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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 2.0093, china 2. Department of Mathematics,{2., 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.

Research on the method for retrieving soil moisture using thermal inertia model

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Science china Earth Sciences 2006年第5期49卷 539-545页

作者： LIU Zhenhua1 & ZHAO Yingshi2.1. Information College, south china Agricultural {2., guangzhou 510642. china 2. Graduate {2. of Chinese Academy of Sciences, Beijing 100049, china Information College South China Agricultural University Guangzhou China Graduate university of Chinese Academy of Sciences Beijing China

In order to improve accuracy of soil moisture inversion using remote sensing, a new thermal inertia model is proposed in this paper. The improved model needs only surface maximum temperature as the temperature parameter input instead of input of the surface temperature difference, as well as the surface sensible and latent fluxes are introduced into boundary conditions of thermal conductivity equation. Furthermore, surface soil conductive heat transfer equation of two-layer model is used to solve the soil thermal inertia so that the remote sensing thermal inertia method can be ap- plied to regions with better-covered vegetation, but usually only for the bare areas or worse vegetation covered areas. The model has been tested at several locations in the area of west Inner Mongolia. Comparing the simulation of the new model with the measurements obtained by apparent thermal inertia and by field test, the result shows that the inertia thermal model can be used to estimate soil moisture in more reasonable accuracy.

关键词： thermal model, thermal conductivity equation, soil initial, sensible flux, latent flux, two-layer model.

Quasirational dynamic system

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Chinese Science Bulletin 2000年第14期45卷 1277-1279页

作者： SUN Daochun & YANG Lo1. Department of Mathematics, south china normal university, guangzhou 510631,{2. 2. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080,{2. Department of Mathematics South China Normal University Guangzhou China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Using the iterations of quasirational mappings, the theorems on dynamic system are generalized to the quasirational dynamic system. Some different results are also obtained.

关键词： quasirational mapping dynamic system covering surface.

A note for preconditioning nonsymmetric matrices

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Applied Mathematics(A Journal of Chinese Universities) 2010年第1期25卷 93-100页

作者： CHEN Xiao-shan LI Wen School of Mathematics, south china normal university, guangzhou 510631,{2. School of Mathematics South China Normal University Guangzhou China

In this paper, we consider preconditioners for generalized saddle point systems with a nonsymmetric coefficient matrix. A constraint preconditioner for this systems is constructed, and some spectral properties of the ... 详细信息

关键词： Preconditioner saddle point matrix minimal polynomial Schilder's factorization.

On the diophantine equation X^2.(1+a^2.Y^4 =-2.

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Science china Mathematics 2010年第8期53卷 2143-2158页

作者： YUAN PingZhi 1 & ZHANG ZhongFeng 2.1 School of Mathematics,south china {2. university,guangzhou 510631,china 2.School of Mathematics & Computational Science,Sun Yat-Sen university,guangzhou 5102.5,china School of Mathematics South China Normal University Guangzhou China School of Mathematics & Computational Science Sun Yat-Sen University Guangzhou China

Let a≥1 be an *** this paper,we will prove the equation in the title has at most three positive integer solutions.

关键词： algebraic approximations continued fractions elliptic curves quartic equations

Estimates on Bloch constants for planar harmonic mappings

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Science china Mathematics 2009年第1期52卷 87-93页

作者： LIU MingSheng School of Mathematical Sciences, south china normal university, guangzhou 510631,{2. School of Mathematical Sciences South China Normal University Guangzhou China

The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Gri... 详细信息

关键词： Bloch constant quasiregular harmonic mapping open planar harmonic mapping 30C99 30C62

Self-trapping and Self-focusing of Light Beams in Uniaxial Crystals

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Chinese Journal of Lasers 1996年第4期B5卷 313-318页

作者： GUO Qi(Institute of Quantum Electronics,south china {2. university,guangzhou 510631, china) south china {2. Univ Guangzhou China

Ｓｅｌｆ－ｔｒａｐｐｉｎｇａｎｄＳｅｌｆ－ｆｏｃｕｓｉｎｇｏｆＬｉｇｈｔＢｅａｍｓｉｎＵｎｉａｘｉａｌＣｒｙｓｔａｌｓ￥ＧＵＯＱｉ（ＩｎｓｔｉｔｕｔｅｏｆＱｕａｎｔｕｍＥｌｅｃｔｒｏｎｉｃｓ，ＳｏｕｔｈＣｈｉｎａＮｏ... 详细信息

Ｓｅｌｆ－ｔｒａｐｐｉｎｇａｎｄＳｅｌｆ－ｆｏｃｕｓｉｎｇｏｆＬｉｇｈｔＢｅａｍｓｉｎＵｎｉａｘｉａｌＣｒｙｓｔａｌｓ￥ＧＵＯＱｉ（ＩｎｓｔｉｔｕｔｅｏｆＱｕａｎｔｕｍＥｌｅｃｔｒｏｎｉｃｓ，ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｇｕ...

关键词： self-trapping self-focusing uniaxial crystal

The generalized Roper-Suffridge extension operator in Banach spaces (Ⅲ)

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Science china Mathematics 2009年第11期52卷 2432-2446页

作者： ZHU YuCan1 & LIU MingSheng2.1 Department of Mathematics,Fuzhou university,Fuzhou 350002.china 2.Department of Mathematics,{2. china normal university,guangzhou 510631,china Department of Mathematics Fuzhou University Fuzhou China Department of Mathematics South China Normal University Guangzhou China

Suppose that X is a complex Banach space with the norm ||·|| and n is a positive integer with dim X ≥n≥ 2. In this paper,we consider the generalized Roper-Suffridge extension operator Φn,β2.γ2....,βn+1,γn+1(f)... 详细信息

关键词： Roper-Suffridge extension operator biholomorphic starlike mapping almost spirallike mapping of type β and order α spirallike mapping of type β and order α