Technology is recognized for its potential to implement exploration tasks. The ease and speed with which it becomes possible to observe many cases of a situation, allows the development of conjectures and brings conviction about their veracity. Mathematical proof, assumed as the essence of Mathematics, tends to appear to the students as something dispensable. Based on KTMT – Knowledge for Teaching Mathematics with Technology model, this study intends to understand the impact of the teachers’ knowledge on mathematical proof in a context of technology integration. The study adopts a qualitative and interpretative methodology, based on case study, analyzing the practice of one teacher. The conclusions emphasize the relevance of the teacher’s MTK – Mathematics and Technology Knowledge, and TLTK – Teaching and Learning and Technology Knowledge. The teacher's MTK guides her decisions, leading her to focus on helping students understand the meaning of conjecture and proof, valuing, at the same time, the relevance of algebraic manipulations. However, the teacher’s TLTK guides her practice, where the knowledge about the students is determinant. The study provides evidence about the difficulty of articulating proof and technology, but it also clarifies the relevance of this articulation and of how the teacher’s KTMT can impact the teacher’s decisions.

Thyroid diseases affect a considerable portion of the population, with hypothyroidism being one of the most commonly reported thyroid diseases. Levothyroxine (T4) is clinically used to treat hypothyroidism and suppress thyroid stimulating hormone secretion in other thyroid diseases. In this work, an attempt to improve T4 solubility is made through the synthesis of ionic liquids (ILs) based on this drug. In this context, [Na][T4] was combined with choline [Ch]+ and 1-(2-hydroxyethyl)-3-methylimidazolium [C2OHMiM]+ cations in order to prepare the desired T4-ILs. All compounds were characterized by NMR, ATR-FTIR, elemental analysis, and DSC, aiming to check their chemical structure, purities, and thermal properties. The serum, water, and PBS solubilities of the T4-ILs were compared to [Na][T4], as well as the permeability assays. It is important to note an improved adsorption capacity, in which no significant cytotoxicity was observed against L929 cells. [C2OHMiM][T4] seems to be a good alternative to the commercial levothyroxine sodium salt with promising bioavailability.

The algebraic variety defined by the idempotents of an incidence monoid is investigated. Its irreducible components are determined. The intersection with an antichain submonoid is shown to be the union of these irreducible components. The antichain monoids of bipartite posets are shown to be orthodox semigroups. The Green’s relations are explicitly determined, and applications to conjugacy problems are described. In particular, it is shown that two elements in the antichain monoid are primarily conjugate in the monoid if and only if they belong to the same -class and their multiplication by an idempotent of the same -class gives conjugate elements in the group.

In this paper, the influence of salt fog and ambient condition exposure on CFRP-to-steel bonded joints (CSJs) with a near end mechanical anchorage was studied. The tests of the CSJs were carried out with a monotonic loading history respectively with and without a near end mechanical anchorage both unaged and after being exposed to the ageing conditions. The results revealed failures in the adhesive for some CSJs with a near end mechanical anchorage, among which also exhibited the best bond performance both in aged and unaged specimens. Due to the high state of degradation after ageing exposure, local damage of the CFRP located at the gap position of the CSJs was induced by a torsion action during the fixation of the specimen in the tensile machine even prior to the testing, which caused, although locally, severe delamination of the CFRP of the aged CSJs. From the torsion test results, a decrease in the torsional capacity of the CFRP after aging revealed the degradation of the carbon fiber-to-matrix interface. Additional results reflected that a drop in the initial stiffness of the load vs. slip relationship can be observed, caused by a pre-crack with a length of 30 mm in the CSJs. © 2021 Elsevier Ltd

In different industries, the bonding technique has gained several advances in recent years. However, due to the specificity of each industry, the bonded joints may present different configurations. For instance, in the case of metallic truss bridges, the use of Carbon Fibre Reinforced Polymers (CFRP) bonded on the steel surface members may require circular or even tubular transitions between these materials. Although the bonded transitions between a metal and a composite material have been deeply studied with flat surfaces the information on circular or tubular hybrid bonded joints is still scarce. Therefore, the present study aims to mitigate some of this lack of knowledge by proposing an analytical solution able to describe the interfacial debonding process between a circular or tubular bonded transition between two materials. The proposed model also aims to simulate the interfacial debonding of double butt (or stepped) lap joints. Under these circumstances, a bilinear local adhesive model is adopted which required the quantification of the elastic and the softened stiffnesses as well as the pure Mode II fracture energy. The Finite Element Method (FEM) is used for the validation of the proposed model. The behaviour of the adhesive joint between materials is numerically modelled through the Cohesive Zone Modelling (CZM) in which the same bilinear shape used in the analytical solutions is adopted. Different situations were analyzed thoroughly and the numerical simulations tracked very closely the analytical results obtained from the proposed closed-form solutions. © 2021 Elsevier Ltd