arXiv subjects

Pyotr N. Ivanshin

Publications and source records attributed to Pyotr N. Ivanshin.

4 recordsLinked to original sources

arXiv2023

The approximate conformal mapping of a disk onto domain with an acute angle

The method of boundary curve reparametrization is applied to construction of the approximate analytical conformal mapping of the unit disk onto an arbitrary given finite domain with a boundary smooth at every point but fininte number of acute angle points. The method is based on both the Fredholm equation solution and spline-interpolation. This approach consists of approximate solution of a linear system with unknown Fourier coefficients and construction of correction splines. The approximate mapping function has the form of a Cauchy integral. The method presentation is supported by demonstration of some examples. This method is applicable to the case of multiply connected domains with boundary angle points.

math.CV↗

arXiv2019

Construction of complex potentials for multiply connected domains

The method of reduction of a Fredholm integral equation to the linear system is generalized to construction of a complex potential --- an analytic function in an infinite multiply connected domain with a simple pole at infinity which maps the domain onto a plane with horizontal slits. We consider a locally sourceless, locally irrotational flow on an arbitrary given $n$-connected infinite domain with impermeable boundary. The complex potential has the form of a Cauchy integral with one linear and $n$ logarithmic summands. The method is easily computable.

math-ph↗

arXiv2018

Continued fractions and conformal mappings for domains with angle points

Here we construct the conformal mappings with the help of continuous fractions approximations. These approximations converge to the algebraic roots $\sqrt[N]{z}$ for $N \in \mathbb{N}$ and $z$ from the right half-plane of the complex plane. We estimate both the convergence rate and the compact set of convergence. Also we give the examples that illustrate the introduced technique of a conformal mapping construction.

math.MG↗

arXiv2008

The mapping of compact into the set of its Chebyshev centres is Lipschitz in the space l^n_{\infty}

In this article the authors prove strong stability of the set of all Chebyshev centres of the bounded closed subset of the metric space. We endow the set of all compacts of the space $l^n_{\infty}$ with Hausdorff metric and prove that the map which puts in correspondence to each compact of $l^n_{\infty}$ the set of its Chebyshev centres is Lipshitz.

math.MG↗