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The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： CHEN Ercai and XIONG Jincheng department of mathematics , Nanjing normal university , Nanjing 210097, china department of mathematics , south china normal university, guangzhou 510631 , china department of mathematics Nanjing Normal University Nanjing China department of mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

A problem of complex oscillation for homogeneous linear differential equations

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Chinese Science Bulletin 1998年第20期43卷 1709-1712页

作者： GAO Shian and YANG Ronghua department of mathematics,south china normal university,guangzhou 510631, china department of mathematics, Guangdong Educational College, guangzhou 510303, china department of mathematics South China Normal University Guangzhou China department of mathematics Guangdong Educational College Guangzhou China

Under a combined dominant condition, an open problem of complex oscillation for the equation \%w (k) +Aw=0\% is set, where \%k≥3, a(z)\% is a transcendental entire function.

关键词： meromorphic function differential equation complex oscillation.

The counting series for (k+1)-uniform linear acyclic hypergraphs

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Chinese Science Bulletin 2001年第3期46卷 197-200页

作者： SHAN Zhilong & LIU Bolian department of mathematics, south china normal university, guangzhou 510631, china department of Computer Science, Guandong Polytechnical normal university, guangzhou 510633, china department of mathematics South China Normal University Guangzhou China department of Computer Science Guandong Polytechnical Normal University Guangzhou China

The explicit formula for (k+l)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k +1)-uniform linear acyclic hypergraphs are obtained.

关键词： hypergraph linear hypergraph hypertree bipartite tree Polya’s Enumeration Theorem.

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,south china normal university,guangzhou 510631,china 1. department of mathematics Fuzhou University Fuzhou 350002 China 2. department of mathematics South China Normal University Guangzhou 510631 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

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 210093, 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.

ON A PROPERTY OF SOLUTIONS OF M-MATRIXEQUATIONS

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Systems Science and Mathematical Sciences 1997年第2期10卷 129-132页

作者： LI Wen (department of mathematics, south china normal university, guangzhou 510631, china) 华南师范大学数学系广东广州

For M-matrix equations, we provide a necessary and sufficient condition for that the solution of the equations has the property p, which improves and generalizes the corresponding results of [1] and [2].

关键词： Linear system of equations property p M-matrix.

The generalized Roper-Suffridge extension operator on bounded complete Reinhardt domains

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Science china mathematics 2007年第12期50卷 1781-1794页

作者： Yu-can ZHU~(1+) Ming-sheng LIU~2 ~1 department of mathematics,Fuzhou university,Fuzhou 350002,china ~2 department of mathematics,south china normal university,guangzhou 510631,china department of mathematics Fuzhou University Fuzhou 350002 China department of mathematics South China Normal University Guangzhou 510631 China

The generalized Roper-Suffridge extension operatorΦ(f) on the bounded complete Rein- hardt domainΩin C^n with n≥2 is defined byΦ_(n,β_2,γ_2,...,β_n,γ_n)~r(f)(z)=rf((z_1)/r),((rf(z_1)/r)/(z_1))^(β2)(f′((z_1)/r)^(γ2)z_2,...,((rf(z_1)/r)/(z_1))^(β_n)(f′((z_1)/r))^(γ_n)z_n) for (z_1,z_2,...,z_n)∈Ω,where r=r(Ω) = sup{|z_1|:(z_1,z_2,...,z_n)∈Ω},0≤γ_j≤1-β_j,0≤β_j≤1, and we choose the branch of the power functions such that ((f(z_1))/(z_1))^(β_j)|_(z_1=0)=1 and (f′(z_1))^(γ_j)|_(z_1=0)= 1,j=2,...,*** this paper,we prove that the operatorΦ_(n,β_2,γ_2,...,β_n,γ_n)~r(f) is from the subset of S_α~*(U) to Sα~*(Ω)(0≤α0,j=1,2...,n),U is the unit disc in the complex plane C,and S_α~* (Ω) is the class of all normalized starlike mappings of orderαonΩ.We also obtain thatΦ_(n,β_2,γ_2,...,β_n,γ_n)~r(f)∈S_α~*(D_p) if and only if f∈S_α~*(U) for 0≤α<1 and some suitable constantsβ_j,γ_j,p_j.

关键词： Roper-Suffridge extension operator, biholomorphic starlike mapping, spirallike of type β, complete Reinhardt domain

On the Construction of the Conjugate Hull of Brandt Semigroups

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Acta Mathematica Sinica,English Series 1998年第4期14卷 519-526页

作者： Zhang Moucheng, department of mathematics, south china normal university, guangzhou 510631, chinaKan Haibing, Institute of mathematics, Fudan university, Shanghai 200433, chinaLi Yonghua, department of mathematics, Yunnan university, Kunming 650000, china department of mathematics, south china normal university, guangzhou 510631, china department of mathematics South China Normal University 510631 Guangzhou China

In this paper the characterizations of conjugate hulls Ψ(S), φ(S), T(S) and θ(S) on a Brandt semigroup S are given. By using these results we can prove that T(S) is self-conjugate in Ψ(S) for a Brandt semigroup S.

关键词： Conjugate hull Self-conjugate Linked bitranslation Brandt semigroup

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, china 2. Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, china 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.