103,692 research outputs found
Translation dual of a semifield
No full textIn this paper we obtain a new description of the translation dual of a semifield introduced in [G. Lunardon,
Translation ovoids, J. Geom. 76 (2003) 200–215]. Using such a description we are able to prove that
a semifield and its translation dual have nuclei of the same order. Combining the Knuth cubical array and
the translation dual, we give an alternate description of the chain of twelve semifields in the table of [S. Ball,
G.L. Ebert, M. Lavrauw, A geometric construction of finite semifields, J. Algebra 311 (2007) 117–129]
A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3
No full textWe give a geometrical description of the spin-embedding esp of the symplectic dual polar space Δ ≅ DW (5, 2r) by showing how the natural embedding of W (5, 2r) into PG (5, 2r) is involved in the Grassmann-embedding egr of Δ. We prove that the map sending every quad of Δ to its nucleus realizes the natural embedding of W (5, 2r). Taking the quotient of egr over the space spanned by the nuclei of the quadrics corresponding to the quads of Δ gives an embedding isomorphic to esp. © 2007 Elsevier Inc. All rights reserved
Comment on “Wang et al. (2005), Robust estimating functions and bias correction for longitudinal data analysis”
No full textThis note provides a discussion on the manuscript by Wang et al. (2005) who aim to robustify inference for longitudinal data analysis by replacing the ordinary generalized estimating function with an influence-bounded, possibly biased, version. To adjust for the bias of the ensuing robust estimator, the authors provide its analytic approximation by means of asymptotic expansions, and estimate it by plugging-in a nonrobust estimate of the parameter of interest. In this letter, we argue that the proposed bias-corrected estimator is, in fact, nonrobust
Blocking sets of size q(t)+q(t-1)+1.
No full textAbstractWe prove that in the desarguesian plane PG(2, qt) (t>4) there are at least three inequivalent blocking sets of size qt+qt−1+1. The first one has q+1 Rédei lines, the second one has exactly one Rédei line, and the third one is not of Rédei type. For GF(q) the largest subfield of GF(qt), our results disprove a conjecture quoted by A. Blokhuis (1998, in “Galois Geometry and Generalized Polygons,” Gent)
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