信息论用数学精度捕获噪声影响的定理概括了这一思想。
Information theory generalises this idea via theorems that capture the effects of noise with mathematical precision.
我们可以把斯图尔特定理直接应用于三角形的中线上。
We can apply Stewart's theorem directly to the median of a triangle.
有时被称为,经典的能量均分定理。
Sometimes it's called the classical equipartition of energy theorem.
那么散度定理究竟讲的是什么？
现在我们要用，平行移轴定理。
有些程序可以证明数学定理。
如前所述，证明以公理和定理做为其论据。
As I mentioned before, proofs use axioms and theorems to make their case.
为什么定理选择逆时针积分而不是顺时针呢？
Why does the theorem choose counterclockwise over clockwise?
他们能保持对社会的既定理念吗？
Can they preserve their static conception of their societies?
其实有很多种证明勾股定理的方法。
And it turns out there's a variety of proofs of the Pythagorean Theorem.
另一件事是，这个定理在物理学上有什么含义？
OK, so the other thing I wanted to say is, what does this theorem say physically?
这就是散度定理。
那就是散度定理。
“这是一个非常有趣的定理，”Brualdi说。
该领域充满了美妙的定理，等待着人们去采撷和整理。
The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order.
我将讲述一些，关于Stokes定理的曲面独立性。
So, I'm going to say a couple of words about surface independence in Stokes theorem.
定理1表明了缺省推理的非单调性这一特点。
Theorem 1 indicates the feature of non-monotonicity for default reasoning.
公布一个程序的源代码与公布一个定理的证明是一样的。
Publishing the source code of a program is the equivalent of publishing the proof of a theorem.
在散度定理中的约定是,将曲面的定向取为外法线的方向。
The convention in the divergence theorem is that we orient the surface with a normal vector pointing always outwards.
会得到完全相同的答案，我觉得用功能定理，会更加的简洁。
You get exactly the same result, and I find this somehow more pleasing to use the work-energy theorem.
定理是基本的原理，我们可以将其组合起来以获得更多的成果。
Theorems are fundamental truths that can be combined to more easily achieve further results.
您还应该对Perl引用和SQL数据库有一定理解。
You should also have some understanding of Perl references and SQL databases.
实际上，这不是一个容易证明的定理，直觉上，先任取一曲面。
So, actually, that's kind of a not so obvious theorem to prove, but maybe intuitively, start by finding any surface.
这就是最终的证明了，证明的思路和证明格林定理的是一样的。
So, that's the end of the proof. OK, so you see, the idea is really the same as for Green's theorem.
为了能够应用Stokes定理，我需要找一个曲面来应用它。
Well, to be able to use Stokes theorem, I need, actually, to find a surface to apply it to.
理论上说，存在排除某些人使用某句诗歌或某个数学定理的可能。
It is theoretically possible to exclude some from the use of a poem, or a mathematical theorem, but exclusion is generally quite difficult.
定理（theorems）由公理推论得到的关于程序的陈述。
theorems which are statements about the program inferred from the axioms.
“证明这个定理”就是要证明这个蕴涵式是一个重言式。
To "prove the theorem" means to show that the implication is a tautology.
散度定理为我们提供了一种，计算向量场通过闭曲面的通量的方法。
So, the divergence theorem gives us a way to compute the flux of a vector field for a closed surface.
所以那是通过散度定理得到的，其中使用了S是封闭曲面这一事实。
So, that's by the divergence theorem using the fact that s is a closed surface.
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