数学模型

A generalized mathematical model was developed to describe the distribution of over-potential.Dimensionless variables μ and ω that characterize the polarization and influence of side electrode reaction in the system,were derived from modeling.Adomian's decomposition methodADM）was used to solve the nonlinear differential equation of the model to obtain an approximate analytical solution,which was in the form of algebraic expressions of infinite power series.By the solution,the relationship between over-potential distribution and average selectivity could be easily calculated without solving the nonlinear model time and again.

建立了描述超电势分布的普遍化数学模型，归纳出表征电极极化和副反应影响的量纲1数μ和ω，并用ADM（Adomian's decomposition method）对该非线性微分方程模型求解；所获得的逼近解代数表达式，可方便地计算不同参数下超电势分布对平均选择性的影响，而毋需反复求解模型微分方程。

Distribution ratios of complex extraction for different operation conditions were forecasted. Using mass action law, the liquid-liquid equilibrium models of complex extraction of monobasic and polybasic carboxylic acid have been successfully induced, and physical extraction were also considered in the model. On the basis of orthogonal experiments, the models of equilibrium distribution ratios were established. The processes of complex extraction were tested and verified. Comparing experimental data with model values, it could be held that the regression precision of model was rather high and the model supplied fundamental data for industrial amplification and practical use of complex extraction.

采用质量作用定律分析方法，成功地推导了同时考虑物理萃取的一元及多元羧酸络合萃取通用液-液平衡数学模型，并在正交试验基础上建立了磷酸三丁酯络合萃取丁酸、三烷基胺（7301）萃取丁酸、丁二酸、柠檬酸的平衡分配系数模型，从平衡角度对络合萃取过程进行了验证与预测，通过实验数据与模型计算值比较，表明模型的拟合精度较好，从而为络合萃取技术的工业放大与实际应用提供了重要依据。

In the present paper, a theoretical model of the mobility for multidisperse particles is developed. The present model is the extension of the previous theoretical model and the semi-empirical model for the monodisperse partcles. This model includes the influence of particle size distributions and is suitable for all particles with different materials and with different size distributions.

通过理论分析，本文提出了多分散性尘粒电迁移率数学模型；此模型是典型的电迁移率模型和单分散性尘粒电迁移率半经验模型的扩展，它考虑了粒度分布的影响，适用于各种物质的尘粒和各种粒度分布的尘粒。

Model of two-phase flow on the precess of launch of gun for balance is established.

本文针对以固体弹丸为平衡体的平衡炮发射技术进行理论研究，对平衡炮发射过程建立相应的经典内弹道模型与两相流内弹道的物理模型与数学模型，通过数值模拟的方法，对平衡炮发射过程进行了一些研究，主要研究内容如下：(1)建立经典内弹道模型，通过数值计算，分析平衡炮发射过程中的膛内压力分布特征及平衡发射特征。

Based on the research of the predecessor's production and the theoretic study, and establishs a mechanics and mathematical model of the horizontal well testing string and optimizes the composition and parts of the testing string. And the plunger effect, spiral bending effect, temperature effect and tympanites effect of the pipe string-packer system are analysed. At the same time, both the model of thermal field and pressure field are studied in accordance with technical peculiarity on site.

本文通过对前人研究成果的调研，建立了水平井测试管柱的力学模型和数学模型，并对测试管柱的结构及配件进行了优化；建立了管柱-封隔器系统的活塞、螺旋屈曲、温度和鼓胀四种基本效应的模型，同时也根据现场工艺特点建立了温度场和压力场的分布模型。

Based on Darcys law and material balance principle, mathematical model of three-dimensional three-phase was derived in porous medium with artificial fractures, and the gravity was considered in the model.

根据物质平衡原理和达西定律，考虑基质和人工裂缝作用下三维三相渗流模型，并考虑了重力作用影响，结合应变孔隙度模型、应变渗透率模型，建立了流固耦合整体压裂数学模型。

The activation energy for deformation in W18Cr4V high speed steel, 40CrMnNiMo tool steel for plastic molding and AISI H13 hot-work tool steel are investigated intensively. The investigation shows that the activation energy for deformation of both 40CrMnNiMo tool steel for plastic molding and AISI H13 hot-work tool steel decrease with the increasing of temperature.

分别将这两种钢的变形激活能数学模型用于蠕变模型，并采用这一改进后的蠕变模型对W18Cr4V高速钢和40CrMnNiMo塑模钢的热变形流变应力进行预测，结果表明，此模型不仅能精确描述蠕变条件下工模钢的流变应力变化规律，也能精确描述工模钢非蠕变条件下的流变应力。

This paper summarizes the commonly math model, Hedonic model and Logistic model for this problem.And simply analyses the three percepts' advantages and disadvantages.

本文总结了针对此问题的一般数学模型、Hedonic模型、Logistic模型等三种决策模型，并简单地分析了这三种方案的优缺点。

This thesis mostly includes main part models of the second loop system, for example, the steady state model and transient state model of the turbine, the transient state models of the condenser、steam emission system.

本论文的主要内容是：首先，建立二回路系统主要部件的数学模型，包括汽轮机稳态模型和动态模型，凝汽器和排放系统动态模型。

Firstly, on the basis of defining the characteristics of project and reviewing the mathematical models for RCPSP, we constructed the mathematical model for RCPSP under the condition that there is non-fixed duration and splittable tasks in project; In order to solve above model, we emphatically discussed the basic principle of the swarm intelligence algorithm--the particle swarm optimization algorithm as well as improvement research for current algorithm, and then proposed a new improved particle swarm optimization algorithm and analyzed its application process in the resource-constrained project scheduling problem; Lastly, in order to confirm the validity of the model and the algorithm, we took an experiment based on 108 instances that produced by problem instance generator which was developed by our team.

首先，在对RCPSP项目特征进行界定以及对项目进度优化模型回顾的基础之上，构建了基于活动工期不固定、任务可拆分特征的RCPSP的数学模型；为了求解上述模型，本文详细阐述粒子群优化算法(Particle Swarm Optimization，PSO)的基本原理以及当前对其改进的研究成果，提出了一种新的改进PSO算法，并对其在RCPSP的应用过程进行了设计；最后，为了检验模型的有效性及算法的优越性，基于梯队内部开发的案例生成器生成的108个算例，进行了仿真试验。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。