Fourth , the theoretical model of optimum technological growth rate under discrete change is erected . technology is a unique production factor because technological growth experiences a mutation when technological increase accumulates to a certain extent . under this condition , the point - mutation model in tom ’ s mutation theory is applied to explain the phenomenon of technological 将技术作为不同于劳动和资本的特殊生产要素进行考察，即当技术量的积累达到一定程度时，技术增长会产生突变，在此条件下，运用汤姆突变理论中的尖点突变模型，解释了技术突变现象，讨论了劳动和资本的不同组合变化下，在临界点附近技术突然跃升或下降的突变性质；构建了技术突变完成后的技术增长率优化理论模型。
The modeling method can solve not only the problem of the number and the location of breaks which the multiple structural changes theory requires , but also take the break kinds of every structural change into consideration , which is likely to be of particular relevance in practice 这种建模方法,不仅能够解决多结构突变理论要求解决的结构突变个数和结构突变点的定位问题,而且能够同时考虑每个结构突变点的突变类型,从全局出发考虑多个突变点,搜索出显著的多个结构突变点,符合实际情况。
The reference index system for the appraisal of logistics partners is established , and two multi - objective decision making approaches for the partner appraisal are analyzed , the appraisal approach based on the ahp - topsis and the appraisal approach based on the catastrophe theory . the comparative research is held with the appraisal results from the different approaches with their practical applications in the field cases 建立了物流合作伙伴评价的参考指标体系，剖析了物流合作伙伴评价的两种多准则决策方法? ?基于ahp - topsis的评价方法和基于突变理论的评价方法，并针对仿真实例对几种评价方法的评价结果进行了比较研究。
A new method is proposed in this paper for analysis of the stability of slope in unsaturated soil affected by rain infiltration based on catastrophe theory , take into account that rainfall infiltration is one of the major factor causing the slope failure of unsaturated soil and the failure is usually abrupt 降雨入渗往往是非饱和土基坑边坡失稳的主要诱发因素之一，同时边坡失稳又具有突发性。本文基于突变理论，提出了考虑降雨入渗影响的非饱和土基坑边坡稳定性分析方法。
