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The article covers the full research on such aspects as mathematic description, numerical analysis method and their practical applications. The diphase heating surface is divided into a hot water section, a evaporation section and a micro overheat section , the problems of model switching are avoided successfully between subcritical and supercritical working condition in the model of The diphase heating surface, and the model can be used for between subcritical and supercritical working condition without causing the model stiff infinity prick up problem. The mathematical model and dynamic characteristic account is unified and predigested for the diphase heating surface of once—through boiler under subcritical and supercritical pressure, and propose that the working conditions at phase change point could be used as divide criterion between water region and steam region under supercritical pressure, the problems are solved successfully between water and steam phase change point under supercritical pressure.

本文在过程的数学描述、数值分析以及实际应用等方面进行了系统的研究分析，将双相受热面统一划分为热水段、蒸发段和微过热段三段，所建立的双相受热面模型不但成功地避免了超临界工况与亚临界工况间的模型切换，而且消除了由区段划分欠妥所引起的模型刚性无限加剧的问题，统一并简化了超临界及亚临界压力下直流锅炉双相区段的数学模型和动态特性计算，而且提出了利用相变点工况作为超临界压力下划分汽水区域的标准，解决了超临界压力下水与蒸汽的相变点问题。

According to the mapping principle of stereographic projection, the combinatorial relationships of line and plane can be solved by use of mathematic analysis.

摘要根据赤平投影的成图原理，利用数学解析的方法，可直接求解有关线与面的组合关系。

The system structure and the mathematic model of least square method to evaluate the straightness errors are introduced.

介绍了系统结构原理以及空间直线度误差的最小二乘评定法数学模型。

From the basic formula of coulomb force and ampere force,together with the concept of electric stress tensor , the mathematic formula of electric force and magnetic force is deduced in this article.

从库仑力和安培力的基本公式出发，引用电应力张量和磁应力张量的概念，导出计算电场力和磁场力的简单数学表示式。

The measurement errors of the single stria section contour sensor are analyzed based on the mathematic model and the relationship between the structural parameters of the sensor and the measurement errors is obtained.

在综合分析各结构参数对测量误差的影响的基础上，得出了传感器结构参数设计的依据，并给出了结构参数设计及标定的实例。

Therefore, the oxygen storage submodel should be taken into account for the three-way catalytic converter mathematic computation.

因此，对三效催化转化器的数值模拟中应加入储放氧模型。

Symbolization is one of the most important inner powers in the development of mathematics. There are three main periods in the development of the mathematic symbols.

符号化是数学发展的内在动力之一，因此分析数学符号对数学发展的影响作用就会有很大意义。

The characteristics of postures, crown form, branch appearance and the leaf shape of Syringa oblata were analyzed by practical measurement of individual plant Mathematic method and model were adopted to analyze the sample data and deeply explore the vegetation quantity of Syringa oblata in Harbin. A quantitative method was put forward for vegetation quantity of Syringa oblata distributed in Harbin and the information management system of vegetation quantity of Syringa oblata for Harbin has been established.

本项研究选取了哈尔滨市园林绿化上数量最多、应用最广的木犀科丁香属植物中的紫丁香为研究对象，立足于哈尔滨市的环境特点，采用逐株实测的方法，具体分析紫丁香姿态、冠形、枝形、叶形的特点，采用数学方法和模型研究对紫丁香样本数据进行分析，并深入研究紫丁香"绿量"的内涵，探索出了哈尔滨市紫丁香"绿量"的量化方法，建立了哈尔滨市紫丁香绿量信息管理系统。

An infiltrating-carbon furnace is a nonlinear system, changing with time and distributed parameters; it is difficult to express its characteristic using precise mathematic model.

渗碳炉是一个非线性、时变和分布参数的系统，用精确的数学模型表示其特性显然是十分困难的。

Carburizer is a nonlinear system with time variation and distributed parameters and it is difficult to describe its characteristics by precise mathematic model.

文章摘要：渗碳炉是一个非线性、时变和分布参数的系统，用精确的数学模型表示其特性较为困难，将带有自整定功能的模糊控制算法引入传统的渗碳炉温度控制系统。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。