Purpose The antique structures are part of the inheritance that our elders left, being important to preserve their memories. It is important to preserve, rehabilitate and restore the historic buildings protecting the cultural patrimony, attending to the actual comfort and habitability requirements. It is necessary to study the behaviour of the various elements that compose antique structures (masonry and wood) in order to develop assessment measures according to the characteristics of the original materials. The paper aims to discuss these issues. Design/methodology/approach An experimental campaign to characterize the mechanical behaviour of the wood of the roof of the �sequeiro� of �Quinta Lobeira de Cima�, a building from the twentieth century located in Minho, was carried out. The tested wood specimens are from two different species: chestnut and oak. Compression, tension and static flexion tests according to parallel to the grain direction were performed. Other parameters, such as density, moisture content and longitudinal modulus of elasticity in compression and in tension, were also obtained. The measurement of displacements was made with Digital Image Correlation (DIC). Findings The results of this study show the similarity between experimental and empirical values for the studied woods species. Originality/value This original study aimed at characterizing the mechanical properties using DIC of wood of the roof of the �sequeiro� of �Quinta Lobeira de Cima�, a building from the twentieth century located in Minho (Portugal). This study is part of master thesis of Jo�o Martins, an original research work.

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The cyclic shift graph of a monoid is the graph whose vertices are the elements of the monoid and whose edges connect elements that are cyclic shift related. The Patience Sorting algorithm admits two generalizations to words, from which two kinds of monoids arise, the $\belr$ monoid and the $\bell$ (also known as Bell) monoid. Like other monoids arising from combinatorial objects such as the plactic and the sylvester, the connected components of the cyclic shift graph of the $\belr$ monoid consists of elements that have the same number of each of its composing symbols. In this paper, with the aid of the computational tool SageMath, we study the diameter of the connected components from the cyclic shift graph of the $\belr$ monoid.

Within the theory of monoids, the cyclic shift relation, among other relations, generalizes the relation of conjugacy for groups. We examine several of these relations for both the $\belr$ and the $\bell$ monoids.

Kashiwara's crystal graphs have a natural monoid structure that arises by identifying words labelling vertices that appear in the same position of isomorphic components. The celebrated plactic monoid (the monoid of Young tableaux), arises in this way from the crystal graph for the q-analogue of the general linear Lie algebra gln, and the so-called Kashiwara operators interact beautifully with the combinatorics of Young tableaux and with the Robinson–Schensted–Knuth correspondence. The authors previously constructed an analogous ‘quasi-crystal’ structure for the related hypoplactic monoid (the monoid of quasi-ribbon tableaux), which has similarly neat combinatorial properties. This paper constructs an analogous ‘crystal-type’ structure for the sylvester and Baxter monoids (the monoids of binary search trees and pairs of twin binary search trees, respectively). Both monoids are shown to arise from this structure just as the plactic monoid does from the usual crystal graph. The interaction of the structure with the sylvester and Baxter versions of the Robinson–Schensted–Knuth correspondence is studied. The structure is then applied to prove results on the number of factorizations of elements of these monoids, and to prove that both monoids satisfy non-trivial identities.

Abstract This paper addresses the durability of bond between concrete and carbon fibre reinforced polymer (CFRP) strips installed according to the near-surface mounted (NSM) technique (NSM CFRP-concrete systems) under the effects of two main groups of environmental conditions: (i) laboratory-based ageing conditions; (ii) real outdoor ageing conditions. The bond degradation was evaluated by carrying out direct pullout tests on aged specimens that were previously subjected to distinct environmental conditions for different periods of exposure. Moreover, the degradation of the mechanical properties of the involved materials was investigated. The digital image correlation (DIC) method was used to document the evolution of the deformation fields at the surface over the whole region of interest consisting of concrete and epoxy adhesive at the ligament region. This information supported the discussion about the evolution of the bond resistant mechanism developed in \{NSM\} CFRP-concrete specimens during testing, as well as the assessment of the bond quality of the system. In general, the results obtained from the durability tests conducted have shown that the different exposure environments, which may be considered as quite severe, did not result in significant damage on \{NSM\} CFRP-concrete system. The maximum decrease of about 12% on bond strength was obtained for real outdoor environments. Conversely, a maximum increase of 8% on bond strength was obtained on the specimens exposed to the temperature cycles between -15��C and +60��C. \{DIC\} allowed to document the stress transfer mechanisms established between the \{CFRP\} and the concrete substrate, revealing the crack patterns and the influence widths of the \{CFRP\} reinforcement strips, which were shown to be important for avoiding group effect when using multiple parallel strengthening \{CFRP\} strips.

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This paper considers whether non-trivial identities are satisfied by certain ‘plactic-like’ monoids that, like the plactic monoid, are closely connected with combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic, and taiga monoids satisfy identities. The existing state of knowledge is discussed for the plactic and Bell monoids.

{We consider a velocity tracking problem for the Navier-Stokes equations in a 2D bounded domain. The control acts on the boundary through an injection-suction device, and the flow is allowed to slip against the surface wall. We study the well-posedness of the state equations, linearized state equations, and adjoint equations. In addition, we show the existence of an optimal solution and establish the first order optimality condition.}

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