渐近的

Under the appropriate assumptions, the asymptotic solutions of the problem with different forms are obtained according to the multiple number of the root of some equation, which is satisfied by the boundary value of the reduced problem, by giving the general expressions for the coefficients of outer solution expansion and the corresponding boundary conditions.

在适当的假设下，通过给出外部解展开式系数及其对应边界条件的一般表达式，根据退化问题的边值作为某方程的根的重数，得到了此问题不同形式的渐近解。

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。

The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .

通过Banach不动点原理和算子半群理论证明了方程解的存在性和唯一性，并证明了KS方程在给定的边界反馈条件下是全局指数稳定的及广义的KS方程在给定的边界反馈条件下是全局指数稳定和渐近稳定的。

In the case of NA samples, the parameter for scale exponential family is discussed using empi- rical Bayes methods. Moreover, we investigate the statistical analysis of life data in reliability tests. Firstly, based on the LINEX loss function, we obtain the empirical Bayesian estimator for parameter of the one-side truncated-type distribution families and the scale exponential family under NA samples, also discuss the estimators?

在非对称的LINEX损失函数下，我们首先给出了一类单边截断型分布族、刻度指数族参数的经验Bayes估计NA样本情形），并讨论了该估计的收敛性质，在某些条件下，证明了本文给出的经验Bayes估计是渐近最优的，且给出了收敛速度。

To our knowledge, this is the first work for the existence of periodic solutions for neutral systems by generalized Schaefer fixed point theorem of seperate contraction mapping.

第四章，讨论了两类依赖于参数的泛函微分系统，用锥上的Deimling不动点定理，证明了系统的正周期解的个数与参数的取值以及非线性项的渐近行为有关。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

The existence of global solutions of equations is the precondition to consider the asymptotic properties.

方程的整体解的存在性是考虑方程解的渐近性质的前提条件，线性增长条件是保证方程的整体解存在的最简单条件。

This paper deals with global existence and blow-up profiles for the solutions of some classes of reaction-di...

本文讨论几类反应扩散方程解的定性性质：具有局部源的初值问题和具有非局部源的初边值问题解的整体存在性和有限时刻爆破的条件，同时爆破，爆破集，爆破解的爆破率、渐近行为等。

By spectral analysis of the system, we find that 0 is the uniquespectral point of system on the imaginary axis.

同时通过研究系统算子的谱特征，证明了系统算子的谱点均位于复平面的左半平面且虚轴上除0外无谱，进而得到系统的渐近稳定性，特别在范数意义下系统的动态解收敛到稳态解。

In accordance with the acting mode of the actuator in aerospace control engineering,and based on infinite dimensional model of the system,a kind of simple and easily implemented variable structure control law is presented.

针对航天控制工程中执行机构的工作模式，基于系统的无穷维模型，本文设计了简单易行的变结构控制方案，并证明了相应的闭环系统的渐近稳定性。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。