Sharp mixed norm spherical restriction

Let $d\geq 2$ be an integer and let $2d/(d-1) < q \leq \infty$. In this paper we investigate the sharp form of the mixed norm Fourier extension inequality \begin{equation*} \big\|\widehat{f\sigma}\big\|_{L^q_{{\rm rad}}L^2_{{\rm ang}}(\mathbb{R}^d)} \leq {\bf C}_{d,q}\, \|f\|_{L^2(\mathbb{S}^{d-1},{\rm d}\sigma)}, \end{equation*} established by L. Vega in 1988. Letting $\mathcal{A}_d \subset (2d/(d-1), \infty]$ be the set of exponents for which the constant functions on $\mathbb{S}^{d-1}$ are the unique extremizers of this inequality, we show that: (i) $\mathcal{A}_d$ contains the even integers and $\infty$; (ii) $\mathcal{A}_d$ is an open set in the extended topology; (iii) $\mathcal{A}_d$ contains a neighborhood of infinity $(q_0(d), \infty]$ with $q_0(d) \leq \left(\tfrac{1}{2} + o(1)\right) d\log d$. In low dimensions we show that $q_0(2) \leq 6.76\,;\,q_0(3) \leq 5.45 \,;\, q_0(4) \leq 5.53 \,;\, q_0(5) \leq 6.07$. In particular, this breaks for the first time the even exponent barrier in sharp Fourier restriction theory. The crux of the matter in our approach is to establish a hierarchy between certain weighted norms of Bessel functions, a nontrivial question of independent interest within the theory of special functions.Comment: 21 page

Vulnerability assessment of Angolan university web applications

Vulnerability assessment is one of the technical procedures that can help prevent serious security breaches, which, when exploited, can undermine brand credibility and or the continuity of a business. Universities hold and process important relevant and sensitive student and staff information appealing to attackers and might affect the organisations' credibility if such information is disclosed. This work presents a study conducted to assess the security status of the Angolan universities' web applications, identifying the most frequent security vulnerabilities and their criticality, based on OWASP Top 10 and CWE Top 25 references to identify and validate the findings discovered during the automatic vulnerability assessment process.info:eu-repo/semantics/acceptedVersio

Desenvolvimento de um plano de manutenção preventiva na rede de distribuição de água de Lisboa

O presente relatório de estágio enquadra-se no âmbito do trabalho final de Mestrado do curso de Engenharia Civil, área de especialização em Hidráulica, do Instituto Superior de Engenharia de Lisboa, e incide na temática dos sistemas de distribuição de água. O estágio decorreu na empresa EPAL – Empresa Portuguesa das Águas Livres, S.A., e teve como objecto o desenvolvimento de um plano de manutenção preventiva para a rede de distribuição de água de Lisboa. Devido à crescente complexidade dos sistemas de abastecimento de água e à grande dispersão territorial dos diversos órgãos integrados na rede, surge a necessidade de desenvolver um sistema que permita simplificar o planeamento e a gestão das intervenções de inspecção e manutenção preventiva dos órgãos. Para esse efeito, recorreu-se a um software SIG (Sistema de Informação Geográfica) para proceder à sectorização da rede de distribuição de água em pequenos grupos (Polígonos), constituídos por um número determinado de órgãos de manobra e segurança. Esta metodologia permite organizar as intervenções em pequenos grupos e optimizar as rotinas de Inspecção diárias. No decorrer do estágio efectuou-se ainda um levantamento dos procedimentos de inspecção e manutenção dos diversos órgãos integrados na rede de distribuição de água de Lisboa, quer por acompanhamento de actividades com as equipas de inspecção, quer por recolha de recomendações junto dos fabricantes dos órgãos. Este levantamento permitiu elaborar fichas de procedimento para as actividades de inspecção e manutenção preventiva dos diversos órgãos, afim de serem usadas como referência pelos trabalhadores.This report falls under the final year Masters course in Civil Engineering, Hydraulics area of expertise, in Instituto Superior de Engenharia de Lisboa, on the subject of water supply systems. The traineeship took place in EPAL – Empresa Portuguesa das Águas Livres, S.A., and consisted in the development of a preventive maintenance plan for the water supply system in the city of Lisbon. Due to the complexity of water supply systems and the wide dispersion of equipments in the water supply network, there is a need to simplify the planning and management of the inspection and preventive maintenance interventions. In order to proceed with the sectorization of the water supply network in small groups (Polygons), it was used a GIS (Geographic Information System) software. This methodology allows to organize the interventions in small groups of equipments and optimize the daily inspection routines. Thanks to the escort of some inspection activities during the traineeship, and also by the gathering of some recommendations provided from the equipment manufacturers, it was possible to elaborate inspection and preventive maintenance procedures forms in order to be used as reference by the workers during the equipments inspections

Fractional diffusion models and option pricing in jump models

Mestrado em Mathematical FinanceO problema de valorização de derivados tem sido o foco da investigação em Matemática Financeira desde a sua conceção. Mais recentemente, a literatura tem-se focado por exemplo em modelos que assumem que as dinâmicas do preço do ativo subjacente são governadas por um processo de Lévy (por vezes chamado um processo com saltos). Este tipo de modelo admite a possibilidade de eventos extremos (saltos), que não são devidamente capturados por modelos clássicos do tipo Black-Scholes, alicerçados no movimento Browniano. Foi também demonstrado ao longo da última década que se as dinâmicas do preço do ativo subjacente seguem certos processos de Lévy, tais como o CGMY , o FMLS e o KoBoL, os preços das opções satisfazem uma equação diferencial parcial fracionária. Nesta dissertação, iremos mostrar que se as dinâmicas do ativo subjacente seguem o denominado Processo Estável Temperado Generalizado, que admite como caso particular os suprareferidos processos CGMY e KoBoL, então os preços das opções satisfazem igualmente uma equação diferencial parcial fracionária. Além disso, iremos implementar um método simples de diferenças finitas para resolver numericamente a equação deduzida, e valorizar opções do tipo europeu.The problem of pricing financial derivatives has been the focal point of research within the field of Mathematical Finance since its conception. In recent years, one of the main areas of focus within the literature has been on models which assume that the dynamics of the price of the underlying asset are governed by a Lévy process (sometimes referred to as a jump process). This type of model admits the possibility of extreme events (jumps), which are not captured by classical Black-Scholes type models based on the Brownian motion. Over the last decades, the literature has further shown that if the dynamics of the price of the underlying is governed by certain Lévy processes, such as the CGMY , the FMLS and the KoBoL, the price processes of European-style options satisfy a variety of fractional partial differential equations (FPDEs). In this dissertation, we will show that if the underlying price dynamic follows a Generalized Tempered Stable process, which admits as particular cases the aforementioned CGMY and KoBoL processes, prices of options satisfy an FPDE of the same type. Further, we will implement a simple finite difference scheme to solve the FPDE numerically to price European-type options.info:eu-repo/semantics/publishedVersio

Assessment of the risk of Hepatitis E virus occurrence in pork carcasses at slaughter in the UK

Hepatitis E virus (HEV) is a RNA virus of the genus Hepevirus. HEV genotype 3 is zoonotic and pigs are the main reservoir. This genotype has been identified in the United Kingdom, in sporadic locally-acquired cases without recent history of foreign travel to endemic countries. The number of HEV-confirmed human cases in the UK has increased significantly, from 124 cases in 2003 to 661 in 2013. Non-travel cases now account for the majority (69%) of cases observed annually in the UK. Our aim was to assess the risk of HEV occurrence in pork carcases at slaughter in the UK. We performed a quantitative exposure assessment using Monte Carlo simulation to estimate the number of carcasses contaminated with HEV produced in a high throughput porcine abattoir during one year. The input data used were: a) true prevalence in British pigs, b) probability of viral shedding in bile and faeces c) number of pig carcases with bile and/or faecal contamination detected during post-mortem inspection. The following assumptions were made when data were unavailable: a) sensitivity and specificity of the RP-PCR diagnostic test; b) meat from viraemic pigs was considered HEV-positive; c) visual faecal and bile contamination only considered since microscopic contamination would not be detected through visual inspection. We estimated through our model that 175,152 (2.4%) of carcases produced in high throughput abattoirs would be infected with HEV in one year period. The number of viraemic pigs slaughtered at the abattoir was the largest driver of the uncertainty in carcass contamination. Variations in this parameter would change the output from 62,982 carcasses up to 306,320. Mitigation strategies at farm level should be explored, as it appears that control at this level would likely result in a higher reduction in HEV contamination in pork meat