本文所研究的光滑函数都有严密的数学推导，以及对正号函数逼近性能的详尽理论证明。

For each smooth function in this paper, the theoretical basis, the detailed derivation process and performance are described.

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华莱士已经提出与达尔文相似的理论，达尔文担心，如果华莱士第一个发表研究成果，那么，自己更详尽的想法将被忽视。

Wallace had developed a similar theory to Darwin's, and Darwin feared his own, more detailed ideas would be neglected if Wallace was the first to publish his results.

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这种理论可能解释为什么睡梦中的情景只和我们记忆中的情景一样详尽。

This theory would explain why dream images are only as detailed as our memories.

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If the dualist were to start offering us some elaborate theory of consciousness, "Well, there's these sorts of soul structures, and those sorts of soul structures, and these create these sensations and those create those sensations.

如果二元论者试图,为我们提供一个详尽的意识理论学说,你看,这是灵魂的什么什么结构,那是灵魂的什么什么结构,这些产生了这种感觉,那些产生了那种感觉

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