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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 {3. of china, hefei 23.026, china)REN GUANGBIN (department of mathematics, university of Science and {3. of china, hefei 23.026, 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 {3. of china, hefei 23.026, 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

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 {3. of china, hefei 23.03., 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

Analysis on cohesive crack opening displacement considering the strain softening effect

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Science china(Physics,Mechanics & Astronomy) 2006年第1期49卷 88-101页

作者： WANG Limin1, XU Shilang2 & ZHAO Xiqiang3.1. Mechanics department, Shandong university of technology, Zibo 255049, {3. 2. Civil Engineering department, Dalian university of technology, Dalian 116024, {3. 3. mathematics department, Ocean university of {3., Qingdao 266071, {3. Mechanics department Shandong University of Technology Zibo China Civil Engineering department Dalian University of Technology Dalian China mathematics department Ocean University of China Qingdao China

In order to investigate the crack propagation in quasi-brittle materials like rock, ceramic and concrete, Hillerborg and his co-researchers abstracted the fracture process zone in front of a stress free crack in terms of a “fictitious crack zone”. On the fictitious crack zone, cohesive stresses distribute following a given softening relationship of stress vs. crack opening. Based on the polynomial or power series expression of cohesive crack opening displacement, the relationship of the cohesive stress vs. the crack opening displacement is established using elastic theory and integral equation, and some unknown physics variables are obtained using variation approach. The calculation results gained in this paper are close to the experimentally test ones.

关键词： cohesive crack, softening, dissipation work, variation approach.

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 {3. of china, hefei 23.026, 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 53.3. 53.10

Congruences on ideal nil-extension of completely regular semigroups

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Chinese Science Bulletin 1998年第5期43卷 379-381页

作者： REN Xueming 1, 2 GUO Yuqi 2 and CEN Jiaping (Shum Kar-ping) 3.. department of mathematics, Xi’an university of Architecture & {3., Xi’an 710055, china 2. department of mathematics, Yunnan university, Kunming 650091, china 3. department of department of mathematics Xi’an University of Architecture & Technology Xi’an China department of mathematics Yunnan University Kunming China department of mathematics Chinese University of Hong Kong Hong Kong

Let S be an ideal nil-extension of a completely regular semigroup K by a nil semigroup Q with zero. A concept of admissible congruence pairs (δ,ω) of S is introduced, where δ and ω are a congruence on Q and a congruence on K respectively. It is proved that every congruence on S can be uniquely respresented by an admissible congruence pair (δ,ω) of S. Suppose that ρ K denotes the Rees congruence induced by the ideal K of S. Then it is shown that for any congruence σ on S,a mapping Γ:σ|→(σ Q,σ K) is an order-preserving bijection from the set of all congruences on S onto the set of all admissible congruence pairs of S,where σ K is the restriction of σ to K and σ Q=(σ∨ρ K)/ρ K. Moreover,the lattice of congruences of S is also discussed. As a special case,every congruence on completely Archimedean semigroups S is described by an admissible quarterple of S. The following question is asked: Is the lattice of congruences of the completely Archimedean semigroup a semimodular lattice?

关键词： completely regular semigroups ideal nil-extension congruences.

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 {3. of mathematics, university of Science and technology of china, hefei 23.026, china {3. 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.

Smoothness for the collision local times of bifractional Brownian motions

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Science china mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3.1 department of mathematics,East china {3. of Science and technology,Shanghai 20023.,china 2 department of mathematics,Anhui Normal {3.,Wuhu 241000,china 3.department of mathematics,Donghua {3.,Shanghai 201620,china department of mathematics East China University of Science and Technology Shanghai China department of mathematics Anhui Normal University Wuhu China department of mathematics Donghua University Shanghai China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2 and YU Yuanhong 3.1. department of Applied mathematics, Beijing Institute of technology, Beijing 100081, {3. 2. department of mathematics, Yunnan university, Kunming 650091, {3. 3. Institute of Applied mathematics, C department of Applied mathematics Beijing Institute of Technology Beijing China department of mathematics Yunnan University Kunming China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.