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ON THE EXACT HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR setS SATISFYING open set condition

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Analysis in Theory and Applications 2008年第1期24卷 93-100页

作者： Shaoyuan Xu Weiyi Su Zuoling Zhou Huaibei Coal Industry Teachers College China Nanjing University China Zhongshan University China

In this paper, we provide a new effective method for computing the exact value of Hausdorff measures of a class of self-similar sets satisfying the open set condition （OSC）. As applications, we discuss a self-simila... 详细信息

关键词： self-similar set Hausdorff measure and Hausdorff dimension open set condition

An Equivalent condition for the Self Similar sets on the Real Line to Have Best Coverings

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Acta Mathematica Sinica,English Series 2013年第9期29卷 1637-1646页

作者： Jian Dong YIN Zuo Ling ZHOU Department of Mathematics Nanchang University Lingnan College Zhongshan University

In this paper, an equivalent condition for the self similar sets on the real line to have best coverings is given. As a result, it partly gives answer to the conjecture which was posed by Zhou and Feng [Zhou, Z. L., Feng, L.： Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17（2）, 493-502 （2004）].

关键词： Self similar set open set condition upper convex density best covering

The Hausdorff Dimension of Sections

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 187-194页

作者： Min NIU Lifeng XI Department of Mathematics and Mechanics Beijing University of Science and Technology Beijing 100083China Institute of MathematicS Zhejimag Wanli University Ningbo 315100 Zhejiang China

The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x=α with ... 详细信息

关键词： Hausdorff dimension Self-similar set Section open set condition

Porosity of Self-affine sets

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Chinese Annals of Mathematics,Series B 2008年第3期29卷 333-340页

作者： Lifeng XI Institute of Mathematics Zhejiang Wanli University Ningbo 315100 Zhejiang China

In this paper, it is proved that any self-affine set satisfying the strong separation condition is uniformly porous. The author constructs a self-affine set which is not porous, although the open set condition holds. ... 详细信息

关键词： Porosity Self-affine set open set condition

A THEORETICAL FRAMEWORK FOR THE CALCULATION OF HAUSDORFF MEASURE-SELF—SIMILAR set SATISFYING OSC

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Analysis in Theory and Applications 2011年第4期27卷 387-398页

作者： Zuoling Zhou Li Feng Sun Yat-Sen University China Albany State University USA

A theoretical framework for the calculation of Hausdorff measure of self-similar sets satisfying OSC has been established.

关键词： Haudorff measure open set condition

A Negative Answer to a Conjecture on Upper Convex Density

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Northeastern Mathematical Journal 2008年第5期24卷 386-394页

作者：尹建东 Department of Mathematics Nanchang University Nanchang 330031

Let E be a self-similar set satisfying the open set condition. Professor Xu conjectures in his doctoral degree thesis that if H^8（E）〈｜E｜^8, then for any x ∈ E, the inequality ^-D^3C（E,x）〉H^8（E）/｜E｜^8hold... 详细信息

关键词： Hausdorg dimension Hausdorff measure upper convex density open set condition contracting-similarity fixed point

A Note on Upper Convex Density

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Communications in Mathematical Research 2010年第4期26卷 361-368页

作者： YIN JIAN-DONG ZHOU ZUO-LING Department of Mathematics Nanchang University Nanchang 330031 Lingnan College Zhongshan University Guangzhou 510275

For a self-similar set E satisfying the open set condition,upper convex density is an important concept for the computation of its Hausdorff measure,and it is well known that the set of relative interior points with upper convex density 1 has a full Hausdorff *** whether the upper convex densities of E at all the relative interior points are equal to 1？ In other words,whether there exists a relative interior point of E such that the upper convex density of E at this point is less than 1？ In this paper,the authors construct a self-similar set satisfying the open set condition,which has a relative interior point with upper convex density less than ***,the above problem is sufficiently answered.

关键词： self-similar set open set condition upper convex density