Information theory generalises this idea via theorems that capture the effects of noise with mathematical precision.
信息论用数学精度捕获噪声影响的定理概括了这一思想。
I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
我把我成功的大部分原因归结于学习数学的收获，尤其是分析复杂原则的那些定理。
Famous Theorems define the mathematical landscape.
著名的定理决定数学的风景。
This analogy is supported by the following theorems.
这种的相似点表现在下面的定理中。
Matrix proofs of several theorems in linear algebra are given.
摘要给出了线性代数中几个定理的矩阵证法。
As I mentioned before, proofs use axioms and theorems to make their case.
如前所述，证明以公理和定理做为其论据。
theorems which are statements about the program inferred from the axioms.
定理（theorems）由公理推论得到的关于程序的陈述。
Remember, the divergence of a vector field What do these two theorems say?
向量场，的散度，这两个定理说了什么呢？
Some theorems about fundamental properties of the digraphs are proved.
本文证明了几个关于有向图基本性质的定理。
He then continues on to establish several key theorems, including this one.
接下来，Dan提出了几个关键的定理，包括下面这个。
AimTo get some important properties and theorems for fuzzy information theory.
目的为得到模糊信息论的一些重要性质和定理。
Theorems are fundamental truths that can be combined to more easily achieve further results.
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。
These theorems improve and generalize many important known results in recent literature.
这些定理改进和推广了近期文献中的许多重要结果。
These theorems improve, unify and generalize many important results in recent literature.
这些定理改进，统一和推广了近期文献中许多重要结果。
The terrain was strewn with beautiful theorems begging to be picked up and arranged in unified order.
该领域充满了美妙的定理，等待着人们去采撷和整理。
Other chapters are focused on Bach's fugues and the theorems of great German mathematician Kurt Gordel.
其他的章节是关于巴赫的赋格曲和伟大的德国数学家Kurt Gordel的定理的。
Each chapter features an introduction to a problem type, definitions, related theorems, and formulas.
每一章特点是一个问题的类型，定义介绍，相关的定理和公式。
This side will be space, this side will be the plane and we are going to start with theorems about work.
这边是空间上的，这边是平面上的，我们来看看关于做功的定理。
In this sense, which is quite easy to define, all mathematical theorems are equally and completely general.
如果按这个意思的话，所有的数学定理都具有同等的和彻底的普遍性。
We evaluated them in completely different ways, and we have a handful of theorems, connecting them to each other.
用完全不同的方法来计算它们，并且有几个定理，把它们相互联系起来。
Static verification and design by contract relay on theorems that are mostly based on deterministic approach.
静态验证和契约式设计理论大部分属于确定性理论的范畴。
They had educated themselves many times over, proved theorems, and acquired and abandoned artistic sensibilities and skills.
在不同的地方，他们一次又一次的接受教育，证明定理，获得艺术灵感和技巧后将其抛弃。
The theorems, formulas and principles in plane geometry reveal the intrinsic relations and basic laws of geometrical concepts.
平面几何的定理、公式、法则反映了几何概念的内在联系，揭示了它们之间的基本规律。
For instance, suppose one has a serviceable lemma that suffices for the task of proving the main theorems of the paper at hand.
比方说某人有一条引理用于证明论文的主命题。
Many mathematicians simply set nettlesome questions like these aside and get back to the more pleasant business of proving theorems.
许多数学家只是把这些恼人的问题简单地弃置一旁，而忙于类似定理证明这样更有趣的事务。
Besides, the two theorems can also solve two large categories of problems about linear and nonlinear computational instability.
此外，文中两个定理还可解决两大类问题的线性和非线性计算不稳定性问题。
In the 1970s, Douglas Lenat's Automated Mathematician automatically generated mathematical theorems, but they proved largely useless.
二十世纪七十年代，道格拉斯·莉娜的“自动数学家”程序自动生成数学定理，但是被证明基本上毫无用处。
It was there when they tried and tried to solve all those tricky 11 theorems; it smiled as they read the "Love across salt desert".
就是在那里，他们一次又一次地努力弄懂那些棘手的数学定理。当他们读到“穿越盐漠的爱”时，教室微笑了。
It was there when they tried and tried to solve all those tricky 11 theorems; it smiled as they read the "Love across salt desert".
就是在那里，他们一次又一次地努力弄懂那些棘手的数学定理。当他们读到“穿越盐漠的爱”时，教室微笑了。
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