Enquadramento cartográfico do Complexo de Granja (NW Ceará, Brasil) e avaliação de sistemas de referenciação geográfica

Este estudo destaca os benefícios da análise metódica da cartografia de base que suporta a produção de Cartografia Geológica. Em certas regiões, as cartas base publicadas estão ainda associadas a redes geodésicas clássicas e, com frequência, são introduzidos erros quando se desconsideram parâmetros essenciais como a Projecção Cartográfica e o Datum Geodésico. Com o uso sistemático dos dispositivos de GPS e dos Sistemas de Informação Geográfica para a elaboração das cartas geológicas, é imprescindível o conhecimento prévio do Sistema de Coordenadas ao qual devem estar ajustados os dados geo-espaciais. Neste estudo de caso, as diferenças e os erros associados à aquisição de coordenadas entre os Data geocêntricos WGS84 e SIRGAS2000 são residuais, atendendo aos parâmetros das cartas base, à região do globo, o campo de acção e a escala, minimizando assim a propagação de erros de posicionamento e georreferenciação subsequentes.

Discrete-time positive periodic systems with state and control constraints

The aim of this paper is to provide an efficient control design technique for discrete-time positive periodic systems. In particular, stability, positivity and periodic invariance of such systems are studied. Moreover, the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability. It is shown how such concept can be used for deriving a stabilizing state-feedback control that maintains the positivity of the closed-loop system and respects states and control signals constraints. In addition, all the proposed results can be efficiently solved in terms of linear programming.

The Riemann sphere in GeoGebra

The stereographic projection is a bijective smooth map which allows us to think the sphere as the extended complex plane. Among its properties it should be emphasized the remarkable property of being angle conformal that is, it is an angle measure preserving map. Unfortunately, this projection map does not preserve areas. Besides being conformal it has also the property of projecting spherical circles in either circles or straight lines in the plane This type of projection maps seems to have been known since ancient times by Hipparchus (150 BC), being Ptolemy (AD 140) who, in his work entitled "The Planisphaerium", provided a detailed description of such a map. Nonetheless, it is worthwhile to mention that the property of the invariance of angle measure has only been established much later, in the seventeenth century, by Thomas Harriot. In fact, it was exactly in that century that the Jesuit François d’Aguilon introduced the terminology "stereographic projection" for this type of maps, which remained up to our days. Here, we shall show how we create in GeoGebra, the PRiemannz tool and its potential concerning the visualization and analysis of the properties of the stereographic projection, in addition to the viewing of the amazing relations between Möbius Transformations and stereographic projections.