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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 {1. 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≥1. 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=1., there is one exception n=3） there exist indecomposable definite unimodular normal Hermitian R1.(R1.- 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

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, {1. china normal university, shanghai 200062, china) E china {1. 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, {1. china normal university, shanghai 200062, china. department of Mathematics, {1. 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

HOMOCLINIC BIFURCATION WITH CODIMENSION 3

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Chinese Annals of Mathematics,Series B 1994年第2期15卷 205-216页

作者： zhu DEMING({1. of Matehematics,east china normal university, shanghai 200062, china) E china {1. UNIV DEPT MATHSHANGHAI 200062PEOPLES R CHINA

First it is proved that both the integral of the divergence and the Melnikov function are invariants of the C2 transformation. Then, the problem of the planar homoclinic bifurcation with codimension 3 is considered. It is proved that, in a small neighborhood of the origin in the parameter space of a Cr (r≥5) system, there exist exactly two Cr-1.semi- stable- limit- cycle branching surfaces, and their common boundary is a unique Cr-1.three-multiple- limit-cycle branching curve. The bifurcation pictures and the asymptotic expansions of the bifurcation functions are given. The stability criterion for the homoclinic loop is also obtained when the integral of the divergence is zero. The proof of the auxiliary theorems will be presented in [1.].

关键词： Homoclinic bifurcation Codimension Semi-stable-limit-cycle branch Three- multiple-limit- cycle branch.

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, {1. china normal university, shanghai 200062, china.) E china {1. 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, {1. china normal university, shanghai 200062, china.) E china {1. 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

On Non-Decomposable Hermitian Forms over Gaussian Domain

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Acta Mathematica Sinica,English Series 1998年第4期14卷 447-456页

作者： zhu {1., department of Mathematics, east china normal university, shanghai 200062, china department of Mathematics East China Normal University 200062 Shanghai China

Methods are presented for the construction of non-decomposable Hermitian forms over the ring of integers of an imaginary quadratic field.

关键词： Non-decomposable form Indecomposable form Odd form Even form Reduced form

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 {1. 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 geodetic numbers of graphs and digraphs

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Science china Mathematics 2007年第8期50卷 1163-1172页

作者： Chang-hong LU~(1.2) 1.department of Mathematics,{1. china normal university,shanghai 200062,china 2 Institute of Theoretical Computing,{1. china Narnal university,shanghai 200062,china 1. department of Mathematics East China Normal University Shanghai 200062 China 2. Institute of Theoretical Computing East China Narnal University Shanghai 200062 China

For every two vertices u and v in a graph G, a u-v geodesic is a shortest path between u and v. Let I(u, v) denote the set of all vertices lying on a u-v geodesic. For a vertex subset S, let I(S) denote the union of all I(u, v) for u, v ∈ S. The geodetic number g(G) of a graph G is the minimum cardinality of a set S with I(S) = V (G). For a digraph D, there is analogous terminology for the geodetic number g(D). The geodetic spectrum of a graph G, denoted by S(G), is the set of geodetic numbers of all orientations of graph G. The lower geodetic number is g ?(G) = minS(G) and the upper geodetic number is g +(G) = maxS(G). The main purpose of this paper is to study the relations among g(G), g ?(G) and g +(G) for connected graphs G. In addition, a sufficient and necessary condition for the equality of g(G) and g(G × K 2) is presented, which improves a result of Chartrand, Harary and Zhang.

关键词： convex set digraph distance geodesic geodetic number 05C1. 05C20