简介:TheauthorpresentssomestraightforwardproofsfortwocomparisontheoremsforGreenfunctionsofMarkovchains,whichslightlyimprovethepreviousresultsbyVaropoulos,DurrettandYanandChen.ArecentresultbyRogersandWilliamsaboutinstantaneousMarkovchainsisalsoimprovedbyusingthesameidea.
简介:ThediscontinuousGalerkin(DG)orlocaldiscontinuousGalerkin(LDG)methodisaspatialdiscretizationprocedureforconvection-diffusionequations,whichemploysusefulfeaturesfromhighresolutionfinitevolumeschemes,suchastheexactorapproximateRiemannsolversservingasnumericalfluxesandlimiters.TheLax-Wendrofftimediscretizationprocedureisanalternativemethodfortimediscretizationtothepopulartotalvariationdiminishing(TVD)Runge-Kuttatimediscretizations.Inthispaper,wedevelopfluxesforthemethodofDGwithLax-Wendrofftimediscretiza-tionprocedure(LWDG)basedondifferentnumericalfluxesforfinitevolumeorfinitedifferenceschemes,includingthefirst-ordermonotonefluxessuchastheLax-Friedrichsflux,Godunovflux,theEngquist-Osherfluxetc.andthesecond-orderTVDfluxes.WesystematicallyinvestigatetheperformanceoftheLWDGmethodsbasedonthesediffer-entnumericalfluxesforconvectiontermswiththeobjectiveofobtainingbetterperfor-mancebychoosingsuitablenumericalfluxes.Thedetailednumericalstudyismainlyperformedfortheone-dimensionalsystemcase,addressingtheissuesofCPUcost,ac-curacy,non-oscillatoryproperty,andresolutionofdiscontinuities.Numericaltestsarealsoperformedfortwodimensionalsystems.
简介:Acousticimpulsesproducedthroughthemechanismofthelaser-inducedbreakdowninwaterhavebeeninvestigatedintherangefrom0℃toroomtemperature.Differentlyfromtheacousticimpulsesproducedviathermalexpansion,thepolarityandtheamplitudeofacousticimpulseproducedvialiquidbreakdownmechanismdonotchangewithwatertemper-ature.Thisindirectlyprovesthattheproductionofacousticimpulseisduetotheexpansionofthecavityitselfwhichincludesplasma.Asemiempiricaldescriptionofthisphenomenonisgiveninthispaper.
简介:ConsiderthelinearsystemAx=b,(1)whereA∈Rn×nisnonsingular.TheadditiveSchwarzmethodwasintroducedinthelastcentury.Recently,themethodhasbeenusedforsolvinggeneralalgebraicsystemoflinearequations(1)inparal-lelcomputer(see[1]).Thisiterativemethodcanbeconsideredasageneralmultisplit-ting,inwhichthecorrespondingiteratesxn,l,l=1,2,…,k,aregivenby
简介:ThelargescalelinearsystemswithM-matricesoftenappearinawidevarietyofareasofphysical,fluiddynamicsandeconomicsciences.Itisreportedin[1]thattheconvergencerateoftheIMGSmethod,withthepreconditionerI+S_α,issuperiortothatofthebasicSORiterativemethodfortheM-matrix.ThispaperconsidersthepreconditionedJacobi(PJ)methodwiththepreconditionerP=I+S_α+S_β,andprovestheoreticallythattheconvergencerateofthePJmethodisbetterthanthatofthebasicAORmethod.Numericalexamplesareprovidedtoillustratethemainresultsobtained.
简介:Inthispaperwestudyreflectedanddoublyreflectedbackwardstochasticdifferentialequations(BSDEs,forshort)drivenbyTeugelsmartingalesassociatedwithL'evyprocesssatisfyingsomemomentconditionsandbyanindependentBrownianmotion.ForBSDEswithonereflectingbarrier,weobtainacomparisontheoremusingtheTanaka-Meyerformula.ForBSDEswithtworeflectingbarriers,wefirstprovetheexistenceanduniquenessofthesolutionsundertheMokobodski'sconditionbyusingtheSnellenvelopetheoryandthenweobtainacomparisonresult.
简介:纸基于准确公平可靠,相对错误函数作为损失功能在被拿开发最佳的Bonus-Malus系统(BMS)的一个图案。在BMS,频率和严厉部件被考虑。这个图案与从古典方形错误的损失功能导出的传统的BMS相比。
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简介:Theprimaryresonancesofaquadraticnonlinearsystemunderweakandstrongexternalexcitationsareinvestigatedwiththeemphasisonthecomparisonofdifferentanalyticalapproximateapproaches.Theforcedvibrationofsnap-throughmechanismistreatedasaquadraticnonlinearoscillator.TheLindstedt-Poincar′emethod,themultiple-scalemethod,theaveragingmethod,andtheharmonicbalancemethodareusedtodeterminetheamplitude-frequencyresponserelationshipsofthesteady-stateresponses.Itisdemonstratedthatthezeroth-orderharmoniccomponentsshouldbeaccountedintheapplicationoftheharmonicbalancemethod.Theanalyticalapproximationsarecomparedwiththenumericalintegrationsintermsofthefrequencyresponsecurvesandthephaseportraits.Supportedbythenumericalresults,theharmonicbalancemethodpredictsthatthequadraticnonlinearitybendsthefrequencyresponsecurvestotheleft.Iftheexcitationamplitudeisasecond-ordersmallquantityofthebookkeepingparameter,thesteady-stateresponsespredictedbythesecond-orderapproximationoftheLindstedtPoincar′emethodandthemultiple-scalemethodagreequalitativelywiththenumericalresults.Itisdemonstratedthatthequadraticnonlinearsystemimpliessofteningtypenonlinearityforanyquadraticnonlinearcoefficients.
简介:Anticipatedbackwardstochasticdifferentialequation(ABSDE)studiedthefirsttimein2007isanewtypeofstochasticdifferentialequations.Inthispaper,weestablishageneralcomparisontheoremforABSDEs.
简介:ThepreparationoftwotypesofmolecularsievesAlPO4-11andMAPO-11isreported.Theparticlesizeofthelatterishundredsofmicrons,about10timeslargerthanthatoftheformer.TheXRD,IRandDTAspectrahavedemonstratedthatmagnesiumhasbeenintroducedintotheframeworkofAlPO4-11.ThesuccessfulpreparationoflargesinglecrystalofMAPO-11willopenupanewareaforthepreparationoflargemolecularsievescrystalsinthefuture.ThelargeMAPO-11crystalcompoundisapromisinghostforthehost-guestassemblyofcompositematerials.
简介:Inthispaper,severalmixtruerulesofsoundvelocityandtheirusefulnessincharacterizingthecomponentsofbiomediumareanalysed.Itispointedoutthatforcharacterizingthecomponentsofbiomedium,therulesarecompatiblewitheachotherundercertainconditions,andtheerrorsbetweeneachruleandrealsoundvelocityarediffferent.Itconcludesthatthereisnogeneralrulesuitableforvariousmediaamongabovementionedrules.