The new series of publications "Mathematics and mathematical

modelling" will present the state of the art in various fields of applied

mathematics with a strong emphasis on mathematical modelling,

numerical simulations, understanding of natural phenomena. It can be

used by scientists working in the corresponding areas of research,

by graduate and undergraduate students.

The second publication of this series concerns the index of elliptic

operators in unbounded domains. A new method to compute the index is

developed. It is based on approximation of elliptic operators in unbounded

domains by the operators in bounded domains. These results have

numerous applications to various models arising in natural sciences.