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The low value appears to be an asymptote; further reductions in toughness do not occur in thicker plates

低值看来是一个渐近值，在更厚的板中韧性值不会进一步减小。

When the errors meet certain requirements, the adaptive law based on the Lyapunov stability further adjusts the weights of networks to ensure the asymptotic convergence of the tracking error to be zero.

当误差满足一定要求时，根据Lyapunov稳定性理论的自适应律进一步调整网络权值，以保证机械手位置误差和速度跟踪误差渐近收敛于零。

Further more,we compute the asymptotic expansion of sums involving generalized harmonic number by singularity analysis method.

进一步地，利用奇异性分析方法，求出涉及广义调和数的一些和式的渐近展开。

By further discussing the asymptoticality of" medial point" for mean value theorem in some references, several new asymptotic estimation formula are obtained under weaker conditions, which unify and extend corresponding results in the references.

对文献中的"中间点"渐近性的有关结果作了进一步讨论，获得几个新的在更弱条件下的渐近估计式，从而在很大程度上推广了文献中的相应结果。

It is proved that, when the value of critical threshold less than 1, the disease free equilibrium point is globally asymptotically stable. Further more, Bursaphelenchtis Xylophilus is used to construct the Lyapunov function, and the stability theory of Lyapunov function is used to prove that the equilibrium point is Global asymptotic stable. It explains that the Bursaphelenchus Xylophilus wiil eventually disappear.

证明了当临界阈值小于1时，无病平衡点是局部渐近稳定的，进一步利用巴尔巴欣公式构造Lyapunov函数，运用Lyapunov稳定性理论证明了该平衡点的全局渐近稳定性，说明松材线虫病会最终消失；当临界阈值大于1时，病虫害平衡点是局部渐近稳定的。

Based on the simulation studies for different kinds of control modes and corresponding algorithms,the features,such as asymptotic of algorithm,the rate of convergence are discovered.Finally,some useful comments are given for further research.

通过对不同控制模式和与之相适应的滤波算法的仿真研究，揭示其算法收敛性和收敛速度等特性。

I hope to receive your further commands at an early date.

我们希望早日收到您的订单。

We hope to have your further order for serge at an early date.

我们希望早日收到您的哔叽订单。

The Contractor shall provide and make at his own expense any further copies required by him.

承包人所需的其余副本由他自己制作并承担费用。

The Contractor shall provide and make at hisown expense any further copies required by him.

承包方应当以自己的费用提供，制作自己额外要求的复印件。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。