简介:Inthispaper,thetwo-dimensionalMarcinkewiczintegralintroducedbySteinμ(f)(x)=(∫0x|∫|x-y|≤1|x-y|Ω(x-y)f(y)dy|2t-3dt)2isshowntobeofweaktype(1,1)andweightedweaktype(1,1)withrespecttopowerweight|x|"if-1<α<0,whereΩishomogeneousofdegree0.hasmeanvalue0andbelongstoLlog+L(S1).
简介:如果对一个简单图G的每一个与G的顶点数同奇偶的独立集I,都有G-I有完美匹配,则称G是独立集可削去的因子临界图.如果图G不是独立集可削去的因子临界图,而对任意两个不相邻的顶点x与y,G+xy是独立集可削去的因子临界图,则称G是极大非独立集可削去的因子临界图.本文刻画了极大非独立集可削去的因子临界图.
简介:Anewspectralproblemisproposed,andnonlineardifferentialequationsofthecorrespondinghierarchyareobtained.Withthehelpofthenonlinearizationapproachofeigenvalueproblems,anewfinite-dimensionalHamiltoniansystemonR2nisobtained.Ageneratingfunctionapproachisintroducedtoprovetheinvolutionofconservedintegralsanditsfunctionalindependence,andtheHamiltonianflowsarestraightenedbyintroducingtheAbel-Jacobicoordinates.Atlast,basedontheprinciplesofalgebracurve,thequasi-periodicsolutionsforthecorrespondingequationsareobtainedbysolvingtheordinarydifferentialequationsandinversingtheAbel-Jacobicoordinates.
简介:如果对一个简单图G的每一个与G的顶点数同奇偶的独立集1,都有G-I有完美匹配,则称G是独立集可削去的因子临界图.如果图G不是独立集可削去的因子临界图,而对任意两个不相邻的顶点x与y,G+zy是独立集可削去的因子临界图,则称G是极大非独赢集可削去的因子临界图.本文刻画了极大非独立集可削去的因子临界图.