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期刊论文

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2005年04月11日

【期刊论文】Some boundary fractal properties of the convolution transform of measures by an approximate identity*

文志雄， Zhi-Ying WEN †， Yiping ZHANG †

，-0001，（）：

-1年11月30日

摘要

We consider the convolution transrms of measures on Rd defined by some approximate identity. We shall establish some relations between the irregular boundary properties of the convolution function between the local Lipschitz exponent of the measure. In particular, the results can be applied to the Poisson and Gauss-Weierstrass kernels. We can then obtain some singular boundary behaviour of positive harmonic or parabolic functions on Rdal by multifractal analysis of measures.

Approximate identity,， Multifraetal,， Logarithmic density

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2005年04月11日

【期刊论文】Dimension of level sets of some Rademacher series

文志雄

，-0001，（）：

-1年11月30日

摘要

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2005年04月11日

【期刊论文】Some remarks on invertible substitutions on three letter alphabet*

文志雄， Wen Zhi-Xiong †， Zhang Yiping ‡

，-0001，（）：

-1年11月30日

摘要

We show by introducing the notion of "prime substitution" that the set of invertible substitutions over an alphabet of more than three letters is not finitely generated. Some examples are given.

invertible substitution,， prime substitution

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2005年04月11日

【期刊论文】A CLASS OF SELF-SIMILAR FRACTALS WITH OVERLAP STRUCTURE*

文志雄， Rao Hui †， Wen Zhi-Ying ‡

，-0001，（）：

-1年11月30日

摘要

Consider the contracting similarities S1(x)=x/3, S2(x)=(x+λ)/3, S2(x)=(x+2)/3 where λε[0, 1]. Assuming Fλ is the invariant set with respect to S1, S2, and S3. In this paper, we study the Hausdorff measure, Hausdorff dimension and the structure of F. Letλ= b a 2 Q \ [0, 1], (a, b)=1. By using combinatorial techniques, we prove that |Fλ|>0 if a≡b 6≠0 (mod 3) and that in the other cases Fλ is a Cantor-like fractal with recursive construction.

Overlap,， Open set condition,， Hausdorff measure and dimension,， Fractal