加倍周期子序列的因子结构

加倍周期序列为一类常见的常长代换序列,对其子序列因子结构的研究具有重要意义.主要利用常长代换序列与二进制展开的关系,结合组合学中的一些技巧,从而得出加倍周期序列子序列的因子结构性质.     

存在趋势和周期特征的非平稳时间序列的建模及其应用

本文研究存在未知周期和趋势的非平稳时间序列的估计问题.将经典的时间序列分解模型写成一个含有未知参数的部分线性模型,首先采用B-样条逼近未知时间趋势,然后利用惩罚最小二乘回归法得到未知周期、周期序列和趋势的估计.本文还给出估计量的理论性质,包括周期估计的相合性以及周期序列和趋势估计的渐近性质.模拟研究展现了本文方法的优越...     

周期相关时间序列与周期自回归模型

介绍了周期相关时间序列和周期自回归模型,并研究了周期自回归时间序列的稳定性及周期性,得到了它为周期相关时间序列的一个充要条件,推广了文献[1]的结论.     

不等长周期时间序列的周期划分方法

针对时间序列周期不等长的情况,提出了一种基于周期划分的时间序列周期分析方法.首先将时间序列变换到频域中获取序列的周期特征,其次根据周期特征计算移动平均的项数来对时间序列做移动平均处理,然后计算移动平均处理后序列中的极值点,最后对极值点按条件进行剔除后得到周期划分点.以划分点为界划分得到时间序列的多个周期段,经过分析采用周期段的中位数线来表示时间序列的周期性变化特征.这种周期划分方法更适用于存在随机波动的长序列,实验表明该方法能较好地对序列做出划分,得到的周期段中位数线的变化特点也与原时间序列基本相符.     

一类广义耦合的非线性波动方程组时间周期解的存在性

研究了一类广义耦合的非线性波动方程组关于时间周期解的问题.首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Laray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

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.     

基于谱分析的非平稳时间序列中的潜周期研究

时间序列的频域分析并不如时域分析应用广泛,但其弥补了时域分析的不足:能够把时间序列分解为具有不同振幅,相位和频率的周期分量的叠加,找出原序列中隐含的主要周期分量,并从周期波动的角度对序列进行解释.针对非平稳时间序列进行研究,利用B样条函数为基底并引入惩罚项,提取序列中的趋势项之后,再根据样本谱密度理论得到时序数据中的潜周期,最终将原始时间序列分解为趋势项,周期项和随机扰动项.数据模拟部分验证了通过B样条估计并提取的趋势项具有较高的精确度,并会对周期项的提取产生积极的影响.实际数据部分使用了黄金价格的月度数据,得到了长,中,短三个波动周期这一有意义的结论,验证了本方法的可行性和有效性.     

带有长期趋势的近似周期时间序列的刻度变换估计

近似周期时间序列具有近似的周期趋势,即近似周期性.所谓近似周期性是指它看起来有周期性,但是每个周期的长度不是常数,比如太阳黑子数序列.近似周期时间序列在社会经济现象建模中有着广泛的应用前景.对于近似周期时间序列,关键在于刻画它的近似周期趋势,因为一旦近似周期趋势被刻画出来它就可以作为一个普通的时间序列来处理.然而,关于近似周期趋势刻画的研究却很少. 本文首先建立一些必要的理论,特别地,提出了带长度压缩的保形变换概念,并且得到了带长度压缩的线性保形变换的充分必要,然后基于此理论作者提出了一种估计尺度变换的方法,该方法可以很好地估计出近似周期趋势.最后,对一个仿真实例进行了分析.结果表明,本文所提出的方法强力有效.     

一类KdV非线性Schr(o)dinger组合微分方程组时间周期解的存在性

本文研究了一类KdV非线性Schr(o)dinger组合微分方程组时间周期解的问题,首先利用Galerkin方法构造近似时间周期解序列,然后利用先验估计和Leray-Schauder不动点原理,证明近似时间周期解序列的收敛性,从而得到该问题时间周期解的存在性.     

分量序列的构造和性质分析

以迹函数和m-序列为基础,对分量序列进行研究,分析其结构和性质.得到其周期、线性复杂度和自相关性的性质,并且证明其满足m-序列的保持性,通过研究得到的结论,给出具有理想二级自相关等良好性质的序列的构造方法.     

Structure in the Enron Email Dataset

We investigate the structures present in the Enron email dataset using singular value decomposition and semidiscrete decomposition. Using word frequency profiles, we show that messages fall into two distinct groups, whose extrema are characterized by short messages and rare words versus long messages and common words. It is surprising that length of message and word use pattern should be related in this way. We also investigate relationships among individuals based on their patterns of word use in email. We show that word use is correlated to function within the organization, as expected. Lastly, we show that relative changes to individuals' word usage over time can be used to identify key players in major company events. Presented at theWorkshop on Link Analysis, Counterterrorism and Security at the SIAM International Conference on Data Mining, 2005. P.S. Keila is a graduate student in the School of Computing at Queen's University. His research area is data mining in text. D.B. Skillicorn is a professor in the School of Computing at Queen's University, where he heads the Smart Information Management Laboratory. His research area is data mining using matrix decompositions, particularly applied to complex datasets in areas such as biomedicine, geochemistry, counterterrorism and fraud.     

The sequence of open and closed prefixes of a Sturmian word

A finite word is closed if it contains a factor that occurs both as a prefix and as a suffix but does not have internal occurrences, otherwise it is open. We are interested in the oc-sequence of a word, which is the binary sequence whose n-th element is 0 if the prefix of length n of the word is open, or 1 if it is closed. We exhibit results showing that this sequence is deeply related to the combinatorial and periodic structure of a word. In the case of Sturmian words, we show that these are uniquely determined (up to renaming letters) by their oc-sequence. Moreover, we prove that the class of finite Sturmian words is a maximal element with this property in the class of binary factorial languages. We then discuss several aspects of Sturmian words that can be expressed through this sequence. Finally, we provide a linear-time algorithm that computes the oc-sequence of a finite word, and a linear-time algorithm that reconstructs a finite Sturmian word from its oc-sequence.     

Palindromic prefixes and episturmian words

Let w be an infinite word on an alphabet A. We denote by (ni)_i?1 the increasing sequence (assumed to be infinite) of all lengths of palindromic prefixes of w. In this text, we give an explicit construction of all words w such that ni+1?2ni+1 for all i, and study these words. Special examples include characteristic Sturmian words, and more generally standard episturmian words. As an application, we study the values taken by the quantity lim supni+1/ni, and prove that it is minimal (among all nonperiodic words) for the Fibonacci word.     

THE ASYMPTOTIC SOLUTION FOR A CLASS OF SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR SINGULAR EQUATION

The singularly perturbed boundary value problem for a class of semilinearsingular equation is considered. Using a simple and special method the asym-ptotic behavior of solution is studied.     

Singular hyperbolicity for transitive attractors with singular points of 3-dimensional <Emphasis Type="Italic">C</Emphasis><Superscript>2</Superscript>-flows

In the context of C^r-flows on 3-manifolds (r ≥ 1), the notion of singular hyperbolicity, inspired on the Lorenz Attractor, is the right generalization of hyperbolicity (in the sense of Smale) for C¹-robustly transitive sets with singularities. We estabish conditions (on the associated linear Poincaré flow and on the nature of the singular set) under which a transitive attractor with singularities of a C²-flow on a 3-manifold is singular hyperbolic.     

非可换的奇异l-群

通过建立奇异元以及奇异l-群的刻划，研究了一般非可换的奇异l-群的性质及相关的结构．     

求矩阵奇异值分解的一种新方法

旨在给出求矩阵奇异值分解的一种新方法.改进和克服了以往方法的缺陷和不足.     

因子谱与诱导序列

对于任意给定的性质${\mathcal{P}}$和序列$\rho$, 词上的组合领域一个重要的研究课题是找出所有的因子$\omega$和序数$p$,使得序列$\rho$中第$p$次出现的因子$\omega$ (记为$\omega_p$) 满足性质${\mathcal{P}}$.这个问题等价于研究``因子谱''.确定因子谱是一个困难的问题. 为了实现目标,我们引入并研究了一系列的概念:核词、包络词、回归词和任意因子的诱导序列. 利用因子谱和诱导序列,我们可以解决序列中的一些计数问题.例如:在序列的任意一个片段中回文或者高次方词的个数. 本文中,我们将结合几个特殊的序列展示相关的研究结果.这些序列包括: Fibonacci序列、Tribonacci序列、Period-doubling序列等等. 我们相信这些概念和方法对于所有的一致常返序列都是有效的.     

On the monotonicity of some singular integral operators

The paper deals with the monotonicity of singular integral operators of the form where is the Cauchy singular integral operator on the interval (0,1) of the real axis and q is a power or logarithmic function. Under suitable assumptions, such singular integral operators are proved to be monotone and maximal monotone in spaces with power weights. Moreover, two related integral equations with weakly singular kernels of logarithmic type are studied. Copyright © 2012 John Wiley & Sons, Ltd.