Packaging waste collection systems are responsible to collect, within a geographic area, three types of packaging materials (paper, glass and plastic/metal) that are disposed by the final consumer into special bins. Those systems are often characterized by having a network with multiple depots that act as transfer and sorting stations, and where the vehicle fleet is based. However, each depot is often managed independently and not as a part of a unique system. In this work, four current tactical/operational practices that contribute to the independent management of each depot are analysed. The change of such practices is investigated and their impact assessed on the total collection cost. A solution methodology based on mathematical formulations is developed to plan service areas, vehicle routes and vehicle schedules taking into account new alternative solutions in managing the system as a whole. Such methodology is applied to a real case study of a company responsible for the collection of the packaging waste in 7 municipalities in mainland Portugal. New service areas, collection routes and vehicle schedules are defined and significant savings are obtained in terms of the total distance travelled as well as in terms of the number of required vehicles, resulting in a decreasing of the total system cost.

Pulsed field gradient spin echo high resolution magic angle spinning nuclear magnetic resonance spectroscopy is a powerful technique to characterize confined biosystems. We used this approach to assess the diffusion of solvent and reaction species within sol–gel matrices differing in enzyme loading.

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Molybdenum and tungsten enzymes require specific chaperones for folding and cofactor insertion. PaoD is the chaperone of the periplasmic aldehyde oxidoreductase PaoABC. It is the last gene in the paoABCD operon in Escherichia coli and its presence is crucial for obtaining mature enzyme. PaoD is an unstable, 35 kDa, protein. Our biochemical studies showed that it is a dimer in solution with a tendency to form large aggregates, especially after freezing/thawing cycles. In order to improve stability, PaoD was thawed in the presence of two ionic liquids [C4mim]Cl and [C2OHmim]PF6 and no protein precipitation was observed. This allowed protein concentration and crystallization using polyethylene glycol or ammonium sulfate as precipitating agents. Saturation transfer difference – nuclear magnetic resonance (STD-NMR) experiments have also been performed in order to investigate the effect of the ionic liquids in the stabilization process, showing a clear interaction between the acidic ring protons of the cation and, most likely, negatively charged residues at the protein surface. DLS assays also show a reduction of the overall size of the protein aggregates in presence of ionic liquids. Furthermore, cofactor binding studies on PaoD showed that the protein is able to discriminate between molybdenum and tungsten bound to the molybdenum cofactor, since only a Mo-MPT form of the cofactor remained bound to PaoD.

Virtual environments are an increasing trend in today’s society. In this scope, the avatar is the representation of the user in the virtual world. However, that relationship lacks empirical studies regarding the nature of the interaction between avatars and human beings. For that purpose it was studied how the avatar’s modeled morphology and dynamics affect its control by the user. An experiment was conducted to measure telepresence and ownership on participants who used a Kinect Natural User Interface (NUI). The body ownership of different avatars was assessed through a behavioral parameter, based on the concept of affordances, and a questionnaire of presence. The results show that the feelings of telepresence and ownership seem to be greater when the kinematics and the avatar’s proportions are closer to those of the user.

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space \(X(\mathbb{R}^n)\) and on its associate space \(X'(\mathbb{R}^n)\), then a pseudodifferential operator \(\operatorname{Op}(a)\) is bounded on \(X(\mathbb{R}^n)\) whenever the symbol \(a\) belongs to the Hörmander class \(S_{\rho,\delta}^{n(\rho-1)}\) with \(0<\rho\le 1\), \(0\le\delta<1\) or to the the Miyachi class \(S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)\) with \(0\le\delta\le\rho\le 1\), \(0\le\delta<1\), and \(\varkappa>0\). This result is applied to the case of variable Lebesgue spaces \(L^{p(\cdot)}(\mathbb{R}^n)\).

We present the δ13C and paleomagnetic stratigraphy for marine strata at the coast of southern Angola, anchored by an intercalated basalt with a whole rock 40Ar/39Ar radiometric age of 84.6 ± 1.5 Ma, being consistent with both invertebrate and vertebrate biostratigraphy. This is the first African stable carbon isotope record correlated to significant events in the global carbon cycle spanning the Late Cenomanian to Early Maastrichtian. A positive ∼ 3‰ excursion seen in bivalve shells below the basalt indicates the Cenomanian-Turonian Boundary Event at 93.9 Ma, during Oceanic Anoxic Event 2. Additional excursions above the basalt are correlated to patterns globally, including a negative ∼ 3‰ excursion near the top of the section interpreted as part of the Campanian-Maastrichtian Boundary Events. The age of the basalt ties the studied Bentiaba section to a pulse of Late Cretaceous magmatic activity around the South Atlantic and significant tectonic activity, including rotation, of the African continent.

Let \(p:\mathbb{R}\to(1,\infty)\) be a globally log-Hölder continuous variable exponent and \(w:\mathbb{R}\to[0,\infty]\) be a weight. We prove that the Cauchy singular integral operator \(S\) is bounded on the weighted variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R},w)=\{f:fw\in L^{p(\cdot)}(\mathbb{R})\}\) if and only if the weight \(w\) satisfies $$ \sup_{-\infty < a < b < \infty} \frac{1}{b-a} \|w\chi_{(a,b)}\|_{p(\cdot)} \|w^{-1}\chi_{(a,b)}\|_{p'(\cdot)}<\infty \quad (1/p(x)+1/p'(x)=1). $$

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The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.

A Matemática é uma das áreas que integra o plano curricular dos Cursos de Educação e Formação (CEF), pelo contributo para o exercício da cidadania em sociedades democráticas e tecnologicamente avançadas, mas esta é, também, frequentemente fonte de exclusão. O programa reconhece-o e enfatiza uma aprendizagem mais ligada ao concreto e à realidade. Mas reconhece também que é ao professor que compete gerir a sua implementação, dando forma às situações de aprendizagem e integrando-as de forma coerente e articulada no curso específico que os alunos frequentam. O estudo que aqui se apresenta teve como principal objectivo analisar e compreender as opções efectuadas pelo professor no decorrer das diferentes etapas da sua prática, dando atenção aos dilemas que enfrentou e às razões que valorizou na tomada de decisões. A abordagem metodológica adoptada é de natureza qualitativa e interpretativa, com a realização dum estudo de caso do professor de Matemática Aplicada dum CEF de Decoração e Pintura Cerâmica. A recolha de dados foi concretizada através de entrevistas, observação de aulas e recolha documental, sendo a análise de dados orientada pelo quadro teórico, conciliado com a interpretação destes. Nas conclusões do estudo a redução dos pré-requisitos, a preocupação em partir dos interesses dos alunos e a intenção de alargar a cultura dos alunos surgem como centrais na selecção das tarefas; enquanto o envolvimento activo dos alunos caracteriza a implementação das aulas. Os dilemas centram-se fundamentalmente na valorização relativa e aprofundamento a atribuir a cada conteúdo e na articulação entre formal e intuitivo.

We here present fossil Crocodylomorpha eggshells from the Upper Jurassic Lourinhã Formation of Portugal, recovered from five sites: one nest from Cambelas with 13 eggs, and three partial eggs and various fragments from, Paimogo N (I), Paimogo S (II), Casal da Rola, and Peralta. All specimens but the nest were found in association with dinosaur egg material. Our research reveals that on a micro- and ultrastructural analysis, all samples present the typical characters consistent with crocodiloid eggshell morphotype, such as the shell unit shape, the organization of the eggshell layers, and the triangular blocky extinction observed with crossed nicols. We assign the material from the Lourinhã Formation to the oofamily Krokolithidae, making it the oldest crocodylomorph eggs known so far, as well as the best record for eggs of non- crocodylian crocodylomorphs. Furthermore, our study indicates that the basic structure of crocodiloid eggshells has remained stable since at least the Upper Jurassic.