简介：Assumethateachcompletelyirrationalnoncommutativetorusisrealizedasaninductivelimitofcirclealgebras,andthatforacompletelyirrationalnoncommutativetorusAwofrankmthereareacompletelyirrationalnoncommutativetorusAρofrankmandapositiveintegerdsuchthattr(Aw)=1/d.tr(Aρ).ItisprovedthatthesetofallC^*-algebrasofsectionsoflocallytrivialC^*-algebrabundlesoverS^2withfibresAωhasagroupsturcture,denotedbyπ1^s(Aut(Aω)),whichisisomorphictoZifEd>1and{0}ifd>1.LetBcdbeacd-homogeneousC^*-algebraoverS^2×T^2ofwhichnonon-trivialmatrixalgebracanbefactoredout.ThesphericalnoncommutativetorusSρ^cdisdefinedbytwistingC^*(T2×Z^m-2)inBcd×C^*(Z^m-3)byatotallyskewmultiplierρonT^2×Z^m-2。ItisshownthatSρ^cd×Mρ∞isisomorphictoC(S^2)×C^*(T^2×Z^m-2,ρ）×Mcd(C)×Mρ∞ifandonlyifthesetofprimefactorsofcdisasubsetofthesetofprimefactorsofp.

简介：ThispapercontinuestheworkofD.MacHale,D.Flannery（Proc.R.Ir.Acad.81A,209—215;83A,189—196）andtheauthor（Proc.R.Ir.Acad,90A,57—62;J.SouthwestChinaNormalUniversity15,No.1,21.—28）onthetopicon“FinitegroupswithgivenAutomorphismgroup”.Thefollowingresultisproved:LetGbeafinitegroupwithAutGaSchmidtgroup.ThenGisisomorphictoS3orKlain4-group.,orDsuchthatAutD=InnD.DisaSchmidtgroupoforder2?p.S2（∈Syl2D）isanormalandspecialgroupexoeptasupersperspecialgroupwithoutcommutativegenerators.

简介：ThispapergivesadefinitionofpermanentoptimaldatapointofLeastAbsoluteDeviation(LAD)problem.Sometheoreticalresultsonnon-degenerateLADproblemareobtained.ForcomputingLADproblem,anefficient,algorithmisgivenaccordingtotheideaofpermanentoptimaldatapoint.Numericalexperienceshowsthatouralgorithmisbetterthanmanyofothers,includingthefamousBRalgorithm.

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简介：Itisprovedthatthereisnochaoticgroupactionsonanytopologicalspacewithfreearc.InthispaperthechaoticactionsofthegrouplikeG×F,whereFisafinitegroup,arestudied.Inparticular,underasuitableassumption,ifFisacyclicgroup,thenthetopologicalspacewhichadmitsachaoticactionofZ×Fmustadmitachatotichomeomorphism.Atopologicalspacewhichadmitsachaoticgroupactionbutadmitsnochaotichorneomorphismisconstructed.

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简介：一、什么是STUDYGROUPSTUDYGROUP是牛津大学的A.B.Tayler博士和当时他的学生J.Ockendon等人在1968年创立的,它的原名是OxfordStudyGroupwithIndustry。这种活动历时一周,是由数学工作者和工业界人士参加的旨在解决实际问题的研讨会。在研讨会的第一天,由工业界代表陈述要解决的问题和目的要求,通常会有5~6个问题。后续2~3天按问题分组讨论,试图建立问题的数学模型和求解方法来解决问题。若问题比较

简介：WeknowthatforacodeC,it‘sveryimportanttofindouttheAutomorphismgroupAutCofC.However,itisverydifficulttoseekentireAutC.Inthispaper,usingtheG.Iofmatricesoverafinitefield,wegiveseveralmethodstojudgewhetherapermutationσ∈S_n.(Symmetricgroup)belongstoAutCornot.Theyarehelpfulforthepurposetoex-

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简介：我们证明为四元数海森堡组上的sublaplacian的限制操作员从Lp被围住到Lp如果1p$\tfrac{4}{3}$\tfrac{4}{3}。这与海森堡组，限制操作员没从Lp在上被围住到Lp不同除非p=1。

简介：WeconsiderHardyspaceswithvariableexponentsdefinedbygrandmaximalfunctionontheHeisenberggroup.ThenweintroducesomeequivalentcharacterizationsofvariableHardyspaces.ByusingatomicdecompositionandmoleculardecompositionwegettheboundednessofsingularintegraloperatorsonvariableHardyspaces.WeinvestigatetheLittlewood-Paleycharacterizationbyvirtueoftheboundednessofsingularintegraloperators.

简介：为海森堡组，我们介绍h-quasiconvexfunctions的概念。我们证明h-quasiconvex功能和h凸的集合的观点是相等的并且h-quasiconvex功能局部地从上面被围住，并且而且导出那h-convexfunctions局部地被围住，因此它是局部地由由Danielli-Garofalo-Nhieu使用最近的结果连续的Lipschitz。最后，我们给第一衍生物ofh-quasiconvex功能的L∞标准的估计。

简介：在这份报纸，作者在homotopy上学习homologically小的symplectic组行动椭圆形的表面E(n)并且得到一些刚硬结果。

简介：Theauthorconstructsthesheafofgeneralizedfundamentalgroupofatopologicalspace.Xandobtainstherelationshipbetweenits1stcohomologysetandallcoveringspacesofXundersuitableconditionsimposeduponX.

简介：ＡＤＭＩＳＳＩＢＬＥＷＡＶＥＬＥＴＳＡＳＳＯＣＩＡＴＥＤＷＩＴＨＴＨＥＴＲＡＮＳＦＯＲＭＧＲＯＵＰＯＮＲＨＥＪＩＡＮＸＵＮＡＮＤＰＥＮＧＬＩＺＨＯＮＧＡｂｓｔｒａｃｔ．ＬｅｔＰｂｅｔｈｅｔｒａｎｓｆｏｒｍｇｒｏｕｐｏｎＲｎ，ｔｈｅｎＰｈａｓａｎａｔｕ...

简介：TheauthorsgivesomeconstructivefactorizationtheoremsforpluriharmonicmapsfromaKaehlermanifoldintotheunitarygroupU(N)andobtainsomeoptimalupperboundsofminimalunitonnumbers.

简介：LetM(2)bethegroupofrigidmotionsoftheplane.TheFouriertransformandthePiancherelformulaonM(2)canbeexplicitlygivenbythegeneralgrouprepresentationtheory.Usingthisfact.weestablishakindofuncertaintyprincipleonM(2).Theresultcaneasilybegeneralizedtohigherdimensionalcases.AnapplicationoftheresultyieldsanuncertaintyprincipleontheEuclideanspacesobtainedbyR.S.Strichartz.

简介：让f在局部性的非各向同性的Sobolev空间W_(loc)~(1，p)(H~n)在n维的海森堡组H~n=C~nxR，在此1≤p<2是的Q和Q=2n+H~n的同类的尺寸。假定椭圆形的坡度是的潜水艇gloabllyL~pintegrable，即，f_(H~n)|▽_(H~n)f|~pdu是有限的。我们在全部spaceH~n上为f证明Poincare是不平等。用我们证明的这不平等，减去某个常数的功能f在thenonisotropicSobolev空间，这在标准下面由C_0~∞(H~n)的结束形成了(∫_(H~n)|f|~((Q_p)/(Q-p)))~((Q-P)/(Q_p))(∫_(H~n)|▽_(H~n)f|~p)~(1/p)。我们将也证明为H~n上的如此的Poincare不平等的最好的常数和extremals与为H~n上的Sobolevinequalities的那些一样。用到L~(2Q)/(Q-2)的锋利的常数和extremalsforL~2上的Jerison和李的结果海森堡组上的Sobolev不平等，我们因此在H~n上为上述的Poincare不平等到达明确的最好的常数什么时候p=2。我们也在HeisenberggroupH~n上在公制的球上为本地Poincare不平等导出最好的常数的更低的界限。

简介：组G的Wielandt亚群，由w(G)表示了，是G的所有低于正常的亚群的normalizers的交叉。在这份报纸，作者为每整数i为最大的班G，为所有整数i的任何一个wi(G)=i(G)或wi(G)=i+1(G)的p组显示出那，并且为在有K1的G的每正常亚群K的w(G/K)=(G/K)。同时，为最大的班的常规p组的一个必要、足够的条件令人满意的w(G)=2(G)被给。最后，如果G是有基本z(G)的non-abelianp组，作者证明力量自守组PAut(G)是基本abelianp组?\mho1(G)\zeta(G)\cap\mho_1(G)。

简介：Thispaperconsiderssingle-machineschedulingproblemsingrouptechnologywiththejobs'processingtimesbeingsimplelinearfunctionsoftheirstarttimes.Theobjectivefunctionsaretheminimizingofmakespanandtotalweightedcompletiontime.SomeoptimalconditionsandalgorithmsaregivenandthefactthattheproblemoftotalweightedcompletiontimesisNP-hardisproved.