公理

Generally, the set of temporal types that can be processed by a system and involved in lots of applications, meet totally ordered relation, and the set of TFDs with a totally ordered set of temporal types is closely related to the Armstrong axioms of traditional functional dependencies.

一般来说，系统所能处理的和相当多的应用所涉及到的时态类型集满足全序关系，并且具有全序时态类型集的TFD集的推导规则与传统函数依赖的Armstrong公理有着紧密的联系。

As a corollary, we solve a conjecture of Liao, i.e., the following four conditions are all equivalent: 1 the system is structurally stable, 2 the system is in the interior of the set of Kupka-Smale systems, 3 the obstruction set and the interior of singularities of the system are empty, 4 the system satisfies Axiom A and the strong transversality condition.

作为一个推论，这解决了廖山涛先生的一个猜测，即下述四个条件等价：1 系统为结构稳定的，2系统及其附近的系统皆为Kupka-Smale系统，3系统的阻碍集为空集，4 系统为公理A且满足横截性条件。3→4，4→1，1→4已经分别由廖山涛， Smale、 Anosov、 Robbin、 Robinson以及Robinson完成。

Our techniques require no detailed representations of objects, and can be applied as long as their mutual distances can be computed and the distance metric satisfies the triangle inequality.

我们的技术不需要表征对象的细节，并且可以应用在当他们的相互距离可以被计算或者距离满足三角不等式公理。

Definition: A demonstration that a mathematical proposition is true based on axioms, definitions, and proven theorems

定义：一个用公理，定义，已证明的定理来证实数学上的命题是真实的一个演绎过程。

A theory in their view is a set of logically interrelated propositions deduced from axioms or underived assumptions.

在他们的观念中，一种理论就是一系列有逻辑关联的论点，这些论点来源于公理或无需证明的观点。

That is to say, we would have nothing more meaningful than an uninterpreted formal language, formal rules of inference, and a subset of the set of well-formed formulas as axioms.

也就是说，我们持有的有意义语言甚至超不过一个尚未解释的形式语言、形式推理规则和作为公理的合式公式子集。

He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous.

他自己造成的恶果，太阳升起的好，并将雨站在正义与公理。

He was zealous for His holiness, and He would surely bring vindication.

祂是圣洁而忌邪的上帝，必要因人的行为而伸张公理的。

This is axiomatically given.

这是以公理的方式提供的。

There continuing efforts to prove the parallel axion do not imply ignorance of Gauss's thoughts.

继续努力去证明平行公理并不意味着不知道高斯的思想。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。