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ON THE VARIATIONS OF G_2

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Chinese Annals of mathematics,Series B 2003年第3期24卷 387-394页

作者： LIU DONG LIN LEI department of mathematics, east china normal university, shanghai 2.0062. china. department of mathematics, east china normal university, shanghai 2.0062. china. department of mathematics East China Normal University Shanghai 200062 China

In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G2. In this paper, the authors investigate their derivation algebras. It is shown that G2 and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of ViG for i = 3,4, 5, 6, and thereby construct some left-symmetric structures on Vi G for i = 3,4,5,6. Some errors about the variations of sl(3, F) in [1] are corrected.

关键词： Variation Derivation Associative form Left-symmetric structure

ON ABELIAN AUTOMORPHISM GROUPS OF SURFACES OF GENERAL TYPE

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Chinese Annals of mathematics,Series B 1996年第1期17卷 43-52页

作者： CAI JINXING(department of mathematics, east china normal university, shanghai 2.0062. china.) E china normal UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

It is proved that for a complex minimal smooth projective surface S of general type, its abelian automorphism group is of order≤36k2s+24, provided x(os)≥8, where Ks is the canonical divisor of S, and X(Os) the Euler... 详细信息

关键词： Projective surface Automorphism group Canonical divisor

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 465-472页

作者： WEI GUOQIANG (department of mathematics, east china normal university, shanghai 2.0062. china.) E china normal Univ Dept Math Shanghai 200062 Peoples R China

The author shows that a rank-preserving *-isorporphism between separable C*-algebras with unity is approximately equivalent to the identity representation. Some applications are made for approximately similarity of n-... 详细信息

关键词： C*-algebra Rank-preserving *-isomorphism Approximately equevalent,Approximately similar n-tuples of operators

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang department of mathematics,east china normal university,shanghai 200241,china Division of Computational Science,E-Institute of shanghai Universities,shanghai normal Benyu Guo department of mathematics,shanghai normal university,shanghai 200234,china Division of Computational Science,E-Institute of shanghai Universities,shanghai,china department of mathematics East China Normal University Shanghai 200241 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Normal University Shanghai 200234 China department of mathematics Shanghai Normal University Shanghai 200234 China Division of Computational Science E-Institute of Shanghai Universities Shanghai China

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Decomposition of integrable holomorphic quadratic differential on Riemann surface of infinite type

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Science china mathematics 2010年第8期53卷 2039-2044页

作者： CHENG Tao department of mathematics,east china normal university,shanghai 200241,china 1. department of mathematics East China Normal University Shanghai 200241 China

In this paper,decomposition of the integrable holomorphic quadratic differential on Riemann surface of infinite type is ***,Schleicher and Shishikura gave a thick-thin decomposition on Riemann surface of finite type with an integrable holomorphic quadratic differential and they thought their result might be generalized to arbitrary hyperbolic Riemann surface of infinite *** confirm what they thought is right and give a proposition(Proposition 2.2) of its own interest.

关键词： holomorphic quadratic differential decomposition collar

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (department of mathematics, shanghai normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (department of mathematics, shanghai normal university, shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

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Science china mathematics 2005年第2期48卷 248-260页

作者： SHUI Shuliang & ZHU Deming College of mathematics and Physics, Zhejiang normal university, Jinhua 321004, china department of mathematics, east china normal university, shanghai 2.0062. china 1. College of mathematics and Physics Zhejiang Normal University 321004 Jinhua China 2. department of mathematics East China Normal University 200062 Shanghai China

Homoclinic bifurcations in four-dimensional vector fields are investigated by setting up a local coordinate near a homoclinic orbit. This homoclinic orbit is principal but its stable and unstable foliations take inclination flip. The existence, nonexistence, and uniqueness of the 1-homoclinic orbit and 1-periodic orbit are studied. The existence of the two-fold 1-periodic orbit and three-fold 1 -periodic orbit are also obtained. It is indicated that the number of periodic orbits bifurcated from this kind of homoclinic orbits depends heavily on the strength of the inclination flip.

关键词： bifurcation, homoclinic orbit, non-resonance, inclination flip, 1-periodic orbit.

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 2.0062. china College of mathematics & Information Science, Northwest normal university, Lanzhou 730070, china 1. department of mathematics East China Normal University Shanghai 200062 China 2. College of mathematics & Information Science Northwest Normal University Lanzhou 730070 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.