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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 {1., east 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 {1., east china normal University, shanghai 200062, china. department of {1., east china normal University, shanghai 200062, china. department of {1. 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 {1., east 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 {1., east 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 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 {1. east china normal University shanghai, 200062 china 1. department of {1. 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

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 {1. east china normal University shanghai, 200062 china department of {1. 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 {1. 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

On the Cayley-Bacharach property and the construction of vector bundles

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Science china {1. 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2 1.department of mathematics and Statistics,Huazhong normal University,Wuhan 430079,china 2 department of mathematics,east china normal University,shanghai 200241,china 1. department of {1. and Statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2 for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1.global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Note on families of semistable curves over P^1.with 4 singular fibers whose Jacobian are non-compact

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Science china {1. 2010年第7期53卷 1710-1713页

作者： YU Fei 1. 2 1.Academy of mathematics and Systems Science, Chinese Academy of Sciences, Beijing 1.01.0, {1. 2 department of mathematics, east {1. normal University, shanghai 200062, {1. Academy of mathematics and Systems Science Chinese Academy of Sciences Beijing China department of {1. East China Normal University Shanghai China

Let f : S → P 1.be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.

关键词： singular fiber adjoint linear system non-compact Jacobian