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- W2393488145 abstract "By modifying the assumptions of Steindl's model as allometric relationships:dP(T)/dT=gP(T),df(T)/dT=-rf(T),where P(T) is the average size of cities of age T,f(T) is the number of cities of age T,parameters g and r represent respectively coefficients of growth of P(T) and f(T),we deduce a set of generalized Beckmann-Davis model of city hierarchies and city-size distribution,namely,δ n-law advanced by the authors,as follows:P m=P 1λ 1-m ,f m=f 1δ m-1 ,where λ=e g,δ=e r,P 1 is the size of the largest city(cities),f 1 is the number of the largest city(cities),and generally,f 1=1, m is the ordinal of city class (m=1,2,...,N).From the generalized Beckmann-Davis model,a three-parameter Zipf model can be derived as P(r)=C(r-α) -dz ,where r is the rank of a city,P(r) is the size of the r th city,as for parameters,C=P 1 dz ,α=1/(1-δ),dz=lnλ/lnδ=g/r.Based on general geometrical measure relationship,P 1/D p m∝f -1/D f m,an equation of fractal dimension is constructed as dz=g/r=D p/D f,where D p is the generalized dimension of P m,and D f,the dimension of f m.In reality,D p→D f,g→r,so dz→1,and when dz=1,we have what is called 2 n-law presented by K.Davis(1978)." @default.
- W2393488145 created "2016-06-24" @default.
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- W2393488145 date "2001-01-01" @default.
- W2393488145 modified "2023-09-25" @default.
- W2393488145 title "Reconstructing Steindl's Model:from the Law of Allometric Growth to the Rank-Size Rule of Urban Systems" @default.
- W2393488145 hasPublicationYear "2001" @default.
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