查询词典 equations

Based on the variable separation method, the governing equations for the film thickness problem have been solved. A reasonable consistent condition of the momentum equations has been found and solved. Based on the methods ofmathematical physics, series expansion solution of the velocity filed in the film has been derived. A boundary condition at the boundary of the spray area was given and the velocity slip phenomenon has been considered.

基于电子器件喷雾冷却技术的研究现状和研究热点，本文对喷雾在热源表面形成的冲击液膜流动及厚度模型、基于CHF(Critical Heat Flux，临界热流密度)准则的倾斜喷射喷嘴轨迹、喷嘴距热源换热最优时的高度、倾斜喷射实验以及针对动态喷射的电磁驱动器件的吸合问题等方面进行了研究：针对圆锥形轴对称喷雾冷却系统，在对喷雾区域进行划分的基础上，引入滑流边界条件，在提出圆锥状喷雾假设的基础上，建立了喷雾区域雾滴密度连续介质等效模型。

The key components in laser gyro is He-Ne ring laser, and the reciprocal action theory between light and medium is the base in studying the ring laser, use the Lamb half classical theory, and on the base of density matrix theory, the optical Brounch equation was established, which described the movement of amplifying medium atom in the ring syntonic cavity, and according to the medium polarize theory the self consistent equations was deduced, which describe the light intensity and phasic of the counter-propagating wave. On the basis of this equations, adopted the simulation software MATLAB and virtual instrument programming language LabWindows/CVI, we can do some simulated experiments in study the phenomenas such as amplify and dispersive characteristic of medium, mode pushing effection, burned hole effection and pattern competition, lock-in of frequency and the characteristic of light intensity and phasic of the counter-propagating wave in laser gyro.

激光陀螺的核心部件为He-Ne环形激光器，而掌握光与介质的相互作用理论是研究激光器的关键，采用拉姆半经典理论为主，在密度矩阵理论的基础上，推导环形谐振腔中描述He-Ne气体增益介质原子运动的光学布洛赫方程，运用介质极化理论得出描述激光陀螺反向行波的光强、位相所满足的自洽场方程组，在此基础上，运用MATLAB仿真软件和虚拟仪器编程语言LabWindows/CVI，对激光陀螺中的介质增益色散特性、频率牵引效应、烧孔效应及模竞争、闭锁效应及环激光的光强和相位特性进行仿真试验研究，并且运用全量子理论，对激光工作原理进行分析，得出二能级系统单模辐射场的光子数密度分布，得出激光场的光子统计分布，仿真激光场的动态建立过程。

From equations eliminated some unknown function and its derivative, are contained only one unknown function with constant coefficient of linear differential equations.

从方程组中消去一些未知函数及其各阶导数，得到只含有一个未知函数的高阶常系数线性微分方程 9。

B double precision real-one-dimensional arrays, length n, storage equations subguadratic constant vector; Return to the solution of the equations vector.

b 双精度实型一维数组，长度为n，存放方程组右端的常数向量；返回方程组的解向量。

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。

This matter overthrew all basises I learned from Sunday school .

这件事把我从周日学校学到的所有道理都颠覆了。

It's one of the cruel ironies of aging: if you want to remember your favorite restaurants, the less you should eat at them.

这是一个老化的残酷讽刺：如果你想记住你最喜欢的餐馆，你应该更少吃到它们。