查询词典 variational problem

Firstly, we discuss the boundary value problem of one dimensional biharmonic equation in an interval and its variational problem,multiresolution analysis in the Sobolev space , then solve it with wavelet-Galerkin methods.

首先本文讨论了一维双调和方程边值问题及其相应的变分问题，定义Sobolev空间的多分辨分析，用小波–伽辽金方法进行数值求解，两组基下得到的系数矩阵为七对角阵和块状对角阵。

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 complementary variational principles are extened to two-medium region problems. The equivalence between variational problem and boundary value problem is proved.

将互补变分原理推广到包含两个区域的问题中，从数学上证明了变分问题与边值问题的等价性。

This integral equation is incorporated into a velocity-pressure variational formulation for the interior region, and a finite element method is used to approximate the resulting variational problem.

本文在绪论中简单介绍了边界元的发展历史及其发展现状，并把边界元和有限元做了简单的比较，介绍了它们各自的优缺点。

Variational problem is a bridge to solve boundary values by variational inequality.

变分问题是用变分不等式解决边值问题的桥梁。

On the basis of the un conditional variational problem of higher order derivatives, this paper studies conditional variational problem .

在含高阶导数的泛函无约束变分问题基础上，进一步研究条件变分问题。

The variational problem of semi-discrete problem is given, the well-posedness of the variational problem is proved, and some error estimates are presented.

给出半离散化问题的变分问题，证明了变分问题的适定性，并给出了误差估计。

In this context a genetic algorithm was applied to the four-dimension (4-D) variational data assimilation, which provided a kind of new and effective method in the initial field optimization. The theoretical basis and detailed algorithm were introduced in this paper. At the same time, according to the property of the variational problem itself, we designed the rational genetic coding, operators and parameters.

本文将遗传算法应用于四维变分资料同化问题，提供了一种新的较为有效的NWP初始场优化方法，给出了相应的理论依据和详细算法，并结合变分问题本身的特点，设计了合理的遗传编码、遗传操作和遗传参数。

In view of the ill-posedness of the diagnosis problem, an effective measure is adopted to make it well-posed. Then the diagnosis problem is transferred into a variational problem which is solved by a regularization method.

&流场诊断技术&是一门综合利用实验测试技术和理论计算技术，进行快速流场分析和流场评估，给出叶轮机械内部流场详细信息和流场优劣判断准则的新兴的综合技术。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。