异速生长定律与城市郊区化的分维刻画

从关于城市人口密度衰减的Smeed模型出发导出城市人口-城区面积异速生长关系式，然后导出刻画城市人口郊区化的Bradford—Kelejian模型；基于前述结果，从Beckmann城市体系异速生长方程出发导出反映城市郊区化的Mills模型，从而建立了Bradford—Kelejian模型、Mills模型与Smeed模型及其参数与分形维数的数理关系．文章证明．关于城市密度的Clark模型不能与Bradford—Kelejian模型及Mills模型有效沟通；进而揭示：Bradford—Kelejian模型和Mills模型的理论基础在于城市结构的自相似性质即分数维特征．城市人口的负指数分布最终会通过自组织机制向呈现幂指数分布的分形几何结构演化。

The law of allometric growth and theoretical foundation of several suburbanization models

This paper presents that the theoretical foundation of the Bradford-Kelejian model and Mills model on suburbanization lie in the law of allometric growth as well as fractal property. From Smeed's model on urban population density, the Bradford-Kelejian model is derived, and then through Beckmann's allometric model and the urban area-population allometric relationship, Mills' model is deduced out. The parameters from different models are integrated with one another and a number of equations are set up based on the mathematical transformation for the models mentioned above. An important conclusion is reached that the negative exponential distribution of urban density conforming to Clark's model will turn into negative power distribution conforming to Smeed's model because of the progress of suburbanization.