查询词典 consistent equations

For the plane wave of laser without pulse shape, we derive the express of electron trajectory by the relative Lorentz and energy equations. Note that the orbit of electron becomes a "fat-8" in the average rest frame. For the plane wave of Gaussian laser, we may know that, through relative Hamilton-Jacobi equation, electrons are accelerated in the front of pulse and decelerated backward. Whereas for the non-plane wave of Gaussian laser, we solve the Lorentz and energy equations by fourth order Runge-Kutta method.

对于无脉冲形状的激光平面波是从考虑了相对论效应的Lorentz方程和能量方程出发，得到了电子的运动轨迹方程表达式，在纵向平均速度参照系下该电子的轨迹呈现"8"字形；对于高斯型单色激光平面波是从相对论Hamilton-Jacobi方程出发，得到激光平面波在脉冲前沿加速电子而脉冲后沿减速电子，电子能量增益为零；而对于高斯型单色激光非平面波是从拉格朗日运动方程和能量方程出发，通过四阶Runge-Kutta法数值求解，得到电子在纵向有质动力、横向电场作用下加速电子，最后在强大的横向有质动力作用下从脉冲侧面散射出去，可以获得很大能量增益本文得到了相应的电子瞬时动量解析表达式。

In the relative coordinate method, the array of the generalized coordinates of the system is formed by the relative coordinates of all rigid bodies. The principle of virtual power and Newton-Euler equations are applied to the system, and arrive at a set of second order differential equations of the generalized coordinates.

在相对坐标法中，系统的广义坐标列阵由系统中各刚体的相对坐标组成，对系统应用牛顿-欧拉方程和虚功率原理，得到系统广义坐标的二阶微分方程组。

Taking generalized coordinates for variables, the differential equations of multiple elastic particles are decomposed into the differential equations in the independent form by introducing generalized coordinates .

通过广义坐标的引入，将多质点弹性体系的运动微分方程分解成以广义坐标为变量的独立微分方程形式。

Moreover, for the treelike system with prescribed motion and the non-treelike system with closed-loop, the generalized coordinates aren't independent completely. Only the dynamical equations of the system and the constrain equations resulting from the prescribed motion and the closed-loop are combined to form DAEs, it can be solved.

另外，对于有指定运动的树系统或带有闭环的非树系统，系统的广义坐标是不完全独立的，系统的动力学方程要与指定运动或系统切断所附加的约束方程一起组成微分--代数方程组才能求解。

The derivatives of the nonsmooth equations are computed to make the generalized derivative matrix nonsingular. Then the nonsmmoth damped Newton method is used to solve them.Analytic solutions of the KdV equation with variable coefficients: Shallow water wave problems belong to problems of free surface wave, and can be molded by the nonsmooth equations model given above in principle.

在前面建立的非光滑方程组数学模型和固定网格法基础上，利用广义导数的概念给出了求解渗流自由面的一种新方法-----非光滑阻尼牛顿法，该法是对非光滑方程组求导，适当的处理广义导数矩阵使其非奇异，利用非光滑牛顿法求解。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

This paper systematically discussed the definition, nature and calculation of two kinds of generalized inverse matrix related to the compatible linear equations, and their relations with the compatible linear equations.

本论文系统地论述与相容线性方程组相关2种广义逆矩阵的定义、性质和计算，以及与相容线性方程组的关系。

The two kinds of symmetries in holonomic and non-holonom-ic mechanical systems,i.e.symmetries of differential equations of motion(ab-breviated as SDEM)and symmetries of Noether-type,and interrela-tions among all kinds of symmetries are investigated.The necessary and suffi-cient conditions of SNT to be SDEM are found out.It is pointed out thatSDEM have distinct geometric properties which are equivalent to the geodesiccharacteristic of differential equations of motion and geodesic deviation.

文中研究了完整与非完整力学系统的两类对称性，即运动微分方程的对称性和Noether型对称性，以及各种对称性之间的相互关系，确定了Noether型对称性为运动微分方程对称性的充分必要条件，并指出运动微分方程的对称性具有明确的几何性质，即它等价于运动微分方程的测地性质以及测地偏离性质。

The topics covered in these sections are the geometric interpretation of systems of linear equations, the classification of finite symmetry groups in two and three dimensions, the exponential of a matrix and its application to solving systems of first order linear differential equations with constant coefficients, and Hurwitz's theorem on the composition of quadratic forms.

这些条文所涉及的主题是线性方程组的几何解释，在两个和三个有限对称群的分类方面，一个矩阵及其应用，以解决一阶常系数线性差分方程，系统指数赫尔维茨定理在二次形式组成。

Now that we have discussed the meaning of a graphical solution of a system of simultaneous equations and the method of plotting a l , we are in a position to find graphical solutions of systems of linear equations.

由于 我们已讨论过联立方程组的图解法和绘制直线的方法，我们就能够找出线性方程组的图解法。

"The operators will suffer a temporary decrease in the number of consumers and short message services as people may not like having to provide their ID cards for a phone number," Xu Junqi, vice-dean with the Policy-Making Institute of the Telecommunications Research Centre under MII, said yesterday.

信息产业部下属的通信决策研究院副主任徐俊其昨天说：&实行手机实名制后，人们可能不太情愿用身份证注册手机号，所以通信运营商会暂时面临用户减少和短信用户减少的问题。&

I don't believe in make-believe!

我不相信这些虚构的故事。