查询词典 inequality sign

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。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

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 Wielandt inequality is an improvement on the general Cauchy-Schwarz inequality, and its applications to statistics were studied. In a note, Wang and Ip (1999) gave the Wielandt inequality in matrix version in terms of the Lo|¨wner partial ordering.

Wielandt不等式是对著名的Cauchy-Schwarz不等式的一种改进，该不等式被广泛应用于统计理论中线型模型的研究方面，因此研究更一般形式的Wielandt不等式有重要的意义。

First, a new integral inequality for quadratic terms is established by using the Park inequality. Next, the integral inequality in combination with the Lyapunov-Krasovskii functional method is used to derive a new delay dependent sufficient condition based on LMI which can guarantee that the closed-loop system is not only internal asymptotically stable but also with the prescribed H-infinity performance via the slow subsystem's memoryless state feedback.

首先利用Park不等式建立了一个基於二次型项的积分不等式，然后利用Lyapunov-Krasovskii泛函方法，获得了系统经慢子系统的无记忆状态反馈后不仅内部稳定，而且具有给定的H性能的，基於LMI的时滞相关充分条件。

Since there is natural different of the kinematic density formula for pairs of intersecting lines in two-dimensional surface and three-dimensional space, the inequalities for double chord-power integrals have studied from two side of two-dimensional surface and three-dimensional space using chord-power intergral inequality. Schwarz inequality. Holder inequality and so on.

由于二维平面和三维空间上的相交直线偶的运动不变密度公式有着本质的不同，本文从二维平面和三维空间两个角度，利用弦幂积分不等式，Schwarz不等式，Holder不等式等不等式分别得到了一系列双弦幂积分不等式。

Motivated by the newψfunctional stability,we can establish some new kinds of stabilities which are different from the exponential stability.With the help of semimartingale convergence theorem,stochastic calculous,moment inequality,Burkholder-Davis-Gundy inequality,Gronwall inequality etc.,we find that the product ofψfunction and the solutions of neutral equations will approach a nonempty set if some specific conditions are satisfied.

我们应用半鞅收敛定理、随机微积分的相关知识以及矩不等式、Burkholder-Davis-Gundy不等式和Gronwall不等式等技巧，得到中立型随机泛函微分方程的解与特定的"ψ函数"的乘积在一定的条件下将趋向某非空集合这一结论，并建立了该中立型方程的随机LaSalle型定理。

By applying the H〓lder inequality, the Gronwall inequality, the Doob's inequality and the properties of the Ito stochastic integral to the integral form of the test equation, several important inequalities related to the analytical solution are proved, and the local order of the numerical solutions in mean square sense is obtained accordingly.

通过对试验方程的积分形式使用Holder不等式、Gronwall不等式、Doob不等式和Ito随机积分的性质，得出了试验方程解析解满足的几个重要不等式，进而得出了数值方法在均方意义下的局部误差阶。

Although translator has turned from being a crystal ball by which the original culture can unrestrainedly penetrate to another crystal ball by which the target culture can freely traverse, the translator's personal embodiment, in the process of cognitive act, are still absent in translation studies. Translators are still subjects without body or simply disembodied subjects.

译者虽然由原语文化可以自由穿透的玻璃球变成了译语文化可以自由穿越的玻璃球，但译者认知过程中的个体体验在翻译研究中依然缺席，译者依然仅仅是一个没有躯体体验的主体。

Chillingly, he claimed our technology is 'not nearly as sophisticated' as theirs and "had they been hostile", he warned 'we would be been gone by now'.

令人毛骨悚然的，他声称我们的技术是'并不那么复杂，像他们一样，和"如果他们敌意"，他警告说，'我们将现在已经过去了。