L~2(R~d)中MRA小波相位的刻画

设A是d×d实扩展矩阵,ψ是以A为扩展矩阵的小波,f是可测函数.如果对任意以A为扩展矩阵的小波ψ,fψ(其中ψ表示ψ的傅立叶变换)的逆傅立叶变换仍是以A为扩展矩阵的小波,则称f是以A为扩展矩阵的小波乘子.主要刻画了L²(R2(R^d)空间中,以行列式绝对值等于2的整数矩阵为扩展矩阵的MRA小波的线性相位.利用该结果,具体给出了二维情况下,Haar型和Shannon型小波在相似意义下的六类整数扩展矩阵的线性相位的表达形式.最后将具有线性相位的MRA不可分离小波应用到二维图象的边缘检测上.     

多线性Fourier乘子算子的加权估计——献给陆善镇教授75华诞

本文考虑多线性Fourier乘子算子在加权Lebesgue空间的乘积空间上的性质,利用多线性Fourier乘子算子的核估计以及多线性奇异积分算子的加权理论,建立多线性Fourier乘子算子的（关于多重Ap/r（R^mn）权函数以及关于一般权函数的）两个加权估计.     

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     

L~2(R~n)中MRA Parseval框架小波和它们的乘子

刻画了L~2(R~n)中具有扩展矩阵伸缩的广义低通滤波器和多尺度分析Parseval框架小波(缩写为MRA PFW).首先,研究了伪逆的尺度函数、广义的低通滤波器和MRA PFW,给出它们的一些刻画.接着,我们给出与MRA PFW相联系的几类乘子的一些刻画.最后,给出了一个例子来证明的结论.     

L~2(R~2)中2进变元低通滤波器

一维2进低通滤波器在一维多分辨分析(MRA)小波的构造和拓扑性质研究中起到重要作用.对于高维小波,其生成要依赖于某个扩张矩阵,所以构造比较复杂.该文讨论由一致矩阵2I_2(2002)生成的MRA小波的低通滤波器(称作2进双变量滤波器.利用2进双变量滤波器乘子完全刻画了2进双变量滤波器,并且证明了所有2进双变量滤波器集合在L~2(T~2)范数拓扑下是道路连通的结论.     

二元多重小波紧框架的矩阵频域乘子

矩阵频域乘子是由本质有界可测函数组成的矩阵,它能将多重小波紧框架映射成多重小波紧框架.引入二元多重小波紧框架的矩阵频域乘子的概念,给出了一个矩阵值函数成为二元多重小波紧框架的矩阵乘子的充要条件,并给出了构造例子.     

L~2(R~n)上的半正交多小波框架

本文研究L2(Rn)上伸缩矩阵A满足|detA|1的半正交多小波框架.本文得到半正交和严格半正交框架的一系列性质及刻画.本文证明半正交Parseval多小波框架与广义多分辨分析(GMRA)Parseval多小波框架是等价的.特别地,本文利用最小频率支撑(MSF)多小波框架和小波集,构造若干半正交多小波框架的例子.     

双线性Fourier乘子在Triebel-Lizorkin和Besov空间的有界性

本文利用Littlewood-Paley分解,Fourier变换和逆变换等方法,研究了双线性Fourier乘子在非齐次正光滑性Triebel-Lizorkin空间和Besov空间的有界性.     

向量值双正交小波的存在性及滤波器的构造

引进了向量值多分辨分析与向量值双正交小波的概念.讨论了向量值双正交小波的存在性.运用多分辨分析和矩阵理论,给出一类紧支撑向量值双正交小波滤波器的构造算法.最后,给出4-系数向量值双正交小波滤波器的的构造算例.     

L2(Rs)中正交尺度函数和正交小波的Fourier变换紧支集的刻画

借助于Fourier变换,在较弱条件下给出了φ(x)是L²(R^s)上正交尺度函数的一个充分必要条件.进一步, 假设 {Ψ_μ } 是正交小波, 且正交小波的Fourier变换紧支集是 ∪_μsupp{ψ_μ} =∏^s_i=1[A_i, D_i] -∏^s_i=1(B_i, C_i),A_i≤B_i≤C_i≤D_i, i =1, 2,… , s. 则在最弱条件“每一个 |ψ_μ| 在ω∈∂(∏^s_i=1[A_i, D_i]) 上连续'下, 该文通过一些不等式和等式给出了正交尺度函数和正交小波的Fourier变换紧支集的刻画.文中的结论全面改进了龙瑞麟和张之华的结果.     

Combinatorial principles between RRT 2 2 and RT 2 2

We study the strength of some combinatorial principles weaker than Ramsey theorem for pairs over RCA0. First, we prove that Rainbow Ramsey theorem for pairs does not imply Thin Set theorem for pairs. Furthermore, we get some other related results on reverse mathematics using the same method. For instance, Rainbow Ramsey theorem for pairs is strictly weaker than ErdSs- Moser theorem under RCA0.     

Infra-red spectral studies of CHF2-CHCl2 and CBrCl2-CBrCl2

The infra-red spectra of two polyhalogenated ethanes, 1, 1-difluoro-2, 2-dichloro ethane and 1, 2-dibromo-1, 1, 2, 2-tetrachloro ethane were obtained in the region of 2·5–38 microns. The spectra of CHF₂-CHCl₂ were obtained in gas, liquid and solid states and also in solvents of widely varying dielectric constants. These spectral studies showed that the molecule exists in the form of two rotational isomers. The fundamental modes of the two isomers were identified on the basis of intensity changes from gas to liquid to solid and in solvents of different dielectric constants. The observed infra-red absorption bands have been assigned in terms of the fundamental absorption bands. Spectra of CBrCl₂-CBrCl₂ were obtained in the solid and vapour phase and in various solvents. These spectra showed that CBrCl₂-CBrCl₂ exists only in the trans form. The infra-red spectra, combined with Raman data available from literature was used for complete assignment of the observed absorption bands.     

P2Q2Iso2D=2D Isoparametric FEM in Matlab

A short Matlab implementation realizes a flexible isoparametric finite element method up to quadratic order for the approximation of elliptic problems in two-dimensional domains with curved boundaries. Triangles and quadrilaterals equipped with varying quadrature rules allow for mesh refinement. Numerical examples for the Laplace equation with mixed boundary conditions indicate the flexibility of isoparametric finite elements.     

Non-symmetric 2-designs modulo 2

Necessary conditions are obtained for the existence of a 2 – (v, k, ) design, for which the block intersection sizess ₁,s ₂, ...,s _n satisfys ₁ s ₂ ... s _n s (mod 2 ^e ), wheree is odd. These conditions are obtained by combining restrictions on the Smith Normal Form of the incidence matrix of the design with some well known properties of self-orthogonal binary codes with all weights divisible by 4.Research done at AT&T Bell Laboratories.     

Descent on 2-Fibrations and Strongly 2-Regular 2-Categories

We consider pseudo-descent in the context of 2-fibrations. A 2-category of descent data is associated to a 3-truncated simplicial object in the base 2-category. A morphism q in the base induces (via comma-objects and pullbacks) an internal category whose truncated simplicial nerve induces in turn the 2-category of descent data for q. When the 2-fibration admits direct images, we provide the analogous of the Beck–Bénabou–Roubaud theorem, identifying the 2-category of descent data with that of pseudo-algebras for the pseudo-monad q ^*Σ _q . We introduce a notion of strong 2-regularity for a 2-category R, so that its basic 2-fibration of internal fibrations c od:F ib(R)→R admits direct images. In this context, we show that essentially-surjective-on-objects morphisms, defined by a certain lax colimit, are of effective descent by means of a Beck-style pseudo-monadicity theorem.     

环$F_2 uF_2 u^2F_2$上的循环码及自对偶码

We give the structures of a cyclic code over ring
R = F2 ＋ uF2 ＋ u^2F2 = {0, 1,u, u^2,v, v^2,uv, v^3},
where u^3 = 0, of odd length and its dual code. For the cyclic code, necessary and sufficient conditions for the existence of self-dual code are provided.     

Comparison of relative risk,attributable risk and logistic response procedures for 2×2×2 andc 2×2×2 contingency tables

Summary A numerical evaluation was made on three different χ² statistics in order to compare mutagenic risk frequencies between two experimental groups in a 2×2×2 contingency table andc 2×2×2 contingency tables. The three methods involve 1) a relative risk approach, 2) an attributable risk approach and 3) a logistic response approach. A relatively large difference was observed among χ² statistics in the three approaches using actual data under the hypothesis that there is no difference between the two groups under scrutiny. With regard to approximate power, it appears that approaches 2) and 3) give fairly stable results. Approach 1) has greater power if there is a small difference in the control groups. It was confirmed that the approximate power of approach 1) is extremely large when the difference in the relative risk frequencies between the two groups under contrast is constant and each relative risk frequency is small. This paper was presented at the 48th annual meeting of Japan Statistical Association in Tokyo, Japan, 1980.