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In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics.

在互补性理论，这是一个相对较新的应用数学领域，数学模型和有关问题的平衡研究几种被认为从物理学的角度和经济的。

Besides, a nonlinear mathematical model is established on the base of non-equilibrium thermodynamic theory and phase equilibrium principle.

从非平衡态热动力学和相平衡的角度，推出了非饱和多孔介质的热湿迁移的数学控制方程，根据本文所研究的对象，对该控制方程进行了简化，建立了蔬菜热湿迁移的一维非线性数学模型，并给出了求解该数学模型的定解条件。

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。

Combining with the characteristics and the principle of analysis on existing bridges, the equipollent load, the mathematical model and the stochastic model for traffic load on existing bridge are studied.

本文结合既有桥梁车辆荷载的特点和分析原则，研究了既有桥梁车辆荷载的等代荷载、数学模型以及随机过程模型。

Operator equitation has always been one of the more active branch in mathematical research.

算子方程历来是数学研究中较活跃的分支之一。

The main problems researched in the dissertation and achievements are as follows: The dissertation explains the science background and the theoretical and actual meaning of the task. The progress and the problems of the flow imaging technique are briefly explained. The advantages of electrical capacitance tomography are discussed. The paper discusses the formation and operating principle of ECT, and builds up the definite mathematical model by detail theoretical analyse, and establishes the Finite Element Model of the system by changing the finite boundary value problem of ECT into equivalence variation problem according to variation principle. On the basis of the FEM of the system, the paper builds the finite element model of the capacitance sensitivity field distribution and programs its finite element simulation software and proves the validity of the FEM of the ECT from different aspects. With the FEM and the qualitative analyse of the effect of each structural parameter of the capacitance transducer on its capability, this paper optimizes the structural parameters of the capacitance transducer, and obviously improves its capability. The compare of the simulated result with the static experimental result shows that the error of them is less than 0.9%.

其主要研究内容包括：阐述课题研究的学术背景及其理论与实际意义，概括总结出流动层析成像技术的发展现状和存在的问题，指出电容层析成像技术的优点；讨论电容层析成像系统的组成及工作原理，进行详尽的理论分析，以变分原理为基础，将ECT的有限元边值问题转换为等价的变分问题，从而建立系统的有限元模型；在系统有限元模型的基础上，建立敏感场的数学模型，编制有限元的仿真软件，并从不同角度证明电容层析成像系统有限元模型的正确性；利用有限元模型，定性地分析电容传感器各结构参数对其性能的影响，并对传感器结构参数进行优化设计，使其性能得到明显的改善。8电极ECT系统的仿真和静态实验结果的比较表明，它们之间的相对误差小于0。

This paper analyses the physical characteristic of MOV and gives out its mathematical model by making it equivalent to inductance, resistance and diode three parts.

对金属氧化物变阻器的物理特性进行了分析，并完成了MOV元件的数学建模，将其等效为电感、电阻、二极管三部分。

A novel method for monitoring the state of transformer windings by identifying parameter of leakage inductance is presented in this paper, using Least Square techniques based on the equivalent equation of transformer leakage inductance. The mathematical model is derived for on-line identification of winding electrical parameter.

以变压器漏电感方程作为绕组参数在线计算的模型，提出了一种利用最小二乘算法进行绕组漏电感参数实时辨识从而实现绕组变形在线监测的方法，推导了用于变压器漏电感参数辨识的方程，针对参数的不可辨识问题提出了解决方案，分析了辨识结果产生误差的原因。

For example, the Maximum Membership Function Principle is proposed in Chapter 2 on which the presently"scattered" ones among fuzzy mathematical operations for fuzzy control methods such as the acquisition of fuzzy relation, the composition of fuzzy relations and the fuzzy set projection algorithms can be unified to within a common theoretic frame; the geometric criterion for the redundant design parameters is developed for a class of fuzzy supervisory control algorithm in Chapter 4; such concepts as the metric equivalent distance between fuzzy rules are defined to realize the highly efficient reasoning process; consequently the strategy and algorithm for a dynamically commissioned fuzzy controller is given.

如在第二章中，提出了最大隶属度原则，从而将现有模糊控制方法中诸如模糊关系的获得、模糊关系的合成、模糊集的投影等"零碎"模糊数学运算统一到一个共同的理论框架之中；在第四章中，还针对一类模糊监督控制算法推导了其冗余设计参数的几何选取准则；为实现高效推理过程而定义了模糊规则间的距离当量等概念，在此基础上，提出了动态构造模糊控制器的策略和算法。

A new and applied mathematical model for the equivalent resistance based on force analysis of semi-circle drawbead is established, and a device for testing the resistance is developed.

基于半圆形拉深筋的受力分析，构建了一种新型实用的拉深筋等效约束阻力模型，并开发了一套测试拉深筋阻力的试验装置。

I can still vividly recall the impressive scenes you gave. You were among my friends and relatives who accompanied me from my house to the seaport and when the porters were slow to show up, you obligingly carried my suitcase for me.

你对我的种种感人情意，使我记忆犹新，那天你随着我的亲友从家里送我上轮船，搬运工迟迟不来，你毅然替我提着皮箱上船。

St. Nicholas became the patron saint of Russia, where he was famous for his red cape, flowing white beard, and bishop's mitre.

圣尼古拉成了俄罗斯人的守护神，在那里，他以身披红斗篷，留着飘逸的白胡须，戴着主教法冠而闻名。