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In this paper we discuss the optimal approximation of matrices and its numerical algorithm on some closed convex cone .

讨论矩阵在闭凸锥上的最佳逼近及其数值算法，在对称半正定矩阵集上，给出了最佳逼近数值算法的MATLAB程序和数值例子。

Based on theory of convex cone s,our extensions of robust linear optimization are done in three directions.

本文基于凸锥理论对鲁棒线性最优化作了若干拓展。

This paper introduces the definition of common quadratic Lyapunov functions and proves that the set which consists of all the common quadratic Lyapunov functions is a convex cone .

给出了共同二次Lyapunov函数的定义，并证明了全体共同二次Lyapunov函数所组成的集合是凸锥

In 1985,Guo Dajun proved that an increasing and α concave operator is of cone contraction,however,is an increasing and α convex operator of cone expansion ?

5年 ，郭大钧证明了增的α-凹算子是锥压缩的，那么增的α-凸算子是否是锥拉伸的呢？

Using the convex cone theory of nonlinear functional analysis, thesufficient condition is obtained in which the system has at least two non-trival w-periodicsolutions.

点定理讨论了n维非自治系统，给出了该系统存在两个非零周期解的充分条件。

The author illustrates in this article the properties of fuzzy convex cone based on the fuzzy normed space;furthermore, testifies the two relevant propositions in the fuzzy normed space.

在模糊赋范空间的背景上，得到了模糊凸锥的若干性质，同时，还给出了模糊赋范空间中两个相关命题的证明。

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。

In addition, the return mapping algorithm is built in negative normal convex cone of violated constraints of level sets to conveniently give an initial structure with multi-constraints, multi-materials and non-design domains.

在这些研究的基础上，提出了适用于一般目标函数、多材料、多约束和多载荷工况的结构拓扑优化的水平集算法4.1，并给出了刚性结构、柔性机构和复合材料微结构设计算法5.1、6.1和7.1，以及大量的数值算例。

In Chapter 3,we discuss theconvergence of Newton's method for nonlinear inclusion problems with values in aclosed convex cone,using the new theory developed by Wang Xinghua,we generalizeRobinson's Kantorovich theorem for this problem to a more widely function classes,inthe same time our results take Smale theorem as a special case.

在第三章，我们利用王兴华最近提出的理论框架研究在闭凸锥中取值的非线性包含问题的Newton方法，将Robinson在特殊Lipshitz条件下建立的Kantorovich型收敛性定理推广至满足中心Lipshitz条件的函数类，我们建立的一般的收敛性定理同时将Smale型收敛性定理包容其中。

Qiang pottery pots, it's very strange with its style, at first glance it looks like a sheep head, the sheep head is one of the Qiang's totom, the two handles on the pot looks like the sheep's ear, on the two side ,it has two cone shaped convex, like sheep's eyes.

纵目双耳陶罐，它的造型非常奇特，乍看像一个羊头，羊头是羌族人的图腾之一，陶罐的两只把手像羊的耳朵，两侧各有两个圆锥状凸起，像羊的眼睛。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。