简介:Letx=(xn)n≥1beamartingaleonanoncommutativeprobabilityspace(M,τ)and(wn)n≥1asequenceofpositivenumberssuchthatWn=∑nk=1wk→∞asn→∞.Weprovethatx=(xn)n≥1convergesinE(M)ifandonlyif(σn(x))n≥1convergesinE(M),whereE(M)isanoncommutativerearrangementinvariantBanachfunctionspacewiththeFatoupropertyandσn(x)isgivenbyk=1Ifinaddition,E(M)hasabsolutelycontinuousnorm,then,(σn(x))n≥1convergesinE(M)ifandonlyifx=(xn)n≥1isuniformlyintegrableanditslimitinmeasuretopologyx∞∈E(M).
简介:我们为其内核满足一个一般同质条件的线性不可分的操作符的一个类在空格BV关于变化获得估计和集中结果。近似的率也被获得。作为应用,我们把我们的一般理论用于Mellin卷绕旋转操作员的盒子,到一个时刻操作员到部分顺序的操作员的一个班。
简介:Withthevigorousexpansionofnonlinearadaptivefilteringwithreal-valuedkernelfunctions,itscounterpartcomplexkerneladaptivefilteringalgorithmswerealsosequentiallyproposedtosolvethecomplex-valuednonlinearproblemsarisinginalmostallreal-worldapplications.ThispaperfirstlypresentstwoschemesofthecomplexGaussiankernel-basedadaptivefilteringalgorithmstoillustratetheirrespectivecharacteristics.ThenthetheoreticalconvergencebehaviorofthecomplexGaussiankernelleastmeansquare(LMS)algorithmisstudiedbyusingthefixeddictionarystrategy.ThesimulationresultsdemonstratethatthetheoreticalcurvespredictedbythederivedanalyticalmodelsconsistentlycoincidewiththeMonteCarlosimulationresultsinbothtransientandsteady-statestagesfortwointroducedcomplexGaussiankernelLMSalgonthmsusingnon-circularcomplexdata.Theanalyticalmodelsareabletoberegardasatheoreticaltoolevaluatingabilityandallowtocomparewithmeansquareerror(MSE)performanceamongofcomplexkernelLMS(KLMS)methodsaccordingtothespecifiedkernelbandwidthandthelengthofdictionary.
简介:Amodifiedsequentiallinearprogrammingalgorithmispresented,whosesubproblemisalwayssolvable,fortheextendedlinearcomplementarityproblem(XLCP),theglobalconvergenceofthealgorithmunderassumptionofX-rowsufficiencyorX-columnmonotonicityisproved.Asaresult,asufficientconditionforexistenceandboundednessofsolutiontotheXLCPareobtained.
简介:LetT:X→XbeanAxiomAdiffeomorphism,mtheGibbsstateforaHldercontinuousfunctionɡ.Assumethatf:X→R~disaHldercontinuousfunctionwith∫_X~(fdm)=0.Ifthecomponentsoffarecohomologouslyindependent,thenthereexistsapositivedefinitesymmetricmatrixσ~2:=σ~2(f)suchthatS~fn√nconvergesindistributionwithrespecttomtoaGaussianrandomvariablewithexpectation0andcovariancematrixσ~2.Moreover,thereexistsarealnumberA>0suchthat,foranyintegern≥1,Π(m*(1√nSfn),N(0,σ~2)≤A√n,wherem*(1√nS~fn)denotesthedistributionof1√nS~fnwithrespecttom,andΠistheProkhorovmetric.
简介:ThenonconformingWilson’sbrickclassicallyisrestrictedtoregularhexahedralmeshes.LesaintandZlamal[6]relaxedthisconstraintforthetwo-dimensionalanalonueofthiselementInthispaperweextendtheirresultstothreedimensionsandprovethatandwhereuistheexactsolution,u_histheapproximatesolutionandistheusualnormfortheSobolevspaceH~1(?).
简介:1.IntroductionTherehasbeenalotofliterature(see[1]--[61and[12])ontheparalleliterativemethodsforthelarge--scalesystemoflinearequationsinthesenseofmatrixmultisplittingsincethepioneeringworkofO’LearyandWhite(see[l])waspublishedin1985.Oneofthemostrecentre...
简介:为在间隔上可测量的某局部地围住的功能f[0,)我们在那些点x估计了修改Szasz-Mirakyan操作员Mnf的集中的率[0,)在哪个站在一起的限制f(?敢慨楶畯?景琠敨洠汵楴瘭牡慩整?牥獮整湩瀠汯湹浯慩獬??湯琠敨搠搭浩湥楳湯污猠浩汰硥匠?d
简介:Theauthorsgiveaproofoftheconvergenceofthesolutionoftheparabolicapproximationu^εt+divf(x,t,u^ε)=ε△u^εtowardstheentropicsolutionofthescalarconservationlawut+divf(x,t,u)=0inseveralspacedimensions.Foranyinitialconditionu0∈L^∞(R^N)andforalargeclassofHuxf,theyalsoprovethestrongconvergeinanyL^plocspace,usingthenotionofentropyprocesssolution,whichisageneralizationofthemeasure-valuedsolutionsofDiPerna.
简介:Inthispaper,someapproximationformulaeforaclassofconvolutiontypedoublesingularintegraloperatorsdependingonthreeparametersofthetype(Tλf)(x,y)=∫ba∫baf(t,s)Kλ(t-x,s-y)dsdt,x,y∈(a,b),λ∈A[0,∞),(0.1)aregiven.HerefbelongstothefunctionspaceL1(〈a,b〉2),where〈a,b〉isanarbitraryintervalinR.Inthispaperthreetheoremsareproved,oneforexistenceoftheoperator(Tλf)(x,y)andtheothersforitsFatou-typepointwiseconvergencetof(x0,y0),as(x,y,l)tendsto(x0,y0,l0).Incontrasttopreviousworks,thekernelfunctionsKl(u,v)don'thavetobe2p-periodic,positive,evenandradial.Ourresultsimproveandextendsomeofthepreviousresultsof[1,6,8,10,11,13]inthreedimensionalframeandespeciallytheveryrecentpaper[15].