离散数学

In this research, the plane 2D mathematical model under Cartesian coordinate system and the

首先建立了直角坐标系正交网格下的平面二维数学模型及复杂边界适体坐标条件下的三维紊流数学模型，对方程的离散差分格式、控制方程的求解、初始边界条件、动边界处理等问题进行了分析研究，并编制相应的计算程序。

This makes more and more people pay more attention to studies and applications of numerical simulation in thermal recovery. In this research, we have developed a reliable mathematical model for thermal recovery, which takes a full consideration of the effect of viscos, gravitical and capillary forces on the three-phase flow of gas, water and oil, the effect of the temperature on the medium characteristics of liquid and solid, the phase equilibrium of gas-liquid in each component, heat transportation including connection, conduction and radiation as well as heat losses in both the overburn and underlying strata. In the space discreation of the mathematical model, we have proposed a new method based on the improvement of the conventional nine-points difference approximation, which has a higher difference accurancy.

本项研究以热力采油的主要机理为基础，充分考虑在粘性力、重力和毛管力作用下油水气三相流动，考虑温度对各种流体和固体介质物性的影响，考虑每一组分中汽液两相的相平衡，考虑热在地层中的传导、对流和辐射以及上下盖层的热损失，利用热力学第一定律、质量守恒定律和流体迁移定律，建立了正确可靠的注蒸汽数学模型；在对数学模型进行空间离散时，利用控制有限体积积分法，对以往的九点差分近似作了合理的改进，使其具有较高的差分近似精度：结果表明，该公式的近似精度要比以往文献中所给的九点差分近似精度高，可以认为，在油藏数值模拟中，如果遇到非均质情况，使用这种九点差分近似更合理。

For the dynamic system of discrete coupled and nonlinear three phase voltage source PWM rectifier, the cycle switch average operator is introduced to transform the discrete system into continuous andthe small signal perturbation method is used to transform the nonlinear system into linear, the small signal dynamic mathematical models are set up.

中文摘要：针对三相电压型PWM整流器这个离散的、耦合的、非线性的动态系统，引入开关周期平均算子将离散的系统变换为连续的系统，应用小信号扰动法将非线性的系统化解为线性的系统，进而分析系统的小信号动态数学模型。

Cellular automata are dynamical systems in which space and time are discrete.

元胞自动机是一种有自组织行为的时空离散、状态离散的并行数学模型。

Because the modern manufacturing system is a kind of discrete systems with nonlinearity, discreteness, randomness and complexity, it is difficult to describe the structure and control of the system with common mathematics models.

现代制造系统是一类具有高度非线性、离散性、随机性和复杂性的离散系统，这类系统的结构和控制问题难于用一般的数学模型来描述。

The mathematical programming formulation and related solution procedure are established by the traditional BEM. Through the discretization of space and time, the elastoplastic stress simulation method and reduce-basis technique are adopted to construct the self-equilibrium stress field. The numbers of variables and constraint equations in the resulting mathematical programming formulation are reduced greatly and then the dimension obstacle of computation in 3-D limit and shakedown analysis is overcome.

采用常规边界元方法建立了三维结构极限与安定分析的数学规划格式，通过对时间和空间的离散化，并采用弹塑性模拟法构造自平衡应力场和引入减缩基技术，大大减少了所形成的数学规划格式中的未知变量和约束方程的数目，有效地克服了三维结构极限与安定分析中的维数障碍问题。

According to fully implicit method, seepage model of low-permeability fractured gas reservoirs are discretized with finite difference method, and corresponding numerical model, coefficient matrix and matrix element are obtained; then based on modern software engineering, numerical simulation software was correspondingly developed with Fortran95 programming language

按照全隐式离散化方法，采用有限差分方法对低渗裂缝性气藏渗流数学模型进行了离散，得到了相应的数值模型、系数矩阵和矩阵元素。然后基于现代软件工程的基本思想，用Fortran95语言开发了相应的数值模拟软件

The use of CAE on the analysis of motor rotor-bearing system, During the numeric model processes, the finite element method is used to build the discrete model and analytical theory of the rotor-bearing system. The entire system is divided into several dividable substructures, each of which develops individual systematic mathematic model. Finally, the motion equation of whole structures is combined by the integrity of the dynamic variables and force balances on connections of each substructure.

本文探讨马达转子-轴承-框架系统之结构动态特性，提供动态特性之关系设计过程中，其转子-轴承系统的动态设计考量方法，利用电脑辅助工程技术，以有限元素方法，先将马达转子-轴承-框架系统分离各个部位成为子结构，将子结构个别的数学模型加以离散化，最后以各子结构结合面上节点的动态参数一致性及力系平衡，连结离散化子结构成为整体结构的运动方程式。

And then, using Matlab, we give some examples on regular surfaces. For example, plane, helicoidal, 3-dimensional Gauss profile, etc.

最后利用数学软件Matlab，给出了一系列的由光滑曲面上的参数曲线网经过离散化得到的离散参数曲线网，如平面，正螺面，三维Gauss型分布图，由3dMax生成的一般曲面等。

It further proves the distinct element method simulation model of charging of bell-less top blast furnace is true, and indicates this mathematics model not only has great theory research significance, but also have full practical worth. The distinct element method simulation model of charging of bell-less top blast furnace is a computer model.

本文还对实际无钟炉顶高炉开炉布料进行了离散单元法模拟研究，模拟结果与实测结果也基本符合，这进一步证明了高炉无钟炉顶布料离散单元法模拟模型的正确性，并且表明此数学模型不仅具有理论研究意义，而且具有实用价值。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。