简介:Wegiveaconstructionofthemaximum,andtheminimumofthesetofnondecreasmgapproxmantsinthediscretecase,whereisapositiveconoexfunction.Acharacterizationofthatsetisalsoobtained.
简介:Thispaperstudiestheinteractionofshockandgradientwave(soundwave)ofsolutionstothesystemofinviscidisentropicgasdynamicsasamodelforthecorrespondingproblemsfornonlinearhyperbolicsystems.Theproblemcanbereducedtoaboundaryvalueprobleminawedgeddormain,ByusingthemethodofconstructingasymptoticsolutionsandNewton'siterationprocessitisprovedthatifaweakshockhitsagradientwave,thenthegrandientwavewillsplitintotwogradientwaves,whiletheshockcontinusespropagating.Inthispapertheauthorreducestheproblemtoastandardformandconstructsasymptoticsolutionoftheproblem.Theexistenceofthegenuinesolutionwillhegiveninthefollowingpaper.
简介:Theauthorintroducesanotionofweak1sequencesandcharacterizessuchsequencesbymeansofhomologicalmethods.ThisnotionextendsthenotionofweekM-sequencesandthusextendsthenotionsofgeneralizedCohen-MacaulaymodulesandBuchsbaummodulestomoregeneralcases.
简介:ThemultivariatesplineswhichwerefirstpresentedbydeBooorasacompletetheoreticalsystemhaveintriguedmanymathematicianswhohavedevotedmanyworksinthisfieldwhichisstillintheprocessofdevelopment.Theauthorofthispaperisinterestedintheareaofinter-polationwithspecialemphasisontheinterpolationmethodsandtheirapproximationorders.ButsuchB-splines(bothunivariateandmultivariate)donotinterpolateddirectly,soIap-proachedthisprobleminanotherwaywhichistoextendmyinterpolatingsplineofdegree2n-1inunivariatecase(See[7])tomultivariatecase.Iselectedtriangulatedregionwhichisinspiredbyothermathematicians’works(e.g.[2]and[3])andextendtheinterpolatingpolynomialsfromunivariatetom-variatecase(See[10])Inthispapersomeresultsinthecasem=2arediscussedandprovedinmoreconcretedetails.Basedonthesepolynomials,theinterpolatingsplines(itisdefinedbymeaspiecewisepolynomialsinwhichtheunknownpar-tialderivativesaredeterminedundercertaincontinuousconditions)arealsodiscussed.Theapproximationordersofinterpolatingpolynomialsandofcubicinterpolatingsplinesareinverstigated.Welunitedourdiscussionontherectangulardomainwhichispartitionedintoequalrighttriangles.Astothecaseinwhichtherectangulardomainispartitionedintounequalrighttrianglesaswellasthecaseofmorecomplicateddomains,wewilldiscussinthenextpa-per.
简介:TheauthorsconsiderthemultilinearoscillatorysingularintegraloperatordefinedbyTA1,A2,…,Akf(x)=∫R^ne^ip(x,v)k/∏/j=1Rmi(Ajix,y)(Ω(x-y))/(│x-y│^n+M)f(y)dy,whereP(x,y)isareal-valuedpolynomialonR^n×R^n,Ωishomogeneousofdegreezero,Rmj(Aj;x,y)denotesthemj-thorderTaylorseriesremainderofAjatxexpandedabouty,M=k/∑j=1mj,ItisshownthatifΩbelongstothespaceLlog^+L(S^n-1)andhasvanishingmomentuptoorderM,then‖TA1,A2,…,Akf‖q≤ck/∏/j=1(∏/│α│=mj‖D^αAj‖rj)‖f‖p,providedthat1
简介:Tikhonov正则化方法是求解不适定问题最为有效的方法之一,而正则化参数的最优选取是其关键.本文将混沌粒子群优化算法与Tikhonov正则化方法相结合,基于Morozov偏差原理设计粒子群的适应度函数,利用混沌粒子群优化算法的优点,为正则化参数的选取提供了一条有效的途径.数值实验结果表明,本文方法能有效地处理不适定问题,是一种实用有效的方法.
简介:TheYang-Mills-HiggsfieldgeneralizestheYang-Millsfield.TheauthorsestablishthelocalexistenceanduniquenessoftheweaksolutiontotheheatflowfortheYang-Mills-HiggsfieldinavectorbundleoveracompactRiemannian4-manifold,andshowthattheweaksolutionisgauge-equivalenttoasmoothsolutionandthereareatmostfinitesingularitiesatthemaximumexistingtime.
简介:Intheintroductionapreliminaryconsiderationofthesenseofconcepts“set”,“structure”,“system”,and“model”,aswellasoftheconnectionbetweenthemisproposedandonthebasisofitsresultsthetaskofinvestigationofabstractbasesofsystem(inparticularreconsiderationofconcept“abstractset”),ofabstractstructure,abstractsystemandofS-Modelisformulated.Thefirstsectionisdevotedtoformulationofanapproachtoconstructionofaggregatetheoryregardedasananalogofmoderateconstructivesettheory:therelations“inclusion”and“equivalence”betweenaggregatesandtheoperationsonaggregates“union”,“intersection,“difference”and“compliment”areintroduced.Definitionoftheconcept“a-system”aswellasofitsa-structureonthespaceofaggregatesisdefined.AspecialattentionisshowntosimilarityandessentialdifferencebetweenaggregatetheoryandsettheoryaswellastothefactthatthefamousparadoxesofCantorandRussellintheCantor’ssettheorytakenoplaceintheaggregatetheory.FurtheravariantofCantor’ssettheorycalledrestricteddiscretesettheoryisconsidered.Thesecondsectionisdevotedtoformulationofanapproachtoconstructionofalgebraofa-systems.Attheendtheconceptofsystemofsuccessivesystems(SSS),isintroduced.