查询词典 polynomial equation

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

Compared with the traditional Euclidean algorithm, the proposed algorithm can easily get error value polynomial and error locator polynomial in the process of solving key equation. Moreover, it can simplify the complexity of hardware circuit and improve decoding speed.

与传统欧几里德算法相比，该算法在求解关键方程的过程中能够较容易地得到错误值多项式和错误位置多项式，从而可以减少硬件电路的复杂性，提高译码速度。

Compared with the traditional Euclidean algorithm, the proposed algorithm can easily get error value polynomial and error locator polynomial in the process of solving the key equation. Moreover, it can simplify the complexity of hardware circuit and improve RS decoding speed.

与传统欧几里德算法相比，该算法在求解关键方程的过程中能够更方便地得到错误值多项式和错误位置多项式，并且能够减少硬件电路的复杂性，提高RS码的译码速度。

Orthogonal polynomials with weight equaling 1 are used to make least square approximation, so morbidity phenomenon in solving equation is avoided and better results can be obtained. Advantages and disadvantages of Legendre polynomial and Gram-Schmidt polynomial are also discussed.

比较了Legendre多项式和Gram-Schmidt正交化构造的多项式在处理时间漂移方面的优缺点，并介绍了通过随机误差的平稳性来检验处理结果优劣。

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

As long as the system of first order polynomial DDEs in (1+1)-dimensions is given, no matter whether a single equation or the coupled equation, CLawDDEs can automatically output the scaling symmetries of the variables and a series of possible polynomial conservation laws for different rank.

只要输入多项式形式的等秩DDE，无论是单个方程还是耦合方程组，CLawDDEs都能自动确定变量的标度变换特性和不同秩的多项式守恒律。

Then we establish a polynomial equation representing the relation between the distance of CCD apart from human face and the gap of human eyes in the CCD image through a set of experimental data.

最后是探讨CCD拍摄的不确定性，对影像量测工作可能造成的影响，并藉由统计的方式计算拍摄不确定性的范围，以调整齿轮尺寸的公差，提高量测的可信度及检验的准确度。

An approximation method is presented. Through the use of the Taylor expansion in the vicinity of the scatterer,the problem is directly reduced to the solution of a polynomial equation which is simpler to treat.

给出了一种反演方法，通过在散射域附近Taylor展式的应用，使得问题直接转化为易为处理的多项式方程的求解。

We propose a new algorithm for a sample and all Nash equilibria by using heuristic search in game supports and the solution techniques of polynomial equation systems.

摘要应用搜索博弈支持集和方程组求解技术，提出了一个计算单一和全部纳什均衡点的启发搜索方法。

For a series spatial and planar mechanism synthesis, synthetic equation set can be established according to the kinematics requirement and characters of the mechanism. Then trigonometric functions are rationalized so as to create a polynomial system =0 , and the polynomial solution=0 is obtained with synthetic elimination method.

对于平面机构与空间机构的各类综合问题，根据各种机构的运动综合要求和机构的特点，建立机构的综合方程组，然后通过三角函数的有理化，将综合方程组化成多项式方程组=0，并采用综合消元法求得其多项式解=0，进而求得待定的机构参数。

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。