F2＋vF2上生成M序列的非奇异反馈函数的性质

M序列是一类最长的非线性伪随机序列．本文研究了在F2＋vF2上生成M序列的非奇异反馈函数f（x1，X2，…，xn）所具有的3条性质：1）Rf≠f；2）Djf为互不相同的生成M序列的非奇异反馈函数（j=1，v，1＋v）；3）在f的多项式表达式中，常数项j。一定不为0；若线性项x2，x3，…，xn全出现，则它们的系数不能全为1或j。     

前馈序列与反馈序列的关系

本文引入移位寄存器序列的向量值表示讨论了线性移位寄存器的前馈序列与反馈序列同时为ｍ序列时的关系,得到了它们在向量值表示下的一个关系式。     

变系数反馈移位寄存器及其序列的几个性质

本文给出了一类新的密钥流生成器一变系数反馈移位寄存器,得到了该密钥流生成器序列的几个重要的密码学性质,并在文中给出了严格的数学证明。     

一类非奇反馈函数的自同构函数

本文定义了ｋ元ｄｅＢｒｕｉｊｎ－Ｇｏｏｄ图Ｇｎ的ｉ对偶自同构及反自同构，并利用同构的性质，给出了一类ｋ元非奇异反馈函数的自同构函数的表达式。     

序列的一种无组合系数的根表示

本文在讨论了组合数C_x~k等在GF(q)上的多元多项式表示的基础上,给出了序列的一种避免组合系数的根表示法,并利用它对两个有重根的反馈多项式生成序列之积的线性复杂性进行了讨论.     

关于某一类非奇反馈函数的自同构函数

本文定义了ｋ元ｄｅＢｒｕｉｊｎ－Ｇｏｏｄ图Ｇｎ的拟ｉ对偶同构及拟对偶自同构，并利用同构的性质，给出了一类ｋ元非奇反馈函数的自同构函数的表达式．     

F_2+vF_2上的循环码

本文研究了环F_2+vF_2上的循环码.利用标准形生成元集刻画了环F_2+vF_2上的循环码的代数结构,证明了环F_2+vF_2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的.     

Dn型非线性反馈移位寄存器

研究了一类Dynkin型非线性反馈移位寄存器,给出了n长码是Dn型反馈函数的周期码的充分必要条件,并得出了所有周期码及其周期。     

环F_2+vF_2上码的覆盖半径

通过研究环F2+vF2上线性码的结构特征,根据Gray映射,定义了两个二元码,从而证明了环F2+vF2上线性码关于李距离的覆盖半径等于两个二元码的覆盖半径之和,并得到环F2+vF2上对偶码的覆盖半径的一些结论,给出了覆盖半径的几个上下界.     

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.     

Non-Holonomicity of Sequences Defined via Elementary Functions

We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results, e.g., non-holonomicity of the logarithmic sequence is extended to rational functions involving log n. Moreover, we show that the sequence that arises from evaluating the Riemann zeta function at an increasing integer sequence with bounded gap lengths is not holonomic. Martin Klazar: ITI is supported as project 1M0021620808 by Ministry of Education of the Czech Republic.     

Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions

In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class of all rational functions of order (n,m) are considered. Let ρ _n,m = ρ _n,m (f;E) be the distance of f in the uniform metric on E from the class . We obtain results characterizing the rate of convergence to zero of the sequence of the best rational approximation { ρ _n,m(n) } _n=0 ^∞ , m(n)/n → θ ∈ (0,1] as n → ∞ . In particular, we give an upper estimate for the liminf _{n →∞} ρ _n,m(n) ^1/(n+m(n)) in terms of the solution to a certain minimum energy problem with respect to the logarithmic potential. The proofs of the results obtained are based on the methods of the theory of Hankel operators. June 16, 1997. Date revised: December 1, 1997. Date accepted: December 1, 1997. Communicated by Ronald A. DeVore.     

具有可选服务、反馈、一般重试时间的M/G/1排队系统

本文考虑了一个具有可选服务、反馈的M／G／1重试排队系统。在假定重试区域中只有队首的顾客允许重试的情况下，重试时间具有一般分布时，得到了系统稳态的充分必要条件。求得稳态时系统队长和重试区域中队长分布及相关指标。     

一类具有到达损失、可选服务、反馈的M/G/1重试排队系统

考虑一个具有到达损失、可选服务、反馈的M/G/1重试排队系统.在假定重试区域中顾客具有相互独立的指数重试时间的情况下,得到了系统的转移概率矩阵和系统稳态的充分必要条件.列出微分方程,求得稳态时系统队长和重试区域中队长分布及相关指标.     

环F_2+uF_2上长度为2n(n为奇数)的循环码

研究了环F2+uF2上长度为2n(n为奇数)的循环码,给出了循环码及其对偶码的生成多项式,以及循环码为自对偶码的充要条件,最后进一步给出了循环码极小Lee重量的一些相关结论