A networking method to compare theories: metacognition in problem solving reformulated within the Anthropological Theory of the Didactic

An important role of theory in research is to provide new ways of conceptualizing practical questions, essentially by transforming them into scientific problems that can be more easily delimited, typified and approached. In mathematics education, theoretical developments around ‘metacognition’ initially appeared in the research domain of Problem Solving closely related to the practical question of how to learn (and teach) to solve non-routine problems. This paper presents a networking method to approach a notion as ‘metacognition’ within a different theoretical perspective, as the one provided by the Anthropological Theory of the Didactic. Instead of trying to directly ‘translate’ this notion from one perspective to another, the strategy used consists in going back to the practical question that is at the origin of ‘metacognition’ and show how the new perspective relates this initial question to a very different kind of phenomena. The analysis is supported by an empirical study focused on a teaching proposal in grade 10 concerning the problem of comparing mobile phone tariffs.     

The effect of organoclay and graphene on the crystallization of PP in ABS/PP blends

In the present research, the isothermal and non-isothermal crystallization of polypropylene (PP) phase in PP-rich poly(acrylonitrile–butadiene–styrene)/polypropylene (ABS/PP) blends was studied. The effect of nanofillers’ incorporation and specialty of organically modified montmorillonite (OMMT) and graphene, into the prepared blends on the isothermal and non-isothermal crystallization of PP phase, were investigated. Moreover, kinetic study of their isothermal crystallization process was carried out, by applying the Avrami equation. The addition of ABS to the PP matrix increased the crystallization rate of PP at 130 °C. The incorporation of OMMT in pure PP accelerated slightly the crystallization process, whereas in ABS/PP blends, it seemed to retard crystallization, due to interactions between ABS phase and organoclay. The incorporation of graphene in pure PP accelerated impressively its isothermal crystallization, while the addition of ABS in graphene/PP nanocomposite slowed down the crystallization rate of PP. The effect of ABS and nanofillers, separately or in combination, on the crystallization of PP phase was reflected on the kinetic parameters of the Avrami equation. Regarding the non-isothermal crystallization, ABS/PP blends presented higher crystallization temperature (T _c) compared to pure PP. The organoclay reinforcement did not have any obvious effect on this temperature, whereas graphene caused significant increase, acting as nucleating agent. The presence of ABS to PP increased the concentration of the β-crystalline phase, reaching its maximum value at 30 mass% ABS content. The organoclay decreased the β-PP in ABS/PP blends, whereas graphene eliminated it.     

Mass spectrometry detection as an innovative and advantageous tool in ligand exchange capillary electrophoresis

The copper(II) complex of a modified cyclodextrin, namely 6-mono-deoxy-6-[4-(2-aminoethyl)imidazolyl]-β-CD (CDmh), previously synthesized and characterized in our laboratory and already used as chiral selector for ligand exchange capillary electrophoresis (LECE) with optical detection, is investigated here in LECE using electrospray-mass spectrometry (ESI-MS) as the detection device. The potential of this hyphenated method is compared with the results previously obtained with optical detection by studying the chiral resolution of tryptophan racemate. Chiral separation conditions compatible with LECE-ESI-MS could be achieved based on the figures of merit obtained by LECE-UV. Interestingly, the values of LOD obtained by LECE-ESI-MS were significantly better than those obtained by LECE-UV and thus, ESI-MS detection seems to open new perspectives in chiral separations by LECE.     

Microwave-assisted aminocarbonylation of ynamides by using catalytic [Fe3(CO)12] at low pressures of carbon monoxide

The microwave-assisted aminocarbonylation of ynamides at low pressures of CO is reported. A new class of (E)-acrylamides that are potentially suitable for several applications has been regioselectively synthesized after microwave irradiation for only 20 min by using eco-friendly [Fe(3)(CO)(12)] as the catalyst precursor and triethylamine as the ligand. This transformation is atom economic as all reactants are used in stoichiometric quantities. Furthermore, the transformation is efficiently applied to the alkoxycarbonylation of alkynes as well. Moreover, running these reactions under microwave irradiation allows the simplification of the reaction conditions with remarkable reductions in time, temperature and gas pressure.     

First-return integrals

Properties of first-return integrals of real functions defined on the unit interval are explored. In particular, first-return integrals are shown to be continuous but not absolutely continuous.     

Preparation and photoactivity of nanostructured anatase, rutile and brookite TiO2 thin films

Photoactive films consisting of pure anatase, brookite or rutile TiO2 were prepared by dip coating from water dispersions obtained by using TiCl4 as the precursor under similar mild experimental conditions.     

A polynomial path-following interior point algorithm for general linear complementarity problems

Linear Complementarity Problems (LCPs) belong to the class of \mathbbNP{\mathbb{NP}} -complete problems. Therefore we cannot expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of the original problem or detects the lack of property P_*([(k)\tilde]){\mathcal{P}_*(\tilde\kappa)} , with arbitrary large, but apriori fixed [(k)\tilde]{\tilde\kappa}). In the latter case, the algorithms give a polynomial size certificate depending on parameter [(k)\tilde]{\tilde{\kappa}} , the initial interior point and the input size of the LCP). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following interior point algorithms.     

C–H⋅<Emphasis Type="Italic">s</Emphasis>O hydrogen bond networks in <Emphasis Type="Italic">E</Emphasis>- and Z-unsaturated esters of C-glycosides

Methyl E(Z)-4,7 anhydro-5-benzamido-6,8-di-O-benzoyl-2,3,5-trideoxy-d-allo-oct-2-enoate have been synthesized like intermediates and isolated as single crystals during the synthesis of pyrazole-related C nucleosides as synthetic product with cytotoxic activity.¹ Crystal structures of E(Z) isomers were determined by X-ray analysis. E isomer crystallizes in the triclinic crystal system, space group P1, a = 5.319(1) Å, b = 10.758(2) Å, c = 12.229(2) Å, α = 72.38(2)^∘, β = 89.97(2)^∘, γ = 87.07(2)^∘, D_x = 1.320 Mgm⁻³ and Z isomer in the orthorhombic crystal system, space group P2₁2₁2₁, a = 5.1297(13) Å, b = 19.667(5) Å, c = 25.871(6) Å, D_x = 1.348 Mgm⁻³. The molecular structure was solved by direct method on the basis of 2609 and 2727 unique reflections recorded at the temperature 293 K (E-isomer) and 173 K (Z-isomer) up to the final R-factor 0.0378 and 0.0435, respectively. C–H⋅sO contact networks were analyzed and the correlation established between the existence of the weak C–H⋅sO hydrogen bonds and the melting point of the single crystals.