查询词典 asymptotic density

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。

This note is a revision and complement to [1]. The author proved that alonglower half of the curve C_1 in Fig. 11 of [1] not only m/a→∞ but also a→-∞,and that the upper half of C_1 has its asymptotic direction the straight linem=-2a. Thus, we have revised the original estimation, which stated that theupper half of C_1 has asymptotic direction m=-a.

本文是对文[1]的修正和补充，证明了沿着文[1]图11中的分岐曲线C_1的下半支应当由α→-∞，而它的上半支以直线m=-2α为渐近方向，从而修正了原来对C_1上半支以m=-α为渐近方向的结论，再利用文[1]中原有的知识也就修正了分歧曲线C_2~*的渐近方向。

The strong consistency, asymptotic normality and asymptotic efficiency of these methods are proved.

我们研究了这些方法的强相合性，渐近正态性和渐近有效性。

We discuss asymptotically best linear unbiased estimators of the Logistic population based on selected order statistics and give the formula of computing the ABLUE, the variance and the covariance of the ABLUE in limit, and properties of the ABLUE, and so on. We give the optimum chosen of spacing which is the ABLUE with maximum asymptotic relative efficiency based on complete sample when selected order statistics number is less than 10, and obtain its maximum asymptotic relative efficiency.

讨论基于Logistic总体Ⅱ型截尾样本的若干个样本分位数的总体分布参数的近似最佳线性无偏估计；给出了该近似最佳线性无偏估计的计算公式，估计方差与协方差的极限表达式及估计量的大样本性质等；给出了全样本，样本分位点个数固定，但不超过10情形下，使上述近似最佳线性无偏估计有最大相对联合估计效率时，样本分位数选取法及最大相对联合估计效率；为大样本情形下，该近似最佳线性无偏估计的应用提供了理论依据。

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric estimation and testing.

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：(bootstrap 和 jackknife方法)；稳健性；独立数据的估计，非参数估计和经验。

Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：（bootstrap 和 jackknife方法）；稳健性；独立数据的估计，非参数估计和经验。

STAT 581 Advanced Theory of Statistical Inference (3) Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability:; robustness; estimation for dependent data, nonparametric estimation and testing.

高级统计推断理论：极限理论，渐进方法，渐进有效和估计的效率，加大似然估高级统计推断理论：计，贝叶斯方法，泛函数的微商渐进性，基于样本的估计：(bootstrap 和 jackknife 方法)；稳健性；独立数据的估计，非参数估计和经验。

Basing on this, the formal asymptotic expansion of solution for the original problem is obtained. Finally, under suitable conditions, existence and its uniform validity of asymptotic expansion of solution for the initial boundary value problem are proved,by using theory of differential inequalities.

在这基础上得到了原问题解的形式渐近展开式；最后，在适当的条件假设下，利用微分不等式理论，证明了原初边值问题解的存在性及其渐近展开式的一致有效性。

Under a given assumption, the author of this paper obtained the uniformly powerful asymptotic expansion of M order and made an estimation of the remainder in asymptotic series.

研究拟线性双曲型方程柯西问题，在一定假设下，得到解的M阶一致有效的渐近展开式，并作出余项估计

In this paper the defect of the traditionary boundary layer methods (including the method of matched asymptotic expansions and the method of Visik-Lyusternik) is noted, from those methods we cannot construct the asymptotic expansion of boundary layer term really.

本文指出传统的边界层方法包括匹配法和Vi(？ik—Lyusternik方法的不足：不能作出边界层项的渐近展开式。提出多重尺度构造边界层项的方法，得到符合实情的结果。

Now she was hungry and angry.She began to smoulder.

现在她又饿又气，她开始流露难以抑制的怒火。

You have placed our iniquities before You, Our secret sins in the light of Your presence.

诗90：8 你将我们的罪孽摆在你面前、将我们的隐恶摆在你面光之中。