http://hdl.handle.net/10071/5554 Mon, 13 Apr 2026 15:47:58 GMT 2026-04-13T15:47:58Z http://hdl.handle.net/10071/36266 Título próprio: Semigroup real characters generated by quasicharacters Autoria: Bettencourt, G.; Mendes, S. Resumo: Let S be an infinite, finitely generated semigroup, endowed with a probability measure. Based on the work [A. Erschler and A. Karlsson, Homomorphisms to ℝ constructed from random walks, Ann. Inst. Fourier (Grenoble) 60 2010, 6, 2095–2113], we construct a real character of S using a random walk approach. In our construction, the word length used in Erschler and Karlsson’s work is replaced by a quasicharacter. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/10071/36266 2026-01-01T00:00:00Z http://hdl.handle.net/10071/33660 Título próprio: On Wigdersons' approach to the uncertainty principle Autoria: Dias, N. C.; Luef, F.; Prata, J. N. Resumo: We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of a simultaneous sharp localization in time and frequency. Moreover, it requires no specific properties of the Fourier transform and can therefore be easily applied to all operators satisfying the primary uncertainty principle. A. Wigderson and Y. Wigderson also suggested many generalizations to higher dimensions and stated several conjectures which we address in the present paper. We argue that we have to consider a more general primary uncertainty principle to prove the results suggested by the authors. As a by-product we obtain some new inequalities akin to the Cowling-Price uncertainty principle, a generalization of the Heisenberg uncertainty principle, and derive the entropic uncertainty principle from the primary uncertainty principles. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10071/33660 2025-01-01T00:00:00Z http://hdl.handle.net/10071/32970 Título próprio: Optimal control of microcephaly under vertical transmission of Zika Autoria: Yapışkan, D.; Silva, C. J.; Torres, D. F. M. Resumo: The Zika virus, known for its potential to induce neurological conditions such as microcephaly when transmitted vertically from infected mothers to infants, has sparked widespread concerns globally. Motivated by this, we propose an optimal control problem for the prevention of vertical Zika transmission. The novelty of this study lies in its consideration of time-dependent control functions, namely, insecticide spraying and personal protective measures taken to safeguard pregnant women from infected mosquitoes. New results provide a way to minimize the number of infected pregnant women through the implementation of control strategies while simultaneously reducing both the associated costs of control measures and the mosquito population, resulting in a decline in microcephaly cases. Mon, 01 Jan 2024 00:00:00 GMT http://hdl.handle.net/10071/32970 2024-01-01T00:00:00Z http://hdl.handle.net/10071/32470 Título próprio: Quaternionic essential numerical range of complex operators Autoria: Carvalho, L.; Diogo, C.; Mendes, S.; Soares, H. Resumo: We study the essential numerical range of complex operators on a quaternionic Hilbert space and its relation with the essential S-spectrum. We give a new characterization of the essential numerical range relating it to the complex essential numerical range. Moreover, we show that the quaternionic essential numerical range of a normal operator is the convex hull of the essential S-spectrum. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10071/32470 2025-01-01T00:00:00Z