简介:Anewspectralproblemisproposed,andnonlineardifferentialequationsofthecorrespondinghierarchyareobtained.Withthehelpofthenonlinearizationapproachofeigenvalueproblems,anewfinite-dimensionalHamiltoniansystemonR2nisobtained.Ageneratingfunctionapproachisintroducedtoprovetheinvolutionofconservedintegralsanditsfunctionalindependence,andtheHamiltonianflowsarestraightenedbyintroducingtheAbel-Jacobicoordinates.Atlast,basedontheprinciplesofalgebracurve,thequasi-periodicsolutionsforthecorrespondingequationsareobtainedbysolvingtheordinarydifferentialequationsandinversingtheAbel-Jacobicoordinates.
简介:Therelativisticproblemofspin-1/2fermionssubjecttovectorhyperbolic(kink-like)potential(~tanhkx)isinvestigatedbyusingtheparametricNikiforov-Uvarovmethod.TheenergyeigenvalueequationandthecorrespondingnormalizedwavefunctionsareobtainedintermsoftheJacobipolynomialsintwocases.
简介:Inthispaper,weshowthatnewmodifieddoublecosinetrigonometricsumsintroducedin[1]areinappropriate,theclassofdoublesequencesJdintroducedthereisunusableforsuchsumsandconsequentlytheresultsobtainedinitarecompletelyincorrect.WehereintroduceappropriatemodifieddoublecosinetrigonometricsumsmakingtheclassJdusableconsideringaparticulardoublecosinetrigonometricseries.
简介:AgraphGiscalledchromatic-choosableifitschoicenumberisequaltoitschromaticnumber,namelych(G)=χ(G).Ohba’sconjecturestatesthateverygraphGwith2χ(G)+1orfewerverticesischromaticchoosable.ItisclearthatOhba’sconjectureistrueifandonlyifitistrueforcompletemultipartitegraphs.Recently,Kostochka,StiebitzandWoodallshowedthatOhba’sconjectureholdsforcompletemultipartitegraphswithpartitesizeatmostfive.Butthecompletemultipartitegraphswithnorestrictionontheirpartitesize,forwhichOhba’sconjecturehasbeenverifiedarenothingmorethanthegraphsKt+3,2*(k-t-1),1*tbyEnotomoetal.,andKt+2,3,2*(k-t-2),1*tfort≤4byShenetal..Inthispaper,usingtheconceptoff-choosable(orL0-size-choosable)ofgraphs,weshowthatOhba’sconjectureisalsotrueforthegraphsKt+2,3,2*(k-t-2),1*twhent≥5.Thus,Ohba’sconjectureistrueforgraphsKt+2,3,2*(k-t-2),1*tforallintegerst≥1.
简介:首先介绍选举理论中的5种投票方法(简单多数、单轮决胜、系列决胜、Coombs法、Borda计数)和5条公平性准则(多数票、Condorcet获胜者、Condorcet失败者、无关候选人独立性、单调性),并用政治和社会领域的若干实例给以解释。然后给出著名的Arrow不可能性定理的两种不同的版本,以及对Arrow一条公平性准则的修正;按照修正后的准则,存在满足所有公平性准则的投票方法。
简介:给出了Banach空间中线性离散时间系统一致与非一致多项式膨胀性的概念,使其在相应空间中范数的增长速度不快于指数型增长,并用实例阐释了二者的关系.借助于指数型膨胀性的研究方法,讨论了其非一致多项式膨胀性的离散特征.作为应用,利用Lyapunov函数给出了相应概念的充要条件.得到了指数膨胀性理论中一些经典结论在非一致多项式膨胀情形下的变形.