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This paper mainly introduces several different methods to prove the mid-value theorem, at the same time the mid-value theorem is applied in the mathematical theory, such as the application and mathematical modeling.

本文主要推荐几种不同的方法证明微分中值定理，同时对微分中值定理加以应用，如在数学理论中和数学建模中的应用。

We will introduce some definitions in the Mathematics Ecology and the mathematical theories and methods. Methods for studding the population ecology or the more ordinary ecology are by setting up the mathematical modelings. We will give the examples of the single population models and the population with interaction models.

简单介绍数学生态学中的一些常用的名词和研究问题所用的数学手段-通过数学建模的方法，将一个实际的生态问题量化为一个数学问题，给出常用的单种群增长的数学模型和具有种间关系的多种群数学模型。

On the base of building mathematical models of tractive performance and economic performance, synthetical optimization model of transmission parameters is presented;And building mathematical models of flexibility coefficient of correlative parame...

其次，基于动力传动系参数优化及分析模型的建立，结合MATLAB与Visual C++编程语言的各自优点，开发了一套基于PC机的动力传动系参数分析及优化设计软件。

On the basis of the mathematical models got by different measuring methods, a complete universal mathematical model was put forward by which different tappets lifts can be converted from one to another.

针对凸轮升程测量量具及方法不统一而造成升程转换困难及转换误差较大等问题，在研究凸轮升程各种测量方法数学模型的基础上，提出一个不同形式推杆升程相互转换的通用数学模型。

The dynamical and kinematic specialty of hydraulic hammer is analyzed during piling. At the same time, the mathematical model is presented of each process. Based on mathematical model of each stage, simulation and analysis is made. The changing rule of displacement, velocity, acceleration can come to a decision from simulation plot during falling process of pile hammer.

提出桩锤在各个打击过程中的数学模型，并对各阶段进行仿真及分析，研究桩锤下打过程中，桩锤位移、速度、加速度变化规律，为进一步研究生产样机提供了理论依据。

A 3D two-fluid model is also built in order to describe more accurately the fluid flow on distillation trays by comparing the computational results of quasi-single phase mathematical model with of two-fluid mathematical model.

本文采用有限体积法及计算流体力学软件&STAR-CD&对单块板以及首次对全回流下的全塔流体流动、传质过程进行了计算，计算结果如下：1。

The mathematical model of the system is divided into mathematical models of trawler, warp and fishing net, which are connected by boundary conditions reflecting the influence of each other. By using this modeling method, the dynamic simulation of the process of drawing in and giving out the fishing net is realized.

在建模过程中，将单船中层拖网系统的数学模型分为渔船、拖网曳纲以及网具系统的数学模型，并通过边界条件实现了数学模型之间的耦合，从而可以进行单船中层拖网作业过程中收放网过程的动态仿真。

This paper studies the mathematical simulation of the "properties-temperature" curve of ductile-brittle transition process for materials and finds the best mathematical model of ductile-brittle transition.

研究了Cr24Al2Si铁素体不锈钢韧脆转移过程的性能-温度曲线的数学模拟，找到了其最佳的韧脆转移数学模型。

The basic orientation of this auditing system and the database of fire protection law about high-rise building is established. And the problem how to audit the building fire design with the fire protection law is solved. Evacuation, fire water supply, smoke-preventing and fire power supply can be auditing in this system. On the base of this improvement, the mathematical result of the smoke-preventing air curtain is gained by using its mathematical mode.

本文对建筑防火设计审核系统的功能需求、系统设计、系统开发等基本问题进行了探讨，确立了系统的基本定位，建立了高层建筑的防火设计消防法规数据库，可对相应建筑的防火间距以及相应的消防法规进行查询，并解决了如何采用对照法规方法对建筑的防火设计进行审核的问题，可对建筑的消防布局、疏散距离、消防给水、防排烟系统和消防电气进行建筑防火设计审核。

Firstly, the relationship between the magnetic pole state of active magnetic pole and the running state of passive magnetic pole was analyzed. The electromagnet's four magnetic pole state and switch sequence, which can drive permanent magnet rotate, were ascertained. Secondly, taking one of magnetic pole state NS (N denotes electromagnet's left magnetic pole and S right magnetic pole) as an example, the distribution of space magnetic field was studied. In addition, the mathematical model of space magnetic field was set up based on the magnetic circuit fundamental and using the method of magnetic analysis and modeling. Lastly, the four states' mathematical model of space magnetic field was solved by using the MATLAB.

首先，分析系统主动磁极磁极状态和从动磁极转动状态之间的关系，确定驱动永磁体转动的电磁体4个磁极状态及切换顺序；其次，基于磁路基本原理，通过磁场分析和建模，以电磁体4个磁极状态之一的NS（N表示其左极、S为右极）为例，对电磁体的空间磁场分布进行研究并建立空间磁场数学模型；最后，以MATLAB为平台对4个磁极状态的空间磁场数学模型进行求解，将求解结果与实验数据进行对比。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。