学科分类
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111 个结果
  • 简介:LetT=(T(t))t≥0beaboundedC-regularizedsemigroupgeneratedbyAonaBanachspaceXandR(C)bedenseinX.WeshowthatifthereisadensesubspaceYofXsuchthatforeveryx∈Y,σu(A,Cx),thesetofallpointsλ∈iRtowhich(λ-A)^-1Cxcannotbeextendedholomorphically,isatmostcountableandσr(A)NiR=Ф,thenTisstable.AstabilityresultforthecaseofR(C)beingnon-denseisalsogiven.Ourresultsgeneralizetheworkonthestabilityofstronglycontinuoussenfigroups.

  • 标签: G-正半群 稳定性 巴拿赫空间 生成子 强连续
  • 简介:TwospectralsequencesaredronedrespectivelyforcohomologiesH^P(Ωf1k-,0)andH^P(Af,k-,0)ofsingularitiesofC^∞mappings.Theyarefinitelydimensiionalnewinvarancesunderrightequivalencesandcontacttransformationsrespectively.FormuLaetobecomputedbylinearalgebrsareproved.

  • 标签: 谱序列 上同调 奇异性 C^∞映射
  • 简介:Inthispaper,weintroduceaconditionweakerthantheLpdifferentiability,whichwecallCpcondition.Weprovethatifafunctionsatisfiesthisconditionatapoint,thenthereexiststhebestlocalapproximationatthatpoint.WealsogiveanecessaryandsufficientconditionforthatafunctionbeLpdifferentiable.Inaddition,westudytheconvexityofthesetofclusterpointsofthenetofbestappoximationsoff,{Pe(f)}ase→0.

  • 标签: 最佳局部逼近 充分必要条件 函数 可微
  • 简介:Inthispaper,weapplythecontractionmappingtheoremtoestablishsomeboundedandunboundedadditiveperturbationtheoremsconcerninglocalC-semigroups.SomegrowthconditionsofperturbationsoflocalC-semigroupsarealsoestablished.

  • 标签: 扰动定理 局部C半群 映射定理 生长条件 有界
  • 简介:LetGbeasecondcountablelocallycompactgroupoidwithHaarsystem{λuH},HbeaclosedsubgroupoidcontainingG^0withHaarsystem{λuH}.T.MasudaintroducedtheC^*-Groupoiddynamicsystem(G,A,α)anditsreducedcrossedproductCrea(G,A)in[2]:whereAisC^*-algebraαisthekomomorphismG→Aut(A).InthispapertheauthorintroducestheC^*-groupoiddynamicsystems(H,A,α/H)and(H\G2,A,^-α)inducedby(G,A,α)andprovesthatC*red(H,A)andC^*red(H\G^2,A)arestronglyMoritaequivalentMoreovertheinducedrepresentationfromC^*red(H,A)toC^*red(G,A)isgot.

  • 标签: C^*-群力学系统 听觉系统 群代数 交叉乘积
  • 简介:Risler&Trotmanin1997provedthatthemultiplicityofananalyticfunctiongermisleft-rightlipschitzinvariant,whichprovidedapartialanswertoZariskiconjecture.Inthisnote,basedontherecentworkofComte,Milman&Trotman,wegeneralizetheworkofthemtoprovethatthemultiplicityofaC~∞-differentiablefunctiongermisalsoleft-rightlipschitzinvariant.

  • 标签: 光滑函数 多样性 lipschitz变量
  • 简介:ThispapershowsthattheC1-curvedfiniteelementdevelopedbyBernadoningeneralcannotsatisfytheessentialboundaryconditionsonapproximateboundary.Furthermore,amodifiedC1-curvedfiniteelementisgiven,whichiscompatiblewiththeelementofArgyristriangleandcansatisfythehomogeneousDirichletboundaryconditionsonapproximateboundary.

  • 标签: Curved boundary DOMAIN Argyris TRIANGLES C1-curved
  • 简介:ThispaperintroducestheconceptoflocalC-cosins-familyandinverstigateitsbasicproperties,Inparticular,acharacterizationofthecompleteinfinitesimalgeneratorofalocalC-cosinefamilyisobtained,AsanapplieationofthistheorytothesecondordersbstractCauchyproblems,acharacterizationofthelocalC-well-posednessoftheseproblemsisgivenintermsofthelocalC-cosinefamilytheory.

  • 标签: 余弦族 完全生成元 二阶柯西问题 半群
  • 简介:LetιbeatriangulationofapolygonaldomainDR2withverticesV={v1:1≤i≤N,}andRSk(D,τ)={u∈Ck(D):(T∈τ,u|τisarationalfunction}.Thepurposeofthispaperistostudytheexist-enceandconstructionofCμ-rationalsplinefunctionsonanytriangulationτforCAGD.TheHermiteprob-lemHμ(V,U)={findu∈

  • 标签: TRIANGULATION spline CAGD polygonal rational vertex
  • 简介:Thispaperderivesfirstordernecessaryandsufficientconditionsforunconstrainedconed.c.Programmingproblemswheretheunderlinedspaceispartiallyorderedwithrespecttoacone.Theseconditionsaregivenintermsofdirectionalderivativesandsubdifferentialsofthecomponentfunctions.Moreover,conjugatedualityforconed.c.Optimizationisdiscussedandweakdualitytheoremisprovedinamoregeneralpartiallyorderedlineartopologicalvectorspace(generalizingtheresultsin[11]).

  • 标签: 锥d.c.最优化 共轭对偶 弱对偶定理 次梯度 多目标优化 方向导数
  • 简介:Weintroducethenotionofproperty(RD)foralocallycompact,Hausdorffandr-discretegroupoidG,andshowthatthesetS2^l(G)ofrapidlydecreasingfunctionsonGwithrespecttoacontinuouslengthfunctionIisadensespectralinvariantandFreehet*-subalgebraofthereducedgroupoidC^*-algebraCr^*.(G)ofGwhenGhasproperty(RD)withrespecttol,sotheK-theoriesofbothalgebrasareisomorphicunderinclusion.EachnormalizedcoeycleconG,togetherwithaninvariantprobabilitymeasureontheunitspaceGoofG,givesrisetoacanonicalmapTconthealgebraCo(G)ofcomplexcontinuousfunctionswithcompactsupportonG.WeshowthatthemapTccanbeextendedcontinuouslytoS2^l(G)andplaysthesameroleasann-traceonCr^*(G)whenGhasproperty(RD)andcisofpolynomialgrowthwithrespecttol,sotheConnes'fundamentparingbetweentheK-theoryandthecycliccohomologygivesustheK-theoryinvariantsonCr^*(G).

  • 标签: GROUPOID C^*-algebra property (RD) SPECTRAL INVARIANCE
  • 简介:A.simplicialmesh(triangulation)isconstructedthatgeneralizesthetwo-dimensional4-directionmeshtoR~m.Thismesh,withsymmetric,shift-invariantvaluesatthevertices,isshowntoadmitaboundedC~1interpolantifandonlyifthealternatingsumofthevaluesattheverticesofany1-cubeiszero.Thisim-pliesthaiinterpolationattheverticesofanm-dimensional,simplicialmeshbyaC~1piecewisepolynomialofdegreem+1withonepiecepersimplexisunstable.

  • 标签: invariant INTERPOLATION TRIANGULATION PIECEWISE symmetric cube
  • 简介:LetAbeaunitalC*-algebra,n∈N∪{∞}.Itisprovedthattheisomorphism△n:Un0(A)/DUn0(A)→AffT(A)/△n0(π1(Un0(A)))isisometricforsomesuitabledistances.Asanapplication,theauthorhasthesplitexactsequence0→AffT(A)/△n0(π1(Un0(A)))iA→Un(A)/DUn(A)πA→Un(A)/Un0(A)→0withiAcontractive(andisometricifn=∞)undercertainconditionofA.

  • 标签: 迹空间 不变量 酉群 C^*代数 同胚群 等距群
  • 简介:Thispapergivesthedefinitionsandsomepropertiesofε-directionalderivateandε-subgradientsofcone-convexfunction.Fromthem,theoptimalityconditionsoflocalandglobaloptimalpointofunconstrainedcone-d.c.programmingaregained.Atlast,thedualitytheoremsofthisprogrammingarepresented.

  • 标签: ε-定向导出数 ε-子斜度 最优化条件 对偶定理 凸函数