参数方程

In the light of the complex, high-level and non-linear feature of the mathematical model which describe the transport of the coalbed methane, this paper study the fully-implicit solving method of the mathematical model in detail. Based on the complexity of the algebraic equations which are formed eventually, according to the alternating direction implicit difference pattern, this paper use the iterative method and the fully main element Gauss-Jordan eliminating method to solve equations, which is to use the iterative method to determine coefficient matrix and use the fully main element Gauss-Jordan method to solve th linear algebraic equation group, at the same time of studying the solving method of the mathematical model, according to the devising requirement of FORTRAN77 program structure, this paper draw up computer program and form the corresponding computer model, and verify the validity and reliability of the model in theory by operating the model.

重点研究了模型内、外边界及有关参数的处理，针对描述煤层甲烷运移的数学模型是一个复杂、高阶非线性数学模型的特点，详细研究了模型的全隐式求解方法，根据最后形成的代数方程组的复杂性，按交替方向隐式差分格式，采用迭代与全选主元高斯约当消去法相结合的方法求解方程：即确定系数矩阵采用迭代法，求解线性方程组时采用全选主元高斯约当消去法，在研究模型解法的同时按FORTRAN结构化程序设计的要求，编制计算机程序，形成相应的CBMRS计算机模型，并通过模型的运行从理论上证明了模型的正确性与可靠性。

In the fourth chapter, we build the model of coefficient on one dimension partial differential equation and adopt finite element method to discrete partial differential equation and in the fifth chapter, we employ GP to identify and build the model of right-side function and adopt over-relaxation or alternating direction implicit method to solute difference equation.

在求解这些偏微分方程连续系数反演或右端连一一一~武卫1里鱼立二大一至」夔里匕崖匕位止透二立一一一一续函数的适应值评价中，我们都采用H'一范数正则化来解决连续参数的识别问题。

The analytic studies of the MITA procedure based on dynamics and the function of thermo-diffuse and thermo-conduction combine these three physic field systematically. Compared with situation function with thermo-balance method, the analytic studies based on dynamics have less parameters approximation, and more precision. Meanwhile, the discipline of the microwave energy absorbed by tissue is should studied also.

基于动力学和热扩散、传导方程的微波热致超声波机制解析解的分析，将上述三类物理场有机地结合在了一起，与基于热平衡的状态解析分析相比，这一方法更少地对三物理场所涉及的参数进行近似，能更准确地反映微波热致超声波机制。

The operator can bedetermined through some ancilla differential equations.Using this operator,theexact solution of the ion's motion can be obtained.

通过对一组辅助的微分方程的求解，可以得到演化算子中的各个参数，并可用这一演化算子精确求解囚禁离子的含时量子运动。

The static model of torsion joint is based on that of bending joint. The effects of structure parameters inside air pressure, initial angle, rube average radius, rube shell thickness on the turning angle are analyzed and the following conclusions are drawn: the relationship between the angle of torsion joint and the inside air pressure is basically linear, the angle of torsion joint increases with the initial angle and rube average radius, the angle of torsion joint decreases while the rube shell thickness increases. The kinetic equation is built for torsion joint. Simulating experiment implies that the time of inflating and deflating process is extremely shorter than that of kinetic process. So the pneumatic process can be ignored in actual system design and control. The factors that affect the dynamic features of torsion joint, such as shell thickness of rubber tube, average radius, initial angle, connector's outlet area, moment of inertia and viscous damping coefficient, are analyzed and the following conclusions are drawn: the change of rube shell thickness has no effects on the dynamic process of FPA inside air pressure while greatly affects the turning angle of torsion joint; when the rube shell thickness is small, the torsion joint has a bigger turning angle, no overshoot and long risetime, when the shell thickness is big, the turning angle of torsion joint is small, but has high response speed, overshoot and low shock; when the rube average radius increases, the turning angle of torsion joint increases and the overshoot increases too; when the initial angle of torsion joint is big, the turning joint is big, the overshoot is small and shock is low, but the risetime is big; the connector's outlet area affects the dynamic process of FPA inside air pressure greatly, but has no effects on the dynamic process of turning angle; moment of inertia and viscous damping coefficient have no effects on the dynamic process of FPA inside air pressure, but affect the dynamic process of turning angle greatly.

在弯曲关节模型推导的基础上，建立扭转关节的静态模型，并分析了扭转关节内腔压力，初始转角，橡胶管平均半径，橡胶管壁厚等参数对关节转角的影响，得出扭转关节的转动角度与充入FPA内腔的压缩气体压力之间基本呈线性关系，扭转关节的转角随初始角度和橡胶管平均半径的增大而增大，扭转关节的转角随橡胶管壁厚的增大而减小的结论；建立了扭转关节的动力学方程，仿真实验表明FPA的充放气过程与扭转关节的动力学过程相比时间极短，在实际系统设计和控制过程中可以忽略不计；分析讨论橡胶管壁厚，平均半径，初始角度，气体节流口面积，转动惯量，粘性阻尼系数等因素对扭转关节动态特性的影响，得出橡胶管初始壁厚的变化对扭转关节FPA内腔压力的动态响应几乎没有影响而对关节转角的响应曲线影响比较明显，壁厚较小时，关节可以得到较大的转角，并且转角的响应曲线没有超调，但上升时间长，壁厚较大时，关节转角变小，响应加快，但是有超调和轻微振荡现象，橡胶管平均半径越大，得到的关节转角越大，但是转角响应的超调量也随之增大，FPA的初始角度越大，关节的转角越大，并且超调量减小，振荡减弱，但是上升时间增大，管接头出口面积的大小对关节FPA内腔压力的建立过程影响较大，但对关节转角的动态响应几乎没有影响，转动惯量和粘性阻尼系数对FPA内腔压力的动态过程几乎没有影响而对扭转关节转角有较大影响等结论。

The mathematical equation of dependence of anolyte volume on fractional conversion, the expression of reaction rate, and the macro-kinetic model were established, and the macro-kinetic parameters were calculated.

建立了阳极液体积随转化率变化的数学方程、反应速率表达式和宏观动力学模型，确定了宏观动力学参数。

According to the equation deduced by the author, the thickness of the strata and the relative sizes of the electromagnetic parameters in the media on the two sides of the bottom interface of the strata can be determined by measuring the frequency of the antinode.

测定波腹频率，就可以根据文中给出的推导方程，计算出地层厚度，以及地层底界面两侧介质电磁参数的相对大小。

Because of appearing empty aggregates in the time zone (the time zone do not include the information), we only establish the indeterminate grey differential equation according to the approximate condition of the differential equation.

利用灰色微分方程中的最小二乘估计参数：进而得到灰色神经网络初始的权值及阈值，这样使初始的权值和阈值更接近准确值，克服了以往BP网络中初始权值的随机性和不确定性，减少了网络的训练次数，提高了网络收敛速度和输出的精度，为避免网络训练陷入局部极小值也起到了重要的作用。

Based on the equation of the model, the acceleration, displacement and story shear of a seven- story building with a three-story appurtenant structure under three control systems including only rubber-bearing base, rubber-bearing and damper and no rubber-bearing are computed under the earthquake record of 1940 EI- Centrol, respectively.

根据控制系统方程，在无橡胶垫、仅设橡胶垫和同时布置橡胶垫和阻尼器的三种工况下，运用1940EI-Centrol加速度波，对具有三层裙房的七层建筑结构进行了分析，得到了七层建筑的加速度、位移和楼层剪力等参数。

In this thesis, we take the delay r as a bifurcation parameter to investigate the Hopf bifurcation phenomenon in system (1). By analyzing the associated characteristic transcendental equation of system (2), and using the Hopf bifurcation theorem, we obtain one condition for the existence of Hopf bifurcation in system (1). Furthermore, based on the center manifold theorem and the method of normal form, some interesting results about the properties of Hopf bifurcation are obtained, including the direction of Hopf bifurcation and stability of Hopf bifurcating periodic solutions.

我们以时滞T作为分支参数，研究了系统(1)的Hopf分支现象：通过分析系统(2)的特征超越方程，结合利用Hopf分支定理获得了系统(1)的Hopf分支存在的一个条件；利用中心流形定理和正规形方法分析了系统(1)的Hopf分支的性质，包括分支的方向和分支周期解的稳定性。

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。