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ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (department of mathematics, east china normal university, shanghai 200062, china) E china normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2) in error estimation.

关键词： matrix unitarily invariant norm condition number

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 200062, china. department of mathematics, east china normal university, shanghai 200062, 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 200062, 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 200062, 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

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数学文化的一些新视角

数学教育学报 2003年第1期12卷 37-40页

作者：张奠宙梁绍君金家梁华东师范大学数学系上海200062 渝西学院重庆400000 常熟高等专科学校江苏常熟215500

数学作为一种文化现象已引起国内外众多学者的重视.但在众多研究中尚存在2方面不足:第一,数学文化的研究,不能只说数学的重要性,强调数学对人类文明的贡献.第二,数学文化必须走进课堂,在实际数学教学中使得学生在学习数学的过程中真正... 详细信息

数学作为一种文化现象已引起国内外众多学者的重视.但在众多研究中尚存在2方面不足:第一,数学文化的研究,不能只说数学的重要性,强调数学对人类文明的贡献.第二,数学文化必须走进课堂,在实际数学教学中使得学生在学习数学的过程中真正受到文化感染,产生文化共鸣,体会数学的文化品位和世俗的人情味.

关键词：数学文化理性思维数学史数学方法

On Indecomposable Definite Unimodular Hermitian Forms

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Acta Mathematica Sinica,English Series 1994年第2期10卷 113-120页

作者： Zhu Fuzu department of mathematics east china normal university shanghai, 200062 china 1. department of mathematics East China Normal University 200062 Shanghai China

For any natural numbers m and n≥17 we can construct explicitly indecomposable definite unimodular normal Hermitian lattices of rank n over the ring of algebraic integers Rm in an imaginary quadratic field (-m1/2). It is proved that for any n （in case m=11, there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R15(R11- lattices of rank n, and we exhibit representatives for each class. In the exceptional case there are no lattices with the desired properties. The method given in this paper can solve completely the problem of constructing indecomposable definite unimodular normal Hermitian Rm-lattices of any rank n for each m.

关键词： show On Indecomposable Definite Unimodular Hermitian Forms Math

Orbits Heteroclinic to Invariant Manifolds

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Acta Mathematica Sinica,English Series 1996年第4期12卷 372-373,375-378页

作者： Zhu Deming department of mathematics east china normal university shanghai, 200062 china department of mathematics East China Normal University Shanghai China

Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic i... 详细信息

关键词： Invariant manifold Exponential dichotomy Heteroclinic orbit Transversality

The Relative Canonical Algebra for Genus 4 Fibrations

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Acta Mathematica Sinica,English Series 1995年第1期11卷 44-52页

作者： Cai Jinxing department of mathematics east china normal university shanghai,200062 china harm.showa-u.ac.jp

In this paper,we prove that for the genus 4 fibration,the relative canonical algebra is generated in degrees ≤3.

关键词： HO The Relative Canonical Algebra for Genus 4 Fibrations

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 200062, 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.