Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

Large-time behavior of some numerical schemes: application to the sonic-boom phenomenon

In this thesis we highlight the necessity of employing numerical schemes that preserve the large-time dynamical properties of the continuous system. We focus on Burgers- like equations, which are well known to develop N-waves as intermediate or asymptotic profiles. As we show, not only forward simulations can be distorted; the efficiency of solutions of optimization and inverse design problems might be affected too. In particular, we apply our results to the case of the prediction and control of the sonic- boom phenomenon, modeled by the augmented Burgers equation

Compliance with the Municipal Agro-Environmental Legislation in Francisco de Orellana, Ecuador

The Decentralized Autonomous Municipal Government of the Francisco de Orellana canton is made up of the following rural parishes: Alejandro Labaka, Armenia, Dayuma, El Dorado, El Edén, García Moreno, Guayusa, Inés Arango, La Belleza, Nuevo Paraiso, Taracoa and the Urban Parish of El Coca. The Constitution of the Republic of Ecuador (2008) establishes the rights of nature and protects the biodiversity of the Amazon ecosystem. This is complemented by the provisions of the Organic Code of Territorial Organization, Autonomy and Decentralization (2010), the Organic Code of the Environment (2017) and also the Organic Law for the Integrated Planning of the Special Amazon Territorial District (2018). This article reviewed compliance with municipal agro-environmental legislation in the Decentralized Municipal Autonomous Government of the Francisco de Orellana canton. This analysis was based on the publication of the Organic Law for the Integrated Planning of the Special Territorial District of the Amazon in the Official Registry Supplement 245, dated May 21, 2018. A qualitative methodology was used. Data were collected through analysis of public policies, regulations, legislation and ordinances, and interviews with the main actors of the Decentralized Municipal Autonomous Government. The results suggested that the Municipal Government seeks to protect the biodiversity of the Amazon ecosystem by adopting sustainable development and conservation policies, but it is clear that ordinances are needed for agro-environmental education, garbage classification, recycling, organic gardens, and greater integration into municipal agro-environmental projects. Keywords: agriculture, Amazon, environment, biodiversity, municipal, Ecuador. Resumen El Gobierno Autónomo Descentralizado Municipal del cantón Francisco de Orellana está integrado por las Parroquias Rurales: Alejandro Labaka, Armenia, Dayuma, El Dorado, El Edén, García Moreno, Guayusa, Inés Arango, La Belleza, Nuevo Paraiso, Taracoa y la Parroquia Urbana de El Coca. La Constitución de la República del Ecuador (2008), establece los derechos de la naturaleza y protege la biodiversidad del ecosistema amazónico, esto se complementa con lo establecido en el Código Orgánico de Organización Territorial Autonomía y Descentralización (2010), el Código Orgánico del Ambiente (2017) y ademas la Ley Orgánica para la Planificación Integral de la Circunscripción Territorial Especial Amazónica (2018). Este artículo revisa el cumplimiento de la legislación agroambiental municipal en el Gobierno Autónomo Descentralizado Municipal del cantón Francisco de Orellana, este análisis se realiza a partir de la publicación de la Ley Orgánica para la Planificación Integral de la Circunscripción Territorial Especial Amazónica en el Registro Oficial Suplemento 245, de fecha 21 de mayo del 2018. La metodología utilizada se basó en un análisis cualitativo usando técnicas y herramientas como la obtención de datos, análisis de las políticas públicas, normativa, legislación, ordenanzas y entrevista con los principales actores del Gobierno Autónomo Descentralizado Municipal del cantón Francisco de Orellana. Los principales resultados sugieren que el Gobierno Municipal busque precautelar la biodiversidad del ecosistema amazónico, adoptando políticas de desarrollo sostenible y de conservación, pero es evidente que son necesarias ordenanzas encaminadas a la educación agroambiental, clasificación de la basura, reciclaje, huertos orgánicos, y una mayor integración en proyectos agroambientales municipales. Palabras clave: agricultura, Amazonía, ambiente, biodiversidad, municipal, Ecuador

A splitting method for the augmented Burgers equation

In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of first order. We also analyze the large-time behavior of the approximated solution by obtaining the first term in the asymptotic expansion. We prove that, when time increases, these solutions be have as the self-similar solutions of the viscous Burgers equation

Jet shapes in ep collisions at HERA

New measurements of the jet shape in ep collisions at HERA using the k_T-cluster jet algorithm are presented.Comment: 7 pages, 3 figures; plenary talk given at the 3rd UK Phenomenology Workshop on HERA Physics, Durham, UK, September 199