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Erd\H{o}s conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36 - O(1). I ...
A diameter graph in is a graph whose set of vertices is a finite subset of and whose set of edges is formed by pairs of vertices that are at diameter apart. This paper is devoted to the study of different extremal properties of diameter graphs in and on a ...
In this report, we use a variety of tools from differential geometry to propose a nonlinear extension of the principal components analysis (PCA) into manifolds setting. This extension, that we shall call principal geodesics analysis (PGA), attempts to find ...
Piezoelectricity is the propriety of materials that relates mechanical deformation as a function of applied voltage and vice-versa. The advantage of using these materials as actuators is the fast response and low power consumption when compared with tradit ...
This contribution presents an ongoing study focused on how location awareness feature modifies collaboration in the context of mobile computing. First it describes the environment we designed and implemented in the form of a mobile game called CatchBob!. T ...
The crystal structure of the new synthetic compound Ba-5[B20O33(OH)(4)] . H2O was established by the methods of X-ray diffraction (a Stoe IPDS diffractometer, lambda MoKalpha, 1860 independent reflections, anisotropic refinement, R = 1.95%, localization of ...
Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning for T is a subset R of the rooms such that each vertex of T is in exactly one room in R. Given a room-partitioning R for T, the exchange ...
The Benary cross is a classical demonstration showing that the perceived brightness of an area is not solely determined by its luminance, but also by the context in which it is embedded. Despite the fact that two identical grey triangles are flanked by an ...
A new method for measuring shape rectangularity is introduced. The new shape measure is invariant with respect to similarity transformations, ranges over the interval (0,1] and picks the value 1 if and only if the measured shape is a rectangle. The measure ...
A study of non-anchored tanks found in Switzerland (Koller, 2003) revealed that the plastic rotation of the shell-to-bottom connection in four of the six tanks studied did not satisfy the 0.2 radians limit established by the Eurocode (Eurocode-8, 2005). Th ...
