简介：ThisarticleconsidersweightedapproximationofmultivariatefunctioninreproducingkernelHilbertspace,andgivesarelationbetweennthminimalerrorsforstandardandlinearinformationintherandomizedsetting.Usingthisrelationwecanestimatethenthminimalerrorforstandardinformationbythenthminimalerrorforlinearinformation,andstudythetractabilityandstrongtractabilityforthesetwoclassesofinformation.

简介：Theauthorsdefinethesceneryflowofthetorus.Theflowspaceistheunionofallflat2-dimensionaltoriofarea1withamarkeddirection(orequivalently,theunionofalltoriwithaquadraticdifferentialofnorm1).Thisisa5-dimensionalspace,andtheflowactsbyfollowingindividualpointsunderanextremaldeformationofthequadraticdifferential.Theauthorsdefineassociatedhorocycleandtranslationflows;thelatterpreserveeachtorusandarethehorizontalandverticalflowsofthecorrespondingquadraticdifferential.Thesceneryflowprojectstothegeodesicflowonthemodularsurface,andadmits,foreachorientationpreservinghyperbolictoralautomorphism,aninvariant3-dimensionalsubsetonwhichitisthesuspensionflowofthatmap.Theauthorsfirstgiveasimplealgebraicdefinitionintermsofthegroupofaffinemapsoftheplane,andprovethattheflowisAnosov.Theygiveanexplicitformulaforthefirst-returnmapoftheflowonconvenientcross-sections.Then,inthemainpartofthepaper,theauthorsgiveseveraldifferentmodelsfortheflowanditscross-sections,intermsof:●stackingandrescalingperiodictilingsoftheplane;●symbolicdynamics:thenaturalextensionoftherecodingofSturmiansequences,ortheS-adicsystemgeneratedbytwosubstitutions;●zoomingandsubdividingquasi-periodictilingsoftherealline,oraperiodicquasicrystalsofminimalcomplexity;●thenaturalextensionoftwo-dimensionalcontinuedfractions;●inductiononexchangesofthreeintervals;●rescalingonpairsoftransversemeasurefoliationsonthetorus,ortheTeichmiillerflowonthetwice-puncturedtorus.

简介：WeshowthatmanyharmonicanalysisoperatorsintheBesselsetting,includingmaximaloperators,Littlewood–Paley–Steintypesquarefunctions,multipliersofLaplaceorLaplace–StieltjestransformtypeandRiesztransformsare,orcanbeviewedas,Calderón–Zygmundoperatorsforallpossiblevaluesoftypeparameterλinthiscontext.Thisextendsresultsexistingintheliterature,butbeingjustifiedonlyforarestrictedrangeofλ.

简介：Inthispaper,westudyoptimalrecovery(reconstruction)offunctionsonthesphereintheaveragecasesetting.WeobtaintheasymptoticordersofaveragesamplingnumbersofaSobolevspaceonthespherewithaGaussianmeasureintheLd-1q(S)metricfor1≤q≤∞,andshowthatsomeworst-caseasymptoticallyoptimalalgorithmsarealsoasymptoticallyoptimalintheaveragecasesettingintheLdq(S-1)metricfor1≤q≤∞.

简介：这篇论文为第一份订单的夸张椭圆形的联合系统的边界值问题被奉献给边界条件的合适的设置的学习。相应边界价值问题的wellposedness也被建立。为椭圆形的系统的边界价值问题的Lopatinski条件然后为夸张椭圆形的联合系统被扩大到盒子。在这篇论文的结果能在液体动力学被用于Euler系统，到特别给描述亚声的流动的很好提出的边界价值问题。

简介：ManyworkshaveinvestigatedtheproblemofreparameterizingrationalBéziercurvesorsurfacesviaMbiustransformationtoadjusttheirparametricdistributionaswellasweights,suchthatthemaximalratioofweightsbecomessmallerthatsomealgebraicandcomputationalpropertiesofthecurvesorsurfacescanbeimprovedinaway.However,itisanindicationofveracityandoptimizationofthereparameterizationtodopriortojudgewhetherthemaximalratioofweightsreachesminimum,andverifythenewweightsafterMbiustransformation.What’smoretheusersofcomputeraideddesignsoftwaresmayrequiresomeguidelinesfordesigningrationalBéziercurvesorsurfaceswiththesmallestratioofweights.Inthispaperwepresentthenecessaryandsufficientconditionsthatthemaximalratioofweightsofthecurvesorsurfacesreachesminimumandalsodescribeitbyusingweightssuccinctlyandstraightway.Theweightsbeingsatisfiedtheseconditionsarecalledbeinginthestablestate.Applyingsuchconditions,anygivingrationalBéziercurveorsurfacecanautomaticallybeadjustedtocomeintothestablestatebyCADsystem,thatis,thecurveorsurfacepossessesitsoptimalparametricdistribution.Finally,wegivesomenumericalexamplesfordemonstratingourresultsinimportantapplicationsofjudgingthestablestateofweightsofthecurvesorsurfacesanddesigningrationalBéziersurfaceswithcompactderivativebounds.

简介：在这篇论文，我们在不同计算设定在n宽度上从空格l_p(1≤p≤2)为斜操作符T把一些最佳的算法给l_2。