简介:这篇文章与库仑潜在的x考虑3D-Hartree-type方程的一个家庭(?1),其起始的数据震荡以便一苛性出现。在线性几何光学盒子中,由使用Lagrangian积分,对答案在外面的一致描述苛性、近苛性被获得。给词调音:Hartree方程;几何光学;Lagrangian积分
简介:这份报纸使描述有弹性的字符串的一个3-dimensional网络的颤动的非线性的波浪方程的一个系统担心。作者导出方程和适当节的条件,决定平衡解决方案,并且,由使用quasilinear的方法夸张系统,证明那因为树联网天赋起始,边界值问题有古典解决方案在拉长的平衡解决方案的邻居存在。然后,这的本地可控制性近联网在某个指定时间间隔的配置被证明的如此的平衡。最后,它被证明那,给二不同平衡状态令人满意某些条件,在足够地大的时间间隔上在第二平衡的一位合适的邻居在一平衡的一位足够小的邻居从状态控制网络到任何状态是可能的。
简介:Itisprovedthatevery3-connectedlooplessmultigraphhasmaximumgenusatleastone-thirdofitscyclerankplusoneifitscyclerankisnotlessthanten,andifitscyclerankislessthanten,itisupper-embeddable.Thislowerboundistight.Thereareinfinitelymany3-connectedlooplessmultigraphsattainingthisbound.
简介:Inthispaper,wefirstshowtheglobalexistence,uniquenessandregularityofweaksolutionsforthehyperbolicmagnetohydrodynamics(MHD)equationsinR~3.ThenweestablishthatthesolutionswithinitialdatabelongingtoH~m(R~3)∩L~1(R~3)havethefollowingtimedecayrate:║▽~mu(x,t)║~2+║▽~mb(x,t)║~2+║▽~(m+1)u(x,t)║~2+║▽~(m+1)b(x,t)║~2≤c(1+t)~(-3/2-m)forlarget,wherem=0,1.
简介:<正>LetMbeacompactminimalsurfaceinS3.Y.J.Hsuprovedthatif‖S‖2≤2(21/2π,thenMiseithertheequatorialsphereortheCliffordtorus,where5"isthesquareofthelengthofthesecondfundamentalformofM,‖·‖2denotestheL2-normonM.Inthispaper,wegeneralizeHsu’sresulttoanycompactsurfacesinS3withconstantmeancurvature.
简介:InthispaperwestudythecomputationalperformanceofvariantsofanalgebraicadditiveSchwarzpreconditionerfortheSchurcomplementforthesolutionoflargesparselinearsystems.Inearlierworks,thelocalSchurcomplementswerecomputedexactlyusingasparsedirectsolver.Therobustnessofthepreconditionercomesatthepriceofthismemoryandtimeintensivecomputationthatisthemainbottleneckoftheapproachfortacklinghugeproblems.InthisworkweinvestigatetheuseofsparseapproximationofthedenselocalSchurcomplements.TheseapproximationsarecomputedusingapartialincompleteLUfactorization.Suchanumericalcalculationisthecoreofthemulti-levelincompletefactorizationsuchastheoneimplementedinpARMS.Thenumericalandcomputingperformanceofthenewnumericalschemeisillustratedonasetoflarge3Dconvection-diffusionproblems;preliminaryexperimentsonlinearsystemsarisingfromstructuralmechanicsarealsoreported.