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Fuzzy Logic for Incidence Geometry [PDF]
The Scientific World Journal, 2016 The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly
Alex Tserkovny
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Convex subspaces of Lie incidence geometries [PDF]
Combinatorial Theory, 2022 Let \(\Gamma\) be a hexagonic Lie incidence structure, e.g.\ a long root geometry of a (thick irreducible) spherical Tits building; compare \textit{E. E. Shult} [Points and lines. Characterizing the classical geometries. Berlin: Springer (2011; Zbl 1213.51001)]. The authors classify all convex subspaces of \(\Gamma\) under the assumption that \(\Gamma\)
Jeroen Meulewaeter +1 more
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Critical ion velocities for nanostructure formation on metal surfaces by slow highly charged ions at arbitrary incidence angles [PDF]
Scientific ReportsSurface nanostructuring of metal targets induced by irradiation with slow, highly charged ions at various incidence angles is investigated. We extend our recently developed cohesive energy model to analyze the influence of impact geometry.
Milena D. Majkić +4 more
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Ruled surface theory and incidence geometry [PDF]
, 2016 This is an expository paper about applications of ruled surface theory in incidence geometry. It surveys the results that have been proven, gives an overview of the methods, and discusses some open problems and further directions. It will appear in the book Journey Through Discrete Mathematics, a Tribute to Jiri Matousek, edited by Martin Loebl ...
Larry Guth
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Groups represented by incidence geometries [PDF]
The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. More precisely, to any group G, we attempt to associate an incidence system whose group of type-preserving automorphisms is Inn(G), the group of inner automorphisms of G, and ...
Dimitri Leemans +2 more
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Incidence geometry in a Weyl chamber I: GL
Advances in Applied Mathematics, 2020 We study the central hyperplane arrangement whose hyperplanes are the vanishing loci of the weights of the first and the second fundamental representations of $\mathfrak{gl}_n$ restricted to the dual fundamental Weyl chamber. We obtain generating functions that count flats and faces of a given dimension.
Mboyo Esole +3 more
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Large Incidence-free Sets in Geometries [PDF]
The Electronic Journal of Combinatorics, 2012 Let $\Pi = (P,L,I)$ denote a rank two geometry. In this paper, we are interested in the largest value of $|X||Y|$ where $X \subset P$ and $Y \subset L$ are sets such that $(X \times Y) \cap I = \emptyset$. Let $\alpha(\Pi)$ denote this value. We concentrate on the case where $P$ is the point set of $\mathsf{PG}(n,q)$ and $L$ is the set of $k$-spaces in
Stefaan De Winter +2 more
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Association between left ventricular remodeling and coronary chronic total occlusion in hypertensive coronary artery disease patients [PDF]
Scientific ReportsHypertensive left ventricular (LV) remodeling may influence coronary artery pathology due to anatomical proximity, yet its association with coronary chronic total occlusion (CTO) remains unclear. This cross-sectional, hypothesis-generating study included
Wujian He +4 more
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Sum-product theorems and incidence geometry
Journal of the European Mathematical Society, 2007 In this paper we prove the following theorems in incidence geometry. The main ingredients used are the subspace theorem, Balog–Szemerédi–Gowers Theorem, and Szemerédi–Trotter Theorem. We also generalize the theorems to high dimensions, extend Theorem 1 to \Bbb F_p^2
Mei-Chu Chang, József Solymosi
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