共查询到20条相似文献,搜索用时 15 毫秒
1.
设F_q为有限域,f_i(x)=a_(i1)x_1~(d_(i1))+…+a_(in)x_n~(d_(in))+c_i(i=1,…,m)为F_q上一组对角多项式,用N(V)表示由f_i(i=1,…,m)确定的簇中的F_q.有理点的个数.通过应用Adolphson和Sperber所引进的牛顿多面体方法,证明了ord_qN(V)≥[1/d_1+…+1/d_n]-m,其中d_i=max{d_(1i),…,d_(mi)}.该结果在许多情形下可以改进Ax- Katz定理,并推广了Wan在m=1时得到的一个定理,而且我们对Wan的定理给出了一个不同的证明. 相似文献
2.
V. V. Khlobystov 《Journal of Mathematical Sciences》2001,104(6):1672-1676
We give solutions of two extremal problems, a generalization of a result of W. Porter on an interpolation polynomial in L2(a,b) with minimal norm, which we get here in an abstract Hilbert space with a measure, and an analogue of a theorem of M. Golomb and H. Weinberger for a bounded set of operator interpolants. 相似文献
3.
利用Chebyshev多项式定义了一类双向单叶解析函数,并得到了该函数类的系数估计及Fekete-Szeg?不等式问题. 相似文献
4.
单纯形上的Stancu多项式与最佳多项式逼近 总被引:8,自引:2,他引:6
作为Bernstein多项式的推广,本文定义单纯形上的多元Stancu多项式.以最佳多项式逼近为度量,建立Stancu多项式对连续函数的逼近定理与逼近阶估计,给出Stancu多项式的一个逼近逆定理,从而用最佳多项式逼近刻划Stancu多项式的逼近特征. 相似文献
5.
Given a set of points S={p
1
,. . ., p
n
} in Euclidean d -dimensional space, we address the problem of computing the d -dimensional annulus of smallest width containing the set. We give a complete characterization of the centers of annuli which
are locally minimal in arbitrary dimension and we show that, for d=2 , a locally minimal annulus has two points on the inner circle and two points on the outer circle that interlace anglewise
as seen from the center of the annulus. Using this characterization, we show that, given a circular order of the points, there
is at most one locally minimal annulus consistent with that order and it can be computed in time O(n log n) using a simple algorithm. Furthermore, when points are in convex position, the problem can be solved in optimal Θ(n) time.
Received June 25, 1997, and in revised form March 5, 1998. 相似文献
6.
A new family of trigonometric summation polynomials, Gn,r(f;θ), of Bernstein type is constructed. In contrast to other trigonometric summation polynomials, the convergence properties of the new polynomials are superior to others. It is proved that Gn,r(f;θ) converges to arbitrary continuous functions with period 2π uniformly on (-∞, ∞) as n→∞. In particular, Gn,r(f;θ) has the best convergence order, and its saturation order is 1/n2r 4. 相似文献
7.
Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′ are real. We show that there is a zero ζ of f′ such that |f(ζ)/ζ|≤2/3, and that this inequality can be taken to be strict unless f is of the form f(z)=z+cz
3. 相似文献
8.
This paper introduces a new notion of weighted least-square orthogonal polynomials in multivariables from the triangular form. Their existence and uniqueness is studied and some methods for their recursive computation are given. As an application, this paper constructs a new family of Pade-type approximates in multi-variables from the triangular form. 相似文献
9.
10.
Bart De Bruyn 《Journal of Algebraic Combinatorics》2003,18(1):41-46
Let S be a near polygon of order (s, t) with quads through every two points at distance 2. The near polygon S is called semifinite if exactly one of s and t is finite. We show that S cannot be semifinite if s = 2 and derive upper bounds for t. 相似文献
11.
《复变函数与椭圆型方程》2012,57(6):379-389
We prove that any quaternionic polynomial (with the coefficients on the same side) has two types of zeroes: the zeroes are either isolated or spherical ones, i.e., those ones which form a whole sphere. What is more, the total quantity of the isolated zeroes and of the double number of the spheres does not outnumber the degree of the polynomial. 相似文献
12.
14.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2004,121(4):2508-2510
An algorithm for computing the invariant polynomials and the canonical triangular (trapezoidal) matrix for a polynomial matrix of full column rank is suggested. The algorithm is based on the Δ W-1 rank-factorization method for solving algebraic problems for polynomial matrices, previously suggested by the author. Bibliography: 3 titles. 相似文献
15.
In this paper, we investigate the convergence rate to the normal law of the distribution of the logarithm of the degree of the splitting field of a random polynomial over a finite field F
q. The exact convergence rate is obtained. A similar result is proved for the distribution of the order of a random permutation. 相似文献
16.
Every Set of Disjoint Line Segments Admits a Binary Tree 总被引:1,自引:0,他引:1
Given a set of n disjoint line segments in the plane, we show that it is always possible to form a tree with the endpoints of the segments
such that each line segment is an edge of the tree, the tree has no crossing edges, and the maximum vertex degree of the tree
is 3. Furthermore, there exist configurations of line segments where any such tree requires degree 3. We provide an O(nlog n) time algorithm for constructing such a tree, and show that this is optimal.
Received September 14, 1999, and in revised form January 17, 2001. Online publication August 29, 2001. 相似文献
17.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2004,121(4):2511-2518
The paper considers the problem of computing the invariant polynomials of a general (regular or singular) one-parameter polynomial matrix. Two new direct methods for computing invariant polynomials, based on the W and V rank-factorization methods, are suggested. Each of the methods may be regarded as a method for successively exhausting roots of invariant polynomials from the matrix spectrum. Application of the methods to computing adjoint matrices for regular polynomial matrices, to finding the canonical decomposition into a product of regular matrices such that the characteristic polynomial of each of them coincides with the corresponding invariant polynomial, and to computing matrix eigenvectors associated with roots of its invariant polynomials are considered. Bibliography: 5 titles. 相似文献
18.
Heinz Marbes 《Mathematische Nachrichten》1989,142(1):19-26
In [2] Th. Friedrich described a twistor-holomorphic immersion of a surface M2 into R4 by an explicit formula. Using this formula we prove a criterion for the property of a point of M2 to be umbilical. In the first section of this paper we explain the notion of a twistor-holomorphic immersion. In section two the explicit formula for a twistor-holomorphic immersion into R4 is described. The main result of this paper is formulated and proved in section three. In the last section two examples are studied with the help of the criterion of section three. 相似文献
19.
20.
F. M. Al-Oboudi 《Complex Analysis and Operator Theory》2011,5(3):647-658
Let A denote the class of analytic functions f, in the open unit disk E = {z : |z| < 1}, normalized by f(0) = f′(0) − 1 = 0. In this paper, we introduce and study the class STn,al,m(h){ST^{n,\alpha}_{\lambda,m}(h)} of functions f ? A{f\in A}, with
\fracDn,al fm(z)z 1 0{\frac{D^{n,\alpha}_\lambda f_m(z)}{z}\neq 0}, satisfying
\fracz(Dn,al f(z))¢Dn,al fm(z)\prec h(z), z ? E,\frac{z\left(D^{n,\alpha}_\lambda f(z)\right)'}{D^{n,\alpha}_\lambda f_m(z)}\prec h(z),\quad z\in E, 相似文献
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