简介：TheMelnikovmethodwasextendedtoperturbedplanarnon-Hamiltonianintegrablesystemswithslowly-varyingangleparameters.Basedontheanalysisofthegeometricstructureofunperturbedsystems,theconditionoftransverselyhomoclinicintersectionwasestablished.ThegeneralizedMelnikovfunctionoftheperturbedsystemwaspresentedbyapplyingthetheoremonthedifferentiabilityofordinarydifferentialequationsolutionswithrespecttoparameters.ChaosmayoccurinthesystemifthegeneralizedMelnikovfunctionhassimplezeros.

简介：Amultilayerflowisastratifiedfluidcomposedofafinitenumberoflayerswithdensitieshomogeneouswithinonelayerbutdifferentfromeachother.Itisanintermediatesystembetweenthesingle-layerbarotropicmodelandthecontinuouslystratifiedbaroclinicmodel.Sincethissystemcansimulatethebarocliniceffectsimply,itiswidelyusedtostudythelarge-scaledynamicprocessinatmosphereandocean.Thepresentpaperisconcernedwiththelinearstabilityofthemultilayerquasi-geostrophicflow,andtheassociatedlinearstabilitycriteriaareestablished.Firstly,thenonlinearmodelisturnedintotheformofaHamiltoniansystem,andabasicflowisdefined.ButitcannotbeanextremepointoftheHamiltonianfunctionsincethesystemisaninfinite-dimensionalone.Therefore,itisnecessarytoreconstructanewHamiltonianfunctionsothatthebasicflowbecomesanextremepointofit.Secondly,thelinearizedequationsofdisturbancesinthemultilayerquasi-geostrophicflowarederivedbyintroducinginfinitesimaldisturbancessuperposedonthebasicflows.Finally,thepropertiesofthelinearizedsystemarediscussed,andthelinearstabilitycriteriainthesenseofLiapunovarederivedundertwodifferentconditionswithrespecttocertainnorms.

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

简介：Newton定律是描述物体运动的基本定律,Hamiltonian方程则为运动的基本规律提供了另外一种表达.由Hamiltonian方程发展而来的Hamiltonian可积系统是现代孤立子理论的重要组成部分.本文是介绍从Newton运动定理到Hamiltonian可积系统的演化的系列文章的一部分,文中证明了一个关于线性斜对称算子为广义Hamiltonian的一个充分和必要条件.

简介：Newton定律是描述物体运动的基本定律，Hamiltonian方程则为运动的基本规律提供了另外一种表达。由Hamiltonian方程发展而来的Hamiltonian可积系统是现代孤立子理论的重要组成部分。文中证明了一个关于Korteweg—devries（KdV）类型的非线性发展方程的在加权Sobolev空间中的估计式。这一估计式对证明一类一般的非线性扩散型发展方程的不变性质是非常有用的。