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"The point is this the growth of a country is a function of how many entrepreneurs they have,"
VOA: standard.2010.01.31
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And this is a function of space.
这是空间函数。
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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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This is going to be a function, I only need two variables, and here I've got three variables down.
我们只，需要两个变量，而现在这里有三个变量。
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You can be reflect about how you do this, but there is slightly different function that person giving a presentation has.
你可以想想你可以怎么做这个，对于做陈述的那个同学来说,要求有一点不同。
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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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As I see it, the official function of this simile is to give us a sense of the size of Satan's shield and thereby to give us a sense of the size of Satan himself.
在我看来，这个比喻的正式的作用,是要给我们展现出撒旦的屏障的规模,因此来展现撒旦自身的伟岸。
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Language of this source is a device, and in relation to other devices it's called a "function."
语言是一种工具，和其他工具一样有功能“
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Because certainly there is a theory that art's main function is to provide succor and solace in this "vail of tears". -Right.
因为确实有一种理论认为艺术的主要,功能是提供帮助与安慰,因为世界纷繁而痛苦，-对的。
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If you're writing a one line function, whose sole purpose in life is addition, and, clearly, this is about addition, well, then it's, in fact, A reasonable to use a shorter symbol like A, but I do have to specify it's type.
如果你在写一个一行的函数，它唯一的目的是,做加法，显然这是关于加法的，好的，实际上，用一个短的标识符是合理的，像，但是我必须指明它的类型。
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This is another way of doing exponentiation, but this one's a recursive function. All right?
但这是一种递归的方法对不对？,好，让我们看看这种方法？
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This is a discontinuous payoff function, so differentiating isn't going to get you very far.
这是一个不连续的收益函数,所以不会涉及太多微分的东西
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Since this is a concave function, it's not just the expected value.
由于这是一条凹曲线,它不只是期待值
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As we'll discuss in the class, and most of you probably know this, your body weight is a function of how many calories you take in and how many calories you burn off through metabolic processes but also physical activity.
我们将会讲到,而且你们中的大部分人可能也知道,你的体重随着卡路里的摄取量,和代谢中的消耗量而变化,还跟肢体活动有关
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So, in the language of calculus, x is a function of time and this is a particular function.
所以,从微积分的角度来看,x是一个关于时间的函数,而且是个很特殊的函数
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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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H for an ideal gas is only a function of temperature. This is not true for a real gas fortunately, but it's true for an ideal gas.
不正确的,但是幸运的是,对于理想气体是完全正确的。
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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 just to hammer home this point, for now, a function really is like a black box.
现在再三强调，让你们彻底了解这一点，一个函数就像是一个黑盒子。
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Poetry, you remember--this is a scientist-- is no more true than religion, but it can perform the function of religion and is therefore capable of saving us.
科学家曾说过-,诗歌并不比宗教更真实，但是诗歌具有宗教的作用,并因此可以拯救人类。
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This is the creation of a function.
这就是创建函数。
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Dialysis - and this is a method to replace or augment the function of your kidneys, to remove waste products really from the blood, which is something the kidney does continuously.
透析技术,这种技术用来替代,或者增强肾脏功能,以去除血液中的各种废物,就像肾脏持续进行的那样
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And the person we have to thank for actually giving us this more concrete way to think about what a wave function squared is is Max Born here.
需要感谢，马克思，波恩,给了我们，这个波函数平方的,具体解释，事实上。
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Remember this is our bond axis here, and you can see there is this area where the wave function is equal to zero all along that plane, that's a nodal plane.
记住这是我们的键轴，你可以看到在这些区域,波函数在这个面内全都是零，这是节点面。
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But luckily we don't have to worry about how we're going to picture all this, now that I said that, no physical interpretation f or a wave function, there is a physical interpretation for what a wave function squared means.
如何想象这些图像,我这么说，虽然波函数，物理解释,但波函数的平方，有物理解释,当我们说到。
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Now this is not a particularly compelling pace just yet of implementing your own function.
这里没有一个特别的强制性的步骤,来执行你自己的函数。
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So this symbol here is actually what we call a wave function.
这里的这个符号,实际上是一个波函数。
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This particular one down here, this portion here is a heart/lung machine and this is a machine that can take over the function of a patient's heart and lungs during the period when they're undergoing open heart surgery, for example.
下面这是一个特别的设备,这一块是,心肺机,这台机器能够,在病人接受心脏手术的时候,替代病人的,心脏和肺的功能
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So, also about Max Born, just to give you a little bit of a trivial pursuit type knowledge, he not only gave us this relationship between wave function squared, This is her grandfather, I don't know if you can see from the eyes, I feel like there's a little bit of a resemblance there.
这里有些，关于它的，花边新闻,他不仅带给我们，这个波函数平方的关系,还给我们带来了，他是她的外祖父，我不知道,你们能不能看出来，我觉得,他们眼睛长得很像。
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So, what this means is that when we're looking at an actual wave function, we're treating it as a wave, right, so waves can have both magnitude, but they can also have a direction, so they can be either positive or negative.
这意味着,当我们看一个波函数时,我们把它看做一个波，波不仅有幅值，还有方向，所以它们可正可负，如果。
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