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ID:39145279
大小:2.03 MB
页数:41页
时间:2019-06-25
《自相似集的Hausdorff测度与上凸密度的估计与计算》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、AbstractABSTRACT.Inthisthesis,wemainlystudyhowtocalculatetheexactHausdorffmeasureofaclassofself-similarsetsandhowtoestimatetheupperboundofupperconvexdensityofsomeconcretepointsinsomeself-similarsets.Inaddition,wepresentanecessaryandsufficientconditionforaclassofself-similarsetsonreallinet
2、ohavebestcoveringsandsomesufficientconditionsforanalmosteverywherebestcoveringtobeabestonefortheself-similarsetssatisfyingtheopensetcondition.Thisthesisisdividedintofourchapters.Inthefirstchapterweintroducetheresearchbackgroundaboutfractal,anddescribeadetailedbasicdefinitionsandlemmasabou
3、tfractal.InthesecondchapterwestudytheproblemofcalculationofHausdorffmeasureofaclassofself-similarsetsinaregularhexahedron.Whenthesimilarratiossatisfiescertainconditions,weprovethatthenaturalcoveristhebestshapeforupperconvexdensity.Itmeansthatthenaturalcoverisabestone,thentheexactvalueofHa
4、usdorffsmeasureofthisclassofself-similarsetsis3,wheresisHausdorffmeasure.InthethirdchapterwefirstprovethatthefamilyofbestshapsofthevertexsofaclassofSierpinskicarpetsisacoveringoftheSierpinskicarpets,thenprovetheminimumoftheupperconvexdensityisachievedattheirvertexs.Thisresultextendssome
5、recentresults.Intheforthchapter,wefirsttakeadvantagedofanimportantcharacteristicthatthebestshapofself-similarsetsonreallinemustbeclosedinterval,thenpresentanecessaryandsufficientconditionforaclassofself-similarsetsonreallinetohavebestcoverings,andsomesufficientconditionsforanalmosteverywh
6、erebestcoveringtobeabestonefortheself-similarsetssatisfyingtheopensetcondition.KeyWords:selfsimilarset;Hausdorffmeasure;Hausdorffdimension;Upperconvexdensity;naturalcovering;bestcoveringIII万方数据目录目录第一章绪论.......................................................................................
7、......................................11.1分形研究背景及现状...........................................................................................11.2分形基本概念.........................................................................................................3第二章一类正六面
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