In this paper, we study permutations on n elements that are even on every subset of size t. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral. In this context, we define and study monoids that generalize both monoids of order-preserving mappings and monoids of orientation-preserving mappings.

The pursuit of strategies that minimize the number of individuals needing vaccination to control an outbreak is a well-established area in mathematical epidemiology. However, for certain diseases, public policy tends to prioritize immunizing vulnerable individuals over epidemic control. As a result, optimal vaccination strategies may not always be effective in supporting real-world public policies. A similar situation happens when a new vaccine is introduced and is in short supply, as target priority groups for vaccination have to be defined. In this work, we focus on a disease that results in long-term immunity and spreads through a heterogeneous population, represented by a contact network. We study four well-known group centrality measures and show that the GED-Walk offers a reliable means of estimating the impact of vaccinating specific groups of individuals, even in suboptimal cases. Additionally, we depart from the search for target individuals to be vaccinated and provide proxies for identifying optimal groups. While the GED-Walk is the most useful centrality measure for suboptimal cases, the betweenness (a related, but different centrality measure) stands out when looking for optimal groups. This indicates that optimal vaccination is not concerned with breaking the largest number of transmission routes, but interrupting geodesic ones.

Incorporating technologies with Generative Artificial Intelligence (GenAI) into education requires a shift in teaching methodologies. However, little is known about how pre-service teachers perceive the relevance and challenges of this incorporation, particularly in mathematics education. This study investigates pre-service teachers’ interactions with GenAI, addressing the relevance and challenges of integrating it in mathematics teaching and discussing possible implications for their knowledge and professional development. Specifically, it intends to understand: How does the pre-service teachers’ interaction with GenAI during the design and implementation of teaching activities relate to their professional knowledge? And how does this relation impact the relevance they ascribe to GenAI? In this qualitative and interpretative study, involving seven pre-service mathematics teachers, we analyse the interplay between participants’ knowledge and use of a GenAI (in this case, ChatGPT), guided by KTMT – Knowledge for Teaching Mathematics with Technology model. The main conclusions revealed a landscape characterised by promise and challenge, where GenAI can be a valuable educational
tool when used to facilitate discussion and promote critical thinking, highlighting the relevance and development of KTMT. The ability to evaluate and reflect on AI-generated responses can promote professional development, preparing pre-service teachers for an increasing presence of technology in educational environments.

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A exploração de diferentes representações promove a compreensão dos tópicos de funções. Partindo deste pressuposto, com este estudo pretende-se analisar o contributo da representação gráfica na aprendizagem da noção de função inversa e da paridade de uma função por alunos do 10.º ano de escolaridade e identificar dificuldades na exploração dessa representação. Na procura de responder a este objetivo, adotou-se uma abordagem qualitativa e interpretativa para compreender as ações dos alunos na resolução das tarefas
propostas. A análise das resoluções mostra que a representação gráfica serviu de suporte para a instituição das definições dos tópicos em estudo. E isto apesar de alguns alunos revelarem dificuldades ao interpretar e ao construir gráficos; ao identificar imagens e imagens inversas em gráficos de funções; ao representar determinadas características gráficas associadas a alguns conceitos, como é o caso da relação entre a paridade de uma função e a simetria na sua representação gráfica (confundindo eixo de simetria e de reflexão). Globalmente, este estudo mostra como a abordagem de conceitos a partir da representação gráfica pode contribuir para a sua compreensão.

Green and lean are manufacturing management paradigms that identify new opportunities to improve the business to be more competitive. The purpose of this research is to contribute for the understanding of how to address green–lean approaches in a supply chain. The objective is to provide basic mechanisms to implement an organization’s supplychain based on an integrated green and lean approach. To attain this objective, some relevant initiatives for a green and lean transformation were considered first. Second, a multiple case study was conducted in the automotive industry to test qualitatively the several integrated green and lean initiatives and see how they are being implemented in the real world. Based on the literature review and the case study, an oriented-tool is suggested, which involves a roadmap to achieve a green–lean supply-chain transformation. The proposed roadmap can serve as the basis for further research in green and lean supply chain management, providing insights into the implementation of a green–lean approach.

The aim of the present study was to proceed to a numerical analysis of the gravity load effects on the behaviour of reinforced concrete beam critical zones when subjected to cyclic loads. A parametric study to assess the influence of different levels of gravity load on RC beam critical zones subjected to cyclic loading was carried out. For this purpose, assuming the level of gravity load as a variable parameter, a nonlinear numerical model of a beam-column connection, previously calibrated with experimental data, was used. In order to evaluate the gravity load effects in the global response, a numerical study of a RC frame system is also presented. The numerical results are analysed in terms of global hysteretic response, accumulated energy dissipation and equivalent viscous damping ratio. In this numerical study, it was observed that the hysteretic response depends on the load path. In the presence of higher gravity load levels, the structure hysteretic behaviour exhibits higher damage levels, associated to a failure mechanism corresponding to the formation of four span plastic hinges. Thus, the proper test procedure should involve the imposition of a reverse cyclic displacement history starting each cycle from the gravity load effects.

Accumulative Roll Bonding (ARB) was used to fabricate Graphene Oxide-reinforced Al-matrix composites.
Graphene Oxide reinforcement was suspended in a stabilized aqueous solution and applied, prior to each ARB
cycle, through airgun spraying. Different concentrations (graphene oxide/milipore water) were used and for
each concentration, samples produced have undergone up to 5 rolling cycles.
Optical and electron scanning microscopies were used for microstructural characterization which revealed a
non-homogenous deformation of the layers across the composite's thickness.
Although the presence of graphene-oxide promoted an increase in the microhardness, higher values were
obtained with its lowest concentration for similar samples. The number of ARB cycles and the direction of the
tested sections also influenced the microhardness results since the 5-cycle samples and the rolling direction
sections for all the samples achieved higher hardness results. Graphene Oxide revealed to be a major contributor
to the increase of stiffness during bending of the tested samples.