查询词典 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。

Secondly, we consider stochastic LQ optimal control problem driven by Lévy processes and Brownian motion. By applying the -Lévy formula, Gronwall's inequality, Young's inequality and Cauchy-Schwarz inequality, we obtain the closeness property of the solution of multi-dimensional backward stochastic Riccati differential equations.

第二部分首先研究由布朗运动和Lévy过程共同驱动的随机LQ最优控制问题，接着利用-Lévy公式、Gronwall不等式、Young不等式及Cauchy-Schwarz不等式证明多维倒向随机Riccati微分方程适应解的闭性质，并利用此性质证明一维BSRDE解的存在唯一性。

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

First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and accuracy of the-th approximate value is estimated by the n-tb approximate value.

首先利用Cauchy场不等式证明了一个基本不等式；其次采用Galerkin方法来构造适当的基函数，并利用Cauchy不等式给出了其特征值计算的误差佑计式；最后得到计算梁横向振动问题的特征值的近似值的算法，而且可以用第n次近似值来估计第n-1次的近似值的精确度。

In this paper,quadratic form theory,the European space inner product nature and Jensen inequality are three ways to prove cauchy inequality,and bthe relation between Cauchy inequality and higher mathematics was illustrated briefly.

本文运用二次型理论、欧式空间中内积性质和詹森不等式三种方法证明柯西不等式，并简要说明柯西不等式与高等数学之间的联系。

The asymptotic behavior of the weak solution is obtained when an enthalpy function is made in L(superscript 2 subscript +) and a differential inequality is proved after using Cauchy inequality, Poincare inequality and the definition of weak solution.

在L(上标2 下标+)空间上构造了一个熵函数，利用带ε的Cauchy不等式和poincare不等式及弱解的定义，推导出了此函数满足的一个微分方程不等式，通过求解微分方程，证明了弱解的渐近性问题。

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。

Anna: No, I've got a hangover.

不是，我昨晚宿醉了。

We head into the mountains in Su's new Land Cruiser, stop for lunch at a scenic restaurant and then hang around drinking beer and eating fruit as two of his employees attempt to lure the birds with a tape recording of the fowl's mating call.

我们坐上苏的巡逻车向山顶出发，在一家风景优美的餐馆吃了中饭。然后我们喝着啤酒吃着水果四处逛。