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Dimension and measure theoretic entropy of a subshift in symbolic space

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Chinese Science Bulletin 1997年第14期42卷 1193-1196页

作者： CHEN Ercai and XIONG Jincheng1. department of Astronomy, nanjing University, Nangjing {2., china 2. department of mathematics, South china Normal University, Guangzhou 510631, china department of Astronomy Nanjing University Nangjing China department of mathematics South China Normal University Guangzhou China

1 Definitions and resultsWITH the development of the theory of dynamical systems and fractal geometry, one provedthat symbolic dynamics is a powerful tool to study chaos and fractals. It is useful to study thefractal characteristics of symbolic dynamics. In the present note we shall point out the relationbetween the dimension and measure theoretic entropy of any subshift in symbolic space. Weprove here that the Bowen’s formula for Hausdorff dimension holds without Markov struc-ture. A variational principle for dimension is obtained.

关键词： symbolic space subshift measure theoretic entropy dimension.

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. department of mathematics, Hangzhou Normal University, Hangzhou 310036,{2. 2. department of Applied mathematics, School of Mathematical Sciences, South{2. University of Technology, Guangzhou 510640,{2.) department of mathematics Hangzhou Normal University Hangzhou 310036 China department of Applied mathematics 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. department of mathematics, Yunnan University, Kunming 650031,{2. 2. department of mathematics, Shangrao Teachers College, Shangrao 334000,{2. department of mathematics Yunnan University Kunming China department of mathematics 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. department of mathematics, Beijing Normal University, Beijing 100875,{2. 2. Institute of Applied Physics and Computational mathematics, Beijing 100080,{2. 1. department of mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational mathematics 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.

A new sequential learning algorithm for RBF neural networks

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Science china(Technological Sciences) 2004年第4期47卷 447-460页

作者： YANG Ge1, LV Jianhong1 & LIU Zhiyuan2.1. department of Power Engineering, Southeast University, nanjing 2.0096,{2. 2. department of Power Engineering, nanjing Institute of Technology, nanjing 2.0013,{2. 1. department of Power Engineering Southeast University 210096 Nanjing China 2. department of Power Engineering Nanjing Institute of Technology 210013 Nanjing China

Due to their inherent imperfections, it is hard to use the static neural networks for nonlinear time-varying process modeling and prediction, and the minimal resource allocation network (MRAN) is difficult to be realized for its too many regulation parameters. A new sequential learning algorithm for radial basis function (RBF) neural networks based on local projection named Local Projection Network (LPN) is proposed in this paper. The results of validation for several benchmark problems with the new algorithm show that the presented LPN not only has the same level as M-RAN in network size and precision of the outputs, but also has fewer regulation parameters and is more predictable.

关键词： radial basis functions, local projection network, minimal resource allocation network, learning algorithm.

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. department of mathematics, Nankai University, Tianjin 300071,{2. 2. department of mathematics, Hebei University, Baoding 071002.{2. department of mathematics Nankai University Tianjin China department of mathematics 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.

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. department of mathematics, Sichuan University, Chengdu 610064,{2. 2. department of mathematics, Shaanxi Normal University, Xi’an 710062.{2. department of mathematics Sichuan University Chengdu China department of mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

Lipschitz classes on local fields

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Science china mathematics 2007年第7期50卷 1005-1014页

作者： Wei-yi SU~(1+) Guo-xiang CHEN~2.1 department of mathematics,{2. University,{2. 2.0093,china 2.department of mathematics,{2. Audit University,{2. 2.1815,china 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Nanjing Audit University Nanjing 211815 China

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is ***,those important characteristics on the Euclidean space R^n and the local field K are compared,so that one may interpret the essential differences between the analyses on R^n and ***,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2.ln 3).

关键词： local field Holder type space Lipschitz class Cantor type fractal function 11F85 46F05 43A2. 2.A80 2.A78

Characteristic analysis for a polynomial-like iterative equation

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Chinese Science Bulletin 1998年第3期43卷 192-196页

作者： Janusz Matkowski 1 and ZHANG Weinian 2.1. department of mathematics, Technical University, 43_300 Bielsko_Biala, Poland {2., Sichuan Union University, Chengdu 610064, china department of mathematics Technical University Bielsko-Biala Poland department of mathematics Sichuan Union University Chengdu China

In the light of Euler’s idea for differential equations,a polynomial_like n _order iterative equation is discussed through analyzing its characteristic polynomial. An unproved result is verified rigorously for the fi... 详细信息

关键词： iterative dynamics functional equation characteristic.