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简介：<正>IthasbeenconjecturedthatthereisahamiltoniancycleineveryfiniteconnectedCayleygraph.Inspiteofthedifficultyinprovingthisconjecture,weshowthatalmostallCayleygraphsarehamiltonian.Thatis,astheordernofagroupGapproachesinfinity,theratioofthenumberofhamiltonianCayleygraphsofGtothetotalnumberofCayleygraphsofGapproaches1.

简介：§1.IntroductionInthepresentpaper,westudyfollowingHamiltoniansystemofSecond-order:(1)withtheboundaryconditionx(0)=x(2jr),x’(0)=x’(2w),(2)wherep(t)￡O(R,Rn'),G(t,x)￡O(RxR',R).P(-)and&(,x)are25F-periodiofunctions.Vj,orG’x(t,a/)willdenotethegradientwithrespecttox.Moreover,weshallalwaysassumethatG’x(t,x)iscontinuous.

简介：Inthispaper,thelinearstabilityofsymplecticmethodsforHamiltoniansystemsisstudied.Inparticular,threeclassesofsymplecticmethodsareconsidered:symplecticRunge-Kutta(SRK)methods,symplecticpartitionedRunge-Kutta(SPRK)methodsandthecompositionmethodsbasedonSRKorSPRKmethods.ItisshownthattheSRKmethodsandtheircompositionspreservetheellipticityofequilibriumpointsunconditionally,whereastheSPRKmethodsandtheircompositionshavesomerestrictionsonthetime-step.

简介：Inthispaper,HamiltoniancyclesanddecompositionsofCayleydigraphsareinvestigat-ed.Sufficientconditionsaregivenforthesetwoproblemsrespectively.Furthermore,theconditionsarealsonecesaaryfor2-regularCayleydisraphs,Inaddition,someknownresultsabouttheCartesianproductsoftwodirectedcyclesarealsodeduced.

简介：LetGbeafinitegroup,andSbeasubsetofG.Thebi-CayleygraphBCay(G,S)ofGwithrespecttoSisdefinedasthebipartitegraphwithvertexsetG×{0,1}andedgeset{(g,0),(gs,1)|g∈G,s∈S}.Inthispaper,wefirstprovidetwointerestingresultsforedge-hamiltonianpropertyofCayleygraphsandbi-Cayleygraphs.Next,weinvestigatetheedge-hamiltonianpropertyofΓ=BCay(G,S),andprovethatΓishamiltonianifandonlyifΓisedge-hamiltonianwhenΓisaconnectedbi-Cayleygraph.

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简介：ThispaperstudiestheexistenceofperiodicsolutionsfornonautonomousasymptoticallylinearHamiltoniansystems.ByusingtheZ_pindextheorysomemultiplicityresultsfornonautonomoussystemsaregiven,whichgeneralizesomeresultsforautonomoussystemsduetoAmmanandZenhder.

简介：§I.IntroductionInthispaperwearelookingforsolutionsofthefollowingHamiltoniansystemofsecondorder:wherex=（x1,x2）andVsatisfies（V.1）V:R×R2→RisaC1-function,1-periodicInt,（V.2）Visperiodicinx1withtheperiodT>0,（V.3）V→O,Vx→Oas|x2|→∞,uniformlyin（t,x1）.

简介：Abstract.LetSnbethesymmetricgroup

简介：SameexistenceandmultiplicityofhomoclinicorbitforsecondorderHamiltoniansystem¨↑x-a（t)x+Wx(t,x)=0aregivenbymeansofvariationalmethods,wherethepotentialV(t,x)=-1/2a（t)|s|^2+W(t,s)isquadraticinsatinfinityandsubquadraticinsatzero,andthefunctiona（t)satisfiesthegrowthconditionlimt→∞∫t…t+la（t)dt=+∞，A↓ι∈R^1.

简介：Anewdiscreteisospectralproblemisintroduced,fromwhichthecoupleddiscreteKdVhierarchyisdeducedandiswritteninitsHamiltonianformbymeansofthetraceidentity.ItisshownthateachequationintheresultinghierarchyisLiouvilleintegrable.Furthermore,aninfinitenumberofconservationlawsareshownexplicitlybydirectcomputation.

简介：Inthispaperwestudytheexistenceofinfinitelymanyperiodicsolutionsforsecond-orderHamiltoniansystems{ü(t)+A(t)u(t)+▽F(t,u(t))=0,u(0)-u(T)=(0)-(T)=0,whereF(t,u)iseveninu,and▽(t,u)isofsublineargrowthatinfinityandsatisfiestheAhmad-Lazer-Paulcondition.

简介：WepresentanewdiscreteintegrablecouplingsystembyusingthematrixLaxpairU,V∈sl(4).AnovelspectralproblemofmodifiedTodalatticesolitonhierarchyisconsidered.Then,anewdiscreteintegrablecouplingequationhierarchyisobtainedthroughthemethodoftheenlargedLaxpair.Finally,weobtaintheHamiltonianstructureoftheintegrablecouplingsystemofthesolitonequationhierarchyusingthematrix-formtraceidentity.ThisdiscreteintegrablecouplingsystemincludesakindofamodifiedTodalatticehierarchy.

简介：InthispaperwedevelopakindofdissipativediscreteschemeforthecomputationofhomoclinicorbitsnearTB-pointinHamiltoniansystems.Itisprovedbyusingcontinuationmethodthatwhenthedissipativetermanditscoefficientaresuitablychosen,thisschemepossessesdiscretehomoclinicorbits,whichapproximatethecontinuoushomoclinicorbitswithsecondorderaccuracyw.r.totime-stepsize.

简介：Uponusingthedenotativetheoremofanti-HermitiangeneralizedHamiltonianmatrices,wesolveeffectivelytheleast-squaresproblemmin‖AX-B‖overanti-HermitiangeneralizedHamiltonianmatrices.WederivesomenecessaryandsufficientconditionsforsolvabilityoftheproblemandanexpressionforgeneralsolutionofthematrixequationAX=B.Inaddition,wealsoobtaintheexpressionforthesolutionofarelevantoptimalapproximateproblem.

简介：作者调查eigen的系统或2的根向量的完全性