关于多项式系数的整除性

设n是正整数,k1,k2,…+k1=n的非负整数,正整数[nk1k2…ks]=n！/k1!k2!…k5!称为多项式系数,本文讨论了当n=a0+a1p+a2p^2+…arp^r,其中p为素数且p≤n,0≤ai&;lt;p(0≤i≤r);ki=a0^(i)+a1^(i)p+…+ar^(i)p^r,其中ki≤0,∑^si=1,ki=n,0≤ak^(i)p(0≤i&;lt;s)时多项式系数的整除性问题,得出的结果推广了著名的Lucas定理^[1].     

关于多项式系数的整除性

设 n是正整数 ,k1 ,k2 ,… ,ks 是适合 k1 +k2 +… +ks=n的非负整数 ,正整数 nk1 k2 … ks=n!k1 !k2 !… ks!称为多项式系数 .本文讨论了当n=a0 +a1 p+a2 p2 +… +arpr ,其中 p为素数且 p≤ n,0≤ ai相似文献   

一类整除性定理

本给出复域上多元多项式环C[x1,x2…，xn]的一类整除性定理，它是[1]中整除定理的直接推广。     

关于高等代数多项式理论的教学探讨

本文探讨高等代数多项式理论的教学策略以帮助师生减缓教与学的压力.     

矩阵函数计算的插值多项式方法

矩阵函数是数学专业课程中的重要内容之一,也是部分非数学类专业课程中的内容.关于矩阵函数符号计算的传统教学方法,是借助矩阵的Jordan标准形,这种方法需要求出矩阵到Jordan标准形的过渡矩阵,运算相对复杂.利用插值多项式计算矩阵函数的方法,可以避开计算过渡矩阵,节省教学时间,并能起到很好的教学效果.     

求解多项式重根时修正的Ehrlich法之改进

1引言次数大于4的多项式的根已没有一般的公式解法,但多项式求根有很多应用背景,因此有不少文献讨论多项式根的迭代解法,如文献[1-9]。对多项式f(x)=sum from j=0 to na_jx~j(a_n=1),(1.1)若其根全是单根,则已有一些收敛快效率高的迭代解法,如著名的Newton法,Durand- Kerner算法。特别是Ehrlich L W在文[1]中提出的同时决定多项式(1.1)的全部单根     

多项式环中的Fermat定理

本文首先介绍了基本多项式与多项式的根的个数的关系,然后得到了定理:对于闭域K上任意互素的多项式f(x),g(x),h(x),且不全为常数,以及任何自然数n(?)3,等式f(x)~n g(x)~n=h(x)~n永远不成立.并将此结论推广到整环上也成立.     

一类整除性定理的推广

「１」给出复数Ｃ上多元多项式环Ｃ「ｘ１,ｘ２,…,ｘｎ」的一类整除性定理,本把它推广为任意代数闭域ｋ上多元多项式环ｋ「ｘ１,ｘ２,…,ｘｎ」的情形。     

关于一个多项式重根迭代法的收敛性

讨论一个同时求解多项式重根的迭代法,给出其收敛性定理及其简洁证明,数值结果是满意的.     

Bernstein多项式的升阶定理

本文给出了Ｂｅｒｎｓｔｅｉｎ多项式升阶定理及其凸性、正性的说明，同时讨论了多项式凸与网凸的关系。     

On the Multidimensional Tarry Problem for a Cubic Polynomial

Mathematical Notes - A new upper bound for the exponent of convergence of a special integral in the Tarry problem is obtained. The result is based on the representation of a special integral as a...     

The General Problem of Polynomial Spline Interpolation

We study the general problem of interpolation by polynomial splines and consider the construction of such splines using the coefficients of expansion of a certain derivative in B-splines. We analyze the properties of the obtained systems of equations and estimate the interpolation error.     

一类基函数的构造问题

对文[1]中给出的基函数作了改进,改进后的基函数不仅形式简单,而且具有良好的几何性质.然后引进多项式树的概念,从更广泛意义出发讨论了一类基函数的构造问题.给基函数的构造提供了一个直观的途径.     

A Linear System Arising from a Polynomial Problem and Its Applications

A linear system arising from a polynomial problem in the approximation theory is studied, and the necessary and sufficient conditions for existence and uniqueness of its solutions are presented. Together with a class of determinant identities, the resulting theory is used to determine the unique solution to the polynomial problem. Some homogeneous polynomial identities as well as results on the structure of related polynomial ideals are just by-products.     

The Frobenius Problem for Classes of Polynomial Solvability

The Frobenius problem is to find a method ( $ =$ algorithm) for calculating the largest “sum of money” that cannot be given by coins whose values $b_0 ,{\text{ }}b_1 ,{\text{ }} \ldots {\text{, }}b_w$ are coprime integers. As admissible solutions (algorithms), it is common practice to study polynomial algorithms, which owe their name to the form of the dependence of time expenditure on the length of the original information. The difficulty of the Frobenius problem is apparent from the fact that already for $w = 3$ the existence of a polynomial solution is still an open problem. In the present paper, we distinguish some classes of input data for which the problem can be solved polynomially; nevertheless, argumentation in the spirit of complexity theory of algorithms is kept to a minimum.     

On Polynomial Solvability of One Quadratic Euclidean Clustering Problem on a Line

Doklady Mathematics - We consider the problem of partitioning a finite set of points in Euclidean space into clusters so as to minimize the sum, over all clusters, of the intracluster sums of the...     

An Extremal Problem Concerning the Derivatives of a Polynomial at Its Roots

Let w be a monic polynomial of degree n +1 with roots x_j in the interval [−1, 1]. We consider the problem of finding the roots x_j for which the minimum of ¦ w '( x_j )¦, for 0≤ j ≤ n , is as large as possible. We prove that the Clenshaw–Curtis points cos( j π/ n ) are the only solution when n is even and that they get asymptotically close to the solution for odd values of n , as n goes to infinity. Our problem is related to the problem of minimizing the norm of inverse Vandermonde matrices.