The goal of this article is to obtain observability estimates for non-homogeneous elliptic equations in the presence a potential, posed on smooth bounded domain Ω R2 and observed from non-empty open subset ω⊂Ω. More precisely, V∈L∞(Ω;R), our main result shows that, when Ω⊂R2 has finite number holes, constant operator −Δ+V, with H2(Ω)∩H01(Ω), form C exp (C‖V‖L∞(Ω)1/2 log 1/2(‖V‖L∞(Ω))) where pos...

Using density functional perturbation theory, we computed the phonon frequencies and Raman IR activities of hafnia polymorphs (P42nmc, Pca21, Pmn21, Pbca OI, brookite, baddeleyite) for phase identification. We investigated evolution with respect to epitaxial strain provide plots frequency differences as a function experimental calibration identification state sample. found signatures different ...

The results of calculating the dielectric and optical characteristics solid polymorphic phases water ices I h , II lattices hydrates sI, sH are presented. Static tensors ε ik complex frequency-dependent (ω) calculated for these materials. It is shown that, in terms properties, crystal uniaxial, tensor components xx yy coincide them, hydrate lattice sI isotropic. Based on functions ε' ε'' (ω), i...