数学模型

The following points are emphasized:The operation models of adiabatic and diabatic distillation have been set up and the operation block, thermodynamics model and mathematical model in the simulation have been determined as well;(2)Based on the simulation and exergy analysis with Aspen Plus program, shortcut distillation design—DSTWU model and rigorous distillation design—RADFRAC model, the author has determined the heat duty, exergy losses and the distribution of exergy losses along the adiabatic column, which will help the simulation and optimization of the diabatic distillation;(3)Diabatic distillation under various operation conditions has been simulated by using energy balance method and exergy analysis;(4)How the different mixture and the various degree of separation, number of trays and feed location influence exergy saving in diabatic distillation have also been discussed;(5)On the basis of the total exergy losses along the column, different schema of the heat transfer distribution along the column have been compared and analyzed;they can be classified in three categories: heat duty equipartition approach, empirical approach, separation degree matching approach. In conclusion, different heat transfer distribution along the column will have effect on total exergy losses. In particular, most satisfactory results have been obtained by using separation degree matching approach. In order to diminish the exergy losses, heat transfer distribution should meet the needs of the request of separation degree.And on this premise, the author makes his suggestion in increasing the proportion of heat supplied to the tray with minimum exergy losses and decreasing the proportion of heat supplied to the tray with the maximum exergy losses.

本文对透热精馏过程进行了模拟并对其节能效果的影响因素做了较为全面的分析和深入的研究，主要研究内容如下：(1)建立了常规精馏和透热精馏过程的模拟操作模块、热力学模型以及数学模型；(2)利用化工模拟软件Aspen Plus并分别采用DSTWU简捷模型和RADFRAC严格计算模型对常规精馏进行模拟计算和有效能分析，确定常规精馏塔的公用工程热负荷、有效能损失及有效能损失在塔内的分布，为透热精馏的模拟和优化提供数据参考；(3)对不同物系在不同分离度条件下进行透热精馏的模拟，分别采用能量衡算法和有效能分析法进行计算和分析；(4)探讨了各种因素如物系的选择、不同分离度、塔板数、进料位置对透热精馏节能效果的影响；(5)以全塔总有效能损失为比较基准，对热量在塔内的三种分布方案即热负荷平均分配法、经验法和分离度匹配法进行了对比分析并得出结论：塔内热量的不同分布方案对于全塔总有效能损失会产生影响，其中以分离度匹配法的节能效果最为理想，为减少有效能的损失，应使塔内的热量分布满足各塔板的分离度要求，并在此前提下，尽量减小有效能损失大的塔板的热负荷和增加有效能损失小的塔板的热负荷。

The clock models of computer, including the early Fuzzball clock model and the present-day Unix clock model, are analyzed. On the basis of the analysis, a universal mathematic model for local clock is established.

接着分析了计算机时钟模型，包括早期的模糊球时钟模型和现在的Unix时钟模型，并建立了通用的本地钟数学模型。

The model has overlay and index method as the basic, mathematical model and statistical method embedded to form an integrated model. The HYDRUS model is performed to obtain the rating system, and principal component analysis and factor analysis are used to get the weighting system.

该模型以参数系统法为基础，将数学模型和统计方法嵌入该综合模型中，通过HYDRUS模型进行数值模拟来建立评价因子的评分体系，权重体系由主成分－因子分析法得到。

The variation of gas parameters in the real compression process of the compressor is worked out in the computer simulation, and effects of some parameters on the performance of the system are studied.

本文建立了这种压缩机的热力模型、泄漏模型、传热模型、和吸气加热损失模型等构成的综合数学模型，进行了计算机仿真研究，给出实际工作过程中气体参数的变化规律和对性能的影响。

Taking Changling County, Zhenlai County and Da'an City of Jilin Province as researchareas, based on remote sensing data, graphics operation and spatial analysis are carried out indifferent points of views, including temporal, spatial, scale and landscapeetc; all aspects analysis of this dissertation are abstractively expressed by digital graphics andseries of curves which are not stick to one pattern to discussing multi-dimension andcomplicated attributes of the salinized process. Linking up temporal-spatial characteristicswith landscape indices while combining mathematics model and Geo-informatic TUPUmodel, this dissertation puts forward the fundamental frame: temporal-spatial evolvementpattern, spatial extension process analysis and landscape characteristics analysis of salinizedland. Temporal-spatial evolvement pattern analysis extracts the essential quantity features andtransformation modes of salinized land, and also analyzes patches spatial geometricalparameters scale feature; spatial extending process analysis discusses the change rate andecological modes; landscape feature analysis utilizes landscape graphics indices to describesalinized land microcosmic graphics features and changes.

信息图谱模型为土地盐碱化研究提供了一种谱系化、定量化与定位化相结合的研究方法，本文选取吉林省西部盐碱化典型区域长岭县、镇赉县、大安市作为研究区，以遥感影像为基础数据，在GIS技术支持下，从时空变化、尺度效应、景观特征等多个角度对盐碱化土地进行图形运算、空间分析，通过不拘一格的数字化图形、曲线系列抽象表达出不同维度上的特征与规律，探讨土地盐碱化过程的多维性与复杂性，将盐碱化土地时空特征与景观特征衔接、数学模型与图谱模型结合，以盐碱化土地时空演变基本模式、空间扩展过程和景观特征分析为框架构建盐碱化土地信息图谱模型研究体系，发挥图谱模型数据挖掘、知识发现的特长，将宏观动态变化与微观特征相联系，进一步挖掘土地盐碱化过程与人类活动影响的关系，为探索研究区盐碱化土地成因、过程，预测其未来发展变化趋势及其对环境影响提供相关科学依据。

The development of the forecast models shows that the foreign forecast models evolved from monocyclic ones to multi-cyclic ones emphasized the models'vertical development,whereas Chinese models such as the Weng's model and many others emphasized their horizontal development.

摘要追溯了石油峰值理论的起源，对国内外一系列关于石油峰值理论模型的定量研究表明，石油峰值理论模型大体有3种类型：①基于生命有限体系的生命模型；②基于概率论和统计学理论的随机模型；③基于生产实践和理论推理的广义数学模型。

This paper firstly introduces the methods and developments about workshop scheduling inside and outside country; secondly expatiates the basic conception and principle about genetic algorithm; then analyses the flow shop and job shop scheduling problem, also predigests the mathematic depiction so as to convenience further program design.

其次对所研究的流水车间调度和作业车间调度进行了详细的数学分析，并对数学描述进行了简化，为下一步算法设计建立数学模型。

For studying of several problems in mathematical physics, the mathematical foundation of quantizing theory is an important subject, and nonlinear Schrodinger equation is a fundamental model in quantum mathematics mechanics.

在现代数学物理的若干问题研究中，量子化理论的数学基础是一个重要课题，非线性Schrdinger方程是量子力学中的基础数学模型。

To solve this problem, it is necessary not only to consider the relationship caused by the difference of the method of projection, by that of the elements of ellipsoids and by that of the original data between the new and the old coordinates, but also to consider the observation errors caused by the two measurements.

解决这一问题必须考虑两种坐标间投影方法、椭圆体元素、起算数据等不同所引起的数学关系，而且还必须考虑到两次测量所引起的测量误差。本文所提出的数学模型确保以上所述数学关系准确，在此条件下，采用最小二乘法，使得由于地图投影等因素和测量误差所引起的新、旧坐标间的差异，一次加以处理。

D models are the most widely spread in the world of turbo-machinery for its simplicity, but they are indeed purely empirical correlations which not only fail to provide detailed information inside one or more components, but also require significant effort to recreate themselves if engine operating conditions or component representations change; quasi 3-D models have been the workhorses for compressor and turbine design for many years, and the primary benefit of using quasi 3-D system models is to facilitate the design and detail analysis of a particular component across the range of possible boundary conditions; Full 3-D models are gradually replacing quasi 3-D ones by virtue of requiring no exit flow angle model and loss model and being capable of predicting secondary flow in cascade.

零维模型由于使用时简单易行，因此在涡轮发动机的仿真中得到广泛应用，但零维模型作为纯粹的经验关系式无法反映部件内部的流动细节，并且一旦部件有少许改动则新特性的建立耗费巨大；准三维模型由于能够详细地提供部件内部的流动情况，方便设计而成为涡轮和压气机设计的主要工具；全三维数学模型正逐步取代准三维模型在涡轮设计中的主导作用，同后者相比前者能够预测叶轮机械内的二次流动，在粘性流计算时不需要气流角和损失的经验公式，因此拥有巨大的发展前景。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐