简介：Inthispaper,someteststatisticsOfKolmogorovtypeandCramervonMisestypebasedonprojectionpursuittechniqueareproposedfortestingthesphericityproblemofahigh-dimensionaldistribution.Thelimitingdistributionsoftheteststatisticsarederivedunderthenullhypothesis.TheasymptoticpropertiesofBootstrapapproximationareinvestigatedandthetailbehaviorsofthestatisticsarestudied.

简介：Testingequalityofcovariancematrixhaslongbeenaninterestingissueinstatisticsinference,Toovercomethesparsenessofdatapointsinhigh-dimensionalspaceanddealwiththegeneralcases,theauthorsuggestsseveralprojectionpursuittypestatistics.Someresultsonthelimitingdistidbutionsofthestatisticsareobtained.Somepropertiesofbootstrapapproximationareinvestigated.Furthermore,forcomputationalreasonsanapproximationforthestatisticsbasedonnumber-theoreticroethodisapplied.Severalsimulationexperimentsareperformed.

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简介：Inthispaper,westudyatwo-speciesperiodicBeddington-DeAngelispredator-preymodelwithdelayinatwo-patchenvironment,inwhichthepreyspeciescandispersebetweentwopatches,butthepredatorspeciescannotdisperse.Onthebasisofthecomparisontheoremofdifferentialequations,weestablishsufficientconditionsforthepermanenceandextinctionofthesystem.

简介：AnA.D.I.Galerkinschemeforthree-dimensionalnonlinearparabolicintegro-differen-tialequationisstudied.Byusingalternating-direction,thethree-dimensionalproblemisreducedtoafamilyofsinglespacevariableproblems,thecalculationissimplified;byusingalocalapproxima-tionofthecoefficientsbasedonpatchesoffiniteelements,thecoefficientmatrixisupdatedateachtimestep;byusingRitz-Volterraprojection,integrationbypartandothertechniques,theinfluencecomingfromtheintegraltermistreated;byusinginductivehypothesisreasoning,thedifficultycomingfromthenonlinearityistreated.ForbothGalerkinandA.D.I.Galerkinschemesthecon-vergencepropertiesarerigorouslydemonstrated,theoptimalH~1-normandL~2-normestimatesareobtained.

简介：Inthisarticle,weestablishtheglobalstabilityofanendemicequilibriumofmulti-groupSIRepidemicmodels,whichhavenotonlyanexchangeofindividualsbetweenpatchesthroughmigrationbutalsocrosspatchinfectionbetweendifferentgroups.Asaresult,wepartiallygeneralizetherecentresultinthearticle[16].

简介：1.IntroductionThetwcawayerrorcomponentregressionmodelmsybeexpressedasif=o+

简介：Fortheimprovedtwo-sidedprojectedquasi-Newtonalgorithms,whichwerepresentedinPartI,weproveinthispaperthattheyarelocallyone-steportwo-stepsuperlinearlyconvergent.Numericaltestsarereportedthereafter.ResultsbysolvingasetoftypicalproblemsselectedfromliteraturehavedemonstratedtheextremeimportanceofthesemodificationsinmakingNocedal&Overton’soriginalmethonpractical.Furthermore,theseresultsshowthattheimprovedalgoritnmsareverycompetitiveincomparisonwithsomehighlypraisedsequentialquadraticprogrammingmethods.

简介：InthispaperweprovethataclassoftrustregionmethodspresentedinpartⅠissuperlinearlyconvergent.Numericaltestsarereportedthereafter.Resultsbysolvingasetoftypicalproblemsselectedfromliteratureshavedemonstratedthatouralgorithmiseffective.