Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

An efficient, approximate path-following algorithm for elastic net based nonlinear spike enhancement

Unwanted spike noise in a digital signal is a common problem in digital filtering. However, sometimes the spikes are wanted and other, superimposed, signals are unwanted, and linear, time invariant (LTI) filtering is ineffective because the spikes are wideband - overlapping with independent noise in the frequency domain. So, no LTI filter can separate them, necessitating nonlinear filtering. However, there are applications in which the noise includes drift or smooth signals for which LTI filters are ideal. We describe a nonlinear filter formulated as the solution to an elastic net regularization problem, which attenuates band-limited signals and independent noise, while enhancing superimposed spikes. Making use of known analytic solutions a novel, approximate path-following algorithm is given that provides a good, filtered output with reduced computational effort by comparison to standard convex optimization methods. Accurate performance is shown on real, noisy electrophysiological recordings of neural spikes.

Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators

2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.

Modelo de um observatório municipal do desporto no concelho de Setúbal

A presente dissertação tem como objetivo geral apresentar uma proposta de um modelo de observatório municipal do desporto na administração local, nomeadamente no concelho de Setúbal. Podem ser verificados alguns estudos sobre a temática dos observatórios no sector do desporto (Leite, 2013; Gaspar 2014). Em plena sociedade de informação, as organizações têm de gerir grandes fluxos de dados. Têm de ter capacidade de adaptação à realidade, mas acima de tudo, uma atitude pró-ativa no sentido de anteciparem novos cenários. Segundo Albornoz e Herschmann (2006), os observatórios costumam recolher, registar, acompanhar, interpretar dados, produzir indicadores estatísticos, criar metodologias para codificar, classificar e categorizar informações, estabelecendo conexões entre pessoas que trabalham em áreas similares, bem como monitorizar e analisar tendências. É exigido à administração local, serviços de qualidade e de transparência na adoção das suas politicas desportivas e a existência de um instrumento de recolha de informação, estruturado com base num modelo de análise que permita conhecer, analisar e compreender o estado de um dado contexto desportivo em tempo real, irá permitir a criação de uma base de dados contendo informação atualizada e confiável. Neste contexto, os sistemas de informação, quando desenvolvidos e aplicados, vão permitir a recolha de informação fundamental sobre o comportamento interno da organização (Claudino, 2005). A presente pesquisa representa uma investigação descritiva, tratando-se de um estudo de caso a aplicar na Câmara Municipal de Setúbal. Em termos da recolha de dados, foram utilizadas fontes primárias, com base numa análise documental. Os resultados deste estudo, permitem apresentar uma primeira abordagem de estrutura e processos de funcionamento de um modelo de observatório municipal do desporto com aplicação prática, tendo sido estabelecidos sete categorias de análise fundamentais: i) Atividades Desportivas; ii) Instalações Desportivas, iii) Associativismo; iv) Recursos Humanos; v) Sector Privado; vi) Consumo Desportivo; vii) Divisão Desporto. As estratégias das políticas públicas desportivas adotadas, o planeamento desportivo ou o acesso ao apoio financeiro, exigem que estejam disponíveis um conjunto de informações rigorosas e fidedignas sobre o desempenho, a evolução e as tendências do sector a nível local pelo que a estrutura de um observatório do desporto, irá permitir de uma forma eficiente, eficaz e participativa que se desenvolvam e projetem as políticas desportivas locais que melhor se ajustem à sua realidade. Acreditamos que a existência de um observatório municipal do desporto acrescenta benefícios para os municípios. As mudanças e os desafios económicos colocados hoje, obrigam a novas dinâmicas competitivas.

Modelo Estocástico para bloqueio de poros e redução de permeabilidade

Modeling transport of particulate suspensions in porous media is essential for understanding various processes of industrial and scientific interest. During these processes, particles are retained due to mechanisms like size exclusion (straining), adsorption, sedimentation and diffusion. In this thesis, a mathematical model is proposed and analytical solutions are obtained. The obtained analytic solutions for the proposed model, which takes pore and particle size distributions into account, were applied to predict the particle retention, pore blocking and permeability reduction during dead-end microfiltration in membranes. Various scenarios, considering different particle and pore size distributions were studied. The obtained results showed that pore blocking and permeability reduction are highly influenced by the initial pore and particle size distributions. This feature was observed even when different initial pore and particle size distributions with the same average pore size and injected particle size were considered. Finally, a mathematical model for predicting equivalent permeability in porous media during particle retention (and pore blocking) is proposed and the obtained solutions were applied to study permeability decline in different scenarios

Modelagem matemática para o transporte de partículas sujeitas a múltiplos mecanismos de retenção

Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media

Les enjeux juridiques concernant les nouveaux modèles d’affaires basés sur la commercialisation des données

Cet essai est présenté en tant que mémoire de maîtrise dans le cadre du programme de droit des technologies de l’information. Ce mémoire traite de différents modèles d’affaires qui ont pour caractéristique commune de commercialiser les données dans le contexte des technologies de l’information. Les pratiques commerciales observées sont peu connues et l’un des objectifs est d’informer le lecteur quant au fonctionnement de ces pratiques. Dans le but de bien situer les enjeux, cet essai discutera d’abord des concepts théoriques de vie privée et de protection des renseignements personnels. Une fois ce survol tracé, les pratiques de « data brokerage », de « cloud computing » et des solutions « analytics » seront décortiquées. Au cours de cette description, les enjeux juridiques soulevés par chaque aspect de la pratique en question seront étudiés. Enfin, le dernier chapitre de cet essai sera réservé à deux enjeux, soit le rôle du consentement et la sécurité des données, qui ne relèvent pas d’une pratique commerciale spécifique, mais qui sont avant tout des conséquences directes de l’évolution des technologies de l’information.

STUDY OF A DIRECT SAMPLING METHOD FOR THE INVERSE MEDIUM SCATTERING PROBLEM

Direct sampling methods are increasingly being used to solve the inverse medium scattering problem to estimate the shape of the scattering object. A simple direct method using one incident wave and multiple measurements was proposed by Ito, Jin and Zou. In this report, we performed some analytic and numerical studies of the direct sampling method. The method was found to be effective in general. However, there are a few exceptions exposed in the investigation. Analytic solutions in different situations were studied to verify the viability of the method while numerical tests were used to validate the effectiveness of the method.

Les enjeux juridiques concernant les nouveaux modèles d’affaires basés sur la commercialisation des données

Cet essai est présenté en tant que mémoire de maîtrise dans le cadre du programme de droit des technologies de l’information. Ce mémoire traite de différents modèles d’affaires qui ont pour caractéristique commune de commercialiser les données dans le contexte des technologies de l’information. Les pratiques commerciales observées sont peu connues et l’un des objectifs est d’informer le lecteur quant au fonctionnement de ces pratiques. Dans le but de bien situer les enjeux, cet essai discutera d’abord des concepts théoriques de vie privée et de protection des renseignements personnels. Une fois ce survol tracé, les pratiques de « data brokerage », de « cloud computing » et des solutions « analytics » seront décortiquées. Au cours de cette description, les enjeux juridiques soulevés par chaque aspect de la pratique en question seront étudiés. Enfin, le dernier chapitre de cet essai sera réservé à deux enjeux, soit le rôle du consentement et la sécurité des données, qui ne relèvent pas d’une pratique commerciale spécifique, mais qui sont avant tout des conséquences directes de l’évolution des technologies de l’information.

Hydrolysis of Ammonia Borane as a Hydrogen Source: Fundamental Issues and Potential Solutions Towards Implementation

In todays era of energy crisis and global warming, hydrogen has been projected as a sustainable alternative to depleting CO2-emitting fossil fuels. However, its deployment as an energy source is impeded by many issues, one of the most important being storage. Chemical hydrogen storage materials, in particular B?N compounds such as ammonia borane, with a potential storage capacity of 19.6 wt?% H2 and 0.145 kg?H?2?L-1, have been intensively studied from the standpoint of addressing the storage issues. Ammonia borane undergoes dehydrogenation through hydrolysis at room temperature in the presence of a catalyst, but its practical implementation is hindered by several problems affecting all of the chemical compounds in the reaction scheme, including ammonia borane, water, borate byproducts, and hydrogen. In this Minireview, we exhaustively survey the state of the art, discuss the fundamental problems, and, where applicable, propose solutions with the prospect of technological applications.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

Analytic Benchmark Solutions for Open-Channel Flows

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.

Exact and analytic-numerical solutions of lagging models of heat transfer in a semi-infinite medium

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.