TheR-function method in boundary-value problems with geometric and physical symmetry

This paper is devoted to developing constructive methods of the theory of R-functions. It gives the first discussion of methods of constructing the equations of loci with symmetry of translation type for duplicated domains not separated by lines and with point symmetry of cyclic type for regions both possessing and lacking axial symmetry. The possible applications are illustrated by numerous examples carried out using the POLE system, including solutions of boundary-value problems involving the influence of cyclically located circular and star-shaped insulators on an electric field.