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A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS

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Journal of Computational mathematics 1998年第2期16卷 141-151页

作者： Dao-qi Yang (department of mathematics, Wayne State university, Detroit, MI 48202, usa) Wayne State Univ Dept Math Detroit MI 48202 USA

An iterative nonoverlapping domain decomposition procedure is proposed and analyzed for linear elliptic problems. At the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires that Neumann data be passed to it. This procedure is suitable for parallel processing. A convergence analysis is established. Standard and mixed finite element methods are employed to give discrete versions of this domain decomposition algorithm. Numerical experiments arc conducted to show the effectiveness of the method.

关键词： Domain decomposition methods finite element methods parallel computing

AN INTERIOR TRUST REGION ALGORITHM FOR NONLINEAR MINIMIZATION WITH LINEAR CONSTRAINTS

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Journal of Computational mathematics 2002年第3期20卷 225-244页

作者： Jian-guo Liu (department of mathematics, university of North Texas, Denton, TX 76203, usa) department of mathematics University of North Texas 美国 Denton

Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented; Vectors for each updating step in the algorithm proposed; Establishment of the convergence properties of the proposed algorithm.

关键词： Nonlinear programming Linear constraints Trust region algorithms Newton methods Interior algorithms Quadratic convergence

A note on certain square functions on product spaces

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Science China mathematics 2006年第1期49卷 98-108页

作者： WANG Meng, CHEN Jiecheng2 & FAN Dashan department of mathematics, Zhejiang university (at Yuquan campus), Hangzhou 310027, China department of mathematics, Zhejiang university (at Xixi campus), Hangzhou 310028, China department of mathematics, university of Wisconsin-Milwaukee, Milwaukee, WI53201, usa department of mathematics Zhejiang University [at Yuquan campus] Hangzhou 310027 China department of mathematics Zhejiang University [at Xixi campus] Hangzhou 310028 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI53201 USA

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × ca and ca × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

关键词： square function, Marcinkiewicz integral, product space.

On the rigidity theorem for harmonic functions in Khler metric of Bergman type

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Science China mathematics 2010年第3期53卷 779-790页

作者： LI Song-Ying 1,2, & WEI DongHuan 1 1 School of mathematics and Computer Science, Fujian Normal university, Fuzhou 350007, China 2.department of mathematics, university of california, irvine, ca 92.97-3875, usa 1. School of mathematics and Computer Science Fujian Normal University Fuzhou 350007 China2. Department of Mathematics University of California Irvine CA 92697-3875 USA

The paper gives a method to generate the potential functions which can induce Khler metrics u = uij dz idz j of Bergman type on the unit ball B n in C n . The paper proves that if h ∈ C n (B n ) is harmonic in these metrics u ( u h = 0) in B n , then h must be pluriharmonic in B n . In fact, it is a characterization theorem, as a consequence, the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails. The results in this paper generalize the theorems of Graham (1983) and examples constructed by Graham and Lee (1988).

关键词： rigidity pluriharmonic Laplace-Beltrami operators u-harmonic

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.