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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 university 美国

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

L~∞ CONVERGENCE OF QUASI-CONFORMING FINITE ELEMENTS FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1995年第2期13卷 108-122页

作者： Wang Ming (department of mathematics, Peking university, Beijing, China) 北京大学数学系北京

In this paper we consider the L∞ convergence for quasi-conforming finite ele-ments solving the boundary value probzlems of the biharmonic equation and give the nearly optimal order L∞ estimates.

关键词：双调和方程拟共形有限元 L↑∞收敛性 L↑∞估计

Regular n-simplices in R^n with vertices in Z^(n)

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Science China mathematics 2004年第1期47卷 104-113页

作者： XIA Jianguo & QIN Hourongdepartment of mathematics, Nanjing Normal university, Nanjing 210097, China (email: jgxia@***) department of mathematics, Nanjing university, Nanjing 210093, China Dept. of Math. Nanjing Normal Univ. Nanjing 210097 China Dept. of Math. Nanjing Univ. Nanjing 210093 China

In this paper the Ⅰ and Ⅱ regular n-simplices are introduced. We prove that the sufficient and necessary conditions for existence of an Ⅰ regular n-simplex in Rn are that if n is even then n = 4m(m + 1), and if n is odd then n = 4m + 1 with that n + 1 can be expressed as a sum of two integral squares or n = 4m - 1, and that the sufficient and necessary condition for existence of a Ⅱ regular n-simplex in Rn is n = 2m2 - 1 or n = 4m(m+1)(m 6 N). The connection between regulars-simplex in Rn and combinational design is given.

关键词： regular n-simplex in Rn, quadratic form.

The cohomology group of weak entwining structure

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Science China mathematics 2007年第5期50卷 665-674页

作者： Ling JIA & Fang LI department of mathematics, Ludong university, Yantai 264025, China department of mathematics, Zhejiang university, Hangzhou 310027, China department of mathematics Ludong University Yantai China department of mathematics Zhejiang University Hangzhou China

In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.

关键词： weak entwining structure cohomology group 16W80 16W99

A FAMILY OF HIGH-ODER PARALLEL ROOTFINDERS FOR POLYNOMIALS

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Journal of Computational mathematics 2000年第3期18卷 283-288页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus,Zhejiang university, Hangzhou, 310028, China) 浙江大学浙江杭州 310028

Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.

关键词： parallel iteration zeros of polynomial order of convergence

A COLUMN RECURRENCE ALGORITHM FOR SOLVING LINEAR LEAST SQUARES PROBLEM

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Journal of Computational mathematics 1996年第4期14卷 301-310页

作者： J.X. Zhao(department of mathematics, Nanjing university, Nanjing China) 南京大学数学系江苏南京

A new column recurrence algorithm based on the classical Greville method and modified Huang update is proposed for computing generalized inverse matrix and least squares solution. The numerical results have shown the ... 详细信息

关键词： Math A COLUMN RECURRENCE ALGORITHM FOR SOLVING LINEAR LEAST SQUARES PROBLEM ABS

An algebraic invariant for Jordan automorphisms on B(H):The set of idempotents

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Science China mathematics 2005年第12期48卷 1585-1596页

作者： CUI Jianlian & HOU Jinchuan department of Mathematical Science, Tsinghua university, Beijing 100084, China department of Applied mathematics, Taiyuan university of Technology, Taiyuan 030024, China department of mathematics, Shanxi Teachers university, Linfen 041004, China department of Mathematical Science Tsinghua University Beijing 100084 China department of Applied mathematics Taiyuan University of Technology Taiyuan 030024 China department of mathematics Shanxi Teachers University Linfen 041004 China

Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism.

关键词： Hilbert space operators,Jordan automorphisms,idempotents.

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) department of mathematics University of Science and Technology of China Hefei 230026 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

Minimal regular 2-graphs and applications

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Science China mathematics 2006年第2期49卷 158-172页

作者： FAN Hongbing, LIU Guizhen & LIU Jiping department of Physics and Computer Science, Wilfrid Laurier university, Waterloo, ON., N2L 3C5 canada School of mathematics and System Science, Shandong university, Jinan 250100, China department of mathematics and Computer Science, university of Lethbridge, Lethbridge, AB., T1K 3M4, canada department of Physics and Computer Science Wilfrid Laurier University Waterloo Canada School of mathematics and System Science Shandong University Jinan China department of mathematics and Computer Science University of Lethbridge Lethbridge Canada

A 2-graph is a hypergraph with edge sizes of at most two. A regular 2-graph is said to be minimal if it does not contain a proper regular factor. Let f2(n) be the maximum value of degrees over all minimal regular 2-graphs of n vertices. In this paper, we provide a structure property of minimal regular 2-graphs, and consequently, prove that f2(n) = n+3-i/3, where 1 ≤ i ≤ 6, i ≡ n (mod 6) and n ≥ 7, which solves a conjecture posed by Fan, Liu, Wu and Wong. As applications in graph theory, we are able to characterize unfactorable regular graphs and provide the best possible factor existence theorem on degree conditions. Moreover, fa(n) and the minimal 2-graphs can be used in the universal switch box designs, which originally motivated this study.

关键词： graph regular factor 2-graph switch box design.