By way of the tip-point model of sudden change theory, the paper studies the physical process of single grain matter breaking.

本文利用突变理论的尖点模型研究了单颗粒物料破碎的物理过程。

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Accordingly, the radiant scopes of different factors between Zhengzhou and other cities concerned are analyzed by using the theory of breaking point.

以此为基础，用裂点法对郑州与周边相邻、相关城市的不同城市要素相互作用的范围进行了分析。

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