写一个我特别感兴趣的 非交换拓扑（Non-Commutative Topology, NCT)和一元域(Field with one element, \mathbb F_1 ） 一、非交换拓扑简介 所谓的 “NCT” ...

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这个问题非常有趣。数学家通常致力于改进复杂繁琐的证明，因此这样的例子肯定是相当多的，但一下子也不太好想起来。这里我找到了几个代数的例子，如果以后看到更有趣的再来继续更新。 有限群的Cauchy定理 定理1(Cauchy 定理). 若 p 是有限群 G 的阶的素因子，则 G 中有 p 阶元。 大多数抽象代数教科书上都会这样证明： 考虑 G 中 p ...

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Title: Algorithms for the synthesis of complex technical systems with ill-defined parameters Abstract: The work aims to improve the conditions for solving the problem of increasing the productivity ...