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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。
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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。
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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"
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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
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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
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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
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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
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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。
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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
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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
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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。
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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
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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。
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There are mathematical theorem-proving programs.
有些程序可以证明数学定理
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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
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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
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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
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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
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This is the "Median Voter Theorem"; thank you.
中间选民定理,谢谢你
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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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