简介:Inthispaperwestudytheexistenceoflimitcycleforcubicsystem(E)3,ofKolmogorovtypewithaconicalgebraictrajectoryF2(x,y)=ax2+2bxy+cy2+dx+ey+f=0Ithasbeenprovedinmyformerpapersthat(E)3doesn’thaveanylimitcycleonthewholeplaneIfb2-ac≠0,Nowweareinvestigatingthecasewhereb2-ac=0.Weprovethesufficientandnecessaryformula(2)or(13)witbwhich(E)3musthaveaparabolictrajectoryF2(x,y)=0.Thentherewillnotbeanylimitcycleonthefullplane.Onthebasisofthis,weconclude:ThecubicsystemofKolmogorovtypewithanon-degeneratedquadraticalgebraictrajectoryonthewholeplanehasnolimitcycle.
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简介:§1.IntroductionLetEbeanon-zerocomplexBanaohspace,&(JET)theBanaohalgebraofalltheoperatorsfromEintoitself.Operatormeans'boundedlinearoperator'throughout.Anoperatorfunction/fromadomain(openset)Dinthecomplexplaneto@l(T£}issaidtobeanalytic,ifforanyx^Eandq>£E*(thedualspaceofE\9>(/(z)aOisanalyticintheclassical’senseinD([1],p.92).Wedenotebyja/B(D)thesetofalltheanalyticoperatorfunctionsfromDinto
简介:让x:Mn是有非零主管弯曲的脐的免费hypersurface。然后,x与Laguerre公制的g被联系,Laguerre张肌\mathbbL\mathbb{L},Laguerre形式C,和一个Laguerre秒基础形成\mathbbB\mathbb{B}它是在Laguerre下面的x的invariants转变组。如果它的Laguerre形式消失,hypersurfacex被称为Laguerreisoparametric并且\mathbbB\mathbb的特征值{B}是不变的。在这份报纸,我们在4分类所有Laguerreisoparametrichypersurfaces。
简介:WiththedevelopmentofWeb2.0,moreandmorepeoplechoosetousetheInternettoexpresstheiropinions.Allthisopinionstogetherintoanewformtextwhichcontainsalotofvaluableemotionalinformation,thisiswhyhowtodealwiththesetextsandanalysistheemotionalinformationissignificantforus.Wegetthreemaintasksofsentimentanalysis,includingsentimentextraction,sentimentclassification,sentimentapplicationandsummarization.Inthispaper,basedontheRsoftware,weintroducedthestepsofsentimentanalysisindetail.Finally,wecollectthemoviereviewsfromtheInternet,anduseRsoftwaretodosentimentanalysisinordertojudgetheemotionaltendencyofthetext.
简介:让f:M→R~3是有非退化的秒的面向的表面基本形式。我们由H和K表示它的吝啬的弯曲和高斯弯曲。然后f的Laguerre体积,由L(f)=∫(H~2定义-K)/KdM,一在Laguerre转变下面不变。功能的L的批评表面被称为Laguerre最小的表面。在这篇论文,我们学习在由使用拉久雷·高斯的R~3的最小的表面印射的theLaguerre。这被知道最小的表面有的genericLaguerre有一样的高斯地图的双Laguerre最小的表面。在这篇论文,我们证明不是Laguerre的任何表面最小被它的LaguerreGaussmap特别地决定。我们也证明圆范围是在R~3的唯一的紧缩的Laguerre最小的表面。并且我们与消失的Laguerre形式在R~3给表面的一条分类定理。
简介:ADMISSIBLEWAVELETSASSOCIATEDWITHTHETRANSFORMGROUPONRHEJIANXUNANDPENGLIZHONGAbstract.LetPbethetransformgrouponRn,thenPhasanatu...
简介:LetX,YbeUMD-spacesthathaveproperty(α),I<p<∞andletMbeanR-boundedsubsetin()(X,Y).Itisshownthat{T(Mk)k∈z:Mk,k(Mk+1-Mk)∈Mfork∈Z}isanR-boundedsubsetof()(Lp(0,2π;X),Lp(0,2π;Y)),whereT(Mk)k∈zdenotestheLp-multipliergivenbythesequence(Mk)k∈z.ThisgeneralizesaresultofVenni[10].TheauthorusesthisresulttostudythestronglyLp-well-posednessofevolutionequationswithperiodicboundarycondition.AnalogousresultsforoperatorvaluedLp-multipliersonRarealsogiven.
简介:LetGbeagraphwithvertexsetV(G)andedgesetE(G)andletgandfbetwointeger-valuedfunctionsdefinedonV(G)suchthat2k-1≤g(x)≤f(x)forallx∈V(G).LetHbeasubgraphofGwithmkedges.Inthispaperitisprovedthatevery(mg+m-1,mf-m+1)-graphGhas(g,f)-factorizationsrandomlyκ-orthogonaltoHandshownthattheresultisbestpossible.