And the solution to this equation looks like this where it is written in terms of a quantity called a wavefunction.

这个方程的解法是,看起来像是写成数学符号就是,波函数。

麻省理工公开课 - 固态化学导论课程节选

Suppose f of x, y, z equals k1, that is my equation, s1 and it gives me a solution s1.

假设我的方程是这样，然后给出了一个解。

麻省理工公开课 - 固态化学导论课程节选

So I have two solutions here; one, what would be sort of the obvious sort of hackish or solve it fast solution?

我这里有两个解决方案，一是有没有一个明显的,独创性的，快速地解决方案？

哈佛公开课 - 计算机科学课程节选

Well, you won't be surprised to hear it's the same solution. So let's look at that code.

好了，听到二者是一样你可别惊讶,让我们看看代码。

麻省理工公开课 - 计算机科学及编程导论课程节选

As I see it, there is only one solution to all the foregoing difficulties.

在我看来，解决这种困境只有一个办法。

耶鲁公开课 - 文学理论导论课程节选

Jell-o is just a hydrated solution of collagen and it contains a lot of water.

吉露果冻就是一种水合的胶原蛋白溶液,它含水极多

耶鲁公开课 - 生物医学工程探索课程节选

But if you can accept the purity of the statement I just made, it is at the root of the thing you have a solution.

但如果你能够遵从原教旨主义的方式,那么这就是你解决此问题的根本

耶鲁公开课 - 古希腊历史简介课程节选

But the mathematicians told Dirac, "You cannot ignore the negative energy solution because it tells you there's a second solution and you cannot throw them out."

但数学家们告诉狄拉克,你不能忽略负的能量,因为数学告诉我有两个根,你不能随便丢掉

耶鲁公开课 - 基础物理课程节选

So in this case, the communication worked but am I right in thinking that the communication isn't such an instant solution as it was in the game we saw last time?

在这个博弈中,交流起到了作用,但是能说这和上一讲的博弈一样吗,交流并没能直接给出解决的方案

耶鲁公开课 - 博弈论课程节选

And so frequently what we try and do is, we take a new problem and map it onto an old problem so that we can use an old solution.

我们经常做的一件事就是，我们处理一个新问题时,把它归结为一个老问题,以便我们能采取老的解决方式。

麻省理工公开课 - 计算机科学及编程导论课程节选

Now for the hacker edition, if you are feeling up to a bit more of a challenge you'll find that when you run the game, one it's not all that hard to use some ASCII art just make it a little fancier as the teaching fellow who implemented this solution did.

对于升级版，如果你能应付更大的,挑战，你会发现当你在玩这个游戏时，用一些字符画把它做得,比那些教学人员做的更有新意,并不是那么困难。

哈佛公开课 - 计算机科学课程节选

It's in solution, it's refrigerated, and it's very difficult to transport refrigerated vaccines to all the remote parts of the world where you would like to transport them.

疫苗需要溶解在水中,还要冷藏,而将这些冷藏的疫苗运送到,世界上所有的偏远地区是十分困难的

耶鲁公开课 - 生物医学工程探索课程节选

The solution is so simple, give us $2, we'll give you a ticket and yet it takes nine steps to do that.

解决方案也简单，给我们2美元，我们将给你一张票,但是你需要9个步骤来处理。

哈佛公开课 - 计算机科学课程节选

We call that a base case. It's basically the simplest possible solution to the problem.

我们说这是一个基础案例,这是这个问题最简单的解决方案。

麻省理工公开课 - 计算机科学及编程导论课程节选

PROFESSOR: Great question. So the question is, how do you choose an algorithm, why would I choose to use a pseudo-polynomial algorithm when I don't know how big the solution is likely to be, I think that's one way to think about it.

教授：问得好，所以问题是，你怎样选择算法，为什么当我,不知道解决方案会有多大的时候,我要选伪多项式算法呢，我想这是一种思考问题的方式。

麻省理工公开课 - 计算机科学及编程导论课程节选

But you can ask, "Why is it giving me a second solution?"

但你可能会问,为什么会得到两个解

耶鲁公开课 - 基础物理课程节选