渐近的

To make our approach to be practical, we also discuss the asymptotic expansion of the operator in chapter 6 which is based on the non-abelian Stokes theorem.

但是由于格点上的算符是path-order变量的乘积，并且其构成非常复杂，按照正常的方式展开实际上是不可能的，为了使我们的算法实际可行，本文接着讨论了格点上算符的渐近展开问题，并且给出了基于non-abelStokes定理的方法，这种方法克服了以前各种办法的缺点，并且简单可行，适用于任意的Wilson算符。

Thus the universal nature of frac-tal structures in the weak interactions of solitary waves is analytically established. Tounderstand the fractal regime further, using asymptotic methods along separatrix orbits,a simple second-order map is derived.

为了更深入的理解分形出现的机制，沿着separatrix轨道运用渐近分析，我们得到一个简单的二阶映射，这个映射描述了动力学方程中动量的变化关系，经过变量变换以后，它不含任何参数，因此对于广义非线性Schro¨dinger方程中孤立波的弱相互作用都是成立的。

He wore a brand-new uniform with the creases still in it where it had been folded, and rich gold epaulettes, which seemed to stand up instead of lying down on his thick shoulders.

这个团长是个易于激动的、须眉均已苍白的渐近老境的将军，他体格结实，胸背之间的宽度大于左右两肩之间的宽度。

Based on the above result, we reveal that the asymptotic behavior of solutions of nonlinear atmospheric system with forcing and dissipation shows itself on the structure of attractor, and that the system has nonlinear adjustment process to the external forcing and the characteristic of decay of effect of initial field.

从而揭示出强迫耗散的非线性大气系统解的渐近行为表现在吸引子的结构上、系统具有向外源强迫的非线性适应过程和初始场作用衰减的特征。

Consistency and asymptotic normality of the proposed quantile estimators are established under mild conditions, allowing for global misspecification of parametric copulas and marginals, and without assuming any mixing rate condition.

一致性和建议的分位数估计的渐近正态性温和的条件下成立，让全球误设的参数Copula函数和边缘人，没有担任任何混合率的条件。

Consistency andasymptotic normality of the proposed quantile estimators are establishedunder mild conditions, allowing for global misspecification of parametriccopulas and marginals, and without assuming any mixing rate condition.

一致性和建议的分位数估计的渐近正态性温和的条件下成立，让全球误设的参数Copula函数和边缘人，没有担任任何混合率的条件。

A nonlinear adaptive speed controller based on adaptive backstepping approach for permanent magnet synchronous motors with nonlinear coupling and parameter uncertainties is presented. With the preposed controller, the parameter uncertainties are compensated and high performance speed controller for permanent magnet synchronous motors is shown to be globally asymptotically stable. The scheme is robust to the parameter uncertainties and load torque disturbance.

针对永磁同步电动机系统的非线性耦合特性以及参数的不确定性，采用自适应反步控制实现永磁同步电动机的非线性控制，在补偿参数不确定性影响，提高系统的抗干扰能力的同时，实现了永磁同步电动机的高性能全局渐近稳定速度跟踪控制。

Firstly, based on the sliding mode control and backstepping technique, a new attitude tracking controller is derived to control the attitude motion of spacecraft, the stability of the system is analyzed via Lyapunov method and the reaction wheel dynamics is also considered from the real applications point of view. The whole design process is divided into two steps: the first step is to use sliding control technique to design suppositional adaptive variable structure controller; and the second step is to design attitude tracking controller based on SMC and backstepping technique. Numerical simulations are performed to show that both tracking maneuver and vibration suppression can be accomplished effectively.

首先，采用自适应后步法结合主动振动控制技术设计了姿态跟踪鲁棒控制器，基于Lyapunov方法分析了系统的渐近稳定性；在此基础上，显性地考虑了执行机构动态特性问题，将整个设计过程分为两个步骤：第一步采用滑模控制技术设计了变结构虚拟控制器，给出自适应控制律的设计方法；第二步，将后步法与滑模控制技术相结合，设计了姿态跟踪鲁棒控制器，给出飞轮电压的输入算法及稳定性分析；最后，将提出的控制方法应用于挠性航天器的姿态跟踪控制，通过数值仿真对所提方法的可行性与有效性进行分析和验证。

Finally, the adaptive control strategy of active balancing for a strictly positive and real rotor with actuator saturation is successfully extended to a flexible rotor with single collocated plane and actuator saturation and a flexible rotor with multiple collocated planes and actuator saturation. A series of numerical simulations show that the proposed adaptive control law can evidently reduce the original imbalance-induced vibration of these rotors and the actuator movement asymptotically approaches to its target value, the opposite of the original imbalance.

最后，把提出的自适应控制策略成功地推广到带作动器饱和、单并置平面的柔性转子和带作动器饱和、多并置平面的柔性转子，一系列数值模拟显示：该控制律能显著减小这些转子原始不平衡引起的振动，作动器的移动能渐近收敛到与原始不平衡相反的目标值。

Then, aerodynamic parameters in different flight conditions are used to imitate the uncertainty of the system, and the digital simulation of closed-loop system designed is performed. The results show that the system can accomplish asymptotic decoupling of roll angle, sideslip angle and head-on angle for aircraft, and the system is provided with the function for restraining uncertainty in the system. This illustrates that the flight control system designed has not only good decoupling characteristic, but also better robustness.

然后用不同飞行条件下的空气动力参数变化来模拟系统的不确定性，并进行闭环系统数字仿真，结果表明，所设计的控制律不仅可实现对飞机滚转角、侧滑角、迎角等的渐近解耦控制，而且对系统不确定性具有较强的抑制作用，说明系统具有较好的解耦性和较强的鲁棒性。

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。