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Chinese Science Bulletin 1997年第3期42卷 259-260页

作者： MAI Jiehua and GU Rongbao1.Institute of mathematics, Shantou university, Shantou 515063,{2. 2. department of mathematics, anhui university, hefei 2.0039,{2. Institute of mathematics Shantou University Shantou China department of mathematics Anhui University Hefei China

IN this letter we discuss the necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C^r(r≥2. flow is trivial, but it is possible for a C^0 flow to contain non-trivial minimal sets. Thus C^0 flows on closed surfaces are more complicated than C^r(r≥2. flows.

关键词： Necessary and sufficient condition of C^0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property

Generic modules for tilted algebras

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Chinese Science Bulletin 1997年第3期42卷 177-180页

作者： DU Xiannengdepartment of mathematics,{2., hefei 2.0039, china department of mathematics Anhui University Hefei China

IN the theory of infinite abelian groups, the concepts of torsion-free groups and divisible groups are well known. We know that there exists, up to isomorphism, one and only one abelian group which is both torsion-free and divisible at the same time. This is the additive group Q of the rational numbers. Q plays an important role in the study of infinite-abelian groups. The theory of infinite-dirnensional modules over a finite-dimensional algebra runs similarly to the theory of infinite abelian groups but there are also some substantial differences.

关键词： tilting modules tilted algebras tame hereditary algebras generic modules.

Characteristic modules of quasi-hereditary algebras with three samples

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Chinese Science Bulletin 1997年第6期42卷 450-454页

作者： ZHANG Pu and LIN Yanan1. department of mathematics, {2. of Science and Technology of china, hefei 2.002., china 2. department of mathematics, Xiamen {2., Xiamen 361005, china department of mathematics University of Science and Technology of China Hefei China department of mathematics Xiamen University Xiamen China

CLINE et al. have introduced the concept of quasi-hereditary algebra, which provided a

关键词： tilting module characteristic module quasi-hereditary algebra.

ON　THE　UPPER　ESTIMATES　OF　FUNDAMENTAL　SOLUTIONS　OF　PARABOLIC　EQUATIONS　ON　RIEMANNIAN　MANIFOLDS

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Chinese Annals of mathematics,Series B 1995年第1期16卷 119-130页

作者： LI JIAYU SHAO XIN (Departmellt of mathematics, anhui university,{2., china.Basic department, anhui Agricultural College, hefei 2.0036, china.) anhui UNIV DEPT MATHHEFEI 230039PEOPLES R CHINA anhui AGR COLL DEPT BASICHEFEI 230036PEOPLES R CHINA

The authors first derive the gradient estimates and Harnack inequalties for positive solutions of the equation on(x, t)An(x, t) + b(x, t)' ac(￣, t) + h(x, t)u(x, t) ￣ m ￣ 0on complete Riemannian manifolds, and then derive the upper bounds of any positive L2.undamental solution of the equation when h(x, t) and b(x, t) are independent of t.

关键词： Parabolic equation Gradient estimate Harnack inequality Fundamentalsolution Riemannian manifolds.

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of mathematics, {2. of Science and Technology of china, hefei 2.002., china 2. department of mathematics, Beijing Normal {2., Beijing 100875, china department of mathematics University of Science and Technology of China Hefei China department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

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, {2. of Science and Technology of china, hefei 2.002., china)REN GUANGBIN (department of mathematics, {2. of Science and Technology of china, hefei 2.002., china) Univ Sci & Technol china Dept Math Anhua 230026 Peoples R 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, {2. of Science and Technology of china, hefei 2.002., china) UNIV SCI & TECHNOL china DEPT MATHHEFEI 230026PEOPLES R CHINA

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

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 mathematics, Shanghai {2., Shanghai 2.1800, china 2. department of mathematics, Zhongshan {2., Guangzhou 5102.5, china department of mathematics Shanghai University Shanghai China department of mathematics 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.

Perturbations of the radical of nest algebras

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Chinese Science Bulletin 1998年第7期43卷 556-560页

作者： LU Fangyan 1 and LU Shijie 2.1. department of mathematics, Suzhou {2., Suzhou 2.5006, china 2. department of mathematics, Zhejiang {2., Hangzhou 31002., china department of mathematics Suzhou University Suzhou China department of mathematics Zhejiang University Hangzhou China

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.

关键词： nest algebras radical perturbation.

On SS-quasinormal subgroups and the structure of finite groups

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Science china mathematics 2011年第3期54卷 449-456页

作者： WEI XianBiao1,2.& GUO XiuYun2. 1department of mathematics and Physics, {2. Institute of Architecture and Industry, hefei 2.002., china 2.0} of mathematics, Shanghai university, Shanghai 2.0444, china 1. department of mathematics and Physics Anhui Institute of Architecture and Industry Hefei 230022 China2. Department of Mathematics Shanghai University Shanghai 200444 China

A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpotent if there is a subgroup D of P with 1 2.D| whenever p = 2.and |D| = 2.is SS-quasinormal in G, where p is the smallest prime dividing the order of G and P is a Sylow p-subgroup of G.

关键词： S-quasinormal subgroups SS-quasinormal subgroups p-nilpotent groups supersolvable groups