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【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
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
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文志雄 , Zhi-Ying WEN †, Yiping ZHANG †
,-0001,():
-1年11月30日
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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【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
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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【期刊论文】Some dimensional results for homogeneous Moran sets∗
文志雄 , FENG De-Jun, WEN Zhi-Ying, WU Jun
Science in China (Series A), 40(1997)475-482,-0001,():
-1年11月30日
Let M({nk}k≥1, {ck}k≥1) be the collection of homogeneous Moran sets deter-mined by {nk}k≥1 and {ck}k≥1, where {nk}k≥1 is a sequence of positive integers and {ck}k≥1 a sequence of positive numbers. In this paper, we determine the maximal and minimal values of Hausdorff dimensions for elements in M. We also prove that for any value s between the maximal and minimal values, there exists an element in M({nk}k≥1, {ck}k≥1) such that its Hausdorff dimension is equal to its. The same results hold for Packing dimension. In the meantime, some other properties of homogeneous Moran sets are discussed.
Homogeneous Moran set,, Homogeneous Cantor set,, Partial homogeneous Cantor set,, Hausdorff dimension,, Packing dimension.,
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【期刊论文】HANKEL DETERMINANTS OF THE THUE-MORSE SEQUENCE
文志雄 , by J.-P. ALLOUCHE, J. PEYRI ERE, Z.-X. WEN (*), Z.-Y. WEN (**)
Ann. Inst. Fourier, Grenoble 48, 1 (1998), 1-27,-0001,():
-1年11月30日
Thue-Morse sequence, Period doubling sequence, Automatic sequences,
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