Browsing by Author "Morais, J."
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- Hyperbolic linear canonical transforms of quaternion signals and uncertaintyPublication . Morais, J.; Ferreira, M.This paper is concerned with Linear Canonical Transforms (LCTs) associated with two-dimensional quaternion-valued signals defined in an open rectangle of the Euclidean plane endowed with a hyperbolic measure, which we call Quaternion Hyperbolic Linear Canonical Transforms (QHLCTs). These transforms are defined by replacing the Euclidean plane wave with a corresponding hyperbolic relativistic plane wave in one dimension multiplied by quadratic modulations in both the hyperbolic spatial and frequency domains, giving the hyperbolic counterpart of the Euclidean LCTs. We prove the fundamental properties of the partial QHLCTs and the right-sided QHLCT by employing hyperbolic geometry tools and establish main results such as the Riemann-Lebesgue Lemma, the Plancherel and Parseval Theorems, and inversion formulas. The analysis is carried out in terms of novel hyperbolic derivative and hyperbolic primitive concepts, which lead to the differentiation and integration properties of the QHLCTs. The results are applied to establish two quaternionic versions of the Heisenberg uncertainty principle for the right-sided QHLCT. These uncertainty principles prescribe a lower bound on the product of the effective widths of quaternion-valued signals in the hyperbolic spatial and frequency domains. It is shown that only hyperbolic Gaussian quaternion functions minimize the uncertainty relations.
- Quaternion Hyperbolic Fourier Transforms and Uncertainty PrinciplesPublication . Ferreira, M.; Morais, J.The present study introduces the two-sided and right-sided Quaternion Hyperbolic Fourier Transforms (QHFTs) for analyzing two-dimensional quaternion-valued signals defined in an open rectangle of the Euclidean plane endowed with a hyperbolic measure. The different forms of these transforms are defined by replacing the Euclidean plane waves with the corresponding hyperbolic plane waves in one dimension, giving the hyperbolic counterpart of the corresponding Euclidean Quaternion Fourier Transforms. Using hyperbolic geometry tools, we study the main operational and mapping properties of the QHFTs, such as linearity, shift, modulation, dilation, symmetry, inversion, and derivatives. Emphasis is placed on novel hyperbolic derivative and hyperbolic primitive concepts, which lead to the differentiation and integration properties of the QHFTs. We further prove the Riemann–Lebesgue Lemma and Parseval’s identity for the two-sided QHFT. Besides, we establish the Logarithmic, Heisenberg–Weyl, Donoho–Stark, and Benedicks’ uncertainty principles associated with the two-sided QHFT by invoking hyperbolic counterparts of the convolution, Pitt’s inequality, and the Poisson summation formula. This work is motivated by the potential applications of the QHFTs and the analysis of the corresponding hyperbolic quaternionic signals.
- The health impacts of poor housing conditions and thermal discomfortPublication . Vasconcelos, J.; Freire, E.; Morais, J.; Machado, J.R.; Santana, P.On summer and winter months, cardiovascular morbidity and mortality rates vary throughout Europe. For example, areas with mild winters seem to be the ones with higher number of seasonal mortality. In fact, Portugal is one of the southern countries together with Ireland that have higher mortality in winter. However, the number of studies relating cold weather with morbidity/mortality is still very rare. These occurrences are suspected to be associated with housing quality especially thermal insulation. In order to assess the relation between the incidence of coronary events and housing conditions in Portugal, a survey on inpatients with any form of acute coronary syndromes was undertaken during winter months, in order to get some data about houseability and residents behavior attitudes against cold exposure. It remained clear that poor housing conditions and/or lack of protective measures against cold exposure are common in Portugal. A better knowledge about the impact of weather and climate on health may be applied to built up a set of regulations for housing design (for new but also for old dwellings restoration); but also it is essential for the establishment of adaptation and mitigation policies and strategies, as well as on health planning and on the development of early warning systems.