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Three elements should be calculated in first-order circuit, which can synthesise analytical solution. Second-order series RLC and parallel RLC both can be calculated by the general function, which uses the Matlab to calculate differential equations. Generally, second-order and high-order circuits use Laplace transformation to formulate circuit equation, and get analytical solution by using Laplace inverse transform.

一阶电路先计算3要素，后合成解析结果；RLC串联和并联的二阶电路采用自编的通用函数计算，自编函数采用了Matlab求解微分方程的符号运算方法；一般的二阶电路和高阶电路采用拉氏变换列写电路方程，再用拉氏反变换得到解析结果。

At first, this paper surveys nonlinear control and the applications of neural networks in control respectively. Then it studies definitions, mathematical descriptions and conditions of invertibility for nonlinear systems, which are used to analyze the feasibility of inverse system control method. Conclusions about the feasibility of inverse control and the realizability of αth-order inverse systems in engineering are achieved. Furthermore, this paper discusses the feasibility, structure and identification of neural network αth-order inverse system for general single-input single-output continuous or discrete nonlinear systems and various composite control methods based on the αth-order inverse. At last, as a part work of an actual project, this paper focuses on the design of neural network αth-order inverse control method for thyristor controlled series compensation in power systems and its effect in improving the stability of power systems.

本文首先分别概述非线性系统的控制与人工神经网络在控制中的应用；然后研究非线性系统各种可逆性的定义、数学描述及可逆性条件，并用于分析逆系统控制方法的可行性，得出有关逆系统控制方法可行性的结论，阐明一般情况下α阶逆系统才工程可实现；接着本文针对一般单输入单输出连续、离散非线性系统，研究神经网络α阶逆系统的可行性、结构与辨识以及基于神经网络α阶逆系统的各种复合控制方法，并给出应用例子；最后本文结合实际项目，针对采用可控串补的电力系统，设计神经网络α阶逆系统控制方法，研究其对提高电力系统稳定性的作用。

The detailed comparisons between the higher—order near tip solution and the well—known modified Prandtl field are also given in this paper.For the compressible materials, in order to satisfy the higher-order compatibility equation of the rate of deformation in the centered fan sector, which is a quite difficult problem unresolved in the previous studies, a particular term must be added to the expansions of the stress components in the regular logarithmic power series adopted by many researchers before. A higher-order near tip field with tangential velocity jump ahead of the crack tip is derived first, of which the dominant terms are the solution widely accepted.

对可压缩材料，本文首先采用非规则的对数幂级数渐近展开方法，克服了过去研究中存在的中心扇形区变形率协调方程的高次渐近式不能被满足的困难，并得到了一个切向速度在裂尖前方存在间断的高阶渐近解，该解的主项就是目前被广泛接受的关于可压缩材料的尖端场解。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

As a result of conservative perturbations, the first order Melnikov function for a perturbed system is identically equal to zero, so the second order Melnikov function has to be considered. The perturbation parameters which make no use in the first order Melnikov function may be important in the second order Melnikov function.

此时一阶Melnikov函数恒等于零，必须考虑二阶Melnikov函数，而在一阶Melnikov函数中不起作用的扰动参数在二阶Melnikov函数中却起着非常重要的作用，因此扰动部分极为复杂。

By analyzing the theory of higher order cummulants and higher order spectrum ,the methods of machine fault feature extraction are researched based on higher order spectral analysis by using the character that higher order spectrum can restrain the gauss noise.

在分析高阶累积量与高阶谱的理论基础上，利用高阶谱可以抑制加性高斯噪声的性质，研究了基于高阶谱分析的机械故障特征提取方法，提出了基于双谱估计的齿轮故障诊断的方法。

Trilemma effect is an important criteria for the self-convergence deflection system.The influence of the higher order Trilemma effect should be taken into account for the correction of the higher-order deflection aberrations.In this paper,when up to the seventh-order Trilemma constants are adjusted,the expression of the influence of 2n-pole multipole field on n-th order Trilemma constant has been deduced and this influence has been calculated.

Trilemma效应［1，2］是在彩色显像管中应用自会聚偏转系统对偏转像差校正时所必须考虑的一个重要问题，在大偏转角下对高级偏转像差的校正必须考虑高阶Trilemma效应的影响，文献［3］应用多极场偏转像差校正理论［4，5，6］，采用区域分割的方法，对直至七阶的Trilemma效应进行了分析，在文献［3］中对Trilemma效应分析时，用到了下面的近似

The total war regime was built to mobalize political, economic, and thought forces to conduct expansive warfares in East Asia in order to change existent regional order that was dominated by West imperial states. Subsequently the statism turned into ultranationalism that ambitiously created Great East Asia Co-prosperity Circle and a new metropolitan Japan-colony-new occupied territory order to solve Japan's dilemma of modernization. The state highly penetrated society during this period. Nevertheless, the defeat of the Pacific War set the demise of ultranationalism and terminated the Japan-center regional order; thirdly, democratization and non-militarization after WWII made Japan a U.S. ally in the west Pacific. Incrementally the revitalization of Keiretsu and civil society shrank the clout of the state to shape national identity. The rise of civic-nationalism became the focal point to understand post-war nationalistic movements.

这种国家主义的统合方式扩大了国家机关对於社会的渗入，也强化了「帝国臣民」的实质意义，然而，随著太平洋战争的毁灭性战败，终止了国家主义扩张的限度；第三，第二次世界大战以后，军事上日本在美国占领下纳入西太平洋安全体系，经济上日本企业走向国际化，使得国家对於国民认同的影响松动，以国民为主体的认同形成成为理解日本战后国民认同的主要途径，由冷战结构下，非官方、建构性、民主的「国民主义」到一九八○年代以后的新国家主义，展现了历史结构下进步与保守两种国民认同的辩证。

The conclusion is drawn through analyze and comparison between the solutions of zero and first order, second and first order that the particle drifts in the vertical direction of the magnetic field and its crosswise gradient in the approximation of first order. While the particle makes superimposed circle movement of uniform velocity in the approximation of second order.

通过分析比较1阶近似解与0阶近似解；2阶近似解与1阶近似解，得出由于1阶近似而引起粒子在与磁场方向以及磁场横向梯度方向垂直的方向发生漂移；由于2阶近似使得粒子在xy平面内做12W、3W、4W、5W、6W叠加的匀速圆周运动。

The solution of zero order is taken into the first order approximate of equation of motion. Then we make the equation linearization to get the solution of first order. So is way to obtain the solution of second order.

均匀、恒定解作为0阶解代入1阶近似运动方程，使之线性化，求出1阶近似解，同理将1阶解代入2阶近似运动方程，使其线性化，求出2阶近似解。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？