Three projects in arithmetic geometry: torsion points and curves of low genus

2019 Fall.Includes bibliographical references.This paper is an exposition of three different projects in arithmetic geometry. All of them consider problems related to smooth curves with low genus and the torsion points of their Jacobians. The first project studies curves over finite fields and two invariants of the p-torsion part of their Jacobians: the a-number (a) and p-rank (f). There are many open questions in the literature about the existence of curves with a certain genus g and given values of a and f. In particular, not much is known when g = 4 and the curve is non-hyperelliptic. This is the case that we focus on here; we collect and analyze statistical data of curves over Fp for p = 3, 5, 7, 11 and their invariants. Then, we study the existence of Cartier points, which are also related to the structure of J[p]. For curves with 0 ≤ a < g, the number of Cartier points is bounded, and it depends on a and f. The second project addresses the problem of computing the endomorphism ring of a supersingular elliptic curve. This question has gained recent interest as the basis of alternative cryptosystems that hope to be resistant to quantum attacks. Our strategy is to generate these endomorphism rings by finding cycles in the l-isogeny graph which correspond to generators of the ring. We were able to find a condition for cycles to be linearly independent and an obstruction for two of them to be generators. Finally, the last chapter considers the Galois representations associated to the n-torsion points of elliptic curves over Q. In concrete, we construct models for the modular curves associated to applicable subgroups of GL₂(Z/nZ) and find the rational points on all of those which result in genus 0 or 1 curves, or prove that they have infinitely many. We also analyze the curves with a hyperelliptic genus 2 model and provably find the rational points on all but seven of them

Profit Analysis of Papaya Crops under Greenhouses as an Alternative to Traditional Intensive Horticulture in Southeast Spain

The high-yield agricultural model in Almería is based on eight different crops. Having led fruit and vegetable exports in Spain for more than 50 years, a decrease in melon and watermelon growing areas in Almería caused a change in supply that affected the model’s profit. Papaya cultivation could reactivate the profit of the agricultural model in Almería and also improve the available product range. The papaya crop needs greenhouse infrastructures high enough to contain the growth and size of the plants during a cycle crop, which is possible in most of the greenhouses of the Horticultural production model of Almería. The papaya harvests obtained in the region meet the quality requirements demanded by European markets. Furthermore, yields obtained are equal or higher than yields obtained by other producing countries. This crop improves profit compared with the profit obtained from the rotation of other horticultural crops that have been traditionally grown in the region

Classification of some nilpotent class of leibniz superalgebras

The aim of this work is to present the description of Leibniz superalgebras up to isomorphism with characteristic sequence (n|m − 1, 1) and nilindex n + m

Evaluation of piezodiagnostics approach for leaks detection in a pipe loop

Pipe leaks detection has a great economic, environmental and safety impact. Although several methods have been developed to solve the leak detection problem, some drawbacks such as continuous monitoring and robustness should be addressed yet. Thus, this paper presents the main results of using a leaks detection and classification methodology, which takes advantage of piezodiagnostics principle. It consists of: i) transmitting/sensing guided waves along the pipe surface by means of piezoelectric device ii) representing statistically the cross-correlated piezoelectric measurements by using Principal Component Analysis iii) identifying leaks by using error indexes computed from a statistical baseline model and iv) verifying the performance of the methodology by using a Self Organizing Map as visualization tool and considering different leak scenario. In this sense, the methodology was experimentally evaluated in a carbon-steel pipe loop under different leaks scenarios, with several sizes and locations. In addition, the sensitivity of the methodology to temperature, humidity and pressure variations was experimentally validated. Therefore, the effectiveness of the methodology to detect and classify pipe leaks, under varying environmental and operational conditions, was demonstrated. As a result, the combination of piezodiagnostics approach, cross-correlation analysis, principal component analysis, and Self Organizing Maps, become as promising solution in the field of structural health monitoring and specifically to achieve robust solution for pipe leak detection.Peer ReviewedPostprint (author's final draft

Parto pre término asociado a dengue en gestantes de Hospital José Cayetano Heredia Piura 2017-2019

A pesar del empeño de los estados miembros para reprimir el impacto de la epidemia, el dengue sigue siendo un dilema de salud pública en las Américas. No ha sido fácil establecer las complicaciones específicas asociadas a dengue en gestantes, sin embargo, las investigaciones a nivel mundial mencionan como principal problema obstétrico el parto pre término. Debido a la falta de investigación comparativa en nuestra ciudad, se consideró desarrollar el presente estudio porque, aparte de haber poca literatura donde asocian el dengue con el embarazo, no existe un tratamiento detallado para este grupo vulnerable de pacientes. OBJETIVO: Determinar si el parto pre término está asociado a dengue en gestantes atendidas en el Hospital III José Cayetano Heredia de Piura durante el 2017-2019. MATERIAL Y MÉTODO: Se realizará una investigación observacional, analítica y retrospectiva. Así mismo se analizarán las historias clínicas de 192 gestantes. RESULTADO: En el año 2017 se registró mayor cantidad de casos (97,4%). El grupo etario 18-29 años (casos: 47,4%, controles: 60,3%), procedencia Piura (casos: 75,6%, controles: 51,3%), paridades multíparas (casos y controles: 64,1%) y método de control FUR (casos: 67,9%, controles: 59,0). Diagnóstico de parto pre término (casos: 43,6%, controles: 34,6%). Relación infección por dengue y parto pre término con un OR 1,460 (IC: 0,765-2,786). Relación severidad de dengue parto pre término con un OR 8,33(IC95%: 2,997-23,175; p <0.05) CONCLUSIONES: El dengue se presentó frecuentemente en las gestantes entre 18-29 años de edad y provenientes de la provincia de Piura. El parto pre término no es una complicación asociada a gestantes con dengue. La edad gestacional al nacimiento en su mayoría se dio entre 37-41 semanas. Las gestantes que tuvieron dengue con signos de alarma mostraron una mayor probabilidad de presentar parto pre término a diferencia de las gestantes que tuvieron dengue sin signos de alarma.Despite the efforts of member states to curb the impact of the epidemic, dengue continues to be a public health dilemma in the Americas. It has not been easy to establish the specific complications associated with dengue in pregnant women, however, worldwide research mentions preterm delivery as the main obstetric problem. Due to the lack of comparative research in our city, it was considered to develop the present study because, apart from having little literature where dengue is associated with pregnancy, there is no detailed treatment for this vulnerable group of patients. OBJECTIVE: Determine if pre-term delivery is related to dengue in pregnant women treated at Hospital III José Cayetano Heredia de Piura during 2017-2019. MATERIAL AND METHOD: An observational, analytical and retrospective investigation will be carried out. Likewise, the medical records of 192 pregnant women will be analyzed. RESULT: In 2017, a greater number of cases were registered (97.4%). The age group 18-29 years (cases: 47.4%, controls: 60.3%), origin Piura (cases: 75.6%, controls: 51.3%), multiparous parities (cases and controls: 64, 1%) and FUR control method (cases: 67.9%, controls: 59.0). Preterm delivery diagnosis (cases: 43.6%, controls: 34.6%). Relationship between dengue infection and pre-term delivery with an OR 1.460 (CI: 0.765-2.786). Dengue severity relationship preterm delivery with an OR 8.33 (95% CI: 2.997-23.175; p <0.05) CONCLUSIONS: Infection by dengue virus in pregnant women was more frequent between 18-29 years of age and from the province of Piura. Preterm delivery is not a complication associated with pregnant women with dengue. The gestational age at birth was mostly between 37-41 weeks. Pregnant women with warning signs had a greater probability of presenting preterm birth than those who had dengue without warning signs.Tesi

What drives industrial energy prices?

Understanding whether the drivers of industrial energy prices are worldwide, group-specific or country-specific is a key issue in economics. This requires flexible econometric models to examine large data sets containing a significant variety of industrial sectors in different countries. To this end, we propose an extension of a dynamic factor model with group structure to account for observable country-specific explanatory variables and develop Monte Carlo simulations to show its good finite sample performance. Using data from 12 industrial sectors in 30 countries during the period from 1995 to 2015, we find three drivers of energy prices: (i) a common factor, the main driving force, captures the worldwide dynamics; (ii) country-specific variables, mainly related to inflation and the use of renewable and waste resources; and (iii) group-specific factors, which are more related to country affiliation than to sector classification.We are also very grateful to professors Andres Alonso, Tomohiro Ando and Pedro Galeano for making available their codes. M. Camacho is grateful for the support provided by grant PID2019-107192GB-I00 funded by MCIN/AEI/10.13039/501100011033, A. Caro was in receipt of an FPU grant from the Spanish Government and D. Peña for grant AEI/PID2019-109196GB-I00

PCA based stress monitoring of cylindrical specimens using PZTs and guidedwaves

Since mechanical stress in structures affects issues such as strength, expected operational life and dimensional stability, a continuous stress monitoring scheme is necessary for a complete integrity assessment. Consequently, this paper proposes a stress monitoring scheme for cylindrical specimens, which are widely used in structures such as pipelines, wind turbines or bridges. The approach consists of tracking guided wave variations due to load changes, by comparing wave statistical patterns via Principal Component Analysis (PCA). Each load scenario is projected to the PCA space by means of a baseline model and represented using the Q-statistical indices. Experimental validation of the proposed methodology is conducted on two specimens: (i) a 12.7 mm (1/2”) diameter, 0.4 m length, AISI 1020 steel rod, and (ii) a 25.4 mm (1”) diameter, 6m length, schedule 40, A-106, hollow cylinder. Specimen 1 was subjected to axial loads, meanwhile specimen 2 to flexion. In both cases, simultaneous longitudinal and flexural guided waves were generated via piezoelectric devices (PZTs) in a pitch-catch configuration. Experimental results show the feasibility of the approach and its potential use as in-situ continuous stress monitoring application.Peer ReviewedPostprint (published version

Formación del concepto límite mediante dos registros de representación: representaciones gráficas y el uso algebraico

Uno de los problemas centrales que se presentan, para abordar el tema de límite, es sin duda cuando nos enfrentamos al concepto de infinito. Generalmente el docente al enseñar el concepto de infinito utiliza metáforas didácticas basadas en conjuntos muy grandes, esto para fijar la idea de infinitud. De acuerdo con la real academia española, esto permite crear la noción de infinito en un lenguaje cotidiano, lo que lleva a generar una mala formación de este concepto, dentro de un lenguaje matemático, ya que la imprecisión del lenguaje cotidiano hace ver al concepto de infinito muy vago y se aleja de la idea matemática como unidad total (Ortiz, 1994). El interés de nuestro trabajo se centra precisamente en el diseño de actividades, donde el estudiante pueda realizar y observar un proceso infinito, a través de ejemplos geométricos donde se presente la situación límite (proceso infinito culminado), permitiendo la formación del concepto de límite

On naturally graded Lie and Leibniz superalgebras

In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of solvable ones. In fact, many families of relevant solvable algebras have been obtained by extensions of naturally graded nilpotent algebras, i.e. solvable algebras with a well-structured nilradical. Thus, the aim of this work is introducing the concept of naturally graded for superalgebra structures such as Lie and (non-Lie) Leibniz. After having defined naturally graded Lie and Leibniz superalgebras, we characterize natural gradations on a very important class of each of them, that is, those with maximal super-nilindex