A new model based on Finite Fracture Mechanics (FFMs) has been proposed to predict the open-hole tensile strength of composite laminates [1]. Failure is predicted when bothstress-based and energy-based criteria are satisfied. This model is based on an analytical solution, and no empirical adjusting parameters are required, but only two material properties: the unnotched strength and the fracture toughness. In the present work, an extension of the proposed FFMs model to predict the notched response of composite laminates with notch geometries other than a circular opening [2] is presented and applied to the prediction of size effects on the tensile and compressive notched strength of composite laminates. The present model is also used to assess the notch sensitivity and brittleness of composite laminates by means of versatile design charts and by the identification of a dimensionless parameter designated as notch sensitivity factor. A further extension of the FFMs model is proposed, which takes into account the crack resistance curve of the laminate in the model's formulation, and it is used to predict the large damage capability of a non-crimp fabric thin-ply laminate [3].

ABSTRACT We report here a new elasmosaurid from the early Maastrichtian at Bentiaba, southern Angola. Phylogenetic analysis places the new taxon as the sister taxon to Styxosaurus snowii, and that clade as the sister of a clade composed of (Hydrotherosaurus alexandrae (Libonectes morgani + Elasmosaurus platyurus)). The new taxon has a reduced dorsal blade of the scapula, a feature unique amongst elasmosaurids, but convergent with cryptoclidid plesiosaurs, and indicates a longitudinal protraction-retraction limb cycle rowing style with simple pitch rotation at the glenohumeral articulation. Morphometric phylogenetic analysis of the coracoids of 40 eosauropterygian taxa suggests that there was a broad range of swimming styles within the clade.

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The influence of mathematical communication over the students’ learning led to this research, whose main goal is to understand the impact on problem solving of the students’ communication difficulties. The study adopts a qualitative and interpretative methodology, undertaking two case studies of 10th grade students. The reached conclusions point to the students’ difficulties at the interpretation of the problem, namely at the interpretation of figures, and at the interpretation of the available data, especially when part of them is irrelevant to the problem. Some difficulties were also identified at the communication level, in relation to the arguments used by the students to support their ideas, where a clear preference to restrict them to mathematic calculations was identified.

Resumo
A importância da comunicação matemática sobre a aprendizagem dos alunos, levou à realização desta investigação que pretendeu compreender o impacto sobre a resolução de problemas das dificuldades de comunicação evidenciadas pelos alunos. Optou-se por uma metodologia de natureza qualitativa e interpretativa e pela realização de estudos de caso envolvendo dois alunos do 10.º ano. As conclusões alcançadas apontam para dificuldades na interpretação do enunciado, nomeadamente relativamente às figuras e a dados em quantidade superior ao necessário. Também ao nível da comunicação da resolução foram identificadas dificuldades em fundamentar ideias, evidenciando uma preferência pelo recurso ao cálculo.

Let \(\mathcal{M}_{X,w}(\mathbb{R})\) denote the algebra of the Fourier multipliers on a separable weighted Banach function space \(X(\mathbb{R},w)\). We prove that if the Cauchy singular integral operator \(S\) is bounded on \(X(\mathbb{R},w)\), then \(\mathcal{M}_{X,w}(\mathbb{R})\) is continuously embedded into \(L^\infty(\mathbb{R})\). An important consequence of the continuous embedding \(\mathcal{M}_{X,w}(\mathbb{R})\subset L^\infty(\mathbb{R})\) is that \(\mathcal{M}_{X,w}(\mathbb{R})\) is a Banach algebra.

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