We now derive, based on the above results, sufficient conditions for a Cartesian product network.

我们现在得出，基于上述结果，有足够的条件，笛卡尔积网络。

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Attempted analyses of concepts in terms of necessary and sufficient conditions, even where they fail, abet discovery.

试图从必要条件和充分条件的角度来分析概念，即便失败了，也能有所发现。

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There will also be a large number of proposed analyses of the concept of an artwork, articulated in terms of necessary and sufficient conditions.

也有理论家提出的许多关于艺术品这个概念的分析，是以必要条件和充分条件这种方式得到陈述的。

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Intelligence and wit were necessary but not sufficient conditions.

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The Bottom line: Billions can buy many amenities and trophies, the necessary conditions to getting a good life, but they cannot buy peace of mind, sanity, and friendship, the sufficient conditions for maintaining a good life.

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In their latest FOMC meeting, the committee agreed to set numerical thresholds for rate hikes, which are necessary but not sufficient conditions: the unemployment rate must fall to 6.5% or below, and the one-to-two year inflation projection should be at or below 2.5%.

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