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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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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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So what is the function of Kallipolis, ? this perfect, this beautiful city?
因此，到底，Kallipolis，的功用为何，这个完美的美丽之城？
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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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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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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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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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The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.
解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件
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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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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 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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The author is a signal, is what Foucault calls a "function."
作者是一个标志，就像福柯所说的“功能“
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If we overlay what the actual molecular orbital is on top of it, what you see is that in the center you end up cancelling out the wave function entirely.
如果我们把真实的分子轨道覆盖在上面，你可以看到中间的,波函数是完全抵消掉了。
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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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So, we do this here for the photoelectric effect, and in terms of the photoelectric effect, what we know the important point is that the incoming photon has to be equal or greater in energy then the work function of the metal.
所以，我们做这个是为了说明，光电效应，在光电效应方面，我们知道的最重要的事情,就是入射的光子能量必须等于,或者大于金属的功函数。
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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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So again if we look at this in terms of its physical interpretation or probability density, what we need to do is square the wave function.
如果我们从物理意义或者,概率密度的角度来看这个问题，我们需要把波函数平方。
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So what is the wave function squared going to be equal to?
波函数的平方等于什么？
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So, if we look at this graph where what we're charting is the internuclear distance, so the distance between these two hydrogen atoms, as a function of energy, -- what we are going to see is a curve that looks like this -- this is the general curve that you'll see for any covalent bond, and we'll explain where that comes from in a minute.
因此，如果我们来看一看这幅曲线图,这里我们画的横坐标是核间距，也就是这两个氢原子之间的距离，纵坐标是能量，我们看到的这是能量关于核间距的曲线-,这是一条普遍的曲线，在研究任何共价键时你都会遇到，我们马上就会解释一下它是怎么来的。
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So in hydrogen atom a, I'll depict that here where the nucleus is this dot, and then the circle is what I'm depicting as the wave function.
在氢原子A里，我在这里把原子核画成一个点，这圆就是波函数。
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You can also have angular notes, and when we talk about an anglar node, what we're talking about is values of theta or values of phi at which the wave function, and therefore, the wave function squared, or the probability density are going to be equal to zero.
我们也可以有角向节点，当我们说道一个角向节点时，我们指的是在某个theta的值,或者phi的值的地方，波函数以及波函数的平方，或者概率密度等于零。
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In contrast when we're looking at a p orbital, so any time l is equal to 1, and you look at angular part of the wave function here, what you see is the wave function either depends on theta or is dependent on both theta and phi.
相反当我们看ｐ轨道时，任何时候ｌ等于１,你们看它的角向波函数，你们可以看到它要么是和theta有关,要么是和theta和phi都有关。
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