单调性

The first part is introduction in which some excellent results are given. For example, LeachandSholander mean of two variables E and its monotonicity, Some results of paper and [4] are also given. In Chapter l,mean function and mean family of n variables in one dimension are given. On the base of mean function of n variables of paper [1], weproof that is mean function and discuss its monotonicity andcontinuity.

第一部分是引言，主要介绍了一些已有的结果，如：一般的两个变元的Leach and Sholander均值B以及它的单调性，又介绍了文[1][4]中一些已有的结果，第一章主要介绍了一维n元平均函数和平均族，在已有的文[1]中给出的参差域K上的n元平均函数概念的基础上，证明一般形式的是平均函数，讨论了它的单调性和连续性，其中还将已有的二元Stolarsky平均推广到了n元平均。

In this paper, we generalized the reverse Shebyshev inequality and obtained the integral inequality of two vector function s, whose monotone of correspondence elements is reverse.

推广了反向Chebyshev不等式，得到了对应分量的单调性相反的连续向量函数的积分不等式和模的单调性相反的连续向量函数的积分不等式。

The interpolation formula can be compiled into standard computer code.

在此，我们首先论述了保单调性的插值方法，根据分布函数的逆函数具有单调性的特点，用保单调的插值曲线去逼近分布函数的逆函数，进而用得到的插值公式进行随机变量的抽样，这样做可以节省抽样的时间，并且在分布函数具有一定的光滑性条件时，插值公式具有比较好的收敛阶。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundle For a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained.

中文摘要：本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In this paper we will mainly study the gauge fixing Yang-Mills heat flow of a principal bundleFor a principle bundle with a compact seme-simple Lie group as its structure group over a compact Riemannian manifold without boundary, the evolutions of the curvature and its higher derivatives under the flow above will be derived, and the energy inequality and the Bochner type estimates will be obtained. Then, the monotonicity formula and the small action regularity theorem can be proved. We will give the locally uniform estimates for the higher derivatives of the curvature.

本论文主要讨论主丛上的规范固定Yang-Mills热流我们在紧致无边黎曼流形上的以半单紧致李群为结构群的主丛上，推导了在规范固定Yang-Mills热流下曲率及其高阶导数的演化方程，得到了该热流的能量不等式和Bochner估计，由此可推出单调性公式和小作用量正则性，以及曲率各阶导数的局部一致估计。

In order to solve this problem, based on monotone approximation of inverse distribution functions, synchronization is achieved.

论文也给出了在函数不具有单调性的假定下，公共随机数法可以衰减方差的一个定理和函数具有单调性时的两个推论。

Secondly,it is proved that monotonicity is equivalent to the law of proof by contradiction,and a simpler equivalent condition to monotonicity is given.

首先，讨论了择优逻辑的若干基本性质，并给出了单调性的一个充要条件；其次，证明了单调性与反证律等价，并给出了单调性的一个更为简洁的充要条件；最后，讨论了解释集合是归纳集时的单调性，证明了单调性与择优蕴涵的退化等价。

In this paper,we show firstly the equivalence of Maskin monotonicity and strategy-proofness on the single peakedness preference domain ,and furthermore that of Maskin monotonicity and coalitional strategy-proofness.

本文证明了在单峰偏好域上Maskin单调性与防策略条件是等价的，并进一步证明了Maskin单调性与联盟防策略是等价的。

The aim of this contribution is to draw a general perspective of the liveness and safeness for Asymmetric Choice nets.

文章讨论了活性具有单调性的非对称选择网活性与安全性的条件，并给出一个多项式时间算法来判定一个给定的非对称选择网是否是活的、安全的与活性满足单调性。

In chapter 6, we discussed the wavefront solution of a kind of lattice differential equation which derives from diverse fields. We obtained the wavefront solution by using sup-subsolution iteration when the coupled functions are quasimonotone, and by applying Schauder fixed point theorem, we also obtained the wavefront solution when the coupled functions have a different quasimonotone property.

在第六章中，我们对一类从实际问题中抽象出来的二阶时滞格微分方程的行波解进行了讨论，用单调迭代的方法讨论了耦合函数具有拟单调性时行波解的存在性，用不动点的方法讨论了耦合函数具有指数拟单调性时行波解的存在性。

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