关于正项级数收敛性

本在Cauchy判别法和D’Alembert判别法基础上，对正项级数的收敛性提出了一个新的判别方法。     

一类三角级数的收敛性

利用Euler公式求三角级∞∑m=1 sinmx/n与∞∑m=1 cosmx/m的和函数并讨论其一致收敛性.     

用莱布尼茨判别法判别一般级数的收敛性

在高等数学和数学分析的教科书中 ,莱布尼茨判别法是用来判别交错级数的收敛性的。若用以下定理 ,我们还可以用它来判别一般级数的收敛性。定理 A　常数项级数 ∞n=1un加括号得到的新级数 ∞k=1( unk+1+unk+2 +… +unk+ 1)。若对每个 k,unk+1,unk+2 ,… ,unk+ 1同号 ,则 ∞n=1un 收敛的充要条件是 ∞k=1( unk+1+unk+2 +… +unk+ 1)收敛。证明　只需证明充分性。设 Sn= nk=1uk,则 limk→∞ Snk=S收敛。因此 ,对每个ε>0 ,存在 k0 ,使 k>k0 ,就有 S -ε相似文献   

小波级数的一些讨论

本文针对小波变换数学中,学员对于小波变换多分辨率分析概念理解困难的问题,提出了小波级数教学方法,通过分析小波多分辨分析概念的本质,建立起与傅立叶级数之间的比较和联系,清楚地描述了小波多分辨分析的本质,从而对加深对小波多分辨分析的理解有明显的效果,最终提高了整个小波课程教学效果。     

一道试题引出的级数收敛性判别法

以命题形式给出证明的一道习题,提供了判断级数收敛与否的一种方法。     

交错级数收敛性的一个判别法

当交错级数∑∞n=0(-1)n-1un中un含有阶乘、连乘职、幂次等的商的复杂形式时,运用命题中所给出的判别法,判断其收敛性比较方便.     

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.     

关于具有拟单调系数的三角级数L1-收敛性的注记

假设三角级数的系数具有拟单调性，给出了级数按L^1[0，2π]中的范数收敛于其和函数的一个判别条件，推广了文献中的有关结果．     

拉普拉斯级数收敛性的一种简单证明

拉普拉有数的收敛性有多种证明方法。本给出了一种非常简单的证明,其中主要只用到了正项级数的一个基本定理,相比之下,本的方法是很容易理解的,在工科的教学中采纳比较合适。     

三角级数一致收敛性问题在复空间的完整推广

本文研究了三角级数在复空间中的一致收敛性问题.利用Abel变换等方法,获得了三角级数在复空间中满足上确界有界变差(SBVS)条件下一致收敛的充分必要条件,推广了Korus在实空间中的结论.     

Pointwise convergence of a class of non-orthogonal wavelet expansions

Non-orthogonal wavelet expansions associated with a class of mother wavelets is considered. This class of wavelets comprises mother wavelets that are not necessarily integrable over the whole real line, such as Shannon's wavelet. The pointwise convergence of these wavelet expansions is investigated. It is shown that, unlike other wavelet expansions, the ones under consideration do not necessarily converge pointwise to the functions at points of continuity, unless a more stringent condition, such as bounded variation, is imposed.

     

Asymptotic behavior of gibbs functions forM-band wavelet expansions

In this paper the asymptotic behavior of Gibbs function for a class ofM-band wavelet expansions is given. In particular, the Daubechies’ wavelets are included in this class. The authors are partially supported by the Chinese National Natural Science Foundation (19571972), the Key Project Foundation (69735020) and the Zhejiang Provincial Science Foundation of China (196083)     

A local convergence theorem for partial sums of stochastic adapted sequences

In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.     

ND序列部分和的大偏差和强收敛性

利用ND随机变量序列的矩不等式、极大值不等式以及随机变量的截尾方法,重点研究了ND随机变量序列部分和的大偏差结果和强收敛性,推广了文献中一些相依随机变量序列的若干相应结果.     

ON CONVERGENCE OF WAVELET PACKET EXPANSIONS

It is well known that the-Walsh-Fourier expansion of a function from the block spaceB _q([0,1]), 1B _q in certain periodized smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of L^p-functions, 1相似文献   

On convergence of wavelet packet expansions

It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.     

PA序列部分和完全收敛性的进一步探讨

通过讨论矩的存在性与部分和尾概率级数收敛性的关系,给出了PA序列部分和的完全收敛性,获得了PA序列与独立序列类似的强极限性质.     

Inversion of the wavelet transform using Riemannian sums

We study the approximation of the inverse wavelet transform using Riemannian sums. For a large class of wavelet functions, we show that the Riemannian sums converge to the original function as the sampling density tends to infinity. When the analysis and synthesis wavelets are the same, we also give some necessary conditions for the Riemannian sums to be convergent.     

The convergence space of minimal USCO mappings

A convergence structure generalizing the order convergence structure on the set of Hausdorff continuous interval functions is defined on the set of minimal usco maps. The properties of the obtained convergence space are investigated and essential links with the pointwise convergence and the order convergence are revealed. The convergence structure can be extended to a uniform convergence structure so that the convergence space is complete. The important issue of the denseness of the subset of all continuous functions is also addressed.      

On the convergence of expansions in polyharmonic eigenfunctions

We consider expansions of smooth, nonperiodic functions defined on compact intervals in eigenfunctions of polyharmonic operators equipped with homogeneous Neumann boundary conditions. Having determined asymptotic expressions for both the eigenvalues and eigenfunctions of these operators, we demonstrate how these results can be used in the efficient computation of expansions. Next, we consider the convergence. We establish the key advantage of such expansions over classical Fourier series–namely, both faster and higher-order convergence–and provide a full asymptotic expansion for the error incurred by the truncated expansion. Finally, we derive conditions that completely determine the convergence rate.