arXiv subjects

I. R. Kayumov

Publications and source records attributed to I. R. Kayumov.

3 recordsLinked to original sources

arXiv2021

Estimates for integrals of derivatives of rational functions in multiply connected domains in the plane

We obtain estimates for integrals of derivatives of rational functions in multiply connected domains in the plane. A sharp order of the growth is found for the integral of the modulus of the derivative of a finite Blaschke product in the unit disk. We also extend the results of E.P. Dolzhenko about the integrals of the derivatives of rational functions to a wider class of domains, namely, to domains bounded by rectifiable curves without zero interior angles, and show the sharpness of the obtained results.

math.CV↗

arXiv2019

On the sum of squares of the coefficients of Bloch functions

In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved

math.CV↗

arXiv2013

Exact analytical solution for one nonlinear variational problem of the cavitation theory

In this paper we investigate the limiting values of the lift and drag coefficients of profiles in the Helmholtz--Kirchhoff (infinite cavity) flow. The coefficients are based on the wetted arc length of profile surfaces. Namely, for a given value of the lift coefficient we find minimum and maximum values of the drag coefficient. Thereby, we determine maximum and minimum values of the lift-to-drag ratios.

math.CA↗