Bounding the gap between a free group (outer) automorphism and its inverse

For any finitely generated group $G$, two complexity functions $\alpha_G$ and $\beta_G$ are defined to measure the maximal possible gap between the norm of an automorphism (respectively outer automorphism) of $G$ and the norm of its inverse. Restricting attention to free groups $F_r$, the exact asymptotic behaviour of $\alpha_2$ and $\beta_2$ is computed. For rank $r\geqslant 3$, polynomial lower bounds are provided for $\alpha_r$ and $\beta_r$, and the existence of a polynomial upper bound is proved for $\beta_r$.Comment: 24 pages; To appear in Collectanea Mathematic

O fim do mundo antigo : uma discussão historiográfica

Com este artigo, pretendemos refletir sobre a maneira pela qual as transformações observadas no conhecimento histórico a partir do século XVIII proporcionaram múltiplas interpretações sobre a "queda" do Império Romano. Nesse sentido, analisamos como a mudança na concepção de tempo, a crítica às noções de progresso e decadência e a superação do paradigma positivista permitiram que a transição da Antigüidade para a Idade Média adquirisse um novo significado dentro da historiografia.With this article, we intend to discuss how some writers since 18th century treated the "decline" of the Roman Empire connected with their historical views. Therefore, we analyze the emergence of a new conception of time, the refutation of progress and decadence as useful historical concepts and the dissolution of the positivist paradigm trying to show how the theme of the passage from Antiquity to Medieval Age acquired a new meaning according to these deep and important theoretical changes

The end of Ancient World : a historical debate

With this article, we intend to discuss how some writers since 18th century treated the “decline” of the Roman Empire connected with their historical views. Therefore, we analyze the emergence of a new conception of time, the refutation of progress and decadence as useful historical concepts and the dissolution of the positivist paradigm trying to show how the theme of the passage from Antiquity to Medieval Age acquired a new meaning according to these deep and important theoretical changes

ENVIE Co-ordination action on indoor air quality and health effects; WP3 Final report – Characterisation of spaces and source

Human exposure to environmental pollutants occurs via various pathways. For many pollutants, especially the volatile ones, air exposure is the dominant pathway. Exposure via air occurs both outdoors and indoors, with diverse types of indoor spaces playing a role, e.g., home, workplace, and passenger cabins of means of transportation. In average people spend over 90% of their time indoors, that percentage being particularly high for some specific groups as new-born, elderly, disabled or sick people. The global exposure to air contaminants is therefore drastically determined by indoor conditions. It is now well established that indoor air pollution contributes significantly to the global burden of disease of the population. For a majority of indoor air contaminants, particularly in the presence of common indoor sources, however, indoor concentrations usually exceed outdoor concentrations, for some pollutants even with an indoor/outdoor ratio of 10 or 20. Emissions are identified, accordingly to the EnVIE approach and grouped into four categories: building materials and related sources, including dampness and moulds; ventilation, natural and mechanical, including, or not, heating, cooling and humidification/ dehumidification; consumer products, furnishing, cleaning and household products; and occupant activities. Emission of chemical substances from construction materials and products in buildings to the indoor air have been reported and reviewed for a wide range of substances, including those formed during secondary reactions, causing complaints of irritation and odour. During the last two decades there has been increasing advances in construction technology that have caused a much greater use of synthetic building materials. Whilst these improvements have led to more comfortable buildings, they also provide indoor environments with contaminants in higher concentrations than are found outside. Wood and cork are now frequently used as a building product for floor coverings, because the material is often regarded as “natural” and “healthy”. However, industrial products, even based on natural raw materials, may contain a number of artificial ingredients and the chemical emissions will strongly depend on the type of additives and the manufacturing process. Modern interior paints are usually based on a polymeric binder. In order to fulfil requirements on e.g., durability, paint contains various functional chemicals. Water-borne paints usually also contains small amounts of approved biocides. Polymeric binders with a very low content of residual monomers have been developed for paint. Besides the release of substances to the indoor air due to primary emission, damp building materials may give rise to volatile substances formed during secondary reactions. Semi-volatile organic compounds (SVOCs) are now receiving much more attention than heretofore. The HVAC (Heating, Ventilation and Air Conditioning) systems as providers, among others, of services of cleaning and dilution of pollutants in the indoor air are also recognized as potential pollution sources. Several studies have shown that the prevalence of SBS symptoms is often higher in air conditioned buildings than in buildings with natural ventilation. 8 The outdoor air introduced indoors through either ventilation systems or natural means is also an important and not always controllable source for the intake of some outdoor pollutants. Outdoor air used for ventilation may also be source of pollution containing particulate matter, particulates of biological origin (microorganisms, pollen, etc.) and various gases like NOx and O building structures which is a driving force for the airflows which will transport to indoors water vapour and gaseous or particulate contaminants. Volatile organic compounds are emitted from a wide variety of household and consumer products with emission rates that are strongly dependent on the type of application and are distributed over several orders of magnitude. A number of product classes are identified and information on ingredients and available data on emissions from individual products are presented. Human activities and the associated use of products encompass a wide range of indoor sources involving release of inorganic gases, particles and organic compounds as a consequence of the activity. For some releases such as with air fresheners the release is a necessary part of the activity to achieve the intended effect whereas for others, such as the release of combustion fumes from a gas appliance, the purpose of the action (in this case generation of heat) is different from the emission. Combustion processes are an important source of a range of air pollutants as carbon monoxide, nitrogen dioxide, sulphur dioxide, particulates and associated inorganic and organic chemicals, organic vapours e.g. formaldehyde, acetaldehyde, and benzene. Sources of these are present in both ambient and indoor environments. The concentrations present in the ambient air provide a baseline for the level of pollutant found indoors as this air enters indoors by processes of infiltration and ventilation. However, the concentration indoors will be modified by processes of sorption to surfaces and chemical reaction depending on the chemical and physical properties of the pollutant and internal surfaces. People themselves are a source of emissions of chemicals and gases, notably CO range of organic compounds that are referred to as body odours. The removal of such body odours is a prime objective of ventilation in order to achieve a satisfactory indoor environment. WP3 aims at to characterize spaces and sources in order to understand where and how to act to guarantee good IAQ. From the two strategies for good IAQ, source control and ventilation, the precautionary principle suggests that first priority shall be given to source control, avoiding, mitigating or simply managing sources of emissions. An overview of all policies on IAQ or related to IAQ, existing or in preparation, directly related to indoor air sources, but also covering outdoor air and industrial emissions, which could affect indirectly IAQ is made. Considering the presented it could be concluded that IAQ is yet poorly regulated at EU level, and in view of that some recommendations are made. The recommendations on policies have taken into account the existing related to IAQ policies such as new EU policies on chemicals (REACH; 2006/121/EC), consumer products (GPSD; 2001/95/EC), construction products (CPD; 89/106/EC) and energy performance of buildings (EPBD; 2002/91/EC) all refer to IAQ issues - suggesting that they could, and probably should, contribute to IAQ policy development and advocate an integrative and comprehensive policy approach centred

Estudos gráficos das variaçôes dos coeficientes da funçâo quadrática com o auxílio do software geogebra

Pretendemos, neste trabalho, observar como os estudantes estudam a variação dos coeficientes da função quadrática f (x) =ax²+ bx+c (a, b e c e a 0), com a utilização do software GeoGebra e verificar se isto facilita a compreensão do desenho gráfico desta função. Para isto elaboramos e aplicamos um teste em uma turma de alunos de um Curso de Licenciatura em Matemática e, em seguida, ministramos um minicurso sobre o GeoGebra para os mesmos. Após a realização do minicurso, reaplicamos o teste. No primeiro teste, os estudantes tiveram facilidade de compreensão em relação ao sinal do coeficiente a, porém, a variação modular foi um desafio e constatamos um alto índice de erros relacionados ao coeficiente b. Quanto ao coeficiente c, houve facilidade. Após a intervenção com o software GeoGebra, houve uma evolução no entendimento da conseqüência da variação do coeficiente b no gráfico da função

Prova em dupla como oportunidade para diálogo e socialização de saberes

Discutimos neste trabalho resultados relativos a mudanças metodológicas realizadas pela prova escrita para alunos de uma escola brasileira. Partimos da experiência docente aliada ao estudo de pesquisas científicas que consideram a prova um momento de aprendizado. Porém acreditamos que isso pode ser potencializado por meio de prova escrita feita com duplas formadas por livre escolha dos alunos, mas duas provas distintas para propiciar a cada dupla o diálogo. Além disso, as duplas devem ser escolhidas com antecedência, sendo a nota obtida pela média aritmética das notas de cada um dos alunos

Redesign e teste de viga seletora em sistema de transporte de volumes

The parcel and postal market is requesting higher and higher sorting capacities of Vanderlande sorters. One of the companies line of sorters is the Compaxorter which uses a beam to sort a parcel instead of a shoe. Compared to the shoe, a sort beam has some disadvantages regarding machine and human safety. Redesigning the sort beam in order to be flexible would reduce or solve the disadvantages. During the development procedure, two prototypes were created and tested along with a multi-body mathematical model to simulate the motion of one component of the prototype, the bracket. The first prototype was created after several concepts were generated. Once the concept that best fitted the key requirements was chosen, it was improved and turned into the first prototype. After testing prototype alpha, valuable information was created regarding its design and the bracket movement. Afterwards, based on the generated information, either the sort beam and bracket went through a new redesign phase. Therefore, the second prototype was produced and tested. The results were positive for the bending event but the bracket mechanism was still not ideal. Therefore, the multi-body mathematical model was created to predict manually its motion and, then, helping with its design.O mercado de encomendas e correio está a exigir cada vez mais altas capacidades das máquinas sorteadoras da Vanderlande. Uma das máquinas da empresa é o Compaxorter que usa uma viga para sortear uma encomenda em vez de um sapato. Comparando ao sapato, a viga seletora tem certas desvantagens no que toca à segurança da máquina e dos operadores. Redesenhar a viga sorteadora de maneira a torná-la flexível pode reduzir ou até eliminar as desvantagens. Durante o processo de desenvolvimento, dois protótipos foram produzidos e testados juntamento com um modelo matemático multi-corpo que simula o movimento de um componente do protótipo, o bracket. O primeiro protótipo foi produzido após várias ideas serem geradas. O conceito que mais se adequava aos requesitos foi escolhido, melhorado e depois transformado então no primeiro protótipo. Após testar o protótipo alfa, foi gerada informação importante relativamente ao seu design e ao movimento do bracket. Com base nessa informação, a viga e o bracket foram novamente redesenhados. Desta maneira, o segundo protótipo foi produzido e testado. Os resultados foram positivos no que diz respeito à flexibilidade da viga mas o mecanismo do bracket ainda não era ideal. Portanto, o modelo matemático multi-corpo foi criado para prever manualmente o seu movimento, culminando com o seu redesign.Mestrado em Engenharia Mecânic

HUMAN EXPOSURE TO FOOD CONTAMINANTS THROUGHOUT DIET: ASSESSMENT THROUGH TDS, BIOACCESSIBILITY AND CYTOTOXICITY ASSAYS IN VITRO

Human health and environmental sustainability are interlinked through diet since food inges- tion is one of the main routes of exposure to several contaminants in humans. In this sense, the transformation of healthy diets from sustainable food systems is crucial to achieving the Sustainable Development Goals defined by the United Nations, namely goals 2 and 3, related to food security and ensuring healthy lives, respectively. The present thesis aimed at i) char- acterising the presence of chemical contaminants in essential food items of the Portuguese diet; ii) evaluating the geographical influence and the importance of diffuse sources on trace ele- ments levels in food; iii) assessing the potential risk of halogens, metals and metalloids to hu- mans through food, and iv) estimating the bioaccessibility of food contaminants and their po- tential toxicity in intestinal cells. The results revealed that regarding the consumption of rele- vant food groups in the Portuguese population, the seafood group presented the highest As, Br, Cd and Pb levels compared to other analysed food groups, with an increased relative risk for total As and a clear progression of Cd relative risk with increasing consumption frequency of seafood. The results also demonstrated that the trace elements in areas affected by wildfires identified a hazard, especially for As, and other trace elements such as Cd, Br, Cr and Sr. More- over, the bioaccessible fractions of As obtained after in vitro digestion of seafood were higher than the EC50 obtained for human intestine cells. This thesis contributed to increasing the knowledge about chemical contamination in food and their risk to the human population, as well as to the importance of using different approaches, including TDS methodology, risk as- sessment strategies, and in vitro assays, as essential tools for developing new monitoring meth- odologies in sustainable food systems and SDGs achievement.A saúde humana e a sustentabilidade ambiental estão interligadas através da dieta, sendo a ingestão uma das principais vias de exposição a contaminantes nos seres humanos. Neste sen- tido, a transformação de dietas saudáveis a partir de sistemas alimentares sustentáveis é cru- cial para alcançar os Objetivos de Desenvolvimento Sustentável definidos pelas Nações Uni- das, nomeadamente os objetivos 2 e 3, relacionados com a segurança alimentar e a garantia de vidas saudáveis, respetivamente. A presente tese visa i) caracterizar a presença de contami- nantes químicos em alimentos essenciais da dieta portuguesa; ii) avaliar a influência geográ- fica e a importância de fontes difusas nos níveis de elementos vestigiais nos alimentos; iii) avaliar o potencial risco de halogéneos, metais e metalóides nos seres humanos através de alimentos, iv) estimar a bioacessibilidade de contaminantes alimentares e a sua potencial toxi- cidade em células intestinais. Os resultados revelaram que em relação ao consumo de grupos alimentares relevantes na população portuguesa, o grupo de produtos do mar apresentou os níveis mais elevados de As, Br, Cd e Pb comparativamente aos outros grupos analisados, um aumento do risco relativo de As total e uma progressão do risco relativo de Cd aumentando com a frequência de consumo de produtos do mar. Os resultados também demonstraram que os elementos vestigiais nas áreas afetadas pelos incêndios identificaram um risco, especial- mente para As, Cd, Br, Cr e Sr. Evidenciaram que as frações bioaccessíveis de As após digestão in vitro dos produtos do mar foram superiores ao EC50 obtido nas células intestinais humanas. Esta tese contribuiu para aumentar o conhecimento sobre a contaminação química nos alimen- tos e o seu risco para a população humana, bem como para a importância de utilizar diferentes abordagens, incluindo a metodologia TDS, estratégias de avaliação de risco, e ensaios in vitro, para o desenvolvimento de novas metodologias de monitorização em sistemas alimentares sustentáveis e o alcance de ODS