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AN EXTREMAL APPROACH TO BIRKHOFF QUADRATURE FORMULAS

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Journal of Computational mathematics 2001年第5期19卷 459-466页

作者： Ying-guang Shi (department of mathematics, hunan Normal university, Changsha 410081, china) 湖南师范大学湖南长沙 410081

Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.

关键词： an extremal approach Birkhoff quadrature formulas

A DISCRETE CHARACTERIZATION OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES AND ITS APPLICATIONS

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Acta Mathematica Scientia 2004年第3期24卷 412-420页

作者： XuJingshi departmentofmathematics HunanUniversityChanysha410082China

In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.

关键词： Herz-type space Triebel-Lizorkin space discrete characterization pseudo-differential operator maximal operator

THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 401-408页

作者： LIU TAISHUN (department of mathematics, university of science and Technology of china, Hefei 230026, china)REN GUANGBIN (department of mathematics, university of science and Technology of china, Hefei 230026, china) Univ Sci & Technol china Dept Math Anhua 230026 Peoples R China

The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular *** type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent *** theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.

关键词： Starlike mappings Growth theorem Starlike circular domains

THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS

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Chinese Annals of mathematics,Series B 1996年第3期17卷 271-278页

作者： GONG SHENG(department of mathematics, university of science and Technology of china, Hefei 230026, china) UNIV SCI & TECHNOL china DEPT MATHHEFEI 230026PEOPLES R CHINA

The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the ... 详细信息

关键词： Bounded symmetric domain Bloch mapping Bloch constant,Locally biholomorphic mapping

SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENTSUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENT

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Journal of Computational mathematics 2000年第5期18卷 541-550页

作者： Qi-ding Zhu (department of mathematics, hunan Normal university, Changsha 410081, china ) 湖南师范大学湖南长沙 410081

In this paper, we construct a projection interpolation for cubic triangular element by using othogonal expansion triangular method. We show two fundamental formulas of estimation on a special partion and obtain a superconvergence result of 1- ∈order higher for the placement function and its tangential derivative on the third order Lobatto points and Gauss points on each edge of triangular element.

关键词： Finite element Superconvergence Projection interpolation.

TYPE X MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION

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Chinese Annals of mathematics,Series B 1996年第3期17卷 335-342页

作者： JIANG JIFA(department of mathematics, The university of science and Technology of china, Hefei 230036, china.) department of mathematics University of Science and Technology of China Hefei 230036 China

The author considers the asymptotic behavior of solutions of a class of ordinary dmerentialequations x = F(x) in the nonnegative orthant R7. Suppose that F(o) = o, Fi(x1,..., xn) isnondecreasing in xk for all k≠ i and that F possesses an order-increasing invarian *** it is shown that every bounded solution to such a system converges to a single equilibrium.

关键词： Type K monotone system Monotone flow Invariant function Equilibrium Convergence

Lie bialgebras of generalized Witt type

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science china mathematics 2006年第4期49卷 533-544页

作者： SONG Guang’ai & SU Yucai College of mathematics and Information science, Shandong Institute of Business and Technology, Yantai 264005, china department of mathematics, university of science and Technology of china, Hefei 230026, china department of mathematics, Shanghai Jiaotong university, Shanghai 200240, china College of mathematics Information science Shandong Institute of Business Technology Yantai 264005 China department of mathematics University of Science Technology of china Hefei 230026 China department of mathematics Shanghai Jiaotong University Shanghai 200240 China

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.

关键词： Lie bialgebras, Yang-Baxter equation, Lie algebra of generalized Witt type.

On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates

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science china mathematics 2010年第8期53卷 2069-2084页

作者： WANG HaiBing 1,2 & LIU JiJun 1 1 department of mathematics,Southeast university,Nanjing 210096,china 2 School of mathematics and Computational science,hunan university of science and Technology,Xiangtan 411201,china 1. department of mathematics Southeast University Nanjing 210096 China2. School of Mathematics and Computational Science Hunan University of Science and Technology Xiangtan 411201 China

Consider the determination of Dirichlet-to-Neumann(D-to-N) map from the far-field pattern in inverse scattering problems,which is the key step in some recently developed inversion schemes such as probe ***,this problem is related to the reconstruction of the scattered wave from its far-field *** firstly prove the well-known uniqueness result of the D-to-N map from the far-field pattern using a new scheme based on the mixed reciprocity *** advantage of this new proof scheme is that it provides an efficient algorithm for computing the D-to-N map,avoiding the numerical differentiation for the scattered *** combining with the classical potential theory,a simple and feasible regularizing reconstruction scheme for the D-to-N map is *** the stability estimate for the reconstruction with noisy input data is rigorously analyzed.

关键词： inverse scattering Dirichlet-to-Neumann map regularization mixed reciprocity principle stability

Convergence analysis for general linear methods applied to stiff delay differential equations

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Progress in Natural science:Materials International 2002年第6期12卷 16-22页

作者： ZHANG Chengjian(department of mathematics, Huazhong university of science and Technology, Wuhan 430074, china) Huazhong Univ Sci & Technol Dept Math Wuhan 430074 Peoples R China

For Runge-Kutta methods applied to stiff delay differential equations (DDEs), the concept of D-convergence was proposed, which is an extension to that of B-convergence in ordinary differential equations (ODEs) . In this paper, D-convergence of general linear methods is discussed and the previous related results are improved. Some order results to determine D-convergence of the methods are obtained.

关键词： D-convergence general linear methods stiff delay differential equations.