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Quasisymmetric property for conjugacies between Anosov diffeomorphisms of the two-torus

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Science China mathematics 2010年第3期53卷 663-670页

作者： HU HuYi 1 & JIANG YunPing 2, 1 department of mathematics, Michigan State university, East Lansing, MI 48824, usa 2 department of mathematics, the Graduate Center and Queens College of CUNY, Flushing, NY 11367, usa 1. department of mathematics Michigan State University East Lansing MI 48824 USA2. Department of Mathematics the Graduate Center and Queens College of CUNY Flushing NY 11367 USA

We prove that the restrictions of the conjugacy between two Anosov diffeomorphisms of the twotorus to the stable and unstable manifolds are quasisymmetric homeomorphisms.

关键词： quasisymmetry Anosov diffeomorphisms conjugacy Hlder condition Markov partition

Constructing super Gabor frames:the rational time-frequency lattice case

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Science China mathematics 2010年第12期53卷 3179-3186页

作者： LI ZhongYan 1 & HAN DeGuang 2, 1 department of mathematics and Physics, North China Electric Power university, Beijing 102206, China 2 department of mathematics, university of Central Florida, Orlando, FL 32816, usa 1. department of mathematics and Physics North China Electric Power University Beijing 102206 China2. Department of Mathematics University of Central Florida Orlando FL 32816 USA

For a time-frequency lattice Λ = A Z d × B Z d , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if |det( AB) | = 1 L . The proof of this result involves various techniques from multi-lattice tiling and operator algebra theory, and it is far from constructive. In this paper we present a very general scheme for constructing super Gabor frames for the rational lattice case. Our method is based on partitioning an arbitrary fundamental domain of the lattice in the frequency domain such that each subset in the partition tiles R d by the lattice in the time domain. This approach not only provides us a simple algorithm of constructing various kinds of orthonormal super Gabor frames with flexible length and multiplicity, but also allows us to construct super Gabor (non-Riesz) frames with high order smoothness and regularity. Several examples are also presented.

关键词： super Gabor frame orthonormal super frame full rank lattice tiles

Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

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Acta Mathematica Sinica,English Series 2000年第3期16卷 405-444页

作者： Guozhen Lu department of mathematics,Wayne State university,Detroit,MI 48202,usa department of mathematics Wayne State University Detroit USA

This paper consists of three main *** of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie *** the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be *** interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector *** main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on *** very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own *** the existence of such polynomials is the second main part of this *** results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given *** construct a linear extension operator which is bounded on different Sobolev spaces *** particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev *** are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

关键词： Poincaré inequalities Extension theorems Interpolation inequalities Anisotropic Sobolev spaces A_p weights (ε,δ)domains Vector fields Polynomials on stratified groups

Discrete calderón-type Reproducing Formula

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Acta Mathematica Sinica,English Series 2000年第2期16卷 277-294页

作者： Yongsheng Han department of mathematics,Auburn university,Auburn,Alabama 36849-5310,usa department of mathematics Auburn University Auburn Alabama 36849-5310 USA

In this paper we use the calderón-Zygmund operator theory to provide a discrete calderón- type reproducing *** translation,dilation and,in particular,the Fourier transform are never used in the proofs,all results still hold on spaces of homogeneous type introduced by Coifman and Weiss. As a consequence,we obtain a class of frames with the minimum regularity properties.

关键词： Spaces of homogeneous type calderón reproducing formula Frame

SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE

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Journal of Computational mathematics 2001年第5期19卷 475-488页

作者： Xiao-wu Lu (department of mathematics and Computer Science, Emory university, Atlanta, GA 30322, usa) Emory university 美国 30322

Presents a class of finite difference methods of first and second order accuracy for the computation of solutions to the quasilinear wave equations. Overview of general symplectic schemes and generating functional; Nu... 详细信息

关键词： Symplectic integration Sine-Gordon equations Finite difference method.

Equivalence problem for Bishop surfaces

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Science China mathematics 2010年第3期53卷 687-700页

作者： HUANG XiaoJun 1, & YIN WanKe 2 1 department of mathematics, Rutgers university, New Brunswick, NJ 08902, usa 2 School of mathematics and Statistics, Wuhan university, Wuhan 430072, China 1. department of mathematics Rutgers University New Brunswick NJ 08902 USA2. School of Mathematics and Statistics Wuhan University Wuhan 430072 China

The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of the recent studies of Bishop surfaces, which, in particular, includes the work of the authors. In the second part of the paper, we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant. More precisely, we let M be a real submanifold of C 2 defined by an equation of the form w = zz + 2Re(z s + az s+1 ) with s≥ 3 and a a complex parameter. We will prove in the second part of the paper that for s≥ 4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation. When s = 3, we show that surfaces of this type with two different real parameters are not holomorphically equivalent.

关键词： equivalence problem Bishop surface Chern-Moser theory elliptic and hyperbolic complex tangents normal form and modular space

Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States

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Acta Mathematica Sinica,English Series 2000年第1期16卷 161-180页

作者： G.Yin~(1)) department of mathematics,Wayne State university,Detroit,MI 48202,usaQ.Zhang~(2)) department of mathematics,university of Georgia,Athens,GA 30602,usaG.Badowski~(3)) department of mathematics,Wayne State university,Detroit,MI 48202,usa department of mathematics Wayne State University Detroit MI 48202 USA department of mathematics University of Georgia Athens GA 30602 USA

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing *** focuses on both unscaled and scaled occupation *** mild conditions,a mean-square estimate is *** averaging the fast components,we obtain an aggregated *** the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state ***,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

关键词： Singularly perturbed Markov chain Occupation measure Aggregation Absorbing state Weak convergence Switching diffusion

Comparison of PBDE congener profiles and concentration levels in human specimens from China and the US and identification of human exposure sources

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Science China Chemistry 2010年第5期53卷 995-1002页

作者： SHE JianWen 1,SHE YiFan 2 &SONG WenLu 2 1 Biochemistry Section,Environmental Health Laboratory Branch,california department of Public Health,Richmond,ca 94804,usa 2Chemistry Section,Food and Drug Laboratory Branch,california department of Public Health,Richmond,ca 94804,usa 1. Environmental Health Laboratory Branch California Department of Public Health Biochemistry Section Richmond CA 94804 USA2. Food and Drug Laboratory Branch California Department of Public Health Chemistry Section Richmond CA 94804 USA

In an effort to investigate the status of human exposure to PBDEs in China,available monitoring data in human specimens(including breast milk,serums,and blood) was collected from the general population as well as specific groups that are occupationally *** exposure profiles and concentration levels were compared with their counterparts in the United States of *** was found that PBDE burdens in general Chinese population are one order lower and have different congener profiles from that in the US,showing higher percentages of BDE-28 or BDE-153 in human specimens from *** and residents in electronic wastes recycling regions or areas of commercial PBDE manufacturing have the highest PBDE exposure levels reported worldwide,which are close or higher than the exposure levels of the general population in the US. Highly brominated congeners,such as BDE-207 and 209,are among the major PBDE congeners,and BDE-209 has the highest percentage(above 50%) for all occupational populations *** components analysis(Pca) demonstrates that the exposure of the general population in the US is closely related to penta-BDE while the human burden in China is *** PBDE in indoor air(gas phase) in the US is highly correlated with the PBDE burden in the general population in the US,indicating a major exposure *** the occupationally exposed populations in China,the congener profiles are closely related to the commercial deca-BDE *** of exposure profiles for general and occupational populations in China suggests that it is essential to include more highly brominated congeners,such as BDE-207 and 209,in future human exposure studies,in order to assess the real burdens and profiles of PBDEs exposure in *** pollution prevention and occupational protection procedures are in need in China to avoid the PBDE contamination problem that has occurred in the US.

关键词： human exposure PBDEs congener profiles concentration levels source source identification China and usa

On the direct path problem of s-elementary frame wavelets

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Science China mathematics 2010年第12期53卷 3187-3196页

作者： DAI XingDe 1 , DIAO YuanAn 1 & GUO XunXiang 2,1 department of mathematics and Statistics, university of North carolina at Charlotte, Charlotte, NC 28223, usa 2 department of mathematics, Southwestern university of Finance and Economics, Chengdu 611130, China 1. department of mathematics and Statistics University of North Carolina at Charlotte Charlotte NC 28223 USA2. Department of Mathematics Southwestern University of Finance and Economics Chengdu 611130 China

In this paper, we discuss the path-connectivity between two s-elementary normalized tight frame wavelets via the so-called direct paths. We show that the existence of such a direct path is equivalent to the non-existence of an atom of a σ-algebra defined over the defining sets of the corresponding frame wavelets, using a mapping defined by the natural translation and dilation operations between the sets. In particular, this gives an equivalent condition for the existence of a direct path between two s-elementary wavelets.

关键词： wavelets frame wavelets frame wavelet sets path-connectivity of wavelets direct path