多项式

Some new formulae for the derivative bounds of parametric curves, such as the general polynomial curves and rational polynomial curves in CAGD, are presented.

对CAGD中常见的多项式曲线和有理多项式曲线的导矢的界提出了新的估计公式。

Since an analytic function can be arbitrary approximated by a polynomial, the provided methods can be applied to robust stability analysis of polynomial family with general non-linear perturbation parameters.

由于非线性解析函数可用多项式任意逼近，故该方法也可用于具有一般非线性参数摄动的多项式族的鲁棒稳定性分析。

Also the constructed curve is a shape-preserving curve for the original curve. We can also adjust the shape of curves by parameters of trigonometric uniform polynomial curve to approach the polygon closer. The general trigonometric polynomial curves with m degree and C(superscript 2m-1)(m=1, 2, 3) continuity are further presented.

除了通过切点参数，还可以通过三角均匀多项式曲线参数来调整曲线形状，使所得曲线更加逼近多边形，并可进一步、类似地可构造与给定多边形相切的C(上标 2m-1)(m=1， 2， 3)连续的m次三角多项式曲线。

It's the first time that from the angle of computational mathematics combined with the structure model of parallel machine, the parallel degree of the relevant algorithms in orthopaedics clinic engineering modeling system, such as piecewise cubic Lagrange interpolation formula, piecewise cubic Hermite's interpolation formula, cubic spline, Chebyshev multinomial fitting algorithms, least square method and contour curve multinomial algorithms, were discussed.

论文首次从计算数学的角度并结合并行机的结构模式出发，讨论了在骨科临床工程造型系统中可能涉及的如分段三次拉格郎日插值公式、分段三次埃尔米特插值公式、三次样条函数、切比雪夫多项式拟合算法，最小二乘法以及轮廓曲线多项式求值算法的并行度。

Osculatory Rational interpolation is similar to the polynomial Hermite interpolation, and for binary Osculatory rational interpolation, Similar to polynomial interpolation formulas haven't appeared from now on.

切触有理插值是类似于多项式插值中的Hermite插值的一种插值，而对于二元切触有理插值，目前还没有构造出类多项式的插值公式。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

Consequently, a series of important topological indices such as σ-index(Merrifield-Simmons index), Clar number, the number of Kukule structures, and the first Herndon number are obtained.

给出了他们对应的独立集多项式和Clar覆盖多项式的简单显式表示，进而从中获得了一系列重要的拓扑指标：σ-指标(Merrifield-Simmons指标)，Clar数，Kekule结构数和第一Herndon数。

By comparing and analyzing, we think that using normal hyperbola function in multi-surface model is better than using inverse hyperbola function in multi-surface model, as i...

将该方法与传统的Taylor多项式、Legendre多项式和曲面函数建模方法进行了比较，表明该方法具有较高的精度和可靠性。

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。

This thesis is devoted to singular point quantities and integrability conditions of complex polynomial differential systems with resonant singular point, and center-focus determination and bifurcation of limit cycles of planar polynomial differential systems.

在第二章中，对具p∶-q共振奇点的复自治多项式微分系统引入广义奇点量的概念，它是文[103]中奇点量概念的推广，它以在实平面多项式微分系统的中心焦点判断与极限环分支中有着极为重要意义的焦点量和鞍点量作为特例。

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。