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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】ON THE LEADING TERM AND THE DEGREE OF THE POLYNOMIAL TRACE MAPPING ASSOCIATED WITH A SUBSTITUTION

文志雄， WEN Zhi-Xiong ，， and WEN Zhi-Ying

Journal of Staistical Physies Vol. 75, Nos 341, 1994，-0001，（）：

-1年11月30日

摘要

Let F be the free group generated by the letters a and b. let φ be a homomorphism from P to SL2(￠). Lei χ=Trφ(a), y=Trφ(b), z=Trφ(ab) and let w ε F, then Trφ(w) will be a polynomial of variables x, y. z. The main aim of this note is to determine the leading term of Trφ(w). Let σ be an endomorphlsm of F, then σ witl indite a mapping φσ:(Z[x, y, z])3→(Z[x, y.=1)3 which is called the trace mapping associated with σ. We wig establish the recurrence relations of the reading terms and degrees of the iterations of φσ, Moreover, some typical examples are studied.

Trace mapping,， Substitution,， Leading tenn.，

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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