简介：LetAbearealsquarematrixandVTAV=GbeanupperHessenbergmatrixwithpositivesubdiagonalentries,whereVisanorthogonalmatrix.ThentheimplicitQ-theoremstatesthatoncethefirstcolumnofVisgiventhenVandGareuniquelydetermined.Inthispaper,threeresultsareestablished.First,itholdsareverseorderimplicitQ-theorem:oncethelastcolumnofVisgiven,thenVandGareuniquelydeterminedtoo.Second,itisprovedthatforaKrylovsubspacetwoformulationsoftheArnoldiprocessareequivalentandinonetoonecorrespondence.Finally,bytheequivalencerelationandthereverseorderimplicitQ-theorem,itisprovedthatfortheKrylovsubspace,ifthelastvectorofvectorsequencegeneratedbytheArnoldiprocessisgiven,thenthevectorsequenceandresultingHessenbergmatrixareuniquelydetermined.

简介：

简介：Inthispaper,thecorrespondencetheoremfortheusualalgebraicsystemsisgeneralizedtocoalgebra.Moreover,oneexample,whichillustratethepreimageofasubcoalgebraneednottobeasubcoalgebraforgeneralcoalgebrahomomorphism,isgiven.

简介：Inthispaperweproveanonvariationalformofarain-maxproblemin[l]andgiveitsapplicationtoaperiodicalproblem.

简介：AnonlinearversionofKreinRutmanTheoremisestablished.ThispaperpresentsaunifiedproofoftheKreinRutmanTheoremforlinearoperatorsandfornonlinearoperators,andofthePerron-Frobeniustheoremfornonnegativematricesandfornonnegativetensors.

简介：LetpdenoteaprimeandP2denoteanalmostprimewithatmosttwoprimefactors.Theauthorprovesthatforsuffcientlylargex,sumfromp≤xp+2=P21>(1.13Cx)/(log~2x),wheretheconstant1.13constitutesanimprovementofthepreviousresult1.104duetoJ.Wu.

简介：<正>WeareconcernedwiththefollowingDirichletproblem:-△u（x）=f（x,u）,x∈Ω.u∈H01（Ω）.（P）wheref（x,t）∈C（Ω×R）,f（x,t）/tisnondecreasingint∈RandtendstoanL∝-functionq（x）uniformlyinx∈Ωast→+∝（i.e.,f（x,t）isasymptoticallylinearintatinfinity）.Inthiscase.anAmbrosetti-Rabinowitz-typecondition,thatis.forsomeθ>2.M>0,0<θF（x.s）≤f（x,s）s,forall|s|≥Mandx∈Ω,（AR）isnolongertrue,whereF（x,s）=integralfromn=0tosf（x,t）dt.Asiswellknown,（AR）isanimportanttechnicalconditioninapplyingMountainPassTheorem.Inthispaper,withoutassuming（AR）weprove,byusingavariantversionofMountainPassTheorem,thatproblem（P）hasapositivesolutionundersuitable,conditionsonf（x,t）andq（x）.Ourmethodsalsoworkforthecasewheref（x,f）issuperlinearintatinfinity.i.e.,q（x）≡∞.

简介：AssumethatBisacompactsubsetontherealaxiscontainingatleastn+1points,C（B）thenormedlinearspaceofallcontinuousfunctionsdefinedonB,withChebyshevnorm‖·‖,andG=span（g1,…,gn）ann-dimensionalsubspaceofC（B）.LetGR={g=sumfromj=1tonajgj:v（x）≤g（x）≤u（x）,qi≤sumfromj=1tondijaj≤pifori=1,…,l}whereu,vareextendedreal-valuedfunctionsonBsubjectto-∞≤v（x）

简介：In1972,Fullerprovedthatacompleteadditivesubeategory_RCofR-Modisequivalenttoamodulecategory⊿-Modifandonlyif_RC=Gen(_RU)forsomequasiprogenerator_RUand⊿≌End_RUcanonically.Inthisnotetheauthorgivesacharacterizationof_RCwhichmakes_RUaprojectiveR-moduleinthecasewhenRisarightperfectringwithidentity,andshowsthatR-ModistheuniquecompleteadditivesubcategoryofR-ModwhichisequivalenttoR-ModforaleftArtinianringR.

简介：Weprovethat,fornon-uniformlyhyperbolicdiffeomorphismsinthesenseofYoung,thelocalcentrallimittheoremholds,andthespeedinthecentrallimittheoremisO(1/√n).

简介：

简介：Aboundoduesscriterionissetup/orsomeconvolutionoperatorsonacompaotLiegroup,BythiscriterionaHoermandermultipliertheoremisprovedintheHardyspacesonSU(2).

简介：我们证明为四元数海森堡组上的sublaplacian的限制操作员从Lp被围住到Lp如果1p$\tfrac{4}{3}$\tfrac{4}{3}。这与海森堡组，限制操作员没从Lp在上被围住到Lp不同除非p=1。

简介：InthispaperwepresentacorrectionoftheproofofustronguniquenesstheoremgivenbyH.Struuss[1]in1992onapproximationbyreciprocalsoffunctionsufann-dimensionalspace(u,…un)satisfyingcoefficientconstraints.

简介：Apicardtypetheoremisproved,andacounterexampleisgiventoshowthattheBlochLawisnottruegenerally.

简介：在这篇论文，一条新非线性的闭图定理被建立，其结果实质地改进一条最近知道重要结论。

简介：<正>Inthispaper,weinvestigatethegeneralizedSublaplacian.Wegivetheexpressionoftherestrictionoperatorsexplicitly.Byintroducingthegeneralizedλ-twistedconvolutions,weobtaintheestimatesoftherestrictionoperatorsinthemixedL~Pspaces.Finally,wegetarestrictiontheoremassociatedwiththegeneralizedSublaplacian.

简介：在这篇论文，由介绍等轴的联盟者Pc0性质，集中定理的一种分离形式被介绍；结果概括；在最近的年里统一几个有趣的结论。

简介：InthispaperwepresentacorrectionoftheproofofastronguniquenesstheoremgivenbyH.Straussin1992onapproximationbyreciprocalsoffunctionsofann-dimensionalspacespan（u1,…,un）satisfyingcoefficientconstraints.

简介：Aseveryoneknows,theclassicalJacksontheoreminapproximationtheorywasgeneralizedinLpspacesbyR.A.Devore.Inthispaper,weprovedtheJacksontheoreminB,spaceswhichintroducedbyDingXiaXi,