充分条件

By analytical method and comparison theorem, some sufficient conditions for uniformly persistent of two populations and the whole system are obtained.

利用分析法和比较定理，得到两种群分别一致持续生存以及整个系统一致持续生存的充分条件。

In the forth chapter, by employing the comparison theorem in theory of difference equations together with pure analysis, we get sufficient conditions for permanence of a class of ratio-dependent discrete system.

第四章运用差分方程理论中的比较定理和纯分析的方法得到离散系统持久性的充分条件。

2By constructing a completely continuous operator in a functional space and employing the cone compression and expansion fixed point theorems, we obtain some sufficient conditions which guarantee the existence of positive periodic solutions for Eq.

通过在一个函数空间构造一个全连续算子，再利用锥压缩锥拉伸不动点定理，得到了一些保证方程(1)，(2)至少存在一个周期正解的充分条件，所得结论改进了文[1]和[6]中的结果。

In the preceding example, womanhood and the right royal lineage are each individually necessary conditions for princesshood and conjointly they comprise a sufficient condition for princesshood.

在这个例子中，女人身份和合法的皇家血统，各自是公主身份的必要条件，合起来就构成公主身份的充分条件。

In this paper, we review some back ground and recent advances in the field of complex networks, and give the sufficient conditions guaranteeing the local and global synchronization stability of the complex connected dynamical networks with asymmetrical coupling matrix and time delay in coupling by using Lyapunov functional.

在这篇论文中，较全面地介绍了复杂网络研究的背景，发展和现状，着重讨论了动态网络模型的同步性质，应用Lyapunov泛函，考察了带有更一般的不对称连接矩阵以及时滞的复杂动态网络的同步性质，给出了局部和全局同步的充分条件。

Moreover, the smallest degree sum on potentially K(p,1,1)-graphic sequences and k-cycle-graphic sequences are given respectively; bounds on m-restricted edge connectively and 3,4-restricted edge cut of graphs are also characterized respectively.

此外，还分别给出了蕴含k圈和（p，1，1）-部图可图序列度和的下界；分别给出连通图含m-限制边割的充分条件和必要条件及连通度的界。

The conservation of energy and momentum is also considered.

在Reich研究工作的基础上，我们把PRK方法应用到这种多辛Hamiltonian PDEs上，给出了它是多辛的一些充分条件，同时，对这种多辛PRK法关于线性能量和动量的保持也作了相应的探讨，这些都在一定程度上发展和拓广了现有的结果。

This feature helps to get a sufficient condition with less conservativeness for the discrete system by using parameter-dependent Lyapunov function.

这个特性有助于通过依赖于参数的Lyapunov函数得到一个关于此类系统保守性更小的充分条件。

By giving the example, explains that theorem 4 in the refuted paper is not the necessary condition of the continued fraction convergences, by discussing the indeterminacy of the lever function and citing the counterexamples, expounds that the theorem 4 is not sufficient condition of the parameters W and W -1 neutralizing each other, and so shows algorithm 1 and 2 in the refuted paper to be incorrect.

通过举例说明了"攻文"定理4不是连分式收敛项的必要条件，并通过对杠杆函数不确定性的讨论和反例的举证说明了"攻文"定理4不是W与W –1相互抵消的充分条件，从而证明了"攻文"算法1和2及其衍生方法是错误的。

Furthermore,we obtain a sufficient and necessary condition about continuity of functional series and integral with parameter,and show the sufficient condition about differential .

将数学分析中一致收敛性的概念加以推广，分别对函数项级数和含参量积分引入次一致收敛的概念，证明了函数项级数、含参量非正常积分连续性的充要条件和可微性的充分条件，推广了数学分析中的相应结

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。