As soon as you allow anything to mix, like you might if you want to do any chemistry, entropy changes.
只要你允许物质混合,就像你做任何化学实验的时候要做的,熵就会发生变化。
He's doing what he can, but change will be slow.
他在做他所能做的一切,但是变化却很缓慢。
Certainly in principle we know how to calculate this and other stuff for a change in state of this sort, for lots of changes of state.
的确原则上我们可以对某个状态变化,计算这些物理量,或者其他物理量,对其他的变化也可以做相同的计算。
Let's hope that all the changes I mad have not introduced a syntax error.
希望我要做的所有这些变化,不会有什么句法错误。
So now in this problem, we can do something slightly different, and let's use this expression here,and I will do that, then I'll stop for today.
对于这个问题,我们可以稍微做点变化,让我们用这个式子,就是这样,今天就讲到到这里
Because it's a makeup class, we'll do something a little special.
因为本堂是新增的课程,所以我们要稍微做些变化。
So what we can do then is for those schizophrenics that on typical neuleptics A we can actually switch them to the A typical neuleptics and run them under the same experiment again and look at what's happening.
我们接下来要做的是,对于那些服用典型药物的精神病患者,我们让他们转用药物,然后再对他们做相同的试验,来看看有什么变化。
And in this context, the length of that array is stored in Arg C. Well, let's take a look at a slight variance of this that reveals further what we can do and reveals what a string really is.
关于这点,那个数组的长度被存储在ArgC中,好的,让我们看看这个轻微的变化,那个揭示了我们可以做的,和字符串实际上是什么。
Not really. it was kind of noodling around with it, varying it a little bit.
不完全是,它在主题的旋律上,做了一点变化
Now, we can do the same procedure for the pressure change.
下面我们对压强变化,做相同的事,我们所要做的是。
So add up all the changes or what you mean by integral.
将全部变化量加在一起,或者做积分
This is real, unlike the Joule coefficient which is very small so that most gases have tiny Joule coefficients. So if you do a Joule experiment, you hardly measure a temperature change. With real gases, here you do actually measure it. You can feel it with your finger on your bicycle tire.
系数那样小以至于,大多数气体的焦耳系数,都很小,所以如果你做焦耳实验,很难测量出温度的变化,对于真实气体,你可以测量它,你能通过手指按在,自行车轮胎上来感觉到它。
So he's up to something here with this rate of harmonic change.
他在这里准备做一点什么,泛音的速度发生了变化。
As long as we understand that, we can do this cancellation and this says on the left-hand side the change in the quantity v square over 2 is a times the change in the quantity x.
只要我们明白这一点,我们就可以这样做简化,在等号左边,v^/2的变化量,为a乘以x的变化量
And then one of the things that I suggested was that if we could figure out some way to order it, and in particular, if we could order it in n log n time, and we still haven't done that, but if we could do that, then we said the complexity changed a little bit.
这就涉及到了排序,如果可以想出一种来将其进行排序,甚至可以在n,log,n的时间内完成,虽然目前我们没做这件事,但是一旦开始做这件事,那么复杂性就是发生一些变化。
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