充分条件

We first show some properties of such operators and give an explit description about the image of a linear bounded operator on a linear normed space. Then based on these results, we show the mean ergordic theorem on a C*-bial-gebra and get a sufficient and necessary condition for a linear functional to be Haar measure. Finally we discuss the sufficent conditions for the existence of Haar measure on C*-bialgebras.

本文首先通过考察这样算子的性质和刻画赋范线性空间中连续线性算子的像集的性质，证明了C*－双代数中的一个平均遮历定理，得到了C*－双代数中的线性泛函是 Haar 测度的充分必要条件；利用遍历定理和这个充分必要条件探讨了C*－双代数中 Haar 浏度存在的一些充分条件。

The switching law is given out according to convex combination condition and the sufficient condition of the stabilization is obtained by switching among a finite number of controllers under the assumption that a single controller cannot make the systems stable and has H-infinity disturbance attenuation.

在假定每个单一的控制器均不能使系统稳定且具有H扰动衰减度的条件下，利用凸组合条件给出了切换律的设计方案，通过在有限个控制器间的切换得到了镇定的充分条件。

A sufficient condition is firstly established such that a nonsymmetric saddle point matrix is diagonalizable with real and positive eigenvalues.

首先给出使得非对称鞍点矩阵具有实正特征值且可对角化的充分条件，该条件比已有著名条件更弱。

Furthermore, based on the ergodic theory of Markov process we analyze the stationary distribution of network residual series, and prove the efficient conditions under which the unique asymptotic stationary distribution exists.

同时，根据马氏过程的遍历理论，对网络输出残差的平稳条件进行了研究，证明了网络输出平稳残差的充分条件，给出了残差序列存在唯一的渐近平稳分布的条件。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

In Chapters 3 and 4, we investigate the existence of periodic solutions of a class of second order functional differential equation and a class of third order functional differential equation, respectively, and obtain new sufficient conditions of their existence result of periodic solutions under growth conditions and linear growth condition, respectively. Compared with some known results in the literature, the equations discussed by us are more general, and our results are concise and easy to be verified.

第三章与第四章分别研究了一类二阶泛函微分方程及一类三阶泛函微分方程的周期解存在性，分别在增长条件及线性增长条件下，获得了这两类方程周期解存在性的新的充分条件，与文献中已知结果比较，我们所讨论的方程更为一般，所得结果较简洁且易于验证。

Under the conditions that the system without impulse effect satisfies the one-side Lipschitz condition, and the impulsive terms satisfy the corresponding Lipschitz conditions, a sufficient condition which can be easily checked the stability of the analytic solution is obtained.

在不受脉冲影响的原方程满足单边Lipschitz条件，及脉冲项满足相应的Lipschitz条件的情况下，给出了一个容易判别的解析解渐近稳定的充分条件。

The result showed that,if only the necessary but insufficient condition,the equilibrium condition ,was adopted to deal with the infinite uncertain boundary condition,the solution to the stress was non-unique due to the fact that the boundary problem here was a mal posed mathematic problem.

通过两个典型的半无限体实例，对水平表面作用无限均布压力下弹性地基的应力和位移解答进行研究，结果表明：对边界条件不明确的无限边界仅采用解答的必要非充分条件——平衡条件来等效处理，其应力解答不是唯一的，因为此时该边值问题不是一个适定的数学问题。

We prove that the well limit behavior can be used to get sufficient conditions for an infinite object to be limit decidable.

本文发现了统一的充分条件保证可以使用极限判定方法，这一充分条件正是形式系统序列的良极限行为。

Again, for antiquarians (I include myself in this harmless avocation), Morishima provides as a Class B theorem his useful generalization of my equal-internal-composition sufficiency condition to a wider "linear dependence" sufficiency condition.

再次，对于文献研究者（包括我自己也有这个无害的嗜好），作为等级B定理森岛通夫为他关于我的相同内部构成的充分条件到更广的&线性相关&的有用的总结提供了充分条件。

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。