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MNDO calculations and group theory were carried out on tetraphenyl porphyrine(TPP) to obtain its optimum molecular geometry.

运用MNDO计算和群论,优化较满的中四苯基卟啉(H2TPP)的分子构型。

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interdependence, interdependency, interdependeney, interdependent, interdependently, interdialling, interdict, interdiction, interdictory, interdiffuse,

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3G, 401(K), a,

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高等数学之美

These permutation groups go by the name S sub n, and they play an important role in group theory.

这些排列群的名称为 S sub n,它们在群论中发挥着重要作用

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TED-Ed(视频版)

And, in fact, that's exactly what most solvers do, even using a group theory notation indicating turns.

而且,事实上,这正大多数求解器所做的,甚至使用指群论符号。

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TED-Ed(视频版)

However, using group theory we can analyze the cube and determine a sequence of permutations that will result in a solution.

, 使用群论,我们可以分析立方体并确定将产生解决方案的排列序列。

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高等数学之美

This is one of many different examples where understanding the nature of these simple groups, these atoms, actually matters outside of group theory.

多不同例子之一,在这些例子中,理解这些简单群、这些原子的本质实际上在群论之外很重要

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高等数学之美

Well, it's the size of the monster, but to explain what that means, we're gonna need to back up and talk about group theory.

嗯,这的大小, 但为了解释这意味着什么,我们需要支持并讨论群论。

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TED-Ed(视频版)

That question doesn't make a lot of sense at first, but an abstract mathematical field called group theory holds the answer, if you'll bear with me.

这个问题一开始并没有多大意义,但如果你能忍受我的话,一个叫做群论的抽象数学领域就有了答案。

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高等数学之美

When you have a correspondence where this remains true for all products, it's called an " isomorphism" , which is maybe the most important idea in group theory.

当你有一个对所有产品都成立的对应关系时,它被称为“同构” ,这可能群论中最重要的想法

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高等数学之美

In your mathematical life, you'll see more examples of a given group arising from seemingly unrelated situations, and as you do, you'll get a better sense for what group theory is all about.

在你的数学生活中, 你会看到更多由看似无关的情况产生的给定群的例子,当你这样做时, 你会更好地理解群论的全部内容。

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高等数学之美

To give a hint for why this is useful, remember how we said that group theory can be used to prove that there's no formula for a degree-5 polynomial the way there is for quadratic equations?

为了提为什么它有用,还记得我们如何说过群论可以用来证明 5 次多项式不存在像二次方程那样的公式吗?

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高等数学之美

In the 1970s, mathematician John McKay was making a switch to studying group theory to an adjacent field, and he noticed that a number very similar to this 196,883 showed up in a completely unrelated context, or at least, almost.

20 世纪 70 年代, 数学家约翰·麦凯 (John McKay) 而研究邻近领域的群论,他注意到一个与 196,883 非常相似的数字出现在完全不相关的背景中,或者至少几乎不相关的背景中。

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interdome, interdominion, interdorsal, interdotting, inter-drain, interdupe, interedependency, interelectric, interelectrode, interelectrodetransconductance,

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3G, 401(K), a,
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