Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

The 12 prophets dataset

The "Ajeijadinho 3D" project is an initiative supported by the University of S\~ao Paulo (Museum of Science and Dean of Culture and Extension), which involves the 3D digitization of art works of Brazilian sculptor Antonio Francisco Lisboa, better known as Aleijadinho. The project made use of advanced acquisition and processing of 3D meshes for preservation and dissemination of the cultural heritage. The dissemination occurs through a Web portal, so that the population has the opportunity to meet the art works in detail using 3D visualization and interaction. The portal address is http://www.aleijadinho3d.icmc.usp.br. The 3D acquisitions were conducted over a week at the end of July 2013 in the cities of Ouro Preto, MG, Brazil and Congonhas do Campo, MG, Brazil. The scanning was done with a special equipment supplied by company Leica Geosystems, which allowed the work to take place at distances between 10 and 30 meters, defining a non-invasive procedure, simplified logistics, and without the need for preparation or isolation of the sites. In Ouro Preto, we digitized the churches of Francisco of Assis, Our Lady of Carmo, and Our Lady of Mercy; in Congonhas do Campo we scanned the entire Sanctuary of Bom Jesus de Matosinhos and his 12 prophets. Once scanned, the art works went through a long process of preparation, which required careful handling of meshes done by experts from the University of S\~ao Paulo in partnership with company Imprimate.Comment: Full dataset online at http://aleijadinho3d.icmc.usp.br/data.htm

A supergeometric approach to Poisson reduction

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to describe the corresponding reductions.Comment: 40 pages. Final version accepted for publicatio

Stellar population analysis on local infrared-selected galaxies

To study the stellar population of local infrared galaxies, which contain star-forming galaxies, composite galaxies, LINERs, and Seyfert 2s. We also want to find whether infrared luminosity and spectral class have any effects on their stellar populations. The sample galaxies are selected from the main galaxy sample of SDSS-DR4 and then cross-correlated with the IRAS-PSCz catalog. We fit our spectra (stellar absorption lines and continua) using the spectral synthesis code STARLIGHT on the base of the templates of Simple Stellar Population and the spectra of star clusters.Among the 4 spectral classes, LINERs present the oldest stellar populations, and the other 3 sub-samples all present substantial young and intermediate age populations and very few old populations. The importance of young populations decreases from star-forming, composite, Seyfert 2 to LINER. As to different infrared luminosity bins, ULIGs & LIGs (log($L_{IR}/L_{\odot})\geq$11) present younger populations than starbursts and normal galaxies. However, the dominant contributors to mass are old populations in all sample galaxies. The fittings by using the spectra of star clusters with different ages and metallicities as templates also give consistent results. The dominated populations in star-forming and composite galaxies are those with metallicity $Z=0.2Z_\odot$, while LINERs and Seyfert 2s are more metal-rich. The normal galaxies are more metal-rich than the ULIGs & LIGs and starbursts for the star-forming galaxies within different infrared luminosity bins. Additionally, we also compare some synthesis results with other parameters obtained from the MPA/JHU catalog.Comment: 13 pages, 11 figures, accepted for publication by A&

Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

In this paper, we study the following degenerate critical elliptic equations with anisotropic coefficients $$-div(|x_{N}|^{2\alpha}\nabla u)=K(x)|x_{N}|^{\alpha\cdot 2^{*}(s)-s}|u|^{2^{*}(s)-2}u {in} \mathbb{R}^{N}$$ where $x=(x_{1},...,x_{N})\in\mathbb{R}^{N},$ $N\geq 3,$ $\alpha>1/2,$ $0\leq s\leq 2$ and $2^{*}(s)=2(N-s)/(N-2).$ Some basic properties of the degenerate elliptic operator $-div(|x_{N}|^{2\alpha}\nabla u)$ are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As a consequence, we obtain some nonexistence results for solutions of this equation.Comment: 29 page

Jacobi-Nijenhuis algebroids and their modular classes

Jacobi-Nijenhuis algebroids are defined as a natural generalization of Poisson-Nijenhuis algebroids, in the case where there exists a Nijenhuis operator on a Jacobi algebroid which is compatible with it. We study modular classes of Jacobi and Jacobi-Nijenhuis algebroids

Reconstructing hominin diets with stable isotope analysis of amino acids: new perspectives and future directions

Stable isotope analysis of teeth and bones is regularly applied by archeologists and paleoanthropologists seeking to reconstruct diets, ecologies, and environments of past hominin populations. Moving beyond the now prevalent study of stable isotope ratios from bulk materials, researchers are increasingly turning to stable isotope ratios of individual amino acids to obtain more detailed and robust insights into trophic level and resource use. In the present article, we provide a guide on how to best use amino acid stable isotope ratios to determine hominin dietary behaviors and ecologies, past and present. We highlight existing uncertainties of interpretation and the methodological developments required to ensure good practice. In doing so, we hope to make this promising approach more broadly accessible to researchers at a variety of career stages and from a variety of methodological and academic backgrounds who seek to delve into new depths in the study of dietary composition.Investigating hominin diets and environments Factors affecting isotope values - Food processing. - Digestion and metabolic processes. - Isotopic variation of dietary sources. Statistical analyses Analytical considerations Applications in archeology and paleoecology Perspectives for hominin studie

Automated PECVD System for Fabrication of a-Si:H Devices

AbstractThis paper reports a fully automated plasma-enhanced plasma chemical vapor deposition (PECVD) system for thin-film deposition. This system can be used for the deposition of hydrogenated amorphous silicon (a-Si:H) and nanocrystalline silicon for devices like solar cells or optical sensors with good film homogeneity and material properties reproducibility. The control software enables two modes of system operation: semi-manual and full-auto. In the semi-manual mode the user sets all process parameters and controls all depositions steps. In the full-auto mode, the program performs the process steps according to script commands in a recipe file. This way, complex multilayered devices can be fabricated, with a high degree of reproducibility of the device characteristics