定理

Boundednesses of population and toxin in population and in the environment are shown by comparison theorem.

通过比较定理得到了种群的有界性，及种群体内毒素和环境中毒素的有界性。

In the process of calculation, by comparison theorem and strict calculation, some sufficient conditions for persistent and extinct of three populations are obtained.

推导过程中主要应用了比较定理，并且通过严密的计算，得到了三种群持续生存性和绝灭性的充分条件。

Making use of the comparison theorem, some sufficient conditions are derived for permanence of the system and non-permanence of predators.

运用比较定理，得到了系统持久生存和捕食者灭绝的充分条件。

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。

Establishing a novel Razumikhin type comparison theorem, input-to-state stability of Hopfield neural networks is studied.

建立新的Razumikhin型比较定理，用以研究Hopfield延迟神经网络的输入—状态稳定性。

By using of the comparison theorem and some results, some sufficient and necessary conditions are derived for permanence of the periodic system and non-permanence of predators.

运用比较定理和一些主要结果，得到了系统永久持续生存和捕食者灭绝的充分必要条件。

In the first chapter, we research the dynamics of population which were in the polluted environment, we will: give the corresponding mathematical model;(2): obtain the explicit conditions for the threshold of the population by means of comparison theorem.

第一章是研究污染环境中种群的动力学行为，首先给出相应受污染系统的数学模型，然后研究系统中种群的持久生存和灭绝问题，在具体模型中，运用比较定理研究种群生存的阈值。

Under the most elementary conditions for backward stochastic differential equation introduced by Peng S., we put forward and prove a general converse comparison theorem.

在由彭实戈引入的倒向随机微分方程的最基本的条件下，提出并证明了一个一般的反比较定理。

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。

In this paper, we study the comparison theorem of backward doubly stochastic differ-ential equtions with continuous coefficient by Tanaka-Meyer formula.

利用Tanaka-Meyer公式研究了双重倒向随机微分方程在连续条件下的比较定理。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新