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。
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。
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。
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。
Comparison theorems of nonlinear equations.
非线性方程的比较定理。
Two principles are presented and three theorems are proved.
给出两条法则，证明三条定理。
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。
All this leads up to the most fundamental of theorems of calculus.
综上所述就导出了微积分学中的最基本的定理。
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。
Some new generalized KKM type theorems are proved in noncompact FC - Spaces.
在非紧fc-空间中证明了一些新的广义kkm型定理。
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。
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。
Accordingly, we extended several important theorems of complex matrix theory to the quaternion field.
由此，把复数域上矩阵论的若干重要定理推广到了四元数体。
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。
Physics is a strict reasonable logical system, which consists of physical concepts, physical laws and physical theorems.
物理学是由物理概念、物理定律、物理定理所构成的能自圆其说的严密逻辑体系。
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。
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。
In the present paper some theorems for variational inequalities and minimax inequality are obtained in hyperconvex metric spaces.
摘要文章给出了超凸度量空间中的一些变分不等式定理和极大极小不等式定理。
I think mathematics can benefit by acknowledging that the creation of good models is just as significant as proving deep theorems.
创建好的模型正如证明深刻的定理一样有意义。我想，承认这一点，数学会从中受益。
In this paper two theorems have been proved and a method of sensitivity analysis of switched capacitor circuits has been described.
本文证明了两个定理，并由此提出了开关电容电路灵敏度分析的一种方法，此方法特别适合于用计算机程序来实现。
In spite of the very close affinity between the variational theorems and the principle of virtual work the study of the former is worth-while.
尽管变分定理与虚功原理之间有很紧密的相似关系，然而对前者的研究仍然是有价值的。
In this paper, symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
针对对称导数、对称偏导数，给出了一些新形式的微分中值定理。
Based on some basic theorems in theory of Numbers this program takes advantage of probabilistic algorithm to test a large number for primality.
基于初等数论中的一些基本定理，本程序利用概率算法，快速判定一个大数是否为素数。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
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