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Via studying the relation between isosceles orthogonality and the lengths of segments contained in the unit sphere, existing results on the uniqueness of isosceles orthogonality are improved. 相似文献
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Du Nailin 《Numerical Functional Analysis & Optimization》2013,34(6):675-708
This work presents some basic principles concerned with two general settings for stable approximating orthogonal generalized inverses in Hilbert spaces. In these two settings, perfect convergence and perfect uniform convergence are two important concepts for making theoretical or numerical analysis. Our basic principles characterize the two important concepts by some necessary conditions: stability with other compensated conditions. These basic principles include as simple corollaries some well-known results. 相似文献
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This paper deals with the problems of best approximation in β-normed spaces.With the tool of conjugate cone introduced in [1] and via the Hahn-Banach extension theorem of β-subseminorm in [2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of a β-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convex β-normed space must be Chebyshev is proved at last. 相似文献
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We investigate the stability constants of convex sets in linear spaces. We prove that the stability constants of affinity
and of the Jensen equation are of the same order of magnitude for every convex set in arbitrary linear spaces, even for functions
mapping into an arbitrary Banach space. We also show that the second Whitney constant corresponding to the bounded functions
equals half of the stability constant of the Jensen equation whenever the latter is finite. We show that if a convex set contains
arbitrarily long segments in every direction, then its Jensen and Whitney constants are uniformly bounded. We prove a result
that reduces the investigation of the stability constants to the case when the underlying set is the unit ball of a Banach
space. As an application we prove that if D is convex and every δ-Jensen function on D differs from a Jensen function by a bounded function, then the stability constants of D are finite. 相似文献
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Doklady Mathematics - Let E be a nonseparable rearrangement invariant space, and let E0 denote the closure of the set of all bounded functions in E. We study elements of E orthogonal to the... 相似文献
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Felipe Rincón 《Discrete and Computational Geometry》2013,50(3):700-713
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Malcolm Greig 《Designs, Codes and Cryptography》2002,27(1-2):25-47
Batten and Beutelspacher have characterized Finite Linear Spaces with lines of size n,n + 1 and n + 2, and with v (n + 1)2for n 22, and some of the cases for smaller n. In this article, using the structuredapproach we presented in our earlier article [8], we complete this characterization for smalln. 相似文献
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We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p
e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in
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. We also give slightly weaker bounds for more general finite classical polar spaces. Another application is the determination of certain explicit bases for the code of PG(2, p) using secants, or tangents and passants, of a nondegenerate conic. 相似文献
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Abstract This paper gencralizes the result about linear isometries of S~ spaces given by W.P.Novingerand D.M.Oberlin[2]for the unite dise of C to the bounded symmetric domains of C~n 相似文献
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This paper generalizes the result about linear isometries of S^pspaces given by W.P.Novinger and D.M.Oberlin[2] for the unite dise of C to the bounded symmetrie domains of C^n。 相似文献