简介:§1.IntroductionLetEbeanon-zerocomplexBanaohspace,&(JET)theBanaohalgebraofalltheoperatorsfromEintoitself.Operatormeans'boundedlinearoperator'throughout.Anoperatorfunction/fromadomain(openset)Dinthecomplexplaneto@l(T£}issaidtobeanalytic,ifforanyx^Eandq>£E*(thedualspaceofE\9>(/(z)aOisanalyticintheclassical’senseinD([1],p.92).Wedenotebyja/B(D)thesetofalltheanalyticoperatorfunctionsfromDinto
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:LetGbeagraphwithvertexsetV(G)andedgesetE(G)andletgandfbetwointeger-valuedfunctionsdefinedonV(G)suchthat2k-1≤g(x)≤f(x)forallx∈V(G).LetHbeasubgraphofGwithmkedges.Inthispaperitisprovedthatevery(mg+m-1,mf-m+1)-graphGhas(g,f)-factorizationsrandomlyκ-orthogonaltoHandshownthattheresultisbestpossible.
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:LetB(E,F)bethesetofallboundedlinearoperatorsfromaBanachspaceEintoanotherBanachspaceF,B+(E,F)thesetofalldoublesplittingoperatorsinB(E,F)andGI(A)thesetofgeneralizedinversesofA2B+(E,F).InthispaperweintroduceanunboundeddomainW(A,A^+)inB(E,F)forA2B+(E,F)andA^+2GI(A),andprovideanecessaryandsufficientconditionforT2W(A,A^+).Thenseveralconditionsequivalenttothefollowingpropertyareproved:B=A^+(IF+(T??A)A^+)??1isthegeneralizedinverseofTwithR(B)=R(A^+)andN(B)=N(A^+),forT2W(A,A^+),whereIFistheidentityonF.Alsoweobtainthesmooth(C¥)diffeomorphismMA(A^+,T)fromW(A,A^+)ontoitselfwiththefixedpointA.LetS=fT2W(A,A^+):R(T)\N(A^+)=f0gg,M(X)=fT2B(E,F):TN(X)R(X)gforX2B(E,F)g,andF=fM(X):8X2B(E,F)g.UsingthediffeomorphismMA(A^+,T)weprovethefollowingtheorem:SisasmoothsubmanifoldinB(E,F)andtangenttoM(X)atanyX2S.ThetheoremexpandsthesmoothintegrabilityofFatAfromalocalneighborhooldatAtotheglobalunboundeddomainW(A,A^+).Itseemstobeusefulfordevelopingglobalanalysisandgeomatricalmethodindifferentialequations.
简介:Analgorithmofcontinuousstage-spaceMCMCmethodforsolvingalgebraequationf(x)=0isgiven.Itisavailableforthecasethatthesignoff(x)changesfrequentlyorthederivativef'(x)doesnotexistintheneighborhoodoftheroot,whiletheNewtonmethodishardtowork.Letnbethenumberofrandomvariablescreatedbycomputerinouralgorithm.Thenafterrn=O(n)transactionsfromtheinitialvalueXo,X^*canbegotsuchthat[f(x^*)|<e-^cm|f(xo)|bychoosingsuitablepositiveconstantc.Anillustrationisalsogivenwiththediscussionofconvergencebyadjustingtheparametersinthealgorithm.