Korovkin type approximation theorem via Ka−convergence on weighted spaces

In this paper, we study the Korovkin type approximation theorem for K_a‐ convergence, which is an interesting convergence method on weighted spaces. We also study the rate of K_a?convergence by using the weighted modulus of continuity and afterwards, we present a nontrivial application.     

Implementation of the nonlinear imperfect transmission conditions between dissimilar materials into commercial FEM software MSC.Marc using Fortran user subroutine: Plane strain case

Thin soft elasto-plastic interphase adhesively bonded materials are replaced by nonlinear imperfect transmission conditions in commercial FEM software MSC.Marc using Fortran user subroutine. The idea of replacement is based upon iteratively finding artificial stiffness of springs which maps elasto-plastic behaviour of interphase. Plane strain case is considered.     

Correlation between the intensities of intermultiplet electric dipole transitions and the fine features of the stark structure of multiplets of Pr3+ ions in the LaCl3 compound

The Stark structure of the multiplets of Pr³⁺ ions in the LaCl₃ compound is described and the even and odd parameters of the crystal field, as well as the covalency parameters, are determined in the approximation of an intermediate interconfiguration interaction. The covalency parameters thus obtained agree well with the parameters calculated in the framework of microscopic models. The intensity parameters of intermultiplet electric dipole transitions are calculated using the odd parameters of the crystal field and the covalency parameters. The results of the calculations are in satisfactory agreement with the experimental data. This allows the conclusion that there is a correlation between the fine features of the Stark structure of the multiplets and the intensities of the intermultiplet electric dipole transitions.     

Charging effects in biased molecular devices

The influence of charging effects on the transport characteristics of a molecular wire bridging two metallic electrodes in the limit of weak contacts is studied by the generalized Breit–Wigner formula. Molecule is modeled as a quantum dot with discrete energy levels, while the coupling to the electrodes is treated within a broad-band theory. Owing to this model we find self-consistent occupation of particular energy levels and orbital energies of the wire in the presence of transport. The nonlinear conductance and current–voltage characteristics are investigated as a function of bias voltage in the case of symmetric and asymmetric coupling to the electrodes. It is shown that the shape of those curves are determined by the combined effect of the electronic structure of the molecule and by electron–electron repulsion.     

Synthesis of a novel constrained α-amino acid with quinoxaline side chain: 7-amino-6,7-dihydro-8H-cyclopenta[g]quinoxaline-7-carboxylic acid

A novel constrained 7-amino-6,7-dihydro-8H-cyclopenta[g]quinoxaline-7-carboxylic acid derivative was prepared starting from 4,5-dimethyl-o-phenylenediamine.