区域双核结构模式的数学推导

The Mathematical Derivation of the Model of Regional Dual-nuclei Structure

研究表明,现有关于区域可达性的计算公式,其实质都是给定区域中某一质点的居中性的测量,因此,现有的区域可达性其实仅指区内可达性。据此,将区域可达性理解成由区内可达性和区外可达性2部分组成,并重点讨论了区外可达性的测算方法。研究表明,区外可达性定量模型的建立无法简单地套用现有的区内可达性的测算方法,原因是门户质点的区外可达性值由于距离为0故无法运用现有的公式予以测算,为此我们通过区外虚拟质点的引入巧妙地解决了这一难题。依据重新定义的区域可达性,本文在均质平原背景的假设条件下推导出了区域双核结构模式的形成机制及相应的参数条件。流域作为双核结构模式形成的理想区域,也在此得到了验证。由于区域双核结构模式仅是区域空间结构类型的一种,因此,随着模型参数的改变,即可进一步推导出其它的空间结构类型。这样,本文建立的关于区域可达性的系列测算公式,显然已不仅仅适合于区域双核结构模式的验证,而是一个适用于区域空间结构演化与区域空间结构类型分析的具有普适意义的数学工具。

In order to derive the regional dual-nuclei structure by the method of building mathematical model, this paper redefines regional accessibility and establishes the formula to calculate it. Our research indicates that the present formula of accessibility measures materially the centrality of one point in a special region. So the present regional accessibility is only the regional internal accessibility. Based on this, this paper divides the regional accessibility into two parts as regional external accessibility and regional internal accessibility. The method to measure regional external accessibility is discussed in detail. The present method fails to measure regional external accessibility because it is impossible to get the value of the regional external accessibility of the gate point. We hypothesize a virtual point located outside the region to resolve the problem. Using the new concept of regional accessibility, this paper derivates the mechanism of the model of dual-nuclei structure and parameters of its existence under the hypothetical background of homogeneous plain. It is also verified that river basin is the best background for dual-nuclei structure to appear. Other spatial structure models can be derived by varying the parameters, because regional dual-nuclei structure is merely one of the spatial structure models.