And all this is, is saying that when you take a mixed second derivative, it doesn't matter in which order you take the two derivatives.

麦克斯韦关系的本质是,当你考虑混合的二阶导数时，求导的顺序不影响最后的结果,现在，我们利用这些关系。

麻省理工公开课 - 热力学与动力学课程节选

This first slide shows a graph of the impact of having metabolic syndrome on heart disease and its consequences.

这张图表明了代谢综合征,对心脏病的影响以及造成的结果

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

There's nothing profound about this, other than the understanding that the details of how you set these things up can matter a lot.

只是说我们要理解，一开始设定时候的值,会对结果有很大影响。

麻省理工公开课 - 计算机科学及编程导论课程节选

As long as you're dealing with state functions it doesn't matter to get at the same results here.

不影响结果,我们的推导就基于这一点。

麻省理工公开课 - 热力学与动力学课程节选

I want to discuss the consequence of rationality in playing games, slightly philosophical for a few minutes.

我们来讨论下理性对博弈结果的影响,这稍微有点哲学的色彩

耶鲁公开课 - 博弈论课程节选

Reason, science, art is the capacity to transform nature by making it, imposing on it, a method that will produce like effects after similar consequences.

理性，科学，艺术是一种能力,是通过创造，施加影响力改变自然的能力，是一种在类似的结果发生后,产生类似结果的能力。

耶鲁公开课 - 政治哲学导论课程节选

If you toss a coin twice and the first experiment doesn't influence the second, we say they're independent and there's no relation between the two.

如果你抛两次硬币,第一次的结果并不影响第二次的结果,所以我们说他们是相互独立的,这两次试验没有关系

耶鲁公开课 - 金融市场课程节选

And, of course, all that's left is this positive pudding. So that's not going to do anything either. And what he found when he did this experiment, was that the count rate with still 132 000 counts per minute.

剩下的是带正电的布丁,也不会产生什么影响,结果他实验上观测到,计数器测得每分钟132000下,所以到目前为止,他可以说实验。

麻省理工公开课 - 化学原理课程节选

Everyone knows from calculus that if you're trying to find a function about which you know only the derivative, you can always add a constant to one person's answer without changing anything.

学过微积分的人都知道,如果你想根据已知的导数,求出其原函数,你总是可以给某人的答案,随便加一个常数,且不影响结果

耶鲁公开课 - 基础物理课程节选

We know that there were many candidates in the '92 election and the 2000 election, and we know that "not voting" is important.

我们知道在92年和2000年,有多个候选人参与了大选,还有弃权票对结果也有很大影响

耶鲁公开课 - 博弈论课程节选

So this one I'm going to let you see whether it makes a difference.

我们来看看这些条件会不会影响结果

耶鲁公开课 - 博弈论课程节选

Again, there's no advertising affecting this, there's no parents being irresponsible and buying sugary cereals for the poor little animals.

此外,这个结果并不受广告营销的影响,也不因为有父母不负责任,给这个可怜的小动物买高糖的谷物

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

So this is true, but it doesn't actually change the result.

纵使它是现实,但它对结果没有影响

耶鲁公开课 - 博弈论课程节选

But it turns out that if you make the voters distributed more realistically, let's say like on a bell-curve shape, it makes actually no difference to the result at all.

但事实上,就算我们让选民分布更符合实际情况,比如说是按钟形分布的,但这实际上对结果没有什么影响

耶鲁公开课 - 博弈论课程节选

But actually there is a little bit of an energy cost into doubling up into a single orbital, because, of course, it takes energy when you create more electron repulsion, that's not something we want to do, but we have to do it here, and it turns out that that effect predominates over, again, the energy that we gain by increasing the atomic number by one.

但实际上，在一个轨道上放两个电子,确实会亏损一点能量，因为，当你加入更多电子，引起更大的排斥能,这显然会消耗能量，这不是我们想要做的，但是在这种情况下我们不得不做，结果这一影响，超过了增加一个,原子序数所得到的能量。

麻省理工公开课 - 化学原理课程节选

What this is, is you take a group of studies on an issue, you pool them all together, and then you weight studies differently depending on factors like how large they were, how good their methods were, and then you come out with overall estimates about the impact of something, in this case the Mediterranean Diet, on health outcomes.

所谓荟萃分析就是将某一问题的一组研究,汇总起来,并根据某些因素,赋予这些研究不同的权重,如基于研究的大小,研究方法的好坏等,然后得出关于某事物的影响的总体评估,在地中海式饮食中就是指健康结果

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

So for a literal definition of what strategic means: it's a setting where the outcomes that affect you depend on actions, not just on your own actions, but on actions of others.

策略形势书面定义是,行为影响结果,然而结果不仅,取决于你的行为 还取决于其他人的行为

耶鲁公开课 - 博弈论课程节选

So this is not even thinking about the other electron shielding, just if we think of the fact, all we need to think about is that the effect of going to a further away n n as we go down the table.

到现在我们甚至还没有考虑,其它电子的屏蔽效果，即使我们要考虑这个因素，我们需要考虑也就是,沿着周期表的某一列往下走，距离会逐渐变远,将起最重要的作用，actually，dominates,这一结果所产生的影响。

麻省理工公开课 - 化学原理课程节选

You can add something else to the answer without invalidating it, and that is anything with one power of t in it, because if you take one derivative it'll survive, but if you take two derivatives, it'll get wiped out.

你可以往答案后面加上其它东西,而且不影响结果,也就是任何t的一次项,因为你求一次导数之后它还在,但如果你求两次导数,这一项就不存在了

耶鲁公开课 - 基础物理课程节选

It wouldn't make any difference to the outcome.

它不会给结果带来任何影响

耶鲁公开课 - 博弈论课程节选