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简介：§1.IntroductionIn[1],R.SchoenandS.T.Yanusedharmonicmaptostudythetopologyofanon-compactcompletestablehypersurfaceinamanifoldofnon-negativecurvature.Essentiallythemethodistoprovefirstthenonexistenceofsomekindofnonconstantharmonicmapandthentodrawtherelativeconclusionsconcerningthetopology.Suchnonexistencetheoremshavebeenobtainedin[3]and[4]incaseswheretheconcernedmanifoldsarecompact.Theaimofthispaperistostudythenon-compactcompletecase.Ourmainresultscanbestatedasfollows.

简介：ThispaperstudiestheuniquenessoftheharmonicmapsfromRnintoSn-1.Atfirstitisprovedthatthemapψ（x）=x|x|:Bn→Sn-1istheuniqueenergyminimizingharmonicmap.ThentheuniquenessoftheharmonicmapswithidentityboundaryvaluefromBntoSn-1follows.

简介：LetG(m,s,t,λ)bethenumberofwaysofλ-coloringalltherootednonseparableouterplanarmapswhicharesimpleandhavetheedgenumberm,thevalencysoftheroot-face,andthevalencytoftheroot-vertex.Thechromaticenumeratingfunctiong(x,y,z;λ.)=G(m,s,t;λ)x~my~sz~tisdetermined.Meanwhile,anumberofexplicitformulaeforenumeratingthiskindofmapsingeneralcaseandinLipartitecaseareprovided.

简介：在这篇文章，作者讨论二种新平面地图：平底锅扇子地图和电路边界地图，并且关于他们的枚举的功能向明确的表情提供不同参数。同时，为电路的二个明确的数公式有二个参数的立方的边界地图：尺寸和根脸的原子价，也被提取。关键词生根的地图-枚举功能-枚举-电路边界地图先生(2000)题目分类05C10-05C30

简介：Thisnoteshowsthatthenumberofrootedcubicplanarmaps(loopsandmulti-edgesareallowed)with2n-3non-root-vertices,n≥3,is

简介：Thispaperprovidesafunctionalequationsatisfiedbythedichromaticsumfunetionofrootedouterplanarmaps.Bytheequation,thedichromaticsumfunetioncanbefoundexplicitiy.

简介：<正>AconjugaeybetweenC1+αΣ-hyperboliccirclecoveringmapsisC1+αifithasapositivederivativeonsomepointintheΣ-set.

简介：Inthispaper,thenumberofcombinatoriallydistinctrootednonseparableouterplanarmapswithmedgesandthevalencyoftheroot-facebeingnisfoundtobe(m-1)!(m-2)!:(n-1)!(n-2)!(m-n)!(m-n+1)!and,thenumberofrootednonseparableouterplanarmapswithmedgesisalsodeterminedtobe(2m-2)!:(m-1)!m!,whichisjustthenumberofdistinctrootedplanetreeswithm-1edges.

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简介：Inthispaper,wediscusstherank-l-preservinglinearmapsonnestalgebrasofHilbertspaceoperators.WeobtainseveralcharacterizationsofsuchlinearmapsandapplythemtoshowthataweaklycontinuouslinearhijectiononanatomicnestalgebraisidempotentpreservingifandonlyifitisaJordanhomomorphism,andinturn,ifandonlyifitisanautomorphismorananti-automorphism.

简介：Thispaperstudiesthedynamicsoftheanalyticfamilyz+1/z+banddescribesthetopologyoftheparameterspace,structuralstabilityandJ-stability.Themappingclassgroupofalmostallmapsoftheabovefamilyisdetermined.

简介：在里面[加拿大数学。公牛。22，pp。513515，1979]，作者延长了一有趣(最好的近似)Ky扇子的定理[看见定理2，数学。Z。112，pp。234240]到在一个Banach空格在一个关上的球定义并且在一个Hilbert空格在一个关上的凸的子集上定义的压缩地图。在里面[J。近似理论52，pp。141148，1988]，作者和日元进一步在一个Hilbert空格扩大了它到1-set-contractive地图。在这份报纸，我们将探讨几个相关问题。首先，我们扩大林，日元为1-set-contractive地图，但是到结果满足更弱的状况，它允许我们包括概括收缩地图。第二，我们让路为nonexpansive地图构造最好的近似(不仅仅存在结果)。第三，我们给上的条件最好的近似{un|n=1,2，}收缩的一个序列{fn|n=1,2，}将收敛到收缩f的最好的近似u。第四，为nonexpansive地图的普通最好的近似定理被证明。到为弱里面的地图和其它的固定的点定理的应用为所有那些四个话题被给。

简介：BymeansofthetheoryofharmonicmapsintotheunitarygroupU(N),theauthorsstudyharmonicmapsintothesymplecticgroupSp(N).Thesymplecticunitonandsymplecticex-tendedunitonareintroduced.ThemethodofthesymplecticBacklundtransformationandtheDarbouxtransformationisusedtoconstructnewsymplecticunitonsfromaknownone.

简介：LetUn（C）,GLn（C）andMn（C）bethen-degreeunitarygroup,thenn-degreegenerallineargroupandthesemigroupsofalln×nmatricesovercomplexnumberfieldCrespec-tively.Hochwaldin[1]showedthatiff:Un（C）→Mn（C）isaspectrum-preservingmulti-plicativemap,thenthereexistsamatrixRinGLn（C）suchthatf（A）=R-1ARforallA∈

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简介：TheauthorsgivesomeconstructivefactorizationtheoremsforpluriharmonicmapsfromaKaehlermanifoldintotheunitarygroupU(N)andobtainsomeoptimalupperboundsofminimalunitonnumbers.

简介：让G是代数学是其谎言的一个谎言组二次。在纸，“非可交换的Weil代数学”，Alekseev和Meinrenken构造了明确的G微分的空间同形并且。他们显示出那)并且Hbas*(和是的超级谎言代数学的通用包围代数学照宗规地与二次的谎言代数学联系了。基本cohomology戒指Hbas*()和Hbas*(并且分别地。因此他们证明了的，等价于超级Duflo地图随超级谎言代数学的伴随行动变换的事实，并且当限制了为invariants的空间时，超级Duflo地图是代数学同形。

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简介：<正>InthispaperwestudysurfacesinS~4andtheirtwistorGaussmaps.SomenecessaryandsufficientconditionsthatthetwistorGaussmapisharmonicaregiven.Wefindmanyexamplesofnonisotropicharmonicmapsfromasurfaceto(?)P~3.