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The new elementary catastrophe -The thermal stability of continuous stirred tank reactor

机译:新的基本灾难-连续搅拌釜反应器的热稳定性

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Catastrophe theory is a new branch of mathematics regarding the discontinuous phenomena in nature. It classifies the critical points according to the potential function and studies discontinuity near them. Generally speaking, the catastrophe is mainlyelementary catastrophes. There are seven elementary catastrophes according to Thom's deducing, namely, fold, cusp, swallowtail, butterfly, elliptic umbilic, hyperbolic umbilic and parabolic umbilic. But Thorn's deduction is restricted to those functions which embed in the structural stable group depending on finite expansion parameters, and abandons these functions, such as y=exp(-1/x~2), which cannot be analyzed by finite expansion.
机译:突变理论是关于自然界中不连续现象的数学的一个新分支。它根据潜在功能对临界点进行分类,并研究临界点附近的不连续性。一般而言,灾难主要是基本灾难。根据Thom的推论,有7种基本的灾难,即折叠,尖,燕尾,蝴蝶,椭圆形脐,双曲线脐和抛物线脐。但是,Thorn的推论仅限于依赖于有限扩展参数嵌入到结构稳定组中的那些函数,而放弃了这些函数(例如y = exp(-1 / x〜2)),而这些函数无法通过有限扩展进行分析。

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