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Minimal symmetric submanifolds in compact Riemannian symmetric spaces

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Chinese Science Bulletin 1998年第21期43卷 1786-1789页

作者： LIANG Ke 1.and JIN Quanqin 1.2.1. {1. of mathematics, Nankai University, Tianjin 300071.{2. 2. department of mathematics, hebei University, baoding 071.02,{2. department of {1. Nankai University Tianjin China department of {1. Hebei University Baoding China

A necessary and sufficient condition for a symmetric submanifold to be minimal in its ambient compact Riemannian symmetric space is given. By this condition a complete classification of non- minimal symmetric submanif... 详细信息

关键词： symmetric space symmetric submanifold mean curvature vector.

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. {1. of mathematics, Shanghai University, Shanghai 2.1.00,{2. 2. department of mathematics, Zhongshan University, Guangzhou 51.2.5,{2. department of {1. Shanghai University Shanghai China department of {1. 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. {1. of mathematics, Suzhou University, Suzhou 2.5006,{2. 2. department of mathematics, Zhejiang University, Hangzhou 31.02.,{2. department of {1. Suzhou University Suzhou China department of {1. 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.

Shape blending of artistic brushstroke represented by disk B-spline curves

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Progress in Natural Science:Materials International 2007年第12期17卷 1501-1507页

作者： Cheng Min1.2.and Wang Guojin1.1. {1. of mathematics, Zhejiang University, Hangzhou 31.02.,{2. 2. department of mathematics, Zhejiang University of Technology, Hangzhou 31.032.{2.) department of {1. Zhejiang University Hangzhou 310027 China 2. department of mathematics Zhejiang University of Technology Hangzhou 310032 China

This paper presents an algorithm for automatically generating in-between frames of two artistic brushstrokes. The basic idea of the algorithm is to represent the two key frames of artistic brushstrokes in disk B-spline curves, and then make blending of their geometric intrinsic variables. Given two key frames of artistic brushstrokes, the skeleton curves can be obtained by certain skeleton-based techniques. After disk B-spline representation of the key frames is generated, interpolation of the intrinsic variables of the initial and the target disk B-spline curves is carried out. Examples show that this method can efficiently create in-between frames of artistic brushstrokes.

关键词： computer aided calligraphy shape blending brushstroke disk B-spline curve skeleton.

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1.and WU Congxin 2.1. {1. of mathematics,Inner Mongolia Normal University, Huhhot 01.02.,{2. 2. department of mathematics, Harbin Institute of Technology, Harbin 1.0006,{2. department of {1. Inner Mongolia Normal University Huhhot China department of {1. Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1.US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1.*, YOU Fei 1.and PENG Jiayin 2.1. {1. of mathematics, Beijing Normal University, Beijing 1.0875,{2. 2. department of mathematics, Neijiang Teacher's College, Neijiang 641.1.0}{2.) Beijing Normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1.and Liu Shenquan2.1. {1. of mathematics, Hangzhou Normal University, Hangzhou 31.036,{2. 2. {1. of Applied mathematics, School of Mathematical Sciences, South{2. University of Technology, Guangzhou 51.640,{2.) department of {1. Hangzhou Normal University Hangzhou 310036 China department of Applied {1. School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

Exponential attractors of the nonlinear wave equations

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Chinese Science Bulletin 1998年第16期43卷 1331-1335页

作者： DAI Zhengde 1.and MA Dacai 2.1. {1. of mathematics, Yunnan University, Kunming 650031.{2. 2. department of mathematics, Shangrao Teachers College, Shangrao 334000,{2. department of {1. Yunnan University Kunming China department of {1. Shangrao Teachers College Shangrao China

The (E, E)-type exponential attractors for the nonlinear wave equation were obtained by using the decomposition of operators and finite covering *** results solves the open problem of Eden et al.

关键词： nonlinearity wave equations exponential attractors.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1.& GUO Boling2.1. {1. of mathematics, Beijing Normal University, Beijing 1.0875,{2. 2. Institute of Applied Physics and Computational mathematics, Beijing 1.0080,{2. 1. department of {1. Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational {1. Beijing 100080 China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.