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EXISTENCE OF INFINITELY MANY SOLUTIONS FOR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT

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Acta Mathematica Scientia 2004年第3期24卷 395-402页

作者：傅红卓沈尧天 department of mathematics South China University of Technology Guangzhou 510640 China Department of Mathematics University of Science and Technology of China Hefei 230026 China department of mathematics South China University of Technology Guangzhou 510640 Chinahis paper is concerned with the following nonlinear Dirichlet problem:where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u Ωis a bounded domain in Rn (n > 3) 1 < p < n p = -pn/n-p is the critical exponent for the Sobolev imbedding λ> 0 and f(x u) satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p = 2 or f(xu) = |u|q-2u where 1 < q < p are generalized.

This paper is concerned with the following nonlinear Dirichlet problem:where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u, Ω is a bounded domain in Rn (n > 3., 1 0 and f(x, u) satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p = 2 or f(x,u) = |u|q-2u, where 1 < q < p, are generalized.

关键词： critical Sobolev exponent concentration compactness principle genus infinitely many solutions

On conformal measures for infinitely renormalizable quadratic polynomials

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Science china mathematics 2005年第10期48卷 1411-1420页

作者： HUANG Zhiyong~1 JIANG Yunping~(2,3. & WANG Yuefei~3.1. School of Information,Renmin university of china,Beijing 100872,china 2. {3. of mathematics,Queens College,City university of New York,NY 113.7,USA {3. of mathematics,Graduate School,City university of New York,New York,NY 10016,USA 3. Academy of mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,china School of Information Renmin University of China Beijing China department of mathematics Queens College City University of New York NY USA department of mathematics Graduate School City University of New York New York USA Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China

We study a conformal measure for an infinitely renormalizable quadratic polynomial. We prove that the conformal measure is ergodic if the polynomial is unbranched and has complex bounds. The main technique we use in t... 详细信息

关键词： Julia set, conformal measure, three-dimensional puzzle, infinitely renormalizable quadratic polynomial.

BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS

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Journal of Computational mathematics 2002年第4期20卷 349-362页

作者： Xiao-yuan Qian (department of Applied mathematics, Dalian university of {3., Dalian 116024, china) department of Applied mathematics Dalian University of Technology Dalian 116024

Non-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced. The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.

关键词： fractal bivariate functions interpolation

ARNOLDI TYPE ALGORITHMS FOR LARGE UNSYMMETRICMULTIPLE EIGENVALUE PROBLEMS

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Journal of Computational mathematics 1999年第3期17卷 257-274页

作者： Zhong-xiao Jia(department of Applied mathematics, Dalian university of {3., Dalian 116024, china) 大连理工大学应用数学系辽宁大连

As is well known, solving matrix multiple eigenvalue problems is a very difficult topic. In this paper, Arnoldi type algorithms are proposed for large unsymmetric multiple eigenvalue problems when the matrix A involved is diagonalizable. The theoretical background is established, in which lower and upper error bounds for eigenvectors are new for both Arnoldi's method and a general perturbation problem, and furthermore these bounds are shown to be optimal and they generalize a classical perturbation bound due to W. Kahan in 1967 for A symmetric. The algorithms can adaptively determine the multiplicity of an eigenvalue and a basis of the associated eigenspace. Numerical experiments show reliability of the algorithms.

关键词： Arnoldi's process large unsymmetric matrix multiple eigenvalue diagonalizable error bounds

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of mathematics, university of Science and {3. of china, hefei 23.026, china 2. department of mathematics, Beijing Normal university, Beijing 100875, china department of mathematics University of Science and Technology of China Hefei China department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, Beijing 100871, {3.) 北京大学数学系北京

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

Algorithm of graph isomorphism with threedimensional DNA graph structures

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Progress in Natural Science:Materials International 2005年第2期15卷 86-89页

作者： LIU Guangwu 1,2*, YIN Zhixiang 1,3. XU Jin1 and DONG Yafei1(1. department of Control Science and Engineering, Hua Zhong university of Science and technology, Wuhan 43.074, {3. 2. College of Transportation, Wuhan university of technology, Wuhan 43.063. {3. 3. department of mathematics and Physics, Anhui university of Science and technology, Huainan 23.001, {3.) Dept. of Control Science and Eng. Huazhong Univ. of Sci. and Technol. Wuhan 430074 China Coll. of Transportation Wuhan Univ. of Technology Wuhan 430063 China Dept. of mathematics and Physics Anhui Univ. of Sci. and Technol. Huainan 232001 China

An algorithm for solving the graph isomorphism problem with 3.D DNA structures is proposed in this paper. The k-armed branched junction molecules are used to code k-degree vertices. Double stranded molecules are used to code edges. Then the molecules are mixed in a tube to be ligated. The result can be detected by gel electrophoresis. The time complexity of the algorithm is O(n2), where n is the number of vertices of the graph.

关键词： DNA computing DNA graph structure graph isomorphism

Characterization for commutators of n-dimensional fractional Hardy operators

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Science china mathematics 2007年第10期50卷 1418-1426页

作者： Zun-wei FU~(1,2) Zong-guang LIU~3.Shan-zhen LU~(1+) Hong-bin WANG~3.~1 School of Mathematical Sciences,Beijing Normal university,Beijing 100875,china ~2 department of {3.,Linyi Normal university,Linyi 276005,china ~3.department of mathematics,china university of Mining and technology (Beijing),Beijing 100083.china School of Mathematical Sciences Beijing Normal University Beijing China department of mathematics Linyi Normal University Linyi China department of mathematics China University of Mining and Technology (Beijing) Beijing China

In this paper,it was proved that the commutator H_(β,b)generated by an n-dimensional fractional Hardy operator and a locally integrable function b is bounded from L^(p1)(R^n)to L^(p2)(R^n)if and only if b is a CMO(R^... 详细信息

关键词： n-dimensional fractional Hardy operator, commutator, C(M)O function, homogeneous Herz space

Free orthodox semigroups and free bands with inverse transversals

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Science china mathematics 2010年第11期53卷 3015-3026页

作者： TANG XiLin department of mathematics, South china {3. of technology, Guangzhou 510640, china department of mathematics South China University of Technology Guangzhou China

It is well known that the subclass of inverse semigroups and the subclass of completely regular semigroups of the class of regular semigroups form the so called e-varieties of semigroups. However, the class of regular semigroups with inverse transversals does not belong to this variety. We now call this class of semigroups the ist-variety of semigroups, and denote it by IST . In this paper, we consider the class of orthodox semigroups with inverse transversals, which is a special ist-variety and is denoted by OIST . Some previous results given by Tang and Wang on this topic are extended. In particular, the structure of free bands with inverse transversals is investigated. Results of McAlister, McFadden, Blyth and Saito on semigroups with inverse transversals are hence generalized and enriched.

关键词： inverse transversal ist-variety free orthodox semigroup free band