A note on primes of the form a2 + 1

In this note I prove using an algebraic identity and Wilson's Theorem

On reduction curves and Garside properties of braids

In this paper we study the reduction curves of a braid, and how they can be used to decompose the braid into simpler ones in a precise way, which does not correspond exactly to the decomposition given by Thurston theory. Then we study how a cyclic sliding (which is a particular kind of conjugation) affects the normal form of a braid with respect to the normal forms of its components. Finally, using the above methods, we provide the example of a family of braids whose sets of sliding circuits (hence ultra summit sets) have exponential size with respect to the number of strands and also with respect to the canonical length.Comment: 20 pages, 3 figure

Implementation of Rio Principles into Latin American Environmental Laws

This paper evaluates the way Latin American Environmental Law have incorporated Rio Declaration´s principles. The survey includes a detailed revision of legal regimes of Mexico Brazil, Argentina, Chile, Colombia and Costa Rica where Environmental Law is more developed but few references to other Ibero-American countries are taken into consideration as well. Although the study focuses more in the 27 principles of Rio Declaration but it also evaluates the level of compliance with the commitments assumed by signatory parties of Climate Change and Biodiversity Convention

Conjugacy problem for braid groups and Garside groups

We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).Comment: New version, with substantial modifications. 21 pages, 2 figure