Planning and defining places for the installation of police facilities are fundamental to improving public security service in urban space. Geographic Information Systems connecting spatial distribution occurrences, budgetary restrictions, maximum distance covered state-of-the-art innovations addressing need preventive responsive management. The present work proposes a management information sy...

The torsion index is a positive integer associated by Grothendieck to any connected compact Lie group G [10]. Knowing the torsion index of a group has direct consequences for the integral cohomology of the classifying space BG, the complex cobordism of BG, the Chow ring of BG, and the classification of G-torsors over fields. These applications of the torsion index are summarized in my paper [25...

In this paper, we study properties of rank metric codes in general and maximum rank distance (MRD) codes in particular. For codes with the rank metric, we first establish Gilbert and sphere-packing bounds, and then obtain the asymptotic forms of these two bounds and the Singleton bound. Based on the asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is exceeded by MRD co...

In this paper, we extend the concepts of demand data aggregation error to location problems involving coverage. These errors, which arise flora losses in locational information, may lead to suboptimal location patterns. They are potentially more significant in covering problems than in p-median problernsIbecause the distance metric is binary in covering problems. We examine the Hillsirtan and R...

Two different relaxed versions of Gummelt’s aperiodic cluster covering rules are considered. These relaxed covering rules produce certain random tiling type structures, which are precisely characterized, along with their relationships to various other random tiling ensembles. One variant of the relaxed covering rules allows for a natural realization in terms of a vertex cluster. It is shown wit...