变分问题

This paper deals with an existence theorem for a class of quasi-equilibrium problem s in com-pletp metric spaces.

研究完备度量空间中一类拟均衡问题的可解性，由此导出著名的Ekeland变分原理。

In some real-world problems, the mapping of the variational inequalities does not have any explicit forms and only the function value can be evaluated or observed for given variables.

现实世界中，变分不等式问题中的映射没有具体表达式而只能在计算过程中对给定的自变量观测到相应的函数值。

Then we apply the above results to discuss the density of extremal points in the variational principle.

随后应用上述结论讨论变分原理中端点的稠密性问题。

In Chapter 4, the related mathematical knowledge, methods and principles are presented which include mathematical morphology, Fourier transform and discrete cosine transform, illposed problem and corresponding regularization methods, basic iteration methods and preconditioning technologies.

回顾并比较了传统线性和非线性滤波方法，详细综述了从变分到PDE在图像滤噪与模糊恢复上的应用和发展，模型基本形式为无约束极小化问题：〓（1）惩罚算子L扩散形式为〓（2）Κ为扩散项，是调整扩散程度的关键因子。

The first prob-lem is rotating tubro impeller,and by introducing the periodic free surface variable we obtainall complementary variational principles.

其一是旋转叶轮问题，通过引进周期性自由面变量，揭示了隐含的一类对偶变分原理，从而给出了可能存在的全部互补原理。

Finally, For the first time, the Ritz variational based mode matching method using new basis functions is proposed to deal with a discontinuity region. The general process to construct the linear equation group is developed, and the equation group's rank is only half of that of the cascading treatment. Thus the efficiency can be increased.

还首次采用新型基函数并利用里兹变分法和模式匹配法提出了构造处理一段不连续性问题的线性方程组的一般理论，方程阶数可比常规的级联处理方法降低一倍，可提高计算效率。

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。

In Chapter 6, we study a kind of system of nonlinear variational inequalities and its related auxiliary problems in real Hilbert space.

针对一类非线性变分不等式系统，我们研究了其相关辅助问题，建立了辅助问题解的存在性定理。

In this paper, we first introduce a class of mixed variational-like inequalities problems.

本文中，我们首先给出了一类混合似变分不等式问题。

To a mass of computation iteration of Chambolle model in solving the inverse problem of image zooming, a class of new model that is based on Besov space is put forward.

摘要在解决图像放大中的反问题时，Chambolle变分模型需要大量的计算迭代。

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。