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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 {3. University, shanghai 200062, china. department of Mathematics, east china {3. 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 {3. 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≤3.k2s+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

Impact on the Yangtze (Changjiang) Estuary from its drainage basin: Sediment load and discharge

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Chinese Science Bulletin 2001年第S1期46卷 73-80页

作者： CHEN Zhongyuan & ZHAO YiwenState Key Laboratory for Estuarine and Coastal Research, east china normal University,{3., china department of geography, east china normal University,{3., china 1. State Key Laboratory for Estuarine and Coastal Research East China Normal University 200062 Shanghai China 2. department of geography East China Normal University 200062 Shanghai China

This paper focuses on the sediment transport and freshwater discharging from upper Yangtze drainage basin downstream, primarily on the basis of multiyear hy-drological data collected from three major hydrological gauge stations (Yichang, Hankou and Datong). Data indicate highest sediment load in Yichang (5.6×108 t/a), lowest in Hankou (5.1×108t) and second highest in Datong (5.4×108 t). This fluctuations are identical with what has been observed from the annual flood season. About one thirds of the sediment load are trapped in the middle Yangtze River course, where meandering river pattern prevails; rest of them are directly transported to the river mouth area via lower Yangtze River channel, where the river is typically confined by the exposed base rock and almost none is being trapped, instead, minor being drained to the mainstream from the local tributaries. To recognize this sediment delivery and river flow media is vital, because it can highlight morphologic/topographic correlation between the

关键词： sediment load discharge estuarine impact the Yangtze River.

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 {3. 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

CONSTRUCTION OF INDECOMPOSABLEDEFINITE HERMITIAN FORMS

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Chinese Annals of Mathematics,Series B 1994年第3期15卷 349-360页

作者： ZHU FUZU (department ofMathematics, east china {3. University shanghai 200062,china) E china normal UNIV DEPT MAHTSHANGHAI 200062PEOPLES R CHINA

This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n *** is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.

关键词： Indecomposable lattice(form) Minimum of a lattice(form) Minimal、ctor Irreduclble vector.

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(department of Matehematics,east china {3. University, shanghai 200062, china) E china normal 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 [16].

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

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 {3. 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

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 {3. 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

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 {3. 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