Knowledge for Teaching Mathematics with Technology (KTMT) is a theoretical model that seeks to articulate previously existing models on professional knowledge and the conclusions that the investigation around the integration of technology has achieved. KTMT is a dynamic knowledge, informed by the practice, that develops from the knowledge on the base domains (Mathematics, Teaching and Learning, Technology and Curriculum), evolving as knowledge in the base domains interacts and as this promotes the development of inter-domain knowledge, which continue to interact, strengthening relations and leading to the development of an integrated knowledge, where knowledge on the base domains and on the two sets of inter-domains appears deeply integrated into a global knowledge.

Acetylcholinesterase (AChE) inhibition is one of the most currently available therapies for the management of Alzheimer’s disease (AD) symptoms. In this context, NMR spectroscopy binding studies were accomplished to explain the inhibition of AChE activity by Salvia sclareoides extracts. HPLC-MS analyses of the acetone, butanol and water extracts eluted with methanol and acidified water showed that rosmarinic acid is present in all the studied samples and is a major constituent of butanol and water extracts. Moreover, luteolin 4′-O-glucoside, luteolin 3′,7-di-O-glucoside and luteolin 7-O-(6′′-O-acetylglucoside) were identified by MS2 and MS3 data acquired during the LC-MSn runs. Quantification of rosmarinic acid by HPLC with diode-array detection (DAD) showed that the butanol extract is the richest one in this component (134 μg mg−1 extract). Saturation transfer difference (STD) NMR spectroscopy binding experiments of S. sclareoides crude extracts in the presence of AChE in buffer solution determined rosmarinic acid as the only explicit binder for AChE. Furthermore, the binding epitope and the AChE-bound conformation of rosmarinic acid were further elucidated by STD and transferred NOE effect (trNOESY) experiments. As a control, NMR spectroscopy binding experiments were also carried out with pure rosmarinic acid, thus confirming the specific interaction and inhibition of this compound against AChE. The binding site of AChE for rosmarinic acid was also investigated by STD-based competition binding experiments using Donepezil, a drug currently used to treat AD, as a reference. These competition experiments demonstrated that rosmarinic acid does not compete with Donepezil for the same binding site. A 3D model of the molecular complex has been proposed. Therefore, the combination of the NMR spectroscopy based data with molecular modelling has permitted us to detect a new binding site in AChE, which could be used for future drug development.

This research has been motivated by a real-life problem of a waste cooking oil collection system characterized by the existence of multiple depots with an outsourced vehicle fleet, where the collection routes have to be plan. The routing problem addressed allows open routes between depots, i.e., all routes start at one depot but can end at the same or at a different one, depending on what minimizes the objective function considered. Such problem is referred as a Multi-Depot Vehicle Routing Problem with Mixed Closed and Open Inter-Depot Routes and is, in this paper, modeled through a Mixed Integer Linear Programming (MILP) formulation where capacity and duration constraints are taken into account. The model developed is applied to the real case study providing, as final results, the vehicle routes planning where a decrease of 13% on mileage and 11% on fleet hiring cost are achieved, when comparing with the current company solution.

Let \(\mathcal{M}(\mathbb{R}^n)\) be the class of bounded away from one and infinity functions \(p:\mathbb{R}^n\to[1,\infty]\) such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R}^n)\). We show that if \(a\) belongs to the Hörmander class \(S_{\rho,\delta}^{n(\rho-1)}\) with \(0<\rho\le 1\), \(0\le\delta<1\), then the pseudodifferential operator \(\operatorname{Op}(a)\) is bounded on the variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R}^n)\) provided that \(p\in\mathcal{M}(\mathbb{R}^n)\). Let \(\mathcal{M}^*(\mathbb{R}^n)\) be the class of variable exponents \(p\in\mathcal{M}(\mathbb{R}^n)\) represented as \(1/p(x)=\theta/p_0+(1-\theta)/p_1(x)\) where \(p_0\in(1,\infty)\), \(\theta\in(0,1)\), and \(p_1\in\mathcal{M}(\mathbb{R}^n)\). We prove that if \(a\in S_{1,0}^0\) slowly oscillates at infinity in the first variable, then the condition \[ \lim_{R\to\infty}\inf_{|x|+|\xi|\ge R}|a(x,\xi)|>0 \] is sufficient for the Fredholmness of \(\operatorname{Op}(a)\) on \(L^{p(\cdot)}(\mathbb{R}^n)\) whenever \(p\in\mathcal{M}^*(\mathbb{R}^n)\). Both theorems generalize pioneering results by Rabinovich and Samko [RS08] obtained for globally log-Hölder continuous exponents \(p\), constituting a proper subset of \(\mathcal{M}^*(\mathbb{R}^n)\).

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The use of agar-based biomaterials for the development of emerging areas, such as tissue engineering or ‘smart materials’ production has recently gained great interest. Understanding how these gel-forming polysaccharides self-organise in aqueous media and how these associations can be tuned to meet the specific needs of each application is thus of great relevance. As an extension of previous pioneering research concerning the application of the microwave-assisted extraction (MAE) technique in the recovery of native (NA) and alkali-modified (AA) agars, this article focuses on the different molecular assemblies assumed by these novel NA and AA when using different MAE routes. The molecular architectures in dilute (5, 10, 50 and 100 mg mL
1) and concentrated (1.5% (w/w)) aqueous media were imaged by AFM and cryoSEM, respectively. Relevant structural and physicochemical properties were investigated to support the microscopic data. Different extraction routes led to polysaccharides with unique properties, which in turn resulted in different molecular assemblies. Even at 5 mg mL
1, AFM images included individual fibers, cyclic segments, aggregates and local networks. At higher polymer concentrations, the structures further aggregated forming multilayer polymeric networks for AA. The more compact and denser 3D networks of AA, imaged by cryoSEM, and their higher resistance to large deformations matched the 2D-shapes observed by AFM. Depending on the nature of the AA chains, homogeneous or heterogeneous growth of assemblies was seen during network formation. The obtained results support well the view of double helix formation followed by intensive double helix association proposed for agar gelation.

Non-catalytic cellulosomal carbohydrate-binding modules (CBMs) are responsible for increasing the catalytic efficiency of cellulosic enzymes by selectively putting the substrate (a wide range of poly- and oligosaccharides) and enzyme into close contact. In the present work we carried out an atomistic rationalization of the molecular determinants of ligand specificity of a family 11 CBM from thermophilic C. thermocellum (CtCBM11), based on a NMR and molecular modeling approach. We have determined the NMR solution structure of CtCBM11 at 25 and 50 ºC and derived information on the residues of the protein involved in ligand recognition and on the influence of the length of the saccharide chain on binding. We obtained models of the CtCBM11/cellohexaose and CtCBM11/cellotetraose complexes by docking in accordance with the NMR experimental data. Specific ligand/protein CH-π and Van der Waals interactions were found to be determinant for the stability of the complexes and for defining specificity. Using the order parameters derived from backbone dynamics analysis in the presence and absence of ligand and at 25 and 50 ºC, we determined that the protein’s backbone conformational entropy is slightly positive. This data in combination with the negative binding entropy calculated from ITC studies supports a selection mechanism where a rigid protein selects a defined oligosaccharide conformation.

A novel porous polymer-ionic liquid composite with poly(2-hydroxyethyl methacrylate) (PHEMA) and 1-butyl-3-methylimidazolium hexafluorophosphate (BMIPF6) has been synthesized by γ-irradiation without heat or chemical initiators. The products can be reversibly converted into organogels. The composites are potential candidates for electrochemical applications. The use of γ-radiation can be a simple and versatile alternative way to obtain these materials.

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