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Inequalities for polars of mixed projection bodies

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Science china mathematics 2004年第2期47卷 175-186页

作者： LENG Gangsong, ZHAO Changjian, HE Binwu & LI Xiaoyandepartment of mathematics, shanghai University, shanghai 20043., china department of mathematics, Binzhou Teachers College, Binzhou 256604, china department of mathematics Shanghai University Shanghai China department of mathematics Binzhou Teachers College Binzhou China

In 1993.Lutwak established some analogs of the Brunn-Minkowsi inequality and the Aleksandrov-Fenchel inequality for mixed projection bodies. In this paper, following Lutwak, we give their polars forms. Further, as app... 详细信息

关键词： convex body, mixed volume, projection body, mixed projection body, polar of mixed projection body, John basis.

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 University, shanghai 201800, china 2. department of mathematics, Zhongshan University, Guangzhou 510275, 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.

Anticoagulation property and security of artificial heart valve material

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Science china(Technological Sciences) 2005年第2期48卷 145-162页

作者： WANG Xianghui1, , LIU Xianghuai1,22, 3. ZHANG Feng2, LI Changrong2, YU Liujiang2, ZHENG Zhihong2, WANG Xi2, JIANG Zhenbin4, CHEN Anqing4 & XU Jingfang3.1. department of Physics, East china Normal University, shanghai 200062, china 2. Ion Beam Lab, shanghai Institute of Mini-system and information, Chinese Academy of Sciences,shanghai 200050, china 3. department of Electronics, School of Information Science and Technology, East china Normal Univer- sity, shanghai 200062, china 4. shanghai Cardiovascular Institute, Zhongshan Hospital, shanghai 20003., china department of Physics East China Normal University Shanghai China Ion Beam Lab Shanghai Institute of Mini-system and information Chinese Academy of Sciences Shanghai China department of Electronics School of Information Science and Technology East China Normal University Shanghai China shanghai Cardiovascular Institute Zhongshan Hospital Shanghai China

Heart valve diseases threaten human health. One reliable way to save lives of such patients is to replace the pathologically changed heart valves by artificial ones. Over 2 million patients have received LTI-carbon heart valve’s implantation. However, the thrombosis after the implantation is one of the difficulties that need to be solved. In order to improve the blood compatibility and security of mechanical heart valves, ion beam technology was used to modify the surface properties of the materials. The investigation results have been summarized in this paper.

关键词： artificial heart valve, ion implantation, plasma immersed ion implantation, ion beam enhanced deposition.

GENERAL CAUCHY PROBLEM FOR THE LINEAR SHALLOW-WATER EQUATIONS ON AN EQUATORIAL BETA-PLANE

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Journal of Hydrodynamics 2006年第3期18卷 303-309页

作者： SHEN Chun SHI Wei-hui School of mathematics and Information Yantai Normal University Yantai 264025 China shanghai Institute of Applied mathematics and Mechanics Shanghai University Shanghai 200072 China department of mathematics Shanghai University Shanghai 200444 China

Based on the theory of stratification, the well-posedness of the initial value problem for the linear shallow-water equations on an equatorial beta-plane was discussed. The sufficient and necessary conditions of the existence and uniqueness for the local solution of the equations were presented and the existence conditions for formal solutions of the equations vere also given. For the Cauchy problem on the hyper-plane {t = O}, the local analytic solution were worked out and a special case was discussed. Finally, an example was used to explain the variety of formal solutions for the ill-posed problem.

关键词： stratification initial value problem,well-posedness shallow-water equations

An Improved Method in Synchronization ofChaotic Systems

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Communications in Nonlinear Science and Numerical Simulation 1998年第3期3卷 140-143页

作者： Jiong RUAN and Lijuan LI(department of mathematics, Fudan University, shanghai 20043., {3.) department of mathematics Fudan University Shanghai 200433 China

An improved strategy in srnchrohization of chaotic dynamics as contrastedwith PC(*** and ***) method and KSC(Kocarev L, Shang A, Chua,L.O.)control idea is presented in this paper. Computer simulations are included to ... 详细信息

关键词： synchronization conditional Lyapunov exponents drive-response

Chen's Theorem with Small Primes

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Acta Mathematica Sinica,English Series 2002年第3期18卷 597-604页

作者： Ying Chun CAI department of mathematics, shanghai University, shanghai 20043.. P. R. china department of mathematics Shanghai University Shanghai P. R. China

Let N be a sufficiently large even integer. In this paper it is proved that the equation N=p+P_2, p≤N^(0.95), is solvable, where p denotes a prime and P_2 denotes an almost prime with at most two prime factors.

关键词： Chen's theorem Sieve Mean value theorem

Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value

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Acta Mathematica Sinica,English Series 2001年第2期17卷 197-206页

作者： Yuan Di WANG department of mathematics, shanghai University, shanghai 20043.. P. R. china department of mathematics Shanghai University Shanghai 200436 P. R. China

Recently much work has been devoted to nonlocal problems. However, very little has been accomplished in the literature for nonlocal initial problems with nonlinear boundary conditions. It is the purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDE with linear homogeneous boundary conditions, and to other ones with nonlinear boundary conditions, provided the ordered upper and lower solutions are given. Semigroup, fractional order function spaces and generalized Poincare operators play an important role in proving the existence of solutions.

关键词： Nonlocal problem Nonlinear boundary condition Palabolic equation Solution Existence Generalized Poincaree operator

Synchronization of Chaotic Systems by Linear Feedback Controller

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Communications in Nonlinear Science and Numerical Simulation 1998年第1期3卷 27-30页

作者： Zhenxun HUANG and Jiong RUAN (department of mathematics, Fudan University, shanghai 20043., {3.) department of mathematics Fudan University Shanghai 200433 China

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关键词： control and synchronization of chaos heterogeneous synchronization ω limit point global asymptotical stability

GLOBALLY CONVERGENT INEXACT GENERALIZED NEWTON METHODS WITH DECREASING NORM OF THE GRADIENT

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Journal of Computational mathematics 2002年第3期20卷 289-300页

作者： Ding-guo Pu (department of mathematics, Tongji University, shanghai 2003.1, {3.) department of mathematics Tongji University 上海 200331

Presents information on a study which proposed a type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems. Theorems on inexact generalized Newton algorithm with decre... 详细信息

关键词： nonsmooth optimization inexact Newton method generalized Newton method global convergence superlinear rate