参数方程

The thesis can be divided into five parts as follows: First, the structural characteristics of finned-pipe evaporator are analyzed. After selecting suitable microelement controller, the heat-transfer and mass-transfer processes are analyzed for every microelement under the conditions of dryness, wetness and frostiness. Based on previous equations, some parameters of frostiness are confirmed and the frost-growing model is set up under frost condition. Some hypotheses are postulated and with the help of the equation of mass-conservation, energy-conservation and momentum-conservation, the evaporation model which fits in the dynamic simulation is built, which set a solid foundation for system simulation. Second, the starting and stopping behaviors under disturbed condition are analyzed and calculated by using the dynamic concentrative parameter model, which gives some advice to better prescribe refrigeration system and set theoretic foundation for carrying out automatic control of refrigeration system. Third, the normal running process is analyzed and calculated by means of rational matching theory, which gives some advice on how to better understand the parameter change under steady state and the affection of inlet-parameter on evaporator. Fourth, the simulation software with dynamic characteristic is designed, which can be applied to calculate thernio-parameter of cryogen, air humidity and frost thickness under different initial and boundary conditions, and to carry out dynamic simulation under conditions of dryness, wetness and frostiness, at the same time, to achieve detection and simulation at any stage from starting to stopping.

本文的主要内容如下：1对翅片管蒸发器结构特点进行分析，选取适当的微元控制体，就干、湿和霜工况下对每个微元分别进行传热传质分析，基于经验关系式确定霜的有关参数，对于霜工况下的霜生长建立模型，经适当假设，运用质量守恒、能量守恒和动量守恒方程建立适合动态仿真的蒸发器数学模型，为系统仿真奠定基础； 2对蒸发在大扰动下的开、停机过程，运用动态集中参数模型进行分析和计算，为更好地描述制冷系统运行的全过程奠定基础，同时也为制冷系统实现自动控制提供一定的理论基础； 3对蒸发器正常运行过程，运用动态分布参数和参数间定量耦合的观点来分析和计算，为更好地了解稳态工况下各点参数的变化情况及各入口参数对蒸发器动态特性的影响即蒸发器性能对各参数变化的敏感性； 4编写翅片管蒸发器动态特性仿真计算程序，可以计算不同边界条件和初始条件下的制冷剂热力参数、空气温湿度和霜厚度分布场，实现对翅片管蒸发器在干、湿和霜工况下的动态仿真。

It was found that the multi-parameter model describing the relation of vapor enthalpy and temperature ( Clapeyron-Clausius equation ) is obviously superior to the commonly used two parameters model and the Antoine equation in term of residual square sum and statistic distribution rule of error.

以乙醇为例利用非线性拟合技术和文献报道的实验数据，探讨了纯物质蒸气压和温度关系及其参数的拟合问题。从拟合的残差平方和和误差的统计分布规律考虑，基于蒸发焓与温度关系( Clapeyron-Clausius方程)的多参数模型明显优于常用的二参数模型和Antoine方程

The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

However, we can not get the film parameters directly because the ellipsometer equation is a transcendental equation. We can hardly get the analytical solution for film parameters from the measured ellipsometric parameters Ψ and Δ. Therefore, to find an algorithm to inverse the measured data Ψ and Δ becomes a primary but important problem.

但是通过椭圆偏振测量只能得到椭偏参数Ψ和Δ，由椭偏参数求解薄膜结构参数的椭偏方程是一个超越方程，很难得到精确的解析解，因此一般采用数值反演迭代不断逼近测量数据，将最优解作为测量结果。

The non-isothermal kinetic data were analyzed with the Achar equation, Coats-Redfern equation, Kissinger equation, Flynn-Wall-Ozawa equation and Starink equation.The mechanism function and kinetic parameters of the thermal decomposition in the third step were obtained.The chemical reaction mechanism (F3) controlled the third thermal decomposition process.The apparent activation energy and the pre-exponential factor were 351 kJ·mol-1 and 2.57×10 30s-1 respectively.

采用Achar方程、Coats-Redfern方程、Kissinger方程、Flynn-Wall-Ozawa方程和Starink方程对非等温动力学数据进行了分析，得到了第3步热分解反应的机理函数、动力学参数和热分解反应动力学方程，其热分解反应过程受F3机理控制，表观活化能为351 kJ·mol-1，指前因子为2.57×

In the formulas of stochastic input and output, when the coefficient of direct consumption and final demand are exponentially distributed, the interrelationship between parameters of stochastic variables can be divided into three types: all the parameters are the same; parameters are inequivalent to each other; some of the parameters are the same, but the rest are inequivalent to each other.

在随机投入产出方程中，当直接消耗系数和最终需求为指数型随机变量时，方程中随机变量分布中参数间的关系有3种基本情况：所有参数都相等、所有参数两两不相等、有部分相等而其余则两两不相等。实际上，前2种情况是第3种情况的特殊形式。

The relations between the parameters of the saturated porous micropolar theory and those of the corresponding one_phase medium are established by means of the Greetsma theory. It has merits that the physics parameters in our dynamic equations of the saturated porous micropolar medium have a definite physics meaning and are easy to be tested in laboratory.

借鉴Greetsma理论，建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系，使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义，易于在试验中确定。

Stability of solutions of the cavitated bifurcation equation is discussed in each region by using the minimal potential principle, and the catastrophic phenomenon of cavity formation is explained. 2. In Chapter 4, problems of cavitated bifurcation for two spheres, which are composed of two different kinds of imperfect compressible hyper-elastic materials, were examined, respectively. The parametric analytic solutions of the radially deformed function and the parametric cavitated bifurcation solutions are all obtained for the two spheres.

利用奇点理论给出了空穴分岔方程在分岔点的等价正规形，将缺陷参数分成若干个区域，证明了当缺陷参数属于某些区域时，具有缺陷的超弹性材料球体发生空穴分岔时的临界载荷比无缺陷的小；并利用最小势能原理讨论了空穴分岔方程的解在各个参数区域内的稳定性，解释了空穴生成的突变现象。

Analysis of ship parametric rolling in head sea;2. A numerical simulation method based on ITTC recommendation was used to investigate the occurrence and magnitude of parametric rolling in longitudinal regular waves.

基于ITTC推荐的参数横摇运动方程，采用估算方法确定方程中的阻尼系数和复原力矩系数，数值模拟出船舶在规则波中的参数横摇情况，将上述方法具体应用于一艘滚装船船模的参数横摇预报，并与试验数据进行对比，验证了所采用方法的有效性。

In this paper the equations of the stability and shear, flexural vibration of the straight bars with varying cross-section and the equations of motion of one degree of freedom systems with varying parameters are written as a unified self-adjoint differential equation of the second order eq.

本文将变截面杆的稳定与剪切、弯曲振动方程，以及具有变参数的单自由度体系的振动方程等均化为统一的二阶自共轭微分方程：并对，且的情形，将二阶自共轭方程化为贝塞尔方程。

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。