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Recent observations had suggested that 2 of the 4 spiral arms hold most of the older stars in the Milky Way galaxy.
VOA: special.2009.01.20
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Well, it looks like it took 1 in this case or it involves-- we can put it another way, merging those two lists involved looking at two numbers, 1, 2, and that's it.
在这种情况下看起来只用了1次-,我们可以从另一个角度看，合并这两个列表涉及到了,2个数字，1，2，就是这样。
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So already, just from Firm 2's production the price has been driven all the way down to costs.
这样公司2的产量会,导致价格下降直到成本价格
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I came here in 1992 And then I had a mini epiphany half way through my sophomore year.
我1992年来到哈佛求学2,大二期间，突然顿悟了。
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test two, it's a little bit over 100, and for test one it's way over 100.
在试验2中比一百稍大，而在试验1中比100大得多。
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px 2py So we need to fill all the way up to the pi 2 p x, and the pi 2 p y.
我们需要填到。
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The sum of path number 2 and path number 3 get me to the same place, so the energy change by going through this time path, this intermediate point here back all the way to final state should be the same the red path.
而经过路径2和3可以3,到达同样的末态，因此经过路径,2和3带来的能量的变化，与路径1带来的,能量变化相同。
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But mathematically, we've mentioned this before, log N or really to be precise, log base 2 of N, is the way you express this mathematically.
但从数学上说，之前我们已经提到过了，准确地说是log，N，以2为底N的对数，这就是它在数学上的表示。
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So let's fill it out in this way, 2p keeping in mind that we're going to fill sigma out the pi 2 p's before the sigma.
让我们这样填上去，记住我们先填π,轨道再填。
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Well, I solve 2 or 3 exponential problems before breakfast every day. You know things like, how to find my way to the bathroom is inherently exponential, but I manage to solve it anyway.
你要知道如何找到,我的浴室就是一个，固有的指数型问题,但是我还是能解决它。
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So Firm 2--if Firm 2 produces all the way up to here then any product produced by Firm 1 is going to push prices even lower.
如果公司2的产量一直增加到这里,那么公司1的每一件产品必须降价出售
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They were the sets 1, 2, 3, all the way up to 100.
这个集合由1 2 3 一直到100组成
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When they started to calculate how much rice would be need to fill up all blocks, all the way to 2 to the power 63.
当他们开始计算,需要多少粒米填满所有方格时，从第二格到第63格。
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One in the so called hundreds columns, a two in the so called tens column 2 so that's 10 times 1 plus 10 times 2 is 120, 123 plus 3 times 1, 123 alright, so completely uninteresting, if this is something long familiar to you, but it turns out computers work in exactly the same way.
这里的1处于百位，2处于十位,所以100乘以1加上10乘以，再加上1乘以3，好的，完全正确就是，但是毫无趣味，这对你是一件极其熟悉的事，但是电脑结果也是以同样的方式运行的。
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Let's just... We'll get there, just to remind you, the way we read this is you give me a quantity of Firm 2, I find Firm 1's best response by going across to the pink line and dropping down.
我们当然也能算出来,提醒一下各位,这个图像的个意思是任意给出公司2产量,然后通过这条粉色的线,就可找出与之对应的公司1的最佳对策
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But since in drawing Lewis structures actually, in some cases you do, you can draw a dotted line that means a 1 and 1/2 bond, but most in most cases, we just draw out both resonance structures, and the way that we say it's a resonance structure is that we put it in the brackets and we put an arrow between it.
但是由于在画路易斯结构时,其实，在某些情况下是可以的，你可以画一条虚线来表示一又二分之一键，但是在多数情况下，我们就把两个结构都画出来，而我们说这是一个共振结构的表示的方法是,把它们放在括号里，并在中间放一个双箭头。
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that's one way to think about it, and there's also another way, and this is the way that your book presents it. If you, in fact, have two of the same atom right next to each other, let's say you have a crystal, or let's say you're talking about a metal, what you can do is just look at the distance between the two nuclei, and split that in 1/2, and take the atomic radius that way.
这只是一种定义的思路，另外还有其它方法，也就是你们课本上的方法，如果你，事实上，有两个相同的原子彼此靠在一起，比如说你有一个晶体，或者说你讨论的是一个金属，你所要做的就是,看看这两个原子核之间的距离，然后将距离除以二，就得到了这个原子的半径。
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She costs C for sure, that's a wash because B, the way we've worked things out, B was $2, C was $1, So B/2-C is a wash.
她承担C的成本,收益是零,因为B,按我们设定的金额,B是2美元,C是1美元,所以B/2-C是零
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And unlike n, l can start all the way down at 0, and it increases by integer value, so we go 1, 2, 3, and all the way up.
不像n，l可以从0开始取，然后每次增加一个整数，所以我们可以去1，2，3，一直下去。
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We can go all the way down -- magnesium aluminum, all the way to this noble gas, 3s23p6 argon, which would be n e and then 3 s 2, 3 p 6.
我们可以继续，镁，铝,一直到惰性气体，氩它是Ne然后。
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If Player II chooses 4, then the synergy leads Player I to raise his best response all the way up to 2, but these strategies up here above 2 are never a best response for Player I. Is that right?
如果参与人II选4,协同导致,参与人I的最佳对策变成2,参与人I的那些大于2的策略,也永远不会成为最佳对策,对不对
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I've found Player 2's best response as a function of q1, and the way I did it, just remember, the way I did was I applied a little bit of 112 and high school calculus, so that's your single variable calculus.
以及参与人2的最佳对策是q1的函数,而且我们用到的数学知识,只是稍微与112和高中微积分有关,仅仅是单变量微积分的知识
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