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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

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 ({1. of mathematics, shanghai normal university, shanghai 200234, china) department of {1. 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.

Population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1.and DAI Yonglong 2 1. department of {1., shanghai university, shanghai 201.00, china 2. department of {1., Zhongshan university, Guangzhou 51.275, china department of {1. Shanghai University Shanghai China department of {1. Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1.as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. P(Z n=0 for some n)=1. and noncertain extinction (i.e. P(Z n=0 for some n)1. are studied.

关键词： Markov chains in random environments stochastic population models branching processes.

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

FLOATING QUANTIZATION EFFECTS ON MULTIRATE SAMPLED-DATA NONLINEAR CONTROL SYSTEMS

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Acta Mathematica Scientia 2007年第3期27卷 635-644页

作者：余宏旺汪志鸣 department of {1. East China Normal University

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

关键词： Multirate sampled-data control systems quantization Schur stable uniformly ultimately bounded

Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips

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Science china {1. 2005年第2期48卷 248-260页

作者： SHUI Shuliang & ZHU Deming College of mathematics and Physics, Zhejiang {1. university, Jinhua 321.04, china department of mathematics, East china {1. university, shanghai 200062, china 1. College of mathematics and Physics Zhejiang Normal University 321004 Jinhua China 2. department of {1. 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.