简介：在控制理论和控制工程中，镇定控制器的设计是一个经典问题。许多有关这个问题的结论一般都是针对线性系统。对于非线性系统，很少见到有构造性结果能用于控制工程中。本文针对一类广泛的非线性控制系统，我们构造了一些控制器，这些判据在工程实际问题中将具有一定的指导意义。

简介：ThispapercharacterizestheirrationalrotaionC^*-algebraassociatedwiththeToeplitxC^*-algebraovertheZ-shapeddomaininC^2inthesenseofthemaximalradicalseries,whichisanisomorphisminvariant.

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简介：定义了向量筐函数的C-Stieltjes近似可表示算子，并研究了它的性质。另外，我们定义了向量值函数的近似C-Stieltjes积分，并证明了它的收敛定理。

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.

简介：TwospectralsequencesaredronedrespectivelyforcohomologiesH^P(Ωf1k-,0)andH^P(Af,k-,0)ofsingularitiesofC^∞mappings.Theyarefinitelydimensiionalnewinvarancesunderrightequivalencesandcontacttransformationsrespectively.FormuLaetobecomputedbylinearalgebrsareproved.

简介：Inthispaper,weintroduceaconditionweakerthantheLpdifferentiability,whichwecallCpcondition.Weprovethatifafunctionsatisfiesthisconditionatapoint,thenthereexiststhebestlocalapproximationatthatpoint.WealsogiveanecessaryandsufficientconditionforthatafunctionbeLpdifferentiable.Inaddition,westudytheconvexityofthesetofclusterpointsofthenetofbestappoximationsoff,{Pe(f)}ase→0.

简介：Inthispaper,weapplythecontractionmappingtheoremtoestablishsomeboundedandunboundedadditiveperturbationtheoremsconcerninglocalC-semigroups.SomegrowthconditionsofperturbationsoflocalC-semigroupsarealsoestablished.

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.

简介：Risler&Trotmanin1997provedthatthemultiplicityofananalyticfunctiongermisleft-rightlipschitzinvariant,whichprovidedapartialanswertoZariskiconjecture.Inthisnote,basedontherecentworkofComte,Milman&Trotman,wegeneralizetheworkofthemtoprovethatthemultiplicityofaC~∞-differentiablefunctiongermisalsoleft-rightlipschitzinvariant.

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简介：ThispapershowsthattheC1-curvedfiniteelementdevelopedbyBernadoningeneralcannotsatisfytheessentialboundaryconditionsonapproximateboundary.Furthermore,amodifiedC1-curvedfiniteelementisgiven,whichiscompatiblewiththeelementofArgyristriangleandcansatisfythehomogeneousDirichletboundaryconditionsonapproximateboundary.

简介：ThispaperintroducestheconceptoflocalC-cosins-familyandinverstigateitsbasicproperties,Inparticular,acharacterizationofthecompleteinfinitesimalgeneratorofalocalC-cosinefamilyisobtained,AsanapplieationofthistheorytothesecondordersbstractCauchyproblems,acharacterizationofthelocalC-well-posednessoftheseproblemsisgivenintermsofthelocalC-cosinefamilytheory.

简介：LetιbeatriangulationofapolygonaldomainDR2withverticesV={v1:1≤i≤N,}andRSk（D,τ）={u∈Ck（D）:(T∈τ,u|τisarationalfunction}.Thepurposeofthispaperistostudytheexist-enceandconstructionofC^{μ-rationalsplinefunctionsonanytriangulationτforCAGD.TheHermiteprob-lemHμ（V,U）={findu∈}

简介：Thispaperderivesfirstordernecessaryandsufficientconditionsforunconstrainedconed.c.Programmingproblemswheretheunderlinedspaceispartiallyorderedwithrespecttoacone.Theseconditionsaregivenintermsofdirectionalderivativesandsubdifferentialsofthecomponentfunctions.Moreover,conjugatedualityforconed.c.Optimizationisdiscussedandweakdualitytheoremisprovedinamoregeneralpartiallyorderedlineartopologicalvectorspace(generalizingtheresultsin[11]).

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）.

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简介：A.simplicialmesh(triangulation)isconstructedthatgeneralizesthetwo-dimensional4-directionmeshtoR~m.Thismesh,withsymmetric,shift-invariantvaluesatthevertices,isshowntoadmitaboundedC~1interpolantifandonlyifthealternatingsumofthevaluesattheverticesofany1-cubeiszero.Thisim-pliesthaiinterpolationattheverticesofanm-dimensional,simplicialmeshbyaC~1piecewisepolynomialofdegreem+1withonepiecepersimplexisunstable.

简介：获得了HilbertC^*-模之间的两个同构定理．作为推论，证明了C^*-代数上每个可数生成的HilbertC^*-模均稳定酉等价于A。

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.