On quadratic Hom-Lie algebras with equivariant twist maps and their relationship with quadratic Lie algebras

Hom-Lie algebras having non-invertible and equivariant twist maps are studied. Central extensions of Hom-Lie algebras having these properties are obtained and shown how the same properties are preserved. Conditions are given so that the produced central extension has an invariant metric with respect to its Hom-Lie product making its twist map self-adjoint when the original Hom-Lie algebra has such a metric. This work is focused on algebras with these properties and we call them quadratic Hom-Lie algebras. It is shown how a quadratic Hom-Lie algebra gives rise to a quadratic Lie algebra and that the Lie algebra associated to the given Hom-Lie central extension is a Lie algebra central extension of it. It is also shown that if the 2-cocycle associated to the central extension is not a coboundary, there exists a non-abelian and non-associative algebra, the commutator of whose product is precisely the Hom-Lie product of the Hom-Lie central extension. Moreover, the algebra whose commutator realizes this Hom-Lie product is shown to be simple if the associated Lie algebra is nilpotent. Non-trivial examples are provided

Interpretación de anisotropías petrográficas en granitos ornamentales basada en la medida de la velocidad de las ondas P

The existence of a possible anisotropy, determined by the orientation of any mineral or by micro­crack network in granite rock, isn´t easily detected by the naked eye. Five granitic rocks from Galicia (Spain), namely Albero, Gris Alba, Gris Mondariz, Rosa Porriño and Traspielas, were characterized petrographically by means of textural and mineralogical studies, using optical polarizing microscopy, and fractographic studies were carried out under scanning electron microscopy. Longitudinal wave propagation velocity was measured in three orthogonal directions on cubic samples, oriented according to rift surface (known in quarry works like the preferential partition surface visible in the blocks). Vp was measured on dry and water saturated samples. All the dry samples showed an anisotropic behaviour of Vp. Models of microcrack network distribution and possible mineral grain orientation were developed based on the obtained data.La existencia de una posible anisotropía originada por orientación de minerales y/o redes de microfisuración en rocas graníticas no es fácilmente detectable a simple vista. Cinco rocas graníticas de Galicia, denominadas comercialmente Albero, gris Alba, gris Mondariz, rosa Porriño y Traspielas, se car­acterizaron petrográficamente, mediante estudios texturales y mineralógicos utilizando microscopía óptica de polarización, realizándose también estudios fractográficos bajo microscopía electrónica de barrido. Se midieron las velocidades de propagación de las ondas longitudinales (Vp) en tres direcciones ortogonales en muestras cúbicas orientadas según el rift (denominado así en cantería como la superficie preferente de partición). Vp se midió en muestras secas y saturadas. Todas las muestras secas mostraron un comportamiento anisótropo de Vp. A partir de los datos obtenidos se han interpretado las redes de distribución de microfisuras y la orientación de minerales

3D Modelling of archaeoseismic damage in the Roman site of Baelo Claudia (Gibraltar Arc, south Spain)

This study deals with the morphometric characterization and quantification of earthquake damage in the ancient Roman city of Baelo Claudia in South Spain (Gibraltar Arc) by means of the use of 3D modelling from drone imagery. Baelo Claudia is a world-renowned archaeological site recording recurrent earthquake destruction during the first and third centuries AD. The first earthquake destroyed the lower littoral zone of the city, allowing its reconstruction from the year c. 60–70 CE, but the second earthquake in 365–390 CE led to the complete destruction of the renewed city and its eventual abandonment. This second earthquake imprinted important deformations in the main monumental zone of the city, including the basilica temples, macellum, city walls, aqueducts and funerary monuments, as well as in the main paved zones of the city. This is the case for the Forum, Decumanus and Cardos, which show a variety of folds, pop-up structures, conjugate fractures and impact marks susceptible to be measured in a 3D format. The current study presents detailed (up to 3 mm/pixel) surface models of iconic monuments within the city. The 3D models were obtained by means of serial orthophotos taken with a UAV Mavic Pro 2 (DJI) Drone device equipped with a 20 mpx camera and a 1” CMOS sensor. Each individual image was captured in a geo-referenced jpg format and processed with the Agisoft Metashape Professional software®. Depending on the measured monument, the final images consisted of 250 to 700 photographs clustered by 50,000 to 150,000 tie points. In all studied items (Decumanus, city walls and bath dish), we follow the same workflow of analysis: (1) alignment of photos with support points; (2) building a dense cloud of points; (3) creation of the surface texture; (4) creation of the Digital Elevation Model (DEM); (5) creation of the orthomosaic; and finally, (6) the building of the high-quality 3D tiled surface models. The obtained models allow the geometric quantification of earthquake deformations (displacements, amplitudes, orientation, etc.) in a GIS-based 3D environment suitable to quantify oriented damage of seismic origin. In a complementary way, these 3D models deserve to be considered for their potential role as digital seismoscopes of ancient archaeological sites and/or heritage building

Photoionization models of the CALIFA HII regions. I. Hybrid models

Photoionization models of HII regions require as input a description of the ionizing SED and of the gas distribution, in terms of ionization parameter U and chemical abundances (e.g. O/H and N/O). A strong degeneracy exists between the hardness of the SED and U, which in turn leads to high uncertainties in the determination of the other parameters, including abundances. One way to resolve the degeneracy is to fix one of the parameters using additional information. For each of the ~ 20000 sources of the CALIFA HII regions catalog, a grid of photoionization models is computed assuming the ionizing SED being described by the underlying stellar population obtained from spectral synthesis modeling. The ionizing SED is then defined as the sum of various stellar bursts of different ages and metallicities. This solves the degeneracy between the shape of the ionizing SED and U. The nebular metallicity (associated to O/H) is defined using the classical strong line method O3N2 (which gives to our models the status of "hybrids"). The remaining free parameters are the abundance ratio N/O and the ionization parameter U, which are determined by looking for the model fitting [NII]/Ha and [OIII]/Hb. The models are also selected to fit [OII]/Hb. This process leads to a set of ~ 3200 models that reproduce simultaneously the three observations. We find that the regions associated to young stellar bursts suffer leaking of the ionizing photons, the proportion of escaping photons having a median of 80\%. The set of photoionization models satisfactorily reproduces the electron temperature derived from the [OIII]4363/5007 line ratio. We determine new relations between the ionization parameter U and the [OII]/[OIII] or [SII]/[SIII] line ratios. New relations between N/O and O/H and between U and O/H are also determined. All the models are publicly available on the 3MdB database.Comment: Accepted for publication in A&