充分条件

This paper consists of three parts: Firstly, we discuss a nonautonomous -species two-patches cooperative Lotka-Volterra diffusion system. Using Brouwer fixed-point theory and Liapunov function, under some conditions, we obtain that the system has a unique globally asymptotically stable positive periodic solution. Secondly, we consider a kind of nonautonomous predator-prey model, in which preys are with stage structure and the predator are with two patches.

中文摘要：本文分三部分讨论三类生态模型周期解或概周期解的存在性及全局渐近稳定性等内容：第一部分讨论了两斑块种群的互惠Lotka-Volterra扩散系统，运用不动点理论和构造Liapunov函数，得到了系统存在唯一一个全局渐近稳定的正周期解的充分条件。

A sufficient condition for the systems to be asymptotically stable, which is dependent on whether LMI is feasible, is presented.

给出了以线性矩阵不等式组的形式表示的该控制器存在的充分条件。

These algorithms contain rich information of system structure, especially, the information of coupling and structure at infinity.

给出非正则反馈线性化问题有解的一系列构造性的充分条件以及必要条件，以及求解线性化反馈变换的递推算法。

Based on the existence of the solution to a LMI, a sufficient condition is obtained under which the composite systems can be quadratically stabilized with a H〓 norm bound constant on disturbance attenuation for all admissible uncertainties and a necessary and sufficient condition is obtained using BMI.

采用线性矩阵不等式方法，给出了系统可鲁棒H〓分散镇定的充分条件；采用双线性矩阵不等式方法，给出了系统可鲁棒H〓动态输出反馈分散镇定的充要条件，并给出了算法。

By means of augmented Lyapunov functional and free-weighting matrix approach,a delay-dependent sufficient condition is presented,which can make the resulting closed-loop systems asymptotically stable and satisfy a prescribed H∞ norm-bounded constraint.

利用增广Lyapunov泛函并结合自由权矩阵方法，得到使得闭环系统鲁棒渐近稳定且具有给定的H∞性能的时滞相关充分条件。

Global asymptotic stability of a class of nonlinear rational difference equation s was studied by means of setting up an auxiliary equation,so that a sufficient condition was obtained.

运用建立辅助方程的方法研究一类非线性有理差分方程正平衡点的全局渐近稳定性，得到一个充分条件。

In chapter 5,we introduce the De Morgan algebra of metric and investigate the pseudo-metric Uniformity and the pseudo-metric topology and the separation axioms in De Morganalgebra of metric.We establish the Baire category theorem and the Banach contraction theo-rem,the Edelstein contraction theorem and other fixed quasi-atom theorems in De Morganalgebra of metric.In final,we give a sufficient condition for the metrization of a De Morganalgebra of topology.

在第五章里，我们地德摩根代数中引进了伪度量，探讨了伪度量一致和伪度量拓扑以及德摩根度量代数的分离公理，得到了Baire范畴定理、Banach收缩定理、Edelstein收缩定理以及其它不动拟原子定理，最后给出一个德摩根拓扑代数可度量化的充分条件。

The positive solutions of the equations are given by using method of directstructure in the Banach space.

直接利用构造的方法，在Banach空间给出了方程的正解，建立了一系列比较定理，给出了方程正解存在的充分条件。

The purpose of this part is to study the delay differential systems in Banach space using the method of fixed point theorem.

一方面在非时滞的情况下通过构造比较函数，利用Brouwer不动点定理得到非时滞微分方程正周期解的存在唯一性，及周期解全局吸引的充分条件。

The sufficient conditions for the existence of the local bifurcations of two semi-trivial solutions (θr,0) and(0,θd) are proved,and stability of the local bifurcate solution from semi-trivial solution(θr,0) is obtained.

利用局部分歧理论及线性稳定理论，证明了两个半平凡解(rθ，0)和(0，θd)局部分歧解存在的充分条件，并且证明了半平凡解(rθ，0)产生的局部分歧解是无条件稳定的。

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％。