一類曲線的Minkowski容度.pdf

1、華中師范大學碩士學位論文一類曲線的Minkowski容度姓名：曾宇申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：陳世榮20050501碩士學位論文MASTER’STHESISAbstractWesaythatthesetisMinkowskimeasurableiftheMinkowskieonl—cntofthesetexistsTheMinkowskicontentsofthesetsmaybefiniteorinfi—nite(pos

2、siblyzero)，whichisconcernedbymanyscholarsEspecially，inthepaperthatLapidusstudiedtheWeyl—BerryconjectureoftheffactaldrumhetransformedtheproblemofestimatingeigenvaluenumbersoftheLaplace’sequationintotheproblemofcalculating

3、theMinkowskicontentonthefractalboundarySothestudyoftheMinkowskicontentsofsomesetsbecomestheworktobepaidcloselyattentiontoNowmanygoodresultshavebeenob—tainedfortheMinkowskicontentsofsomesetsinRForexample，AssociateProfesso

4、rShirongCheninCCNUstudiedthecountablesetsintheinterval[0，1]andobtaineditsMinkowskicontentanddimensionBesides，F(xiàn)alconerandLapidusalsomadesomegoodresearchesOilthemButlittlewbrkhasbeencarriedoutforMinkowskicontentsofthesetsi

5、nR”(扎≥2)Forexample，VonKochcurve、CantordustandSierpinskigasketarethefamousfractalsetsButtheirMinkowskicontentsareunsolvedyetInthispaperwestudyVonKochcurveardCantordustfirstly汀givesolYlepropertiesofVonKochcurveandCantordus

6、tandthengetestimationformulaeofupperandlowerMinkowskicontentsofthemrespectivelybysomeskillThusweeasilyobtainthattheMinkowskicontentsofthemdon’texistBesides，throughanotherdefinitionandmethod，wecalculatetheupperIVlinkowski

7、contentM(d，E)andthelowerMinkowskicontent壇(d，E)ofSierpinskigasketErespectivelyThatisM4∽，E)≈1814and蠔(d，F(xiàn))≈1811ThereforeweobtainthatSierpinskigasketisnotMinkowskimeasurablebyanewmethodKeywords：Minkowskicontent；Minkowskimeas