数学基础

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。

On the base of Frege's study, Russell put forward the theory of types to settle Russell's paradox. On the base of non-set, Russell brought forward axiom of infinity and axiom of option as the premises and built a system. He tried to defined the non-negative integer in logic terms and derive the theorems of arithmetic from the laws of logic by deductive method.

罗素在弗雷格研究的基础上，提出逻辑类型论来解决罗素悖论，以非集合论理论为基础，以无穷公理和选择公理为前提，利用逻辑概念定义数学概念，并构造系统，通过逻辑演绎法从逻辑公理推导数学定理。

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。

Introduce the elementary knowledge related to dimension chain; Propose mathematical model of dimension chain, and analyze the process to build mathematical model; Analyze the search process to generate dimension chain using deep first search method.

介绍尺寸链的相关基础知识；提出尺寸链数学模型，分析了以图论为基础的数学模型的建立；分析了以深度优先搜索法进行尺寸链自动生成的搜索过程。

With the investigation of the domestic and foreign literature systematically, the bases on the domestic and foreign present research and the comprehensive utilizations of the various knowledge of fluid mechanics in porous medium, reservoir engineering, mathematical physics, perforation completion, numerical simulation and so on, this article takes numerical simulation of gas reservoir of water solubility as the research aim which has completed following research works and obtained the corresponding research results: it analyzes the nature of the Water-soluble gas and formation water as well as the influent factors of the solubility through the study of massive materials; It establishes mathematical models three-dimension, the dual medium, the gas-water phase through the way of finite difference in the migration of water-soluble gas, which describes the entire process of release, migration and production in formation, where it considered the problems of variable bubble point; According to the numerical models of gas reservoir of water solubility it provides solution procedure that based on black oil model; It discovers that there will obtain the good effects in the lowly speed of development through simulation; the reinjection of formation water may largely enhance the produce degree of water-soluble gas when we consider reinjection in simulator; It considered the influence of perforated completion on development so as to increase the simulator"s versatility, It discovers that the simulator may reflect the conditions of development when we exanimate he simulator"s reliability with the empirical datum.

本文以水溶性气藏数值模拟研究为研究目标，在系统调研国内外文献、深入分析国内外研究现状的基础上，综合利用渗流力学、油气藏工程、数学物理方法、射孔完井以及数值模拟理论等多方面的知识，完成了以下研究工作并取得相应的研究成果；①通过对大量的资料调研，分析了水溶气、地层水性质、储层地质性质以及影响气体在水中溶解度的因素。②考虑到由于高压产生的大量水力裂缝，采用有限差分方法建立水溶气运移的三维、双重介质、气-水两相全隐式数学模型，该模型描述了水溶气在地层中的释放、运移和采出的整个过程。③在原有黑油模型的基础上，根据水溶性气藏数值模型编制了该数值模型的求解程序，该程序可以求解单重、双重介质两种情况。④通过模拟不同开采速度对水溶气开发效果的影响，发现开采速度较慢的时候可以取得较好的开采效果。⑤在模拟器中考虑了注水对水溶性气藏开发的影响，地层水回注可以大幅度提高水溶气的采出程度。⑥为增加模拟器的通用性，在模拟器中考虑了射孔完井方式对开采的影响。⑦检验模拟器计算的可靠性，发现在使用实验数据对水溶性气藏进行模拟时，模拟器可以很好的反映气藏开发的状态。

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。

Partial and total differentials, Vector analysis, Orthogonal curvilinear coordinates, Matrices and

基础物理数学( S0043)(0，3)/基础应用数学( S0249)(0，3)偏微及全微分(1)、向量分析(7)、正交曲线座标系(3)、矩阵及本徵值问题(4)、常系数全微分方程式(1)。

In the process of calculation ,not only the decouplable feature of symmetrical elements in the coordinate system of symmetrical components is fully utilized,but also the symmetrical parts and unsymmetrical parts are treated as separate blocks, thus the efficiency of calculation is rasied moreover.

建立用于故障分析的网络的数学模型是计算机编程计算的基础。当前在电力网络中最常用的网络参数矩阵有节点参数矩阵和支路参数矩阵。在故障分析计算中一般采用网络节点参数矩阵作为电力网络的数学模型，又主要使用节点导纳矩阵作为分析的基础。

On the condition of remote observation and quasi- monochromatic observation,a compact image-plane interference mathematical model is deduced with OAS optical transfer function and the property of Fourier transform.

在观测目标相当遥远及准单色观测条件下，根据光学综合孔径光学传递函数以及傅里叶变换性质建立了一个简化的像面干涉光强分布数学模型，此数学模型的物理含义符合光学综合孔径成像观测的实际情况；根据光学综合孔径瞳面干涉条件，在光学综合孔径像面干涉数学模型的基础上得到瞳面干涉的数学模型。

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。