Hodge polynomials of the moduli spaces of pairs

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\phi)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\phi\in H^0(E)$ is a holomorphic section. In this paper, we determine the Hodge polynomials of the moduli spaces of rank 2 pairs, using the theory of mixed Hodge structures. We also deal with the case in which $E$ has fixed determinant.Comment: 23 pages, typos added, minor change

On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Normal Modes of Black Hole Accretion Disks

This paper studies the hydrodynamical problem of normal modes of small adiabatic oscillations of relativistic barotropic thin accretion disks around black holes (and compact weakly magnetic neutron stars). Employing WKB techniques, we obtain the eigenfrequencies and eigenfunctions of the modes for different values of the mass and angular momentum of the central black hole. We discuss the properties of the various types of modes and examine the role of viscosity, as it appears to render some of the modes unstable to rapid growth

Estrategias de cooperación inter-empresa para el desarrollo de mejores prácticas medioambientales en la industria de los astilleros colombianos

The present work aims to develop strategies that allow implementingenvironmental best practices in the Colombian shipyard industry, a sector that has been growing for the last decade and that is identified as a potential world-class industry in the country. Collaborative work was carried out with four of the biggest Colombian shipyards and an international firm to identify legal and operational issues regarding the industrial activity, to reach unified consensus to represent the whole sector. Finally, an environmentalbest practices document was elaborated to guideshipyard operationsin the country, with the potential to be constituted as an official guide of the Colombian Ministry for the Environment.El presente trabajo tiene como objetivo desarrollar estrategias que permitan incorporar buenas prácticasambientales en la industria astillera Colombiana, sector que ha mostrado un crecimiento significativo en la última década y que representa una apuesta productiva para el país. Se efectuó un trabajo colaborativo con cuatro de los astilleros más representativos en el país y una empresa internacional para identificar los aspectos legales y de operación de la actividad industrial que impactan el medio ambiente, de manera que se lograse unificar criterios que tuviesen una representatividad sectorial. Finalmente se consolidóun documento de buenas prácticas ambientales para orientar la operación de astilleros en el país, con el potencial de constituirse como una guía oficial del Ministerio de Ambiente, Vivienda y Desarrollo Territorial colombiano

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Nitrogen Cycle And Ecosystem Services In The Brazilian La Plata Basin: Anthropogenic Influence And Climate Change.

The increasing human demand for food, raw material and energy has radically modified both the landscape and biogeochemical cycles in many river basins in the world. The interference of human activities on the Biosphere is so significant that it has doubled the amount of reactive nitrogen due to industrial fertiliser production (Haber-Bosch), fossil fuel burning and land-use change over the last century. In this context, the Brazilian La Plata Basin contributes to the alteration of the nitrogen cycle in South America because of its huge agricultural and grazing area that meets the demands of its large urban centres - Sao Paulo, for instance - and also external markets abroad. In this paper, we estimate the current inputs and outputs of anthropogenic nitrogen (in kg N.km(-2).yr(-1)) in the basin. In the results, we observe that soybean plays a very important role in the Brazilian La Plata, since it contributes with an annual entrance of about 1.8 TgN due to biological nitrogen fixation. Moreover, our estimate indicates that the export of soybean products accounts for roughly 1.0 TgN which is greater than the annual nitrogen riverine exports from Brazilian Parana, Paraguay and Uruguay rivers together. Complimentarily, we built future scenarios representing changes in the nitrogen cycle profile considering two scenarios of climate change for 2070-2100 (based on IPCC's A2 and B2) that will affect land-use, nitrogen inputs, and loss of such nutrients in the basin. Finally, we discuss how both scenarios will affect human well-being since there is a connection between nitrogen cycle and ecosystem services that affect local and global populations, such as food and fibre production and climate regulation.72691-70

A new extended mixture normal distribution

The normal distribution is the most important model in statistics for analysis of continuous data. We propose a new distribution, called the extended mixture normal distribution, based on a linear mixture model. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions, mean deviations and two measures of entropy. The maximum likelihood and Bayesian methods are used to estimate the model parameters. We prove empirically that the new distribution can be a better model than the normal and other classical distributions by means of an application to real data