简介:ThispaperinvestigatestherelationshipbetweenstatefeedbackandHamiltonicanrealization.Firest,itisprovedthatacompletelycontrollablelinearsystemalwayshasastatefeedbackstateequationHamiltonianrealization.NecessaryandsufficientconditionsareobtainedforittohaveaHamiltonianrealizationwithnaturaloutput.ThensomeconditionsforanaffinenonlinearsystemtohaveaHamiltonianrealizationaregiven.someconditionsforanaffinenonlinearsystemtohaveaHamiltonianrealizationaregiven.Forgeneralizedoutputs,theconditionsofthefeedback,keepingHamiltonian,arediscussed.Finally,theadmissiblefeedbackcontrolsforgeneralizedHamiltoniansystemsareconsidered.
简介:本文利用图的独立数和任意3个独立点集中距离2的点对邻域交,给出了图为Hamilton和Hamilton连通的新的充分条件
简介:ItisshownthatifGisahamiltonianbipartitegraphon2nverticesandδ(G)>2n/5+2,wheren≥60,thenGisbipancyclic.
简介:<正>IthasbeenconjecturedthatthereisahamiltoniancycleineveryfiniteconnectedCayleygraph.Inspiteofthedifficultyinprovingthisconjecture,weshowthatalmostallCayleygraphsarehamiltonian.Thatis,astheordernofagroupGapproachesinfinity,theratioofthenumberofhamiltonianCayleygraphsofGtothetotalnumberofCayleygraphsofGapproaches1.
简介:我们证明那在那里存在位于一种保角的公制、兼容的连接形式,和公制的类型Hamiltonian下面与歧管(我们把它称为几何图画),那能被放进与平常的Hamilton-Lagrange力学的通讯。二的动态等价的要求Hamiltonians打字,momenta由二幅图画产生了相等为乘都,是足够的决定保角的因素的扩大,在几何并列表示上定义,在它有到Hamiltonian-Lagrange图画的潜力的功能决定的所有订单的系数的analyticity的领域,在Hamilton-Lagrange并列表示,和它的衍生物上定义。相反地,如果保角的功能被知道,一幅Hamilton-Lagrange图画的潜力能以一个类似的方法被决定。我们证明在Hamilton-Lagrange图画的轨道的任意的本地变化能被变化在几何图画沿着geodesics产生并且建立为理解在几何图画的不稳定性怎么在不稳定性被表明提供一个基础的通讯原来的Hamiltonian运动。
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简介:ByvirtueoftheEinstein-Podolsky-Rosenentangledstate,whichisthecommoneigenvectoroftwopanicles'relativecoordinateandtotalmomentum,weestablishthebosonicoperatorversionoftheHamiltonianforaquantumpoint-masspendulum.TheHamiltoniandisplaysthecorrectSchroedlngerequationintheentangledstaterepresentation.ThecorrespondingHeisenbergoperatorequationswhichpredicttheangularmomentum-angleuncertaintyrelationarederived.Thequantumoperatordescriptionoftwoquantumpendulumscoupledbyaspringisalsoderived.
简介:Basedonthetheoryofcalculusofvariation,somesuffcientconditionsaregivenforsomeEuler-LagrangcequationstobeequivalentlyrepresentedbyfiniteoreveninfinitemanyHamiltoniancanonicalequations.Meanwhile,somefurtherapplicationsforequationssuchastheKdVequation,MKdVequation,thegenerallinearEulerLagrangeequationandthecylindricshellequationsaregiven.
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.
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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.
简介:二种高度维的谎言代数学和他们的环代数学被介绍,为哪个象TB层次一样包括BroerKaup(放射性元素)层次和散长波浪(DLW)层次的联合integrablecouplings扩展integrable模型的一些被获得。从联合integrablecouplings的减小,BK方程,DLW方程,和TB方程的相应联合integrablecouplings分别地被获得。特别,TB方程联合的联合integrable归结为著名mKdV方程的一些integrablecouplings。分别地,三种soliton层次的联合integrablecouplings的Hamiltonian结构被采用变化身份得出。最后,我们把进化方程的BK层次分解成代表和宽松的对被给其伴随的抑制x的流动和抑制tn的流动。