SOME TOPICS ON WAVELET ANALYSIS

A review of the advance in the theory of wavelet analysis in recent years is given.     

样条共轭插值与L_p模误差估计

[1—5]讨论了各种类型插值样条的L_∞模最优误差估计。本文利用共轭插值样条,给出一些插值样条类的L_1模最优误差界,然后用插值空间理论导出L_p模估计的上界。 一、样条共轭插值 设n≥1并给定[0,1]上的两个分划:     

五次Hermite插值样条的最优误差界

<正> [1]对等距分划下单结点的五次插值样条作出了最优误差估计,本文将给出等距分划下五次Hermite插值样条的最优误差界. 先引入一些记号与定义. 向量(a_1,…,a_n)的弱变号数和强变号数分别记为S~-(a_1,…,a_n)和S~+(a_1,…,a_n).     

加强技术创新 推进产学研结合 为广东经济发展服务

广东省教育部产学研合作计划的实施，给高校科技发展带来了新的机遇和挑战。在省部产学研合作中，中山大学围绕国家创新体系的建设目标和区域经济发展的需要，以制度创新为动力，以科技创新为中心，坚持“基础研究与应用研究并重、知识创新与技术创新并重、提高学术水平与服务地方经济并重”的思路，为建设创新型广东做出了应有的贡献。     

指定结点重数的最优求积公式

本文通过完全样条和单样条之间的对偶关系,证明了关于函数类W_∞~r的(r_1,…r_n)型最优求积公式存在且唯一。     

ON UNIQUENESS OF SOLUTION TO POINTWISE LANDAU PROBLEM ON THE FINITE INTERVAL

1. Introduction Let W_∞~((r)) (β) = {f| f∈W_∞~((r)) [-1,1], ||f||_(C[-1,1]) β, ||f~((r))||_∞ 1}.In this paper, we will consider the following Landau problem:λf~((k))(ξ) + μf~((k-1)) (ξ) →inf, f∈W_∞~((r)) (β), (1.1)where ξ∈[-1,1], 1(?)k(?)r-1, and λ, μ real and not all zero, (if k=1,suppose λ≠0 in addition ). A. Pinkus studied it first. To begin with, we introduce some fundamental definitions anddenotions. The perfect spline f, which satisfies || f~((r))||_∞ = 1 andhas n knots and n+r+1 points of equioscillation in [-1,1], isdenoted by x_(nr), which is refered as Tchebyshev perfect spline. And     

服务社会--大学无法回避的社会责任

科技成果的转化,是中国高校以及大学校长的一个心病。大学之于社会的意义,概括起来有三个方面,一是人才的培养,二是科学研究,三是社会服务。加速高校科技成果的推广转化,促进科技与经济的结合,是大学社会服务功能的一个方面,是大学义不容辞的任务。从某种意义上说,在当今社会,大学的影响力和渗透     

基于L~1度量分析的图象分解与重构算法

Mallat‘s decompositon and reconstruction algorithms are very important in the the field of wavelet theory and its applications to signal processing.Wavelet Anal-ysis,which is based on L^2(R) space,can eliminate redundancy of signals with the help of orthogonality and characterize the processing precision with the meansquare error.In the recent years,it is understood that the mean square measuredoes not match human visual sensitivity well.From the point of view,R.DeVore studied L^1 measure instead.Similarly,considering the principles of image com-pression,Yang introduced and dealt with orthogonality in L^1 space based on thebest approximation theory,and consequently established the corresponding decom-position and reconstruction algorithms for signals.In this paper,error analyses for the algorithms above are taken and the selection of the best parameters in the algorithms are discussed in detail.Finally,the algorithms are compared with the classical Haar and Daubechies‘‘s orthogonal wavelets based on the singal-to-noiseratio data computed.     

Optimal Quadrature Formulas (OQF) and Periodic Monosplines With Multiplicities

For pre-assigned multiplicities (r_i)_1~n, 1≤r_i≤m, and f∈W_q~m, consider the qu-adrature formulas of type (r_i,…, r_n):     

关于混合插值样条

本文中我们提出一类特殊的H-B插值问题,即所谓混合插值.我们首先讨论五次样条,它是将Meir和Sharma的缺插值样条中的二阶导数的逐点插值换成一阶导数与二阶导数的交替插值.然后又讨论了三次样条,将[3]中讨论的(p)型插值改成一阶导数及函数值本身在节点处的交替插值.我们研究了这两类样条的存在、唯一性,并得到了它