A variational analysis of Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian constraint equation, which has been previously studied by other methods.Comment: 15 page

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

Along-strike segmentation in the northern Caribbean plate boundary zone (Hispaniola sector): Tectonic implications

Highlights • Along-strike variations of tectonic framework in northeastern Caribbean margin are studied. • Shallow plate boundary structure related to the slab geometry has been defined. • First-order fault systems and its associated features have been mapped along the margin. Abstract The North American (NOAM) plate converges with the Caribbean (CARIB) plate at a rate of 20.0 ± 0.4 mm/yr. towards 254 ± 1°. Plate convergence is highly oblique (20–10°), resulting in a complex crustal boundary with along-strike segmentation, strain partitioning and microplate tectonics. We study the oblique convergence of the NOAM and CARIB plates between southeastern Cuba to northern Puerto Rico using new swath multibeam bathymetry data and 2D multi-channel seismic profiles. The combined interpretation of marine geophysical data with the seismicity and geodetic data from public databases allow us to perform a regional scale analysis of the shallower structure, the seismotectonics and the slab geometry along the plate boundary. Due to differential rollback between the NOAM oceanic crust north of Puerto Rico and the relative thicker Bahamas Carbonate Province crust north of Hispaniola a slab tear is created at 68.5°W. The northern margin of Puerto Rico records the oblique high-dip subduction and rollback of the NOAM plate below the island arc. Those processes have resulted in a forearc transpressive tectonics (without strain partitioning), controlled by the Septentrional-Oriente Fault Zone (SOFZ) and the Bunce Fault Zone (BFZ). Meanwhile, in the northern margin of Hispaniola, the collision of the Bahamas Carbonate Province results in high plate coupling with strain partitioning: SOFZ and Northern Hispaniola Deformed Belt (NHDB). In the northern Haitian margin, compression is still relevant since seismicity is mostly associated with the deformation front, whereas strike slip earthquakes are hardly anecdotal. Although in Hispaniola intermediate-depth seismicity should disappear, diffuse intermediate-depth hypocenter remains evidencing the presence of remnant NOAM subducted slab below central and western Hispaniola. Results of this study improve our understanding of the active tectonics in the NE Caribbean that it is the base for future assessment studies on seismic and tsunamigenic hazard

Sharp constants in weighted trace inequalities on Riemannian manifolds

We establish some sharp weighted trace inequalities W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M) on $n+1$ dimensional compact smooth manifolds with smooth boundaries, where $\rho$ is a defining function of $M$ and $\sigma\in (0,1)$. This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page

MAPPING THE SPAIN´S EXCLUSIVE ECONOMIC ZONE IN THE GALICIAN MARGIN

MAPPING THE SPAIN´S EXCLUSIVE ECONOMIC ZONE IN THE GALICIAN MARGIN Gómez Ballesteros, M.1(*), González-Aller, J-D. 2, Martín Dávila, J. 3, Carbó, A., 4, Somoza, L. 5, Druet, M. 1, Martínez-Espinosa, S. 2, Catalán, M. 3, Muñoz, A. 4, León, R 5 1 Instituto Español de Oceanografía / C/. Corazón de María, 8, 28020 Madrid 2 Instituto Hidrográfico de la Marina / Pl. San Severiano, 3, 11007 Cádiz 3 Real Observatorio de la Armada, C/. Cecilio Pujazón s/n 11100Cádiz 4 Universidad Complutense de Madrid / Av Séneca, 2, 28040 Madrid 5 Instituto Geológico y Minero de España, Calle de Ríos Rosas, 23, 28003 Madrid (*)Corresponding Author: [email protected] In the context of the Hydrographic and Oceanographic Research of the Spain´s Exclusive Economic program (ZEEE), operated jointly by Instituto Hidrográfico de la Marina (IHM) and Real Observatorio de la Armada (ROA) working in close collaboration with the Instituto Español de Oceanografía (IEO), Universidad Complutense de Madrid (UCM) and Instituto Geológico y Minero de España (IGME) have conducted seven oceanographic cruises in Galician waters (EEZ -01 -02 ZEE , ZEE -03, ZEE -06 -07 ZEE , ZEE- ZEE- 08 and 09). The main objective of the Spain´s Exclusive Economic Zone project is mapping the seafloor, carrying out a systematic bathymetric survey of the 200 miles that comprise this area. In addition, as secondary objectives were performed acquiring that complement other geophysical parameters characterizing the seafloor and seabed from the knowledge of other variables such as the Terrestrial Magnetic Field , Terrestrial Gravity field, sound velocity and seabed internal structure. For the acquisition of detailed and accurate information during these cruises, carried on board the BIO Hespérides, high-resolution geophysical techniques were used to compile the data and the bathymetry of the region was mapped using a multibeam system during which 100 per cent coverage was obtained. At the same time high-resolution parametric seismic reflection profiles, as well as gravity and magnetic, were also recorded in the survey areas. These systems provide data on bathymetry, quality seafloor, acoustics backscatter , gravimetry, magnetometry and subsurface structure and require the use of precise positioning techniques, so were used in conjunction with GPSD and inertial navigation systems. As a result of these oceanographic researches and post-processing, analysis and interpretation of the whole acquired data, a synthesis of 6 maps were published with 1:500.000 scale and corresponding to Bathymetric map, Geomorphology map, Geomagnetic Anomaly map, Bouguer and Free Air Anomaly maps and backscatter map. REFERENCIAS J. Martín Davila, M. Catalán, M. Larrán, Sección de Hidrografía del IHM, A. Carbó, A. Muñoz-Martín, JL Granja, P. Llanes, L. Somoza, R. León, F.J. Gonzalez, M. Gómez-Ballesteros, M. Druet, and J. Acosta, 2014: Zona Económica Exclusiva Española (ZEEE): Margen Continental Gallego. Mapas Generales de batimetría, de anomalías Geomagnéticas, Graviméwtricas de Aire Libre y Bpouguer, Geomorfológico y Mosaico de Imágenes de Reflectividad (E. 1:500.000). Ministerio de Defensa. Secretaria General Técnica, NIPO: 083-12-230-3, DL: M-39518-201

A threshold phenomenon for embeddings of H0mH^m_0 into Orlicz spaces

We consider a sequence of positive smooth critical points of the Adams-Moser-Trudinger embedding of $H^m_0$ into Orlicz spaces. We study its concentration-compactness behavior and show that if the sequence is not precompact, then the liminf of the $H^m_0$-norms of the functions is greater than or equal to a positive geometric constant.Comment: 14 Page

Geomorphology of the Avilés Canyon System, Cantabrian Sea (BayofBiscay)

The Avilés Canyon System (ACS) is a complex, structurally-controlled canyon and valley system constituted by three main canyons of different morphostructural character. They are, from east to west: La Gaviera Canyon, El Corbiro Canyon and Avilés Canyon. In addition to this ACS, a new canyon has been surveyed: Navia Canyon. We present for the first time a high resolution multibeam map showing with great detail the morphological and structural complexity of this segment of the Cantabrian margin. ACS presents a tectonic imprint marked by NW-SE, NNE-SSW and E-W structures. The morphology of their reaches as well as their single mouth, in addition to some rock dredges in their major valleys, demonstrates active down-slope flushing. The continental shelf shows a flat, uniform slope with local and well defined rock outcrops south of Aviles Canyon head. Sedimentary zones are limited, showing thin unconsolidated sedimentary cover. Strong continental margin water dynamics avoid thicker sediment deposition, being littoral sedimentary dynamics responsible for transport to the canyons heads and conduit to the Biscay Abyssal plain. Biscay Abyssal Plain shows evidence of a strong westward current affecting the surveyed strip of this more than 10 km wide plain. Presence of two parallel deep sea channels, erosive scarps, and erosion of gully divides on the lower slope, may indicate that this is part of the distal fan at the termination of the large turbiditic system fed by Cap Ferret, Capbreton and other large canyons (Santander, Torrelavega, Lastres and Llanes) to the west of ACS.Instituto Español de OceanografíaVersión del edito

New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces

We consider a singular Liouville equation on a compact surface, arising from the study of Chern-Simons vortices in a self dual regime. Using new improved versions of the Moser-Trudinger inequalities (whose main feature is to be scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF

Design of a Bovine Low-Density SNP Array Optimized for Imputation

The Illumina BovineLD BeadChip was designed to support imputation to higher density genotypes in dairy and beef breeds by including single-nucleotide polymorphisms (SNPs) that had a high minor allele frequency as well as uniform spacing across the genome except at the ends of the chromosome where densities were increased. The chip also includes SNPs on the Y chromosome and mitochondrial DNA loci that are useful for determining subspecies classification and certain paternal and maternal breed lineages. The total number of SNPs was 6,909. Accuracy of imputation to Illumina BovineSNP50 genotypes using the BovineLD chip was over 97% for most dairy and beef populations. The BovineLD imputations were about 3 percentage points more accurate than those from the Illumina GoldenGate Bovine3K BeadChip across multiple populations. The improvement was greatest when neither parent was genotyped. The minor allele frequencies were similar across taurine beef and dairy breeds as was the proportion of SNPs that were polymorphic. The new BovineLD chip should facilitate low-cost genomic selection in taurine beef and dairy cattle

Breakup reaction models for two- and three-cluster projectiles

Breakup reactions are one of the main tools for the study of exotic nuclei, and in particular of their continuum. In order to get valuable information from measurements, a precise reaction model coupled to a fair description of the projectile is needed. We assume that the projectile initially possesses a cluster structure, which is revealed by the dissociation process. This structure is described by a few-body Hamiltonian involving effective forces between the clusters. Within this assumption, we review various reaction models. In semiclassical models, the projectile-target relative motion is described by a classical trajectory and the reaction properties are deduced by solving a time-dependent Schroedinger equation. We then describe the principle and variants of the eikonal approximation: the dynamical eikonal approximation, the standard eikonal approximation, and a corrected version avoiding Coulomb divergence. Finally, we present the continuum-discretized coupled-channel method (CDCC), in which the Schroedinger equation is solved with the projectile continuum approximated by square-integrable states. These models are first illustrated by applications to two-cluster projectiles for studies of nuclei far from stability and of reactions useful in astrophysics. Recent extensions to three-cluster projectiles, like two-neutron halo nuclei, are then presented and discussed. We end this review with some views of the future in breakup-reaction theory.Comment: Will constitute a chapter of "Clusters in Nuclei - Vol.2." to be published as a volume of "Lecture Notes in Physics" (Springer