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Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顾了高斯之前的数论研究状况，在系统分析高斯的科学与数学成就的基础上，探讨了《算术研究》出现的数学背景和高斯的同余理论；(2)通过对原始文献的系统解读，深入分析了费马小定理发现发展的历程以及在素性检验中的重要作用，指出《算术研究》前三节是高斯在总结并发展了前人对该定理研究的基础上形成的，并揭示了费马小定理在初等数论定理证明中的核心地位；(3)以二次互反律的两个主要来源为线索，详细考察了费马，欧拉，拉格朗目，勒让德，直到高斯的相关工作，揭示了该定律对十九世纪数论发展的巨大推动作用。

This powerful algebraic structure with its finiteness makes itself a concise and beautiful subject of study in the mathematical world.

这种强有力的代数结构再加上有限性这一条件使它成为数学领域中一种简洁、美妙的研究对象。

At last, based on a mathematical tool: algebraic system, this paper gives definition of spatial data cube.

最后，基于数学工具——代数系统，给出了空间数据立方体严格的数学定义。

A programming language based on ALGOL and designed for non-numeric manipulation of mathematical expressions.

一种以ALGOL语言为基础，为数学表达式进行非数值操作而设计的程序设计语言。

A programming language based on ALGOL and designed for nonnumeric manipulation of mathematical expressions.

一种以ALGOL语言为基础，为数学表达式进行非数值操作而设计的程序设计语言。

Fuzzy controller is designed according to human"s controlling experience of systems. After reducing the operator"s controlling experience to a set of qualitatively descriptive conditional statements, and then quantifying them by using the theory of fuzzy set, the controller can transform the natural language of human"s controlling strategies into the algorithmic language acceptable for the computer, then the controller can receive human"s experience, and imitates humans operating strategies and effectively control some objects that can not be constructed into the mathematical model.

模糊控制控制器是以人对被控系统的控制经验为依据而设计的，它把操作人员的控制经验归纳成定性描述的一组条件语句，然后运用模糊集合理论将其定量化，把人的控制策略的自然语言转化为计算机能够接受的算法语言所描述的控制算法，使控制器得以接受人的经验，模仿人的操作策略实现对一些无法构造数学模型的被控对象进行有效的控制。

The text"s main works involve to establishing mathematical models and come true models" algorithmization and found blocking simulation models and simulation application.

建立电力系统数学模型的任务是根据系统仿真目的和系统原型与模型的数学相似原则来构造模型的数学描述。

Mathematical models algorithmization can realize easily through choosing corresponding models and computer language.

在算法实现过程中，选择数值稳定性高、误差可以控制、计算工作量少和尽可能节省内存空间的算法。

The traditional mathematical expectation also results in the problem which puzzled the economist many years such as the Allais paradox and the Ellesberg paradox ...

Choquet(1953)提出了容度的概念以后，Choquet积分作为对传统数学期望的一种改进，被自然的引如到经济学中来。

Therefore, alogical generalization of limit cycle in stochastic models needs to be developed, andinterestingly, the concept of circulation in the mathematical theory of nonequilibriumsteady states [91] actually plays the role.

因此，需要研究随机模型中对应于确定性模型极限环概念的合理推广；而在关于开系统非平衡定态的数学理论[91]中，环流恰好可以扮演这样一个角色。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐