Laws of large numbers for the frog model on the complete graph

The frog model is a stochastic model for the spreading of an epidemic on a graph, in which a dormant particle starts to perform a simple random walk on the graph and to awake other particles, once it becomes active. We study two versions of the frog model on the complete graph with $N + 1$ vertices. In the first version we consider, active particles have geometrically distributed lifetimes. In the second version, the displacement of each awakened particle lasts until it hits a vertex already visited by the process. For each model, we prove that as $N \to \infty$, the trajectory of the process is well approximated by a three-dimensional discrete-time dynamical system. We also study the long-term behavior of the corresponding deterministic systems

A New Multi-Dimensional Framework for Analyzing Regional Integration: Regional Integration Evaluation (RIE) Methodology

Theories of regional integration typically analyze the regional integration process from the perspective of a single discipline, usually economics. However, such one-dimensional analytical frameworks cannot fully capture the richness and complexity of the inherently multi-dimensional regional integration process. To address the problem, we propose the regional integration evaluation (RIE) methodology which is based on four dimensions of development – economic, political, social and technological. The central idea behind the RIE methodology is that regional development promotes regional integration. Our RIE methodology differs from the existing literature in that it is based on a more comprehensive definition of development than just economic development. Our definition of a region's development incorporates the development levels of all regional countries as well as differences in development levels among regional countries. We apply the RIE methodology to assess the regional development and hence integration prospects of NAFTA, ASEAN, MERCOSUR and EU.Economic integration; economic modeling; NAFTA; ASEAN; MERCOSUR; EU

The ecology and life history of the Mexican tetra, Astyanax mexicanus, (Teleostei: Characidae) in the lower Rio Grande Valley, Texas

The Mexican tetra has been found to migrate from shallow waters in the spring and summer months into deeper waters during the winter months when temperatures are too cold for their survival. This fish is omnivorous with insect material being the major source of food. Its food types include green algae, nematoceran larvae, hemipterans, coleopterans, hymenopterans, dipterans, ostracods, fish eggs and amphipods. Furthermore, size classes showed that the Mexican tetras reached their largest size at the River site and smaller sizes at the Bridge and Gate sites and apparently breed year round. They are capable of producing from 300 to just over 7000 eggs per female. The diameter of Mexican tetra eggs range in size from 0.5mm to 1.0mm, and the mean egg size was found to be 0.7mm $\pm$ 0.11mm. In addition, analysis of the relative abundances at the tree sites showed the Mexican tetra to have an overall ranking of six at the Gate site, two at the Bridge site and eight at the River site

Crane Mechanical

This report explains the structural and mechanical design of a crane located in a offshore platform. The introduction summarizes the two main parts of the project, the structural calculus of the crane and the mechanical design of the equipment. The report continues with the structural calculus of the crane, both theoretical and using a software. Following, the structural calculus and the mechanical design of the equipment are detailed. Finally, the conclusions show that, by following the mentioned steps the objectives have been achieved. The integrity of the crane and the possibility to be built have been demonstrated. Regarding to the mechanical design, the suitability of the equipment has been validated and the conditions required to meet by the gear box determined.Departamento de Ciencias de los Materiales e Ingeniería Metalúrgica, Expresión Gráfica en la Ingeniería, Ingeniería Cartográfica, Geodesia y Fotogrametría, Ingeniería Mecánica e Ingeniería de los Procesos de FabricaciónGrado en Ingeniería Mecánic

Sobre un teorema de fröberg y los grafos saturados

Se estudian los Anillos de Cohen-Macaulay (=CM) Saturados y se prueba el Teorema de Fröberg que caracteriza los complejos simpliciales CM con una resolución 2-lineal usando resultados sobre grafos CM de R. H. Villarreal.Saturated Cohen-Macaulay (=CM) Rings are studied and the theorem of Fröberg characterizing the CM simplicial complexes having a 2-linear resolution is proved, using results of R. H. Villarreal on CM graphs