查询词典 variational formulation

Variational problems which are invariant under the actions of symmetric group often possess multiple solutions e.g.

根据Ljusternik-Schnirelman理论，在对称群作用下不变的泛函具有多解（见［1-6］等）。

In this paper we separate the Hamiltonian into three parts: a spherical symmetry Hamiltonian; a z-component of the angular momentum operator, and a non-spherical symmetric potential as the perturbation operator, and provide a propose method by separating the potential containing squared magnetic field B^2 into two parts spherical symmetric and non-spherical symmetric ones so that the first-order energy correction due to the non-spherical symmetric potential is zero, and the second-order correction due to B^2 can be obtained by a simple variational method.

采用变分法和微扰法相结合的方法，把高强度磁场中氢原子的哈密顿H分为三部分：球对称哈密顿；z分量角动量算符相应部分和非球对称势微扰，并用一种特别规定的分解法将哈密顿H中含磁场平方项的势能分解为球对称与非球对称两部分，且使非球对称部分引起的一级修正能量值为零，并采用一种简便的变分法直接求出B^2对能级的二级修正值。

With the application of the Pro-Hellinger-Reissner variational principle, dual equations in the symplectic space are yielded to present an analytical method for the bending of annular sector plates.

然后应用类 Hellinger-Reissner变分原理，导出了辛几何空间的对偶方程，从而将环扇形薄板弯曲问题导入到辛对偶求解体系。

In this paper,some characterizations of solutions for a system of vector variational inequalities are derived under the a.

该文研究了一类向量变分不等式组，在PPM条件下，对其解进行了一些刻画此外，给出了该向量变分不等式组的一个间隙函数，并在强单调条件下，证明了它是弱尖极小的。

By using the projection method, we prove the existence and uniqueness of solutions for this new system of generalized variational inequalities.

在本文中，我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组，通过用度量投影的方法，我们证明了这类广义变分不等式组解的存在性和唯一性。

In Chapter 7, we consider the numerical solution of system of mixed nonlinear variational inequalities in Banach space. The definition ofη—proximal mapping for a proper subdifferentiable functional is introduced.

我们先引入适定次可微泛函的η—逼(来源：ABCa776论文网www.abclunwen.com)近映射的概念，利用η—逼近映射的性质，提出了求解SMNVI的一些迭代算法，并证明了算法的收敛性。

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。

Third, applied the variational function to the analysis of the reservoir property variety predication in three dimension, and the last, It is valuable and useful for low permeability gas field development to use the Darcy law and the permeability tensor analysis to describe the Permeability anisotropy.

本文对储层的宏观及微观非均质性统计分析的研究成果，特别是首次应用地质统计学的实验变差函数，量化分析储层属性变量的空间变异性，为储层参数

On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how freeduan.com variational calculus leads to field theory.

在旅行时，你将发现tensor表达式与矢量微积分有关怎样，几何学建立直觉概念多么不同啊，和freeduan.com variational微积分怎样导致原野理论。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

There had been a moment during the breakfast meeting, though, after the backslapping and the small talk and when all of us were seated, with Vice President Cheney eating his eggs Benedict impassively and Karl Rove at the far end of the table discreetly checking his BlackBerry, that I witnessed a different side of the man.

那次早餐会期间，在表示过关心和寒暄以后，我们所有人坐了下来，我注意观察了一下，副总统切尼面无表情地吃着班尼迪克蛋（Eggs benedict，源自美国，以英式松饼、火腿、水煮蛋以及荷兰酱组合而成），卡尔。罗夫在餐桌的远端谨慎地经常查看他的黑莓手机，我目睹了他所不为人知的一面。

Talk Undelete failed; someone else may have undeleted the page first.

Talk 无法删除选定的页面或图像（它可能已经被其他人删除了）。