Quadrangle Av-10 ‘Oppia’ is one of five quadrangles that cover the equatorial region of asteroid (4) Vesta. This quadrangle is notable for the broad, spectrally distinct ejecta that extend south of the Oppia crater. These ejecta exhibit the steepest (‘reddest’) visible spectral slope observed across the asteroid and have distinct color properties as seen in multispectral composite images. Compa...

Brouwer, A.E, W.H. Haemers, Structure and uniqueness of the (81,20, 1.6) strongly regular graph, Discrete Mathematics 106/107 (1992) 77-82. We prove that there is a unique graph (on 81 vertices) with spectrum 20’2”‘(-7)*“. We give several descriptions of this graph, and study its structure. Let r = (X, E) be a strongly regular graph with parameters (v, k, ;1, p) = (81, 20, 1, 6). Then r (that i...

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We give a characterization of translation ovoids of flock generalized quadrangles. Then we prove that, if q = 2e , each elation generalized quadrangle defined by a flock has a large class of translation ovoids which arise from semifields of dimension two over their left nucleus. Finally, we give some examples when q is odd. © 2003 Elsevier Ltd. All rights reserved. MSC (2000): Primary 51E12; Se...

There are a number of important substructures associated with sets of points of antiregular quadrangles. Inspired by a construction of P. Wild, we associate with any four distinct collinear points p, q, r and s of an antiregular quadrangle an incidence structure which is the union of the two biaffine planes associated with {p, r} and {q, s}. We investigate when this incidence structure is a sem...

An octagon quadrangle is the graph consisting of an 8-cycle (x1, ..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS] is a pair (X,B), where X is a finite set of v vertices and B is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKv defined on X. A 4-kite is the graph ha...

This paper presents a probability method for detecting people in a static image. We simplify people as a torso and four limbs. The torso is fitted by a quadrangle, and each limb is fitted by one or two quadrangles depending on its pose. In order to find people, we should try to find a combination of quadrangles that must satisfy some geometric and topological constrains. Firstly, we try to dete...

We study random constructions in incidence structures, and illustrate our techniques by means of a well-studied example from finite geometry. A maximal partial ovoid of a generalized quadrangle is a maximal set of points no two of which are collinear. The problem of determining the smallest size of a maximal partial ovoid in quadrangles has been extensively studied in the literature. In general...