Non-linear approximations for natural convection in a horizontal annulus

Two different problems are proposed as approximations of the usual system modelling natural convection under the Oberbeck-Boussinesq assumptions. The error is evaluated by means of the norm of its gradient in the Hilbert space. The average Nusselt number is also estimated.     

Bounded Engel elements in groups satisfying an identity

We prove that a residually finite group G satisfying an identity \(w\equiv 1\) and generated by a commutator closed set X of bounded left Engel elements is locally nilpotent. We also extend such a result to locally graded groups, provided that X is a normal set. As an immediate consequence, we obtain that a locally graded group satisfying an identity, all of whose elements are bounded left Engel, is locally nilpotent.     

The acoustical characterization of orchestra platforms and uncertainty estimation of the results

Measurements have been carried out on furnished orchestra platforms in four concert halls in Italy in order to describe the sound field perceived by musicians. The heterogeneous nature of the orchestra suggested a procedure able to take into account the mutual hearing between instrumental sections. The measured parameters were the early, late and total support, the reverberation time, the early decay time and the clarity index. A part of the study has been devoted to the measurement uncertainty estimation. The source directivity and the small displacements of the microphone influence the early decay time to a great extent while the on-platform spatial variability affects both the early decay time and the clarity index. Per-section early support shows differences that render the overall spatial mean inappropriate to describe the stage as a whole. For the other parameters an overall mean platform value can instead be suitable, even though, for the case of clarity a more evident group variability is observed. The values of late support, reverberation time, early decay time and clarity index, proposed in literature as suitable measures of reverberance for musicians, are not all intercorrelated, indicating that not all these parameters can be associated to the same subjective impression.     

EEG topography-specific BOLD changes: a continuous EEG-fMRI study in a patient with focal epilepsy

Blood oxygenation level dependent (BOLD) response related to interictal activity was evaluated in a patient with post-traumatic focal epilepsy at repeated continuous electroencephalogram (EEG)-functional magnetic resonance imaging examinations. Lateralized interictal EEG activity induced a main cluster of activation co-localized with the anatomical lesion. Spreading of EEG interictal activity to both frontal lobes evoked bilateral clusters of activation indicating that topography of BOLD response might depend on the spatial distribution of epileptiform activity.     

Quantum chemical studies of dioxygen activation by mononuclear non-heme iron enzymes with the 2-His-1-carboxylate facial triad

Density functional theory with the B3LYP hybrid functional has been used to study the mechanisms for dioxygen activation by four families of mononuclear non-heme iron enzymes: alpha-ketoacid-dependent dioxygenases, tetrahydrobiopterin-dependent hydroxylases, extradiol dioxygenases, and Rieske dioxygenases. These enzymes have a common active site with a ferrous ion coordinated to two histidines and one carboxylate group (aspartate or glutamate). In contrast to the heme case, this type of weak field environment always leads to a high-spin ground state. With the exception of the Rieske dioxygenases, which have an electron source outside the active site, the dioxygen activation process passes through the formation of a bridging-peroxide species, which then undergoes O-O bond cleavage finally leading to the four electron reduction of O(2). In the case of tetrahydrobiopterin- and alpha-ketoacid-dependent enzymes, the O-O heterolysis yields a high-valent iron-oxo species, which is capable of performing a two-electron oxidation chemistry on various organic substrates. For the other two families of enzymes (extradiol dioxygenases and Rieske dioxygenases) the substrate oxidation and the O-O bond cleavage are found to be coupled. In the extradiol dioxygenases the product of the O-O bond cleavage is a ferric iron with an oxy-substrate with a mixture of radical and anionic character, which is essential for the selectivity of the catechol cleavage.