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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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We can graph out what this is where we're graphing the radial probability density as a function of the radius.
我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。
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When you call a function, what actually happens is that function gets its own chunk of memory that's identical in size to the data type that it expects.
当你调用一个函数，实际上发生的是,函数得到了自己的内存块，相同的类型,是占有一样大小的内存的。
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So let's understand: what is the nature of exponential function so that we can understand the power of one?
让我们先理解指数函数的本质,以便理解“一“的力量？
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What I plot on this graph here is as a function time, years, dates, life expectancy as a function of time.
在这儿的这张图是,一个关于时间,年,日期的函数,将寿命长短作为时间的函数
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Usually what I want to talk about is what's the smallest size class in which this function grows? With all of that, what that says b is that this we would write is order b.
通常我们想要的是,方法增长时最贴切的描述,也就是说，在这个问题上,算法关于。
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I tell you something about the second derivative of a function and ask you what is the function.
我告诉你一个函数的二阶导数,然后问你这个函数是什么
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It's the notion of what the function of that state is, I think, that is most striking.
我认为,这种关于城邦功能的观念,才是最为引人瞩目的
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What I am looking at here is boiling point as a function of atomic number.
我在看的是非典,作为原子序数的功能。
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What is Socrates trying to do here, and what is that metaphor, ? that central metaphor, ? what function does it serve within the work?
苏格拉底倒底想干吗，那个隐喻，那个核心隐喻是啥，它在本书中有啥功用？
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And so the food is a broader constituent of what we consume; the nutrient will be the pieces of the food that affect bodily function.
所以食物的概念要比吃的东西更加广泛,食物中的营养素影响着我们的人体机能
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We assume that unless we're dealing with Scheherazade, it has to have an end, but at the same time we might well ask ourselves, why does it have a middle? What is the function of the middle with respect to a beginning and an end?
而且我们认定一定会有结尾，除非讲故事的是那个，《天方夜谭》中的苏丹新娘，但是我们要问自己了，为什么故事一定要有经过呢？,故事的经过对于开头结尾来说起到什么作用呢？
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What is Firm 2's best response as a function of q1?
1的函数即公司2的最佳对策是什么
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And that...which itself is a function of... who is in power and who was then in power and what type of parties they are in... you know, sort of ruling parties.
只要政府能做出措施就好。,不管前后任的执政者是谁,他们所属的是哪个党派。,谁是执政党。
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Life will become meaningful as a function of your pursuit rather than you're expecting some objective validation because the world is what the traditional, particularlly traditional religions view said it was. Go ahead.
你的生活会因为有所追求而变得有意义,而不是去期待一些客观实在的好处,因为世界就如传统宗教,所定义和限定的那样,你继续说吧。
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It's also about: how banks operate; what their function is in our society; and, why they are such important institutions that have gone back for hundreds of years and remain powerful, central features in our economy.
也会讲到,银行如何运作,银行在社会上的功能,以及为什么几百年来,银行依然在经济生活中拥有,重要的作用
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There's no classical analogy that explains oh, this is what you can kind of picture when you picture a wave function.
可以解释：,哦，这就是，你想象的,波函数的样子啊。
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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.
波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。
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So, first, if I point out when l equals 0, when we have an s orbital, what you see is that angular part of the wave function is equal to a constant.
首先，如果ｌ等于０,那就是ｓ轨道，你们可以看到,它波函数的角度部分是一个常数。
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Well the idea of a hash, in fact, what's called a hash function is to have some way of mapping any kind of data into integers.
我要怎么做？实际上想法还是哈希,通过一个哈希函数,把任何种类的数据都映射成整数。
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What is going on as a function of time?
作为时间的函数它将如何变化
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So, what's the idea? If I know what my hash function does, it maps, in this case characters into a range zero to 256, which is zero to 255, I create a list that long, and I simply mark things.
我知道我的哈希函数做什么,在这个例子中，它将字母，映射成0到255的256个数字，我创建了一个这么长的列表，并且我只是简单的标志这些东西。
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Notice that the relationship between the rhetorical is and the grammatical is is basically the relationship between what Jakobson calls the "poetic function" and the "metalingual function."
注意下,修辞学上的is和语法中的is之间的关系,基本上就是雅各布森所说的,“诗功能“和“元语言功能“之间的关系“
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And just as with variables, you should use some common sense, some style here, and the function's name should X Y communicate what it does, calling it X or Y or Z is generally not all that helpful.
就像变量，你使用一些常识，一些类型，和函数名需要,传达它所做的事情，把它叫做,或者Z通常是没有什么用处的。
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We also talked about well, what is that when we say wave function, what does that actually mean?
我们还说了，当我们讨论波函数时，它到底有什么意义？
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But before we get to that, in terms of thinking just think, OK, this is representing my particle, this is representing my electron that's what the wave function is.
但是在我们谈论那个部分之前，在理解方面，仅仅是理解，好的，它代表了粒子，它代表了电子,这就是波函数。
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And what is plotted below is the actual wave function, so you can see it starts very high and then the decays down.
下面这画的是，波函数，你们可以看见它开始非常高,然后衰减下来。
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This is a table that's directly from your book, and what it's just showing is the wave function for a bunch of different orbitals.
这是一张你们书里的表格，它展示了各种,不同的轨道波函数。
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So, we can think about what is it that we would call the ground state wave function.
我们来考虑一下,基态的波函数，是怎么样的。
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