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Abridgement ）:Mathematics Olympiad entitled to carriers, a mathematical way of thinking on the meaning: mathematical thinking is to understand the nature of mathematical knowledge, from some of the specific content of mathematics and mathematical understanding of the excessive rise in refining a mathematical point of view, is a mathematics knowledge Structure of the essence and soul of the commander in chief and it played the dominant role of mathematical knowledge.

以数学竞赛题为载体，阐述了数学思想方法的涵义：数学思想就是对数学知识的本质认识，是从某些具体的数学内容和对数学的认识过重中提炼上升的数学观点，是数学知识结构的精髓和灵魂，它起到统帅和支配数学知识的作用。

Comprehensively making use of the basic theory, such as Space Analytic Geometry, Gear Meshing Engagement Theory, Method of Mathematical Calculation, Theory for Error Analyzing and Data Processing, the author has established the mathematical models of the new method, which has included the analytic mathematical model for precision orientation, the mathematical model for the ball's diameter and the measuring diameter, the mathematical model about the ball's centre, the calculation model for tooth alignment diviations and the model for tooth alignment error evaluation.

本文综合应用空间解析几何学、啮合原理、计算方法、误差理论与数据处理等有关基础理论，推导建立了新方法的数学模型，包括：确定定位关系的解析法数学模型，测球直径与测量半径的数学模型，测球球心的数学模型，齿向偏差的计算模型以及齿向误差的评定数学模型等。

Chapter 4, lists the teaching cases in teacher's teaching, combined the cases dissecting the teaching methods of mathematics and mathematical cerebration and methods in the point of view of psychology, then infers that to proceed the teaching of mathematical cerebration and methods is necessary. In the other hand, I compared and studied the association between the basic mathematical cerebration and methods and other mathematical knowledge, answer the questions that which mathematical cerebration and methods are more worthy to jut out. At last, infers a mode of the teaching in mathematical cerebration and methods.

第四章列举了教师在授课中的教学案例，结合案例从心理学角度对中学数学教学与数学思想方法教学进行剖析，得出进行数学思想方法教学是十分必要的；同时对中学数学教学中的数学基本思想方法与其它数学知识的关系进行了对比分析，对在中学数学教学中突出哪些数学基本思想方法为好做了解答；最后给出了数学思想方法教学的一个教学模式。

Relativity can't leave Lorentz transformation such interesting mathematical game, from its beginning to its end is from mathematical game to mathematical game, it seems that he wants to use mathematical game to direct physics experiment, it seems that he wants to use mathematical game to change space and construct another universe.

相对论离不开洛仑兹变换这个有趣的数学游戏，从它的开始到它的结束全是从数学游戏到数学游戏，似乎他要用数学游戏去指导物理实验，似乎他要用数学游戏去改造空间和另造宇宙。

To strengthen mathematical symbol language analogy and symbol's suggesting function, to cultivate students' ability to transfer the mathematical narrative language to mathematical symbol language, to lead students to understand the definition of mathematical symbol and to regulate the writing of symbols will all contribute to developing mathematical thinking.

加强数学符号语言类比和符号提示功能教学，培养学生将数学叙述语言转换成数学符号语言的能力，引导学生正确理解数学符号的含义并规范符号书写，促进学生数学思维的发展。

Because the mathematical linguistics are one kind by the mathematical symbol, mathematics terminology and the scientific language which is composed after the improvement natural language, therefore in mathematics teaching, the teacher not suitable direct use mathematical linguistics achievement teaches the language generally, but must act according to student's knowledge foundation and the psychological feature, transforms the mathematical linguistics as easily the language which is accepted by the student.

由于数学语言是一种由数学符号、数学术语和经过改进的自然语言组成的科学语言，因此在数学教学中，教师一般不宜直接使用数学语言作为讲授语言，而必须根据学生的知识基础和心理特征，将数学语言转化为容易被学生所接受的语言。

Psychology}, the paper defines intuition as a cognitive ability to make immediate judgement without analyzing or reasoning and further analyzes the relation and difference between intuition, inspiration, insight, imagination and perceptual intuition, pointing out that mathematical intuitive thinking is a swift judgement on and imagination to the objects of mathematics and their relationship in structure which is featured by illogicality, directness, probability, randomness and unity and aids students in predicting conclusion or direction to solution as well as making definite choice between several options, Furthermore, the paper probes into the foundation of mathematical intuitive thinking in terms of psychological mechanism, and thereupon holds it necessary to develop students mathematical intuition in that it does good to the excitement of creativity, improvement of overall qualities, all- brain development and optimization of mathematical thinking among students.

而数学直觉思维就是人脑对数学对象及其结构关系的一种迅速的判断与敏锐的想象，并探讨了数学直觉思维的生理机理基础，总结其特征有非逻辑性、直接性、或然性、随机性、整体性和综合性。在解题时直觉能帮助学生对结论或解题方向做出预见，也可以在推理面临多种可能性时，帮助学生做出果断的选择。

Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system.

本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C_0 -半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助Matlab工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C_0 -半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础。

For preparing for the researches of text digital watermarking and advantaging other researchers" development when using the Chinese mathematical expression theory, this paper designs and realizes a development platform of Chinese mathematical expression. It has been proved by experiments that the platform"s function, execution speed and stability can satisfy the requirements of conversion and operation of enormous data.This research found out that the structure information of Chinese have plenty redundant information that can be used by the Chinese mathematical expression for the digital watermarking, the data embedded can possess better robustness. Based on this finding, this paper designs a kind of text digital watermarking method of embedding watermarking by using Chinese structure, and realizes the method by using the Chinese mathematical expression platform.Considering the watermarking embedding algorithms importance to the robustness of the text digital watermarking, this paper makes fully use of the advantage of the Chinese mathematical expression theory to design a kind of layered text method, which has being realized by using the Chinese mathematical expression platform. The layered text method can handle the text as a solid structure, and the embedding data havepreferable robustness.Finally, based on the researches of the text digital watermarking method and the text layered method, this paper integrates the method of making use of the Chinese structure embedding watermarking with the robust algorithm based on text layered, and realizes a brand-new text digital watermarking method. Proved by lots of experiments, this brand-new method has good robustness and better invisibility.

为了为研究工作做准备和方便其他使用汉字数学表达式理论体系的人进行开发，本文基于汉字数学表达式理论设计实现了一个汉字数学表达式平台，实现了Unicode汉字集中的汉字、汉字数学表达式、汉字的Unicode码之间的相互转化、依据汉字数学表达式提取汉字的结构信息、由汉字数学表达式在非中文平台上不依赖字库显示汉字的图像等功能，使用复合文档技术和流压缩技术进行数据的存储，使用对汉字数学表达式进行二叉树拆分来处理汉字数学表达式中包含的信息，使用自定义哈希函数来提高运行速度，实验证明，该平台功能、速度和稳定性完全能满足大量数据的转化和运算要求；通过研究表明汉字的结构信息中存在大量可使用汉字数学表达式理论加以利用的水印加载空间，加载在该空间的数据可以具有较好的鲁棒性，基于此，本文设计了一种利用汉字结构加载水印的文本数字水印方法，并使用汉字数学表达式平台将其实现；由于水印嵌入算法对于文本数字水印的鲁棒性至关重要，本文充分利用汉字数学表达式理论的优点，设计了一种文本分层的方法，并使用汉字数学表达式平台将其实现，使文本成为一个立体的空间，使嵌入在其中的数据具有更好的鲁棒性；最后在基于汉字数学表达式的文本数字水印嵌入方法的研究和基于汉字数学表达式的文本分层方法的研究的基础上，结合利用汉字结构嵌入水印的方法和基于文本分层的抗攻击文本水印嵌入算法实现了一种全新的文本数字水印方法，经实验证明，该方法有良好的鲁棒性和较好的隐蔽性。

Language in the Visual C ++ program to prepare the small company's management wages Data Structures Using C language simulation of the car park management, vehicle output reached, departure time and location C language environment in Turbo C 2.0 calculator program to prepare the basic functions, and provide visual interface SQL server database and the use of VC ++"student information management system" 2007,"Higher Education's Cup" National Mathematical Contest in Modeling (China's population growth projections) were third prizes Hubei Division Zhongnan University of Nationalities in 2006 Mathematical Contest in Modeling (the company's best production programme) won by their schools China and South Africa in 2007 by the national schools "Innovation Capability honorary title" 2006 "click space of a series of activities Poetry Speech Competition" The Excellence Awards 2006 - 2007 Zhongnan University of Nationalities professional third prizes August 2007 through selected to participate in the summer school mathematical modeling training September 2007 in "Higher Education's Cup" National Mathematical Contest in Modeling May 2006 Zhongnan University of Nationalities Mathematical Contest in Modeling Participate in the 2006 ACM Programming Contest 2006 Computer Science Institute participate in the "Click space series of activities," Poetry Speech Competition 2006 National University and South Africa to participate in "Click space series of activities," Program Design Contest China and South Africa in 2005 to join the University of the nation "Table Tennis Association"

++语言在Visual C++环境下编写程序实现小型公司的工资管理数据结构使用C 语言模拟停车场管理问题，输出汽车到达、离开时间及位置 C 语言在Turbo C 2.0环境下编写程序实现计算器的基本功能，并提供可视化界面数据库使用SQL server及VC++实现&学生信息管理系统& 2007年&高教社杯&全国大学生数学建模竞赛获湖北赛区三等奖 2006年中南民族大学数学建模竞赛（汽车公司的最佳生产方案）获学校一等奖 2007年获中南民族大学校&创新能手&荣誉称号 2006年&点击空间系列活动之诗歌演讲比赛&获优秀奖 2006年-2007年中南民族大学专业三等奖 2007年8月经过选拔参加学校暑期数学建模培训 2007年9月参加&高教社杯&全国大学生数学建模竞赛 2006年5月中南民族大学数学建模竞赛 2006年参加ACM程序设计大赛 2006年参加计算机科学学院&点击空间系列活动&之诗歌演讲比赛 2006年参加中南民族大学&点击空间系列活动&之程序设计大赛 2005年加入中南民族大学&乒乓球协会&

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。