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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2016, Volume 158, Book 2, Pages 202–220 (Mi uzku1363)  

This article is cited in 5 scientific papers (total in 5 papers)

A parametric method of finding accessory parameters for the generalized Schwarz–Christoffel integrals

N. N. Nakipov, S. R. Nasyrov

Kazan Federal University, Kazan, 420008 Russia

Abstract: An approximate method of finding accessory parameters for the generalized Schwarz–Christoffel integrals has been suggested. The integrals provide conformal mappings of a half-plane onto the polygonal Riemann surfaces with inner branch points. The method is based on including the desired map into a one-parametric family of conformal mappings of the upper half-plane onto the Riemann surfaces which are obtained from some fixed Riemann surface by cutting it along an elongated polygonal slit. A system of ordinary differential equations for parameters of the Schwarz–Christoffel integrals, i.e., for the preimages of their vertexes and branch points, has been deduced. Application of the method consists in solving a number of successive Cauchy problems describing the process of moving of the end of the slit along the chains of the polygon. The solution obtained in the previous step forms the initial data for the Cauchy problem in the next step. A numeric example illustrating the method has been considered. For univalent mappings, a similar method was first suggested by P. P. Kufarev.

Keywords: Schwarz–Christoffel integrals, multivalent functions, parametric method.

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Bibliographic databases:
UDC: 517.5
Received: 18.01.2016

Citation: N. N. Nakipov, S. R. Nasyrov, “A parametric method of finding accessory parameters for the generalized Schwarz–Christoffel integrals”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 158, no. 2, Kazan University, Kazan, 2016, 202–220

Citation in format AMSBIB
\Bibitem{NakNas16}
\by N.~N.~Nakipov, S.~R.~Nasyrov
\paper A parametric method of finding accessory parameters for the generalized Schwarz--Christoffel integrals
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2016
\vol 158
\issue 2
\pages 202--220
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1363}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3545711}
\elib{http://elibrary.ru/item.asp?id=26566376}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. Zhambaa, T. V. Kasatkina, A. M. Bubenchikov, “Primenenie metoda P.P. Kufareva k resheniyu zadachi o dvizhenii gruntovykh vod pod gidrotekhnicheskimi sooruzheniyami”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2017, no. 47, 15–21  mathnet  crossref  elib
    2. I. A. Kolesnikov, “On the problem of determining parameters in the Schwarz equation”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 50–62  mathnet  crossref  elib
    3. S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031  mathnet  crossref  crossref  adsnasa  isi  elib
    4. I. A. Kolesnikov, “Opredelenie aktsessornykh parametrov konformnykh otobrazhenii iz verkhnei poluploskosti na pryamolineinye schetnougolniki s dvoinoi simmetriei i krugovye schetnougolniki”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2019, no. 60, 42–60  mathnet  crossref  elib
    5. I. A. Kolesnikov, “Nakhozhdenie parametrov konformnogo otobrazheniya iz poluploskosti na krugovoi mnogougolnik”, Materialy XVII Vserossiiskoi molodezhnoi shkoly-konferentsii «Lobachevskie chteniya-2018», 23-28 noyabrya 2018 g., Kazan.  Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 175, VINITI RAN, M., 2020, 56–68  mathnet  crossref
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