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Point-line spaces related to Jordan pairs Ghent University
A point-line space is an abstract geometric object that consists of a set of points and a set of lines such that on each line there are at least two points. A large class of point-line spaces with high symmetry comes along with buildings, combinatorial objects that are introduced by Jacques Tits and help to study algebraic objects with geometric methods. To formulate quantum mechanics as abstract and general as possible, the physicist Pascual ...
On exceptional Lie geometries Ghent University
Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular, many of the exceptional Lie incidence geometries occur. In an appendix, we extend our result to the locally disconnected case and discuss the locally disconnected case of some other well-known characterizations.
Generalized hexagons and Singer geometries Ghent University
In this paper, we consider a set L of lines of PG(5, q) with the properties that (1) every plane contains 0, 1 or q + 1 elements of L, (2) every solid contains no more than q(2) + q + 1 and no less than q + 1 elements of L, and (3) every point of PG(5, q) is on q + 1 members of L, and we show that, whenever (4) q not equal 2 (respectively, q = 2) and the lines of L through some point are contained in a solid (respectively, a plane), then L is ...
RF linearity trade-offs for varying T-gate geometries of GaN HEMTs on Si Interuniversity Microelectronics Centre Vrije Universiteit Brussel
Short-channel Gallium Nitride (GaN) high-electron-mobility transistors (HEMTs) often utilize T-shape gates due to their large gate-line cross-sectional area and subsequent f(MAX) increase. In this paper, we report the linearity trade-offs associated with varying the T-gate geometries of AlGaN/GaN HEMTs on Si, specifically the gate extensions which serve as field plates and their impact on the large-signal performance. Small-signal ...
Finite fields and Galois geometries Ghent University
In 1954 Segre proved the following celebrated theorem : In PG(2, q), with q odd, every oval is a nonsingular conic. Crucial for the proof is Segre's Lemma of Tangents, where a strong result is deduced from the simple fact that the product of the nonzero elements of GF(q) is -1. Relying on this Lemma of Tangents he was able to prove excellent theorems on certain point sets in PG(2,q). To this end he also generalized the classical theorem of ...
Classification results for hyperovals of generalized quadrangles Ghent University
A hyperoval of a point-line geometry is a nonempty set of points meeting each line in either 0 or 2 points. We discuss a combination of theoretical and practical techniques that are helpful for classifying hyperovals of generalized quadrangles. These techniques are based on the connection between hyperovals, even sets and pseudo-embeddings of point-line geometries.
A hemisystem of a nonclassical generalised quadrangle Ghent University
The concept of a hemisystem of a generalised quadrangle has its roots in the work of B. Segre, and this term is used here to denote a set of points H such that every line l meets H in half of the points of l. If one takes the point-line geometry on the points of the hemisystem, then one obtains a partial quadrangle and hence a strongly regular point graph. The only previously known hemisystems of generalised quadrangles of order (q, q (2)) were ...
Linear representations of subgeometries Vrije Universiteit Brussel Ghent University
A linear representation $T_n^*(\K)$ of a point set $\K$ in a hyperplane $\PG(n,q)$ of $\PG(n+1,q)$ is a point-line geometry embedded in $\PG(n+1,q)$. We first prove that an isomorphism between two linear representations $T_n^*(\K)$ and $T_n^*(\K')$ is induced by an isomorphism between the two linear representations $T_n^*(\overline{\K})$ and $T_n^*(\overline{\K}')$ of their closures $\overline {\K}$ and $\overline{\K}'$.
This allows ...
This allows ...