Finiteness theorems for matroid complexes with prescribed topology

It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of $h$-vectors, there are finitely many simplicial complexes of bounded dimension with $h_1=k$ for any natural number $k$. In this paper we study the question at the other end of the $h$-vector: Are there only finitely many $(d-1)$-dimensional simplicial complexes with $h_d=k$ for any given $k$? The answer is no if we consider general complexes, but when focus on three cases coming from matroids: (i) independence complexes, (ii) broken circuit complexes, and (iii) order complexes of geometric lattices. We prove the answer is yes in cases (i) and (iii) and conjecture it is also true in case (ii).Comment: to appear in European Journal of Combinatoric

The topology of the external activity complex of a matroid

We prove that the external activity complex $\textrm{Act}_<(M)$ of a matroid is shellable. In fact, we show that every linear extension of LasVergnas's external/internal order $<_{ext/int}$ on $M$ provides a shelling of $\textrm{Act}_<(M)$. We also show that every linear extension of LasVergnas's internal order $<_{int}$ on $M$ provides a shelling of the independence complex $IN(M)$. As a corollary, $\textrm{Act}_<(M)$ and $M$ have the same $h$-vector. We prove that, after removing its cone points, the external activity complex is contractible if $M$ contains $U_{3,1}$ as a minor, and a sphere otherwise.Comment: Comments are welcom

Testing for Unit Roots: Mexico's GDP

The study presents an analysis of the stochastic nature of the gross domestic product of Mexico for the period 1900-2001. Several specifications to test for the existence of unit roots are presented. The conventional tests, Dickey Fuller, Augmented Dickey Fuller and Phillips Perron, indicate that the series is nonstationary and integrated of order 1. The result is robust to the inclusion of exogenously and endogenously determined structural breaks. Interestingly, when structural breaks are determined endogenously, a structural break in 1907 is identified. We interpret this results as suggesting that setting the date of a structural break ex-ante might not be the most efficient procedure when testing for unit roots.Unit Root tests, structural Break and gross domestic product of Mexico.

Diseño de una herramienta para la toma de decisiones en la construcción de sistemas de tratamiento de aguas residuales en urbanizaciones y condominios

Proyecto de Graduación (Licenciatura en Ingeniería Ambiental) Instituto Tecnológico de Costa Rica, Escuela de Química, 2011.El objetivo del presente trabajo fue generar una herramienta dirigida a ingenieros responsables de proyectos urbanísticos que les sirva de guía para la elección y el diseño del mejor arreglo sanitario que debe ser construido para tratar las aguas residuales domésticas, que además organice de forma lógica la tramitología que se debe seguir ante el Instituto Costarricense de Acueductos y Alcantarillados (AyA) y les brinde información hidrogeológica georeferenciada que debe considerarse durante la etapa de concepción de la obra. Para esto, se procedió con la revisión de códigos y documentos técnicos referentes a obras de tratamiento y disposición de aguas residuales, acuerdos de junta directiva de AyA relativos a los trámites para cada tipo de proyecto y expedientes resueltos de solicitudes presentadas en el período 1997-2009 para construir una base de antecedentes. El diseño se materializó en un instrumento digital elaborado a partir de diagramas de Microsoft Office Visio que indican que se debe construir un sistema de tanque séptico más drenaje cuando el terreno presente condiciones de infiltración entre 2 y 24 min /cm, exista un espesor de la zona no saturada en el área del proyecto mayor a 5 m, no se cuente con cobertura o planes de construcción de alcantarillado sanitario y se determine un tiempo de tránsito de contaminantes desde los drenajes proyectados hasta las fuentes de abastecimiento de agua de por lo menos 70 días. En caso de incumplimiento de estos requisitos se debe construir una planta de tratamiento de aguas residuales con su respectiva red de alcantarillado sanitario. A partir de la base de antecedentes se elaboraron 19 mapas de distintas partes del país, cuyo análisis indica que los sitios más favorables para la construcción de tanques sépticos y drenajes son: Alajuela, Liberia, Colón, Grecia y Oreamuno; mientras que los menos convenientes son: Pococí, Siquirres y Guácimo.Instituto Costarricense de Acueductos y Alcantarillado

Painting sampler: un spleen aceleracionista

Mi proyecto se interesa temáticamente por el modo en el que el individuo contemporáneo es afectado por una gran saturación de ofertas de consumo, sobre todo desde el punto de vista de su fuerte potencia visual y de cómo ello puede relacionarse con la práctica de la pintura. Esto es atendido mediante la investigación de las posibilidades de construcción pictórica, abarcando las técnicas de la pintura al óleo, la acuarela, el ensamblaje, el collage, la cerámica y la intervención sobre revistas, libros y catálogos. Por tanto, tomando el collage como base estructural de mi producción, tensiono la violencia compositiva con la necesidad de crear una fuerte unicidad atsmosférica de cada cuadro, para hacer una relectura de ciertos géneros pictóricos como la pintura de interiores, el bodegón, el paisaje y la alegoría desde mi presente, con referencias a tradiciones y estrategias artísticas como el Pop-art, el Neoexpresionismo, el kitsch, la “Bad painting”, el Simbolismo o el Surrealismo, o a autores y corrientes extra-artísticas como la literatura beat, en especial Wiliam Burroughs, o Charles Bukowski, además de otros autores como Baudelaire o el Marqués de Sade, o ámbitos estéticos populares como la ilustración, Instagram o el vaporwave

Aeroelastic simulation of rotorcraft propulsion systems

A close relationship between the aerospace technology level and the capability to model and simulate the physics involved during the flight has been identified throughout the aviation history. The continuous improvement in physical and mathematical models has provided a further understanding of the behaviour of the different components along with the complete vehicle. As a result, the performance modelling has experienced a large improvement. The aviation industry, which is characterised by the use of cutting edge technology, requires large investments when new concepts are introduced. The application of high fi delity simulation tools reduces considerably the investment carried out prototyping and testing. This fact is also applicable to the rotorcraft industry, where a continuous increase in the employment of helicopters has been observed throughout the last decades, expecting a sharp growth within the next 20 years. The forecasted growth in the number of helicopter operations along with the increasing concern about the environmental impact of aviation, lead the governmental bodies to set up a number of goals to reduce the carbon dioxide, nitrogen oxides, and noise emissions. Three paths were identified to reduce the environmental impact and meet the proposed goals. The fi rst one is the reduction in the number of operations. However, a sharp growth in the number of helicopter operations is expected. The second one is the optimisation of the flight procedures. Nevertheless, the potential improvement is limited. The third one is the introduction of a quieter and more,efficient type of rotorcraft. There exist two new rotorcraft con figurations which show enough potential to be studied. These are the tilt-rotor and compound helicopter. Both designs improve the cruise performance using auxiliary lift and propulsive systems, while they still exploit the vertical flight capability of helicopters. Nevertheless, the lack of reliable high fi delity models has made their development long and highly expensive. Within this context, the necessity of a simulation framework able to simulate and predict the detailed performance of novel rotorcraft con figurations is highlighted. The present work aims to lay the foundations of this comprehensive rotorcraft code by developing a computational framework for the aeroelastic simulation of propulsion systems. The tool is characterised by a high fi delity level able to predict the highly unsteady loads at a low computational cost. The fi rst characteristic makes this tool suitable for the design stage and noise calculations; whilst the second one enables its integration into multidisciplinary optimisation procedures. The development of this framework has required a considerable contribution to the knowledge in different areas of study, these included: structural dynamics, in flow aerodynamics, blade aerodynamics, aeroelasticity, and computational acceleration techniques. The individual models have been integrated into a cost efficient aeroelastic simulation framework, which has been extensively validated with experimental data. Very good and in some cases excellent correlation with the experimental measurements has been observed. The main contribution of this work has been the successful development of a computational framework for the aeroelastic simulation of rotorcraft propulsion systems. It accurately simulates and predicts the aerodynamic flow field and the unsteady loads generated by the rotor and transferred to the fuselage. It is easily expandable to account for interactions with other rotors, auxiliary lift surfaces, and fuselage bodies. The simulation tool estimates high fidelity low and high frequency aerodynamic loading, which enables the calculation of impulsive noise emissions. The framework computes accurate predictions of rotor power required, which enables its use as a validation tool for lower order models. The developed framework approximates the third level of Padfi eld's hierarchical paradigm, providing detailed aeroelastic information necessary for design purposes. The additions of parallel computing and an acceleration scheme results in a highly computationally effcient tool suitable for optimisation methodologies. Moreover, a considerable contribution has been made in terms of modelling of: coupled modal characteristics, aeroelastic simulation; computational enhancements of in flow models and investigation of the effect of the fuselage aerodynamic interference and coupled flexible blade modelling

Nonwovens of Ceramic Decorated Cellulose Based Fine Fibers for Leaded Water Purification

Fine fibers of cellulose acetate were Forcespun and used to make nonwoven mats of cellulose. Nonwovens were activated using a solution combustion synthesis which deposited iron nitride onto fibers. Cellulose and cellulose composite mats were tested as adsorbents for lead ion in water. Cellulose showed slightly higher adsorption capacities (mg/g) up to 1300 mg/g lead loading. Adsorption data were further analyzed using several isotherms, of which the Dubinin-Raduskevich gave the best fits