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SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

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Chinese Annals of mathematics,Series B 2005年第4期26卷 651-658页

作者： WANG MENG department of mathematics, {2. university, hangzhou 31002., china School of Mathematical Sciences, Pudan university, Shanghai 2.0433, china. department of mathematics Zhejiang University Hangzhou 310027 China. School of Mathematical Sciences Fudan University Shanghai 200433 China

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(... 详细信息

关键词： Sobolev inequality Complete manifold Riesz transform Potential Heat kernel

Ordinal scheduling problem and its asymptotically optimal algorithms on parallel machine system

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Science in china(Series F) 2004年第2期47卷 161-169页

作者： TAN Zhiyi1,2.& HE Yong1 1. department of mathematics, {2. university, hangzhou 31002., china (email: tanzy@math.zju. *** heyong@math.zju.***) 2. State Key Laboratory of CAD & CG, {2. university, hangzhou 31002., china 1. department of mathematics Zhejiang University 310027 Hangzhou China 2. State Key Laboratory of CAD & CG Zhejiang University 310027 Hangzhou China

Focusing on the ordinal scheduling problem on a parallel machine system, we discuss the background of ordinal scheduling and the motivation of ordinal algorithms. In addition, for the ordinal scheduling problem on identical parallel machines with the objective to maximize the minimum machine load, we then give two asymptotically optimal algorithm classes which have worst-case ratios very close to the upper bound of the problem for any given m. These results greatly improve the results proposed by He Yong and Tan Zhiyi in 2.02.

关键词： scheduling design and analysis of algorithm worst-case ratio.

On the Notion of Cobordism for Bounded Manifolds

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Acta Mathematica Sinica,English Series 1994年第1期10卷 59-63页

作者： Gan Danyan department of mathematics {2. university hangzhou,31002. china 1. department of mathematics Zhejiang University 310027 Hangzhou China

The usual concept of eobordism is concerned with closed *** this paper, we generalise the concept of cobordism to the extent of bouncded manifolds and obtain a homotopy theorem similar to the theorem of Thom.

关键词： On the Notion of Cobordism for Bounded Manifolds

ω-Gorenstein injective modules and dimensions

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Science china mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2.& DING NanQing3 1department of mathematics, {2. university, {2. 31002., china 2.0} of mathematics, {2. university of Technology, {2. 31002., china 3department of mathematics, Nanjing university, Nanjing 2.0093, china 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module

Dynamic behavior of polymer surface and the time dependence of contact angle

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Science china Chemistry 2005年第6期48卷 553-559页

作者： WANG Xinping1, CHEN Zhifang1 & SHEN Zhiquan2.1. Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry, department of Applied Chemistry, zhejiang Institute of Science and Technology, {2. 310033, china 2. department of Polymer Science and Engineering, zhejiang university, {2. 31002., china 1. department of Applied Chemistry Zhejiang Institute of Science and Technology Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry 310033 Hangzhou China 2. department of Polymer Science and Engineering Zhejiang University 310027 Hangzhou China

Time-dependent contact angles were measured by depositing sessile drops of wa-ter on the polymer surfaces and monitoring the drop shape as a function of time. It was found that contact angles decreased sharply with contact time and the equilibrium contact angle was finally attained after a certain time. Values of starting (θ s) and equilibrium contact angles (θ e) obtained by the sessile drop method depend on polymer properties. The Wilhelmy plate technique was used to measure advancing and receding contact angles. The variations of starting (θ s) and equilibrium contact angles (θ e), advancing (θ a) and receding contact angles (θ r) have been studied on the oxidized surface of polymers containing polybutadiene block to explore the cause of time-dependence in contact angle measurement and the meaning of θ s and θ e. The results showed the linear relationships between starting (θ s) and advancing contact angles (θ a), the equilibrium (θ e) and receding contact angles (θ r). The similar relationship was also established between the contact angle hysteresis (θ a?θ r) and differences (θ s ?θ e) in starting contact angles and equilibrium contact angles. Therefore, time-dependence in contact angle measurement was mainly attributed to the surface reconstruction when water drops were deposited on polymer surfaces. The starting contact angle was contributed by the hydrophobic component on polymer surface and the equilibrium contact angle mainly by the hydrophilic component of polymer. These results not only demonstrated the interdependency between two contact angle measurements, the sessile drop method and the Wilhelmy plate technique, but also provided the experimental evidence to explain the cause of time-dependent contact angle. This may also provide a new method to study dynamic behavior of polymer surface.

关键词： contact angle, surface dynamic behavior, polymer surface, dynamic contact angle, time-dependence.

Limit theory of restricted range approximations of complex-valued continuous functions

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Science china mathematics 2007年第10期50卷 1427-1440页

作者： Xian-fa LUO~1 Chong LI~(2.) ~1 School of mathematics and Computer Science,Jishou university,Jishou 416000,{2. ~2.department of mathematics,zhejiang university,hangzhou 31002.,{2. 1. School of mathematics and Computer Science Jishou University Jishou 416000 China 2. department of mathematics Zhejiang University Hangzhou 310027 China

This paper is concerned with the problem of the best restricted range approximations of complex-valued continuous functions. Several properties for the approximating set PΩ such that the classical characterization results and/or the uniqueness results of the best approximations hold are introduced. Under the very mild conditions, we prove that these properties are equivalent that P is a Haar subspce.

关键词： restricted range approximation, Haar subspace, characterization, uniqueness

A theoretical model of turbulent fiber suspension and its application to the channel flow

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Science china(Physics,Mechanics & Astronomy) 2010年第9期53卷 1659-1670页

作者： LIN JianZhong1,2.& SHEN SuHua1 1 department of Mechanics,zhejiang {2.,hangzhou 31002.,china 2.5} Jiliang {2.,hangzhou 310018,china 1. department of Mechanics Zhejiang University Hangzhou 310027 China2. China Jiliang University Hangzhou 310018 China

A theoretical model of turbulent fiber suspension is developed by deriving the equations of Reynolds averaged Navier-Stokes,turbulence kinetic energy and turbulence dissipation rate with the additional term of *** order to close the above equations,the equation of probability distribution function for mean fiber orientation is also *** theoretical model is applied to the turbulent channel flow and the corresponding equations are solved *** numerical results are verified by comparisons with the experimental *** effects of Reynolds number,fiber concentration and fiber aspect-ratio on the velocity profile,turbulent kinetic energy and turbulent dissipation rate are *** on the numerical data,the expression for the velocity profile in the turbulent fiber suspension channel flow,which includes the effect of Reynolds number,fiber concentration and aspect-ratio,is proposed.

关键词： theoretical model turbulent fiber suspension numerical simulation channel flow modification of velocity profile

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.

Line bundles on non-primary Hopf manifolds

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Science china mathematics 2004年第4期47卷 538-551页

作者： LIU Weiming & ZHOU XiangyuInstitute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080,{2. department of mathematics, zhejiang university, hangzhou 31002.,{2. 1. Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. department of mathematics Zhejiang University 310028 Hangzhou China

Let X be a Hopf manifolds with Abelian fundamental group, L any flat line bundle on X, we give a formula for computing explicitly the cohomology Hq(X, Ωp(L) using the method of group action and the generalized Douady... 详细信息

关键词： Hopf surface, cohomology, line bundle, sections.