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With the help of asymmetric parameter, the mechanism of regime against different shocks is analyzed.

借助模型的不对称参数，分析了不同性质冲击下的不同机制。

Particle Swarm Optimization is adopted to detect parameter pattern e.g. circle, ellipse, hyperbola and asymptote.

我们采用一种以粒子群演算法Particle Swarm Optimization 为基础的方法，用来侦测一张影像上的参数图形(如：圆、椭圆、双曲线与双曲线的渐近线)的参数。

In addition, the least squares estimator of unknown parameter is constructed, and its asymptotic behavior is proved.

另外也构造了未知参数的最小二乘估计量，并证明了它的渐近性质。

By a-priori choice of the regularization parameter respectively, the optimum asymptotic convergence order of the regularized solution is obtained.

给出了正则参数的先验选取，并通过正则参数的先验选取证明了正则解的误差具有渐进最优阶。

Algorithm application of neural networks.Ⅲ Implementation of neuro-computers. The main contribution of the dissertation can be summarized as follows: 1 Hopf bifurcation of three kind of neural networks are discussed in detail, including type of discrete time delay, type of time delay with weak kernel and strong kernel as well as the proof of existence of bifurcation. Other problems such as asymptotic stability of bifurcation periodic solution, algorithm of determining the bifurcation direction, asymptotic stability and style of periodic solution are also studied. The average time delay is chosen as the bifurcation parameter, phenomena pertinent to system states of the continuous time delay network with strong kernel evolving from stable to oscillating, then back to stable again are observed.

论文的主要创新之处可以归纳如下： 1）针对目前国内外对神经网络的分岔研究较少的情况，论文中详细讨论了带离散时延神经网络、带弱核的连续时延神经网络、带连续分布时延且具有强核的神经网络的Hopf分岔现象，从理论上证明了Hopf分岔的存在性，并研究了分岔周期解的渐近稳定性，得到了确定周期解的渐近稳定性、分岔方向、周期解的渐近形式的算法；用平均时延作为分岔参数，发现带强核的连续时延神经网络中存在着系统的状态由稳定变化到振荡现象，当继续增加平均时延参数时，又从振荡变为稳定这一特殊的动力学现象。

S data, and get the parameter estimate of ARMA noise by Hannan-Rissanen s linear procedure, then the estimate is of strong consistency and is of asymptotic normal efficiency for Gaussian series.

若用所计算得到的回归残差作为数据，采用Hannan-Rissanen的线性估计法求ARMA噪声的参数估计，则本文证明了估计是强相容的，且对正态序列，估计具有渐近正态优效性。

Describes general methods of point and interval parameter estimation and the small and large sample properties of estimators: method of moments, maximum likelihood, unbiased estimation, Rao-Blackwell and Lehmann-Scheffe theorems, information inequality, asymptotic relative efficiency of estimators.

点估计和区间估计的一般方法，估计量的小样本和大样本性质：矩法，极大似然估计，无偏估计，Rao-Blackwell 和 Lehmann-Scheffe 理论，信息不等式，渐进相对有效估计量。

The basic equations are expanded in asymptotic linear equations of each order according to small parameter of incident wave's field by perturbation method.

近年来随着计算技术的发展，有限元等数值法已广泛应用于波与结构相互作用'的计算分析。

Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third order asymptotic expressions for the Lagrangian particle trajectories and the period of particle motion can be derived directly in Lagrangian form.

藉由一系列连续的Taylor级数展开，於考量波动场中各流体质点之运动轨迹与运动周期下，将已知的Eulerian解转换成完全未知的Lagrangian形式解。

The wave number is expanded into asymptotic series in terms of a small parameter. This method is exact and can approach any accuracy desired.

这一方法本身是精确的，它能达到任意所需的精度，然而四层和五层波导结构的数值计算实例表明，仅二阶近似解就足够精确了。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新