以递推数列为通项的级数判别法

讨论了以递推数列为通项的级数收敛的判别法,证明了递推函数二阶导数存在蕴含级数发散以及适用二阶导数不存在情形的两类判别法.     

交错级数收敛性判别法

研究交错级数收敛性判别法.通过计算级数通项的极限和单调性得到三个判据,并对其中两个结论给出形式简化的推论,最后举例说明所提判别法的应用.     

关于Fourier级数收敛性的判定定理

讨论Fourier级数收敛性判定定理的Dini判别法和Jordan判别法,并通过列举实例说明这两种方法是相互不包含的.     

Fourier级数两个收敛定理的关系及反例

Fourier级数的收敛问题一直是很多数学研究者关注的问题,不同的数学分析教材和高等数学教材对收敛定理的表述各不相同。本文通过实例说明这些收敛定理之间不存在包含关系,并进一步说明这些收敛定理都是判别Fourier级数收敛的充分条件,而不是充要条件。     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.     

Subseries Convergence and Unconditionally Convergence of Compact Operator Series

Let(E,r)bealocallyconvexHausdorfftopologicalvectorspace.AseriesZxiinEissaidtobesubseriesr-convergent(-s.c.),ifforeachstrictlyincreasingsequence{n,}inN,theseriesZx"'isT-convergent.TheseriesZx,issaidtobeunconditionallyr-convergent(r-u.c.),ifforeachpermutationffofN,theseriesZx,<,,ls.,r-convergence.rheseriesZx,issaidtobesubseriesunconditional1yT-convergent(r-s.u.c.)ifforeachstrictlyincreasingseqtience{n,}inN,theseriesZx.,isunconditionallyr-convergent.If(E,r)isasequentiallycompletespace,thenT…     

Pointwise Convergence and Uniform Convergence of Wavelet Frame Series

Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.     

在反思中教学数项级数敛散性的概念

反思是数学活动的核心和动力,学生只有在学习中反思,在反思中学习,才能形成数学思维,才能学会学习;教师只有在行动中反思,在反思中行动,才能成为"研究型的教师",才能学会教学.学生在学习数项级数敛散性概念的过程中,往往因为未能很好地实现与概念扩展相对应的观念更新,而不能深刻地理解数项级数敛散性的概念.为解决此问题可考虑采取以下举措:一是结合Koch雪花的面积和周长问题引起困惑,产生数学反思;二是结合级数敛散性问题乘兴追问,深化数学反思.     

时间序列中参数变点的检测(英文)

The paper considers the problem of testing for a change point in the parameters of AR（p） models.It is shown that the asymptotically limiting distribution of the residual CUSUM of squares test（RCUSQ） is still the sup of a standard Brownian bridge under null hypothesis.We also show via simulations that our asymptotic results provide good approximations in finite samples.     

共轭混合型Jacobi级数的收敛速度(英文)

对于有界变差的连续函数，本文给出了其共轭混合型Jacobi级数的收敛速度．     

The Rate of Convergence for the Conjugate Series of Mixed Jacobi Series

The rate of convergence of the conjugate series of the mixed Jacobi series for continuous function of bounded vartation is given.     

依概率收敛与依分布收敛的关系

本文探讨了随机变量序列依概率收敛与依分布收敛的关系 ,并给出了一个依分布收敛能保证依概率收敛的最弱的条件 ,即 :设分布函数列 { Fn(x) }弱收敛于连续的分布函数 F(x) ,则存在随机变量序列{ξn}和随机变量ξ,它们分别以 { Fn(x) }和 F(x)为其对应的分布函数列和分布函数 ,且 {ξn}依概率收敛于ξ.     

Necessary Conditions for the Convergence of Fourier Series

Various conditions have been claimed in a recent paper as necessary for the convergence of a Fourier series at a point, principally the Lebesgue summability of the series. These conditions are, however, shown to be necessary only in a particular class of functions and the error in the argument is explicated. The relevant facts about Lebesgue summability are reviewed.     

正项级数敛散性的一个判别法

基于正项级数的比较判别法和p-级数的敛散性,给出一个与D’Alembert判别法和Cauchy判别法平行的判别正项级数敛散性的方法.并通过实例对所给判别法的可行性进行检验,发现它是已有方法的一个有效补充.     

共轭Neumann-Bessel级数的收敛速度

给出共轭Neumann-Bessel级数的核函数的渐近表达式，它的精度达到O（），然后利用这个表达式，讨论了该级数的收敛速度．     

幂指型正项级数的判别方法

引人幂指型正项级数的概念,基于比较判别法和正项等比级数的敛散性,建立幂指型正项级数的审敛规则,分析它与Cauchy判别法的关系,并将其推广用以判别普通正项级数的敛散性.实例说明其应用方法.     

Convergence of the Magnus Series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a sufficient condition for convergence, which improves on several earlier results.     

Statistical Convergence of Infinite Series

In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We will discuss some questions related to the convergence of subseries of a given series.