Fibonacci数列的模数列的周期性

对于Fibonacci数列{Fn}以及给定的正整数m,由Fn关于模m的最小非负剩余an,构成一个新的数列{an},称为Fibonacci数列的模数列.本文利用初等数论的知识和数学归纳法,证明了Fibonacci数列的模数列是周期数列,并且是纯周期数列.     

Fibonacci数列的模数列的周期的一个性质

Fibonacci数列的模数列是周期数列,并且是纯周期数列.利用模数列的定义,讨论了Fibonacci数列的模数列的周期的一个性质,证明了下列结果:假设m1与m2为不同的正整数,Fibonacci数列{Fn}的模数列{an(m1)}与{an(m2)}的最小正周期分别为T1与T2,则模数列{an([m1,m2])}的最小正周期为[T1,T2].     

基于混沌序列的密钥生成新方法

设计了一种从混沌序列生成密钥的新方法.其基本原理是从混沌序列依次取若干数据构成实值序列,将其按非线性规则映射成二值序列,再用实值序列和任意指定序列分别置乱这个二值序列,被置乱后的二值序列即为所生成密钥.实验表明,在混沌密码体制研究中,这种密钥较一般序列密钥更具有独立性、均匀性和不可预测性.     

Hilbert空间中有效序列的刻画与扰动

本文研究了Hilbert空间中的有效序列,通过引入序列的伴随序列,给出了有效序列的一个等价刻画,接着讨论了保持向量序列有效性的线性算子的性质,证明了一个线性算子将任意有效序列映射为有效序列当且仅当它是酉算子;最后,给出了正规正交基中添加一个单位向量后所得到的序列是有效序列的一个充要条件.     

定向可图的度偶序列

n为非负整数序列，若存在以该序列为度序列的图，则称n为可图的，特别的，若此图是一个定向图，该序列则称为是定向可图的，本提出了一个判断序列是否为定向可图的充分必要条件，并且在定理的证明过程中给出了一个在定理条件下构造所求定向图的有效算法。     

A Note on Sequences with the Shift and Add Property

A sequence of elements from a finite field satisfies the shift and add property if the componentwise sum of any two shifts of the sequence is either a shift of the sequence or the all zero sequence. A sequence whose elements lie in an arbitrary group satisfies the shift and multiply property if the componentwise product of any two shifts of the sequence is either a shift of the sequence or the all identity sequence. The paper classifies sequences which have the shift and add property or the shift and multiply property.     

星可数k网与序列覆盖s映射

证明了在空间具有星可数ｋ网的条件下,度量空间的１（２）序列覆盖ｓ映象是局部可分度量空间的１（２）序列覆盖、紧覆盖ｓ映象。     

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.     

全变差有界函数列的一致(R)可积性

给出了一致有界单调函数列一致可积性定理 ,由此得出全变差序列有界的收敛函数列的一致可积性 .说明了该结论可判断一些非一致收敛函数列的逐项积分性质 .     

Additive Macaulay Posets

An additive sequence of integers is a finite sequence in which the sum of any number of consecutive terms is less than or equal to the sum of the same number of initial terms in the sequence and greater than or equal to the sum of the same number of final terms in the sequence. If the final several terms in an additive sequence are greater than or equal to, in order, the initial several terms of a second additive sequence, then the juxtaposition of the two sequences is also additive. This simple fact has combinatorial corollaries.     

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。     

整数偶序列为蕴含强连通的Beineke－Harary判准

一个由ｎ个非负整数有序对构造的序列是有向可图的,如果它是某个有向图的度序列．一个有向可图序列是蕴含强连通的,如果它是某个强连通有向图的度序列．Ｂｅｉｎｅｋｅ和Ｈａｒａｒｙ给出了一个有向可图序列为蕴含强连通的判准．Ｂｅｉｎｅｋｅ－Ｈａｒａｒｙ判准的充分性证明是“相当长”的（见［１］）．本文的目的是给出Ｂｅｉｎｅｋｅ－Ｈａｒａｒｙ判准的充分性的一个简短证明．     

Topological sequence entropy for maps of the interval

A result by Franzová and Smítal shows that a continuous map of the interval into itself is chaotic if and only if its topological sequence entropy relative to a suitable increasing sequence of nonnegative integers is positive. In the present paper we prove that for any increasing sequence of nonnegative integers there exists a chaotic continuous map with zero topological sequence entropy relative to this sequence.

     

GR(4,r)上本原序列的元素分布

本文利用GR（4，r)上本原序列的迹表示及二次型的有关结论，给出了本原序列的第一权位序列的元素分布，同时求得本原序列的元素分布。     

Decidability and Specker sequences in intuitionistic mathematics

A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema (which we call ED ) about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set that is not intuitionistic decidable” and show that the existence of a Specker sequence is equivalent to ED . We show that ED is consistent with some certain well known axioms of intuitionistic analysis as Weak Continuity Principle, bar induction, and Kripke Schema. Thus, the assumption of the existence of a Specker sequence is conceivable in intuitionistic analysis. We will also introduce the notion of double Specker sequence and study the existence of them (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Prediction properties of some extrapolation methods

Convergence acceleration methods consist in the construction of a sequence converging faster than the initial sequence. Each member of the new sequence is a guess for the limit and it is computed from a restricted number of terms of the initial sequence. It is shown herein how convergence acceleration methods can be used to predict the next (unknown) term of the initial sequence instead of its limit. Particular emphasis on Aitken's △² process and the E-algorithm is placed.     

Score sequences of oriented graphs

We extend Landau's concept of the score structure of a tournament to that of the score sequence of an oriented graph, and give a condition for an arbitrary integer sequence to be a score sequence. The proof is by construction of a specific oriented graph Δ(S) with given score sequence S. It is shown that Δ(S) is transitive and has the minimum number of arcs among the oriented graphs with score sequence S.     

基于趋势修正的灰预测模型优化研究

针对序列增长趋势不完全满足准指数规律时的灰色预测建模问题,提出基于GM(1,1)模型与序列增长趋势之间偏差修正的建模方法,将GM(1,1)模型还原式中的常数项作为灰变量处理,加入调整系数以缩小拟合值与实际值之间的增长趋势差异,利用灰色离散模型拟合调整系数的变化过程,将得到的调整系数拟合值带入原时间响应函数,进而得到趋势修正的原始序列拟合值;运用新的建模方法对南京市第三产业用电量进行拟合和预测,证明了方法有效提升了GM(1,1)建模精度,并且拟合序列和实际序列的灰色绝对关联度得到提高.     

Applications of Parameterizations of Oblique Duals of a Frame Sequence

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.     

基于谱密度评价随机性

为了评价一个平稳过程的随机性, 我们基于谱密度提出了一个图方法. 当图中的散点呈现线性关系的时候, 我们可以判定这个序列是随机的. 为了说明这个思想, 我们用模拟的办法来检验伪随机数的随机性. 另外, 我们也用了一个实际数据来考察数据的相关性. 这两个例子都说明了我们的图方法是非常有效的.