查询词典 axioms

Under the instruction of the schur axioms, many reasoning concerning schur axiomses produced then, and became a theories system of the schur axioms of integrity, coming up the certificate that the schur axioms and many of its reasonings expanded the likeness of the matrix and the characteristic of the matrix to be worth.

在 定理的指导下，许多关于定理的推论便产生了，并且形成了一个完整的定理理论体系，把定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

Theexpected utility theory based on the axioms isalso very important in modern decision-making theory.Form late fifties lastcentury,some scientists ahead by Allais and Edwards,try to check the facticity ofthe rational decision-making models applied to the real decision-making behavior,but find it unsatisfactory.For example,Allais Paradox and Preference Circleschallenge the axioms critically.

从二十世纪五十年代后期开始，以Allais和Edwards为首的一批学者从心理学的角度参与了实际决策行为的研究，他们从实证的观点去考察理性决策模型在实际决策行为中的真实性，不断地发现这些模型在应用中表现出各种偏差，Allais悖论的设计和克星循环现象的发现对Von Neumann-Morgenstern理性行为公理提出了有力的挑战。

Weak bialgebras and Hopf algebras are generalizations of ordinary bial-gebras and Hopf algebras in the following sense: the defining axioms are the same, but the multiplicativity of the counit and comultiplicativity of the unit, are replaced by weaker axioms.

中文摘要：弱双代数和弱Hopf代数是通常的双代数和Hopf代数的推广：定义的公理不变，但是余单位的乘法和单位的余乘法变得更弱一些了。本文主要将上环理论及其Galois理论运用于弱Hopf代数，得到弱Hopf代数的相应结果。

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 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 axioms mentioned here are a system of axioms, which comprise potential axiom, motivational axiom, reflexive axiom,aesthetic axiom and intermendiate.

这里提出的，是由潜在公理、动因公理，反身公理、美学公理和中介公理所组成的公理体系。

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 book, Boole set forth the formal axioms of logic (much like the axioms of geometry) on which the field of symbolic logic is built.

在这本书里，向前 Boole 装置逻辑的正式公理在上建立了符号逻辑的领域

In the doctoral dissertation,which focuses in lattice-ordered preferencestructure theory and lattice-ordered decision-making theory,lattice-orderedpreference relation displaces complete preference relation in order to makecharacterization of preference structure general,and in order to propose a newthinking of weakening completeness axiom,and also in order to put forward atheoretical base for setting up the rational behavior axioms and utility theorywith lattice-ordered preference structure.

本文有关格序偏好关系理论的研究将Von Neumann-Morgenstern理性行为公理中偏好关系的全序描述推广为格序描述，使得对偏好结构的描述更为一般化，并且为弱化公理体系中完全性或连通性假使提供一条新思路，为建立基于格序理论的理性行为公理及其相关的效用理论提供理论依据。

The circulation, consumption and reproduction of the trilogy have not only testified to its historical significance and literariness, but also invested it with new meanings.

该三部曲的流通、消费与再生产不仅验证了其历史意义及文学性，而切还赋予它以新的意义。

If he thought that he could buy me off, he would be wrong.

如果他认为他可以收买我，那他就大错特错了。