本文引进了一个新的记号，研究色多项式的根全为非负整数的图的色性。
In this paper, a new character is used. When all roots of chromatic polynomials of graphs are not minus integers, the author studies the chromaticity of them.
这些代数条件表示为由椭圆与抛物线，椭圆与双曲线确定的广义特征多项式的根的分布。
The algebraic condition can be represented by the distribution of the roots of the generalized characteristic equation of the ellipse and parabola (hyperbola).
可以利用多项式的根在复平面上的分布构造用于迭代的计算式，使能够对生成图形进行预先设计。
The formulas that used in the iterative procedure are build by means of the distribution of the roots of polynomial equation on the plane, and therefore the generating images are designed in advance.
本文证明了球面有限点集的伪对称性可以完全由其特征多项式的根来刻画，并得到了在度量加运算下伪对称性具有封闭性。
In this paper, we show that the Pseudo-Symmetric property of spherical point set can be characterized by the eigen values of eigenpolynomial and it has the closeness under the metric sum operation.
这种方法能够保证辨识出的参数是最佳的；而且不用求解对应的非线性最小二乘问题，只需求一元多项式的根，从而大大减少计算量。
This approach can guarantee that the identified parameters are optimal, by solving a one-dimensional polynomial equation instead of a nonlinear least square problem.
研究两个多项式的根的相对分布的显式判定问题，得出两个三次多项式的根的相对分布以及二次和四次多项式的根的相对分布的显式判定。
We obtain the relative distribution of roots of two polynomials whose degrees are respectively 2 and 4, and we answer the same problem about the two polynomials of degree 3.
利用匹配多项式根的信息，根据其定义以及图的度序列和匹配多项式的性质推导。
Use the information of the matching roots, and the character of the degree sequence and matching polynomials to compute.
较程序化地给出了实系数多项式函数实数根的求法。
Methods of exploring the real number roots of a real coefficient polynomial function are procedurally given.
由于伴随多项式系数的特点，决定了它的根具有特殊性。
Since the characteristic of its coefficient, adjoint polynomials'roots has some specific property.
考察了除环上的l多项式的左因式、左根与左倍式的性质，给出了导数与左结矩阵的应用。
Left factors, left multiples and left roots of the polynomials over sfield are studed. Applications of derivative and left relative matrices are given.
本文通过几个例子介绍了三次单位根在复数计算、证明与多项式整除中的应用。
This paper, by examples, introduces the application of triple root in the calculation and proof of complex number, and exact division in multinomial.
本文讨论了具有一个零特征根的非线性齐次系统的局部拓扑结构，并给出利用系统右端多项式系数的判断准则。
In this paper, we discuss the locally topological structures of nonlinear homogeneous systems with one zero characteristic root, and give a criteria by the right-hand polynomial coefficients.
本文提出一种确定特征多项式的全部根是否位于左半平面的迭代法。
In this paper, we present an iterative method for determining whether all roots of characteristic polynomial are on the left half-plane.
本文在复数域上证明了哈密尔顿-凯莱定理，并给出方阵A的特征多项式的全部矩阵根。
The paper proved the Hamilton-Cayley theorem in complex number space, and indicated the all matrix root of the sign multinomial of matrix A.
并通过比较这些极值图的最小根得到此类连通图族伴随多项式最小根的序。
Moreover, some ordering relations are determined by comparing the minimum roots of these extreme graphs.
利用初等方法给出了一类包含第一类契贝谢夫多项式——盖根堡多项式的积的求和公式。
Sum formula for a kind of involving the first species of Chebyshev-Gegenbauer LPolynomials are presented by using primary methods.
本文利用分圆多项式的所有根是单位根的性质，直接从给定的多项式入手，提出了判定一个多项式是否为分圆多项式的算法．算法简单明了，易于实现．。
An algorithm for cyclotomic polynomial test is presented based on that all the roots of a cyclotomic polynomial are unity. The algorithm is directed. simple and realized easily.
本文研究用正交多项式逼近非线性趋势，然后对残差进行单位根检验的方法。
Orthogonal polynomial approximation is proposed to estimate the nonlinear deterministic trend and then the residual is used to test the unit root.
介绍了用多项式根的性质与导数极限定理求分段函数在分界点的导数的简单方法。
The paper introduces the property theorem about roots of polynomial and the derivate limit theorem, by which we can study the derived number of a break point of piecewise function.
本文指出了弱粘弹性材料结构的特征值是一组有理分式多项式方程的根，并给出了关于这些有理分式多项式方程根的一个定理。
It is pointed out that the eigenvalues of these structures are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper.
传统多项式根最大模求解算法的求解效率低、计算复杂。
Classic algorithm is slow and complex for solving the maximum module of the roots of polynomials.
针对该问题，提出一种基于多项式根的最大模求解的二分搜索算法。
Aiming at these problems, this paper presents a binary search algorithm based on solving the maximum module of roots of polynomial.
考虑阻尼力后，结构的特征方程应有复数根，因而通常用于求解多项式方程实数根的二分法不再适用。
The consideration of damping force leads to a fact that there exist complex roots to the characteristic equation for the structures.
通过研究多项式的系数来确定整系数多项式的有理根，进而得出整系数多项式的有理根的一个判定定理和根的存在定理。
The paper available mapping of integral coefficient polynomial and rational number, obtain factorization from factorization of polynomial by the way of sieve in true fraction series.
通过研究多项式的系数来确定整系数多项式的有理根，进而得出整系数多项式的有理根的一个判定定理和根的存在定理。
The paper available mapping of integral coefficient polynomial and rational number, obtain factorization from factorization of polynomial by the way of sieve in true fraction series.
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