充分条件

Some sufficient conditions of the existence and uniqueness of the periodic solutions are obtained.

研究了一阶非线性泛函微分方程的周期解，得到了周期解存在唯一的一些充分条件，推广和改进了已有的结果。

And the sufficient conditions for the existence and stability of semi-trivial periodic solution and positive period-1 solution were obtained.

并得到了半平凡周期解和正周期1解存在和稳定的充分条件。

Recently, the authors of [14, 16, 17] considered the above problem and gave the sufficient conditions about the existence of single and multiple solutions by employing the norm-type expansion and compression theorem due to Krasnoselskii.

最近，文献[14，16，17]中，作者考虑了上述问题，并利用Krasnoselskii的范数形式的锥拉伸和压缩定理得到了单个和多个解存在的充分条件。

In this paper, a disease transmission model of SEIRS type with exponential demographic structure is studied. Two sufficient conditions are obtained to guarantee the local or global exponential stability of the disease free equilibrium by using a new technique based on the concept of comparison.

本文研究了一类具指数人口统计与结构的SEIRS传染病模型，利用一种新的基于比较原理的分析，获得了无病平衡点局部和全局指数稳定的两个充分条件。

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

The sufficientcondition is given to prove that Parsons graphs Tb(2, q) is l -- factorable. The author discussesthe directional Parsons graPhs DTb and gives some new conclusions about them. In theend, the author brings forward some new concepts about Parsons graphs and makes someelementary discussions on them.

给出了Parsons图是1—因子可分解的一个充分条件，并证明了部分Parsons图是1—因子可分解的；对有向Parsons图进行了讨论，并给出了一些结论；另外，我们还针对Parsons图提出了一些新的概念，并对其进行了初步讨论。

Many sufficient and necessary conditions for a finite group to be solvable are given, which generalize some known results.

另一方面，我们研究了Sylow-子群的某些特殊子群的半覆盖远离性对有限群结构的影响，给出了一些有限群为p-幂零和超可解的充分条件。

In this paper, the almost periodic solution for a class of two-degree-of-freedom nonlinear oscillating systems is studied by using the Leray-Schauder fixed point theorem and the method of Liapunov function.

运用Leray-Schauder不动点定理和Liapunov函数方法，研究了一类两自由度非线性振动系统的概周期解，得到了该振动系统概周期解存在的充分条件。

Chapter two mainly considers the periodic boundary value problems for impul-sive differential equations. Some existence results, obtained by the help of Schaeffers fixed point theorem and the method of upper and lower solutions coupled with the monotone iterative technique.

第二章讨论了两类周期边值问题，通过利用Schaeffer不动点定理，上下解方法和单调迭代方法，建立了解存在的充分条件。

The sufficient conditions for guaranteeing the permanence of the system and the existence and uniqueness of periodic solution having globally asymptotical stability are obtained by using the extremum principle,fixed point theorem and V function method s together.

讨论一类具 Holling 类功能反应和放养的捕食链非自治扩散系统，应用极值原理和不动点定理及 V函数法，得到该系统的一致持久性以及存在唯一全局渐近稳定周期解的充分条件。

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％。