AI 中文总结
该研究从历史考量出发，探讨数学物理领域对衰老的多种建模尝试，分析施瓦茨空间等形式化的应用，提出需构建能筛选持久结构的新型衰老表征形式化。
AI 中文摘要
从一些历史考量出发，我们研究数学物理领域内对衰老建模的各种尝试。例如，我们研究衰退函数的数学理论，自洛朗·施瓦茨关于分布的研究以来，这类函数通常定义在所谓的“施瓦茨空间”上。我们阐释这种本质上属于分析学的形式化如何适用于生命力（或多种生命功能）衰退的表征。随后，我们表明存在许多其他可能的形式化，它们利用代数的资源，特别是曹、金和鲁什的“倾斜”理论以及关系结构理论，在后者之上可以定义出卡梅隆意义上的代数“年龄”概念。但我们最终认为，一种更具积极性的衰老表征，且与从古到20世纪的诸多文化来源所传达的内容相一致，应当运用另一种形式化，这种形式化能够在生物与其环境的整体博弈中，于其他事物衰退的过程中筛选出不会衰退的持久结构。
英文摘要
Starting with some historical considerations, we examine the various attempts to model old age that fall within the realm of mathematical physics. For example, we study the mathematical theory of declining functions, which, since Laurent Schwartz's work on distributions, are generally defined on what is called a "Schwartz space." We explain how this essentially analytic formalization applies to the representation of the decline of vitality (or of a number of vital functions). We then show that there exist many other possible formalizations that utilize the resources of algebra, in particular the theory of "inclines" of Cao, Kim, and Roush and that of relational structures, on which an algebraic notion of "age," in Cameron's sense, can be defined. But we maintain, in conclusion, that a more positive representation of old age, consistent, moreover, with what a number of cultural sources from Antiquity to the 20th century tell us, should mobilize another type of formalization, capable of selecting, within the overall debate between the living being and its environment, persistent structures that do not decline amidst the decline of others.
Comments39 pages, 6 figures
