Absorption spectra of two orthogonal linearly polarized X-rays in a single CeCoGe3 crystal were measured at the ID12 beamline ESRF for energies near K-edges Ge, Co and L23 edges Ce. The X-ray natural linear dichroism (XNLD) was revealed vicinity all absorption edges, which indicates splitting electronic states crystalline field. Mathematical modelling comparison with experimental data allowed i...

In this note, we compute the fundamental solution for the Hermite operator with singularity at arbitrary point y ∈ R. We also apply this result to obtain the fundamental solution for the sub-Laplacian Lα = − ∑n j=1(X 2 j +X 2 j+n)− iαT on the Heisenberg group. In this note, we first derive the fundamental solution of the Hermite operator n ∑ j=1 ( λjx 2 j − ∂2 ∂xj ) in Rn, i.e., we are looking ...

From a monotonicity property, we derive several results characterizing positive harmonic functions in the unit ball in R and positive measures on the unit sphere Sn−1. Let Bn = {x ∈ Rn : |x| < 1}, n ≥ 2 be the unit ball in Rn and Sn−1 = ∂Bn be the unit sphere. From a monotonicity property, we derive several results characterizing positive harmonic functions in Bn and positive measures on Sn−1. ...

1.1. Let C/S be a smooth proper curve of genus g over a scheme S, and let P be a finite set of prime numbers which includes all residue characteristics of S. For any section s : S → C we then obtain, as in [DM, 5.5], a pro-object π1(X/S, s) in the category of locally constant sheaves of finite groups on S whose fiber over a geometric t̄ → S is equal to the maximal prime to P quotient of π1(Ct̄, s...