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1、SpringerSeriesinStatisticsAdvisors:P.Bickel,P.Diggle,S.Feinberg,U.Gather,I.Olkin,S.ZegerForothertitlespublishedinthisseries,gotohttp://www.springer.com/series/692AlbertW.Marshall•IngramOlkinBarryC.ArnoldInequalities:TheoryofMajorizationandItsApplicationsSecondEditionABCAlbertW.MarshallBarryC.Arnol
2、dDepartmentofStatisticsDepartmentofStatisticsUniversityofBritishColumbiaUniversityofCaliforniaVancouver,BCV6T1Z2Riverside,CA92521CanadaUSAandmailingaddressbarry.arnold@ucr.edu2781W.ShoreDriveLummiIsland,WA98262almarshall@earthlink.netIngramOlkinDepartmentofStatisticsStanfordUniversityStanford,CA94
3、305USAiolkin@stat.stanford.eduISSN0172-7397ISBN978-0-387-40087-7e-ISBN978-0-387-68276-1DOI10.1007/978-0-387-68276-1SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2010931704cSpringerScience+BusinessMedia,LLC2011Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorin
4、partwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissim
5、ilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerS
6、cience+BusinessMedia(www.springer.com)Toourlong-sufferingwivesfortheirpatiencewiththisproject:Sheila(AWM),Anita(IO),Carole(BCA)TothememoryofZ.W.(Bill)BirnbaumandEdwinHewittwhoinitiatedmyinterestininequalities(AWM)Tomystudentsandcolleagueswhohaveenergized,enrichedandenlivenedmylife(IO)TothememoryofP
7、eggyFranklin(BCA)PrefaceandAcknowledgmentsfromtheFirstEditionPrefaceAlthoughtheyplayafundamentalroleinnearlyallbranchesofmath-ematics,inequalitiesareusuallyobtainedbyadhocmethodsratherthanasconsequencesofsomeunde
