A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers’ competence regarding the didactic strategy used and its results, as well as the students’ learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.     

Diagonal multilinear operators on Köthe sequence spaces

We analyse the interplay between maximal/minimal/adjoint ideals of multilinear operators (between sequence spaces) and their associated Köthe sequence spaces. We establish relationships with spaces of multipliers and apply these results to describe diagonal multilinear operators from Lorentz sequence spaces. We also define and study some properties of the ideal of (E, p)-summing multilinear mappings, a natural extension of the linear ideal of absolutely (E, p)-summing operators.     

Theoretical approach to the out-of-plane deformation of 1,3-disubstituted azulenes

Computational calculations at B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) levels were employed to analyze the structure and conformation of 1,3-bis(4-bromophenyl)azulene (1), 1,3-bis(2-thienyl)azulene (2), and 1,3-bis(2-pyrrollyl)azulene (3) in order to rationalize the out-of-plane deformation found in the azulene cores of 1 and 2 in the crystalline state, whereas compound 3 shows a totally planar azulene moiety. Our results indicate that 1,3-disubstituted azulenes possess two almost equally stable and easily convertible minimum energy conformers, which differ in the relative orientation of the substituent groups and in the planarity degree of the azulene core. An absolute planarity index (P) is introduced to quantify the out-of-plane distortion found in the azulenes under study. The aromaticity of minimum energy conformers was evaluated by means of geometric (HOMA), magnetic (NICS), and energetic (the frequency of the lowest out-of-plane vibration, ν_min) aromaticity indicators, which suggest that compound 3 possesses the most aromatic azulene core within the group. Calculated molecular dipole moments suggest that the conformation of 1,3-disubstituted azulenes in the crystalline state can be explained in terms of electrostatic intermolecular interactions rather than relative stability of planar and non-planar conformers.     

Driven reconnection about a magnetic X-line with strong guide component

A two-dimensional, two-fluid model is used to investigate driven magnetic reconnection in collisionless or semicollisional plasmas. The reconnection is driven by externally induced plasma flows in a background magnetic configuration that has a hyperbolic null component in the reconnection plane and a strong component, the so-called guide component, perpendicular to that plane. A dynamic solution is obtained in which the reconnection proceeds in two phases: an initial one whose characteristic rate is a fraction of the Alfvén frequency, and a later one whose rate is determined by the electron collision frequency.     

C-C bond-forming reactions of Ir(III)-alkenyls and nitriles or aldehydes: generation of reactive hydride- and alkyl-alkylidene compounds and observation of a reversible 1, 2-H shift in stable hydride-Ir(III) alkylidene complexes

Nucleophilic attack of the beta-carbon of an Ir(III)-alkenyl functionality onto the alpha-carbon of a coordinated nitrile- or aldehyde occurs intramoleculary to yield initially iridacyclic structures. Nitriles give rise to isolable complexes that contain delocalized five-membered rings (iridapyrroles, e.g. 3'-8') in a reaction catalyzed by H2O (for some of these syntheses, Ir(III)-eta 3-allyl derivatives may be used as the source of the Ir(III)-alkenyl moiety). In contrast, the alkenyl-to-aldehyde C-C coupling gives transient iridacycles that evolve by a fast alkyl-to-alkylidene migration and beta-H elimination. The end products (13* and 14*) contain an elaborated chelating alkoxide-olefin ligand. Addition of [H(OEt2)2][BAr'4] to the iridapyrroles effects stereospecific protonation of the beta-ring carbon. Those iridapyrroles which contain an additional metal-alkyl functionality (e.g. 3a*, alkyl = C2H5) afford highly reactive cationic alkyl-alkylidene intermediates that evolve instantaneously by migratory insertion/beta-H elimination. The end products also contain an elaborated, chelating ligand, although this time with an olefin and imine terminus compared with the previous ligand. Contrary to this result, protonation of the hydride-iridapyrrole complex 8a* in weakly coordinating solvents permits isolation of two unusual cationic cis-hydride-alkylidene compounds 11*, which undergo reversible 1,2-H shifts.     

On the capriciousness of the FCCF Karplus curve

Numerous well-behaved Karplus curves correlating dihedral angle (phi) and NMR coupling constants (3JXY) exist for X-C-Z-Y fragments with X or Y = H, C, F, and P. Absent is the enigmatic F-C-C-F moiety. By calculating the four Ramsey contributions to 3JFF for F-CH2-CH2-F, a pleasing phi/3JFF curve with both positive and negative regions arises. Unlike the H-C-C-H curve, F-C-C-F is PSO vs FC dominated. The latter and the F lone electron pairs cause both the negative J values and the substituent-induced J-leveling effect.     

A practical, one-pot synthesis of highly substituted thiophenes and benzo[b]thiophenes from bromoenynes and o-alkynylbromobenzenes

An efficient synthesis of thiophenes and benzo[b]thiophenes has been developed from easily available bromoenynes and o-alkynylbromobenzene derivatives. This novel one-pot procedure involves a Pd-catalyzed C-S bond formation using a hydrogen sulfide surrogate followed by a heterocyclization reaction. Moreover, in situ functionalization with selected electrophiles further expands the potential of this methodology to the preparation of the corresponding highly substituted sulfur heterocycles.     

Ultrafast irreversible phototautomerization of o-nitrobenzaldehyde

o-Nitrobenzaldehyde is photolabile because of an irreversible phototautomerization, whereas comparable aromatic compounds function as photoprotectors because the tautomerization is reversible. In this experimental and theoretical study we track down the cause of this difference to the electronic changes that occur during the tautomerization.