"The point is this the growth of a country is a function of how many entrepreneurs they have,"
VOA: standard.2010.01.31
And this is a function of space.
这是空间函数。
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。
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。
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。
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
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。
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“
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。
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。
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?
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
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
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
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
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。
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。
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。
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。
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。
This is the creation of a function.
这就是创建函数。
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
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。
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。
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。
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。
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。
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
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。
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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