充分条件

The definition of adjoint pair and equivalent condition are discussed. A sufficient condition of adjoint pair is improved.

讨论伴随对定义及其等价条件，改进伴随对存在的一个充分条件。

The paper is devoted to the quartic invariant algebraic curves in quadratic system.

本文在给定参数满足一定的条件下，研究了一类二次系统的四次不变代数曲线系统平衡点的稳定性态，并运用Dulac函数法给出了该系统不存在极限环的充分条件，这一研究在同类问题中具有一定的拓展性。

The asymptotic behaviour of the solution for the problem is investigated under certain conditions.

在一定条件下讨论了这些问题的解当t→＋∞时的渐近行为，给出了一类高维广义KdV－Burgers型方程解"爆破"的充分条件。

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。

With the help of comparison theorem, sufficient conditions which guarantee permanence of the system are obtained. For the almost periodic case, by constructing a suitable Liapunov function, we obtained that the system has a unique globally asymptotically stable positive almost periodic solution. Finally, we study a multispecies predator-prey system with stage structure and Holling II type functional response.

第二部分考虑具有阶段结构的非自治扩散捕食系统，利用比较定理得到该系统持久生存的充分条件，其后在概周期情形下通过构造合适的Liapunov函数得到了保证该系统存在唯一一个全局渐近稳定的概周期解的条件。

Furthermore, the existing condition of stable controlling for another form of the system is studied and the sufficient condition of making a closed loop system asymptotically stable in local bound is also discussed.

然后，研究了另一形式的滞后离散广义双线性系统稳定控制存在的条件，并给出了使闭环系统局部渐近稳定的充分条件。

Here conditions (1) and (2) are each on their own necessary conditions for bachelorhood and together they are jointly sufficient for bachelorhood.

在这里，条件（1）和（2）各自是单身汉身份的必要条件，合起来构成单身汉身份的充分条件。

Unmarriedness and maleness are each individually necessary conditions for bachelorhood; together, these criteria represent a sufficient condition for bachelorhood.

未婚状态和男人身份，各自是单身汉身份的必要条件；放在一起，这两个条件就是单身汉身份的充分条件。

Furthermore, a conjecture about the stability of the multi-adding-point error model is presented and some corollaries of the conjecture are proved.

摘要提出多综合点误差模型及其孤立部分传递函数的概念，得到了所有孤立部分传递函数都正实的充分必要条件，以此为基础，给出了关于系统稳定性充分条件的一个猜想，并证明了猜想的一些推论。

Thischapter proposes three concepts,i.e.,kernelled quasidifferential,star-kerneland star-differential,and establishes their operational properties.A sufficiencytheorem and a sufficiency and necessity theorem for a quasi-kernel being a ker-nelled quasidifferential are proven.Both the existence of star-kernel for a qua-sidifferentiable function and the existence of star-differential for a directionallydifferentiable function are established.The relationships between sub-and su-per derivatives and Penot differentials are discussed as well.

这一章我们引入了三个概念，即核拟微分，星核与星微分并建立了它们的运算性质；证明了拟核为核拟微分的一个充分条件定理及一个充分与必要条件定理；建立了拟可微函数星核的存在性及方向可微函数星微分的存在性并讨论了Penot微分与上、下导数的关系。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。