Fractals, Wavelets, and their Applications: Contributions from the International Conference and Workshop on Fractals and Wavelets PDF
Preview Fractals, Wavelets, and their Applications: Contributions from the International Conference and Workshop on Fractals and Wavelets
Springer Proceedings in Mathematics & Statistics Christoph Bandt · Michael Barnsley Robert Devaney · Kenneth J. Falconer V. Kannan · Vinod Kumar P.B. Editors Fractals, Wavelets, and their Applications Contributions from the International Conference and Workshop on Fractals and Wavelets Springer Proceedings in Mathematics & Statistics Volume 92 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Christoph Bandt • Michael Barnsley Robert Devaney • Kenneth J. Falconer V. Kannan • Vinod Kumar P.B. Editors Fractals, Wavelets, and their Applications Contributions from the International Conference and Workshop on Fractals and Wavelets 123 Editors ChristophBandt MichaelBarnsley InstitutfürMathematikundInformatik MathematicalSciencesInstitute UniversitätGreifswald AustralianNationalUniversity Greifswald,Mecklenburg-Vorpomm. Canberra,Australia Germany KennethJ.Falconer RobertDevaney MathematicalInstitute MathDepartment UniversityofStAndrews BostonUniversity StAndrews,Fife,UK Boston,MA,USA VinodKumarP.B. V.Kannan DepartmentofBasicSciences DepartmentofMathematics andHumanities andStatistics RajagiriSchoolofEngineering UniversityofHyderabad andTechnology Hyderabad,India Kerala,India ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-3-319-08104-5 ISBN978-3-319-08105-2(eBook) DOI10.1007/978-3-319-08105-2 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014949263 MathematicsSubjectClassification(2010):28A80,81Q35,42C40,65T60 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Fractalgeometryisayoungfield.Itwasinitiallydevelopedinthe1980s,drivenby the motivationto modelrough phenomenain nature, and by new opportunitiesof computervisualization.Towardstheendofthe1980s,waveletswereintroducedfor theneedsofsignalandimageprocessing.Today,thefieldoffractalsandwavelets has grown into a respected mathematical discipline with specific concepts and techniques,andwithplentyofapplicationsinsideandoutsidemathematics. InNovember2013aworkshopandthefirstInternationalConferenceonFractals andWaveletsinIndiatookplaceatRajagiriSchoolofEngineeringandTechnology, Kochi,Kerala. In the workshop, from November 9 to 12, leading experts from all over the world gave comprehensive survey lectures on the state of the art in their areas. In the International Conference from November 13 to 16, new research results were presented by mathematiciansfrom ten countries. There were more than 100 participants from India, revealing that research in fractals and wavelets has taken rootatmanyIndianuniversities,with an emphasison applicationsto engineering, medicine,Internettraffic,hydrology,andotherfields. This volume contains all invited lectures of the workshop as well as selected contributions to the conference. Providing readable surveys, it can be used as a referencebookforthosewhowanttostartworkinthefield.Itdocumentsthepresent state of research in the area, both in India and abroad, and can help to develop cooperationamongwidelyscatteredgroups. TheorganizersoftheconferencewouldliketothankthemanagementofRajagiri SchoolofEngineeringandTechnology,Cochin,Kerala,Indiafortheinspirationand supportprovidedtoconducttheconference. The organizers acknowledge the financial support given by the International Centre for Theoretical Physics, the International Mathematical Union, the Inter- national Council for Industrial and Applied Mathematics, the National Board for Higher Mathematics India, the Department of Science & Technology India, the DefenceResearch&DevelopmentOrganisationIndia,theIndianNationalScience Academy, the Kerala State Council for Science Technology & Environment, and TheSouthIndianBankLimited. v Contents PartI FractalTheory IntroductiontoFractals......................................................... 3 ChristophBandt GeometryofSelf-similarSets................................................... 21 ChristophBandt AnIntroductiontoJuliaandFatouSets....................................... 37 ScottSutherland ParameterPlanesforComplexAnalyticMaps............................... 61 RobertL.Devaney MeasurePreservingFractalHomeomorphisms .............................. 79 MichaelF.Barnsley,BrendanHarding,andMiroslavRypka TheDimensionTheoryofAlmostSelf-affineSetsandMeasures........... 103 KárolySimon CountableAlphabetNon-autonomousSelf-affineSets ...................... 129 MariuszUrban´ski OnTransverseHyperplanestoSelf-similarJordanArcs.................... 147 AndreyTetenov FractalsinProductFuzzyMetricSpace....................................... 157 R.UthayakumarandA.Gowrisankar SomePropertiesonKochCurve................................................ 165 R.UthayakumarandA.NalayiniDevi ProjectionsofMandelbrotPercolationinHigherDimensions.............. 175 KárolySimonandLajosVágó SomeExamplesofFiniteTypeFractalsinThree-DimensionalSpace..... 191 MaiTheDuy vii viii Contents FractalsinPartialMetricSpaces............................................... 203 S.MiniraniandSunilMathew PartII WaveletTheory FramesandExtensionProblemsI ............................................. 219 OleChristensen FramesandExtensionProblemsII ............................................ 235 OleChristensen,HongOhKim,andRaeYoungKim LocalFractalFunctionsandFunctionSpaces................................ 245 PeterR.Massopust SomeHistoricalPrecedentsoftheFractalFunctions........................ 271 M.A.NavascuésandM.V.Sebastián ANewClassofRationalQuadraticFractalFunctionswith PositiveShapePreservation..................................................... 283 A.K.B.Chand,P.Viswanathan,andM.A.Navascués IntervalWaveletSetsDeterminedbyPointsontheCircle .................. 303 DivyaSingh InverseRepresentationTheoremforMatrixPolynomialsand MultiscalingFunctions .......................................................... 319 M.MubeenandV.Narayanan ARemarkonReconstructionofSplines fromTheir Local WeightedAverageSamples...................................................... 341 P.DevarajandS.Yugesh C1-RationalCubic FractalInterpolation Surface Using FunctionalValues ................................................................ 349 A.K.B.ChandandN.Vijender OnFractalRationalFunctions ................................................. 369 P.ViswanathanandA.K.B.Chand PartIII ApplicationsofFractalsandWavelets InnovationontheTortuousPath:FractalElectronics....................... 385 NathanCohen PermutationEntropyAnalysisof EEG of Mild Cognitive ImpairmentPatientsDuringMemoryActivationTask...................... 395 LeenaT.Timothy,BinduM.Krishna,MuraliKrishnaMenon, andUshaNair Contents ix AMultifractal-BasedImageAnalysisforCervicalDysplasia Classification...................................................................... 407 P.Singh,J.Jagtap,C.Pantola,A.Agarwal,andA.Pradhan Self-SimilarNetworkTrafficModellingUsingFractalPoint Process-MarkovianApproach.................................................. 413 RajaiahDasari,RameshRenikunta,andMallaReddyPerati ValidationofVarianceBasedFittingforSelf-similarNetworkTraffic .... 427 Ramesh Renikunta, Rajaiah Dasari, Ranadheer Donthi, andMallaReddyPerati Self-Similar Network Traffic Modeling Using Circulant MarkovModulatedPoissonProcess ........................................... 437 Ranadheer Donthi, Ramesh Renikunta, Rajaiah Dasari, andMallaReddyPerati InvestigationofPriorityBasedOpticalPacketSwitchUnder Self-Similar Variable Length Input Traffic Using Matrix QueueingTheory................................................................. 445 RaviKumarGudimallaandMallaReddyPerati Computationally Efficient Wavelet Domain Solver for FlorescenceDiffuseOpticalTomography ..................................... 457 K.J.FrancisandI.Jose ImplementationofWaveletBasedandDiscreteCosineBased AlgorithmonPanchromaticImage ............................................ 471 JyotiSarup,JyotiBharti,andArpitaBaronia Trend,TimeSeries,andWaveletAnalysisofRiverWaterDynamics...... 479 KulwinderSinghParmarandRashmiBhardwaj An Efficient Wavelet Based Approximation Method to Film-PoreDiffusionModelArisinginChemicalEngineering .............. 491 PandyPirabaharan,R.DavidChandrakumar,andG.Hariharan ANewWavelet-BasedHybridMethodforFisherTypeEquation.......... 501 R.RajaramandG.Hariharan
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