数学分析

This paper studies the development of production of Hunan Potentiometer General Factory with the Analytical Hierarchy Process.

1决策分析的主要方法我们利用层次分析法来进行决策分析，这是一种定性与定量分析相结合的决策方法，它将决策者对复杂问题的思维过程数学化。

Based on the analysis of the mechanism of robot manipulators, a trajectory tracking controlling research model is first built up with ADAMS, and its mathematical model is formulated through the study of robot kinematics and dynamics. After the modeling errors are analyzed in practical robotic systems, a conception of centralized error is brought forward according to the theory of weighting functions. In the case of modeling errors' exist, the robotic uncertain model is derived by introducing an auxiliary control variable into inverse dynamic analysis. The control strategy of robust exponential convergence is applied to the robotic uncertain model, the applicable conditions and the applicable controller with this application are presented. The stable control effect under three main model uncertainties (parametric errors, joint disturbs, joint frictions) are systematically studied on the previously built research model. The problems of robust exponential convergence controller which often results in unstable output and so produces a large relative error when the input trajectory is in a small range are resolved by adjusting the control parameters based on the controller's structure.

本文在机械手的机械结构分析基础上，利用ADAMS建立了用于机械手轨线跟踪控制研究的机械手模型；通过对机器人运动学和动力学问题的研究，建立了机械手研究的数学模型；分析了机器人系统中模型误差的主要来源，根据加权函数法分析，提出了模型集中误差的概念；在存有模型误差的情况下，采用逆动力学结构并引入辅助控制量，由机器人误差模型推导了机器人非确定性模型；提出了采用鲁棒指数收敛法对上述机器人非确定性模型进行鲁棒镇定的控制策略，并给出了对机器人进行鲁棒指数收敛控制时系统不确定因素应满足的匹配条件；针对机械手研究模型，深入研究了鲁棒指数收敛控制器对机器人系统中常见的模型参数误差、关节扰动、关节摩擦等不确定因素的镇定控制效果；针对鲁棒指数收敛控制器易产生控制量振荡的问题以及在小范围内系统轨线跟踪的稳态误差过大问题，本文分别提出了基于控制器结构的控制参数调整法和基于轨线跟踪范围大小的控制参数分段切换法。

Secondly, the steady-state productivity model for horizontal well in gas reservoir is established. On the basis of solving the model, this thesis elicits the binomial deliverability equation by which absolute open flow potential and inflow performance relationship can be got and we can forecast the production performance of horizontal well in gas reservoir. In the end, on the basis of the theoretical analysis, this thesis explores homologous nodal analysis program.

其次，在建立水平气井不稳定渗流数学模型并求得其解的基础上，推导出了考虑地层伤害及非达西渗流影响水平气井产能方程，通过该产能方程可求出水平气井的绝对无阻流量，绘制流入动态关系曲线来预测生产动态；最后，在理论分析的基础上建立了水平气井节点分析方法，并开发了相应的节点分析程序。

Second, in the viewpoint of crypto analysis, the practical requirement for the cryptographic function is to construct the function that can resist all the known crypto analysis and attacks. In advanced, the main cryptographic properties are compared, and the relation among these cryptographic properties is analyzed, including the trade-off ones. Get the conclusion that the construction of cryptographic Boolean function is to find out the proper Boolean function in the whole vector space under the restriction of several cryptographic properties required for the security system.

然后本文从密码分析的角度，讨论了密码函数的实际需求，即构造能够抵抗已有密码分析与攻击的布尔函数；分析了布尔函数的主要的密码学性质，并比较了这些性质之间的相互关系，包括制约的关系；得出了构造布尔函数的实质的结论，即在向量空间中构造全体布尔函数，以所需的若干密码学性质作为限制条件，用有限域上的多项式、Walsh谱、Hadamard矩阵等数学工具找出适当的布尔函数用于加密体制的设计。

Using the sectional force and torque balance method to consider the effects of load force and temperature,provides a more completeness and systematic mathematical model.The working characteristic of bimetal strip is expressed by equivalent network.

采用综合考虑负载作用力及温度影响的分析条形双金属片的截面力－力矩平衡法，给出了较完整系统的数学模型；将双金属片用等效网络表示，用网络分析手段求解温度继电器、热继电器的工作参数；分析了在比弯曲最大的条件下各层界面、表面应力关系。

On the basis of analyzing the reason that produce hydraulic impact, the dynamics of vibration wheel of vibration compactor and dynamics of vibration hydraulic system were analysed, the mathematics model of vibration hydraulic system was set up and its output models for pressure and flow were deduced.

在分析液压冲击产生原因的基础上，进行了振动压路机振动轮的动力学分析和振动液压系统的动态分析，建立了振动液压系统的数学模型，同时推导出系统压力和流量的输出模型。

Aiming at the mathematic model of shafting crankle coupling vibration based on the subsection continuous mass model,the multidimensional frequeney analysis method is put forward and developed.Combining frequency change with shafting configuration parameter,it's more favorable to have direct analysis.The method...

针对基于分段连续质量模型的轴系弯扭耦合振动数学模型，进一步简化并提出多维频率分析方法，将频率变化与轴系的结构参数联系起来，有利于直观分析，同时给出分析振型、共振频率及共振模态等的方法

Mathematics and Physics in the 19th century, another major achievement - Fourier analysis of the development of the simulator played a direct role in promoting. The late 19th century and early 20th century, have made a variety of computing the Fourier coefficients of the differential analyzer differential analysis reconciliation and so on.

19世纪数学物理的另一项重大成就——傅里叶分析，对模拟机的发展起到了直接的推动作用。19世纪后期和20世纪前期，相继制成了多种计算傅里叶系数的分析机和解微分方程的微分分析机等。

In mathematics, Chinese scholars have achieved important results in fields such as number theory, theorem-proving by computer, differential geometry, topology, complex analysis, probability and mathematical statistics, PDE, functional analysis, numerical analysis and control theory and so on.

在数学方面，据我所知，中国数学家在诸如数论、定理机器证明、微分几何、拓扑学、复分析、概率论与数理统计、偏微分方程、泛函分析、数值分析和控制论等领域里也都取得了具有国际水平的成果。

After a brief summary on data mining and rough set theory, the research works in the thesis can be descript as follows: 1. To the problem that finding rules in enormous data is very timeconsumable and the expansibility of existed algorithms is not very good, the thesis proposes a new method to discompose large data table based on the concepts of positive region and the importance of attribute in rough set theory.

Rough集理论是一种新型的处理不确定性知识的数学工具，围绕着数据挖掘领域存在的问题，本文利用Rough集理论与Rough分析工具，提出若干解决方案，同时在具体处理问题过程中引入了信息理论、因子分析等方法，与Rough分析结合使用，讨论了Rough集技术在知识发现、关联规则挖掘、模式分类以及数据清洗等问题中的应用。

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。