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ON NON-ISOTROPIC JACOBI PSEUDOSPECTRAL METHOD

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Journal of Computational mathematics 2008年第4期26卷 511-535页

作者： Benyu Guo Keji Zhang Department of mathematics,shanghai normal university,shanghai 200234,china Scientific Computing Key Laboratory of shanghai Universities Division of Computational science of E-Institute of shanghai Universities Department of mathematics Shanghai Normal University Shanghai 200234

In this paper, a non-isotropic Jacobi pseudospectral method is proposed and its appli- cations are considered. Some results on the multi-dimensional Jacobi-Gauss type interpolation and the related Bernstein-Jackson type inequalities are established, which play an important role in pseudospectral method. The pseudospectral method is applied to a twodimensional singular problem and a problem on axisymmetric domain. The convergence of proposed schemes is established. Numerical results demonstrate the efficiency of the proposed method.

关键词： Jacobi pseudospectral method in multiple dimensions Jacobi-Gauss type inter-polation Bernstein-Jackson type inequalities Singular problem Problem on axisymmetricdomain.

Study on the dual-frequency oscillations in galactose-BZ system

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Chinese Journal of Chemistry 1997年第1期15卷 25-30页

作者： LI, He-XingDepartment of Chemistry, shanghai normal university,shanghai 200234, china Department of Chemistry Shanghai Normal University Shanghai 900234 China

Three types of dual-frequency oscillations in KBrO3-galactose-acetone-MnSO4-H2SO4 have been observed in a batch reactor depending on the initial concentration of H2SO4 or Br-. Similar phenomena were also observed when galactose was replaced by other aldosugars such as glucose, arabinose, lactose and maltose. However no dual-frequency oscillation has been found when ketosugar like fructose was used instead of galactose as the substrate. The roles of acidity, bromide ion and acetone in dual-frequency oscillations have been analyzed. The mechanism of dual-frequency oscillations has been discussed.

关键词： galactose dual-frequency oscillations acidity bromide

THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS

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Chinese Annals of mathematics,Series B 2000年第3期21卷 367-374页

作者： XU QINGXIANG(Department of mathematics, shanghai normal university, shanghai 200234, china.) E-mail:qxxu@*** Department of mathematics Shanghai Normal University Shanghai 200234 China

Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (G). It is proved that if G is amenable and GF≠G+, then Ker γGF,G+ is exactly the minimal closed non-trivial ideal of G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.

关键词： Discrete group Toeplitz algebra Minimal ideal

Functors of the Category of Abelian Sheaves on Regular Affine Scheme

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Acta Mathematica Sinica,English Series 1996年第4期12卷 413-414页

作者： Zhou Caijun Department of mathematics shanghai normal university shanghai, 200234 china Department of mathematics Shanghai Normal University Shanghai China

In this short paper, we prove that if R is a regular local ring of unequal characteristic, then there exists an additive covariant functor G from the category of abelian sheaves on SpecR to the category of abelian groups such that id_R(G(R))>dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative.

关键词： Affine scheme Abelian sheaf Additive covariant functor

JACOBI SPECTRAL METHODS FOR MULTIPLE- DIMENSIONAL SINGULAR DIFFERENTIAL EQUATIONS

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Journal of Computational mathematics 2003年第3期21卷 325-338页

作者： Li-Han Wang Ben-yu Guo (Department of mathematics, shanghai normal university, shanghai 200234, china) Department of mathematics Shanghai Normal University 上海 200234

Jacobi polynomial approximations in multiple dimensions are investigated. They are applied to numerical solutions of singular differential equations. The convergence analysis and numerical results show their advantages.

关键词： Jacobi approximations Multiple dimensions.

Short cycle structures for graphs on surfaces and an open problem of Mohar and Thomassen

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science china mathematics 2006年第2期49卷 212-224页

作者： REN Han & DENG Mo Department of mathematics, East china normal university, shanghai 200062, china college of mathematics & Information science, Northwest normal university, Lanzhou 730070, china Department of mathematics East China Normal University Shanghai China college of mathematics & Information science Northwest Normal University Lanzhou China

In this paper we investigate cycle base structures of a (weighted) graph and show that much information of short cycles is contained in an MCB (i.e., minimum cycle base). After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be an MCB. Furthermore, we show that the structure of MCB in a (weighted)graph is unique. The property is also true for those having a longest length (although much work has been down in evaluating MCB, little is known for those having a longest length). We use those methods to find out some unknown properties for short cycles sharing particular properties in (unweighted) graphs. As applications, we determine the structures of short cycles in an embedded graph and show that there exist polynomially bounded algorithms in finding a shortest contractible cycle and a shortest two-sided cycle provided such cycles exist. Those answer an open problem of B. Mohar and C. Thomassen.

关键词： cycle base facial cycle graph embedding.

A FILTER SECANT METHOD WITH NONMONOTONE LINE SEARCH FOR EQUALITY CONSTRAINED OPTIMIZATION

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Journal of Systems science & Complexity 2010年第4期23卷 846-860页

作者： Chao GU Detong ZHU School of mathematics and Informatics Shanghai LiXin University of Commerce Shanghai 201620 China Business college Shanghai Normal University Shanghai 200234 China

This paper proposes a filter secant method with nonmonotone line search for non-linearequality constrained *** Hessian of the Lagrangian is approximated using the BFGSsecant *** new method has more flexibility for the acceptance of the trial step and requires lesscomputational costs compared with the monotone *** global and local convergence of the proposedmethod are given under some reasonable ***,two-step Q-superlinear convergence rateis established by introducing second order correction *** numerical experiments are reported toshow the effectiveness of the proposed algorithm.

关键词： Convergence filter method line search nonmonotone secant update

ON THE EXISTENCE OF FIXED POINTS FOR LIPSCHITZIAN SEMIGROUPS IN BANACH SPACES

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Chinese Annals of mathematics,Series B 2001年第3期22卷 397-404页

作者： ZENG LUCHUAN, YANG YALI Department of Matematics, shanghai normal university, shanghai 200234, china. Department of mathematics Shanghai Normal Univeristy Shanghai 200234 China

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. ... 详细信息

Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.

关键词： Fixed points Lipschitzian semigroups Asymptotic regularity normal structure coefficient Asymptotic center

Finite element analysis for general elastic multi-structures

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science china mathematics 2006年第1期49卷 109-129页

作者： HUANG Jianguo, SHI Zhongci & XU Yifeng Department of mathematics, shanghai Jiao long university, shanghai 200240, china Division of Computational science, E-lnstitute of shanghai Universities, shanghai normal university, shanghai 200234, china Institute of Computational mathematics, Academy of mathematics and Systems science, Chinese Academy of sciences, Beijing 100080, china Department of mathematics, Chinese university of Hong Kong, Shatin, N. T., Hong Kong, china Department of mathematics Shanghai Jiao Tong University Shanghai China Division of Computational science E-Institute of Shanghai Universities Shanghai Normal University Shanghai China Institute of Computational mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of mathematics Chinese University of Hong Kong Hong Kong China

A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.

关键词： elastic multi-structures, finite elements, generalized Korn's inequality, unique solvability, error estimates.