极小

The Enneper's minimal surface is the unique cubic parametric polynomial minimal surface one can find and one can not find any high order polynomial minimal surface in the differential Geometry literatures.

极小曲面被广泛应用于建筑设计，飞机轮船制造业，在结构化学，材料科学，植物学，动物学等领域被用作各种模型，在这些应用领域已有很多文献出现，但是，在CAGD领域几乎还没有关于极小曲面造型方面的工作。

This paper introduces the concept of minimal perturbation efficient solution in minimal perturbation constraints programming.

文中引进了极小扰动约束规划的极小扰动有效解概念。

In [33] and [34], a nice generalization of minimal Lagrangian submanifolds called Hamiltonian-minimal submanifold was introduced and investigated by Y.G.

Oh在[33]和[34]中最先引进的哈密尔顿极小拉格朗日子流形，此类子流形式是对极小拉格朗日子流形一种很好的推广，同时他对此类子流形作了相应的研究。

The result not only enriched the theory of minimal surface in differential geometry, but also enhanced the application of minimal surfaces in CAD systems.

本研究不仅丰富了微分几何中的极小曲面理论，对极小曲面在CAD系统中的应用也有重要意义。

It is the first time that the rational Bézier surfaces modeling problem has been proposed and approached successfully, which make it possible for us to research on minimal surface modeling of general conicoid.

在CAGD领域内首次提出了有理Bézier极小曲面造型问题并进行了成功的尝试，使得统一地研究一般二次曲面的极小曲面造型成为可能。

Objective Focusing on minimality of dynamical systems,equivalent descriptions of minimality of some special systems are given.

目的主要对动力系统的极小性进行研究，针对几种特殊的系统给出该系统为极小的等价描述。

Since Von Neumann proved the first minimax theorem in 1928, rich fruits have been obtained about research on minimax theory.

自从Von Neumann于1928年证明了第一个极大极小定理以来，关于极大极小理论的研究已经取得了丰硕的成果。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space,—△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.

在前言中，简要介绍了变分法的产生、发展过程，在第二章中我们介绍了有关变分法的一些基本知识，包括Sobolev空间，—△算子，弱解，极小化序列方法和一些极小极大定理，在第三章中我们介绍了非线性项有界或满足次线性条件，以及它满足推广的Ahmad-Lazer-Paul条件时，二阶Hamiltonian系统和半线性椭圆问题的研究历程，最后在第四章中我们证明了本论文的主要定理，并把它应用到第三章的问题中，使得前面的几种共振的情形都可以统一到这个抽象的结果中。

We construct a kind of special matrix function, which is used to characterize the minimization property of this iterative method, and prove that the approximate solution, generated by this iterative method, minimizes this kind of matrix function over a special affine subspace, which means that the Frobenius norm of the residual sequence is strictly monotone decreasing.

通过构造一类特殊的矩阵函数来刻画该迭代方法的极小化性质，并证明了由该迭代方法计算出来的逼近解，可使得这类矩阵函数在一个仿射子空间上达到极小，而且所得到的残差序列的Frobenius范数是严格单调递减的。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失