Çàñåäàíèå 370 (10 ìàðòà 2017 ã.)

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Áðþõîâ Ä. À.
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Mappings Associated with Classical Conformal of the
Second Kind in R ^{3} and Problems of Stationary
Meridional Velocity Fields in Inhomogeneous Media
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In 1992 Leutwiler in modified quaternionic analysis in R^{3} characterized each
C^{2}-function of the reduced quaternionic variable u= u_{0}+iu_{1}+ju_{2}=u_{0}(x_{0};x_{1};x_{2})
+iu_{1}(x_{0};x_{1};x_{2}) +ju_{2}(x_{0};x_{1};x_{2}) on open sets from R^{3}={(x_{0};x_{1};x_{2})}, satisfying
the special condition x_{1}u_{2}=x_{2}u_{1} in the framework of Fueter’s 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 R^{3}. Properties of some quadratic and cubic gradient dynamical
systems with variable dissipation in R^{3} were studied.

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But now geometric properties of singular sets of generalizations of conformal
mappings of the second kind in modified quaternionic analysis in R^{3} are insufficiently studied. Important hypothesis about the Jacobian matrix of generalizations
of conformal mappings of the second kind in R^{3} in the framework of Fueter’s 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 Fueter’s 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 R^{3}. In particular, problems of meridional velocity fields
corresponding to the generalized Joukowski transformation of order n in R^{3} are
studied.