简介:Anumbilicalfreeorientedhypersurfacex:M→Rnwithnon-zeroprincipalcurvaturesiscalledaLaguerreisoparametrichypersurfaceifitsLaguerreformC=iCiωi=iρ1(Ei(logρ)(rri)Ei(r))ωivanishesandLaguerreshapeoperatorS=ρ1(S1rid)hasconstanteigenvalues.Hereρ=i(rri)2,r=r1+r2+···+rn1n1isthemeancurvatureradiusandSistheshapeoperatorofx.{Ei}isalocalbasisforLaguerremetricg=ρ2IIIwithdualbasis{ωi}andIIIisthethirdfundamentalformofx.Inthispaper,weclassifyallLaguerreisoparametrichypersurfacesinRn(n>3)withtwodistinctnon-zeroprincipalcurvaturesuptoLaguerretransformations.
简介:<正>Newkindsofstronglyzero-dimensionallocalesareintroducedandcharacterized,whicharedifferentfromJohnstone’s,andalmostallthetopologicalpropertiesforstronglyzero-dimensionalspaceshavethepointlosslocalicforms.Particularly.theStone-Cechcompactificationofastronglyzero-diluensionallocaleisstonglyzero-dimensional.
简介:Foranasymmetricmatrix,thezero-nonzeropatternPofentriescanbedescribedbyadigraphΓ(P)whichhasanarcifanentryisnonzero.Theminimumrankofazero-nonzeropatternisdefinedtobethesmallestpossiblerankoverallrealmatriceshavingthegivenzero-nonzeropattern.Definitionsofvariousgraphparametersthathavebeenusedtoboundminimumrankofazerononzeropattern,includingpathcovernumberandeditdistance,andthetrianglesizetri(P).Inthispaper,byconvertingadigraphintoanundirectedbipartitegraphG(U,V),wepresentanalgorithmforconstructingasub-bipartitegraphwiththeuniquemaximumperfectmatchingM',andobtainthattri(P)=|M'|forP.
简介:Countdatawithexcesszerosareoftenencounteredinmanymedical,biomedicalandpublichealthapplications.Inthispaper,anextensionofzero-inflatedPoissonmixedregressionmodelsispresentedfordealingwithmultileveldataset,referredashierarchicalmixturezero-inflatedPoissonmixedregressionmodels.AstochasticEMalgorithmisdevelopedforobtainingtheMLestimatesofinterestedparametersandamodelcomparisonisalsoconsideredforcomparingmodelswithdifferentlatentclassesthroughBICcriterion.AnapplicationtotheanalysisofcountdatafromaShanghaiAdolescenceFitnessSurveyandasimulationstudyillustratetheusefulnessandeffectivenessofourmethodologies.
简介:Forfirst-orderquasilinearhyperbolicsystemswithzeroeigenvalues,theauthorestablishesthelocalexactcontrollabilityinashortertime-periodbymeansofinternalcontrolsactingonsuitabledomains.Inparticular,undercertainspecialbutreasonablehypotheses,thelocalexactcontrollabilitycanberealizedonlybyinternalcontrols,andthecontroltimecanbearbitrarilysmall.
简介:Theimportanceofthezerosofmultwariablelinearsystemsiswell-knoiunintermsofmeasureobstructionstothecontrollabilityandthe.observability.Inthispaper,arecursivedecarnposiAmojinterconnectedsystemsisoutlinedbytakingintoaccountthesequentialstructureoftheconnnections.Thepaperextendsthe,coordinate,module-theoreticstudiesfromtheelementaryalgebraicsystemstheorytoincludethecaseojsuchlinearinterconnectedsystemswhichneednottobecontrollableorobservable.Also,thepropertiesofcontrollabilityandobservability,thedecouplingzerosandthesignalMakingissuesarecharacterized.
简介:In[1],Dingetal.studiedthenonhomogeneousBurgersequationThispaperwillprovethatwhenμ→0thesolutionof(1.1)willapproachthegeneralizedsolutionofTheauthorsnoticethattheequation(1.2)isbeyondthescopeofinvestigationsbyOleinikO.in[2].Thesolutionshereareunboundedingeneral.Thepaperalsostudiestheδ-wavephenomenonwhen(1.2)isjointedwithsomeotherequation.
简介:ThispaperpresentssomeresultsaboutboundsforcoincidenceindicesofNielsencoincidenceclassesformapsbetweennonorientablesurfaces.DenotingbyKnthenonorientablesurfaceconstructedbyaconnectedsumofntoruswithaKleinbottle,theauthorproves:(i)forpairsofmapsbetweentwoKleinbottlesorforpairsofmapsfromaKleinbottletoasurfaceKnthecoincidenceclassindexisbounded.(ii)forpairsofmapsfromKntotheKleinbottlethecoincidenceclassindexisunbounded.Otherboundednessresultsaregivenformoretechnicalconditions,includingoneforselfmaps.
简介:Inthispaper,thetotallynon-positivematrixisintroduced.Thetotallynon-positivecompletionaskswhichpartialtotallynon-positivematriceshaveacompletiontoatotallynon-positivematrix.Thisproblemhas.ingeneral,anegativeanswer.Therefore,ourquestionisforwhatkindoflabeledgraphsGeachpartialtotallynon-positivematrixwhoseassociatedgraphisGhasatotallynon-positivecompletion?IfGisnotamonotonicallylabeledgraphormonotonicallylabeledcycle,wegivenecessaryandsufficientconditionsthatguaranteetheexistenceofthedesiredcompletion.
简介:Leta,b,cberelativelyprimepositiveintegerssuchthata2+b2=c2.Je′smanowicz’conjectureonPythagoreannumbersstatesthatforanypositiveintegerN,theDiophantineequation(aN)x+(bN)y=(cN)zhasnopositivesolution(x,y,z)otherthanx=y=z=2.Inthispaper,weprovethisconjectureforthecasethataorbisapowerof2.
简介:InthispaperweconsidertheeigenvalueproblemofsemilinearellipticequationinR~n(n≥~3)-△u+α(x)u=λf(x,u),u∈H~1(R~n).
简介:ThepaperistogeneralizetherigiditytheoremthatthespecialWeingartensurfaceisthespheretothecaseofsubmanifolds.Itisprovedthatanon-negativelyimmersedcompactsubmaifnoldinspaceformofconstantcurvatureisaRiemannianproductofseveraltotallyumbilicalsubmanifoldsifthemeancurvatureandthescalarcurvatureofthesubmanifoldsatisfyacertainfunctionrelation.