简介：让x：Mn是有非零主管弯曲的脐的免费hypersurface。然后，x与Laguerre公制的g被联系，Laguerre张肌\mathbbL\mathbb{L}，Laguerre形式C，和一个Laguerre秒基础形成\mathbbB\mathbb{B}它是在Laguerre下面的x的invariants转变组。如果它的Laguerre形式消失，hypersurfacex被称为Laguerreisoparametric并且\mathbbB\mathbb的特征值{B}是不变的。在这份报纸，我们在4分类所有Laguerreisoparametrichypersurfaces。

简介：让f：M→R~3是有非退化的秒的面向的表面基本形式。我们由H和K表示它的吝啬的弯曲和高斯弯曲。然后f的Laguerre体积，由L(f)=∫(H~2定义-K)/KdM，一在Laguerre转变下面不变。功能的L的批评表面被称为Laguerre最小的表面。在这篇论文，我们学习在由使用拉久雷·高斯的R~3的最小的表面印射的theLaguerre。这被知道最小的表面有的genericLaguerre有一样的高斯地图的双Laguerre最小的表面。在这篇论文，我们证明不是Laguerre的任何表面最小被它的LaguerreGaussmap特别地决定。我们也证明圆范围是在R~3的唯一的紧缩的Laguerre最小的表面。并且我们与消失的Laguerre形式在R~3给表面的一条分类定理。

简介：在无界的域检验合成legendre近似的开发。一个建议计划的稳定性和集中的证明；二维的外面的问题的讨论；错误评价。

简介：在这篇论文，我们介绍同类的Besov类型空格MiloudAssal电子邮件：Miloud.Assal@fst.rnu.tn全文预览(小，大)[2]。Bourdaud，G.：RéalisationdesespacesdeBesovhomogènes。Arkiv地席，26，4154(1988)[3]。Triebel，H.：功能空格II的理论，Birkhaüs嗯，(1992[4]。杨，D.C.：分数维图形上的Besov空格的一些应用程序。ActaMathematicaSina，Engish系列，21(5)，12091218(2004)[5]。杨，D.C.，Yangsheng，H.：Besov和Triebel-Lizorkin的一些新空格在同类的空格打字。StudiaMathematica，156(1)，6797(2003)[6]。杨，D.C.：在空格嵌入Besov空格和Triebel-Lizorkin空格的定理哦同类的类型。在中国的科学，系列A，46(2)，12091218(2003)[7]。Bahouri，H.，Gérard，P.，徐，C.J.：EspacesdeBesovet评价deStrichartzgénéraliséessurlegroupede海森堡。杂志d'AnalyseMathématique，82，93118，(2000)[8]。Betancor，J.J.，Rodríguez方山，L.：在Besov-Hankel空格。数学。Nachr，171，517(1995)[9]。Assal，M.，Hacen，B.：LaguerreHypergroup上的概括Besov类型空格。Annales马特马蒂丘斯·布莱塞·帕斯卡，12，117145(2005)[10]。Bami，M.L.：L1(K,ω的Semisimplicity)加权的可交换的HypergroupK。ActaMathematicaSinica，英语系列，24(4)，606610(2008)。[11]。本森，C.，Jenkins，J.，Ratcliff，G.：海森堡组上的Schwartz功能的球形的变换。功能的分析的杂志，154，379423(1998)[12]。Nessibi，M.M.，Trimèche，K.：由使用的Laguerre亢奋的组上的氡变换的倒置概括了小浪。数学分析和申请的杂志，208，337363(1997)[13]。Kortas，H.，Sifi，M.：Lévy-Khintchine公式和与Laguerre和bessel功能联系的双卷绕旋转半组。潜在的分析，15，4358(2001)[14]。Faraut，J.，Harzallah，K.�

简介：Opticalspinsplittinghasattractedsignificantattentionowingtoitspotentialapplicationsinquantuminformationandprecisionmetrology.However,itistypicallysmallandcannotbecontrolledefficiently.Here,weenhancethespinsplittingbytransmittinghigher-orderLaguerre–Gaussian(LG)beamsthroughgraphenemetamaterialslabs.TheinteractionbetweenLGbeamsandmetamaterialresultsinanorbital-angularmomentum-(OAM)dependentspinsplitting.TheupperboundoftheOAM-dependentspinsplittingisfound,whichvarieswiththeincidentOAMandbeamwaist.Moreover,thespinsplittingcanbeflexiblytunedbymodulatingtheFermienergyofthegraphenesheets.Thistunablespinsplittinghaspotentialapplicationsinthedevelopmentofspin-basedapplicationsandthemanipulationofmid-infraredwaves.

简介：AnalgorithmforsimultaneouscomputationoftheadjointG(s)anddeterminantd(s)ofthematrixpolynomials2JsA1-A2ispresented,whereJisasingularmatrix.BothG(s)andd(s)areexpressedrelativetoabasisofLaguerreorthogonalpolynomials,ThisalgorithmisanewextensionofLeverrier-Fadeevalgorithm.

简介：Laguerre–Gaussianbeams,asaspecialmodelwithspiralphasestructure,havebeenintensivelyinvestigated.HolographicgratingmethodisaconvenientmethodofgeneratingLaguerre–Gaussianbeamsandmeasuringtheirorbitalangularmomenta.Butduetosomeinevitableadversefactorssuchaslateraldisplacement,angulardeflectionandellipticalincidentprofileofincidentbeam,thepracticaleffectivenessshouldbereevaluated.Thispaperisdevotedtothestudyontheinfluencesoftheabovementionedthreeadversefactorsontheholographicgratingmethod.Thecharacteristicsofthemodedecompositionofdiffractiveorderandtherelativepowersoftheorbitalangularmomentumeigen-statesarealsogiven.

简介：ALegendrespectralelement/LaguerrecoupledmethodisproposedtonumericallysolvetheellipticHelmholtzproblemonthehalfline.Rigorousanalysisiscarriedouttoestablishtheconvergenceofthemethod.Severalnumericalexamplesareprovidedtoconfirmthetheoreticalresults.TheadvantageofthismethodisdemonstratedbyanumericalcomparisonwiththepureLaguerremethod.

简介：TakingtwoLaguerre–Gaussianbeamswithtopologicalchargel=±1asanexample,thispaperstudiesthecompositeopticalvorticesformedbytwononcollinearLaguerre–Gaussianbeamswithdifferentphases,amplitudes,waistwidths,off-axisdistances,andtheirpropagationinfreespace.Itisshownbydetailednumericalillustrativeexamplesthatthenumberandlocationofcompositevorticesatthewaistplanearevariablebyvaryingtherelativephaseβ,amplituderatioη,waistwidthratioξ,oroff-axisdistanceratioμ.Thenettopologicalchargelnetisnotalwaysequaltothesumlsumofchargesofthetwocomponentbeams.Themotion,creationandannihilationofcompositevorticestakeplaceinthefree-spacepropagation,andthenetchargeduringthepropagationremainsunchangedandequalstothenetchargeatthewaistplane.

简介：WepresentbeamsolutionsofthestronglynonlocalnonlinearSchrodingerequationinleft-handedmaterials(LHMs).DifferentLaguerre-Gaussian(LG)necklacebeams,suchassymmetricandasymmetricsinglelayerandmultilayernecklacebeamsarecreatedbythesuperpositionoftwosinglebeamswithdifferenttopologicalcharges.SuchsuperpositionsarethenpropagatedthroughLHMs,displayinglineardiffraction.ItisfoundthatthesuperpositionoftwoLG_(nm)beamswithoppositetopologicalchargesdoesnotshowrotationalbehaviorandthatthereexistsrotationforothertopologicalchargecombinations.OurtheorypredictsthattheaccessiblesolitonscannotexistinLHMs,

简介：Anumbilicalfreeorientedhypersurfacex:M→Rnwithnon-zeroprincipalcurvaturesiscalledaLaguerreisoparametrichypersurfaceifitsLaguerreformC=iCiωi=iρ1(Ei(logρ)(rri)Ei(r))ωivanishesandLaguerreshapeoperatorS=ρ1(S1rid)hasconstanteigenvalues.Hereρ=i(rri)2,r=r1+r2+···+rn1n1isthemeancurvatureradiusandSistheshapeoperatorofx.{Ei}isalocalbasisforLaguerremetricg=ρ2IIIwithdualbasis{ωi}andIIIisthethirdfundamentalformofx.Inthispaper,weclassifyallLaguerreisoparametrichypersurfacesinRn(n>3)withtwodistinctnon-zeroprincipalcurvaturesuptoLaguerretransformations.

简介：针对无限域上一维热传导方程的解析解为反常积分形式,直接计算往往比较困难.首先采用Fourier变换给出问题解析解,其次结合解析解的形式和无限域上Gauss型数值积分法精度高的优点,将半无限域上的一维热传导方程问题利用Gauss-Laguerre数值积分计算数值解,对无限域上的一维热传导方程的解析解转化为半无限域上的形式后用Gauss-Laguerre数值积分计算.实验结果表明,本文给出的数值解方法具有很高的精度.

简介：Inthispaper,ageneralizedLaguerre-sphericalharmonicspectralmethodisproposedfortheCauchyproblemofthree-dimensionalnonlinearKlein-Gordonequation.Thegoalistomakethenumericalsolutionstopreservethesameconservationasthatfortheexactsolution.Thestabilityandconvergenceoftheproposedschemeareproved.Numericalresultsdemonstratetheefficiencyofthisapproach.WealsoestablishsomebasicresultsonthegeneralizedLaguerre-sphericalharmonicorthogonalapproximation,whichplayanimportantroleinspectralmethodsforvariousproblemsdefinedonthewholespaceandunboundeddomainswithsphericalgeometry.