数学分析

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。

It is just for the above reasons, statistical theory and simulated mathematical models, such as fuzzy mathematics, grey system theory, analytic hierarchy process, set pair analysis as well as the remote-sensing technology of geographic information systems are more and more emphasized so as to heighten the scientific value of such assessments.

综述了最近几年环境评价中应用较广或新出现的综合评价方法及其在环境评价中的应用，重点介绍了模糊数学方法、灰色系统理论、层次分析法和集对分析等数学模型评价方法，以及地理信息系统技术的原理和有关应用。

In the situation, this paper brought up the risk analysis and evaluation method on the basis of intelligent control and network communication technology for Network Communication System. The risk analysis and evaluation of Network Communication System firstly discussed the character of network communication and its risk. At the following we estimate a risk evaluation model according the distribution of the systems risk by time and space. Otherwise, we combined Fuzzy Comprehensive Evaluation with Analytic Hierarchy Process, and set up the multi-grade fuzzy comprehensive evaluation model for Network Communication System.

该方案主要通过讨论网络通信系统及其风险的特性，根据风险的时间和空间分布规律，以"风险"为整个网络通信系统安全模型的评估和分析对象，确立网络通信系统风险分布的量化评估模型，同时，就不同区域和不同时段的风险通过引入层次分析的一般方法来确定它们的权重系数，最后，通过模糊综合评判法则对系统中模糊不确定性因素进行数学化的抽象，建立一个反映其本质特征和动态过程的理想化的数学评估模型。

The construction of the models is based on such theories as Theoretical Mechanic,Advanced Mathematics,Space Analytic Geometry,the Theory of Ship and Sea-keeping Theory.

在比较、分析国内外有关船舶波浪稳性的研究成果的基础上，运用理论力学、流体力学、高等数学、空间解析几何的基本原理和船舶原理、船舶耐波性、船舶抗沉性、势流理论的专业理论知识，提出了计算船舶波浪稳性的数学模型，并针对客滚船在波浪中的稳性变化进行了定量的计算和分析。

It is very interesting to study the boundedness for the commutators related to some integral operator on the functions spaces.

Marcinkiwicz算子作为分析数学中一个重要的积分算子，对它的研究一直是分析数学学者们十分感兴趣的问题。

I tried to discover that when student's solving problems, the developing level of students adapt the dialysis of the mathematical cerebration and methods. Then I try to give some advices of my teaching on how to permeate the basic mathematical cerebration.

鉴于此，我在教学实践中，对学生解决数学问题的表现进行了收集、分析、总结；同时也对教师在授课中数学思想方法的体现进行了分析研究。

At first, according to the mechanical vibrationtheory and detailed analysis on coiling the different stage mathematical models of coiling are set-up. The correlation equations of the models are also given. Then, the paper presents an analysis ofthe moment of inertia of coiler in hot strip mill in detail, the equation of the inertia moment and theanalysis.

本课题首先从振动理论出发，对卷取的整个过程做了详尽的动力学分析，建立了不同卷取阶段的数学模型；接着分析了卷筒的惯性力矩，建立了卷筒张力控制的数学模型，推导了惯性力矩的理论表达式。

The course is divided into two parts: Part 1: Signal representations - discrete and continuous; System representations; Linear time invariant systems (Superposition, Causality, Impulse response, Stability, Transfer functions); Discrete and continuous convolution.

通过 本课程的学习，学生应能掌握信号分析与线性系统的基本理论及分析方法，应能建立简单电路与系统的数学模型，并对数学模型求解，为后续课程的学习打好基础。

To further enhance the autoleveling technology of drawing frame, a new type of dual open-loop control system was issued based on the analysis of the quality of the current autoleveling control system of drawing frame. This paper presented a mathematical model of the new control system, analyzed its mathematical theory, and elucidated the theoretical basis of dual open-loop autoleveling control system.

为进一步提高并条机自调匀整技术，在分析纺织并条机自调匀整控制系统优劣的基础上，提出一种新的双开环控制系统，给出了新型控制系统的数学模型，详细分析了其数学原理，阐述了双开环自调匀整控制系统的理论基础。

This paper proposes that the antagonistic relations between the two views parallel the debate between behaviourism and constructivism in mathematics education through the analyses of its philosophical position, and shows that philosophy of mathematics has important influences on the actual activity.

基础主义和拟经验主义是数学哲学的两个主要派别，通过对其哲学立场的分析提出这两种哲学观的对立表现在数学教育中就是行为主义和建构主义的对立，从一个侧面表明数学哲学对实际数学活动的影响。

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。