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And what's fallen out when we do that, because in each case, one of the first derivatives gives us the entropy.
当我们这样做时就得到了结果，因为在这些例子中，一阶导数是熵。
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OK, in each case, what these things are doing, is they're doing, what sometimes gets referred to as operator overloading.
这将会是个默认的或者说是，通用的来比较对象是否相同的方法，好，在每个例子中，这些事情正在做的，就是,一些与操作符重载有关的东西。
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So we know that in each case the heat is going to be the opposite of the work, but the work isn't the same in these two different ways of getting from here to here, right. So let's just see it explicitly. Here's our qA.
所以我们知道在每种情形下功,与热量相差一个负号,但从这里到这里，在这两条路径,中的功是不同的，对吧？,那么让我们明确地看一下。
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In this case, 6 valence electrons for each oxygen, so we have 18 total valence electrons.
在这种情况下，每个氧原子都有六个价电子，因此我们总共有十八个价电子。
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And then confronted with a new case, we found ourselves reexamining those principles, revising each in the light of the other.
当我们面临新的情况时，我们重新检验这些原则，根据新的情况修正这些理由或原则。
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So Alpha in this case is better against Alpha, and Beta is better against Beta, but neither dominates each other.
所以对方选α时我应该也选α,她选β我也应该选β,这里没有优势策略
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Two pieces of memory actually touching each other or you touching memory that you don't actually own, in which case the computer doesn't really know what to do and just, bam.
两块内存相互覆盖,或者你覆盖了不存在的内存，那样的话计算机不知道,该怎么做，只有崩溃。
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Sidney's talking about the various kinds of discourse: - divinity, hymnody, science, philosophy, history-- in other words, all the ways in which you can contribute to human betterment and human welfare. He says in the case of all but one of them, each discourse is a "serving science."
西德尼进行了很多方面的阐述：,神学，赞美诗，科学，哲学，历史-,换句话说，所有你能想到的,对人类福祉有益处的方式,他说这里面除了诗学，其他都是“服务性学科“
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But it's a valuable thing. It says, in each case, I return some useful value from this procedure.
但是这就是变量，是在每个例子中，我从这个程序中返回了一些有用的值。
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In fact, it took the same number of steps as it did in the other case, because each time I'm cutting it down by a half.
因为每次我都把问题的规模,缩小一半，这很棒，好，接下来让我们这么做。
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In the second case, if both firms undercut each other, you end up with low prices, that's actually good for consumers but bad for firms.
在第二个案例中,如果两家企业互相削弱,最终会压低价格,这对消费者有利,但对企业不利
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The first grade corresponds to the row player, me in this case, and the second grade in each box corresponds to the column player, my pair in this case.
单元格内第一个成绩是我的成绩,每个单元格第二个成绩是,我对手的成绩
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How many moles of gas are there in each case, in reactants and products? If that changes, of course you know that the pressure in there is going to change at constant volume if the amount of gas in there is changing.
在反应物和生成物中，各有多少摩尔的气体？,如果它发生了变化,当然在等体条件下，如果气体的总量,发生了变化，压强也会发生变化。
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Right? If that was the case in that code, then my complexity is no longer log, because I need linear access for each time I've got to go to the list, and it's going to Lisp be much worse than that.
这里的复杂度不再是对数的了，因为每次在列表中，查找需要线性访问,可能还要糟糕,其实，有些编程语言，如。
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H2 So the simplest case we can think of is with h 2 where we have two unpaired electrons, each in a 1 s orbital of a separate h atom.
最容易想到的例子是2,我们有两个未配对电子，每个都在一个分开的1s轨道上。
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And in this case, we go from 8 to 4 to 2 to 1 three times and then on each iteration of this algorithm, each pass across the board I'm touching N numbers, so that means I'm doing N things, log N times.
在这个例子中，我们从8得到4，到2，再到1，是3次,在这个算法的每次迭代中，每一趟我都会操作N个数，也就是所我每次要做N步操作，一共要做，log，N，次。
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