数学

It's pointed out that soft sensor will play more important role in field bus network control system. According to this, a crude solution was addressed. At last, we point out that soft sensor technology must used to build an information warehouse for the whole enterprise, combined with data fusion, data warehouse, data rectification and other related technologies. The main contributions of this dissertation are as follows: The background, requirement, and application situation of soft sensors are expounded, the theories, methods and skills of soft sensing technology are analyzed, and the fruits and problems in current soft sensor technologies are summarized. Some new methods of soft sensor is proposed: A principal component analysis-based secondary variable selection method are proposed; A new conception which modeling data should have gross error detection is addressed, and then a cluster analysis-based modeling data gross error detection method is given.

本文的主要贡献有：对软测量技术根据实践的要求进行了一定的理论研究，针对具体问题提出了新的方法：讨论了辅助变量选择问题，研究了基于主元分析的辅助变量选择方法，该方法克服了传统方法只能利用数学模型产生的仿真数据进行最优辅助变量选择的缺点，可以根据历史数据进行辅助变量选择；提出了建模数据显著误差侦破的概念，指出传统的显著误差侦破研究的是已知过程数学模型的情况，而建模时数学模型是未知的，但是直接来自现场的数据并不能保证不含显著误差，并用基于聚类分析的方法解决了该问题，该方法利用聚类分析原理，直接面对过程数据，不需以过程模型为基础，在此基础上给出了软测量建模过程中样本数据的处理方法。

This subject combines the basic principle of the calculus of variation and and reply and change basic theories of the function according to fracture mechanics, use mechanics, mathematics knowledge to set up corresponding mathematical model, derive out a series of mechanics and mathematics theory formula, work out procedure carry on number value calculate, to include edge crackle round stress intensity factor of component go on, ask, solve.

本课题结合变分法的基本原理并根据断裂力学和复变函数的基本理论，运用力学、数学知识建立相应的数学模型，推导出一系列的力学及数学理论公式，编制程序进行数值计算，对含边缘裂纹圆形构件的应力强度因子进行求解。

On one hand,as a typical content of mathematical subject,reasoning and proof embodies the mathematical rational spirit;on the other hand,to cultivate students' thinking ability as the main function,the mathematics without reasoning and proof.

一方面，推理与证明作为数学学科的典型内容，体现了数学的理性精神；另一方面，数学以培养学生的思维能力为主要功能，它离不开推理与证明。

There are two major divisions of mathematics: pure and applied.

数学有两个主要的分支：纯粹数学和理论数学。

In correspondence to the functions of the three phase, mathematics teaching is classified into three teaching patterns as theoretical teaching, empirical teaching and practical teaching, so that purposefulness.

三。三教学模式根据数学认知结构构成的三个要素及其相互关联和递进的关系，将数学学习和数学认知结构的形成分为知识习得、能力提高、素质养成三个阶段。

Through teaching the Pythagoras theorem and the make-square method of quadric equation with one unknown, the teaching practice of using mathematics history during mathematics teaching of the secondary school is researched deeply, so the educational value of mathematics history is embodied well.

第四、通过勾股定理的教学和一元二次方程的配方法的教学，更深入地进行了中学数学教学中利用数学史的教学实践研究，更好地体现了数学史的教育价值。

The paper, taking Pythagorean Theorem for example, analyzes the function, effect and the practice in the modern teaching.

分析了数学定理演变的原因及其对数学发展的作用，并以数学教材中典型的定理"勾股定理"为例，分析其在历史演化中的作用与影响，以及在现代中学里的教学。

After questionary,the circumstance of college students of science and engineering mastering the mathematical induction is obtained:many students knew how to use the mathematical induction,but they didn't know its logical basis and logical theory.

通过问卷调查，了解到理工科学生掌握数学归纳法的状况，绝大多数人会用数学归纳法，但他们不知道数学归纳法的逻辑基础和逻辑原理。

Only like this can we form our own way which will meet the requirements of the new era. Facing the reform, our teachers should renew our opinion, rerealize some basic matters such as education, Maths study and Maths teaching, and rechange our role through the study of the new subject theory and teaching case concerned. Teachers should put the theory into effect.

面对数学新课程改革，教师要及时更新观念，正确认识教育、数学学习和数学教学等基本问题，并通过对新课程理念和有关案例的学习，重新认识和转换自己的角色，以学习者、课程的开发者、教材的编写者和评价的参与者的角色，真正把新课程的理念落实到实处。

According to the definition of axis straightness error ,a mathematical model was developed to evaluate axis straightness error by way of least square method in the rectangular coordinates.

根据轴线直线度误差的定义，建立了在直角坐标采样时该项误差的最小二乘评定法数学模型，该模型的采样数据不需要等角度间隔采样；并用计算机进行仿真分析·结果表明，所建立的数学模型编程简单，计算出的轴线直线度误差值与真实情况的误差小于 10 -6μm·因此由本模型引入的误差可忽略不计·所建立的数学模型为研制形位误差虚拟测量系统提供了理论基础

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。