Enhancing urban analysis through lacunarity multiscale measurement

Urban spatial configurations in most part of the developing countries showparticular urban forms associated with the more informal urban development ofthese areas. Latin American cities are prime examples of this sort, butinvestigation of these urban forms using up to date computational and analyticaltechniques are still scarce. The purpose of this paper is to examine and extendthe methodology of multiscale analysis for urban spatial patterns evaluation. Weexplain and explore the use of Lacunarity based measurements to follow a lineof research that might make more use of new satellite imagery information inurban planning contexts. A set of binary classifications is performed at differentthresholds on selected neighbourhoods of a small Brazilian town. Theclassifications are appraised and lacunarity measurements are compared in faceof the different geographic referenced information for the same neighbourhoodareas. It was found that even with the simple image classification procedure, animportant amount of spatial configuration characteristics could be extracted withthe analytical procedure that, in turn, may be used in planning and other urbanstudies purposes

Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science