数学

Based on intensive investigation of original sources and research literatures on the subject in consideration,and under the paradigm why mathematics was done in the history of mathematics,the dissertation studies systematically the origin and invention of the calculus of variations by means of source analysis and comparative argumentation.

变分法是研究泛函极值的数学分支，它不仅与数学中众多分支联系紧密，而且也为物理学提供了重要的原理，同时又有着十分广泛的应用，凶此，对其历史进行研究，具有极为重要的理论价值和现实意义。

The mathematical model of gas carburization is mathematical description of all kinds of physical and chemical phenomena in the process of carburization.

气体渗碳数学模型是渗碳过程中各种物理、化学现象的数学描述。

In this research, the plane 2D mathematical model under Cartesian coordinate system and the

首先建立了直角坐标系正交网格下的平面二维数学模型及复杂边界适体坐标条件下的三维紊流数学模型，对方程的离散差分格式、控制方程的求解、初始边界条件、动边界处理等问题进行了分析研究，并编制相应的计算程序。

Descartes' influence in mathematics is also apparent, the Cartesian coordinate system allowing geometric shapes to be expressed in algebraic equations being named for him.

笛卡尔在数学中的影响也很显著，因他而命名的笛卡儿坐标系让几何图形可用数学方程表达。

Show model combines growth model, math model and VR technologies to design the proper object structure of each organ of virtual plant. First of all,research background, research content of virtual plant area and Virtual Reality technology are introduced. The concept of VR and research content of virtual plant are defined. Secondly, we analyze math model of virtual plant, including Bezier curve, NURBS curved surface, fractal system, L-system and Catenary curve. Thirdly, we give show model of virtual plant in detail. Finally, the design of the platform and growth model on XML script is introduced , and how to show the virtual plant in the platfrom is discussed too.

本文首先介绍了虚拟植物领域的研究背景、研究内容和虚拟现实技术，明确了虚拟现实的概念和虚拟植物的研究范畴，然后介绍了虚拟植物器官的数学模型，对各个器官展开了拓扑结构分析，建立有针对性的数学模型，先后介绍了Bezier曲线，NURBS曲面，分形系统，L-系统和悬链线曲线，接着详细分类介绍了虚拟植物器官的显示模型，最后介绍了虚拟作物平台的设计，平台中基于XML脚本的生长模型，以及虚拟作物在作物平台中的显示。

Chapter 5, explains emphasizly how to permeate the basic mathematical cerebration and methods into teaching.

第五章着重阐述了如何将数学基本思想方法渗透于中学数学教学中。

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。

And it gives some suggestions to teachers on stressing the cerebration teaching in classroom teaching, explaining mathematical cerebration and methods actively, pointing out the principles and measures of enhancing mathematical cerebration and methods.

对教师在课堂教学中突出思想教学、积极探索数学思想方法教学提出了建议，指出加强数学思想方法教学的原则和具体措施。

If there's any mistake, I beg your pardon to point it out and correct it. There're five chapters totally in this paper, and the each main contents is al follows: Chapter 1, it introduces the mathematical methods, mathematical cerebration's implication and the association between them.

发现学生在解题时，其发展水平与思想方法渗透之间相适应和不相适应的行为表现，据此提出自己对在数学课堂教学中如何渗透数学基本思想方法的一点看法。

After studying of modern pedagogy and modern psychology, and after experiencing the participation pedagogy, and in view of the fact of the characteristic of math teaching in class of kindergartener, the scheme method of combining the traditional teaching mode with the participation pedagogy have been put forward in this paper.

在这一思想的指导下，幼师数学教学中形成了教师与学生参与式教学的四个层次，在使用参与式教学法时提出了对教师与学生的具体要求，对数学概念课进行了参与式教学法设计，并对准备导入环节的设计以及例题课教学的设计等做了较详细的阐述。

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。