Euler, Rey Pastor y la sumabilidad de series

Peer Reviewe

Aspectos de la obra de Cantor apreciados desde la teoría de categorías y funtores

Con los recursos de la teoría de categorías iniciada a mediados del siglo XX y de su fragmento, la teoría de topos a partir de 1970, ha sido posible clarificar algunas de las intuicio-nes originales y profundas de Cantor sobre la naturaleza de los conjuntos abstractos dejadas de lado cuando Zermelo axiomati-zó a principios del siglo la teoría de conjuntos. Este «paraíso de Cantor» defendido por Hilbert frente a los intuicionistas ha sido generalizado por los topos de Grothendieck-Lawvere-Tierney, que proporcionan múltiples modelos formales de teoría de conjuntos en los que interpretar las matemáticas clásicas e intuicionistasWith the resources of category theory initiated in the middle of the twentieth century and its fragment, topos theory from 1970 onwards, it has been possible to clarify some of Cantors orig-inal and profound intuitions about the nature of abstract sets left aside when Zermelo axiomatized set theory at the beginning of the century. This Cantor paradise defended by Hilbert against the in-tuitionists has been generalized by the Grothendieck-Lawvere-Tier-ney topos, which provide multiple formal models of set theory in which to interpret classical and intuitionistic mathematic

Instituciones Matemáticas (1785), by Antonio Gregorio Rosell y Viciano (ca. 1748-1829)

The Royal Printing Office published in 1785 Instituciones Matemáticas by Antonio Rosell, professor since January 1772 at the Royal Studies of San Isidro in Madrid. The author announced two volumes, the first containing numerical arithmetic and the principles of algebra, but the second was unpublished. Rosell claims that he wants to write a «textbook on pure mathematics» for «mathematicians by profession». We present a detailed description of the book, preceded by some biographical notices about the author, and general aspects of the cited work.La Imprenta Real publicó en 1785 Instituciones Matemáticas de Antonio Rosell, catedrático desde enero de 1772 en los Reales Estudios de San Isidro en Madrid. El autor anunció dos volúmenes, el primero contiene la aritmética numérica y los principios del álgebra, pero el segundo quedó inédito. Rosell afirma que quiere escribir un «texto de matemática pura» dirigido a «matemáticos de profesión». Presentamos una descripción detallada del libro, precedida por indicaciones biográficas sobre el autor y aspectos generales de la obra citada

Seabed morphology and bottom water masses related to benthic habitats at the Cristóbal Colón diapir (NW of the Guadalquivir ridge, Gulf of Cádiz)

The seabed morphology and the sub-superficial characteristics of the Cristóbal Colón diapir located on the continental slope of the Gulf of Cadiz have been analysed from data obtained in the framework of the LIFE+INDEMARES/CHICA project. The aim of this study is to recognize the morphological features and the geological processes generated by the bottom water masses and their influence on the habitats and associated benthic communities. The NACW affects the generation of morphological features on the summit, revealing that different oceanographic conditions favoured the carbonate mound growth in the past. The interface between the NACW and the MOW sweeps the bottom from the SE to the NW and the presence of benthic communities dominated by filter feeders on the contouritic drift indicates that this current is strong enough to favour the availability of nutrients and organic particles and to develop both the contouritic deposits on the SE flank and the moats on the N and W flanks.Versión del edito

Submarine deltaic geometries linked to steep, mountainous drainage basins in the northern shelf of the Alboran Sea: Filling the gaps in the spectrum of deltaic deposition

A comprehensive analysis of small deltaic environments linked to short, mountainous, and seasonal fluvial systems in the northern shelf of the Alboran Sea was undertaken in order to define the controlling parameters of the geomorphological variability. The database includes multibeam and backscatter imagery, surficial sediment samples, and high-resolution seismic profiles. Additionally, geomorphological and hydrodynamic modeling and statistical analysis (principal component and cluster analysis) of hydrological and physiographic variables were performed.Most of the studied deltaic systems have high-gradient, coarse-grained deposits with preferential development of the submarine portions to the detriment of the deltaic plains. The geomorphological analysis identified three basic types of plan-viewdistributions according to the length-to-width ratios: elongate, linguoid and lobate. Cross-slope profiles evidence dominant concave-upward geometries, fewer occurrences of planar geometries, and no sigmoid profiles. Sediment depocenters are extremely thick in proximal locations, but thin out rapidly seawards. The geometric distribution patterns of the deltaic systems are characterized by a predictable pattern in plan-view according to the type of fluvial system, ranging from a relatively large river to ephemeral creeks. Prevailing concave and secondary planar profiles support strong sediment progradation in the submarine realmand lowsediment retention in the emerged deltaic environment. Two different types of systems are distinguished: (1) larger rivers,where deltaic deposition is largely controlled by basin dimensions, ultimately dictating themagnitude of water and sediment discharges; and (2) smaller rivers and creeks,where deltaic geometries are related to the basin slopes. The influence of hydrodynamic variables on defining the submarine deltaic geometry has been observed in the case of concave-upward geometries, where geomorphological boundaries are defined by medium- and high-energy wave conditions.Versión del editor2,520

Multidisciplinary study of mud volcanoes and diapirs and their relationship to seepages and bottom currents in the Gulf of Cádiz continental slope (northeastern sector)

The seabed morphology, type of sediments, and dominant benthic species on eleven mud volcanoes and diapirs located on the northern sector of the Gulf of Cádiz continental slope have been studied. The morphological characteristics were grouped as: (i) fluid-escape-related features, (ii) bottom current features, (iii) mass movement features, (iv) tectonic features and (v) biogenic-related features. The dominant benthic species associated with fluid escape, hard substrates or soft bottoms, have also been mapped. A bottom current velocity analysis allowed, the morphological features to be correlated with the benthic habitats and the different sedimentary and oceanographic characteristics. The major factors controlling these features and the benthic habitats are mud flows and fluid-escape-related processes, as well as the interaction of deep water masses with the seafloor topography. Mud volcano eruptions give rise to mud flows and/or aqueous fluid seepage. These processes sustain chemosynthesis-based communities, closely associated with fluid seepage. Large depressions in the nearby area are influenced by collapse-related phenomena, where active fluid escape and the erosive effect of bottom currents have been identified. When the extrusion activity of the mud volcano is low and the seepage is diffuse, authigenic carbonates form within the edifice sediments. The bottom current sweeps the seafloor from the SE to the NW. When the velocity is moderate, sedimentary contourite processes take place on both sides of the edifices. At high velocities, the authigenic carbonates may be exhumed and colonised by species associated with hard substrates. Small carbonate mounds are found at the summits of some volcanoes and diapirs. Living corals have been found on the tops of the shallowest mud volcanoes, revealing different oceanographic conditions and strong bottom currents that favour the availability of nutrients and organic particles. The edifices affected by very high current velocities are located in the channels where erosive processes dominate.Postprint2,517

Episodios de construcción de un delta mediterráneo: Cambio climático y modificaciones antropogénicas en el delta del río Adra

The evolutionary stages of the submarine delta off the Adra River are investigated in this study, under the context of climatic fluctuations entangled with increasing human activities and interventions in the drainage basins and adjacent shores during the Middle to Late Holocene. To achieve that goal, we used an extensive database comprising a set of bathymetric data covering different time slices, a dense grid of high-resolution seismic data and several sediment cores collected in the two submarine lobes of the Adra River delta. Two main evolutionary phases can be identified. The first one extended through most of the construction history and was mediated by major climatic events at the Mediterranean scale; this phase included three major progradational events occurring during the Mid Holocene, the Roman time and the Little Ice Age. The most recent phase is strongly determined by human modifications of the fluvial channels, and resulted in a drastic transformation of the submarine sedimentary environment.Versión del edito

Spatial assessment of trawling activity in a shallow mud volcano field of the Gulf of Cádiz

The Gulf of Cadiz display a wide continental shelf at its northwestern part with a complex oceanographic circulation, large extensions with soft bottoms, diapiric ridges, mud volcanoes, channels, that promote geological and biological heterogeneity and also a wide variety of commercial resources that are exploited by an important fishing sector. Fisheries activity in this area has been studied using VMS and logbooks data during 2011. Fishing effort and captures maps for some important species (Nephrops norvegicus and Parapenaeus longirostris) have been developed for different areas which may be able to improve the spatial and quantitative information on fisheries, and implement measures to improve ecosystem management and conservation of the different vulnerable habitats of the Gulf of CadizVersión del edito

From chemosynthesis-based communities to cold-water corals: Vulnerable deep-sea habitats of the Gulf of Cádiz

The Gulf of Cádiz (GoC) represents an area of ecological importance within the northeastern Atlantic Ocean due to the presence of Mediterranean and Atlantic water masses, a heterogeneous seafloor and a biological confluence. Nevertheless, information on the presence of vulnerable deep-sea habitats is still very scarce and it is of importance for further habitat monitoring within the context of the Habitats and Marine Strategy Framework Directives and for improving conservation and resource extraction management. From 2010 to 2012, fluid migration and emission related edifices (e.g., mud volcanoes, diapirs) from the Spanish continental margin of the GoC have been explored using a remotely operated vehicle (ROV; Liropus 2000) and an underwater camera sled (UCS; APHIA 2012) as well as several devices for collecting sediment and fauna. Different vulnerable deep-sea habitats have been observed, including anoxic bottoms with bacterial mats, sea-pen communities, sponge aggregations, antipatharian and gorgonian communities and also cold-water coral banks. Some of these habitats are included in conservation lists of the habitat directive and in international conventions (OSPAR, RAC/SPA), however some of them are located in areas of the GoC that are exposed to intense trawling. The diversity of habitats detected in the Spanish continental margin of the GoC highlights the importance of seepage related edifices as inducers of seabed and habitat heterogeneity in deep-sea areas.En prens