Housing cycles in the major euro area countries.

The recent burst of the house price bubble in the United States and its spillover effects on real economies worldwide has rekindled the interest in the role of housing in the business cycle. In this paper, we investigate the relationships between housing cycles among the four major euro area countries (Germany, France, Italy and Spain) over the sample 1980q1 – 2008q4. Our main findings are that GDP cycles between 1.5 and 8 years show a high degree of comovement across these four countries, reflecting trade linkages. In contrast comovements in housing market cycles between 1.5 and 8 years are much weaker, idiosyncratic factors playing a major role. House prices are even less related across countries than quantities (residential investment, building permits, housing starts …). We find however much stronger relationships since 1999, i.e. in the common monetary policy period.Housing cycles, synchronisation measures, euro area countries.

The Stationary Phase Method for a Wave Packet in a Semiconductor Layered System. The applicability of the method

Using the formal analysis made by Bohm in his book, {\em "Quantum theory"}, Dover Publications Inc. New York (1979), to calculate approximately the phase time for a transmitted and the reflected wave packets through a potential barrier, we calculate the phase time for a semiconductor system formed by different mesoscopic layers. The transmitted and the reflected wave packets are analyzed and the applicability of this procedure, based on the stationary phase of a wave packet, is considered in different conditions. For the applicability of the stationary phase method an expression is obtained in the case of the transmitted wave depending only on the derivatives of the phase, up to third order. This condition indicates whether the parameters of the system allow to define the wave packet by its leading term. The case of a multiple barrier systems is shown as an illustration of the results. This formalism includes the use of the Transfer Matrix to describe the central stratum, whether it is formed by one layer (the single barrier case), or two barriers and an inner well (the DBRT system), but one can assume that this stratum can be comprise of any number or any kind of semiconductor layers.Comment: 15 pages, 4 figures although figure 4 has 5 graph

A Change of Variables to the Dual and Factorization of Composite Anomalous Jacobians

Changes of variables giving the dual model are constructed explicitly for sigma-models without isotropy. In particular, the jacobian is calculated to give the known results. The global aspects of the abelian case as well as some of those of the cases where the isometry group is simply connected are considered. Considering the anomalous case, we infer by a consistency argument that the `multiplicative anomaly' should be replaceable by adequate rules for factorization of composite jacobians. These rules are then generalized in a simple way for composite jacobians defined in spaces of different types. Implimentation of these rules then gives specific formulas for the anomally for semisimple algebras and also for solvable ones.Comment: 15 pages, no figures, Latex file, A treatment of the global aspects of the abelian and of semisimple duality groups are added. General formulas for the mixed anomaly are derive

Rudiments of Holography

An elementary introduction to Maldacena's AdS/CFT correspondence is given, with some emphasis in the Fefferman-Graham construction. This is based on lectures given by one of us (E.A.) at the Universidad Autonoma de Madrid.Comment: 60 pages, additional misprints corrected, references adde