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Some methods mentioned in the elementary number theory and analytic number theory are used to consider the problems which are related with the Smarandache functions, then a conjecture and an asymptotic formula are given, a special equation is solved and Smarandache-Riemann sequences are generated.

本论文基于对Smarandache问题的学习与研究，运用了初等数论与解析数论中的一些研究方法，对与Smarandache函数相关的问题进行了简单的思考，给出了一个猜想，一个渐近公式，解决了一个特殊的方程，推广了Smarandache-Riemann序列。

This paper consists of three parts:We first consider the non-autonomous predator-prey system with both Beddirigton-DeAngelis functional response and dispersion. By using comparison theorem of differential equation, we study the permanance of the system. After that, by constructing suitable Lyapunov function, we obtain some sufficient condition which guarantee the existence of globally asymptotically stable almost periodic solution of the system.

本文研究三方面的内容：第一部分考虑具有扩散和Beddington—DeAngelis功能反应的捕食-食饵系统，利用微分方程比较原理得到该系统一致持续生存的条件；通过构造适当的Lyapunov函数得到了该系统存在全局渐近稳定概周期解的充分条件。

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。

In Chapter 3, we consider periodic solutions and equilibria at infinity for a generalized Brusselator system.

所以，关于无穷远奇点的一些分析和判断方法也在第二章中给出(来源：bfbfAfbBC论文网www.abclunwen.com)。

Then, we consider the Lyapunov-Schmidt reduction method from the Morse theoretical point of view. We prove that the critical groups at infinity of the reduced functional are isomorphic to those of the original functional.

接下来，我们从Morse理论的角度来考察著名的Lyapunov-Schmidt约化方法，证明了原泛函与约化后的泛函在无穷远处的临界群是同构的。

We should consider the opinion of parents and children at large.

我们应该综合考虑父母和孩子们的意见。

Plenty of time to consider your position at your leisure.

你在闲暇的时候有很多时间来考虑你的处境。

This is one of the myths of science that we shall consider at length.

这是科学的一个神话，我们将在后边对此予以充分考虑。

These organizations have plenty of data on the cost of living as well as other issues that you'll want to consider, and they'll provide it at no charge.

这些机构有很多生活成本方面的数据以及其他你需要考虑的东西，并且是免费提供的。

I have no time to consider all kinds of problems or open the memory at random.

我没有时间考虑种种问题或者随意翻开记忆。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样