中文摘要：

区域密度函数是分析区域空间结构及其变动趋势的有效工具，但其在实证研究中的应用尚比较少见。现有研究大多使用单中心密度函数，研究局限于单中心城市区域。探讨了适用于多中心城市区域的区域密度函数的形式，并进一步将其应用于对京津冀都市圈空间结构特征及区域增长模式的分析。使用探索性空间数据分析方法分析区域人口密度分布发现，京津冀都市圈具有多中心空间结构特征。分别应用单中心和多中心区域密度函数分析京津冀都市圈空间结构与增长模式，单中心密度函数的分析显示京津冀都市圈的主要中心城市尚处于向心集聚的发展阶段，而多中心密度函数的分析则显示京津冀都市圈呈现集聚与扩散并存的空间发展趋势，并且不同层次的中心城市表现出三种不同的增长模式，分别为去中心化扩散、中心增长型扩散和向心集聚。由于多中心区域密度函数综合考虑多个中心对区域人口密度分布的影响，因此能更准确地反映京津冀都市圈人口密度分布的变化趋势。

英文摘要：

The study of regional spatial structure and growth patterns has been of interest to those concerned with regional planning and analysis. Spatial structure can be defined in various ways, and one major perspective relates to investigating the distribution of population densities. The population density function, which has been applied widely within the context of an urban area, can be extended to analyzing regional spatial structure and growth patterns. However, most of the empirical studies so far conducted have employed the density function based on the monocentric model, which is not appropriate for modeling the modern metropolitan region that usually takes a polycentric form. This study first discusses the form of polycentric regional density function, and then applies it to the Beijing-Tianjin-Hebei metropolitan region. The polycentric density function is assumed to be an aggregate of the individual monocentric density functions of the various regional urban centers. Through the exploratory spatial data analysis of the population density distribution, we find that the Beijing-Tianjin-Hebei metropolitan region does have a polycentric spatial structure with four regional density centers： Beijing, Tianjin, Baoding and Shijiazhuang. We test the most commonly used monocentric regional density function form, the square root negative exponential density function, and the results show that it is basically applicable to our analysis. Then we apply both the monocentric and polycentric density functions to study the spatial structure and growth patterns of the Beijing-Tianjin-Hebei metropolitan region during the period from 1990 to 2000. The analysis with the monocentric density function shows population still concentrate into the major urban centers of the region, while the analysis with the polycentric density function finds the coexistence of concentration and dispersion of population in the region, and reveals three different growth patterns of the urban centers at the different levels,which are the dispersion pat