查询词典 necessary and sufficient conditions

At the same time, for the process additive and multiplicative uncertainties mostly encountered in practice, the sufficient and necessary conditions for holding the control system robust stability are analyzed, and thus, an intuitive determination method is provided based on the spectral radius criterion.

同时，对于实际中最常见的被控过程的加性和乘性不确定性，分析了控制系统保证鲁棒稳定性的充要条件，由此给出了基于谱半径判据的直观判定方法。

At the same time, sufficient and necessary conditions for holding the control system robust stability are analyzed in the presence of the process additive and multiplicative uncertainties often encountered in practice, and correspondingly, the on-line rule for tuning the adjustable parameters of the decoupling controller matrix is provided.

同时，对于实际中常见的被控过程的加性和乘性不确定性，分析了控制系统保证鲁棒稳定性的充要条件，从而给出在线整定解耦控制器矩阵的可调参数的规则。

Li and one of his lemmas toabbreviate the nonnormal Cayley digraph 〓 into the case when 〓 is a dicycle.When 〓 is a dicycle,we give the sufficient and necessary conditions for 〓 to benonnormal and the structure of the corresponding automorphism group Aut.

Li定义的一个图〓，其中N是Aut的一个非平凡极小正规子群，和他的一个引理，把对非正规Cayley有向图Γ的讨论简化到〓是一个有向圈的情况，进而决定了当〓为有向圈时，Γ非正规的充要条件和Aut的结构。

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

By using of the comparison theorem and some results, some sufficient and necessary conditions are derived for permanence of the periodic system and non-permanence of predators.

运用比较定理和一些主要结果，得到了系统永久持续生存和捕食者灭绝的充分必要条件。

This article uses the implicit function theorem and the properties of analytic functions,with less limitations for the uniqueness,continuity,continuous differentiability of the implicit functions,and gets the sufficient and necessary conditions of the existence of implicit functions by simplifying them.

从常用隐函数存在性定理出发，放宽对隐函数唯一、连续、连续可微等性质的限制，利用解析函数的性质将其展拓，得到广义隐函数存在的充分必要条件和广义隐函数的分布特征。

Convergence, convergence in probability, and convergence in distribution. And some sufficient and/or necessary conditions are also given.

收敛、统计依概率收敛的充要条件或充分条件，此外还讨论了几种收敛性之间的一些关系。

In the second part, we studied blind source separation in ill conditioned cases, obtained the sufficient and necessary conditions on solvability, and presented the neural network model and corresponding adaptive algorithm. We also discussed the blind digital source separation, established the blind separation and extration models and algorithms. These algorithms can be used to deal with high noise and ill-conditioned cases.

在第二部分，我们研究了奇异混合情形下信号盲分离问题，给出了神经网络模型及相应的自适应算法；我们也研究了数字信号盲分离问题，得到了有关可解性的充要条件，提出了分别处理低噪声问题和高噪声问题的算法，这些算法对感知信号个数少于源信号个数等病态问题也适用。

Firstly, the recent developments in controllability and observability for switched system are reviewed. Secondly, by means of properties of invariant subspace, the controllability for switched systems with continuous-time and discrete-time subsystems, and a class of discrete impulsive switched systems is respectively investigated. Some sufficient and necessary conditions of controllability are proved. In the end, some simple criterions for controllability and observability of switched symmetric composite systems are set up.

首先介绍了切换系统能控性与能观性方面的一些重要结论；其次，用不变子空间的性质分别研究了同时含有连续子系统和离散子系统的切换系统和一类离散脉冲切换系统的能控性，建立了相应的充分性与必要性判别准则；最后，研究了切换对称组合系统的能控性与能观性，得到了此系统能控性与能观性的简单判据。

And the sufficient and necessary conditions of the monotone set function which is continuous of the empty set and the full set are given.

李军[6]引入了强序连续性概念，证明了单调测度空间上实值函数的Lebesgue定理成立的充要条件是单调集函数具有强序连续性。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。