简介：分组数列问题形式新颖，构思精巧，题型丰富多彩，但离不开两个最基本的问题：求通项公式与前n项和．本文就这两个基本问题做如下的讨论．

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简介：Inthispaperwewillshowthatifanapproximationprocess{Ln}n∈Nisshapepreservingrelativetotheconeofallk-timesdifferentiablefunctionswithnon-negativek-thderivativeon[0,1],andtheoperatorsLnareassumedtobeoffiniterankn,thentheorderofconvergenceofDkLnftoDkfcannotbebetterthann2evenforthefunctionsxk,xk+1,xk+2onanysubsetof[0,1]withpositivemeasure.Takingintoaccountthisfact,wewillbeabletofindsomeasymptoticestimatesoflinearrelativen-widthofsetsofdifferentiablefunctionsinthespaceLp[0,1],p∈N.

简介：Inthispaper,wedeterminetheexactestimationofone-sidedn-widthsdn+（wqr（pr）,L1）.q=1,∝,whereWqr（Pr）isaclassofdifferentiable2π-periodicfunctions,andisdeterminedbyadifferentialopera-torPr（D）=Dσ∏j=tl（D-αj）,σ,j∈N,σ≥2,xj≠0,xj∈R.

简介：设G是一个具有顶点集V（G)和边集E（G）的图。设g和f是定义在V（G）上的两个整数值函数，使得g(x)≤f(x)对所有的点x∈V(G)都成立。结果G是一个（mg+n,mf-n）-图，1≤n

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简介：ThecommutatorsofsingularintegraloperatorswithhomogeneouskernelΩ(x)/|x|^narestudied,whereΩishomogeneousofdegreezero,andhasmeanvaluezeroontheunitsphere.ItisprovedthatΩ∈L(logL)^(k+1)(S^(n-1))isasufficientconditionsuchthatthek-thordercommutatorisboundedonL^2(R^n).

简介：ThequalitativepropertiesofapredatorpreysystemwithHolling-(n+1)functionalresponseandafairlygeneralgrowthratearecompletelyinvestigated.Thenecessaryandsufficientconditiontoguaranteetheuniquenessoflimitcyclesisgiven.Ourworkextendsthepreviousrelevantresultsinthereference,

简介：在通常情况下,对于任意的通道结构Γ的理想秘密共享方案不存在.然而,如果|Γ0|n成立,那么通道结构Γ便存在一个理想的秘密共享方案,其中Γ0是Γ的基,n是参与者总量.

简介：R．A．Gordon在[1]中定义了从R^1到Banach空间抽象函数的McShane积分，证明了当X不含C0时，如果，在[a，b]上MeShanef可积，则在[a．b]上Pettis可积．在这篇文章中，我们定义了从R^n到Banaach空间抽象函数的Mcshane积分。证明了fMcShane可积，则f是Pettis可积．于是我们推广了[1]的结果。

简介：作者将证明组2Dp(3)能被它的顺序部件特别地决定，在此p≠2m+1是一个素数，p≥5。更精确，如果OC(G)表示G的顺序部件的集合，我们将证明OC(G)=是OC(2Dp(3))如果并且仅当G对2Dp(3)。我们的结果的主要后果是汤普森的有效性在考虑下面为这些组推测。

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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。