共查询到20条相似文献,搜索用时 0 毫秒
1.
In this paper we establish a sharp result concerning integral mean estimates for self-reciprocal polynomials. 相似文献
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Horst Alzer 《Proceedings Mathematical Sciences》2010,120(2):131-137
Let n ≥ 1 be an integer and let P
n
be the class of polynomials P of degree at most n satisfying z
n
P(1/z) = P(z) for all z ∈ C. Moreover, let r be an integer with 1 ≤ r ≤ n. Then we have for all P ∈ P
n
:
$
\alpha _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt} \leqslant \int_0^{2\pi } {|P^r (e^{it} )|^2 dt} \leqslant \beta _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt}
$
\alpha _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt} \leqslant \int_0^{2\pi } {|P^r (e^{it} )|^2 dt} \leqslant \beta _n (r)\int_0^{2\pi } {|P(e^{it} )|^2 dt}
相似文献
3.
We investigate the distribution of zeros around the unit circle of real self-reciprocal polynomials of even degrees with five terms whose absolute values of middle coefficients equal the sum of all other coefficients. Furthermore, it also give a new inequality and other Eneström-Kakeya types of results as by-products of this investigation. 相似文献
4.
Richárd Rimányi 《Inventiones Mathematicae》2001,143(3):499-521
As an application of the generalized Pontryagin-Thom construction [RSz] here we introduce a new method to compute cohomological
obstructions of removing singularities — i.e. Thom polynomials [T]. With the aid of this method we compute some sample results,
such as the Thom polynomials associated to all stable singularities of codimension ≤8 between equal dimensional manifolds,
and some other Thom polynomials associated to singularities of maps N
n
?P
n+k
for k>0. We also give an application by reproving a weak form of the multiple point formulas of Herbert and Ronga ([H], [Ro2]).
As a byproduct of the theory we define the incidence class of singularities, which — the author believes — may turn to be
an interesting, useful and simple tool to study incidences of singularities.
Oblatum 4-II-1999 & 19-VII-2000?Published online: 30 October 2000 相似文献
5.
P.G.L. Leach 《Journal of Mathematical Analysis and Applications》2006,322(1):288-297
The classical heat polynomials are polynomial solutions of the heat equation. We demonstrate the generation of such polynomials through the medium of the group theoretical properties of the equation. A generalised procedure for the generation of polynomial solutions is presented and this is extended to the construction of related polynomials. 相似文献
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Kevin Cattell Frank Ruskey Joe Sawada Micaela Serra C. Robert Miers 《Journal of Algorithms in Cognition, Informatics and Logic》2000,37(2):267
Many applications call for exhaustive lists of strings subject to various constraints, such as inequivalence under group actions. A k-ary necklace is an equivalence class of k-ary strings under rotation (the cyclic group). A k-ary unlabeled necklace is an equivalence class of k-ary strings under rotation and permutation of alphabet symbols. We present new, fast, simple, recursive algorithms for generating (i.e., listing) all necklaces and binary unlabeled necklaces. These algorithms have optimal running times in the sense that their running times are proportional to the number of necklaces produced. The algorithm for generating necklaces can be used as the basis for efficiently generating many other equivalence classes of strings under rotation and has been applied to generating bracelets, fixed density necklaces, and chord diagrams. As another application, we describe the implementation of a fast algorithm for listing all degree n irreducible and primitive polynomials over GF(2). 相似文献
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Theoretical and Mathematical Physics - We study Landau–Ginzburg orbifolds $$(f,G)$$ with $$f=x_1^n+cdots+x_N^n$$ and $$G=Sltimes G^d$$ , where $$Ssubseteq S_N$$ and $$G^d$$ is either the... 相似文献
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Francesco Belardo Enzo M. Li Marzi Slobodan K. Simić Jianfeng Wang 《Graphs and Combinatorics》2010,26(2):163-172
We consider the following two classes of simple graphs: open necklaces and closed necklaces, consisting of a finite number of cliques of fixed orders arranged in path-like pattern and cycle-like pattern, respectively. In these two classes we determine those graphs whose index (the largest eigenvalue of the adjacency matrix) is maximal. 相似文献
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Gross,Klein和Rieper(1993)计算了项链图的亏格分布,其后,Chen,Liu和Wang(2006)以及Yang,Liu(2007)分别给出了项链图嵌入分布的递推式和显式.本文给出项链图嵌入分布的多项式显式.从计数角度,此式比上述两个表达式更为简洁. 相似文献
20.
The Total Embedding Distributions of Cacti and Necklaces 总被引:5,自引:0,他引:5
Yi Chao CHEN Yah Pei LIU Tao WANG 《数学学报(英文版)》2006,22(5):1583-1590
Total embedding distributions have been known for only a few classes of graphs. In this paper the total embedding distributions of the cacti and the necklaces are obtained. Furthermore we obtain the total embedding distributions of all graphs with maximum genus 1 by using the method of this paper. 相似文献
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