多项式

The basic steps of this method are as follows.The firststep is to derive a necessary condition such that the families of quasipolynomials withone parameter,corresponding to the edges of the polytope,have pure imaginary rootsby using the Dixon's resultant for polynomials.Then to check that the casescorresponding to the parameters obtained in the first step are in fact impossible byusing the generalized Sturm criterion and some stability criteria.

其基本思路是先利用多项式方程组的Dixon结式理论导出使各棱边对应的单参数特征拟多项式有纯虚根时，参数值应满足的一个等式条件，即所谓的Dixon结式等于零，然后由广义Sturm判别法验证对所有参数值，Dixon结式不等于零，或使结式等于零的解不产生特征拟多项式的纯虚根。

A bstract: This paper focus on virtual instrument design of modal parameters identification with curve fitting theory based on rational fraction orthogonal polynomials. Using Forsythe orthogonal polynomials solves the coefficient equation instead of normal power polynomials in order to decrease the morbidity of it, making the orders of coefficient equation reduce to half and increasing computing efficiency.

本文基于有理分式正交多项式曲线拟合理论对振动系统的模态参数辨识进行了虚拟仪器的设计，为了减少系数矩阵的病态，采用 Forsythe 正交多项式代替普通的幂多项式进行求解，使系数矩阵阶次降低近一半，提高了运算速度。

According to the first and second references, a sufficiency and necessity condition on rational root of integral coefficients polynomial is put forward and a reduced method of testing the rational root is also shown in this paper.

摘要给出了整系数多项式有理根的一个必要条件，从而得到整系数多项式有理根检验的一个简化方法，达到了简化整系数多项式有理根检验的目的。

Jacobian Davis iterative method of solving equations AX = B, least squares polynomial fitting, portfolio Simpson formula for integration, with a triangular decomposition method of solving equations AX = B.

拉格朗日插值多项式拟合，牛顿插值多项式，欧拉方程解偏微分方程，使用极限微分求解导数，微分方程组的N=4龙格库塔解法，雅可比爹迭代法解方程AX=B，最小二乘多项式拟合，组合辛普生公式求解积分，用三角分解法解方程

A kind of blending functions with shape parameters is constructed based on trigonometric polynomial functions. Then the method of generating trigonometric polynomial Coons patch is discussed.

给出一类含参数的三角多项式混合函数，在此基础上构造一类三角多项式混合Coons曲面片，提出带形状参数的双三次三角多项式Coons曲面片的表达式。

In order to make up the deficiency of ordinary trigonometric polynomial curves in aspect of shape adjustment, then in view of polynomial spline cannot represent some transcendental curves, a new kind of parametric trigonometric polynomial spline with a shape parameter is constructed by linear singular blending technique.

为了弥补普通三角多项式样条曲线在形状调整方面的不足，同时又考虑到多项式样条曲线不能精确表示一些超越曲线，我们利用奇异混合的思想构造了一种新的带有形状控制参数的三角多项式样条曲线。

Babai, a more accurate estimate vector can be obtained and the coefficients of the multiple polynomial of the interpolation polynomial can be computed.

利用L.Babai最近向量格归约算法得到更精确的估计向量，再计算出插值多项式的倍数多项式的系数，从而计算出原插值多项式的系数。

We analyze formers centers conditions for polynomial Lienard equations, give direct conditions of a nondegenerate center at the origin with elimination theory, and give an algorithm for general situations with algebraic elimination methods of polynomials.

运用多项式的代数消元法，对前人给出的多项式Liénard方程的中心判据进行分析，对多项式的系数给出原点是非退化中心的直接条件，并对较一般的情形给出算法。

Since every computation that can be done in logarithmic space can also be done in polynomial time it follows that if there is a logarithmic-space many-one reduction then there is also a polynomial - time many-one reduction.

若我们提供一个副函式可以在多项式时间解出&Y&，'''又'''可写出呼叫此副函式的程式并在多项式时间解出问题&X&，代表我们可以将&X&多项式时间图灵变换成&Y&。

As an application,generating quasi arc-length parameterization of PH curves is also discussed.

在CAGD中，曲线曲面一般用多项式或有理多项式表示，因此求解多项式函数的反函数是CAGD中的一个基本问题，它在曲线的准弧长参数化、曲线隐式化、曲线求交等问题中都有非常重要的作用[1-2]。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失