Abstract:
Under study is some new problem of integral geometry. All planes are considered in the three-dimensional Euclidean space. The data are given by the integrals over all such planes of an unknown piecewise-smooth function depending both on the spatial variables and the variables characterizing the planes. The sought object is an integrant discontinuity surface of the first kind. The uniquiness theorem of of the desired surface is proved. The research od the papert presents an aspects of the theory of probing an unknown medium by various physical signals.
Keywords:
integral geometry, generalized Radon transform, probing, unknown boundaries.
Citation:
D. S. Anikonov, Ya. A. Kipriyanov, “An underdetermined problem of integral geometry for the generalized Radon transform”, Sib. Zh. Ind. Mat., 19:1 (2016), 18–26; J. Appl. Industr. Math., 10:1 (2016), 21–28
\Bibitem{AniKip16}
\by D.~S.~Anikonov, Ya.~A.~Kipriyanov
\paper An underdetermined problem of integral geometry for the generalized Radon transform
\jour Sib. Zh. Ind. Mat.
\yr 2016
\vol 19
\issue 1
\pages 18--26
\mathnet{http://mi.mathnet.ru/sjim908}
\crossref{https://doi.org/10.17377/sibjim.2016.19.102}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3549854}
\elib{https://elibrary.ru/item.asp?id=25591887}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 1
\pages 21--28
\crossref{https://doi.org/10.1134/S1990478916010038}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84961671425}
Linking options:
https://www.mathnet.ru/eng/sjim908
https://www.mathnet.ru/eng/sjim/v19/i1/p18
This publication is cited in the following 1 articles:
Mukhiddin Muminov, Zarifjon Ochilov, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 020010
Citation in format AMSBIB
Contact us: