Ill-distributed sets over global fields and exceptional sets in Diophantine Geometry

Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that for definable sets $X$ in $\mathbb{R}_{\exp}$ of dimension at most $2$ a conjecture of Wilkie about the density of rational points is equivalent to the fact that $X$ is badly distributed at the level of residue classes for many primes of $K$. This provides a new strategy to prove this conjecture of Wilkie. In order to prove this result, we are lead to study an inverse problem as in the works \cite{Walsh2, Walsh}, but in the context of number fields, or more generally global fields. Specifically, we prove that if $K$ is a global field, then every subset $S\subseteq \mathbb{P}^{n}(K)$ consisting of rational points of projective height bounded by $N$, occupying few residue classes modulo $\mathfrak{p}$ for many primes $\mathfrak{p}$ of $K$, must essentially lie in the solution set of a polynomial equation of degree $\ll (\log(N))^{C}$, for some constant $C$

Uniform bounds for the number of rational points on varieties over global fields

We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sasyk, Roman. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires; Argentin

Uniform bounds for the number of rational points on varieties over global fields

We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least 4 over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the Bε factor by a log(B) factor.Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sasyk, Roman. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires; Argentin

PYMES potencia en crecimiento caracterización enfocada en la cadena de suministro de Palma Africana en el Ecuador

The thesis described below shows a study of the supply chain levels of the African oil palm, in order to find improvement opportunities in the short and long term for the growers, which will have a direct effect on the extractors and the industries; who are the main chain participants. To accomplish this, we selected study cases of SMEs growers, and from there knowing and working with logistic attributes of each participant and the relationship among them. Using the information from the chain’s behavior, we represented it in a dynamic system model, which indicated that the bottleneck is the production of palm fruit due to the lack of proper management of the harvesting process, improving the number of harvesters, the techniques that facilitate the product identification, training and with a better pest control.En la presenta tesis se muestra un estudio realizado a los eslabones de la cadena de suministro de la palma africana, con el fin de buscar oportunidades de mejora, a corto y largo plazo, de los palmicultores los mismos que tendrán un efecto directo a las extractoras e industrias principales participantes de la cadena. Para lograr esto, se tomaron casos de estudio de palmicultores que sean PYMES para caracterizarlos, y a partir de ahí conocer y trabajar con los atributos logísticos de cada uno de los participantes y la relación existente entre ellos. Con la información obtenida se representó el comportamiento de la cadena en un modelo de sistemas dinámicos, el cual indicó que el cuello de botella es la producción de fruta de palma debido a la falta de un manejo correcto del proceso de cosecha, teniendo que mejorar la forma en que lo ejecutan en base al número de cosechadores, a técnicas que faciliten la identificación de productos, capacitaciones y mejor control de plagas

Emotional and cognitive responses to cultural heritage: a neuromarketing experiment using virtual reality in the tourist destination image model context

The research is driven to identify and measure, through electroencephalography the impact of cultural and architectural heritage emulated by virtual reality on the mind of a tourist, in the form of cognitive and emotional responses measured as brain waves, identifies, through electroencephalogram, the cognitive and the emotional responses by subjects immersed in cultural tourist destination virtual reality, takes as conceptual framework the tourist destination image model and focus on tourist destinations characterised by historical, cultural, and architectural heritage. A neuromarketing experiment is caried out in which the cognitive and affective responses can be observed and measured using alpha α and beta β brain bioelectric waves, the data obtained directly from the human brain is used to carry out an analysis using the partial least squares regression algorithm PLS. The results show that the cognitive and emotional response caused by the tourist destination cultural heritage through virtual reality in individuals, is positive

Effects of hydrogen embrittlement on the fracture strength of notched tensile specimens: An Engineering Approach

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Distributed sets on global fields and exceptional sets in diophantine geometry

Esta tesis concierne el estudio de la densidad de puntos racionales en variades algebraicas y conjuntos definibles en estructuras o-minimales. La estrategia consiste en probar que los puntos racionales de estos conjuntos est´an mal distribuidos en clases residuales para muchos módulos primos. Primero, probamos que un conjunto de puntos afines o proyectivos con coordenadas en un cuerpo global, de altura acotada que ocupa pocas clases residuales para muchos módulos primos debe estar esencialmente contenido en el conjunto de ceros de un polinomio de grado y coeficientes de altura peque˜nos. Esto generaliza resultados de Walsh. Luego, aplicamos para estudiar una conjetura de Wilkie acerca de la distribución de los puntos racionales en ciertas estructuras o-minimales, y probamos que esta conjetura es equivalente a que ciertos conjuntos de puntos racionales de altura acotada estén mal distribuidos a nivel de clases residuales para muchos primos.This thesis concerns the study of the density of rational points on algebraic varieties and definable sets in o-minimal structures. The strategy consist in showing that the rational points of these sets are badly distributed in residual classes for many prime moduli. First, we prove that a set of affine or projective points with coordinates lying in a global field, with bounded height, that occupies few residual classes for many prime moduli must be essentially contained in the zero locus of a polynomial of small degree and height. This generalizes results of Walsh. Then, we apply this result to study a conjecture of Wilkie about the distribution of rational points on certain o-minimal structures, and we prove that this conjecture is equivalent to the fact that certain sets of rational points of bounded height are badly distributed at the level of residual classes for many prime moduli.Fil: Paredes, Marcelo Exequiel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina