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991.
In this paper we generalize the notion of cyclic code and construct codes as ideals in finite quotients of non-commutative
polynomial rings, so called skew polynomial rings of automorphism type. We propose a method to construct block codes of prescribed
rank and a method to construct block codes of prescribed distance. Since there is no unique factorization in skew polynomial
rings, there are much more ideals and therefore much more codes than in the commutative case. In particular we obtain a [40,
23, 10]4 code by imposing a distance and a [42,14,21]8 code by imposing a rank, which both improve by one the minimum distance of the previously best known linear codes of equal
length and dimension over those fields. There is a strong connection with linear difference operators and with linearized
polynomials (or q-polynomials) reviewed in the first section.
相似文献
992.
从例外集的角度研究了亚纯函数微分多项式fkQ[f]+P[f]的零点分布,证明了:对于满足δ(∞,f)1-α>0的超越亚纯函数f(z),微分多项式fkQ[f]+P[f]在不含极点的可数个圆盘并集之外有无穷多个零点,其中k>1+ΓP+γP+α1(-1+αΓQ+ΓP-γP),ΓQ是Q[f]的权,ΓP,γP是P[f]的权和次数.本文推广了Hayman,Anderson,Langley等人的结论. 相似文献
993.
Several cubature formulas on the cubic domains are derived using the dis-crete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Cheby-shev weight functions and associated interpolation polynomials on [-1,1]2, as well as new results on [-1,1]3. In particular, compact formulas for the fundamental interpo-lation polynomials are derived, based on n3/4 + (n2) nodes of a cubature formula on [-1,1]3. 相似文献
994.
HICKERNELL Fred J 《中国科学A辑(英文版)》2009,52(11):2309-2320
This article considers universal optimality of digital nets and lattice designs in a regression model. Based on the equivalence theorem for matrix means and majorization theory,the necessary and sufficient conditions for lattice designs being φp-and universally optimal in trigonometric function and Chebyshev polynomial regression models are obtained. It is shown that digital nets are universally optimal for both complete and incomplete Walsh function regression models under some specified conditions,and are... 相似文献
995.
TianLiang Tu 《中国科学A辑(英文版)》2009,52(3):493-506
Let Γ be a closed smooth Jordan curve in the complex plane. In this paper, with the help of a class of fundamental functions
of Hermite interpolation, the author introduces a continuous function interpolation which uniformly approximates to f(z) ε C(Γ) with the same order of approximation as that in Jackson Theorem 1 on real interval [−1, 1]. The accuracy of the order
of approximation is proved. Using the method different from the early works, the author studies simultaneous approximation
to function and its derivatives and the desired results analogues to that in Jackson Theorem 2 on real interval [−1, 1] are
obtained.
相似文献
996.
研究Kac方程的初值问题.证明了该类方程存在唯一的全局分布解.并且使用一种新的线性化方法证明了该类方程的解具有相应的多项式衰减性. 相似文献
997.
利用局部域的方法,研究素数p在有理数域的6次根扩张中的素理想分解问题,并完全确定了素数p在Q(6√u)中分解所可能有的形式(pα︱︱u).为进一步研究素数p在Q(2l√u)中(l为素数)的分解提供了途径. 相似文献
998.
999.
1000.
Richard J. Mcintosh 《The Ramanujan Journal》2009,19(2):183-186
In his last letter to Hardy, Ramanujan defined 17 functions f(q), (|q|<1), which he called mock theta functions. Each f(q) has infinitely many exponential singularities at roots of unity, and under radial approach to every such singularity, f(q) has an asymptotic approximation consisting of a finite number of terms with closed exponential factors, plus an error term
O(1). We give an example of a q-series in Eulerian form having an approximation with an unclosed exponential factor. Complete asymptotic expansions as q→1 of some shifted q-factorials are given in terms of polylogarithms and Bernoulli polynomials.
Supported by the Natural Sciences and Engineering Research Council of Canada. 相似文献