变分方程组

First,the basic formulas solving the artificial earthquake wave compatible with object response spectra are established;the integration equations are translated into the algebraic equations by interpolation function.

首先，从单质点系在地震作用下的反应出发，直接推导了求解与目标反应谱拟合的人造地震动基本公式；随后，利用插值函数将积分方程变换为代数方程组，进而从反应谱的变分求得人造地震动的时域变分。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

The numercial simulation has been carried out, and the experimental results show that this method has been improved significantly comparing with the traditional one in nonlinear optics. Secondly, a second order system of semilinear elliptic equations, which comes from a mathematics model of the electric potential distribution of a media surrounded with the protein, is transformed into a variational problem, the existence of solution of it is proved by using variational principle and Trudinger—Moser inequality, and the relation between the solutions of variational problem and the solutions of its dual problem is obtained.

首先，讨论了非线性光学中的二次谐波产生的耦合方程组，利用变分法证明了耦合方程组非平凡解的存在性，然后进行了数值模拟，实验结果表明文中方法比经典的非线性光学中的方法有较大的改进，这对优化光倍频器件的设计将有所帮助；其次，将一类二阶半线性椭圆型方程组转化为一个变分问题，然后利用变分法和

The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.

研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题；提出并证明了完全泛函的变分问题的定理，采用偏微分算子，给出了完全欧拉方程组。

In a proper condition, U(superscript *) is a generalized solution of the differential equation system.

提出了象凸微分方程组的概念，并用这一概念对一类微分方程组的边值问题提出了一种新的变分迭代解法，此迭代解的极限U存在；在适当的条件下，U为此微分方程组的广义解，应该指出：1。

Firstly, the three-dimension boundary question and its corresponding variation question concerning the point-source electrical field on a 3-D structure are presented. Secondly, the finite element method is used to solve the variational equation. The study area is divided into many tetrahedral elements. Then, we interpolate with a tri-linear function in each element. So, the variational equation is converted into a linear equation system. Finally, taking into account saving of time, we make use of symmetric successive overrelaxation preconditioned conjugate gradient algorithm to solve large linear system, and obtain the potential value of each node, resulting in the calculation of the apparent resistivity values on the ground surface.

首先给出了三维构造中点源电场的边值问题以及相应的变分问题；然后利用有限单元法求解变分问题，采用四面体单元对研究区域进行剖分，在单元中进行三线性函数插值，将变分方程化为线性代数方程组；最后，考虑到节约计算时间，利用对称超松弛预条件共轭梯度迭代算法求解大型线性方程组，得到了各节点的电位值，进而计算出地表的视电阻率。

In the end, we built a model of the 4-D variational data assimilation for a barotropic primitive equation based on GA and compared with the adjoint assimilation model.

同时，以正压原始方程组为例建立了基于遗传算法的变分同化模型，并从多方面与伴随模式变分同化系统进行了分析比较。

The solution of a variational equation system corresponding to this kind of problems is obtained.

该文求得了与此类问题有关的一个变分方程组的解，并且证明了最佳控制的存在性。

The solution of a variational equation system correspondi ng to this kind of problems is obtained.

该文求得了与此类问题有关的一个变分方程组的解，并且证明了最佳控制的存在性。

It is equivalent to solve differential equation for under water explosion. The modes of velocity potential function and movable boundary are chosen, then, a variational equation system is derived by REDUCE procedure on computer.

在此基础上，选取了流场及运动边界的模态，将泛函对选定的自变函数变分，并取驻值；用REDUCE语言由计算机推出变分方程组。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。