Banach空间的张量积及其共轭空间

张量积函子是同调代数中研究模范畴的重要工具。在[1]的基础上,本文对B-空间的张量积做了讨论,得出一些新的结论。设E是B-空间,{E_i,j∈J}是B-空间族,作为赋范空间,则E(?)∪_(i∈J)E_i与∪_(i∈J)(E(?)E_i)等距同构。作为B-空间,E(?)_(?)∪_(i=1)~(?)E_i与∪_(i=1)~(?)(E(?)_(β_(?))E_i)的子空间等距同构。其次本文推广了著名的伴随同构定理([2]Th2.11).设E_1,E_2与F是B-空间,则(?)(E_1(?)_(?)E_2,F)分别与(?)(E_2,(?)(E_1,F)),(?)(E_1,(?)(E_2,F))等距同构.特别(E_1(?)_(?)E_2)分别与(?)(E_2,E_1),(?)(E_1,E_2)等距同构.最后,设E_i,F_i是B-空间,f∈(?)(E_1,F_1),g∈(?)(E_2,F_2),则存在唯一的φ∈(?)(E_1(?)_(β_1)E_2,F_1(?)_(β_2)F_2),记φ=f(?)g.令P={sum from i to f_i(?)g_i},则P与(?)(E_1,F_1)(?)_(?)(?)(E_2,F_2)的稠密子空间(?)(E_1,F_1)(?)(E_2,F_2)等距同构。特别E_1(?)E_2是(E_1(?)_(β_1)E_2)的子空间。本文中的记号同于[1]。文中涉及到张量积的范数都是Cross-范数。     

An evolutionary model of urban bus transport network based on B-space

In this paper, an evolutionary model of bus transport network in B-space is developed. It includes the effect of the overlapping ratio of new route on network performance and overcomes the disadvantage, i.e. lack of economic consideration, in the evolutionary bus transport network model in P-space proposed by Chen et al （2007）. The degree distribution functions are derived by using the mean-field method and the master equation method, separately. The relationship between the new stop ratio of a route, λ, and the error in exponential of degree distribution function from the mean-field method is developed as ASlope= λ/（1 -λ） ＋ ln（1-λ）. Finally, the bus transport networks of Hangzhou and Nanjing are simulated by using this model, and the results show that some characteristic index values of the simulated networks are closer to the empirical data than those from Chen＇s model.