14 citations · 66 across the 17 of their papers we have counts for
19 papers
Projective view at Optimization Problem for Multiband Filter
Andrei Bogatyrev
The best uniform rational approximation of the \emph{sign} function on two intervals separated by zero was explicitly solved by E.I. Zolotarëv in 1877. This optimization problem is…
Metastable states of sub-micron scale ferromagnetic periodic antidot arrays
Andrei B. Bogatyrëv, Konstantin L. Metlov
The magnetic textures on nanoscale possess topological features due to the continuity of the magnetization vector field and its boundary conditions. In thin planar nanoelements, wh…
Blaschke product for bordered surface
Andrei Bogatyrev
It is well known that a ramified holomorphic covering of a closed unitary disc by another such a disc is given by a finite Blaschke product. The inverse is also true. In this note…
Recent Progress in Optimization of Multiband Electrical Filters
Andrei Bogatyrëv
The best uniform rational approximation of the \emph{sign} function on two intervals was explicitly found by Russian mathematician E.I. Zolotarëv in 1877. The progress in math even…
Water flow under rectangular dam
Andrei Bogatyrëv, Oleg Grigor'ev
A new analytical method for calculation the characteristics of the flow in porous medium bounded by a rectangular polygonal path is proposed. The method is based on the usage of hi…
On capacity computation for symmetric polygonal condensers
Sergei Bezrodnykh, Andrei Bogatyrev, Sergei Goreinov +3
Making use of two different analytical-numerical methods for capacity computation, we obtain matching to a very high precision numerical values for capacities of a wide family of p…
What makes magnetic skyrmions different from magnetic bubbles ?
Andrei B. Bogatyrëv, Konstantin L. Metlov
A large enough piece of ferromagnet is usually not magnetized uniformly, but develops a magnetization texture. In thin films these textures can be doubly-periodic. Such are the wel…
Analytical approach to the multiband filter synthesis and comparison to other approaches
Andrei B. Bogatyrev, Sergei A. Goreinov, Sergei Yu. Lyamaev
A novel analytical approach to the synthesis of electrical (e.g. analogue, digital or microwave) filters is proposed. This approach allows to obtain lowest possible degree filters…
Real meromorphic differentials: a language for the meron configurations in planar nanomagnets
Andrei Bogatyrev
In this paper we use the language of real meromorphic differentials from the theory of Klein surfaces to describe the metastable states of multiply connected planar ferromagnetic n…
Topological constraints on positions of magnetic solitons in multiply-connected planar magnetic nano-elements
Andrei B. Bogatyrëv, Konstantin L. Metlov
Here we consider an interplay between the topology of the magnetization texture (which is a topological soliton, or Skyrmion) in a planar magnetic nano-element and the topology of…
Capacity of several aligned segments
Andrei B. Bogatyrev, Oleg A. Grigoriev
In this note we present a universal formula in terms of theta functions for the Log- capacity of several segments on a line. The case of two segments was studied by N.I.Akhiezer (1…
How many Zolotarev fractions are there?
Andrei Bogatyrev
Known properties of Chebyshev polynomials are the following: they have simple critical points with only two (finite) critical values. Those properties uniquely determine the named…
Magnetic states in multiply-connected flat nano-elements
Andrei B. Bogatyrev, Konstantin L. Metlov
Flat magnetic nano-elements are an essential component of current and future spintronic devices. By shaping an element it is possible to select and stabilize chosen metastable magn…
Image of Abel-Jacobi map for hyperelliptic genus 3 and 4 curves
Andrei Bogatyrev
For the evaluation and inversion of abelian integrals we show that the image of the Abel-Jacobi map of genus less than 5 hyperelliptic curve in its Jacobian is the intersection of…
Conformal mapping of rectangular heptagons
Andrei B. Bogatyrev
We propose an analytical approach to the conformal mapping of (rectangular) polygons based on the theory of Riemann surfaces and theta functions.
Elementary construction of some Jenkins-Strebel differentials
Andrei Bogatyrev
We give an explicit multi-parametric construction for Jenkins-Strebel differentials on real algebraic curves. Roughly speaking, the square of any real holomorphic abelian different…
Rational functions admitting double decomposition
Andrei Bogatyrev
J.Ritt has investigated the structure of complex polynomials with respect to superposition. In particular, he listed all the polynomials admitting different double decompositions i…
Pictorial Representation for Antisymmetric Eigenfunctions of PS-3 Integral Equations
Andrei Bogatyrev
Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete l…
Integral equations PS-3 and moduli of pants
Andrei Bogatyrev
More than a hundred years ago H.Poincare and V.A.Steklov considered a problem for the Laplace equation with spectral parameter in the boundary conditions. Today similar problems fo…