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THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS

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Chinese Annals of mathematics,Series B 1996年第3期17卷 271-278页

作者： GONG SHENG(department of mathematics, university of science and technology of china, hefei 230026, china) 中国科学技术大学数学系安徽合肥

The estimations of the bounds of the Bloch constant of locally biholomorphic mappingson irreducible bounded symmetric domains are given. When the domain is a unit circle, theestimation of the lower bounds is just the ... 详细信息

关键词： Bounded symmetric domain Bloch mapping Bloch constant,Locally biholomorphic mapping

The contact Yamabe flow on K-contact manifolds

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science china mathematics 2009年第8期52卷 1723-1732页

作者： ZHANG YongBing department of mathematics, university of science and technology of china, hefei 230026, china department of mathematics University of Science and Technology of China Hefei China

We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds.

关键词： Yamabe problem Yamabe flow contact metric manifold K-contact manifold 53A30 53D10

Lie bialgebras of generalized Witt type

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science china mathematics 2006年第4期49卷 533-544页

作者： SONG Guang’ai & SU Yucai College of mathematics and Information science, Shandong Institute of Business and technology, Yantai 264005, china department of mathematics, university of science and technology of china, hefei 230026, china department of mathematics, Shanghai Jiaotong university, Shanghai 200240, china College of mathematics and Information science Shandong Institute of Business and Technology Yantai China department of mathematics Shanghai Jiaotong University Shanghai China department of mathematics University of Science and Technology of China Hefei China

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.

关键词： Lie bialgebras, Yang-Baxter equation, Lie algebra of generalized Witt type.

Existence and Non-Existence of Periodic Solutions of Generalized Lineard Equations with Damping of No Lower Bound

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Acta Mathematica Sinica,English Series 1996年第4期12卷 361-371页

作者： Jiang Jifa department of mathematics university of science and technology of china hefei, 230026 china department of mathematics University of Science and Technology of China Hefei China

This paper establishes criteria for the existence and non-existence of nonzero periodic solutions of the generalized Lienard equation （?）+f（x,（?））（?）+g（x）=*** main goal is to study to what extent the damping f can be small so as to guarantee the existence of nonzero periodic solutions of such a system. With some standard edditional assumptions we prove that if for a small |x|, ∫±∞|f（x,y）|-1dy=±∞, then the system has at least one nonzero periodic solution, otherwise, the system has no nonzero periodic solution. Many classical and well-known results can be proved as corollaries to ours.

关键词： Generalized Lienard equation Limit cycle

Norm continuity for t>0 of linear operator families

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Chinese science Bulletin 1998年第9期43卷 719-723页

作者： LIANG Jin and XIAO Tijun department of mathematics, university of science and technology of china, hefei 230026, china department of mathematics University of Science and Technology of China Hefei China

Some criteria of norm continuity for t>0 of linear operator families in Hilbert spaces are given.

关键词： linear operator family norm continuity criteria.

Monomial Hopf algebras over fields of positive characteristic

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science china mathematics 2006年第3期49卷 320-329页

作者： LIU Gongxiang & YE Yu Institute of mathematics, Academy of mathematics and Systems science, Chinese Academy of sciences, Beijing 100080, china department of mathematics, university of science and technology of china, hefei 230026, china Institute of mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China department of mathematics University of Science and Technology of China Hefei China

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n)are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.

关键词： monomial coalgebra, Gaussian binomial coefficient, monomial Hopf algebra.

Hamiltonian Formalism of de-Sitter Invariant Special Relativity

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Communications in Theoretical Physics 2007年第7期48卷 27-36页

作者： YAN Mu-Lin XIAO Neng-Chao HUANG Wei Interdisciplinary Center for Theoretical Study,university of science and technology of china,hefei 230026,chinaLI Si department of mathematics,university of science and technology of china,hefei 230026,china Interdisciplinary Center for Theoretical Study University of Science and Technology of China Hefei 230026 China department of mathematics University of Science and Technology of China Hefei 230026 China

The Lagrangian of Einstein's special relativity with universal parameter c(SR_c)is invariant under Poincarétransformation,which preserves Lorentz metric η_μν.The SR_c has been extended to be one which is invariant underde Sitter transformation that preserves so-called Beltrami metric B_(μv).There are two universal parameters,c and R,inthis Special Relativity(denoted as SR_(cR)).The Lagrangian-Hamiltonian formulism of SR_(cR) is formulated in this *** canonic energy,canonic momenta,and 10 Noether charges corresponding to the space-time's,de Sitter symmetryare *** canonical quantization of the mechanics for SR_(CR)-free particle is *** physics related to itis discussed.

关键词： de-Sitter invariance special relativity canonic energy and canonic momenta Beltrami metric

The Degree of Symmetry of Certain Compact Smooth Manifolds II

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Chinese Annals of mathematics,Series B 2007年第2期28卷 195-204页

作者： Bin XU department of mathematics, university of science and technology of china, hefei 230026, china Chern Institute of mathematics, Nankai university, Tianjin 300071, china department of mathematics, Johns Hopkins university, Baltimore, MD 21218, USA. department of mathematics University of Science and Technology of China Hefei China Chern Institute of mathematics Nankai University Tianjin China department of mathematics Johns Hopkins University Baltimore USA

We give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain compact fiber bundles with non-trivial four dimensional fibers in the sense of cobordism, by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau (Topology, 18, 1979, 361-380). As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP2×V, where V is a closed smooth manifold admitting a real analytic Riemannian metric of non-positive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one dimensional cohomology.

关键词： Degree of symmetry Fiber bundle Cobordism Non-positive Curvature Harmonic map First cohomology

A CHARACTERISTIC-BASED FINITE VOLUME SCHEME FOR SHALLOW WATER EQUATIONS

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Journal of Hydrodynamics 2009年第4期21卷 531-540页

作者： GUO Yan LIU Ru-xun DUAN Ya-li LI Yuan department of mathematics University of Science and Technology of China Hefei 230026 China department of mathematics China University of Mining and Technology XuZhou 221116 China

We propose a new characteristic-based finite volume scheme combined with the method of Central Weighted Essentially Non-Oscillatory （CWENO） reconstruction and characteristics, to solve shallow water equations. We apply the scheme to simulate dam-break problems. A number of challenging test cases are considered, such as large depth differences even wet/dry bed. The numerical solutions well agree with the analytical solutions. The results demonstrate the desired accuracy, high-resolution and robustness of the presented scheme.

关键词： shallow water equations finite volume method characteristic method Central Weighted Essentially Non-Oscillatory (CWENO) scheme HLLC flux