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The Riemannian Manifolds with Boundary and Large Symmetry

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Chinese Annals of mathematics,Series B 2010年第3期31卷 347-360页

作者： Zhi CHEN Yiqian SHI bin xu department of mathematics University of Science and Technology of China Hefei 230026 China. department of mathematics University of Science and Technology of China Hefei 230026 China.

Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.

关键词： Riemannian manifold with boundary Isometry Rotationally symmetric metric Principal orbit

THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 401-408页

作者： LIU TAISHUN (department of mathematics, university of science and technology of china, hefei 230026, china)REN GUANGbin (department of mathematics, university of science and technology of china, hefei 230026, china) department of mathematics University of Science and Technology of China Hefei 230026 China

The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular *** type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent *** theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.

关键词： Starlike mappings Growth theorem Starlike circular domains

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

Some new results about Jacobi forms

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Chinese science Bulletin 1997年第3期42卷 181-183页

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

THE one-dimensional Jacobi forms were first systematically investigated by Eichler and Zagier, and a similar theory in a higher-dimensional case was developed by Ziegler, who gave the precise definition and some basic properties of higher-dimensional Jacobi forms. This note tries to give a satisfactory classification for a large kind of spaces of Jacobi forms. To be a little more explicit, we get a rank formula for Jacobi forms and then show that either all the

关键词： Jacobi forms rank coefficient estimation.

Epidemic dynamics on complex networks

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Progress in Natural science:Materials International 2006年第5期16卷 452-457页

作者： ZHOU Tao , FU Zhongqian, and WANG binghong (department of Electronic science and technology, university of science and technology of china, hefei 230026, china department of Modern Physics, university of science and technology of china, hefei 230026, china) department of Electronic science and technology University of Science and Technology of China Hefei 230026 China department of Modern Physics University of Science and Technology of China Hefei 230026 China

Recently, motivated by the pioneer work in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. One of the ultimate goals is to understand how the topological structures affect the dynamics upon networks. In this paper, we give a brief review on the studies of epidemic dynamics on complex networks, including the description of classical epidemic models, the epidemic spread on small-world and scale-free networks, and network immunization. Finally, perspectives and some interesting problems are proposed.

关键词： epidemic dynamics complex networks critical value immunization small-world effect scale-free property.

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

TYPE X MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION

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Chinese Annals of mathematics,Series B 1996年第3期17卷 335-342页

作者： JIANG JIFA(department of mathematics, The university of science and technology of china, hefei 230036, china.) department of mathematics University of Science and Technology of China Hefei 230036 China

The author considers the asymptotic behavior of solutions of a class of ordinary dmerentialequations x = F(x) in the nonnegative orthant R7. Suppose that F(o) = o, Fi(x1,..., xn) isnondecreasing in xk for all k≠ i and that F possesses an order-increasing invarian *** it is shown that every bounded solution to such a system converges to a single equilibrium.

关键词： Type K monotone system Monotone flow Invariant function Equilibrium Convergence