But, that's all changed, but the reality of the situation, that Paris is overly dominant, has not changed at all.

但是今非昔比,实际的情况是,巴黎的绝对支配地位丝毫没有变化过

耶鲁公开课 - 1871年后的法国课程节选

But that's also nice, it lets you see how the recursive thing is simply unwrapping but the complexity in terms of the amount of time it takes is going to be the same.

它让我们看到了，在复杂度依照时间总数来看,没有变化的情况下,递归是怎么一步步的展开的,我欠你一个糖，谢谢。

麻省理工公开课 - 计算机科学及编程导论课程节选

A mule is not spending 1/2 of its time as a donkey, and 1/2 of its time as a horse, we don't see it flickering back and forth between the two, that's not what we see.

骡子并不是一半的时间是驴，另一半的时间是马，我们不会看到它在两者之间来回变化，这不是我们所看到的情况。

麻省理工公开课 - 化学原理课程节选

Then the second derivative gives the change in entropy with respect to the variable that we're differentiating, with respect to which is either pressure or volume.

二阶导数给出熵,随着变量变化的情况，这些变量包括压强或者体积。

麻省理工公开课 - 热力学与动力学课程节选

Things of course have changed since those early times in so many ways.

与早期相比 情况已发生多方面的变化

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

Think about how grossly things have changed starting in those earlier times.

想想随着时间流逝,情况发生了多大的变化

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

Now there's a lot of variation in that: men would be different from women, taller more then shorter, all that sort of thing, but nonetheless let's just use that as a reference.

当然随情况会有不同变化,男人需要的比女人多,高的比矮的多,像这类情况,但我们用这数据做个参考

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 things have changed a lot.

情况发生了很大的变化

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

Let's say you want to see how something like cigarette smoking is changing in the population and the rates of cigarette smoking, and you want to look at people every five years from 1970 to 2000.

比如你想知道,人群中吸烟者的人数变化,和吸烟者的比例,在1970年至2000年每五年的情况

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

And the useful outcome of all that is that p we get to see how entropy changes with one of those variables in terms of only V, T, and p, which come out of some equation of state.

这样做的重要结果是,我们得到了熵随着V，T或者,其中一个变量变化的情况，这些可以从状态方程得到。

麻省理工公开课 - 热力学与动力学课程节选

b OK. In this example I'd use b. All right, as b get-- b is the thing that's changing as I go along here, but it could be things like, how many elements are there in a list if the input is a list, could be how many digits are there in a string if the input's a string, it could be the size of the integer as we go along. All right.?

好，在这个例子里我会用，因为b是一直在变的东西,但是也可能是如下情况：,如果输入是数组的话,变化的就是数组的元素数，如果输入是字符串的话,变化的就是字符串的长度，如果是integer的话,可能就是这个数的大小，对不对？

麻省理工公开课 - 计算机科学及编程导论课程节选