查询词典 necessary and sufficient conditions

In the proof,sufficient conditions are proved mainly by properties of K function and continuity of Lyapunov function:in necessary proof,we separately structure Lyapunov functions which satisfy the conditions of the theorems, such that the results establish.

在定理的证明中充分性主要利用K类函数严格单调递增和Lyapunov函数的连续性；必要性的证明中，分别构造Lyapunov函数，满足定理的条件，使得定理的结论成立。

Chapter 5 is devoted the study of fuzzy optimization in fuzzy convex analysis structure given in chapter 4. We consider the problems of minimizing and maximizing a convex fuzzy mapping over a convex set and develop necessary and/or sufficient optimality conditions.

在第5章中，首先，在第4章所建立模糊凸分析的结构基础上，考虑了凸模糊映射的极值问题，得到了凸模糊映射取得极值的充分/必要条件。

In this paper, we provide a necessary condition and several sufficient conditions for a digraph to have a pair of disjoint quasi-kernels.

在这篇文章中，我们给出了一个有向图有一对不相交的准核的一个必要条件和若干充分条件。

As an extension, we also obtain some sufficient and necessary conditions under which M_c is left Fredholm and left Weyl for some left invertible operator C, respectively.In chapter 2, the sufficient and necessary condition under which the difference of two idempotent operators on infinite dimensional Hilbert spaces is Fredholm (in-vertible) is discussed. In addition, some equivalent conditions under which products and differences of projections in a C~*-algebra are Moore-Penrose invert-ible are obtained.

来源：Ae5BCab论7a文网www.abclunwen.com对给定的算子对，给出存在左可逆算子C使得M_C左可逆的充要条件；存在可逆算子C使得M_C左可逆的充要条件；存在左可逆算子C使得M_C是左Fredholm算子的充要条件；存在可逆算子C使得M_C是左Fredholm算子的充要条件；存在左可逆算子C使得M_C是左Weyl算子的充要条件；存在可逆算子C使得M_C是左Weyl算子的充要条件。

From the matrix theory and the general principle of the iterative convergence of the linear coupled equations, this dissertation firstly proved the sufficient necessary convergent conditions for CMAC batch learning as well as the necessary convergent conditions for CMAC incremental learning, in which no additive conditions were needed. The past researchers'conclusions under the special condition of the positive articulation matrix are generalized and improved.

从矩阵理论和线性方程组迭代收敛的一般性原理出发，首次在不附加特殊条件的情况下，证明了CMAC学习算法在批量和增量两种学习方式下收敛的一般性定理，给出CMAC算法在批量学习方式下收敛的充要条件，以及在增量学习方式下收敛的必要条件，对前人在关联矩阵正定的特殊条件下得出的结论进行了推广和改进。

The influences of derivations and adjoint ideal semigroups of prime ring with characteristic 2 on the prime ring are discussed, and several sufficient conditions for the prime ring being communitive ring or S4-ring and some necessary conditions for a class of prime rings being communitive rings are obtained.

先给出了一个利用导子和理想来判断素环的可交换性结论的证明，然后讨论了特征为2的素环的导子和归联理想半群对这个素环的影响，得到了素环成为交换环或者S4-环的几个充分条件及一类素环成为交换环的必要条件。

In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.

第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。

There is no reason to presume that the concepts that we explore by means of this method will turn out to be analysable in terms of necessary and/or sufficient conditions.

没有什么理由假定我们用这种方法来探索的那些概念，从必要条件和/或充分条件的角度来说，到头来果真是能够得到分析的。

Modeling and stability analysis problem of linear switched system are emphasized in this part and main results include:(1) Through investigation in the projection of 〓 on x, where x denotes continuous state vector, a series of sufficient conditions for stability, asymptotic stability and unstability of linear switched system's equilibrium in the sense of Lyapunov are achieved. And also, a sufficient and necessary condition for state bounded stability of linear switched system is received.(2) For a class of periodical linear switched system whose switching sets are a group of ordinal lines starting from the original point, it's proved that state bounded stability can be defined by the running characteristic in a single period (3) Based on linear switched system, the concept of linear switched system network is put forward. Linear switched system network is a complex network interconnected by many linear switched systems.

这部分着重研究线性切换系统的建模与稳定性分析问题，主要成果包括：（1）通过考察〓在x上的投影，得到线性切换系统的平衡点在Lyapunov意义下稳定、渐近稳定及不稳定的一系列充分条件，并得到了线性切换系统状态有界稳定的一个充要条件；（2）证明了对于一类切换集为从原点出发的一组射线的周期线性切换系统，其状态有界稳定可根据一个周期内的系统运行特性来判定；（3）在线性切换系统的基础上提出了线性切换系统网络的概念，线性切换系统网络是由多个线性切换系统交互作用而形成的复杂网络。

In the second chapter, the stabilities of periodic regular gaits for six-legged robots walking longitudinally and laterally were systematically studied respectively, employing a hexpod's geometric model with outward extension of middle legs. Major progress and achievements reached are: a Both the necessary and the sufficient conditions for static walking of hexapods were established theoretically. b A generalized optimization method of gait stability was investigated. c For all feasible duty factor, stability-optimal gaits were obtained, with the expressions being of wide adaptation.

第二章系统分析研究了轴对称六足步行机器人在&中腿行程外置模型&下沿两个运动主方向运动时周期规则步态的稳定性及步态规划问题，主要取得以下三方面新的进展：（1）从理论上建立了六足步行机静态稳定的必要性定理和充分性定理；（2）探索了步态稳定性计算机择优的一般方法；（3）对于所有可能的有荷因数取值，从理论上证明静态稳定性最优步态的存在，并得到具有相当普遍意义的统一表达式。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。