简介:Thispaperprovesthattheoptimalquadratureformulasoftype(r1,…rn)forWm1isunique,andtheextremalfunctionischaracterizedbyitsoscillatoryproperty.Ontheotherhand,thefundamentaltheoremofalgebraforperiodicmonosplineswithoddmultiplicitiesissolvcd
简介:这篇论文为答案在片是其弱熵的严格地凸的能量守恒定律涉及一个起始的边界价值问题明智的光滑的答案班由组成有限地许多断绝。由相应起始的价值问题和边界熵的弱熵答案的结构,状况开发了byBardos-Leroux-Nedelec,我们把一个构造方法给起始的边界价值问题的弱熵答案。与起始的值问题相比,起始的边界值问题的弱熵解决方案包括下列新相互作用类型:一个扩大波浪与边界碰撞,边界反映是到边界的正切的一个新冲击波。根据结构和弱熵答案的一些全球估计,我们导出全球L~1错误估计为粘滞到由使用匹配旅行的这个起始的边界价值问题的方法挥动答案方法。如果在里面胶粘的答案包括一个扩大波浪与边界碰撞,边界思考的相互作用是到边界的正切的一个新冲击波,或在里面胶粘的答案包括是到边界的正切的一些冲击波,然后的粘性答案的错误在里面胶粘的答案被O(ε~(1/2))在L~1标准围住;否则,处于起始的价值问题,L~1错误界限是O(ε|nε|)。
简介:Inthispaper,wehaveinvestigatedtheproblemoftheconvergencerateofthemultipleintegralwheref∈Cn+1([0,T]n)isagivenfunction,πisapartitionoftheinterval[0,T]and{BtHi,π}isafamilyofinterpolationapproximationoffractionalBrownianmotionBtHwithHurstparameterH<1/2.ThelimitprocessisthemultipleStratonovichintegralofthefunctionf.Inviewofknownresults,theconvergencerateisdifferentfordifferentmultiplicityn.Undersomemildconditions,weobtainthattheuniformconvergencerateis2Hinthemeansquaresense,whereisthenormofthepartitiongeneratingtheapproximations.
简介:WedescribetheestablishingprocessfortheBoson-FermionalgebraofOSP(1,2)startingfromthefundamentalWigneroperatorsofOSP(1,2),andstudyitsstructuréfeatureandrepresentationtheory.WealsogivetheBoson-FermionrepresentationofOSP(1,2),whichisaninfinitedimensionalandgradestarrepresentation
简介:Inthispaper,weshowthatnewmodifieddoublecosinetrigonometricsumsintroducedin[1]areinappropriate,theclassofdoublesequencesJdintroducedthereisunusableforsuchsumsandconsequentlytheresultsobtainedinitarecompletelyincorrect.WehereintroduceappropriatemodifieddoublecosinetrigonometricsumsmakingtheclassJdusableconsideringaparticulardoublecosinetrigonometricseries.
简介:EQrot1nonconformingfiniteelementapproximationtoaclassofnonlineardualphaselaggingheatconductionequationsisdiscussedforsemi-discreteandfully-discreteschemes.Byuseofaspecialproperty,thatis,theconsistencyerrorofthiselementisoforderO(h2)oneorderhigherthanitsinterpolationerrorO(h),thesupercloseresultsoforderO(h2)inbrokenH1-normareobtained.Atthesametime,theglobalsuperconvergenceinbrokenH1-normisdeducedbyinterpolationpostprocessingtechnique.Moreover,theextrapolationresultwithorderO(h4)isderivedbyconstructinganewinterpolationpostprocessingoperatorandextrapolationschemebasedontheknownasymptoticexpansionformulasofEQrot1element.Finally,optimalerrorestimateisgainedforaproposedfully-discreteschemebydifferentapproachesfromthepreviousliterature.
简介:Inthispaper,themodifiedextendedtanhmethodisusedtoconstructmoregeneralexactsolutionsofa(2+1)-dimensionalnonlinearSchr¨odingerequation.WiththeaidofMapleandMatlabsoftware,weobtainexactexplicitkinkwavesolutions,peakonwavesolutions,periodicwavesolutionsandtheir3Dimages.