Equidivisible pseudovarieties of semigroups

We give a complete characterization of pseudovarieties of semigroups whose finitely generated relatively free profinite semigroups are equidivisible. Besides the pseudovarieties of completely simple semigroups, they are precisely the pseudovarieties that are closed under Mal'cev product on the left by the pseudovariety of locally trivial semigroups. A further characterization which turns out to be instrumental is as the non-completely simple pseudovarieties that are closed under two-sided Karnofsky-Rhodes expansion

Recognizing pro-R closures of regular languages

Given a regular language L, we effectively construct a unary semigroup that recognizes the topological closure of L in the free unary semigroup relative to the variety of unary semigroups generated by the pseudovariety R of all finite R-trivial semigroups. In particular, we obtain a new effective solution of the separation problem of regular languages by R-languages

On the group of a rational maximal bifix code

We give necessary and sufficient conditions for the group of a rational maximal bifix code $Z$ to be isomorphic with the $F$-group of $Z\cap F$, when $F$ is recurrent and $Z\cap F$ is rational. The case where $F$ is uniformly recurrent, which is known to imply the finiteness of $Z\cap F$, receives special attention. The proofs are done by exploring the connections with the structure of the free profinite monoid over the alphabet of $F$

Cooperação judiciária penal na União Europeia: entre a desintegração e o desafio do federalismo

O autor parte do reconhecimento da existência da atual crise – à semelhança da crise no pós-guerra – para elaborar sobre o significativo percurso no âmbito da cooperação judiciária penal na União Europeia, que acompanhou, por sua vez, a evolução da integração política. A União Europeia encontra-se hoje numa etapa crucial no que respeita à construção de uma jurisdição penal plena, caminho esse parametrizado pelo Tratado de Lisboa, nomeadamente quanto à criação de uma Procuradoria Europeia. Esta poderá vir a desenhar-se como um órgão "federal", com uma atuação concentrada e uniforme para todo o território da União Europeia, como espaço natural da sua jurisdição territorial.The author firstly recognizes the existence of the current crisis – similar to the crisis in post-war Europe – to elaborate on the significant path that criminal judicial cooperation in the European Union undertook, sustained by the evolution of political integration. Today the European Union is at a crucial stage in regards to the construction of a full criminal jurisdiction, particularly regarding the creation of a European Public Prosecutor's Office, as parameterized by the Lisbon Treaty. This is likely to emerge as a "federal" agency, with a concentrated and uniform action throughout the territory of the European Union, as the natural area of its territorial jurisdiction

Conforming finite elements with embedded strong discontinuities

A kinematically consistent approach for embedded discontinuitie