查询词典 inequalities

For solving problem (1), this dissertation first presents a sufficient and necessary condition by dealing with inequalities using projection operator in convex analysis, and then proposes a kind of new neural network model based on the constraint domain:〓(2) Where P is a projection operator on Q.

本文利用凸分析中的投影算子处理不等式约束，首先给出二次规划问题(1)解存在的充分和必要条件，据于此提出一种新的基于约束区域神经网络模型〓(2)来进行求解，其中P为Q上的投影算子。

First, We discuss the relationship between the width integral of convex body and dual quermassintegrals when i∈R, and we obtain Some inequalities and extremum properties.

我们获得了凸体i—次宽度积分的Blaschke-Santalo不等式，并建立了凸体i—次宽度积分Aleksandrov-Fenchel不等式的局部形式。

As to problem of time varying delay existing in NCSs, a time-varying model including certain system and uncertain system are constructed firstly, and then stability and stabilization of these systems are discussed based on time-delay system theory, cone convex optimization theory and free weighting matrices approach. Conditions of time-dependent stability and stabilization with less conservative are given in the form of linear matrix inequalities.

针对网络时滞问题建立了时变时滞NCSs的模型(包括确定系统和不确定系统)，然后利用时滞系统理论、锥补线性化方法和自由权矩阵方法研究了NCSs的稳定性和镇定性问题，并基于LMIs形式给出具有较小保守性的时滞相关稳定和镇定条件。

Especially, we study the applications of Jensen inequality of convex function in proving inequalities.

在此基础上，利用凸函数的Jensen不等式，证明了一些应用初等数学知识难以证明的初等不等式，显示出凸函数在不等式证明中的重要性。

Then, through quadratic separators, the sufficient condition of the fault tolerant controller existence can be transformed into the problem of solving some limited number of linear matrix inequalities, including each vertex of the convex polyhedron.

然后，通过二次可分原理，求解只包含关于凸多面体各顶点的有限个线性矩阵不等式，给出了容错控制器存在的充分条件。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

In informal but descriptive language ,we say that the definite integral preserves inequalities.

如果在区间上，，则用通俗明了的话说，就是定积分保持不等号。

These two problems are converted to mathematical problems of solving some matrix inequalities and Riccati equations which are dependent on the time delays.

它们的可解充分条件可以化为与时滞相关的矩阵不等式和 Riccati方程的形式。

A design method for pre-compensator in frequency domain of aeroengine multivariable control system based on diagonal dominance and the method of linear matrix inequalities is presented.

摘要提出了以对角占优为基础，结合线性矩阵不等式进行航空发动机多变量控制系统频域预补偿器的设计。

Many scholars abroad and home have obtained lots of criteria for identifying generalized strictly diagonally dominant matrix by using iterative arithmetic and techniques in matrix theory and inequalities, and studied its properties and applications.

国内外许多学者运用矩阵理论上的一些方法、不等式放缩技巧及迭代算法，获得了广义严格对角占优矩阵的许多判定方法，并对其性质、应用进行了研究。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。