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A New Class of Banach Spaces with Uniform Normal Structure 总被引:2,自引:0,他引:2
§ 1.Introduction LetXbeanormedlinearspace ,andletS(X) ={x∈X :x =1 }betheunitsphereofX .In 1 94 8,BrodskiiandMilman[1]introducedthefollowinggeometricconcept: Definition 1 ABounded ,convexsubsetKofaBanachspaceXissaidtohavenormalstructureifeveryconvexsubsetHofKthatconta… 相似文献
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高继 《应用泛函分析学报》2000,2(3):247-263
假设S(X)是Banach空间X的单位球面,作引进了四个新的几何参数:Jε(X)=sup{βε(x),x∈S(X)},jε(X)=inf{βε(x),x∈S(X)},Gε(X)=sup{αε(x),x∈S(X)},gε(X)=inf{αε(x),x∈S(S)},其中≤ε≤1,βε(x)=sup{min{‖x εy‖,‖x-εy‖,y∈S(X)}},αε(x)=inf{max{‖x εy‖,‖x-εy‖,y∈S(X)}},讨论了这些参数的性质,本主要结果是:如果主要结果是:如果有一个ε,0≤ε≤1,使得Jε(X)<1 ε/2或gε(X)>1 ε/3,那末X有一至正规结构。 相似文献
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This paper computationally investigates the RhSin (n = 1 6) clusters by using a density functional approach. Geometry optimizations of the RhSin (n = 1 6) clusters are carried out at the B3LYP level employing LanL2DZ basis sets. It presents and discusses the equilibrium geometries of the RhSin (n = 1-6) clusters as well as the corresponding averaged binding energies, fragmentation energies, natural populations, magnetic properties, and the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. Theoretical results show that the most stable RhSin(n = 1-6) isomers keep an analogous framework of the corresponding Sin+1 clusters, the RhSi3 is the most stable cluster in RhSin (n = 1-6) isomers. Furthermore, the charges of the lowest-energy RhSin (n = 1-6) clusters transfer mainly from Si atom to Rh atom. Meanwhile, the magnetic moments of the RhSin(n = 1-6) arises from the 4d orbits of Rh atom. Finally, compared with the Sin+1 cluster, the chemical stability RhSin clusters are universally improved. 相似文献
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正规六边形和更广泛具有正规结构的Banach 空间 总被引:1,自引:1,他引:0
假设X是一个实Banach空间,S(X)是单位球面。作者引进了一个新的几何参数(H(X),讨论了H(X)和Neumann-Jordan常数CNJ(X)R 性质以及H(X)和其他几何常数的关系,本文主要结果是:H(X)〈2或CNJ(X)〈4/5一致正规结构。 相似文献
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