And some of them might be spinning clockwise, in which case, according to the right-hand rule we would consider them spin-down.
而另一些电子则是在顺时针自旋,在这种情况下,根据右手定理,我们会以为它是在向下转。
So now, now that we've got all three of the major laws of thermodynamics, what I want to start in on is a discussion of what happens spontaneously.
现在既然我们已经得到了,热力学的三个主要定理,我想现在开始讨论的是,什么过程会自发进行。
First of all, it's clear from the Pythagoras' theorem that a is the square root of ^2 + ^2.
首先,根据毕达哥拉斯定理,勾股定理在西方被称为"毕达哥拉斯定理"
So they--in other words, the insurance company--doesn't trust the insurance companies to do the calculations like I showed with the binomial theorem.
因此他们...也就是说,他们不放心让保险公司按照二项式定理,自己计算准备金要求
So there are examples in American History of elections that seem to in which the Median Voter Theorem seems to do well.
因此从美国历史上的选举案例里看,中位数选民定理非常奏效
We prove things in mathematics that have never been proven before or we find new ways to prove these theorems or what have you and we can be creative.
我们用数学去证明从未被证明过的事物,我们探寻新的方法去证明那些定理,或其他诸如此类,总之,我们具有创造力
The mutual fund theory that we gave last time said, no the mutual fund is just supposed to be diversifying for you.
但上节课讲到的共同基金定理认为,共同基金的目的是分散投资
If they're sort of doing their job right, they're actually diversifying away all the risk and relying on the law of large numbers.
如果他们工作得当,那么他们其实是规避了所有的风险,而且依赖大数定理。
Well there are examples in American History in which the Median Voter Theorem looks pretty good.
在美国历史上就有一个案例,此案例中中间选民定理非常奏效
To actually apply this it helps to go to something called the normal approximation to the binomial, because it's kind of difficult to compute this formula.
在实际应用这些公式的时候,需要运用二项分布的正态近似定理,因为二项分布公式的值很难计算
The theory of mutual funds is: nobody is supposed to be holding anything other than-- ... the ideal theory of mutual funds--is holding something other than this tangency portfolio.
共同基金定理是指:,所有人都应该持有-,理想的共同基金定理说,都应该持有这种切线投资组合。
It's called the Median Voter Theorem because the voters at the center, in this case 5 and 6, actually get to decide not just the election, but to decide therefore, what policies are put in place.
它之所以叫中间选民定理是因为,处在中间位置的选民,比如这个案例中立场5和6,实际上他们不止左右了选举结果,而且还决定了那些政策可以施行
A casino does not have a risk that the law of large numbers will be repealed and a roulette table will be a long-term losing proposition or a craps table will be a long-term losing proposition.
一个赌场不会有,大数定理被替代,或者轮盘赌和,双骰赌博会是长期亏本买卖的风险。
There are mathematical theorem-proving programs.
有些程序可以证明数学定理
As a matter of fact, it's so widely believed that asset allocation is the most important tool that I think some people have come to the conclusion that it's some sort of law of finance that asset allocation is the most important tool.
事实上,我们普遍相信,资产配置是最重要的工具,以至有人得出结论,资产配置是最重要的工具,已经算是一条金融学定理了
A lot I'm going to talk about is Modigliani-Miller but I'm not going to get too deep into it, maybe in your review sections you can get more technical.
我会重点谈论MM定理,但也不会过分深入,在复习阶段我可能会讲的更专业一些
If you give me a pair of numbers, Ax and Ay, that's as good as giving me this arrow, because I can find the length of the arrow by Pythagoras' theorem.
如果给我一组数字,Ax 和 Ay,就相当于给了我这个箭头示意图,因为我可以利用毕达哥拉斯定理定理求出模长
It turns out that it's not a financial law that asset allocation takes center stage; it really is more a description of how it is that we behave.
事实上,资产配置的核心地位,还称不上是金融学定理,但它确实已不仅仅是对我们行为的描述
This is the "Median Voter Theorem"; thank you.
中间选民定理,谢谢你
We'll be talking about the Modigliani-Miller Theorem and related issues in this lecture as well as something about the behavior of the stock market and its tendency to go through dramatic movements.
我们会讲到,MM定理,和与其相关的问题,还会讲到,股市行为和,股市戏剧性的运动趋势
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