变分问题

First,we show a compactness theorem in SBH,then byusing this compactness theorem,we discuss variational problems for two different func-tionals.

首先给出了SBH空间的一个紧性定理，然后利用这个定理讨论了两个不同泛函的变分问题。

By using the compactness theorem of SBD space, Poincaréinequality onthe BD functions,we prove the existence for variational problems.

主要利用SBD函数空间的紧性定理，BD函数的Poincaré不等式等给出了变分问题的存在性。

The existence condition of first and second boundary variation was given with boundary variation method. The numerical method was obtained.

应用测度理论，将经典的变分问题，利用线性分析的方法转化为在几个Randon测度空间中寻找最优测度的有限维线性优化问题；从而得到最优控制律。

In the case of strong nonlocality, the response function can be expanded in Taylor's series, so that the variational problem can be found in a closed form.

在强非局域的情况下，通过对介质响应函数进行泰勒展开，可以解析地表示变分问题。

The polynomial function bases are used to form the approximately matching function. Moreover, the discrete values of grey image is transformed to polinomial function that are exact fit at the considered pixel locations. As a result, The mathematical operations performed such as derivation, integration, and gradient evaluation also give out the polynomial functions, therefore, the system of undetermined coefficient equations is derived to be a system of linear algebraic equations.

我们把立体匹配过程看作泛函的极小化过程，因此选用变分问题近似解法的Ritz法构造数值算法，以多项式函数为基构作匹配函数的近似解，进而又利用多项式过样值点的拟合将离散的灰度图象变换为多项式函数，因此计算中所需的求导，积分，及梯度运算的结果仍然是多项式函数，最终将待定系数方程组化为线性代数方程组。

Moreover,the weighted residual method is utilized forestablishing the generalized variational formulation for solving three-dimensional eddy-current problems.

此外，介绍了用加权余量法建立三维涡流问题的等价广义变分问题的基本方法。

This variational inequality is solved with a diagonal algorithm.

用对角算法求解该交通均衡的变分问题。

The second chapter studies the optimal selection of functional weight factors in the variational problem.

第二章研究了变分问题中泛函权重因子的最优选取。

The cartoon-texture decomposition is presented by a variational problem.

构造了一个变分问题来实现图像的纹理结构分解。

Based on the Galerkin Method the variational problem for the point source 2.5-dimensional electricfield is derived and the corresponding finite element equations are obtained.

基于Galerkin法推导了点源2.5维电场的变分问题，得到了对应的有限元方程组。

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。