumerated in a computer search. We have also enumerated all ‐optimal and minimax‐optimal k‐circulant SSDs with (mod 4) and . The computer search utilizes the fact that theses designs are equivalent to certain 1‐rotational resolvable balanced incomplete block designs. Combinatorial properties of these resolvable designs are used to restrict the search space.     

关于强伪压缩算子与强增生算子的Ishikawa型迭代序列收敛性的特征

本文结果表征了用于构造强增生算子方程解,m-增生算子方程解及强伪压缩算子不动点的(带误差的)Ishikawa型迭代序列的收敛性,推广与改进了Chidume与Osilike的定理1,定理2及定理3(Nonlinear Anal.TMA,1999,36(7):863-872)。     

Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument [<Emphasis Type="Italic">t</Emphasis> + 1/2]

In this paper we investigate the existence and uniqueness of pseudo almost periodic solutions and unboundedness of other solutions for the systems of differential equations with piecewise constant argument [t + 1/2] by means of new notion of pseudo almost periodic vector sequences. The case in which the characteristic equation has multiple roots is considered.     

q‐Bernstein polynomials related to q‐Frobenius–Euler polynomials,l‐functions,and q‐Stirling numbers

The aim of this paper was to derive new identities and relations associated with the q‐Bernstein polynomials, q‐Frobenius–Euler polynomials, l‐functions, and q‐Stirling numbers of the second kind. We also give some applications related to theses polynomials and numbers. Copyright © 2012 John Wiley & Sons, Ltd.     

Reliability,signature, and relative quality functions of systems under time‐homogeneous load‐sharing models

For a coherent binary system made of binary components, we consider the assumption that the components' lifetimes are distributed according to a time‐homogeneous, load‐sharing model. Such models are characterized in terms of the so‐called multivariate conditional hazard rate functions. We aim to point out some related properties of the notions of signature, relative quality functions, and reliability functions. On this purpose, we preliminarily collect all the necessary background and review some related literature. This paper concludes with a discussion, also containing some hints for future work.