查询词典 simultaneous equations

The development process of the finite element method is introduced briefly,and the theoretic fundamentals of the quasi conforming element method is analyzed from generalized equilibrium equations,generalized compatibility equations and its weak continuity condition.

简述有限元的发展过程，从广义平衡方程、广义协调方程和拟协调元弱连续条件等方面分析了拟协调元的理论基础，说明了拟协调元是有限元发展的必然趋势，其做法就是广义协调方程的直接解，自然满足平衡对弱连续条件的要求。

The ones, including conservation of mass, conservation of energy, Newtonian equations of motion, conservation of electric charge, linear momentum principle, continuity equation and Maxwell equations for electromagnet etc., are suitable to all substances. They are universal laws in nature.

连续介质力学的基本方程可分为两类：一类适用于所有物体，构成了自然界的普适规律，如质量守恒、能量守恒、电荷守恒，牛顿运动方程，马克斯威尔电磁学方程、熵产率恒正原理等。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

The fundamental equations are the momentum equations of contravariant velocities as unknown variables and the Poisson equation of the pressure correction.

基本方程是以逆变速度为未知变量的动量方程和关于压力修正量的Poisson方程。

The grids can be densified locally where the flow is complicated for the sharp change of water depth.(5) 2-D hydrodynamic equations in the generalized curvilinear coordinates have been derived with the contravariant velocities as main variables. The new equations keep the original styles and physical meanings. Based on the water depth correction method, the 2-D flow numerical model has been established and validated by the measured data.

推导了广义曲线坐标系下以逆变流速张量作为主变量的二维水动力方程，新方程保持原有结构形式及物理含义，采用水位校正法建立了二维水流数学模型，经实测资料验证后的模型，模拟并分析了分流角度、宽深比等因素变化对分汊流平面二维水流结构的影响。

Therefore, it is significant to study the existence and controllability of multivalued functional differential equations and integrodifferential equations.

因此，对多值泛函微分方程和积分微分方程存在性和可控性的研究具有重要意义。

The PSE in the curve coordinate systems are solved by the numerical techniques developed efficiently in this paper. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. The finite-difference of governing equations with fourth-order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations.

对于曲线坐标系下的抛物化稳定性方程，文中发展了求解的高效数值方法：引进法向变换，使得在临界层与壁面之间的扰动量变化最快的区域有更多的法向网格点；导出包含边界邻域在内的完全四阶精度的法向有限差分格式，这对方程精确离散至关重要；采用全局法和局部法相结合的方法及其新的迭代公式，大大加速收敛并得到更精确的特征值。

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。

Don't listen to their haver, nothing of that sort.

别听他们胡说八道，根本就没那回事。

But bank's shares trade below their book value, suggesting that investors are skeptical.

但是，银行股票以低于账面价值的价格交易，这一点反应了投资者的怀疑。