A Generalization of a Levitin and Parnovski Universal Inequality for Eigenvalues

In this paper, we derive “universal” inequalities for the sums of eigenvalues of the Hodge de Rham Laplacian on Euclidean closed submanifolds and of eigenvalues of the Kohn Laplacian on the Heisenberg group. These inequalities generalize the Levitin–Parnovski inequality obtained for the sums of eigenvalues of the Dirichlet Laplacian of a bounded Euclidean domain.     

Refractive,dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared

We report on experimental measurements of the refractive index of twelve organic solvents at five different wavelengths (450, 532, 632.8, 964 and 1,551 nm) and a temperature of 300 K. Based on these new data visible to near-infrared dispersion relations are constructed. Group-velocity dispersion (GVD) is theoretically calculated. Zero- and negative-GVD situations are identified for two common solvents in near-infrared wavelengths. Via comparison with refractive index data available in bibliography, estimated values of thermo-optic coefficients are also presented.     

Electron–Phonon Superconductivity in Boron-Based Chalcogenide (X= S,Se) Monolayers

Electron–phonon mediated superconductivity is deeply investigated in two boron based monolayer materials, namely, $B_{3}S$, a metal exhibiting the ability to superconduct, and a new metal, $B_{3}Se$, presenting perfect kinetic stability. Calculations based on density functional perturbation theory combined with the maximally localized Wannier function also reveal that both materials exhibit anisotropic planar hexagonal structure like graphene. The key parameters involved in the superconductor behavior are all calculated. The electronic density in the Fermi surface is given to provide the environment for enhanced electron–phonon coupling. The longitudinal and transverse vibration modes of optical phonons mainly contribute to the electron–phonon coupling strength. Furthermore, the binding energy between the bosonic Cooper pair superfluid is quantified and determined. The critical temperature for the two materials is 20 and 10.5 K, respectively. The results obtained show the potential use of such materials for superconducting applications.