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Dal'nevost. Mat. Zh., 2007, Volume 7, Number 1-2, Pages 17–29 (Mi dvmg53)  

This article is cited in 3 scientific papers (total in 3 papers)

The generalized reduced modulus in spatial problems of the capacitorial tomography

V. V. Aseev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The external problem of the spatial capacitorial tomography is considered. The notion of capacitorial defect of an object (a compact set) along Möbius directions in the space has been introduced. The criteria for the capacitorial invisibility of an object along the Möbius direction determined by a pair of points in the accessible region of the space has been obtained. The problem of upper estimates for the capacitorial defect along Möbius directions in the space, as well as it's connection with the notion of generalized reduced modulus by V.N. Dubinin, is there also considered in this paper.

Key words: condenser, conformal capacity, conformal modulus, modulus of a set of curves, capacitorial defect, capacitorial tomography, capacitorial invisibility, NED-set, eliminability along direction, Apollonian condenser, generalized reduced modulus.

Full text: PDF file (262 kB)
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Document Type: Article
UDC: 517.54, 517.956
MSC: Primary 31A15; Secondary 30C85
Received: 26.11.2007

Citation: V. V. Aseev, “The generalized reduced modulus in spatial problems of the capacitorial tomography”, Dal'nevost. Mat. Zh., 7:1-2 (2007), 17–29

Citation in format AMSBIB
\Bibitem{Ase07}
\by V.~V.~Aseev
\paper The generalized reduced modulus in spatial problems of the capacitorial tomography
\jour Dal'nevost. Mat. Zh.
\yr 2007
\vol 7
\issue 1-2
\pages 17--29
\mathnet{http://mi.mathnet.ru/dvmg53}
\elib{http://elibrary.ru/item.asp?id=15484738}


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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. V. V. Aseev, “Ned sets on a hyperplane”, Siberian Math. J., 50:5 (2009), 760–775  mathnet  crossref  mathscinet  isi  elib
    2. V. N. Dubinin, “On the reduced modulus of the complex sphere”, Siberian Math. J., 55:5 (2014), 882–892  mathnet  crossref  mathscinet  isi
    3. Abrosimov V N., Mednykh A.D., Mednykh I.A., Tetenov V A., “Vladislav Vasilevich Aseev is 70”, Sib. Electron. Math. Rep., 14 (2017), A43–A57  mathnet  mathscinet  isi
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