基于数理视角的空间界面存在性研究——以河南省城乡界面为例

空间界面理论已显示出强大生命力,但其理论架构还不完善。现有研究基本上是建立在"空间界面确实存在"这一经验判断的前提下进行的,对于其存在性还缺乏理论验证。在提炼空间界面唯象理论的基础上,构建了空间界面的数理模型,并以城乡界面为例,以空间为内生变量,空间中的元素如经济、社会、文化等为外生变量,构建联立方程模型,以河南省108个县域为空间单元,采用三阶段最小二乘法和迭代三阶段最小二乘法进行参数估计,建构了城市系统和乡村系统的函数,并进行了数理推导与求解。研究表明,城市函数与乡村函数存在着交集,且其交集为无穷多个点组成的域面,即存在一个城市与乡村系统空间及其要素相互交织而成的独立系统,进而从理论上证明"城乡界面是存在的"。

Existence of Spatial Interface Based on Mathematical Research: A Case Study of Urban-Rural Interface in Henan Province

The theory of spatial interface has shown a great vitality,but its theoretical framework is not perfect.The existing researches are basically under the premise of "space interface does exist",which based on experiences while lack of theoretical verification.Based on the phenomenological theory of space interface,this research constructed the mathematical model of space interface.Taking the urban and rural interface as an example,the space as the endogenous variable,and the elements in the space,such as economy,society and culture as exogenous variables,it built a simultaneous equation model.And then taking 108 counties in Henan Province as spatial units,using the three stage least square method and the iterative three stage least square method to estimate the parameters.The mathematical derivation and solution was carried out finally.The results show that there are intersections between urban and rural functions.Moreover,these intersections are a region that composed by infinite points,which showed that there is an independent system caused by both space and its elements of urban and rural system.The proposition of "space interface exists" is proved theoretically.