这个动机要达到觉醒应该是二重的一个人为他自己承受幸福并且指出一条道路为他人的幸福。
The motivation for reaching Awakening should be the dual one of finding enduring happiness for oneself and of pointing the way to such happiness for others as well.
这种二重的劳动力市场使得一部分人在市场衰退下得以全身而退，而另一部分主要由临时工，失业人员和非法劳工构成的人却步履艰难。
This two-tier labour market divides workers into a privileged groupcocooned from the reality of recession and the disadvantaged ontemporary contracts, in unemployment or in illegal jobs.
丹尼斯赞扬了富勒在 Valse à laLoie 里的二重唱。
举个简单的例子，想想两个人跳华尔兹，或者弹钢琴二重唱。
As simple examples, think of two people waltzing, or playing a piano duet.
二重对数是对数的积分。
看两只猫的滑稽二重唱！
但是你知道，它给了你一个例证，其中你可以，把复杂的线积分化成简单些的二重积分。
But, you know, it gives you an example where you can turn are really hard line integral into an easier double integral.
如果是一条闭曲线，也可以用二重积分来代替的。
If it is a closed curve, we should be able to replace it by a double integral.
我们已经做过的一个例子是，计算四分之一单位圆上的二重积分。
One example that we did, in particular, was to compute the double integral of a quarter of a unit disk.
这样是为了形成一个“二重奏系统，”即制作视频的专家和教师结合。
The idea is for a "duet system, " where a video expert teaches in tandem with the classroom’s own teacher.
那就可以使用格林公式了，并且我们知道,它就等于的二重积分，结果为0，因为旋度F等于。
Then, yes, we can apply Green's theorem and it will tell us that it's equal to the double integral in here of curl F dA, 0 which will be zero because this is zero.
这就会变成…，如果俯视这个抛物面，所看到的就是单位圆盘，这就应该是单位圆上的二重积分了。
That is just going to be, if you look at this paraboloid from above, all you will see is the unit disk so it will be a double integral of the unit disk.
也就是最终要摆脱曲面积分，回到常规的二重积分。
And this is finally where I have left the world of surface integrals to go back to a usual double integral.
第一点就是，有些你以为是用一重积分来做的，但却通常是用二重积分来完成的。
The first one that I will mention is actually something you thought maybe you could do with a single integral, but it is useful very often to do it as a double integral.
那么我就能名正言顺地,用R上的某个函数的二重积分来替代通量的线积分。
Then I can actually -- --replace the line integral for flux by a double integral over R of some function.
除了这些，旋度还有一个用处，如果你还记得，我们讨论平面的时候,当把线积分转换成二重积分的时候。
But another place where this comes up, if you remember what we did in the plane, curl also came up when we tried to convert line integrals into double integrals.
如果有人问我小说家第二重要的素质是什么，这个答案也很简单：注意力—即集中有限才能完成此刻最为重要的事情的能力。
If I'm asked what the next most important quality is for a novelist, that's easy too: focus - the ability to concentrate all your limited talents on whatever's critical at the moment.
追求揭示了现代大学的二重性。
另一件关于二重积分的是，我们已经讲过了，如何做更复杂的变量变换。
OK, now another thing we've seen with double integrals is how to do more complicated changes of variables.
要计算二重积分，要做的就是要利用切面。
So, to compute this integral, what we do is actually we take slices.
女人会为了这鲁莽而又负责的犯罪二重奏而疯狂，从而使这段荣耀之路的结局显得更加情绪化。
Women went nuts for this simultaneously reckless and in-charge crime duo, making its blaze-of-glory finale even more emotional.
已经众所周知德里布的《花之二重唱》由于被英国航空较近的一个广告宣传活动中引用到而名噪一时。
Already well known, Delibes's Flower Duet was made ever-increasingly popular by British Airway's use of the work in a fairly recent advertising campaign.
而情人在他们的爱情二重唱中使用的言语，不是特里斯坦也不是伊索尔德，老人，在新成为的结合中并不存在。
And the words the lovers' use in their love duet is no more Tristan no more Isolde, that old persons don't exist is this new merged unity they have become.
信息治理是指与企业第二重要的资源即信息资源相关的决策活动。
Information governance represents the decision making activities for the second-most important resource of the enterprise - its information resources.
邻近的大厅安装着汽轮机，这是核电厂里第二重要的单元设备。
In the neighboring hall there is the turbine - the second most important unit in a nuclear power plant.
儿童节目中食品广告的二重形式否认、情感诉求与产品技巧……有这样良好的平衡点吗？
Dual Modality Disclaimers, Emotional Appeals and Production Techniques in Food Advertising Airing in Programs Rated for Children. Is There a Good Balance?
研究者称，发现导致肾癌的第二重要致病基因是一个重大进步。
The researchers said the discovery of a second major gene linked to renal cancer was a major advance.
也就是二重和三重积分的内容，以及平面和空间中的向量积分。
And so that was stuff about double and triple integrals and vector calculus in the plane and in space.
也就是二重和三重积分的内容，以及平面和空间中的向量积分。
And so that was stuff about double and triple integrals and vector calculus in the plane and in space.
应用推荐