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101.
In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S 2. For this purpose we employ commuting pairs of real symmetric matrices H, K
n×n
to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables. 相似文献
102.
Moharram A. Khan 《Czechoslovak Mathematical Journal》2002,52(2):401-413
Let p, q and r be fixed non-negative integers. In this note, it is shown that if R is left (right) s-unital ring satisfying
, respectively) where
, then R is commutative. Moreover, commutativity of R is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results. 相似文献
103.
Zeng Guangxing 《中国科学A辑(英文版)》1999,42(3):272-280
For an ordered field (K,T) and an idealI of the polynomial ring
, the construction of the generalized real radical
ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing
is presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project. 相似文献
104.
The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra
(m/n ) were described by Serganova, leading to her solution of the character problem for
(m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed. 相似文献
105.
TZEKIS P.; KARAMPETAKIS N. P.; VARDULAKIS A. I. 《IMA Journal of Mathematical Control and Information》1999,16(4):391-401
The main purpose of this paper is to determine two new algorithmsfor the division of the polynomial matrix B(s) R[s]pxq by A(s) R[s]pxp (a) based on the Laurent matrix expansion at s = =of the inverse of A(s), i.e. A(s)1, and (b) in a waysimilar to the one presented by Gantmacher (1959). 相似文献
106.
We examine connections between A-hypergeometric differential equations and the theory of integer programming. In the first part, we develop a hypergeometric sensitivity analysis for small variations of constraint constants with creation operators and b-functions. In the second part, we study the indicial polynomial (b-function) along the hyperplane xi=0 via a correspondence between the optimal value of an integer programming problem and the roots of the indicial polynomial. Gröbner bases are used to prove theorems and give counter examples. 相似文献
107.
Sergei Yu. Vasilovsky 《Proceedings of the American Mathematical Society》1999,127(12):3517-3524
The algebra of all matrices over a field has a natural -grading . In this paper graded identities of the -graded algebra over a field of characteristic zero are studied. It is shown that all the -graded polynomial identities of follow from the following:
108.
平面多项式系统及其相伴系统 总被引:8,自引:0,他引:8
引进平面多项式系统的相伴系统的概念 ,分析了多项式系统与其相伴系统之间在极限环不存在性 ,唯一性 ,中心焦点的判定等问题上的相似之处和不同之处 ,提出了几个公开问题 . 相似文献
109.
Alberto Corso William Heinzer Craig Huneke 《Transactions of the American Mathematical Society》1998,350(12):5095-5109
We study content ideals of polynomials and their behavior under multiplication. We give a generalization of the Lemma of Dedekind-Mertens and prove the converse under suitable dimensionality restrictions.
110.
涉及微分多项式的亚纯函数的唯一性 总被引:7,自引:0,他引:7
设f(z)是非常数的整函数,n是正整数,F(z)=f ̄(n)(z)+a_1(z)f ̄(n-1)(z)+…+a_n(z)f(x),其中a_1(z),a_2(z),…,a_n(z)均是f(z)的小函数,本文证明了:若f(z)和F(z)几乎CM分担两个不同的有穷复数a和b,则f(z)≡F(z). 相似文献