简介:<正>Inthispaperwegivethenecessaryandsufficientconditionsforallfinitecriticalpointsofquadraticdifferentialsystemstobeweakfoci,andsolveanopenproblemproposedbyYanqianYe.
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简介:Itisprovedthatfork≥71,thecircumferencec(G)ofa3-connectedk-regulargraphGonnverticesisatleastmin{|G|,3k+5}.Thisresultisessentiallybestpossible.
简介:LetFF_vbethesetoffaultynodesinann-dimensionalfoldedhypercubeFQ_nwith|FF_v|≤n-1andallfaultyverticesarenotadjacenttothesamevertex.Inthispaper,weshowthatifn≥4,theneveryedgeofFQn-FF_vliesonafault-freecycleofeveryevenlengthfrom6to2~n-2|FF_v|.
简介:一张标记的图是订的对(G,L)由图G和它的标记的L组成:V(G)鈫?{1,2,鈥?n},在此n=|V(G)|。在一张标记的图的一条增加的nonconsecutive路径(G,L)任何一个是一条路径(u1,u2,鈥?uk)(k鈮?2)在G以便L(ui)+为所有i=的2鈮?L(ui+1)1,2,鈥?k?1或顺序1的一条路径。增加nonconsecutive路径在的全部的数字(G,L)被d表示(G,L)。如果标记的L生产最大的d,标记的L是最佳的(G,L)。在这份报纸,在Zverovich(2004)的比那简单的一个方法被给获得路径的最佳的标记。象周期和星那样的另外的特殊的图的最佳的标记被获得。
简介:Thispaperinvestigatesthepredator-preysystem:x=k1(x-ax)-k(x)y,y=(-k3+βk(x)ywit.k(x)=k2x,x≤x,k2x,x>τ,whereα,β,τ;k1,k2,k3arepositiveconstants.Themainresultsareasfollows(i)Incasek3-βk2τ≥0system(1)hasnolimitcycle.(ii)Incasek3-βk2τ<0,k1+k3-βk2τ>0,andforO<α<<1,system(1)atleasthastwolimitcycles.
简介:InthispaperweprovethatifTisaregularn-partitetournamentwithn≥>6,theneacharcofTliesonak-cyclefork=4,5,…,n.OurresultgeneralizestheoremsduetoAlspachandGuorespectively.
简介:Inthispaper,HamiltoniancyclesanddecompositionsofCayleydigraphsareinvestigat-ed.Sufficientconditionsaregivenforthesetwoproblemsrespectively.Furthermore,theconditionsarealsonecesaaryfor2-regularCayleydisraphs,Inaddition,someknownresultsabouttheCartesianproductsoftwodirectedcyclesarealsodeduced.
简介:UsingtheaveragingtheoryoffirstandsecondorderwestudythemaximumnumberoflimitcyclesofgeneralizedLinarddifferentialsystems{x=y+εhl1(x)+ε2hl2(x),y=-x-ε(fn1(x)y2p+1+gm1(x))+∈2(fn2(x)y2p+1+gm2(x)),whichbifurcatefromtheperiodicorbitsofthelinearcenterx=y,y=-x,whereεisasmallparameter.Thepolynomialshl1andhl2havedegreel;fn1andfn2havedegreen;andgm1,gm2havedegreem.p∈Nand[·]denotestheintegerpartfunction.
简介:Inthispaper,weinvestigatethenumber,locationandstabilityoflimitcyclesinaclassofperturbedpolynomialsystemswith(2n+1)or(2n+2)-degreebyconstructingdetectionfunctionandusingqualitativeanalysis.Weshowthatthereareatmostnlimitcyclesintheperturbedpolynomialsystem,whichissimilartotheresultofPerkoin[8]byusingMelnikovmethod.Forn=2,weestablishthegeneralconditionsdependingonpolynomial'scoefficientsforthebifurcationlocationandstabilityoflimitcycles.Thebifurcationparametervalueoflimitcyclesin[5]isalsoimprovedbyus.Whenn=3thesufficientandnecessaryconditionsfortheappearanceof3limitcyclesaregiven.Twonumericalexamplesforthelocationandstabilityoflimitcyclesareusedtodemonstrateourtheoreticalresults.
简介:Thepaperapproachestheproblemofthecommandfunctionsofgalvanometer-basedscanners(GS)thatarenecessarytoproducethelinearplusparabolicscanningfunctionoftheGS,whichwehaveprovedpreviouslytoproducethehighestpossibledutycycle(i.e.,timeefficiency)ofthedevice.Wehavecompletedthistheoreticalaspect(whichcontradictedwhathasbeenstatedpreviouslyintheliterature,whereithasbeenconsideredthatthelinearplussinusoidalscanningfunctionwasthebest)withtheexperimentalstudyofthemostusedscanningfunctionsoftheGSs(sawtooth,sinusoidalandtriangular),withapplicationsinbiomedicalimaging,inparticularinopticalcoherencetomography,demonstratingthatthetriangularfunctionisalwaysthebestonetobeapplied,frombothanopticalandamechanicalpointofview.Inthepresentstudytheinputvoltage/commandfunctionwhichshouldbeappliedtotheGStoproducethedesiredtriangularscanningfunction(withcontrollednon-linearityforthefastestpossiblestop-and-turnportions)wasdeterminedanalytically,inrelationshipwiththeactivetorquethatdrivesthedevice.Thiscommandfunctionisanalyzedwithregardtothespecific,respectivelyrequiredparametersoftheGS:naturalfrequencyanddampingfactor,respectivelyscanspeedandamplitude.ThemodelinginanopenloopcontrolstructureoftheGSisfinallydiscussedasatrade-offbetweenusingthehighestpossibledutycycleandminimizingthemaximumpeaksoftheinputvoltage.