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1、LectureNotesinMathematicsAcollectionofinformalreportsandseminarsEditedbyA.Dold,HeidelbergandB.Eckmann,Z0rich167Lavrentiev.RomanovVasilievComputingCenteroftheAcademyofSciencesNovosibirsk/UdSSRMultidimensionalInverseProblemsforDifferentialEquations$Springer-Verla9Berlin-H
2、eidelberg.NewYork1970ISBN3-540-05282-8SpringerVedagBerlinHeidelbergNewYorkISBN0-387-05282-8SpringerVerlagNewYorkHeidelbergBerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallythoseoftranslation,reprinting,re-u
3、seofillustrations,broadcasting,reproductionbyphotocopymgmachineorsimilarmeans,andstorageindatabanks.Under§54oftheGermanCopyrightLawwherecopiesaremadeforotherthanprivateuse,afeeispayabletothepublisher,theamountofthefeetobedeterminedbyagreementwiththepublisher.?bySpringer
4、-VerlagBerlin-Heidelberg1970.LibraryofCongressCatalogCardNumber70-140559.PrintedinGermany.Off~druck:JulimBdtz,Weinhdm/Bergr,.r.CONTENTSINTRODUCTION...................................................IVCHAPTERI-SomeProblemsofIntegralGeometry.................11.ProblemofDe
5、terminingaFunctionfromIntegralsoverEllipsoidsofRevolution................................22.GeneralizationtoAnalyticCurves.......................103.ProblemofDeterminingaFunctioninsideaCirclefromIntegralsalongaFamilyofCurvesInvarianttoRotationabouttheCenteroftheCircle..
6、........................134.OntheProblemofDeterminingaFunctionfromItsMeanValuesoverCircles.....................................19CHAPTER2-LinearizedInverseDynamicProblemfortheTelegraphEquation...........................................22I.StatementoftheInverseProblemand
7、ItsLinearization..222.Linearized0ne-DimenslonalInverseProbleminTwo-DimensionalSpace.......................................245.TwoFormulationsoftheLinearlzedInverseProbleminThree-DimenslonalSpace.................................284.DerivationofaNonlinearDifferentialEquat
8、ionfortheInverseProblem.........................................31CHAPTER3-LinearizedInverseKinematicProblemfo