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:Veryrecently,BelleannouncedtheirobservationofΥ(5S)!bJ!(J=0;1;2),indicatingthattheΥ(5S)!bJ!decaysalsohavelargedecaywidths,i.e.,themeasuredbranchratiosofΥ(5S)!bJ!are<3:410??3,(1:640:23+0:30??0:22)10??3,and(0:570:220:07)10??3withJ=0;1;2,respectively[1].ItshouldbenoticedthateventhoughthetreelevelcontributionstoΥ(5S)!bJ!(J=0;1;2)shouldbestronglysuppressedduetotheOkubo-Zweig-Iizuka(OZI)rule,suchlargedecaywidthsareobserved,whichagaininspiresourinterestinunderstandingsuchquantities.Inthiswork,weproposethatthecontributionfromthehadronicloopshouldbeconsideredinstudyingΥ(5S)!bJ!.
简介:研究了—(p,q)-Laplacian拟线性椭圆方程组.当连续函数V和W在两种情形下,利用Moser迭代技巧和Ljusternik-Schnirelmann畴数理论,建立了方程组正解的存在性和多重性结果.