多项式方程

From the theory, the algorithm for determination of the degree of implicit polynomials is followed: detecting the stationary points in the object boundary based on its features, and then calculating the minimum degree according to the formula derived from the theorem. In addition, the theory can be extended to three-dimensional object.

该方法首先由给定物体边界的轮廓检测出其驻点数，然后根据驻点数得到拟合隐含多项式曲线方程次数的下界，进而推广到三维物体的隐含多项式曲面拟合次数的确定。

The model was solved by the Ritz method, and the orthogonal polynomials generated by the Gram-Schmidt process were employed as admissible function for both disk and blades. With this approach, the matrix derived from kinetic energies becomes diagonal and numerical manipulation can become easy and stable.

采用Gram-Schmidt方法生成正交多项式作为李兹容许函数进行模型的离散化，简化了所得到的频率方程求解过程，有利於求解过程的数值稳定性，并可方便地通过对方程系数性质的分析了解结构振动模态的性质。

For some special cases, the paper gives some important identical theorems, and then establishes a valuable relation between the uniformly almost periodic functions and the trigonometric polynomials.Secondly, on the basis of the identical theorem, the paper investigates the Fourier series of the uniformly B2 almost periodic functions, and further proves that the series is unique.Thirdly, the paper discusses the Parseval equation of the uniformly B2 almost periodic functions, which establishes the relation between these functions and the coefficients of their Fourier series; and next investigates an important approximation theorem-Riesc-Fischer theorem, about the uniformly B2 almost periodic functions and the trigonometric polynomials.

并给出了特殊情况下的几个重要的恒同定理，将一致概周期函数与有限三角多项式联系起来；第二，在恒同定理的基础上，给出了一致B~2概周期函数的Fourier级数，并且级数是唯一的；第三，讨论了一致B~2概周期函数的Parseval方程，建立了函数与其Fourier级数的系数之间的联系；接着给出了关于一致B~2概周期函数和三角多项式之间的一个重要近似定理—Riesc-Fischer定理。

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。

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves.The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value,and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor.Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle...

基于Stroh公式和表面阻抗张量理论，提出了研究界面滑移波动态失稳问题的一种新的方法·该方法将表面阻抗张量概念推广到复波速域，并将摩擦接触界面上的边界条件以表面阻抗张量表示·最终将边值问题化归为求解一个复多项式在单位圆内的根·以弹性半空间与刚体平面相对稳态摩擦滑移为例进行了详细的分析，导出了一个4次复特征方程并讨论了方程在单位圆内解的特性，给出了滑移界面波失稳条件的显式解析表达式

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

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。

A new method of wavefront fitting based on regression analysis of normal equation is proposed using Zernike polynomial s.

介绍了一种干涉波面的Zernike多项式拟合方法，该方法从构造的正规方程入手并对其进行逐步回归分析，从众多的Zernike多项式模式中选取影响显著的模式。

We get a class of refinable distributions which have localpolynomial property and are globally linear independent but are locally lineardependent,So that when M＞N,the Daubechies type scaling functions〓have localpolynomial properties and are globally linear independent but locally lineardependent.

给出了一类细分方程，它们的解具有局部多项式性质并且它们是整体线性无关的但是它们是局部线性相关的。从而得到了当〓时，Daubechies型尺度函数〓具有局部多项式性质并且它们是整体线性无关的但是它们是局部线性相关的。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。