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In this paper,we study the existence.uniqueness and asymptotic stability of the periodic solutions for a class of nonautonomous systems by using the method of Liapunov Function.

利用Liapunov函数方法,研究了一类非自治系统周期解的存在唯一性及渐近稳定性,得到了存在唯一渐近稳定的周期解的充分条件。

This system is permanent by comparative principle and globally asymptotically stable through constructing a Liapunov function; for the periodic case, the research has obtained conditions for existence, uniqueness and stability of a positive periodic solution.

利用比较原理研究了系统的持久性,通过构造Liapunov函数证明了系统的全局渐近稳定性,在假设系统为周期系统的条件下得到了正周期解的存在唯一性和全局渐近稳定的充分条件。

An impulsive control scheme of the Lur'e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur'e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur'e system and impulsive control law are given, a theory of impulsive synchronization of two Lur'e system is also presented.

提出了Lur'e系统的脉冲控制系统,利用关于脉冲系统稳定的几个定理,得到了具变化的脉冲区间的Lur'e系统镇定的充分条件;并且给出了Lur'e系统的适当参数与脉冲控制律,使得两个Lur'e系统脉冲同步。

By structuring a Lyapunov function, and using matrix norm , the stability of the time-delay uncertain systems is analysed with the result of some significant sufficientconditions.

通过构造适当的Lyspunov函数和利用矩阵范数,对时滞扰动多变量系统的鲁棒稳定性进行了较为详细的分析,得出了几个较有意义的充分条件

On the base, using the knowledge about matrix operations, we study the admissibility of parameter estimators in multilinear model and growth curve model.

在此基础上,利用矩阵运算的知识,进一步研究了多元线性模型和增长曲线模型中参数估计的可容许性,获得了参数估计在指定的估计类和全体估计类中可容许的充要条件或充分条件。

In Part 3 we study the mutualism system with several delays Sufficient conditions are obtained for the existence of positive periodic solutions of the system by using the theory of Mawhin coincidence degree .

第三部分考虑了两种群带多时滞的互惠系统我们利用Mawhin重合度理论,得到了系统正周期解的存在性的充分条件,推广了文[28,29]的结果,并且删去[30]的某些条件。

In Part 3 we study the mutualism system with several delaysSufficient conditions are obtained for the existence of positive periodic solutions of the system by using the theory of Mawhin coincidence degree .

第三部分考虑了两种群带多时滞的互惠系统我们利用Mawhin重合度理论,得到了系统正周期解的存在性的充分条件,推广了文[28,29]的结果,并且删去[30]的某些条件。

By using the above conclusions the nondegeneracy condition of systems without steady errors is analyzed successfully.

利用上面的结果,成功地分析了结构无静差问题的非蜕化条件;证明了非蜕化条件不但是实现结构无静差的充分条件之一,而且还是实现结构无静差的必要条件。

Later, we estimate our variational functional to get a nontrivial solution of the new equation and so the second solution for is obtained.

然后我们利用函数平移将原来的非齐次边界问题转化为奇次边界问题,验证了其对应的变分泛函满足不带条件的山路引理的两个条件,并给出了泛函临界点存在的一个充分条件,最后对具体的变分泛函进行估计,得到了新方程非平凡解的存在性结果,从而得到了原方程第二个正解的存在性结果。

The satisfiability of conjunction normal form is a typical NP-complete problem. To study the complexity of SAT problem, a new concept of saturated clause muster has been introduced with using the characteristic of saturated clause muster. The sufficient condition of SAT problem was approved to be a polynomial and has opened out essential distinction of 2SAT and 3SAT problems.

合取范式可满足性问题是典型的NP完全问题,本文引入了一个饱和子句集的新概念,利用饱和子句集的特性,研究了SAT问题的复杂性,证明了SAT问题复杂性为多项式的一个充分条件,并揭示了二元可满足性问题与三元可满足性问题的本质差别。

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