On the critical group of matrices

Given a graph G with a distinguished vertex s, the critical group of (G,s) is the cokernel of their reduced Laplacian matrix L(G,s). In this article we generalize the concept of the critical group to the cokernel of any matrix with entries in a commutative ring with identity. In this article we find diagonal matrices that are equivalent to some matrices that generalize the reduced Laplacian matrix of the path, the cycle, and the complete graph over an arbitrary commutative ring with identity. We are mainly interested in those cases when the base ring is the ring of integers and some subrings of matrices. Using these equivalent diagonal matrices we calculate the critical group of the m-cones of the l-duplications of the path, the cycle, and the complete graph. Also, as byproduct, we calculate the critical group of another matrices, as the m-cones of the l-duplication of the bipartite complete graph with m vertices in each partition, the bipartite complete graph with 2m vertices minus a matching.Comment: 18 pages, 5 figure

Managerial appraisal and compensation: The case of Spain

This paper explores some fundamental tasks associated with corporate governance: manager appraisal and compensation. Most of the empirical research in this area has been centered on Anglo-Saxon countries. Some European countries, such as Spain, have a very different governance tradition. Given this context, the work presented here has two objectives: 1.- To describe existing appraisal and compensation practices in Spain, comparing them with those used in the USA. 2.- To study the determinants of CEO compensation, and the relationship between CEO compensation and certain Board practices, using agency theoryAppraisal; compensation; agency

On the critical ideals of graphs

We introduce some determinantal ideals of the generalized Laplacian matrix associated to a digraph G, that we call critical ideals of G. Critical ideals generalize the critical group and the characteristic polynomials of the adjacency and Laplacian matrices of a digraph. The main results of this article are the determination of some minimal generator sets and the reduced Grobner basis for the critical ideals of the complete graphs, the cycles and the paths. Also, we establish a bound between the number of trivial critical ideals and the stability and clique numbers of a graph.Comment: 23 pages. Some changes over the previous version. Accepted in Linear algebra and its Application

Aportaciones al conocimiento de la flora de Córdoba. Algunas especies interesantes de la cuenca hidrográfica del río Bembézar

Se incluyen en este trabajo las citas de 47 taxones en el área que comprende la cuenca hidrográfica del río Bembézar, parte de las cuales constituyen novedades para la provincia de Córdoba y algunas para Andalucía Occidental. Las citas se acompañan de comentarios bibliográficos acerca de la corología de dichos taxones.In this paper the records of 47 taxa from the bassim of the Bembézar river in Cordoba are included. Most of them are new for the Flora of Córdoba and for Wester Andalucia. Chorological and bibliographical remarks about the plants are also included

Factors impacting sustainability in rural drinking water: an integrated approach in Paraguay

The research assesses the sustainability of a program intervention in drinking-water supply in 100 rural communities in Paraguay and identifies the main factors and good practices that could correlate with higher levels of sustainability for drinking-water supply systems. The research includes an integrated assessment of the technical systems, the governance of the community-based provider, and the user’s participation. A total of 100 drinking-water systems built between 2006 and 2010 were technically and operationally revised. Surveys were conducted to 100 community-based sanitation boards (SB) and 450 beneficiary households, using systematic random sampling in 30 rural communities. Preliminary results suggest that participation of the users, the institutional capacity of the SB, the external support of a public institution – as SENASA in this case - and the reinforcement of maintenance activities seem to be key aspects to keep sustainability in rural water systems in the medium and long term

Congestión vehicular en Medellín: una posible solución desde la Economía

Según la teoría económica el mecanismo de precios es una herramienta adecuada para solucionar el problema de congestión vehicular. El objetivo de este artículo es diagnosticar el grado de congestión vehicular de la ciudad de Medellín (Colombia) y proponer alternativas que den solución a dicho problema desde la óptica de la teoría económica. A diferencia de otros estudios, esta investigación analizó la relación entre el gasto de las familias en transporte y la elección de transporte (público o privado) a través la metodología de elasticidades. Se encontró evidencia a favor de la hipótesis de los precios como mecanismos para desincentivar el uso del automóvil privado, pues a medida que aumenta el nivel de gasto en transporte (asociado a un supuesto peaje urbano), la probabilidad de usar transporte privado disminuye, mientras que la probabilidad de utilizar transporte público aumenta.According to the Economic theory, prices are the most accurate mechanism to solution the traffic congestion problem in urban areas. This article presents a diagnosis on the mobility issue in the city of Medellín (Colombia) and a solution is proposed based on Economic theory. The household expenditures in transportation and the choice between public and private transport were analyzed through the method of elasticity. Evidence has been found proving that the prices mechanism is an efficient mechanism to disincentive the usage of private vehicles, since a rise in the expenditure in transport (due to an hypothetic intra- urban toll) results in a lower probability to use private vehicle and a higher probability to use public transportation

Dust in the Circumgalactic Medium of Low-Redshift Galaxies

Using spectroscopically selected galaxies from the Sloan Digital Sky Survey we present a detection of reddening due to dust in the circumgalactic medium of galaxies. We detect the mean change in the colors of "standard crayons" correlated with the presence of foreground galaxies at z ~0.05 as a function of angular separation. Following Peek & Graves (2010), we create standard crayons using passively evolving galaxies corrected for Milky Way reddening and color-redshift trends, leading to a sample with as little as 2% scatter in color. We devise methods to ameliorate possible systematic effects related to the estimation of colors, and we find an excess reddening induced by foreground galaxies at a level ranging from 10 to 0.5 millimagnitudes on scales ranging from 30 kpc to 1 Mpc. We attribute this effect to a large-scale distribution of dust around galaxies similar to the findings of Menard et al. 2010. We find that circumgalactic reddening is a weak function of stellar mass over the range $6 \times 10^9 M_\odot$ -- $6 \times 10^{10} M_\odot$ and note that this behavior appears to be consistent with recent results on the distribution of metals in the gas phase.Comment: Submitted to Ap