We study the boundedness of Fourier convolution operators \(W^0(b)\) and the compactness of commutators of \(W^0(b)\) with multiplication operators \(aI\) on some Banach function spaces \(X(\mathbb{R})\) for certain classes of piecewise quasicontinuous functions \(a\in PQC\) and piecewise slowly oscillating Fourier multipliers \(b\in PSO_{X,1}^\diamond\). We suppose that \(X(\mathbb{R})\) is a separable rearrangement-invariant space with nontrivial Boyd indices or a reflexive variable Lebesgue space, in which the Hardy-Littlewood maximal operator is bounded. Our results complement those of Isaac De La Cruz-Rodríguez, Yuri Karlovich, and Iván Loreto Hernández obtained for Lebesgue spaces with Muckenhoupt weights.

A aprendizagem dos nossos alunos é fortemente influenciada pelas caraterísticas das tarefas que lhes propomos e a resolução de problemas é frequentemente apontada como uma das tarefas com mais potencial para promover aprendizagens ricas. Mas aprender implica ser capaz de desenvolver raciocínios, de comunicar as nossas ideias e de compreender as dos outros num processo argumentativo e reflexivo. A avaliação das aprendizagens num contexto de resolução de problemas envolve assim, necessariamente como parte importante do processo, uma análise da comunicação que se estabelece entre todos os envolvidos.
Nesta comunicação iremos focar-nos precisamente na comunicação que se estabelece durante a resolução de problemas, abordando as dificuldades dos alunos e dando atenção à interpretação que fazem do enunciado, à compreensão que manifestam das figuras apresentadas, à relação que conseguem estabelecer entre a situação em causa e a informação disponibilizada através de um gráfico, à forma como conseguem explicitar o seu raciocínio e à linguagem matemática que utilizam no decurso do processo de argumentação. Para tal vamos basear-nos num conjunto de problemas propostos a alunos do 10.º ano de escolaridade no decorrer do estudo de funções.

We give a combinatorial characterization of conjugacy in the sylvester monoid, showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids.

Given graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. Let f_H(n) be the smallest number t such that any graph G of order n admits an H-decomposition with at most t parts. Here we study the case when H=C_7, that is, the cycle of length 7 and prove that f_{C_7}(n)=\lfloor n^2/4 \rfloor for all n≥10.

Theropod teeth are particularly abundant in the fossil record and frequently reported in the literature. Yet, the dentition of many theropods has not been described comprehensively, omitting details on the denticle shape, crown ornamentation and enamel texture. This paucity of information has been particularly striking in basal clades, thus making identification of isolated teeth difficult, and taxonomic assignments uncertain. We here provide a detailed description of the dentition of Megalosauridae, and a comparison to and distinction from superficially similar teeth of all major theropod clades. Megalosaurid dinosaurs are characterized by a mesial carina facing mesiolabially in most mesial teeth, centrally positioned carinae on both most mesial and lateral crowns, a mesial carina terminating above the cervix, and short to well-developed interdenticular sulci between distal denticles. A discriminant analysis performed on a dataset of numerical data collected on the teeth of 62 theropod taxa reveals that megalosaurid teeth are hardly distinguishable from other theropod clades with ziphodont dentition. This study highlights the importance of detailing anatomical descriptions and providing additional morphometric data on teeth with the purpose of helping to identify isolated theropod teeth in the future.

Neste texto apresentamos os jogos no ensino da matemática como uma forma de aprendizagem de conteúdos e não apenas como um recurso que cada professor pode usar nas suas aulas para tornar a aula diferente. Analisamos dois jogos desenvolvidos por nós e que utilizámos com alunos dos 7.º e 10.º anos de escolaridade, procurando não só apresentar os jogos, mas também aspetos da sua implementação em sala de aula, ponderando o contributo que trouxeram à aprendizagem dos alunos.
Aprender matemática depende de um grande número de variáveis, o que torna o ensino um processo complexo, pois é necessário que se desenvolva o raciocínio lógico, além de estimular o desenvolvimento das mais variadas capacidades transversais, tais como o pensamento autónomo, a criatividade, o sentido de estratégia e a capacidade de resolver problemas.
Duas das dificuldades frequentemente encontradas pelos professores passam pela falta de motivação para a aprendizagem e pelo desinteresse pela Matemática. A solução para estes problemas pode passar pela utilização de jogos para complementar o estudo, mas também para a aquisição de novos conteúdos. No entanto, apenas a implementação dos jogos não basta. O papel do professor é de extrema importância e a planificação e orientação da aula são fundamentais para que se alcancem os objetivos pretendidos.

Multi-threaded programs allow one to achieve better performance by doing a lot of work in parallel using multiple threads. Such parallel programs often contain code blocks that a thread must execute atomically, i.e., with no interference from the other threads of the program. Failing to execute these code blocks atomically leads to errors known as atomicity violations. However, frequently it not obvious to tell when a piece of code should be executed atomically, especially when that piece of code contains calls to some third-party library functions, about which the programmer has little or no knowledge at all. One solution to this problem is to associate a contract with such a library, telling the programmer how the library functions should be used, and then check whether the contract is indeed respected. For contract validation, static approaches have been proposed, with known limitations on precision and scalability. In this paper, we propose a dynamic method for contract validation, which is more precise and scalable than static approaches.

Abstract The near-surface mounted (NSM) strengthening technique is capable of effectively increase the bearing capacity of structural concrete elements. This technique which basically consists of placing \{FRP\} reinforcements inside small grooves cut in the concrete cover, has been widely investigated in terms of structural performance and ability to improve the flexural and shear behaviour of reinforced concrete beams and columns. However, little research has been carried out concerning to the \{NSM\} long-term performance and durability. Motivated by the need of increasing the knowledge on the expected durability of the \{NSM\} technique using \{CFRP\} laminates, this paper presents an experimental program in which direct pull-out tests are carried out for evaluating the bond behaviour of specimens aged through wet-dry cycles. A total of 30 specimens are tested, analysing the effect of the bond length, the groove width, the groove depth and the aging effect on the bond behaviour. Digital image correlation method is also used to identify the bond resistant mechanism developed in an element strengthened using \{NSM\} technique. Finally, using the experimental results, an analytical�numerical strategy is applied to establish the local bond stress�slip relationship.

Abstract The bond behavior between Fiber Reinforced Polymers (FRPs) and masonry substrates has been the subject of many studies during the last years. Recent accelerated aging tests have shown that bond degradation and \{FRP\} delamination are likely to occur in FRP-strengthened masonry components under hygrothermal conditions. While an investigation on the possible methods to improve the durability of these systems is necessary, the applicability of different bond repair methods should also be studied. This paper aims at investigating the debonding mechanisms after repairing delaminated FRP-strengthened masonry components. FRP-strengthened brick specimens, after being delaminated, are repaired with two different adhesives: a conventional epoxy resin and a highly flexible polymer. The latter is used as an innovative adhesive in structural applications. The bond behavior in the repaired specimens is investigated by performing single-lap shear bond tests. Digital image correlation (DIC) is used for deeper investigation of the surface deformation and strains development. The effectiveness of the repair methods is discussed and compared with the strengthened specimens.

Neste artigo apresentamos um protocolo de controlo de concorrência que garante que a execução concorrente de transações é equivalente à sua execução sequencial por uma ordem predefinida. Isto permite executar programas que usam transações de forma determinista. O protocolo (1) permite, pela primeira vez, a execução determinista de programas que usam memória transacional por hardware; e (2) garante a execução determinista de programas que usam memória transacional por software com um desempenho claramente superior ao estado da arte.

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