Besov spaces with non-doubling measures

Suppose that is a Radon measure on which may be non-doubling. The only condition on is the growth condition, namely, there is a constant 0$"> such that for all and 0,$">

where In this paper, the authors establish a theory of Besov spaces for and , where 0$"> is a real number which depends on the non-doubling measure , , and . The method used to define these spaces is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are obtained.

     

双联齿轮断裂分析

机床传动系统双联直齿轮投入运行不久即发生齿面断裂事故,造成较大经济损失.传动系统所用双联齿轮未达到设计使用寿命,属于早期断裂失效.对现场收集到的断裂齿轮残块进行化学成分分析和硬度测试,对齿廓工作面及断裂形成的断口用扫描电镜进行微观观察,对齿轮残块上出现的裂纹用光学金相显微镜观察其形貌和微观特征,依据检测实验数据和结果,...     

Theta lifting from elliptic cusp forms to automorphic forms on <Emphasis Type="Italic">Sp</Emphasis>(1, <Emphasis Type="Italic">q</Emphasis>)

Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by “Kudla lifting”, i.e. a theta lifting from elliptic modular forms to holomorphic automorphic forms on SU(1,q). We prove that the images of Arakawa’s theta lifting belong to the space of bounded automorphic forms generating quaternionic discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincaré series generating such discrete series. The author was partially supported by JSPS Research Fellowships for Young Scientist for April 2002 to March 2005. The results of this paper were obtained in this period.     

Monomial Ideals and the Gorenstein Liaison Class of a Complete Intersection

In an earlier work, the authors described a mechanism for lifting monomial ideals to reduced unions of linear varieties. When the monomial ideal is Cohen–Macaulay (including Artinian), the corresponding union of linear varieties is arithmetically Cohen–Macaulay. The first main result of this paper is that if the monomial ideal is Artinian then the corresponding union is in the Gorenstein linkage class of a complete intersection (glicci). This technique has some interesting consequences. For instance, given any (d + 1)-times differentiable O-sequence H, there is a nondegenerate arithmetically Cohen–Macaulay reduced union of linear varieties with Hilbert function H which is glicci. In other words, any Hilbert function that occurs for arithmetically Cohen–Macaulay schemes in fact occurs among the glicci schemes. This is not true for licci schemes. Modifying our technique, the second main result is that any Cohen–Macaulay Borel-fixed monomial ideal is glicci. As a consequence, all arithmetically Cohen–Macaulay subschemes of projective space are glicci up to flat deformation.     

Entropy extension

We prove an “entropy extension-lifting theorem.” It consists of two inequalities for the covering numbers of two symmetric convex bodies. The first inequality, which can be called an “entropy extension theorem,” provides estimates in terms of entropy of sections and should be compared with the extension property of ?_∞. The second one, which can be called an “entropy lifting theorem,” provides estimates in terms of entropies of projections.     

Use of Divided Differences and B Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids

In this paper, we construct fast discrete transforms of wavelet type with an arbitrary number of zero moments for nonuniform grids. We obtain explicit formulas for the parameters defining the wavelet transform.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 743–752.Original Russian Text Copyright ©2005 by I. V. Oseledets.     

A Method for the Construction of Families of Biorthogonal Filters with Prescribed Properties

Some necessary and sufficient conditions are given in order to obtain biorthogonal wavelet filters with properties which are usually required in applications, such as symmetry and regularity order, by appropriately choosing the parameters in the lifting scheme. A special class of filters extending the biorthogonal B-spline filters is then proposed and analyzed.     

基于非线性提升格式的边缘检测

针对边缘检测中检测精度与抗噪能力的相互制约的问题，采用非线性提升格式，结合自适应阈值，提出了一种新的边缘检测算法．该算法计算简单、易于并行实现，且在一定程度上协调了检测精度与抗噪声之间的矛盾．实验结果表明该算法在提取边缘的同时能有效地抑制噪声，检测精度高．     

适合于图像压缩的7/5小波基的构造

通过利用提升算法和检验双正交小波稳定性的充分必要条件Cohen-Daubechies准则,构造了一个适合于图像压缩的7/5双正交小波基.为了便于小波变换的硬件实现,选取四个提升系数中的三个为二进制分数,而另一提升因子为1/10的倍数.本文中所构造的7/5小波基虽然在压缩性能上低于CDF9/7小波,但由于提升系数为二进制分数和1/10的倍数,所以该小波基的小波变换更易于采用硬件来实现,并且其小波变换速度比CDF9/7小波要快.实验的结果表明该小波的压缩性能优于Daubechies5/3小波,同时与[6]所构造的两组7/5小波基相比较,该小波变换不仅能方便于硬件的实现,而且其压缩性能优于或相当于[6]中的两组7/5小波基.