On regularity of a quasiconformal mapping at a point of maximal stretching

Local behaviour of a K-quasiconformal mapping f at a point z₀of maximal stretching is studied. A sufficient condition forthe existence of the finite limit lim(f(z) – f(z₀))/(z– z₀)|z – z₀|^1/K–1 as z z₀, and a criterionfor z₀ to be a point of maximal stretching are given.     

On the degenerate Beltrami equation

We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient has the norm Sufficient conditions for the existence of a homeomorphic solution to the Beltrami equation on the Riemann sphere are given in terms of the directional dilatation coefficients of A uniqueness theorem is also proved when the singular set of is contained in a totally disconnected compact set with an additional thinness condition on

     

Solutions with singularities of a certain equation of mathematical physics

A theorem for the representation of solutions with singularities of logarithmic type of a certain equation of mathematial physics in terms of quasiconformal mappings is obtained.Doctor of Physicomathematical Sciences.Candidate of Physicomathematical Sciences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 174–178, February, 1992.     

Effect of an electric field on the energy spectrum and hydrodynamics of superfluid helium

A strong electric field leads to anisotropy of the spectrum of elementary excitations of superfluid helium and affects the hydrodynamics, reducing the superfluid flow perpendicular to the field.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Stekova, AN SSSR, Vol. 120, pp. 25–31, 1982.