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简介：Inthispaper,therelationshipbetweenRiemann-Liouvillefractionalintegralandthebox-countingdimensionofgraphsoffractalfunctionsisdiscussed.

简介：Thispaperpresentssomeresultsoftherelationbetweenwavelettransformandfractaltransform.Thewavelettransformoftheattractoroffractaltransformpossesestranslationalandscaleinvariance.Sowespeedthefractalimageencodingbytestingtheinvarianceofthewavelettransformappropriateforimageencoding.Theclassficationschemeofrangeblocksbywavelettransformisgiveninthispaper.

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简介：在这份报纸，我们首先在帖子上描绘分数维的插值函数(FIF)的有限批评有限自我类似的集合。然后，我们在Sierpinski垫板(SG)上与一致垂直可伸缩因素学习FIF的拉普拉斯算符。作为应用，我们证明SG上的下列Dirichlet问题的答案是有一致垂直可伸缩因素1/5的FIF：u=0在SG上{q1,q2,q3},和u(qi)=i,i=1，2，3qi,i=1，2，3，是SG的边界点。

简介：平行的Liesegang模式猛抛当包含的答案一同沉淀时，乐队们被获得在一个1D胶化矩阵的离子interdiffuse。形成的节俭地可溶的盐，显示磁盘的美丽的层化猛抛对1D试管轴垂直。Liesegang结构从他们的分数维的性质的观点被分析。几何Liesegang模式与象时间，乐队间距和乐队宽度法律那样的著名实验法律在一致被构造。扩散的起始的集中上的乐队间距的依赖(外部)并且不动(内部)电解质(一0并且B0，分别地)被拿跟随Matalon-Packter法律。数学分数维的尺寸和盒子计数尺寸是计算的。分数维的尺寸被发现与增加A增加0并且减少的B0。我们也与雏晶的随机的分发分析马赛克模式，在他们的分数维的性质上比古典Liesegang胶化方法，和报告在不同条件下面成长。最后，乐队在多重谱线被组织的复杂Liesegang模式被学习，并且分数维的性质与复合增加，这被显示出。

简介：Inthispaper,weconstructaclassofnowheredifferentiablecontinuousfunctionsbymeansoftheCantorseriesexpressionofrealnumbers.Theconstructedfunctionsincludesomeknownnondifferentiablefunctions,suchasBushtypefunctions.Thesefunctionsarefractalfunctionssincetheirgraphsareingeneralfractalsets.Undercertainconditions,weinvestigatethefractaldimensionsofthegraphsofthesefunctions,computetheprecisevaluesofBoxandPackingdimensions,andevaluatetheHausdorffdimension.Meanwhile,theHoldercontinuityofsuchfunctionsisalsodiscussed.

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简介：ThesufficientconditionsofHoldercontinuityoftwokindsoffractalinterpolationfunctionsdefinedbyIFS(IteratedFunctionSystem)wereobtained.Thesufficientandnecessaryconditionforitsdifferentiabilitywasproved.ItsderivativewasafractalinterpolationfunctiongeneratedbytheassociatedIFS,ifitisdifferentiable.

简介：Parameteridentificationproblemisoneofessentialprobleminordertomodeleffectivelyexperimentaldatabyfractalinterpolationfunction.Inthispaper,wefirstpresentanexampletoexplainarelationshipbetweeniterationprocedureandfractalfunction.Thenwediscussconditionsthatverticalscalingfactorsmustobeyinonetypicalcase.

简介：ThispaperdefinestheuppercapacitydensitiesofthesubsetsofR^n,getsuniformlowerboundoftheuppercapacitydensitiesforH^s-almostallpointsoftheHausdorffs-setsortheanalyticsetswithHausdorffdimensionsinR^n,whichimprovestheresultsofWenZhiyingandZhangYiping'spaperin[1].

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简介：就时空的分数维的结构而言，在拓扑的尺寸DT=的规模相关性理论2被造。在这一conjecture，这时空的geodesics暗示量力学的水动力学模型。随后，计量器分数维的时空上的重力的地被给。然后，计量器组，gauge-covariant衍生物，计量器地的力量张肌，计量器不变的Lagrangean，计量器潜力的地方程和计量器精力动量张肌被决定。最后，使用这个模型，ReissnerNordstr?m类型度量标准被获得。

简介：Wepresentlowerandupperboundsfortheboxdimensionofthegraphsofcertainnonaffinefractalinterpolationfunctionsbygeneralizingtheresultsthatholdfortheaffinecase.

简介：LetG？R2bearegularanisotropicfractal.WediscusstheproblemofthenegativespectrumfortheSchr¨odingeroperatorsassociatedwiththeformalexpressionHb=id？D＋btrGb,b∈R,actingintheanisotropicSobolevspaceW1,a2（R2）,whereDistheDirichletLaplanianinR2andtrGbisafractalpotential（distribution）supportedbyG.

简介：Inthispaper,wepresentanewmethodfordeterminingthefractaldimensionoftimeseriesandthealgorithmofHindex(Hurstindex).

简介：ItisimportanttocalculatetheHausdorffdimensionandtheHausdorffmesurerespecttothisdimensionforsomefractalsets.Byusingtheusualmethodof“MassDistribution”,wecanonlycalculatetheHausdorffdimension.Inthispaper,wewillconstructanintegralformulabyusinglowerinverses-densityandthenuseittocalculatetheHausdorffmeasuresforsomefractionaldimensionalsets.

简介：Inthispaper,westudyaspecialclassoffractalinterpolationfunctions,andgivetheirHaar-waveletexpansions.Onthebasisoftheexpansions,weinvestigatetheH(o|¨)ldersmoothnessofsuchfunctionsandtheirlogicalderivativesoforderα.

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