应用数学

To solve this problem, based on the concept of graph theory we give a few models and arithmetic designs of virtual backbone in the environment of different application, and propose the corresponding routing mechanism with these virtual backbones. The major achievements are outlined as follows:The state of host's power or the time of host's online plays an important role in keeping stability of a virtual backbone. With a view to this feature, the paper introduces a simple and efficient heuristic algorithm for calculating the virtual backbone by seeking a minimum connected dominating set with maximal weight. The maximality of the weight-based choice of backbone nodes guarantees that the most suitable nodes have been chosen for the role of backbone nodes so that they can properly coordinate all the other nodes and keep stability of the virtual backbone in the network.

为了解决这个问题，本文利用网络图论中的一些理论，在不同的应用环境下给出几种虚拟骨干网的模型、构建及基于稳定性和节能的算法设计，并针对这些骨干网提出相应的分层路由机制，主要研究内容和贡献如下：考虑到主机的功率大小和在线时间长短对虚拟骨干中心的相对稳固性的影响，提出用基于极大权的最小连通支配集模拟虚拟骨干网；并给出其数学模型和相应的启发式算法，确保了性能强的主机担任骨干节点；通过优化规则确保骨干网的极小性，有效地减小了控制分组转发开销；最后进行了仿真验证。

A large quantity of energy and de-ionized water is consumed in the old process. The purpose of this thesis is to apply CD technique to the old process of methyl acetate hydrolysis. In order to prepare for future industry process, we checked the mathematical model that has been established by our experiments.

本论文的目的是将催化蒸馏技术应用于醋酸甲酯水解工艺中，通过实验，对前期所建立的数学模型进行校核，考察各项工艺参数，发现并解决问题，获得第一手详实的数据资料，为进行下一步的工作作好充分准备，为将来的工业化生产提供可靠的数据参考与技术支持。

The uncertainty of travel time of road network is depicted by means of scenario union firstly,then a path finding modal applied minimax theorem is constructed for obtaining most reliable path of all scenarios.

该方法通过场景集描述网络旅行时间的不确定性，应用Minimax理论构建求解所有场景下可靠路径的数学模型，并设计了问题求解算法，分析了算法的时间复杂性，最后通过典型算例对算法进行了验证。

This paper firstly reviews the history of Automated Theorem Proving and Mizar,then gives a description of methods of mechanical theorem proving and verification to mathematical proposition under Mizar system.Based on that basis,the paper has done some Mizar researches on mixed operation of quaternion,differentiati- on of special composite function and the application of Rolle\'s theorem.

本文首先介绍了定理机器证明和Mizar语言系统的发展历史，其次简单描述了Mizar系统下定理机器证明和校验数学命题的方法，在此基础上对四元数的混合运算，特殊复合函数的微分以及洛尔定理的应用等方面进行了Mizar实现。

Thirdly,the paper combines mathematical knowledge with the Rolle\'s theorem implemented in Mizar system already, implements the exert and promotion of Rolle\'s theorem and Cauchy mean value theorem in Mizar system.

将Mizar系统中已实现的洛尔定理与相关数学知识相结合，在Mizar系统中实现了洛尔定理和柯西中值定理的一些应用和推广。

After contrasting and optimizing this paper gets a set of parameters. Then according to these parameters the paper sets up entity model, and after validating and analyzing with finite element it can save time of calculating. On the other hand, it can provide a good method of design of moldboard plow surface.

通过对这四个阶段中土垡的运动学和动力学分析研究，建立了犁体牵引阻力的数学模型；通过对比分析得到较优的一组参数，然后以该组参数为依据进行参数优化，最后以优化后的参数建立犁体实体模型，应用有限元进行分析，节省了计算时间和提高了计算效率，为今后犁体曲面设计提供了一种方法。

This paper analyses and calculates the plow parameters about two kinds of high speed plows LEMKEN and KUHN, and studys the relation between the geometric parameters of shape of moldboard plow surface and soil properties, plowing quality, forces properties, plowing speed, resistance and energy dissipation during the plowing. Then according to the direction of developing high efficiency and saving-energy agriculture, under the premise of good farming quality this article puts forward a kind of method setting the mathematics model about plow resistance through the new cultivation principle and the new design principle.

本文通过对比分析的手段对LEMKEN和KUHN两种高速犁参数两种犁体曲面参数进行量化分析计算，分析犁体曲面形状的几何参数与耕后质量、土壤的力学特性、耕速、阻力和功率消耗等相关关系，结合目前高效节能型农业的发展方向，提出在保证作业质量的前提下，应用新型耕作理论和新型设计理论建立牵引阻力数学模型。

He found that the interval of an octave is rooted in the ratio 2:1,that of the fifth in 32,that of the fourth in 4:3.and that of the whole tone in9:8.the phthagoreans applied these ratios to lengths of a string on an instrument called a canon,or monochord(a board with two bridges between which a string is stretched and a third bridge that divide the string in two parts);and thereby were able to determine mathematically the intonation of an entire musical system.

毕达哥拉斯将这些弦长比例应用于一种叫做卡农的乐器上，卡农也可以称之为单弦琴或者单弦音响测定器（是一个由两个码构成的木板，码子之间有一条被拉伸的琴弦，第三个码子位于琴弦两端的码子之间），因此能够用数学的方法测定整个音乐系统的音调。

They make use of the latest techniques in biochemistry and biotechnology. Their analyses are sprinkled with complex mathematics and multivariate statistics.

他们会应用最新的生物化学和生物科技成果，而他们的分析也充满了复杂的数学和多元统计分析。

As a new branch of mathematics and with a great ability to describe and study natural phenomenon, fractal geometry has attracted a good deal of attention and has been applied in more and more fields.

分形几何作为一个新兴的数学分支，为描述复杂事情提供了一套崭新的工具，在越来越多的领域得到应用。

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。