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In the paper we characterize subspaces and strong subspaces of a semiaffine partial linear space and consider definability
of projective and semiaffine planes, affine lines and parallelity in terms of projective lines. We also give some construction
of a wide class of semiaffine partial linear spaces. 相似文献
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Let L be a non-trivial finite linear space in which every line has n or n+1 points. We describe L completely subject to the following restrictions on n and on the number of points p: p≤n 2+n?1 and n≥3; n 2+n+2≤p≤n 2+2n?1 and n≥3; p=n 2+2n and n≥4; p=n 2+2n+2 and n≥3; p=n 2+2n+3 and n≥4. 相似文献
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Anton Betten Anne Delandtsheer Maska Law Alice C. Niemeyer Cheryl E. Praeger Shenglin Zhou 《数学学报(英文版)》2009,25(9):1399-1436
The paper summarises existing theory and classifications for finite line-transitive linear spaces, develops the theory further, and organises it in a way that enables its effective application. The starting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitive automorphism groups of linear spaces. In two of these cases the group may be imprimitive on points, that is, the group leaves invariant a nontrivial partition of the point set. In the first of these cases the group is almost simple with point-transitive simple socle, and may or may not be point-primitive, while in the second case the group has a non-trivial point-intransitive normal subgroup and hence is definitely point-imprimitive. The theory presented here focuses on point-imprimitive groups. As a non-trivial application a classification is given of the point-imprimitive, line-transitive groups, and the corresponding linear spaces, for which the greatest common divisor gcd(k, v - 1) ≤ 8, where v is the number of points, and k is the line size. Motivation for this classification comes from a result of Weidong Fang and Huffing Li in 1993, that there are only finitely many non-trivial point-imprimitive, linetransitive linear spaces for a given value of gcd(k, v - 1). The classification strengthens the classification by Camina and Mischke under the much stronger restriction k ≤ 8: no additional examples arise. The paper provides the backbone for future computer-based classifications of point-imprimitive, line- transitive linear spaces with small parameters. Several suggestions for further investigations are made. 相似文献
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Hironao Koshimizu 《Central European Journal of Mathematics》2011,9(1):139-146
We characterize finite codimensional linear isometries on two spaces, C
(n)[0; 1] and Lip [0; 1], where C
(n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of
Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C
(n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts. 相似文献
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Let (X, d) be a compact metric space and let (X) denote the space of all finite signed Borel measures on X. Define I: (X) → ℝ by I(μ) = ∫
X
∫
X
d(x, y)dμ(x)dμ(y), and set M(X) = sup I(μ), where μ ranges over the collection of measures in (X) of total mass 1. The space (X, d) is quasihypermetric if I(μ) ≦ 0 for all measures μ in (X) of total mass 0 and is strictly quasihypermetric if in addition the equality I(μ) = 0 holds amongst measures μ of mass 0 only for the zero measure.
This paper explores the constant M(X) and other geometric aspects of X in the case when the space X is finite, focusing first on the significance of the maximal strictly quasihypermetric subspaces of a given finite quasihypermetric
space and second on the class of finite metric spaces which are L
1-embeddable. While most of the results are for finite spaces, several apply also in the general compact case. The analysis
builds upon earlier more general work of the authors [11] [13].
相似文献
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《Journal of Combinatorial Theory, Series A》1987,44(2):229-240
A decent linear space DLS(k) is a linear space with minimal line size at least three and with maximal line size exactly k. Denote by vk (resp. bk) the minimum number of points (resp. lines) in a DLS(k). We determine the numbers vk and bk for all k and prove that each DLS(k) with bk lines has vk points. Thus the DLS(k)'s with bk lines are the minimal linear spaces. 相似文献
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M. Brannigan 《Numerical Functional Analysis & Optimization》2013,34(1):79-91
It has been shown that the theory of H-sets is important in the characterization of best uniform approximation of continuous real-or complex-valued functions. We here extend the theory of H-sets to the more general setting of functions with compact domain and with range contained in a Banach space. Using the definitions of H-sets, we construct a maximal linear functional and obtain inclusion theorems analogous to the classical case. It is then a simple matter to deduce a characterization of best approximation and show when uniqueness and strong uniqueness are achieved. 相似文献
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Roger R. Smith 《Proceedings of the American Mathematical Society》2000,128(11):3461-3462
We show that finite dimensional injective operator spaces are corners of finite dimensional -algebras .
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The coapproximation in linear spaces 总被引:2,自引:0,他引:2
Son Wenhua 《分析论及其应用》1993,9(4):55-65
In this paper, we investigate the properties of strongly coapproximation in normed linear spaces and locally convex spaces.
The relations between strongly coapproximation and strongly unique approximation and of the f-coapproximation and f-approximation
are also considered.
Supported by NSFC 相似文献
17.
We extend the enumeration of regular linear spaces in 1 to at most 19 points. In addition, one of the 5 missing cases in the previous list is settled. The number of regular linear spaces of type (15|215,330) is 10,177,328. © 2005 Wiley Periodicals, Inc. J Combin Designs. 相似文献
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