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1、InteractionofMechanicsandMathematicsFioralbaCakoni·DavidColtonQualitativeMethodsinInverseScatteringTheoryAnIntroductionWith14FiguresABCIMMAdvisoryBoardD.Colton(USA).R.Knops(UK).G.DelPiero(Italy).Z.Mroz(Poland).M.Slemrod(USA).S.Seelecke(USA).L.Truskinovsky(France)IMMispromotedundertheauspice
2、sofISIMM(InternationalSocietyfortheInteractionofMechanicsandMathematics).AuthorsProfessorDr.FioralbaCakoniProfessorDr.DavidColtonDepartmentofMathematicalSciencesUniversityofDelawareNewark,DE19716USALibraryofCongressControlNumber:2005931925ISSNprintedition:1860-6245ISSNelectronicedition:1860
3、-6253ISBN-103-540-28844-9SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-28844-2SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadca
4、sting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliableforprosecutionunde
5、rtheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringeronline.comcSpringer-VerlagBerlinHeidelberg2006PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesar
6、eexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandTechBooksusingaSpringerLATEXmacropackageCoverdesign:design&productionGmbH,HeidelbergPrintedonacid-freepaperSPIN:1133123089/TechBooks543210PrefaceThefieldofinversescatteringtheoryhasbeen
7、aparticularlyactivefieldinappliedmathematicsforthepasttwentyfiveyears.Theaimofresearchinthisfieldhasbeentonotonlydetectbutalsotoidentifyunknownobjectsthroughttheuseofacoustic,electromagneticorelasticwaves.Althoughthesuccessofsuchtechniquesasultrasoundandx-r
