Lagrangian submanifolds and dynamics on Lie affgebroids

We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.Comment: 50 pages. Several sections update

Poisson-Jacobi reduction of homogeneous tensors

The notion of homogeneous tensors is discussed. We show that there is a one-to-one correspondence between multivector fields on a manifold $M$, homogeneous with respect to a vector field $\Delta$ on $M$, and first-order polydifferential operators on a closed submanifold $N$ of codimension 1 such that $\Delta$ is transversal to $N$. This correspondence relates the Schouten-Nijenhuis bracket of multivector fields on $M$ to the Schouten-Jacobi bracket of first-order polydifferential operators on $N$ and generalizes the Poissonization of Jacobi manifolds. Actually, it can be viewed as a super-Poissonization. This procedure of passing from a homogeneous multivector field to a first-order polydifferential operator can be also understood as a sort of reduction; in the standard case -- a half of a Poisson reduction. A dual version of the above correspondence yields in particular the correspondence between $\Delta$-homogeneous symplectic structures on $M$ and contact structures on $N$.Comment: 19 pages, minor corrections, final version to appear in J. Phys. A: Math. Ge

Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups

In this paper, we discuss several relations between the existence of invariant volume forms for Hamiltonian systems on Poisson-Lie groups and the unimodularity of the Poisson-Lie structure. In particular, we prove that Hamiltonian vector fields on a Lie group endowed with a unimodular Poisson-Lie structure preserve a multiple of any left-invariant volume on the group. Conversely, we also prove that if there exists a Hamiltonian function such that the identity element of the Lie group is a nondegenerate singularity and the associated Hamiltonian vector field preserves a volume form, then the Poisson-Lie structure is necessarily unimodular. Furthermore, we illustrate our theory with different interesting examples, both on semisimple and unimodular Poisson-Lie groups.Comment: 17 page

The view on teachers and students using virtual classrooms methodology b-learming

El presente estudio se engloba dentro de un proyecto de innovación llevado a cabo en el curso 2010-2011 en la Universidad de La Laguna. Se desarrolló en las distintas asignaturas del campo o ámbito de la "Tecnología Educativa" y que se imparten actualmente en distintas titulaciones de la Facultad de Educación. El objetivo que se pretende es indagar sobre la opinión y valoración que hace el alumnado y el profesorado sobre el uso de las aulas virtuales como herramienta de apoyo en la modalidad semipresencial o “blended-learning”. Así como explorar si el diseño del aula virtual y el uso de determinadas herramientas y actividades de aprendizaje en el entorno de las aulas virtuales está moldeada por el perfil de la titulación, de la asignatura o de la práctica docente de cada profesor La metodología se estructuró en dos líneas atendiendo a la naturaleza de los sujetos participantes: profesorado y alumnado. En el caso del alumnado se elaboraron dos cuestionarios de opinión on line. Y con respecto al profesorado se elaboró una matriz en la que el docente tenía que describir tanto la metodología utilizada como las herramientas y actividades desarrolladas. De los resultados se desprende que en el diseño del aula virtual interviene fundamentalmente la propia estructuración de las asignaturas en créditos teóricos y prácticos. Y en cuanto a la selección de las herramientas digitales y actividades de aprendizaje parece que de alguna manera está influyendo las teorías y prácticas docentes sobre cómo debe desarrollar y adquirir el alumnado determinadas habilidades y conocimientos.This study is part of an innovation project conducted in 2010-2011 at the University of La Laguna. It was developed in the different subjects of the field or area of "Educational Technology" and currently taught in different degrees of the Faculty of Education. The objective sought is to inquire into the opinion and judgment that makes the students and teachers on the use of virtual classrooms as a support tool in a blended- learning or blen. And explore whether the design of the virtual classroom and the use of certain tools and learning activities in the virtual classroom environment is shaped by the degree profile of the subject or of the teaching practice of each teacher. The methodology is structured in two lines based on the nature of the subjects involved: teachers and students. In the case of students prepared two opinion questionnaires online. And with respect to teachers is developed a matrix in which the teacher had to describe both the methodology and the tools and activities. The results show that in the virtual classroom design itself primarily involved structuring of credit courses in theory and practice. And as for the selection of digital tools and learning activities seems that somehow is influencing educational theories and practices on how to develop and acquire certain skills and knowledge students

Determination of the toxic activity of optimized extracts of Palmaria and Porphyra as a treatment for ischemia-reperfusion injury

La lesión por isquemia-reperfusión (I/R) puede provocar rechazos en los trasplantes de órganos debido al daño a nivel celular que producen los radicales libres de oxígeno (ROS). Se ha comprobado que los antioxidantes naturales pueden reducir este daño. Los extractos de muchas algas poseen una actividad antioxidante notable, pero se necesita comprobar la toxicidad de estos antes de proponerlos como fármacos. En este estudio, se realizaron dos ensayos toxicológicos con queratinocitos humanos inmortalizados (HaCaT) y nauplios de Artemia salina para valorar la toxicidad de dos extractos con actividad antioxidante de Palmaria palmata y Porphyra sp. Se obtuvieron LC 50 de 7,843 % ( v/v ) de concentración de extracto en P. palmata en el ensayo con HaCaT y 3,2583 % ( v/v ) en el ensayo con A. salina , mientras que con Porphyra sp. se obtuvo 10,7463 % ( v/v ) en el ensayo con HaCaT y 6,5688 % ( v/v ) en el ensayo con A. salina . Los niveles sin efecto adverso observable (NOAEL) obtenidos para cada alga en cada ensayo mostraron significativamente una mayor toxicidad del extracto de P. palmata que del de Porphyra sp. (p < 0,05). Finalmente, se propuso un índice que tiene en cuenta la actividad antioxidante y la toxicidad de cada extracto para predecir su eficiencia in vivo , confirmando los resultados anteriores, y por ello se escogió el extracto de Porphyra sp. como el más idóneo para continuar con los ensayos preclínicos en el desarrollo de un fármaco para el tratamiento de la lesión por I/R.The ischemia/reperfusion (I/R) injury can cause rejections in organ transplantation surgeries due to the damage that radical oxigen species (ROS) produce in the cells. It has been proved that natural antioxidants can reduce this damage. Lots of algae extracts show a noticeable antioxidant activity, but there’s a need to test their toxicity before suggesting them as potential drugs. In this study, two toxicologic assays using human immortalized keratinocytes (HaCaT) and Artemia salina nauplii were carried out to test the toxicity of two extracts that showed antioxidant activity from Palmaria palmata and Porphyra sp. LC 50 values of 7.843 % ( v/v ) of extract concentration with P. palmata in the HaCaT assay and 3.2583 % ( v/v ) in the A. salina assay were obtained, while 10.7463 % ( v/v ) of extract concentration for the HaCaT assay and 6.5688 % ( v/v ) for the A. salina assay were obtained for Porphyra sp. The non-observed adverse effect level (NOAEL) obtained for each algae in each assay showed a significantly higher toxicity level in the P. palmata extract than in the Porphyra sp. extract (p < 0.05). Lastly, an index which considers both antioxidant activity and toxicity of each extract was proposed for predicting their in vivo efficiency, supporting the previous results, so Porphyra sp. extract was considered the most suitable for going ahead with the preclinic assays towards the development of a drug for treating the I/R injury.Ciencias Experimentale

Chromium Isotope Behavior During Serpentinite Dehydration in Oceanic Subduction Zones

Fluids released through the dehydration of serpentinite can be rich in Cl −, which enables the significant mobility of Cr in subduction zones. However, the Cr isotope behavior accompanying the mobility of Cr during serpentinite dehydration is still poorly constrained. Here, we report high-precision Cr isotope data for a unique suite of serpentinites that represent metamorphic products at different depths in oceanic subduction zones. Low-grade serpentinites affected by significant Cr loss during serpentinization exhibit remarkably higher δ 53Cr, while samples with Cr contents >∼1,800 ppm typically preserve mantle-like δ 53Cr. Antigorite serpentinites have an average δ 53Cr value of −0.17‰ ± 0.19‰ (n = 12, 2SD), which is statistically lower than those of low-grade serpentinite (−0.05‰ ± 0.30‰, n = 80, 2SD) and higher-grade chlorite harzburgite (−0.10‰ ± 0.27‰, n = 22, 2SD). This suggests that resolvable Cr isotope fractionation occurs during serpentinite dehydration, which is explained by the variability of Cr isotope behavior in the presence of Cl-bearing fluids at different dehydration stages. No obvious Cr isotope fractionation was found during chlorite harzburgite dehydration, probably related to the limited Cr mobility in a Cl-poor fluid. Other processes, such as melt extraction, external fluid influx and retrograde metamorphism, have negligible effects on the Cr isotope systematics of meta-serpentinites. Fluids released by serpentinite dehydration may have a great effect on the Cr isotope heterogeneity of mantle wedge peridotites and arc magmas.National Key Ramp;D Program of ChinaStrategic Priority Research Program (B) of CAS 2018YFA0702600National Natural Science Foundation of China (NSFC) XDB41000000Fundamental Research Funds for the Central Universities 42073029 41973004CNSAMICIN/AEI D020204FEDER program "Una manera de hacer Europa" PID2022-136471N-B-C21 C22 PID2019-111715GB-I00AEIFSE program "FSE invierte en tu futuro" RYC2018-024363-IJunta de AndaluciaEuropean Union (EU) Postdoc_21_00791European Social Fund (ESF)Junta de Andalucia RNM-131 RNM-37

The RoPES project with HARPS and HARPS-N. I. A system of super-Earths orbiting the moderately active K-dwarf HD 176986

We report the discovery of a system of two super-Earths orbiting the moderately active K-dwarf HD 176986. This work is part of the RoPES RV program of G- and K-type stars, which combines radial velocities (RVs) from the HARPS and HARPS-N spectrographs to search for short-period terrestrial planets. HD 176986 b and c are super-Earth planets with masses of 5.74 and 9.18 M$_{\oplus}$, orbital periods of 6.49 and 16.82 days, and distances of 0.063 and 0.119 AU in orbits that are consistent with circular. The host star is a K2.5 dwarf, and despite its modest level of chromospheric activity (log(R'hk) = - 4.90 +- 0.04), it shows a complex activity pattern. Along with the discovery of the planets, we study the magnetic cycle and rotation of the star. HD 176986 proves to be suitable for testing the available RV analysis technique and further our understanding of stellar activity.Comment: 21 pages, 24 figures, 7 table