http://hdl.handle.net/10071/5547 2026-04-17T02:00:17Z http://hdl.handle.net/10071/36406 Título próprio: Ações de grupos finitos no toro n-dimensional: O exemplo do quociente estendido Autoria: Bettencourt, G.; Mendes, S. Resumo: Um matemático, um físico e um químico encontram-se e alguém pergunta qual a estrutura algébrica com mais aplicações nas respetivas áreas. Ao contrário das histórias habituais, é provável que a resposta seja a mesma: a teoria dos grupos. 2025-01-01T00:00:00Z 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. 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. 2025-01-01T00:00:00Z http://hdl.handle.net/10071/33086 Título próprio: Optimal control synchronization of a complex network of predator-prey systems Autoria: Silva, C. J.; Cantin, G. Editor: Bernard Bonnard; Monique Chyba; David Holcman; Emmanuel Trélat Resumo: In this work, we consider a complex network of predator-prey systems, modeling the ecological dynamics of interacting species living in a fragmented environment. We consider non-identical instances of a Lotka-Volterra model with Holling type II functional response. We study optimal control problems, for the minimization of the default of synchronization in the complex network, where the controls reproduce the implementation of ecological corridors. The main goal is to restore biodiversity of life species in a heterogeneous habitat by reaching at least a global coexistence equilibrium, or in a better scenario, a global limit cycle which would guarantee biological oscillations, which means rich life dynamics. 2024-01-01T00:00:00Z