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

A quantitative analysis of cold water for human consumption in hospitals in Spain

An estimation of the water used for human consumption in hospitals is essential to determine possible savings and to fix criteria to improve the design of new water consumption models.The present work reports on cold water for human consumption (CWHC) in hospitals in Spain and determines the possible savings. In the period of 2005–2012, 80 Eco-Management and Audit Schemes (EMAS) from20 hospitals were analysed. The results conclude that the average annual consumption of CWHC is 1.59m3/m2 (with a standard deviation of 0.48 m3/m2), 195.85 m3/bed (standard deviation 70.07 m3/bed), or 53.69 m3/worker (standard deviation 16.64 m3/worker). The results demonstrate the possibility of saving 5,600,000m3 of water per year. Assuming the cost of water as approximately 1.22 €/m3, annual savings are estimated as 6,832,000 €. Furthermore, 2,912MWh of energy could be saved, and the emission of 22,400 annual tonnes of CO2 into the atmosphere could be avoided

A new sauropod titanosaur from the Plottier Formation (Upper Cretaceous) of Patagonia (Argentina)

This paper presents a new titanosaur sauropod, collected from levels of reddish clays assigned to the Plottier Formation (Coniacian-Santonian). The holotype of Petrobrasaurus puestohernandezi gen. et. sp. nov. is a disarticulated specimen, from which teeth, cervical, dorsal and caudal vertebrae, sternal plates, metacarpals, femora, tibia, a fragment of ilium, pubis, haemal arches, and cervical and dorsal ribs have been preserved. This period is of particular interest because it saw the definitive isolation of the vertebrate faunas of Patagonia, with the separation of South America from the rest of Gondwana, a process that had begun during the Early Cretaceous. Although some of the characters observed in Petrobrasaurus gen. nov. suggest a relationship with the South American clade Lognkosauria, this new sauropod is regarded as Titanosauria incertae sedis until a more profound analysis of the Titanosauria that in which it is included is undertaken

Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.Comment: 29 page

Nonholonomic constraints in kk-symplectic Classical Field Theories

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.Comment: 27 page