查询词典 problem of contact

We deal with the biharmonic equation and proved that under our assumptions, the week solution of the natural boundary value problem strongly converges (in H~2) to that of the first boundary value problem.

为克服这一困难，我们用具自然边界条件的边值问题(在二阶椭圆型方程情形为第三边值问题)去逼近相应的第一边值问题，并以重调和方程为例，证明了在一定条件下，其具自然边界条件的边值问题的弱解在H~2的意义下强收敛到相应的第一边值问题的弱解。

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。

In this paper we study the method of interpolation by radial basis functions in H~k(k ≥ 1) and give some error estimates. By means of such interpolation with a special kind of radial basis function, we construct a basis in H~k(k ≥ 1). Combined with the Galerkin method, this theory can be applied to solve boundary value problems for elliptic partial differential equations (such as the third boundary value problem for Poisson equation and the corresponding problem for the biharmonic equation), and some numerical experiments are also given.

本文从求解偏微分方程的角度出发，在被逼近函数u属于一般的Sobolev空间H~k(k≥1)的情形，引入了一种径向基函数插值方法，并建立了相应的误差估计；再利用这种插值性质，从一类特殊径向基函数出发构造Sobolev空间的一组基，针对Poisson方程第三类边值问题和重调和方程类似边值问题，为用无网格算法求解偏微分方程边值问题建立了相应的理论，并通过算例来验证了这一算法。

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。

This paper mainly researches the Clamped Plate problem(or the eigenvalue problem of Dirichlete biharmonic operator) on n-dimensional complex ball,and we obtain an inequality for biharmonic operator on n-dimensional complex ball.

主要对n-维单位复球Bn的Clamped Plate问题(或Dirichlete重调和算子的特征值问题)进行了研究，得到了复球上重调和算子的特征值不等式

The bilinear programming is converted into a max-min problem on the principle of duality, and a linear approximation algorithm for the max-min problem is presented, which proves to be convergent in finite steps.

利用对偶原理，将双线性规划问题转化为极大极小问题，研究了该极大极小问题的线性逼近算法，并证明了该算法在有限步内收敛。

The bilinear programming is converted into a max min problem on the principle of dual ity, and a linear approximation algorithm for the max min problem is presented, which proves to be convergent in finite steps.

利用对偶原理，将双线性规划问题转化为极大极小问题，研究了该极大极小问题的线性逼近算法，并证明了该算法在有限步内收敛。

In Chapter 4, we consider the 2-Catalog Segmentation problem which is equivalent to some kind of bipartite graph partition problem.

在第四章，我们研究二目录分割问题，它等价于一个基于二部图上的某种划分问题。

By using network flow theory, the optimization problem of power conservation is transformed into the optimal bipartition problem of a flow network which can be partitioned by the max-flow mm-cut algorithm.

利用网络流理论，将节约电量的最优化问题转化为一个流网络的最优分割问题，而后者可采用最大流最小切割算法实现最优切分。

By using network flow theory,the optimization problem of power conservation is transformed into the optimal bipartition problem of a flow network which can be partitioned by the max-flow min-cut algorithm.

利用网络流理论，将节约电量的最优化问题转化为一个流网络的最优分割问题，而后者可采用最大流最小切割算法实现最优切分。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。