The bonding technique has received extensive attention in the recent decades. Unlike the use of metallic screws, screws or rivets, some of the advantages of this bonding technique include the elimination of stress concentration, lighter weight and the extension of the life cycle of the adhesively bonded structures. The stiffness and strength of a material are increased after bonding with another reinforced material, but it can only be effective if the interface is able to transfer bond stresses. However, how the bond stress transfer is carried out when the joint, reinforcement and substrate are subjected to a thermal loading is not yet well understood. One way to facilitate and improve such knowledge is to develop analytical solutions that, despite their simplicity, allow parameters to be identified that may directly influence the bond between materials. Therefore, the present study aims to develop a series of closed-form solutions able to describe the debonding process of bonded joints with different characteristics using two different exponential softening laws. The results mainly describe the interfacial slips, bond stresses and strains in both materials during the temperature increase process. In total, 108 examples with different bonding conditions are studied and, at the same time, numerically modelled through the Finite Element Method (FEM). The numerical results were compared to the proposed closed-form solutions and a satisfactory agreement was obtained between the numerical and analytical results, validating the latter. When considered in the simulations, the glass transition temperature (Tg) of the adhesive greatly affected the bond stress transfer between materials and compromising the initial integrity of the adhesively bonded structure. © 2020

No contexto do Observatório de Literacia Oceânica, o estudo da coconstrução de um museu virtual online investiga a aprendizagem dos alunos pertencentes às comunidades piscatórias, contribuindo para a literacia histórica. O envolvimento em tarefas concretas associadas à aprendizagem é considerado, consensualmente, um fator de motivação. No presente estudo trabalharam as artes da pesca artesanal, enquadradas por conteú dos da disciplina de História. Utilizando ambientes tecnologicamente enriquecidos, pretende-se compreender as interações entre o conhecimento formal e informal destes alunos, desenvolvendo-se o estudo de forma a que os conhecimentos sejam signi{\textbackslash}icativos e usáveis, promovendo a intervenção na sociedade, enquanto agentes de mudança. A metodologia assentou num estudo empı́rico qualitativo, com base na etnogra{\textbackslash}ia crı́tica, combinado com design-based research, para a construção do protótipo do museu virtual online. As estratégias de ação, técnicas de recolha e aná lise de dados desenvolveram-se num contexto de observação participativa, notas de campo e aplicação de vários instrumentos, bem como na coconstrução do protótipo por aproximações sucessivas estruturantes da plataforma digital selecionada. Constatou-se a ausência de interação entre os saberes formais e informais dos alunos, um desconhecimento da história das suas comunidades, mas também a valorização das histórias de famı́lia. Os alunos foram observadores crı́ticos das suas práticas reconhecendo, por exemplo, a desvalorização dos seus saberes informais e a sua falta de relação com os conteú dos da disciplina de História. Neste processo identi{\textbackslash}icou-se a necessidade de introduzir temáticas relacionadas com a Literacia Histórica, História das Comunidades Capariquenses e Sustentabilidade, considerando-o o meio privilegiado para a disseminação do seu património cultural.

The cyclic shift graph of a monoid is the graph whose vertices are elements of the monoid and whose edges link elements that differ by a cyclic shift. This paper examines the cyclic shift graphs of `plactic-like' monoids, whose elements can be viewed as combinatorial objects of some type: aside from the plactic monoid itself (the monoid of Young tableaux), examples include the hypoplactic monoid (quasi-ribbon tableaux), the sylvester monoid (binary search trees), the stalactic monoid (stalactic tableaux), the taiga monoid (binary search trees with multiplicities), and the Baxter monoid (pairs of twin binary search trees). It was already known that for many of these monoids, connected components of the cyclic shift graph consist of elements that have the same
evaluation (that is, contain the same number of each generating symbol). This paper focusses on the maximum diameter of a connected component of the cyclic shift graph of these monoids in the rank-$n$ case. For the hypoplactic monoid, this is $n-1$; for the sylvester and taiga monoids, at least $n-1$ and at most $n$; for the stalactic monoid, $3$ (except for ranks $1$ and $2$, when it is respectively $0$ and $1$); for the plactic monoid, at least $n-1$ and at most $2n-3$. The current state of knowledge, including new and previously-known results, is summarized in a table.

This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of tableaux, we present Robinson--Schensted--Knuth-type correspondences (that is, bijective correspondences between word arrays and certain pairs of semistandard tableaux of the same shape), generalizing two known correspondences: a bijective correspondence between standard words and certain pairs of standard tableaux, and an injective correspondence between words and pairs of tableaux.

We also exhibit formulas to count both the number of each type of tableaux with given evaluations (that is, containing a given number of each symbol). Observing that for any natural number $n$, the $n$-th Bell number is given by the number of standard tableaux containing $n$ symbols, we restrict the previous formulas to standard words and extract a formula for the Bell numbers. Finally, we present a `hook length formula' that gives the number of standard tableaux of a given shape and deduce some consequences.

This paper constructs presentations via finite complete rewriting systems for plactic monoids of types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$, using a unified proof strategy that depends on Kashiwara's crystal bases and analogies of Young tableaux, and on Lecouvey's presentations for these monoids. As corollaries, we deduce that plactic monoids of these types have finite derivation type and satisfy the homological finiteness properties left and right $\mathrm{FP}_\infty$. These rewriting systems are then applied to show that plactic monoids of these types are biautomatic.