不等式

Combining RFD with SDS,the program can automatically prove an extensive class of geometric inequalities involving radicals.

将RFD算法和差分代换方法相结合，给出了一大类具有相当难度的几何不等式的机器证明。此前该课题仅有的工作是杨路关于二次根式的结果。

And then it is made a very brief survey for the history and recent advance of Riccati equation and linear matrix inequality, especially their applications in system and control theory.

接着简单介绍Riccati方程和线性矩阵不等式的发展及其在控制领域中的应用。

Look at Picture 3.4—2. Compare the area of Square ABCD with the sum of the areas of four same right-angled triangles , and what inequality can you have?

阅读课本 P110，比较图3.4－2中正方形 ABCD 的面积与4个全等的直角三角形的面积之和的大小，你能得到怎样的不等式？

The linear matrix inequality's application to the control theory is mainly studied.

本文主要研究了线性矩阵不等式在控制理论中的应用。

Chapter 2 discuss firstly the local existence of solutions for a class of abstract functionalintegro-differential equations with unbounded delay by Schauder's fixed point theorem, then byintroducing an inequality condition and applying the continuity property of solutions it obtainsthe global existence of the solutions.

第二章先利用Schauder不动点定理讨论一类具有无限时滞抽象泛函积分微分方程解的局部存在性，然后引入一不等式条件并利用解的延拓性质获得了解的整体存在性

Let x be an immersion of a compact Willmore surface M into the n-dimensional unit sphere Sn. In this thesis we first consider the Willmore surfaces in the unit 3-sphere, and establish an integral inequality for the square of the length of the trace free part of the second fundamental form and the mean curvature.

令x是一个从紧致威尔摩曲面M到n 维单位球面Sn的浸入，在本论文中我们首先考虑3维单位球面中的威尔摩曲面并建立一个包含第二基本型式迹为零部份的张量长度平方与平均曲率之积分不等式。

Under the suitable hypotheses of compactness,convexity,and semicontinuity,an existence theorem of the weak efficient solution for the convex-like vector equilibrium problems is established.

向量变分不等式与向量均衡问题的重要课题之一是研究其解集的连通性，因为它保证了解可连续的移动。

Since the extended value functions are merely semicontinuous, an extension of viscosity solutions to semicontinuous functions is needed.

因此，以往关于拟变分不等式的粘性解的讨论中所使用的方法也就不再适用，需要利用新的方法将粘性解延展到半连续函数中。

Viability Theory is applied to the optimal control problem for this class of hybrid dynamic time varying systems in this dissertation for the first time. And the statement about a characterization of the extended value functions as the unique lower semicontinuous solution to a Bensoussan-Lions type QVI is proved.

本文首次将生存理论应用到这一复杂系统的最优控制问题中来，得到了最优控制问题中的值函数是一类拟变分不等式唯一的下半连续解的重要结论。

At first, two optimal control problems for hybrid dynamic time-varying systems with free-terminal and terminal constraint are considered, value functions of these two optimal problems are respectively proved to be the unique viscosity solution and the unique lower semicontinuous solution to a type of Quasi-Variational Inequality and the relationship between them is addressed.

本文首先分别考虑了有限时间混合动态时变系统在终端自由和终端约束两种情形下的最优控制问题，得到了最优控制问题的解在这两种情形下分别是一类拟变分不等式的唯一的粘性解和唯一的下半连续解的结论，并给出了它们之间的关系。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。