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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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If you start segregating the gases, there are fewer possible configurations that because you're forcing a particular set of circumstances.
如果你开始分离这些气体，整个系统所具有的可能的状态就会变少,你强加了一个特定的条件。
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And if they can identify those things, they can think about a life work, they can think about their calling.
如果他们能明确这些东西，他们就能思考一生的工作，思考一生的使命召唤。
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If there were no voltage on the plates, we would expect everything to be over here in some negative value falling.
如果板子上没有速度，这些可能都在这,都是负值下降的。
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And we can actually better visualize this if we plot how that energy changes as a function of internuclear distance.
而我们就能更清楚地看到这些，如果我们画出,能量随核间距的变化曲线。
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If I want to create a set or a sequence representing these things, I simply insert into that list.
如果我想创建一个集合,或者一个序列表示这些东西，我只要简单的把它插入列表中。
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So realize if it doesn't quite sink in today, not a problems in terms of these low level details.
如果你们没有完全吸收我今天讲的内容，没关系,这些小细节都会在习题集中找得到。
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I wish it didn't say "exit," but it does say "exit," because that kind of weakens my point, but over many auditorium doors a red light just hangs there.
如果这些灯上没有注明出口就好了“,因为这样会削弱我要证明的观点，礼堂的门上一般会挂着一盏红灯。
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To question those beliefs would seem to exhibit a kind of lack of civic faith faith in our ruling opinions.
如果质疑这些信念,似乎是表现出缺乏公民信仰,对我们统治主张的信仰。
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What's going on here, so go back to your Economics 115 or 150, if you took either of those courses.
这到底是怎么回事,回顾一下经济学115或者150,如果你们有人学过这些课的话
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And if any of you here are nodding in agreement at these sentiments, that's not such a good sign.
如果在座有同学,点头同意这些人的观点，这可不是一个好迹象。
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This is something I used to announce near the end, but then some people felt that it's not fair not to know this from the beginning.
这些话我以前都是在期末的时候说的,但后来有些同学反映,如果不在课程一开始知道这些会很不公平
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If they awarded options that were "In the money" -that means already exercisable at profit -then they would be subject to a tax liability immediately, so they don't want to do that.
如果这些奖励的股票期权是价内期权,这说明期权行权即可赢利,这些利润是要交税的,当然他们想避免交税
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And to say, if we believe in these values, if we believe in liberty and democracy and equality and justice and tolerance and humility and faith, then this is what our foreign policy should look like.
如果我们相信这些价值，如果我们相信自由，民主,公平和正义,以及宽容，谦逊和信仰，那我们的外交政策,也该如此。
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If you change the animal's environment and you give it access to these sort of foods, and these are the pictures that I showed in the first class, and you remember I asked you what constituents of this diet promoted obesity and you said it was fat, sugar, and variety that was correct.
如果你改变动物所在环境,再给它们这些食物,这些图片我们在第一课见到过,我问过这些食物中哪些成分使人发胖,你们说脂肪,糖和其他成分,没错
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But in terms of us going to the grocery store and thinking about things, probably we're all breathing sighs of relief.
但是如果我们走进商店,以后想到这些的话，我们都应该松一口气。
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I said that if I was really hygienic, and you can now wonder about how often do I shower?
但是这真的很棒，对不对？,那么为什么我要说这些呢？,我说过如果我真的很讲卫生的话？
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And once I have values, I want to get a hold of them so I can give them names.
如果我有想保存的值，我可以命名这些值,也就是进行了绑定。
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If the bonding energy is very strongly negative, thermal energy isn't great enough to disrupt those bonds and allow those bonds to be broken and then have fluidity.
如果键能非常强，热能并不足以,打破这些化学键,破坏这些化学键,并使它们液化。
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What if I were able to mix the orbitals?
他说如果将这些轨道混在一起会怎么样呢？
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But in fact, if you just run your fingers again and again over this floppy disk you are disorienting those particles or knocking them off perhaps altogether, depending on the medium.
事实上，如果你把手指一次次的在磁盘上面滑动,这些粒子就会变的无极性,或者把它们整个搞坏，而这取决于媒介。
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So, this makes this chart shown in pink make a lot more sense, because if we're way out at very far distances, essentially what we have here is we're talking about two separate atoms.
因此综合考虑这些因素可以发现这条粉红色曲线很合理，因为如果我们离得非常远，本质上来说,我们讨论的就是两个分开的原子。
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Run merge sort on those. By induction, if it does the right thing, I'm going to get back two lists, and I'm going to then merge Them together. Notice what I'm going to do.
在这些上面再运行归并排序，根据归纳，如果这样是正确的,我将重新得到两个列表,然后我会把它们合并在一起。
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It's a way of breaking the code up into modules. Modules that makes sense on their own. Modules that we can reuse in multiple places. Modules that, if you like, Isolate components of the process.
能将代码分解为模块,模块能够独自运作,我们能在很多地方再利用这些模块,如果你喜欢的话，模块可以被看作是过程独立的组成部分。
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So, having other particles around that have the same energy that you could technically add up if you were adding them up like a wave, you can't do the same thing with particles, they're all separate.
所以，如果它们是波,你可以把其他的,拥有相同能量的粒子加起来，但是你不能把这些粒子加起来，因为它们是分离的。
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If you do look down at the Periodic Table and get above 109, Uun Uuu Uub you will see these strange notations here, Uun,Uuu,Uub What is all of this?
如果你看周期表的下面部分,到109号，你会看到这些奇怪的符号,这些是什么呢？
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Because if we think about wave behavior of electrons and we're forming bonds, then what we have to do is have constructive interference of 2 different electrons, right, to form a bond, we want to and together those probabilities.
如果我们考虑,电子的波动行为,并且，我们要成键的话,我们要,把，这些概率，加在一起,如果。
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All right? And if you want to do other things, whoops, sorry-- and add them together, we will get out, again, a concatenation of that string. And these will, we'll let you work through the variations, but these are the simple expressions we can use.
对不对？如果你想要进行一些别的操作，哦，对不起-是加到一块，然后结果值也是，两个字符串的链接，这些会，我们会让大家慢慢学习变量，但是这些是我们能用的最简单的表达式。
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And that idea was, we make a guess in the middle, we test it so this is kind of a guess and check, and if the answer was too big, then we knew that we should be looking over here. If it was too small, we knew we should be looking over here, and then we would repeat.
这些有理数是有序排列的,然后我们的想法是,首先在中间取个数作为猜想数，然后对这个猜想数进行验证，如果由猜想数得到的答案太大,我们知道应该跳过，比猜想数大的那个区间，如果太小的话。
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