Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424

Presentations for some monoids of injective partial transformations on a finite chain.

Communications in Algebra, 33 (2005), p. 587-604

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85

The cardinal of various monoids of transformations that preserve a uniform partition

Bulletin of the Malaysian Mathematical Sciences Society

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

A framework to operate transformations between distinct models differing in modelling concepts

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e de Computadores

A framework for efficient model transformations

The reported productivity gains while using models and model transformations to develop entire systems, after almost a decade of experience applying model-driven approaches for system development, are already undeniable benefits of this approach. However, the slowness of higher-level, rule based model transformation languages hinders the applicability of this approach to industrial scales. Lower-level, and efficient, languages can be used but productivity and easy maintenance seize to exist. The abstraction penalty problem is not new, it also exists for high-level, object oriented languages but everyone is using them now. Why is not everyone using rule based model transformation languages then? In this thesis, we propose a framework, comprised of a language and its respective environment, designed to tackle the most performance critical operation of high-level model transformation languages: the pattern matching. This framework shows that it is possible to mitigate the performance penalty while still using high-level model transformation languages.

Photochemical synthesis and functional transformations of bicyclic vinyl aziridines

Aziridines, a class of organic compounds containing a three membered heterocycle with a nitrogen atom, are extremely valuable molecules in organic and medicinal chemistry. They are frequently used as versatile precursors in the synthesis of natural products, and many biologically active molecules possess the aziridine moiety. The reactivity of aziridines has been studied, for example, in ring-opening reactions with thiols. However, not much interest seems to be given to reactions of aziridines in aqueous media, despite the numberless advantages of using water as solvent in organic chemistry. The nucleophilic ring-opening reaction of aziridines in aqueous media was here explored. Following the Kaplan aziridine synthetic methodology, in which pyridinium salts undergo a photochemical transformation to give bicyclic vinyl aziridines, new aziridines were synthetized. Their nucleophilic ring-opening reaction in water under physiological conditions was investigated and a range of sulphur, nitrogen, carbon and oxygen nucleophiles tested. Thiols, anilines and azide proved to be good nucleophiles to react with the aziridines, giving the ring-opening product in moderate to good yields. The best results were obtained with thiols, more specifically with cysteine-derived nucleophiles. Preliminary results show that these bicyclic vinyl aziridines can modify calcitonin, a peptide containing two cysteine amino acids residues, grating them the potential to be used in bioconjugation as ligands to cysteine-containing proteins, or even as enzyme inhibitors of, for example, cysteine proteases. Additionally, exploratory investigations suggest that the separation of both enantiomers of the bicyclic vinyl aziridine can be performed by taking advantage of an enzymatic methodology for the resolution of racemic secondary alcohols. Both enantiomers would be highly valuable as precursors in the synthesis of enantiomerically pure molecules, as no other method is currently reported for their separation.