数学基础

PSO is a population-based optimization algorithm, which mimics the social behavior of animals in a flock. It makes use of individual and group memory to update each particle position allowing global and local search optimization. The objective function considered was the total weight of the structure subjected to stresses, displacements and forces constraints. The effects of the parameters were investigated as well and such combination of tuning parameters promote a better global search behavior avoiding premature convergence while rapidly converging to the optimal solution. Results showed the effectiveness of the proposed method by comparing with ANSYS Design Optimization Tool (zero-order method). The PSO with the tuning parameters makes it an ideal method for offshore wind turbines foundations optimization tasks.(2) A reliability analysis method for pile foundation bearing axial loads based PSOThe performance function of pile foundation's axially bearing capacity sometimes is nonlinear and complex, on the basis of geometric meaning of structural reliability index, an optimum model with PSO for structural reliability analysis under arbitrary random variables was established, The PSO algorithm is very efficient to solve global optimization problemsIts use in structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. In addition, PSO is a zero order algorithm, for no derivative is necessary for its implementation.

本文的研究针对桩式海上风机基础结构的特点，在国内外有关研究成果的基础上对海上风机基础结构优化设计理论和可靠度方法一些相关问题进行了较为深入的研究，具体做了以下几个方面的工作：(1)基于粒子群优化的桩式海上风机基础确定性优化设计方法桩式海上风机基础的优化设计是一个复杂的、非线性约束的优化问题，针对传统的基于梯度信息的优化方法在处理非线性问题中易陷入局部最优解的问题，本文将一种耦合惩罚函数的PSO算法引入到海上风机基础结构概念设计中，PSO算法是从群体动物聚集觅食这一活动中受到启发而发展的，该算法利用个体和群体的信息共享不断改进自身的位置从而进行局部和全局最优搜索，本文中以桩和三脚架连接段直径及壁厚为设计变量，以基础总重量作为优化的目标函数，在给定的约束条件下建立了三脚架基础优化数学模型，另外本文还研究了PSO参数变化对结果的影响，协调的参数组合可以避免陷入早熟收敛而能够快速的获得全局的最优解，通过与ANSYS优化模块的计算结果比较验证了该方法的有效性，本方法为海上风机基础的确定性设计提供了一条有效的途径。

Professor Chen Xingshen achievements in order to affirm and encourage the development of our young mathematicians to contribute to the cause of China's Mathematical What he has in-depth introduction to the mathematics outside the field of theoretical physics to become an important tool G introduced geometric structure of the equivalent problem, a 20th century one of the major developments of mathematics, Integral geometry for the generalized basis, access to basic kinematics formulas.

为了肯定陈省身教授的功绩，激励我国中青年数学工作者对发展我国的数学事业做出贡献他引入的东西已深入到数学之外的领域，成为理论物理的重要工具，引进了G 几何的结构，研究其等价问题，成为20世纪后数学的主要发展之一，为广义的积分几何奠定基础，获得基本运动学公式。

The theories research part mainly is the foundation that supervises and control by one's own in domestic and international relevant mathematics academics related research cultural heritage up, combine the present condition of the our country mathematics education reform, re- examine mathematics learning process, get:The development of high school student mathematics academics ability is the necessity that the core puts forward mathematics academics ego supervision ability research from here.

理论研究部分主要是在国内外有关数学学科自我监控相关研究文献的基础上，结合我国数学教育改革的现状，重新审视数学学习过程，得出：中学生数学学科能力的培养是关键，由此提出数学学科自我监控能力研究的重要性。

The methods of documental research and experience-summarizing research are used in the thesis.

本文采用文献法、经验总结法，在研究数学阅读教学实施现状和对数学阅读价值分析的基础上，充分论证了高中数学新课程中设立数学阅读内容的必要性。

In Russell's opinion, logic should be the foundation of mathematics. Then he put forward his topic that mathematics is the same as logic and it can be deoxidized to logic.

他认为，数学的基础应是逻辑，从而提出他的数学逻辑主义论题：数学与逻辑等同，全部数学可以化归为逻辑。

In Russells opinion, logic should be the foundation of mathematics. Then he put forward his topic that mathematics is the same as logic and it can be deoxidized to logic.

他认为，数学的基础应是逻辑，从而提出他的数学逻辑主义论题：数学与逻辑等同，全部数学可以化归为逻辑。

This dissertation compares and reflects on classical mathematics between Chinese and Western, points that classical mathematics in Chinese differs from Western, former is a constructing and mechanizing system, and latter is logical and deduct system.

本文通过揭示中国古典数学思想及以古希腊为代表的西方古典数学思想特征的基础上，寻求二者之差异及引起差异的根源、表现及特征，指出中国古典数学的构造性、机械化的算法体系，完全有别于以古希腊为代表的西方数学的逻辑风格和演绎体系。

At last, the software for upper machine and lower machine is introduced.Chapter 3, on the basis of the experiment on the nano feeding control platform, the mathematic modal of drive parts is established considering that the nano feeding under large feeding force has some open air temperature random disturbance phenomenon which influences the feed precision.

第三章，首先对建立数学模型的分步拟合方法进行了介绍，接着，在实验的基础上，通过拟合的方法得出纳米级热驱动部件输入功率与输出位移的数学传递函数以及外界温度干扰与输出位移的数学传递函数，最后建立了干扰情况下的纳米级热驱动部件数学模型。

The base of this point is that firstly, math has become the base of natural science, social science and behavioural science, and the content, ideology and other elements of math have been widespreadly applied to our social life; secondly, math plays a key role in improving the scientific and cultural qualities of a nation because it not only provided us with applying technology but also gibes people capability; thirdly, one of the weak line in math education is the cultivation of the ability of self-supervision and self-control.

另一方面，数学教育应着眼于人的文化素质教育已成为人们对数学教育认识的一个新变化点。这一点是基于：1、数学已成为自然科学、社会科学和行为科学的基础，数学的内容、思想等在人类社会生活中已经得到广泛的应用；2、数学在提高一个民族的科学和文化素质上起着非常关键的作用，他不仅给予应用技术，而且也给人以能力。

The First Part discusses the rationale of cultivating the maths self-learning ability of secondary vocational school students, making an overall theotvlical explanation in the urgency and possibility of cultivating the maths self-lenmmg ability of secondary vocational school students, the learning and teaching features of ninths self-learning ability and the teaching principles of maths self-learning ability cultivation.

第一部份，讨论培养中职学生数学自学能力的理论基础，从培养数学自学能力的迫切性、可能性，数学自学能力的学习特征，教学特征，以及数学自学能力培养的教学原则等方面作了较为全面的理论阐述。

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。