Scaling and duality in the superconducting phase transition

The field theoretical approach to duality in the superconducting phase transition is reviewed. Emphasis is given to the scaling behavior, and recent results are discussed.Comment: ws LaTex, 9 pages, 1 figure; published in "Fluctuating Paths and Fields", Festschrift dedicated to Hagen Kleinert on the occasion of his 60th birthday, Edited by W. Janke et al. (World Scientific, Singapore, 2001

Tunnel number degeneration under the connected sum of prime knots

We study 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one.Comment: 40 pages, 28 figures; Version 2: reference added, minor changes in tex

1º Congresso Internacional de Geologia de Timor-Leste.

Congresso Internacional de Geologia de Timor-Lest

Classical homogeneous multidimensional continued fraction algorithms are ergodic

Homogeneous continued fraction algorithms are multidimensional generalizations of the classical Euclidean algorithm, the dissipative map (x_1,x_2) \in \mathbb{R}_+^2 \longmapsto \left\{\begin{array}{ll} (x_1 - x_2, x_2), & \mbox{if $x_1 \geq x_2$} (x_1, x_2 - x_1), & \mbox{otherwise.} \end{array} \right. We focus on those which act piecewise linearly on finitely many copies of positive cones which we call Rauzy induction type algorithms. In particular, a variation Selmer algorithm belongs to this class. We prove that Rauzy induction type algorithms, as well as Selmer algorithms, are ergodic with respect to Lebesgue measure