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《Journal of Jiangxi Normal University(Natural Sciences Edition)》 2007-03
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A New Sufficient and Necessary Condition Under Which Aself-Similar Set Has a Best-a.e.-Closed-Set Covering

XU Shao-yuan(School of Mathematics and Computer Science,Gannan Teachers College,Ganzhou Jiagxi 341000,China)  
In this paper,a new sufficient and necessary condition for the existence of the best-a.e.-closed-set covering of the self-similar set is obtained.As a result,we improve and generalize a corresponding result which is obtained by Shaoyuan Xu and Guozhen Li in 2004.As applications,a self-similar set satisfying the strong separation open set condition,which is constructed on the real line is well discussed.
【Key Words】: self-similar s-set open set condition(OSC) Hausdorff measure and Hausdorff dimension best-a.e.-closed-set covering
【Fund】: 国家自然科学基金(10571185);; 江西省自然科学基金(061105)资助项目
【CateGory Index】: O174.12
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【Citations】
Chinese Journal Full-text Database 1 Hits
1 XU Shao-yuan~(1,2),LI Guo-zhen~3 (1.Dept. of Math. Huaibei Coal Industry Teachers' College, Huaibei 235000,China;2.College of Mathematics and Scientific Computer, Zhongshan University, Guangzhou 510275,China;3.Institute of Mathematics and Informatics,Jiangxi Normal University, Nanchang 330027,China);A Necessary and Sufficient Condition for a Self-Similar Set to Have Best-a.e. Cover Consisting of Closed Sets[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2004-03
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 SONG Shou bai,\ XIE Ming qin (Department of Mathematics, Anhui Normal University, 241000, Wuhu, Anhui, China);THE HAUSDORFF MEASURE OF KOCH CURVE[J];JOURNAL OF ANHUI NORMAL UNIVERSITY(NATURAL SCIENCE);1999-03
2 Shaoyuan Xu (Gannan Teachers College,China) Weiyi Su (Nanjing University,China);ELEMENTARY DENSITY BOUNDS FOR SELF-SIMILAR SETS AND APPLICATION[J];分析,理论与应用(英文版);2007-04
3 XU Shao-yuan~(1,2),LI Guo-zhen~3 (1.Dept. of Math. Huaibei Coal Industry Teachers' College, Huaibei 235000,China;2.College of Mathematics and Scientific Computer, Zhongshan University, Guangzhou 510275,China;3.Institute of Mathematics and Informatics,Jiangxi Normal University, Nanchang 330027,China);A Necessary and Sufficient Condition for a Self-Similar Set to Have Best-a.e. Cover Consisting of Closed Sets[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2004-03
4 XIE Xian-hua,WU Huo-xiong2,XU Shao-yuan1(1.School of Mathematic Computer Science,Gannan Normal University,Ganzhou Jiangxi 341000,China;2.Department of Mathematics,Xiamen University,Xiamen 361005,China);Boundedness for Integrals Operator Along Subvarieties Curves with Rough Kernels on Multiples[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2009-02
5 WU Jiongqi (Department of Math.,Zhangzhou Teachers College, Zhangzhou 363000,China);An elementary proof for the Hausdorff measure of some Sierpinski carpets[J];Pure and Applied Mathematics;2003-03
6 ZENG Chao-yi , YUAN De-hui (Department of Mathematics, Hanshan Normal University, Chaozhou 710071,China);Hausdorff measure of m-Cantor Dust[J];Pure and Applied Mathematics;2009-02
7 DU Xing\|hua (Dept of Mathematics, Daqing Petroleum Institute, Anda, Heilongjiang 151400, China );Estimation of Hausdorff measure of several deformed Koch curves[J];Journal of Daqing Petroleum Institute;2000-04
8 YAN Kun(Xi'an Modern Nonlinear Science Applying Institute, Xi'an 710061, China);Fractal dimension structure of Cosmos and its mathematical foundations[J];Progress In Geophysics;2004-03
9 LIU Juan,XU Shao-yuan(Department of Mathematics,Huaibei Coal Industry Teachers College,235000,Huaibei,Anhui,China);The Hausdorff Measure of the Cartesian Product of the Middle Third Cantor Set with Itself[J];Journal of Huaibei Coal Industry Teachers College(Natural Science Edition);2006-01
10 XU Shao-yuan,LIU Jing,CHEN Xiao-yun(Department of Mathematics,Huaibei Coal Industry Teachers College,235000,Huaibei,Anhui,China);The Hausdorff Dimension of the General Sierpinski Block Generated by Normal Tetrahedron and the Estimation of Its Hausdorff Measure[J];Journal of Huaibei Coal Industry Teachers College(Natural Science Edition);2007-04
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