极小

Chapter one has introduced the background and classification of minimax theorems; Chapter two summarizes several proof method of minimax theorems, which are illustrated with examples; Chapter three has explained the development general situation of minimax theorems for a function and for two functions with chapter four respectively, and according to the classification of the theorem, has illustrated some important conclusionses in quantitative minimax theorems, topological minimax theorems and quantitative-topological minimax theorems separately.

第一章介绍了极大极小定理的背景及其分类；第二章总结了极大极小定理的几种证明方法，并举出例子进行说明；第三章和第四章分别阐述了单函数的极大极小定理和两个函数的极大极小定理的发展概况，在第三章中，按照极大极小定理的分类，分别对数量极大极小定理，拓扑极大极小定理和数量拓扑极大极小定理的一些重要结论作了介绍。

Soc _RR is a injective left R-module.(4) Soc _RR is a left self-injective ring.|Theorem 4.2.9 Let R be a commutative notherian ring, then the following are equivalent:(1) R is a FS-ring.(2) R is a PS-ring.(3) Every minimal ideal of R is injective.(4) Every minimal ideal of R is p-injective.

定理4.2.9若R是交换的Noethe(来源：Aae0eBe0C论文网www.abclunwen.com)r环，则以下条件等价：R是FS-环；R是PS-环；R的每个极小理想都是内射的；R的每个极小理想都是p-内射的；R是IS-环；R的每个极小理想都是投射的；R的每个极小理想都是平坦的。

Secondly, a finite element method is used to approximate the constrained minimization problem, both existence of minimizer for cost functional in finite demensional space and the convergence of minimizer are proven.

然后利用有限元方法对上述定解问题进行离散，并证明了有限维空间上泛函的极小元存在以及有限维空间上的极小元收敛到无限维空间上的极小元。

Secondly, by using the connection, we prove that the minimal continuous semi-flow is the minimal continuous flow if its time-one map is open, and for any minimal continuous semi-flow, there is an invariant residual set such that the restriction to the set is a minimal continuous flow.

为此，我们首先建立了它与其时间1映射极小集的联系；然后，利用这种联系证明了：若时间1映射为开映射，则它是极小的连续流，并且一般地说来，对任意极小连续半流，存在不变的剩余集，使得它在这不变集上的限制是极小的连续流。

Discussion (1) Mean temperature variations in China in the last millennium synchronize well with the classical solar minimum, such as the Darton minimum, the Maunder minimum, the Sporer minimum and the Oort minimum, suggesting a strong linkage between temperature variations and solar variability in the last millennium.

综合讨论(1)"红原-金川"平均温度变化趋势显示，近千年中国平均温度变化与经典的太阳活动极小期，如Darton极小、Maunder极小、Sporer极小、Oort极小，等等，表现一致。

First, we extend the general finite element method from the function surface to the parameter function. Second, we bring this kind of method into the design of rational Bézier minimal surface. Third, we transform the problem of Dirichlet energy function into the problem of minimizing a discrete objective function.

首先推广了函数曲面中的有限元方法，进而研究如何针对参数曲面使用有限元方法，并把该方法引入到有理Bézier极小曲面造型的设计中，从而将连续的Dirichlet能量函数极小化问题，转化为一个离散形式的目标函数的极小化问题。

In this paper, row distance and minimum row distance of matrix on F2 are presented, and some properties about row distance are given. Two important theorems are proved.

陈勤引进了F2上矩阵的行间距和极小行间距概念，给出了极小行间距的一些基本性质，证明了极小行间距的两个重要定理。

In addition, we study the reduced minimum modulus of the generalized Drazin inverse of an operator on a Banach space and give out lower and upper bounds of the reduced minimum modulus of an operator and its generalized Drazin inverse, respectively.

第四章讨论了左乘算子L_A∈BB(H的约化极小模与A的约化极小模的关系；讨论了广义Drazin可逆算子的广义Drazin逆的约化极小模的上下界及广义Drazin可逆算子的广义Drazin逆的约化极小模与算子的约化极小模的关系。

In chapter 2, we define a new operator—the minimal operator on martingale space, it's well known that the maximal operator controls where given martingale f is large, intuitively, we say that the minimal operator controls where a martingale is small.

第二章引入了鞅空间上极小算子mf的概念，众所周知，极大算子可以控制一个"较大"的鞅，那么形象地说，极小算子就是用来控制那些"较小"的鞅，因此，在研究关于极小算子的加权不等式时，很自然地要估计诸如〓，log mf等算子的值。

In vector optimization one investigates optimal elements such as minimal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space.

前言在向量最优化中，人们研究偏序线性空间中非空子集的最优元，比如极小元，强极小元，真极小元或者弱极小元。

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