数学

LM leads to a school of logicism based onmathematical research.

弗雷格的"数学逻辑主义"的努力引发了数学研究的"逻辑主义"学派。

In preface, Russell's mathematics logicism is introduced in brief. It is thought to be include not only the idea of mathematics can be deoxidized to logic, but also the work of settle Russell' paradox.

在前言中，简要地介绍了罗素的数学逻辑主义思想，认为它除了"将数学还原为逻辑"这一观点外，还包括了解决罗素悖论的工作。

Logicism holes that mathematics can be reduced to logic, but the logicists were beaten by the discovery of the set paradox, because they have not discerned the intrinsic differences between logic and mathematics.

逻辑主义认为数学可以化归为逻辑，集合论悖论的发现给逻辑主义者造成重大的打击，逻辑主义失败的原因在于他们没有看到逻辑与数学之间存在着质的区别。

"Logicists supposed that abstract mathematical objects can be entirely developed starting from basic ideas of sets and rational, or logical, thought; a variant of logicism, known as mathematical Platonism, views these objects as existing external to and independent of an observer"

逻辑主义认为抽象的数学对象全部可以从基本的几组想法以及合理的或逻辑的思想发展出来，称为数学的柏拉图主义的一个变型把这些对象看作是观察者之外的、独立的存在

"Logicists suppose d that abstract mathematical objects can be entirely developed starting from basic ideas of sets and rational, or logical, thought; a variant of logicism, known as mathematical Platonism, views these objects as existing external to and independent of an observer"

逻辑主义认为抽象的数学对象全部可以从基本的几组想法以及合理的或逻辑的思想发展出来，称为数学的柏拉图主义的一个变型把这些对象看作是观察者之外的、独立的存在

The main work of this thesis is that basing on the documents of [77] , [78] , [79] , [80] , [81] probe into the applications of the duality theory in the macroeconomic analysis combining with some important problems in the modern economics, at the same time especially pay attention to the microfoundation of the macroanalysis.

本文的主要工作就是在[77]，[78]，[79]，[80]，[81]等文的基础上，以数学规划中的对偶理论做为基本数学工具，结合现代经济学研究的几个重大课题深入系统地探讨了对偶理论在宏观经济分析中的应用，同时也特别注重了宏观分析赖以存在的微观基础。

The thoughtway of function, it is the most important, one of the basiccest maths thoughtway, it is perforative a masterstroke at maths of whole high school.

函数的思想方法，是最重要的、最基本的数学思想方法之一，它是贯穿于整个高中数学的一条主线。

ABSTRACT It is very difficult to get exact mathematical models of industrial processes, models used in design procedure of control systems are commonly mathematical models through approximation.

在实际工程应用中通常很难得到被控对象的精确数学模型，在控制系统设计过程中所采用的模型常常是在一定程度上的经过近似化处理的数学模型。

The traditional mathematical expectation (i.e.the expectation about additive measure) takes an important role in risk pricing .

传统的数学期望(即关于可加测度的数学期望)在风险定价和效用理论中起者重要的作用。

Mathematical expectation is the random variable one of the important features of mathematics, the average value of random variable response to the size, in practical application has a pivotal role.

数学期望是随机变量的重要数学特征之一，它反映随机变量平均取值的大小，在实际应用中有着举足轻重的作用。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。