370 (10 2017 .)

. . Mappings Associated with Classical Conformal of the Second Kind in R3 and Problems of Stationary Meridional Velocity Fields in Inhomogeneous Media

In 1992 Leutwiler in modified quaternionic analysis in R3 characterized each C2-function of the reduced quaternionic variable u= u0+iu1+ju2=u0(x0;x1;x2) +iu1(x0;x1;x2) +ju2(x0;x1;x2) on open sets from R3={(x0;x1;x2)}, satisfying the special condition x1u2=x2u1 in the framework of Fueters construction, as a function associated with classical holomorphic. Later during ICNAAM in 2011-2014 the author presented some spatial properties of corresponding generalizations of conformal mappings of the second kind. Also the author described the first applications in continuum mechanics in the framework of stationary meridional velocity fields in axially symmetric inhomogeneous medium with specific density. In 2013-2014 the velocity fields was characterized as gradient dynamical systems in R3. Properties of some quadratic and cubic gradient dynamical systems with variable dissipation in R3 were studied.

But now geometric properties of singular sets of generalizations of conformal mappings of the second kind in modified quaternionic analysis in R3 are insufficiently studied. Important hypothesis about the Jacobian matrix of generalizations of conformal mappings of the second kind in R3 in the framework of Fueters construction, published by the author in 2014, was proved jointly with Kahler. Using approach of Jentili and Struppa, in 2016 Bryukhov and Kahler presented a class of slice-monogenic functions of the special type corresponding to Fueters construc- tion. It becomes realistic to describe more general spatial properties of stationary meridional velocity fields in axially symmetric inhomogeneous medium with specific density in the form of mappings associated with classical conformal of the second kind in R3. In particular, problems of meridional velocity fields corresponding to the generalized Joukowski transformation of order n in R3 are studied.