On amenability and co-amenability of algebraic quantum groups and their corepresentations

We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this study, we also investigate the involved tensor C*-categories.Comment: 46 pages, (some misprints corrected, a couple of remarks and a new reference added

Amenability and co-amenability of algebraic quantum groups

We define concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele. We show that co-amenability of an algebraic quantum group always implies amenability of its dual. Various necessary and/or sufficient conditions for amenability or co-amenability are obtained. Co-amenability is shown to have interesting consequences for the modular theory in the case that the algebraic quantum group is of compact type.Comment: 25 pages, with some minor corrections, as to appear in the IJMM

La causa parasitaria de la "seca" de los Quercus

La “Seca” de los Quercus es una enfermedad compleja que, en la península Ibérica, afecta principalmente a encinas y alcornoques, tanto a árboles agrupados como dispersos. La causa parasitaria más importante que contribuye al desarrollo de esta enfermedad es la actuación del hongo Phytophthora cinnamomi Rands. Este parásito primario habitante del suelo se detectó en España a finales de los años 80, estando en la actualidad muy presente en las comunidades autónomas de: Andalucía, Castilla La Mancha, Castilla y León, Extremadura y Madrid. En este artículo se explica de forma compresible los caracteres morfológicos del agente parasitario, su actividad como agente patógeno causal de la enfermedad y su dinámica (reproducción, conservación y dispersión).___________________________________The “Seca” (oak decline disease) of the Quercus trees is a complex disease that in the Iberian peninsula attack the holm oak and corck oak both in clusters and dispersed trees. The parasite cause more important that contributes to develop of these disease is the activity of the fungus Phytophthora cinnamomi Rands. This pathogen is a primary parasite soil habitant and was detected in Spain at the end the 80’s. Current this pathogen is present in the Autonomic Comunities of Andalusian, , Castilla La Mancha, Castilla y León, Extremadura and Madrid. In the text is indicate in understandable way the morpholgical characters of the parasite agent, its pathogen activity as well as its dynamic (reproduction, conservation and dispersion)

Historical flash floods retromodelling in the Ondara River in Tàrrega (NE Iberian Peninsula)

Flash floods in the Ondara River have caused many fatalities and damages in the town of Tàrrega in the last 400 yr. Unfortunately, no flow records are available. <br><br> However, floods can sometimes be reconstructed thanks to available historical information: limnimarks, written accounts and archaeological surveys. Indeed, from these data and using the retromodelling method on three different scenarios to take into account morphology changes, the peak flows of the seven greatest floods occurred in Tàrrega since the 17th century were estimated. <br><br> The results showed that the heaviest flood's specific peak flow (10.7 m<sup>3</sup> s<sup>−1</sup> km<sup>−2</sup>) ranks among the highest ever modelled or measured in similar-sized catchments in the Western Mediterranean region. The results pointed out, as well, that the changes in channel's morphology (mainly, the disappearance of a mediaeval bridge under sediment) caused by one of the floods increased the hydraulic capacity of a crucial cross-section. All this resulted in modest floods invading the town less often, but with much faster and, thus, more destructive flows. <br><br> A preliminary estimation of the results' uncertainty was 4% for great floods and 18% for modest floods. <br><br> The reconstructed peak flows will be introduced in a database for a future use in climatic and hydrological studies