简介:TheauthorobtainsaWeierstrassrepresentationforsurfaceswithprescribednormalGaussmapandGausscurvatureinH3.AdifferentialequationaboutthehyperbolicGaussmapisalsoobtained,whichcharacterizestherelationamongthehyperbolicGaussmap,thenormalGaussmapandGausscurvature.TheauthordiscussestheharmonicityofthenormalGaussmapandthehyperbolicGaussmapfromsurfacewithconstantGausscurvatureinH3toS2withcertainalteredconformalmetric.Finally,theauthorconsidersthesurfacewhosenormalGaussmapisconformalandderivesacompletelynonlineardifferentialequationofsecondorderwhichgraphmustsatisfy.
简介:LetCdenotethesetofallk-subestsofann-set.AssumeAlohtaininCa,andAlohtainin(A,B)iscalledacross-2-intersectingfamilyif|AB≥2forandA∈A,B∈B.Inthispaper,thebestupperboundsofthecardinalitiesfornon-emptycross-2-intersectingfamillesofa-andb-subsetsareobtainedforsomeaandb,AnewproofforaFrankl-Tokushigetheorem[6]isalsogiven.
简介:SomecharacterizationsoftheconditionalexpectationoperatorsonLebesgue-BochnerspacesL_p(μ,X)aregiven,where1≤p<∞,p≠2.AlsoanexampleisgiventoshowthatthecharacterizationsoftheconditionalexpectationoperatorsonL_p(μ,X)aredifferentfromthatonL_p(μ)_zFinally,arepresentationoftheconstant-preservingcontractiveprojectiononspacesL_p(μ,X)isgotwhen0
简介:Animprovedrandomizedalgorithmoftheequivalent2-catalogsegmentationproblemispresented.Theresultobtainedinthispapermakessomeprogresstoanswertheopenproblembyanalyzethisalgorithmwithperformanceguarantee.A0.6378-approximationfortheequivalent2-catalogsegmentationproblemisobtained.
简介:Assumethatm≥2,pisaprimenumber,(m,p(p-1))=1,-1(Z/mZ)~*and[(Z/mZ)~*:]=4.Inthispaper,wecalculatethevalueofGausssumG(X)=Σ_(x∈F_q~*)x(x)ζ_p~(T(x))overF_q,whereq=p~f,f=((m))/4xisamultiplicativecharacterofF_qandTisthetracemapfromF_qtoF_p.Underourassumptions,G(x)belongstothedecompositionfieldKofpinQ(ζm)andKisanimaginaryquarticabeliannumberfield.WhentheGaloisgroupGal(K/Q)iscyclic,wehavestudiedthiscycliceaseinanotherpaper:'Gausssumsofindexfour:(1)cycliccase'(acceptedbyActaMathematicaSinica,2003).Inthispaperwedealwiththenon-cycliccase.
简介:这篇论文为3D在一张无穷地长圆柱的嘴在亚声的流动的全球存在和稳定性上涉及这个问题稳定的潜在的流动方程。如此的一个问题被Courant-Friedrichs显示在[8,p。377]:通过管的流动应该是被考虑一稳定,isentropic,无旋与圆柱的对称流动并且应该由与适当边界条件解决3D潜力流动方程坚定。由介绍一些合适加权的H?lder空格并且建立priori估计,当在否定无穷的亚声的流动的国家被给时,作者在一张3D嘴证明亚声的潜在的流动的全球存在和稳定性。关键词亚声的流动-潜在的流动方程-Bessel功能-加权的H?lder空格-全球存在2000苏布杰克特先生分类35L70-35L65-35L67-国家Basic支持的76N15工程中国(号码2006CB805902)的研究节目,中国(号码10871096)的国家自然科学基础和为江苏大学的先进才能的研究基础。
简介:<正>Weaddressthequestionthatifπ1-surjectivemapsbetweenclosedaspherical3-manifoldshavethesamerankonπ1theymustbeofnon-zerodegree.ThepositiveanswerisprovedforSeifertmanifolds,whichisusedinconstructingthefirstknownexampleofminimalHakenmanifold.Anothermotivationistostudyepimorphismsof3-manifoldgroupsviamapsofnon-zerodegreebetween3-manifolds.Manyexamplesaregiven.