简介：AradialfunctioncanbeexpressedbyitsgeneratorthroughThepositivedefiniteofthefunctionplaysanimportantroteintheradialbasisinterpolation.WecannaturallyuseBochner’sTheoremtocheckifispositivedefinite.Thisrequireshoweveran-dhnensiotialFouriertransformationanditisnotveryeasytocalculate.Furthermoreinalotofcaseswewilluseforspacesofvariousdimensionstoo,thenforeveryfixednweneeddotheFouriertransformationoncetocheckifthefunctionispositivedefiniteinthen-di-mensionalspace.Thecompletelymonotonefunction:,whichisdiscussedin[4]ispositivedefiniteforarbitraryspacedimensions.Withthistechniquetvecanveryeasilycharacterizethepositivedefinite,ofaradialfunctionthroughitsgenerator.Unfortunatelythereisonlyaverysmallsubsetofradialfunctionwhichiscompletelymonotone.Thusthiscriterionexcludedalotofinterestingfunctionssuchascompactlysupportedradialfunction,whcihareveryusefulinapplic

简介：InthispaperweconsidertheeigenvalueproblemofsemilinearellipticequationinR~n(n≥~3)-△u+α(x)u=λf(x,u),u∈H~1(R~n).

简介：LetXbeacomplexBanachspacewithouttheanalyticRadon-Nikodymproperty.TheauthorshowsthatG={f∈H∞(D,X):thereexistse＞0,suchthatforalmostallθ∈[0,2π],limsup‖f(rei)-f(sei)‖＞∈}isadenseopensubsetofH(D,X).Itisalsoshownr,s↑1thatforeveryopensubsetBofT,thereexistsF∈H∞(D,X),suchthatFhasboundaryvalueseverywhereonBcandFhasradiallimitsnowhereonB.WhenAisameasurablesubsetofTwithpositivemeasure,thereexistsf∈H∞(D,X),suchthatfhasnontangentiallimitsalmosteyerywhereonAcandfhasradiallimitsalmostnowhereonA.

简介：Abstract.Theexistenceofpositiveradialsolutionstothesystemsof

简介：Thefollowingresultisestablished:letXbeaBanachspacewithouttheRadon-Nikodymproperty,thereexistsauniformlyboundedharmonicfunctionfdefinedontheopenunitdiskofCwithvaluesinX,suchthatforalmostallθ∈[0,2π],（?）f(reiθ)doesnotexist.

简介：BytheSchauder-Tychonofffixed-pointtheorem,weinvestigatetheexistenceandasymptoticbehaviorofpositiveradialsolutionsoffullynonlinearellipticequationsinR^n.WegivesomesufficientconditionstoguaranteetheexistenceofboundedandunboundedradialsolutionsandconsiderthenonexistenceofpositivesolutioninR^n.

简介：自从球形的Gaussian光线的函数，严格地是积极的明确，作者使用Gaussian内核的翻译的线性联合插入内推在这篇文章的范围上的散布数据。看到目标功能通常在本国的空格外面，并且那不得不解决线性方程的一个大放大系统获得interpolant的组合系数工作，作者首先与Gaussian光线的功能关于插值探查进一些问题。然后，他们由Gaussian光线的功能构造伪插值操作符，并且得到近似的学位。而且，他们看在伪插值和插值之间的错误关系他们什么时候有一样的基础功能。最后，作者与本地支持功能讨论quasi-interpolant的构造和近似。

简介：Thispapergeneralizestheformulasumfromn=nto(Ins（v）Ins＇（v）=δss＇)tothecasewithtwodifferentv.Ins（v）istheradialwavefunctionofanelectroninaconstantmagneticfield.Theseresultsareveryusefulinsynchrotonradiationandastrophysics.

简介：Inthispaper,anewquasi-interpolationwithradialbasisfunctionswhichsatis-fiesquadraticpolynomialreproductionisconstructedontheinfinitesetofequallyspaceddata.Anewbasisfunctionisconstructedbymakingconvolutionintegralwithaconstructedsplineandagivenradialbasisfunction.Inparticular,fortwicelydiffer-entiablefunctiontheproposedmethodprovidesbetterapproximationandalsotakescareofderivativesapproximation.

简介：

简介：TheauthorsdiscussproblemsofapproximationtofunctionsinL^2(R^n)andoperatorsfromL^2(R^n1)toL^2(R^n2)byRadial-BasisFunctions.TheresultsobtainedsolvetheparblemofcapabilityofRBFneuralnetworks,abasicprobleminneuralnetworks.

简介：Thispaperintroducestheuseofpartitionofunitymethodforthedevelopmentofahighorderfinitevolumediscretizationschemeonunstructuredgridsforsolvingdiffusionmodelsbasedonpartialdifferentialequations.Theunknownfunctionanditsgradientcanbeaccuratelyreconstructedusinghighorderoptimalrecoverybasedonradialbasisfunctions.Themethodologyproposedisappliedtothenoiseremovalprobleminfunctionalsurfacesandimages.Numericalresultsdemonstratetheeffectivenessofthenewnumericalapproachandprovideexperimentalorderofconvergence.