查询词典 sufficient condition

A sufficient and necessary condition for nonlinear continuous-time associate memory neural networks to be locally exponentially stable is obtained, and a unction is defined for characterizing the domain of attraction of equilibrium point.

摘要讨论非线性连续联想记忆神经网络平衡点局部指数稳定的判定条件及平衡点指数吸引域的估计，得到了平衡点局部指数稳定的充要条件，并引入一个特征函数，可以判定平衡点的邻域是否为指数吸引域。

On conic optimization, we work over some properties of cone and its dual cone, and solve the relations between special cones (obtuse cone, orthogonal cone, superior and inferior obtuse cones) and their dual cones.Furthermore, sufficient and necessary condition under which they exist are proved detailed .

本文围绕锥规划问题，对锥及其对偶锥的性质进行了研究，解决了一些特殊锥(钝锥、直角锥、优劣钝锥)及其对偶锥之间的关系，并对它们存在的充要条件给予了详细的证明。

Chapter 3 Some properties in Cesaro-Orlicz sequence spaces: In this chapter, the dual spaces of the Cesaro-Orlicz sequence spaces and the criteria for the extreme point are studied and the sufficient and necessary condition of which the spaces has theλ- property and the uniformλ- property is given by the above results.

第三章Cesaro-Orlicz序列空间中的一些基本性质：本章我们主要讨论了Cesaro-Orlicz序列空间的对偶空间，同时给出此空间中端点的判据，然后由此端点的判据我们证明了Cesaro-Orlicz序列空间具有λ-性质，最后我们得到了此空间中一致λ-性质的等价条件。

Also, the paper gives a sufficient and necessary condition for a knot being equivalent to a trivial knot.

给出一个纽结等价於平凡纽结的充要条件。

We present concrete mathematical expressions concerning relationships of P, I, J and R, a sufficient and necessary condition of J = 0, and relationships among transitivity, negative transitivity, semitransitivity, Ferrers properties between R and P and I with W as the t-norm.

主要包括P，I，J，R之间关系的具体表现、J=φ的充要条件，在W_φ意义下，R的传递性、负传递性、半传递性、Ferrers性质与P，I的相关性质之间的联系，得到了与普通情形下相平行的一些结果。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively. Compared with some known results in the literature, the equations discussed by us are more general, and our results are concise and easy to be verified.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

Moreover, we still get an sufficient and necessary condition of uniform sequence of generalized fuzzy integrable functions.

此外，还得到了非负模糊可测函数列广义模糊一致可积的一个充分必要条件。

New technologies were a necessary condition for the green revolution, but not a sufficient one.

而新技术只是绿色革命的必要非充分条件。

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。