查询词典 Jacobi

Nonlinear flexural wave equation is solved by the Jacobi elliptic function expansion method. Two kinds of exact periodic solutions of the nonlinear equations are obtained, that is, the shock wave solution and the solitary wave solution. The necessary condition for existence of exact periodic solutions, shock solution and solitary solution is discussed, which is consistent with the qualitative analysis.

利用Jacobi椭圆函数展开法，对该非线性方程进行求解，得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解，讨论了这些解存在的必要条件，这与定性分析的结果完全相同。

The Jacobi elliptic function-like solution and trigonometric function solution of variable coefficient KP equation.

获得了变系数KP方程新的类孤波解、类Jacobi椭圆函数解和三角函数解。

Firstly, the natural frequencies and normal mode shapes of the fluid-conveying pipe with zero fluid velocity (i.e. U=0) were determined with the transfer matrix method. Next, these natural frequencies and normal mode shapes were used to derive the equation of motion for the fluid-conveying pipe with fluid velocity U.neq.0 by using the expansion theorem. Finally, the free and forced vibration responses of the pipe with flowing fluid were obtained by means of the Jacobi method and the Newmark direct integration method.

首先吾人使用转移矩阵法来求取一流速等於零(即U=0)、跨距数为N之流体输送管的自然频率及其所对应之正规化振态，然后利用振态重叠法原理来推导流速不等於零(即U.neq.0)时，整个流体输送管在外力作用下的运动方程式，最后再以Jacobi法及Newmark直接积分法来计算该水平流体输送管的自然频率及强迫振动反应。

Boley and Golub used Gauss quadrature formula to solve the inverse problem, but I used other different methods and thoughts. I obtained a new decomposition form of orthogonal matrix consisted by the unit eigenvectors of Jacobi matrix and found the direct relations between the first row and the orther rows of this orthogonal matrix.

Boley和Golub的算法是用高斯求积公式，而本人另辟蹊径，推出了关于Jacobi矩阵单位特征向量组成的正交阵的一种分解形式，并找到此正交阵第一行和其它行的直接联系，由此避免了通过求特征多项式计算尾主子阵的特征值，得到了新的稳定解法。

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

By For the Jacobi iterative method of Gauss - Seidel iterative method and the comparison Initial research iterative equation and the nature of the coefficient matrix iteration convergence speed impact.

本文通过了举例对Jacobi迭代法和Gauss-Seidel迭代法进行了比较，研究迭代初值和方程组系数矩阵性质对迭代法收敛速度的影响。

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。

A compound inverse eigenvalue problem of Jacobi matrix and some generalized inverse eigenvalue problems have been discussed in this paper.

本文研究了一类Jacobi矩阵混合逆特征值问题及几类矩阵广义逆特征值问题。

In this paper, hyperbolic tangent function method and its some extensions suchas sine-cosine method, extended tanh method, F-expansion method and Jacobi ellip-tic function method are summarized, the idea and technique of hyperbolic functionmethod are explored.

本文对双曲正切函数法及sine - cosine方法，扩展tanh函数法，Jacobi椭圆函数展开法， F-展开法等一些主要的双曲函数方法及其扩展进行了系统的归纳与总结，揭示了双曲函数法的构造思想与技巧。

In this paper, we will introduce the weighted modulus of smoothness and the weighted K-functional to discuss the direct and the converse theorems, the local saturation results on the simultaneous approximation on an infinite interval with Jacobi-weight by the integral operator, the lin...

本文利用带权光滑模与带权K--泛函讨论定义在无穷区间上的积分型算子Gamma算子线性组合对空间L_∞(0，∞)中函数的带Jacobi权同时逼近的正逆定理以及局部饱和结果，还讨论了Gamma算子的强逆不等式。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。