Abstract

Scwartz-Christoffel Integrals Reducibility to Close-to-Convex

G.Bilchenko (Department of Special Mathematics, Kazan State Technical University, Kazan, Russia)

e-mail: Grigory.Bilchenko@ksu.ru

The problem of study of unit disk images classes under Schwartz-Christoffel mappings with fixed (on unit circle) chain of corner points preimages changes sufficiently if the integrand factors exponents are subjected to permutations. The problem of search of the permutations that the corresponding mapping becomes nonstrict close-to-convex appears. The search of set of permutations reducing the integral to nonstrict close-to-convex one consists of three stages: 1) linear programming problems series solution; 2) finding in complete graph the Hamiltonian circuit passing through distinguished sets of sub-paths; 3) recognition in the group of permutations a residue class corresponding to the Hamiltonian circuits set. All the stages are computer-aided because of large volume of necessary computations. The conditions guaranteed the existence or absence of reducing permutation are obtained for exponents set. The relation of exponents set with subgroup of permutations preserving close-to-convexity is investigated for close-to-convex integrals.

Section : 12