简介:设μ(I,{nk}k≥1,{ck}k≥1)为闭区间I,正整数序列{nk}k≥1及正实数序列{ck}l≥1确定的Moran集,c(I,{nk},{ck})c(I,{nk},{ck})分别为μ{nk}k≥1,{ck}k≥1的齐次Cantor集与偏齐次Cantor集,给出了齐次Cantor集与偏齐次Cantor集的关系及证明。
简介:Contor集是一个具有一定代表性的分形.文章从不同方面、不同角度对Cantor集进行推广,得到一些新的集合,并分别计算出它们的Hausdorff维数.
简介:将三分Cantor集构造的一个性质推广到2n+1(n∈N)分Cantor集,并用它简便计算出2n+1分Cantor集的Hausdorff测度,给出了此类广义Cantor集Hausdorff测度计算的一种新方法.该方法比其它方法更为初等而易于计算,为计算其它分形集的Hausdorff测度提供了一种思路.
简介:Aclassofmetric,compact,andtotallydisconnectedspaces,calledself-similarCantorsetsisintroduced.Aself-similarstructureisdefinedtobeagraphwithweightededges.Theintroductionofultrametricsandquasi-isometriesgivesversatilitytothisconstruction.Thermodynamicalfunctionsasfreeenergyandentropyareassociatedwithself-similarstructures.Multifractalanalysis,basedona“LargeDeviations”inequalityandGibbsmeasures,leadstoafairlygeneralHausdorffdimensiontheorem.
简介:1.Somedefinitionsandnotions1.1.HausdorffgaugeandPackinggaugeAfuncitonh:[0.1]→Rissaidtobeadimensionfunctionifithasthefollowingproperties:(1)h(t)iscontinuousandincreasing,h(0)=0,h(t)>0whent>0.(2)thereexistsaconstantM>0,h(2t)
简介:在客斥原理和Gould—Hsu反演公式的基础上,提出了新词(word)偏序集上的广义二项式系数的性质,并结出了一个反演公式。
简介:研究了一个由6个相似压缩确定的满足开集条件的自相似Cantor集,得到了它的Hausdorff测度的准确值.
简介:WeconsiderthehomogeneousCantorsetswhicharegeneralizationofsymmetricperfectsets,andgiveaformulaoftheexactHausdorffmeasuresforaclassofsuchsets.
简介:Inthispaperthederivativeanditsexceptionalsetaccordingtothealternativelyjumpingfunctionandself-similarfunctionrespectivelyarediscussed.Andintheappendix,aproofofthestatement1.2(2)of“CalculusonCantortriadicset(Ⅱ)—derivative”whichisimportanttothediscussionofexceptionalsetisgiven.