查询词典 cauchy inequality

We prove the corresponding Doob"s maximal inequality, Burkholder-Gundy-Davis inequality, the greater-smaller operator inequality and Rosenthal"s inequality in the framework of rearrangement invariant martingale space on finite interval.

包括重排不变鞅空间及其中的Doob极大不等式，Burkholder-Gundy-Davis不等式，上、下不等式，Rosenthal不等式等。

Cauchy—inequality is an extremely important inequality. Ingeniously applies it or its promoted type nimbly, may cause some more difficult problem to be easily solved.

摘要柯西不等式是一个非常重要的不等式，灵活巧妙地应用它以及它的推广式，可以使一些较为困难的问题迎刃而解。

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwalls type, an energy inequality is got and a priori estimate is established.

接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwall's type, an energy inequality is got and a priori estimate is established.

接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

In chapter 3, we study the Bihari type inequality of integral equation with retarded term, we consider the inequality of integral equation as follows:In this section we will get some new result about the inequality (3.1.1) on t_0,∞.

我们考虑了下面的积分方程不等式这节我们将得到不等式(3.1.1)在t_0，∞上的一些新结论，同时将给出一个反例，修正了文

Retarded term; Impulsive term; Integral inequality; Nonlinear equation; Volterra inequality; Bihari inequality

时滞项；脉冲项；积分不等式；非连续函数； Volterra型不等式； Bihari型不等式

In order to study the popular curve shortening flow in the plane, Gage[3] has shown in 1983 the following inequality, if k is the signed curvature of a closed convex plane curve γ with length L and enclosing area A, then one gets Gage calls it an isoperimetric inequality in [3], but he does not show that the equality holds if and only if the curve γ is a circle, while as an isoperimetric-type inequality, one should prove this kind of result.

Gage称之为等周不等式，但他没有证明其中等号成立当且仅当，γ为圆周，而作为等周型的不等式是应该证明这种结果的，本文我们利用单位速率外法向量流，通过努力证明了这种结果，从而把Gage不等式加强成更加等周的形式。

And then, in this part, following the idea of Topping [51, 52], we will show an isoperimetric inequality (6.3.1) on surfaces of non-positive Gaussian curvature by means of the curve shortening flow on surfaces, this inequality can be considered as a generalization of the Banchoff-Pohl inequality in the Euclidean plane.

然后，仿照Topping[51]和[52]利用平均曲率流证明等周不等式的想法，我们利用曲面上的曲线缩短流在Gauss曲率非正的曲面上证明了一个等周不等式(6.3.1)，它可以看成欧氏平面上Banchoff-Pohl [8]不等式在曲面上的推广。

The stability of Lurie type control systems with multiple time-delays and nonlinearities is considered. Based on the Lyapunov stability theory, using an improved new integral inequality and the method of linear matrix inequality, a refined method called the integral inequality approach is presented.

为了研究具有非线性干扰项的多时滞Lurie控制系统的稳定性问题，依据Lyapunov稳定性理论，利用线性矩阵不等式方法，通过一个改进的新积分不等式，给出了一个新的判断系统稳定的新方法―积分不等式法。

Similarly, current deals with pariahs Sudan and Iran represent a sort of diplomatic arbitrage.

同样，中国目前与不受国际社会欢迎的苏丹和伊朗签署的协议，代表着某种外交套利。

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