多-尺度加细函数及其性质的研究

引入伸缩因子为a的多-尺度加细函数和平移不变子空间的概念．研究了多-尺度加细方程解存在的条件．特别地,给出这种方程的解是正交的充分必要条件．建立了多-尺度加细函数与两尺度加细函数之间的关系．并讨论了它们的一些性质．最后给出相应的构造算例．     

对称反对称多重尺度函数的构造

１　多重小波的定义和双尺度相似变换 作为一种分析工具,小波已经运用在各种领域,并取得了显著的成果．近年来,多重小波成为小波研究的热点．Ｉ．Ｄａｕｂｅｃｈｉｅｓ［１］已经证明,对单重小波,除Ｈａｒｒ基外不存在对称和反对称的有紧支集的小波正交基．而多重小波则不受这一限制． 利用分形插值的方法,Ｇｅｒｏｎｉｍｏ、Ｈａｒｄｉｎ和 Ｍａｓｓｏｐｕｓｔ［２］等构造出了ＧＨＭ多重小波,相应的多重尺度函数和多重小波函数如图１和图２所示．ＧＨＭ多重小波的两个尺度函数都是对称的,相应的小波函数则一个对称另一个反对称;…     

一种对称损失函数下正态总体刻度参数的估计

本文研究正态分布中刻度参数在损失函数L(σ，δ)=[(σ-δ)^2]/σδ下的最小风险同变估计及Bayes估计，并讨论(cT(x) d)^1/2形式估计的可容许性与不可容许性，我们发现在这种损失下σ的极大似然估计是不可容许的．     

正定可对称化矩阵与预对称迭代算法

１．问题的提出 我们引入正定可对称化矩阵定义的背景是为了研究求解二阶椭圆型非自共轭方程的离散迭代有效算法、这类方程的椭圆型是本质的分析性质。是由二阶项决定的,在离散方程中表现为正定性;非自共轭性则是由方程中的一阶项引起的,在相当广泛一类问题中可通过变量代换化为自共轭。因此,我们称这类问题为正定可对称化问题。 例１．高维二阶常系数椭圆型方程其中 Ａ为常系数正定对称（ｓ．ｐ．ｄ）阵, 为正交阵, Ｄ是对角元素为正的对角阵。 先作变量代换,通过演算,偏微分方程对于新变量变成这里进而令可将原非自共轭偏微分算子…     

一个初等对称函数不等式的加强

一个初等对称函数不等式的加强汤子赓（浙江省绍兴市经济管理干部培训中心３１２０００）本文对文［１］给出的关于初等对称函数的一个不等式，通过求得函数的下确解，得到最佳结果．为便于阅读，先将［１］中的有关概念介绍如下：ｎ个正数ｘ１，ｘ２，…，ｘｎ的初等对称...     

a尺度三维八向加细小波尺度函数的构造算法

依据双向小波理论为基础,利用张量积构造a尺度三维八向加细小波尺度函数,研究了具有紧支撑性面具符号的a尺度三维八向加细方程拥有紧支撑分布解的情况,讨论了三维八向a尺度加细小波函数紧支撑区间.     

M带紧支撑正交对称复尺度函数的构造

1 引言 近年来,小波的研究主要集中于实值小波,并得到了许多优美的结果。如Daubechies构造一系列2带正交小波,Chui和Lian构造若干3带既正交又对称的尺度函数和小波,杨守志,程正兴等,构造出既正交又对称的4带尺度函数和小波,对M≥3这样的一般情形,Bi,Dai和Sun给出M带正交的Daubechies类尺度函数的通用滤波器表     

一个对称函数下界的加强

记ｆｋ（ｘ１…，ｘｎ）＝Ｅｋ（１－ｘ１，…，１－ｘｎ）－Ｅｋ（ｘ１，…，ｘｎ），ｋ＝１，…ｎ其中Ｅｋ（ｘ１，…，ｘｎ）为初等对称函数，并规定当ｋ＝０时，Ｅｋ（ｘ１，…，ｘｎ）＝１，当ｋ＜０或ｋ＞ｎ时，Ｅｋ（ｘ１，…，ｘｎ）＝０．笔者在文［１］证明了：...     

关于对称函数的一类不等式

关于对称函数的一类不等式石焕南（北京联大职业技术师院１０００１１）ｎ个正数ｘｌ，ｘＺ，…，ｘ。的初等对称函数是规定当ｋ＝０时，Ｅｋ（ｘｌ，…，。。）一１；当ｋ＜０或ｋ＞。时，Ｅｋ（。１，…，。。）一０．不难验证本文将证明如下两个定理定＆ＩＲ。；＞０，...     

对称双线性函数与线性变换

借助内积关系来推断欧氏空间的变换具有线性性的研究，已取得了丰富的成果［２－６］．与之相对照，关于借助对称双线性函数来推断向量空间的变换具有线性性的研究还很少．为简便，本文中Ｖ均代表数域Ｆ上任意维向量空间；Ｗ均代表任意维欧氏空间；Ｖｖ代表Ｖ的所有变换的...     

预设尺度滤波器的双正交小波矩阵的构造

本文研究尺度滤波器的基本分解问题。基于所得结果，对于任意给定的尺度滤波器，给出了双正交小波矩阵的构造方案。     

Asymptotic regularity of Daubechies' scaling functions

Let , , be Daubechies' scaling function with symbol , and let , be the corresponding Sobolev exponent. In this paper, we make a sharp estimation of , and we prove that there exists a constant independent of such that

This answers a question of Cohen and Daubeschies ( Rev. Mat. Iberoamericana, 12(1996), 527-591) positively.

     

仿射分形插值函数与纵向尺度因子

文中对一类仿射分形插值函数,用纵向尺度因子刻画了函数在特定值域分布的充分必要条件.     

Characterization of scaling functions in a multiresolution analysis

We characterize the scaling functions of a multiresolution analysis in a general context, where instead of the dyadic dilation one considers the dilation given by a fixed linear map such that and all (complex) eigenvalues of have absolute value greater than In the general case the conditions depend on the map We identify some maps for which the obtained condition is equivalent to the dyadic case, i.e., when is a diagonal matrix with all numbers in the diagonal equal to There are also easy examples of expanding maps for which the obtained condition is not compatible with the dyadic case. The complete characterization of the maps for which the obtained conditions are equivalent is out of the scope of the present note.

     

A new approach to interpolating scaling functions

We present a new method to construct interpolating refinable functions in higher dimensions. The approach is based on the solutions to specific Lagrange interpolation problems by polynomials and applies to a large class of scaling matrices. The resulting scaling functions automatically satisfy certain Strang-Fix conditions. Several examples are discussed.     

On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions

Gauss-Lobatto quadrature formulae associated with symmetric weight functions are considered. The kernel of the remainder term for classes of analytic functions is investigated on elliptical contours. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with either the real or the imaginary axis. The results obtained here are an analogue of some recent results of T. Schira concerning Gaussian quadratures.

     

任意矩阵伸缩的正交小波包

1 引言 Coifman和Meyer引入L~2(R)中正交小波包,可以用张量积形式构造L~2(R~2)上的二维正交小波包;Chui和Li研究单变量非正交小波包和对偶小波包;Shen给出矩阵伸缩为2I时L~2(R~s)上非张量积小波包的构造算法;程正兴给出矩阵小波包的构     

Minimizing symmetric submodular functions

We describe a purely combinatorial algorithm which, given a submodular set functionf on a finite setV, finds a nontrivial subsetA ofV minimizingf[A] + f[V A]. This algorithm, an extension of the Nagamochi—Ibaraki minimum cut algorithm as simplified by Stoer and Wagner [M. Stoer, F. Wagner, A simple min cut algorithm, Proceedings of the European Symposium on Algorithms ESA '94, LNCS 855, Springer, Berlin, 1994, pp. 141–147] and by Frank [A. Frank, On the edge-connectivity algorithm of Nagamochi and Ibaraki, Laboratoire Artémis, IMAG, Université J. Fourier, Grenbole, 1994], minimizes any symmetric submodular function using O(|V|³) calls to a function value oracle. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper was presented at the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) in January 1995. This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.     

Classical symmetric functions in superspace

We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under the diagonal action of the symmetric group on the sets of commuting and anticommuting variables. In this work, we present the superspace extension of the classical bases, namely, the monomial symmetric functions, the elementary symmetric functions, the completely symmetric functions, and the power sums. Various basic results, such as the generating functions for the multiplicative bases, Cauchy formulas, involution operations as well as the combinatorial scalar product are also generalized.