收敛域

Firstly, convergence condition of a binomial is discussed, and along with the calculating formula of region of convergence, the matching band of fractance circuit attained by binomial expansion method is indicated definitely.

首先讨论了二项式的收敛条件，并结合收敛域的计算公式，明确指出使用二项展开法所得到的分抗电路的逼近带范围。

The techniques of computing the domain of convergence and sum function and expanding functions in several variables to power series of functions in several variables are mainly discussed by many examples.

引入了多元函数项级数的概念，给出了其收敛域及和函数的定义；通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法。

For a long time, it is a main factor to hamper the real-time application of SHET. The research is carried on aiming to quickening convergence speed. The automatic-changing Homotopy algorithm is proposed in the dissertation. The algorithm, which can change the solving method based on fundamental component, has the advantages of large convergence domain, high convergence rate and high precision. Many trigonometric functions are contained in the mathematical model, during solving equation, the calculated speed and the precision are affected by the calculations of trigonometric functions.

特定谐波消除技术的数学模型是一组非线性方程组，长期以来，方程的求解一直是限制该技术实时应用的关键因素，本文针对特定消谐方程组的快速求解进行细致的研究，提出自动变同伦算法，该算法可根据基波幅值的取值范围来决定采用的求解方法，其对求解方法的可选择性使该算法与其它算法相比具有计算速度快、收敛域宽、计算精度高等优点。

But it is a hard task to solve this equation, one reason is that the TV-norm is nondifferentiable when |▽_u|= 0, so we cant apply a linearizationtechnique such as the Newton method. The other reason is that the Euler-Lagrange equation has a highly nonlinear term. The Newton method for such equation is known to have a very small domain of convergence, and it is very difficult to make sure that the initial value such as the observed image belongs to this domain. So the Newton method is not an ideal method for solving this equation.

但是求解它比较困难，主要是因为TV-范数在|▽u|=0处不可微，不能用诸如牛顿法之类的方法将其线性化；且Euler-Lagrange方程含有一个高度非线性的项，牛顿法只有局部收敛性，对于高度非线性问题它的收敛域很小，因此难以保证所取的初始点在它的收敛域内，故一般不用牛顿法直接求解。

Property 2 (Term-by-Term Integration) Suppose that is the sum of a power series on interval ;that is,Then, if is interior to ,and the radius of convergence of the integrated series is the same as for the orginal series.

性质 2 幂级数的和函数在其收敛域上可积，并有逐项积分公式，，逐项积分后所得到的幂级数和原级数有相同的收敛半径。

In accordance with discrete, non-symmetry and time-delay feedback neural networks, we provide some theoretical criteria to judge the stability for designing the networks. On continuous feedback networks, we built an algorithm to estimate the convergence region. On the HNN feedback networks, an effective optimization algorithm based on the annealing strategy and the chaotic neural network is presented, and some disciplinary conclusions are provided to guide the selection of parameters. Simulation results on benchmark problems demonstrate that the performances of our algorithm are distinctly superior to those of the classic HNN based on gradient descend and stochastic optimization methods based on probabilistic distribution.

针对离散、非对称和时延等三种类型的动态反馈网络，给出了可用于网络设计的稳定性判别准则；针对连续动态反馈网络，建立了其收敛域估计的一个算法；针对以HNN模型描述的动态反馈网络，基于退火策略和混沌神经网络提出了一种高效的优化算法，建立了可用于指导参数选择的一些规律性结论，对典型算例的仿真研究显示，改进算法在各类性能上相对基于梯度下降的传统HNN模型和基于概率分布的随机优化算法，具有明显的优越性。

Leading resistant factor into the necessary condition can also enlarge the quadratic convergence region near optimal solution so that it is very efficient to use the known flash calculations at one condition to iteratively compute another optimal solution at other conditions where pressure, temperature and mole fractions of components are close to known ones respectively.

在极值必要条件式中引入阻尼因子能扩大真解附近的平方收敛域，尤其在利用已知条件下的汽液平衡结果作初值直接用极值条件方程迭代计算压力、温度和组成变化不严重的相邻点的汽液平衡极值解方面效果十分显著，适合于加快组分模型的计算速度。

A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.

文摘：用比较直接的方法证明幂级数的和函数在收敛域内可以逐项微分的公式；并得到了计算傅立叶系数的一种简便方法。

In this method, an interim variable is defined by combining one variable of each subsystem. The interim variable is used to construct the sliding-mode function and the total control law can be derived to guarantee the equilibrium point is reachable in finite time. Using LaSalle invariance theorem, it can be proved further that the equilibrium field only includes one equilibrium point and the equilibrium point is asymptotically stable.

该方法将各个子系统的一个变量进行组合定义成一个中间变量，然后从这个中间变量出发构造滑模函数，通过求取总的控制量保证中间变量在有限时间内收敛到平衡点；进一步利用LaSalle不变性原理证明该收敛域内只有一个平衡点且是渐近稳定的。

The linear segment, convergent area, convergent time and accuracy of clutter-lock in imagery domain are analysed in detail.

对图像域杂波锁定的线性段、收敛域、收敛速度和估计精度进行了细致的讨论。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。