简介:LetMbeacompactminimalhypersurfaceofsphereSn+1(1).Let(M)beH(r)-torusofsphereSn+1(1).AssumetheyhavethesameconstantmeancurvatureH,theresultin[1]isthatifSpec0(M,g)=Spec0((M),g),thenfor3≤n≤6,r2≤n-1/norn≥6,r2≥n-1,thenMisisometricto(M).Weimprovedtheresultandprovethat:ifSpec0(M,g)=Spec0((M),g),thenMisisometricto(M).Generally,ifSpecp(M,g)=Specp((M),g),herepisfixedandsatisfiesthatn(n-1)≠6p(n-p),thenMisisometricto(M).
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简介:Asimplifiedmultisupportresponsespectrummethodispresented.Thestructuralresponseisasumoftwocomponentsofastructurewithafirstnaturalperiodlessthan2s.Thefirstcomponentisthepseudostaticresponsecausedbytheinconsistentmotionsofthestructuralsupports,andthesecondisthestructuraldynamicresponsetogroundmotionaccelerations.Thismethodisformallyconsistentwiththeclassicalresponsespectrummethod,andtheeffectsofmultisupportexcitationareconsideredforanymodalresponsespectrumormodalsuperposition.Iftheseismicinputsateachsupportarethesame,thesupportdisplacementscausedbythepseudostaticresponsebecomerigidbodydisplacements.Theresponsespectruminthecaseofmultisupportexcitationsthenreducestothatforuniformexcitations.Inotherwords,thismultisupportresponsespectrummethodisamodificationandextensionoftheexistingresponsespectrummethodunderuniformexcitation.Moreover,mostofthecoherencycoefficientsinthisformulationaresimplifiedbyapproximatingthegroundmotionexcitationaswhitenoise.Theresultsindicatethatthissimplificationcanreducethecalculationtimewhilemaintainingaccuracy.Furthermore,theinternalforcesobtainedbythemultisupportresponsespectrummethodarecomparedwiththoseproducedbythetraditionalresponsespectrummethodintwocasestudiesofexistinglong-spanstructures.Becausetheeffectsofinconsistentsupportdisplacementsarenotconsideredinthetraditionalresponsespectrummethod,thevaluesofinternalforcesnearthesupportsareunderestimated.Theseregionsareimportantpotentialfailurepointsanddeservespecialattentionintheseismicdesignofreticulatedstructures.
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简介:Ahybridtriplesystemofordervandindexλ,denotedbyHTS(v,λ),isapair(X,B)whereXisav-setandBisacollectionofcyclictriplesandtransitivetriplesonX,suchthateveryorderedpairofXbelongstoλtriplesofB.AnoverlargesetofdisjointHTS(v,λ),denotedbyOLHTS(v,λ),isacollection{(Y\{y},Ai)}i,suchthatYisa(v+1)-set,each(Y\{y},Ai)isanHTS(v,λ)andallAisformapartitionofallcyclictriplesandtransitivetriplesonY.Inthispaper,weshalldiscusstheexistenceproblemofOLHTS(v,λ)andgivethefollowingconclusion:thereexistsanOLHTS(v,λ)ifandonlyifλ=1,2,4,v≡0,1(mod3)andv≥4.
简介:Baiyuneboite-(Ce)isanewfluor-carbonatemineral.Basedonthefinedataonthestructureofthemineral,thefactorgroupandnormalcoordinateanalysesforitsinfraredspectrumhavebeencarriedout.ThefactorgroupanalysesindicatethatthesitegroupandfactorgroupsplittingsoftheinternalvibrationbandsofCO3^2-ionsdonotoccurandthatthedoublebandsofnormalmodesresultfromtwonon-equalsetsofCO3^2-ionsinthecrystalstructure,Thenormalcoordinateanalysesgivethestretchingforceconstants.bendforceconstantsandcalculatedfrequenciesofCO3^2-ions.Thecalculationsofpotentialenergydistributionallowustoassignv3andv4tothestretchingvibrationandthebendvibrationofCO3^2-ions.respectively.
简介:Weintroducefourtypesofspecialeigenvalueswhichlieontheboundaryofcertaininclusionregionsforthespectrumofacomplexsquarematrix,i.e.,R_r(G_c)-,O(a)-,B_r(B_c)-.andOB(a)-eigenvalues.Thenwecharacterizetheseeigenvaluesandtheircorrespondingeigenvectorsforirreduciblematrices,Finallywegivesomenewsufficientconditionsforanirreduciblecomplexmatrixtobenonsingular.
简介:Thereisatypeofnodalsurfaceimposedbysymmetryonwavefunctions.Thesesurfacesarecrucialtotheorderingoflow-lyingstates.Basedonananalysisofthistypeofsurfaceandbasedonexistingtheoreticalresults,thefeatureofthelow-lyingspectrumoftheHe-tetramerisstudied,andthecandidatesofboundstatesandnarrowresonancesaresuggested.