http://hdl.handle.net/10174/31 Tue, 10 Nov 2026 00:55:24 GMT 2026-11-10T00:55:24Z http://hdl.handle.net/10174/42713 Title: Local estimates for functionals rotationally invariant with respect to the gradient Authors: Santos, Telma João Abstract: This paper concerns minimization problems from Calculus of Variations rotationally invariant with respect to the gradient. Inspired by properties associated with results which are valid for elliptic partial differential equations, it presents some local estimates nearby non extremum points as well as nearby extremum points for these problems, generalizing some results obtained by Arrigo Cellina, Vladimir V. Goncharov and myself. As a consequence, some local estimates are obtained for the difference between the supremum and the infimum of any solution to the problem considered Thu, 29 Dec 2022 00:00:00 GMT http://hdl.handle.net/10174/42713 2022-12-29T00:00:00Z http://hdl.handle.net/10174/42518 Title: Factorisation of the Classical Nonstandard Bounded Functional Interpretation Authors: Dinis, Bruno; Gaspar, Jaime Editors: Bezzeghoud, Mourad; Carapau, Fernando; Minhós, Feliz; Vaidya, Ashwin Abstract: Functional interpretations are maps of formulas from the language of one theory into the language of another theory, in such away that provability is preserved, proofs are (essentially) translated into proofs, and information about the proofs is gathered. Functional interpretations have many uses, such as: relative consistency results, conservation results and the extraction of computational content from proofs. We prove the factorisation Ust = Kst Bst of Jaime Gaspar and Fernando Ferreira’s classical nonstandard bounded functional interpretation Ust in terms of an extension of Jean-Louis Krivine’s negative translation Kst and Bruno Dinis and Jaime Gaspar’s intuitionistic nonstandard bounded functional interpretation Bst. We also give some applications of the factorisation. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/10174/42518 2026-01-01T00:00:00Z http://hdl.handle.net/10174/42198 Title: On the intersection of fixed subgroups of Fn × F m Authors: Carvalho, André Editors: Diekert, Volker Abstract: We prove that, although it is undecidable if a subgroup fixed by an automorphism intersects nontrivially an arbitrary subgroup of F n × F m , there is an algorithm that, taking as input a monomorphism and an endomorphism of F n × F m , decides whether their fixed subgroups intersect nontrivially. The general case of this problem, where two arbitrary endomorphisms are given as input, remains unknown. We show that, when two endomorphisms of a certain type are given as input, this problem is equivalent to the Post Correspondence Problem for free groups. Tue, 24 Feb 2026 00:00:00 GMT http://hdl.handle.net/10174/42198 2026-02-24T00:00:00Z http://hdl.handle.net/10174/41513 Title: Modelos geométricos em bambu Authors: Mateus, Luís; Macias Marques, Pedro Abstract: Construção de modelos geométricos em bambu foi uma das sessões práticas que teve lugar no II Encontro STEAM no passado mês de março na Escola Secundária Camilo Castelo Branco, em Oeiras. Esta sessão, dinamizada pela Associação de Professores de Matemática e pela Associação de Professores de Desenho e Geometria Descritiva, ocorreu em duas edições, cada uma com aproximadamente 12 participantes. A realização da sessão assentou num ponto de partida essencial. A ideia de que a matemática e a geometria podem ser utilizadas para representar, interpretar e agir sobre o mundo que nos rodeia, seja o mundo natural seja o mundo artificializado pelo homem. O processo de construção dos modelos estabeleceu uma relação entre a geometria e a materialidade em que intervêm variadas propriedades físicas como a gravidade, o atrito, a elasticidade, a ductilidade, entre outras, que colocam limites ao que se pode construir, e que, por isso, tornam evidente que qualquer representação que se faça é apenas uma aproximação ao fenómeno que se pretende analisar. Wed, 01 Jan 2025 00:00:00 GMT http://hdl.handle.net/10174/41513 2025-01-01T00:00:00Z