Formation of Superoxo Species by Interaction of O2 with Na Atoms Deposited on MgO Powders: A Combined Continuous‐Wave EPR (CW‐EPR), Hyperfine Sublevel Correlation (HYSCORE) and DFT Study

The formation of O₂^? radical anions by contact of O₂ molecules with a Na pre‐covered MgO surface is studied by a combined EPR and quantum chemical approach. Na atoms deposited on polycrystalline MgO samples are brought into contact with O₂. The typical EPR signal of isolated Na atoms disappears when the reaction with O₂ takes place and new paramagnetic species are observed, which are attributed to different surface‐stabilised O₂^? radicals. Hyperfine sublevel correlation (HYSCORE) spectroscopy allows the superhyperfine interaction tensor of O₂^?Na⁺ species to be determined, demonstrating the direct coordination of the O₂^? adsorbate to surface Na⁺ cations. DFT calculations enable the structural details of the formed species to be determined. Matrix‐isolated alkali superoxides are used as a standard to enable comparison of the formed species, revealing important and unexpected contributions of the MgO matrix in determining the electronic structure of the surface‐stabilised Na⁺? O₂^? complexes.     

A discrete Perron-Ta Li type theorem for the dichotomy of evolution operators

Following the Perron-Ta Li line of results, we give a characterization of the uniform exponential dichotomy property for the abstract continuous-time evolution families using a discrete-time approach.     

Finite filtrations of modules and shellable multicomplexes

We introduce pretty clean modules, extending the notion of clean modules by Dress, and show that pretty clean modules are sequentially Cohen–Macaulay. We also extend a theorem of Dress on shellable simplicial complexes to multicomplexes.     

Bessel sequences of exponentials on fractal measures

Jorgensen and Pedersen have proven that a certain fractal measure ν has no infinite set of complex exponentials which form an orthonormal set in L²(ν). We prove that any fractal measure μ obtained from an affine iterated function system possesses a sequence of complex exponentials which forms a Riesz basic sequence, or more generally a Bessel sequence, in L²(μ) such that the frequencies have positive Beurling dimension.     

X‐ray absorption study of the local structure at the NiO/oxide interfaces

This work reports an X‐ray absorption near‐edge structure (XANES) spectroscopy study at the Ni K‐edge in the early stages of growth of NiO on non‐ordered SiO₂, Al₂O₃ and MgO thin films substrates. Two different coverages of NiO on the substrates have been studied. The analysis of the XANES region shows that for high coverages (80 Eq‐ML) the spectra are similar to that of bulk NiO, being identical for all substrates. In contrast, for low coverages (1 Eq‐ML) the spectra differ from that of large coverages indicating that the local order around Ni is limited to the first two coordination shells. In addition, the results also suggest the formation of cross‐linking bonds Ni—O—M (M = Si, Al, Mg) at the interface.     

Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes

The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.     

Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions

Necessary and sufficient optimality conditions are obtained for a nonlinear fractional multiple objective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and duality results are proved using concepts of generalized semilocally preinvex functions.     

Mixed integer programming for a special logic constrained optimal control problem

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L² norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.