Large-radius excitons in polar crystals are considered. It is shown that translation invariant description of interacting with a phonon field leads to nonzero contribution phonons into the exciton ground state energy only case weak or intermediate electron-phonon coupling. A conclusion made self-trapped cannot exist limit strong Peculiarities absorption and emission spectra discussed. Condition...

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn is presented. In particular new examples of Sp(n)Sp(1)-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers [5] and [6].

A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn is presented. In particular new examples of Sp(n)Sp(1)-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers [5] and [6].

We obtain C regularity estimates for nonlocal elliptic equations that are not necessarily translation invariant using compactness and perturbative methods and our previous regularity results for the translation invariant case.

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced maximal invariant measure study its properties. Further, how measures depend on parameters system. These results were illustrated by a simple example or risk management model where appear naturally.