公理

This is because economics is founded upon the premise that individuals make choices among options, and constrained maximization sets an essential restriction on behaviour without which individual choices would become unpredictable.

这是因为经济学主要是探讨人们如何作出选择的行为，而「有条件限制最大化」的公理在行为上建立最主要的限制。由於没有了「有条件限制最大化」的公理，人们的行为便没可能再推测。

As an application of the above proof, we obtain at once that there is an open and dense set in the set of Ω-stable systems such that every system in the set satisfies Axiom A and the no-cycle condition (Axiom A and the strong transversality condition, respectively).

作为上述方法的一个运用，马上可以得出在Ω稳定系统的集合中有一开稠集满足公理 A 和无环性条件(对应的，公理 A 和强横截性条件)。

Byapplying a general large deviation theorem of Kifer and Ruelle's Smale space tech-nique together with his unique equilibrium state result for non-Holder continuousfunctions,we obtain a level-2 LDT for the Axiom A endomorphism with respectto its equilibrium states,and for Axiom A attractors of the endomorphism withrespect to the Lebesgue measure.

利用Kifer的一个一般性的LDT，Ruelle的Smale空间方法及其关于非〓连续函数平衡态的存在唯一性结果，我们证明了公理A自映射相对平衡态的level-2 LDT，以及自映射的公理A吸引子相对Lebesgue测度的level-2LDT。

In section three, we recall the mapping cone and show that the mapping cone is equivalent with the octahedral axiom if the other three axioms are satisfied.

在第三节，我们讨论了预三角范畴中的映射锥，证明了在其它三条公理满足的条件下，"映射锥是三角"与八面体公理等价。

The pointless description of axioms of separation, especially T2 axiom is a question without final result in pointless topology.

中文摘要：分离公理，尤其是T2公理的无点刻划是无点拓扑理论中没有统一结果的问题。

His definitions do not always define, his axioms are not always indemonstrable, his demonstrations require many axioms of which he is quite unconscious.

他的定义并不总是下了定义的，他的公理并不总是不可证明的，他的证明需要许多他还没有完全意识到的公理。

The generally acknowledged truth of traditional logic isn′t the generally acknowledged truth of the traditional logic syllogism ;It isn′t get the law of identity,the law of contradiction,the law of excluded middle and the law of sufficient reason;It isn′t still the two complete formula of Celarent in Aristotle′s system.

传统逻辑的公理不是传统逻辑的三段论的公理，也不是同一律、矛盾律、排中律和充足理由律，还不是亚里士多德系统中第一格的两个全称式。

The contents of the abstract of the short Communication is:"The paper gives a complete differential partition to a Euclidean straight line with a fixed frame, and three axioms for the integral of infinitesimals indexed by real numbers; proves in standard mathematics there are positive infinitesimals outside of real number set; Gives cosmic, macro and micro counterexamples to two axioms in Jordan, Carathéodory, and Lebesgue measure theory; transforms Weierstrass limit into Huang limit, Cantor continuum into Huang continuum, and Newton-Leibniz formula into Huang formula."

这个短的发言的摘要的内容如下："此文对一条确定了固定标架的欧几里德直线给出了完整的微分分拆，并对以实数为标号的无穷小的积分给出了三条公理；在标准数学中证明了在实数集合之外存在正的无穷小；对若当，卡拉特欧多里和勒贝格测度论中的两条公理给出了宇观的，宏观的和微观的反例；将外尔斯特拉斯极限改进为黄氏极限，将康托连续统改进为黄氏连续统，和将牛顿－莱布尼茨公式改进为黄氏公式。"

In the first part, firstly, we introduce the nonstandard analysis theory simply. Using the axioms in nonstandard analysis, the nonstandard model is axiomatic approached, and the existence of nonstandard model and the consistence of axioms in nonstandard analysis are proved by the construction of nonstandard model. Secondly, some properties of nonstandard model are discussed, such as transitivity, Boolean properties, etc. Finally, Loeb measure spaceY,L

在第一部分里，首先对非标准分析理论进行了简单的概述，通过用非标准理论中的公理，给出了非标准模型，进而利用非标准模型的构造，证明了非标准模型的存在性和非标准模型中公理的一致性；其次，讨论了非标准模型的一些简单性质，如传递性，布尔代数运算性质等；最后，在内测度空间Y，

The Generalized Kolmogorov Probability generalized the 1st Kolmogorov's axiom and allows the probability values to be within the whole open real interval of (-infinite,+infinite).

广义的柯尔莫果洛夫概率(Generalized Kolmogorov Probability)推广了柯尔莫果洛夫概率三公理的第一公理：概率可在开区间范围内取值。

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。