POPULATION DENSITY FUNCTIONS: A DIFFERENTIAL EQUATION APPROACH*
提出一种新的数学技术来描述人口密度函数，识别了两个长度尺度，推导出微分方程并得到渐近解，通过匹配渐近展开和多尺度方法应用于大都市和区域层面的人口密度。
"This paper introduces a new mathematical technique to describe population density functions. Two length scales, which characterize the variation of these density functions within a region, are identified. A differential equation is derived and asymptotic solutions obtained. Two specific techniques, the method of matched asymptotic expansions and the method of multiple scales, are introduced and illustrated by application to population densities at both the metropolitan and regional levels."