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Xiu Gui LIU 《数学学报(英文版)》2007,23(3):385-392
In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1). 相似文献
84.
本文应用 Smith周期变换理论 ,根据球面在周期变换下的指数 ,对球面到光滑流形的连续映射做了进一步探讨 ,从而得到了 Munkholm型定理 . 相似文献
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Pauliina Ilmonen 《Linear and Multilinear Algebra》2013,61(5):557-564
In 1861, Henry John Stephen Smith [H.J.S. Smith, On systems of linear indeterminate equations and congruences, Philos. Trans. Royal Soc. London. 151 (1861), pp. 293–326] published famous results concerning solving systems of linear equations. The research on Smith normal form and its applications started and continues. In 1876, Smith [H.J.S. Smith, On the value of a certain arithmetical determinant, Proc. London Math. Soc. 7 (1875/76), pp. 208–212] calculated the determinant of the n?×?n matrix ((i,?j)), having the greatest common divisor (GCD) of i and j as its ij entry. Since that, many results concerning the determinants and related topics of GCD matrices, LCM matrices, meet matrices and join matrices have been published in the literature. In this article these two important research branches developed by Smith, in 1861 and in 1876, meet for the first time. The main purpose of this article is to determine the Smith normal form of the Smith matrix ((i,?j)). We do this: we determine the Smith normal form of GCD matrices defined on factor closed sets. 相似文献
88.
Using Hart Smith’s and curvelet transforms, new necessary and new sufficient conditions for an L 2(?2) function to possess Hölder regularity, uniform and pointwise, with exponent α>0 are given. Similar to the characterization of Hölder regularity by the continuous wavelet transform, the conditions here are in terms of bounds of the transforms across fine scales. However, due to the parabolic scaling, the sufficient and necessary conditions differ in both the uniform and pointwise cases. We also investigate square-integrable functions with sufficiently smooth background. Specifically, sufficient and necessary conditions, which include the special case with 1-dimensional singularity line, are derived for pointwise Hölder exponent. Inside their “cones” of influence, these conditions are practically the same, giving near-characterization of direction of singularity. 相似文献
89.
An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph.
The approach serves well to explain how the path cover number (resp. diameter of a tree T) is related to the maximal multiplicity MaxMult(T) occurring for an eigenvalue of a symmetric matrix whose graph is T (resp. the minimal number q(T) of distinct eigenvalues over the symmetric matrices whose graphs are T). The approach is also applied to a more general class of connected graphs G, not necessarily trees, in order to establish a lower bound on q(G). 相似文献
90.
Carlos A. Alfaro Carlos E. Valencia Adrián Vázquez-Ávila 《Linear and Multilinear Algebra》2018,66(10):2036-2048
Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterization of the digraphs with at most one trivial critical ideal. Which implies the characterizations of the digraphs whose critical group has one invariant factor equal to one, and the digraphs whose Smith group has one invariant factor equal to one. 相似文献