查询词典 simultaneous differential equations

First, the mathematical model of the HT oxide crystal growth is set, and then the dimensionless equations are given out. Finally, the boundary conditions are determined and the equations are solved by FDM. The simulation program is given by the above method.

首先建立了高温氧化物晶体生长的数学模型，然后给出了无量纲方程，最后确定了边界条件，使用有限差分方法求解了方程，并在此基础上编制了仿真程序。

Starting with properties of cubic parabola, it is demonstrated elementarily that solving elliptic equations using Jacobian elliptic functions, analytic solutions for a class of nonlinear wave equations and properties of nonlinear waves can be obtained, especially for solitary waves.

从立方抛物线的特性谈起，用较初浅的方法，借助于雅可比椭圆函数求椭圆方程的解，说明一类非线性波方程可用行波法求解析解。

At first, the velocity which is the outlet velocity of 2-D numerical model by using the VOF and κ~εmodel is used as the inlet velocity of the 3-D numerical model. The control equations of 3-D water and sediment movement are described in the orthogonal curvilinear coordinates, and the equations is segregated by using the Finite Volume Method.

以二维的水气两相流的VOF 模型结合雷诺时均法的κ~ε双方程模型进行水气两相流计算，得到稳定流场作为三维水沙计算的初始进口条件。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

The complete model of locomotive and vehicle and the exact motion equations of wheel-set are established, in which, three-dimension wheel/rail contact geometry is taken into account and the Kalker's creep theory is employed to analyze the effects of the contact region of wheel/rail. An iterative procedure of solving wheel/rail creep force is proposed to improve the existed calculating method. Finally, the motion equations of vehicle with 23 DOFs are derived using the D'Alembert principle.

建立了较完善的机车车辆分析模型和较精确的轮对运动方程：考虑三维非线性轮轨接触几何关系，用Kalker蠕滑理论研究了轮轨接触区的蠕滑效应，建立了较为详细的轮对运动方程，提出用迭代法来求解轮轨蠕滑力从而对现有蠕滑力求解方法进行了改进，并采用D′Alembert原理推导了23个自由度车辆的运动方程。

This article mainly discusses four kinds of solution system of linear equations,such as Elementary operations, the tecnique of Orthogonalization,Gaussian elimination method and Block matrix,and some ways that how to solve the multiple polynomial equations and decomposite the multiple polynomial matrix.

本文主要讨论了利用初等变换、正交化的技巧、高斯消去法和分块矩阵的四种求解线性方程组的解法，以及一些关于多元多项式方程组求解和多元多项式矩阵分解的方法。

In this paper another deductive proof of the algorithms for the recursive solution of the system of linear equations with a Toeplitz coefficient matrix is considered, and formulas for the specific recursive solution of the various forms of the system of linear equations in accordance with a Toeplitz coefficient matrix are given.

本文给出了具有托布里兹系数矩阵线性方程组递推解法算式的另一推导证明方法，并给出了基于托布里兹系数矩阵的各种线性方程组的具体递推解法公式。

And then the influence of two of the damage models, the Kachanov and the gradient dependent constitutive equations, on the well posed properties of the fundamental equations in continuum damage mechanics is studied according to th.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即 Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

The main contents and the contributions are as the follows:(1) The general form of the movement equations in terms of Taylor series is derived, for the first time the movement equations of electric power system is expressed by matrices, the characteristics of the coefficients of Taylor series is studied.

所得的主要研究成果如下：（1）推导了电力系统运动方程的高阶泰勒展开的一般形式，首次将电力系统状态方程的泰勒展开用矩阵表达，研究了泰勒展开系数的特性。

For nonlinear harmonic oscillators, we close the flow equations and acquired an explicit expression of energy-level. For nonlinear-coupled harmonic oscillators, we close the flow equations and diagonalize the Hamiltonian by numerical analysis methods.

对非线性谐振子系统，计算出系统参数随流参数变化的一组方程及系统的能级；对耦合的非线性谐振子系统，得出系统参数随流参数变化的一组非线性方程，数值分析对角化了系统。

Connectors are lines that can be anchored to particular places, called glue points , on the graphic object.

连接符，可固定在图形对象的特定的地方的线条。

Another way of putting it, too many agents have a say in each other's work, and bureaucratic rigor mortis sets in.

另一种表达是，太多的作用物在彼此的工作里都有话语权，官僚的僵尸开始抬头。