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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 8, Pages 1413–1422 (Mi zvmmf269)  

This article is cited in 7 scientific papers (total in 7 papers)

X-ray tomographic determination of the chemical composition and structure of an inhomogeneous medium

V. G. Nazarov

Institute of Applied Mathematics, Far East Division, Russian Academy of Sciences, ul. Radio 7, Vladivostok, 690041, Russia
References:
Abstract: The chemical composition of an inhomogeneous body consisting of several homogeneous parts is determined by x-ray tomography. At the first stage, an indicator of inhomogeneities is used to determine the internal structure of the body. Next, under certain additional assumptions about the properties of the parts, a method is proposed for partial or complete determination of the chemical composition of each part as based on the results of the previous stage. Mathematically, the problem is reduced to solving the radiative transfer equation and systems of linear algebraic equations. Numerical experiments are performed via computer simulation. The numerical results are illustrated by graphs and tomograms.
Key words: radiative transfer equation, x-ray tomography, numerical method for determining the chemical composition of a medium.
Received: 02.05.2006
Revised: 26.03.2007
English version:
Computational Mathematics and Mathematical Physics, 2007, Volume 47, Issue 8, Pages 1358–1367
DOI: https://doi.org/10.1134/S0965542507080131
Bibliographic databases:
Document Type: Article
UDC: 519.65
Language: Russian
Citation: V. G. Nazarov, “X-ray tomographic determination of the chemical composition and structure of an inhomogeneous medium”, Zh. Vychisl. Mat. Mat. Fiz., 47:8 (2007), 1413–1422; Comput. Math. Math. Phys., 47:8 (2007), 1358–1367
Citation in format AMSBIB
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\by V.~G.~Nazarov
\paper X-ray tomographic determination of the chemical composition and structure of an inhomogeneous medium
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 8
\pages 1413--1422
\mathnet{http://mi.mathnet.ru/zvmmf269}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2378186}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 8
\pages 1358--1367
\crossref{https://doi.org/10.1134/S0965542507080131}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548410436}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf269
  • https://www.mathnet.ru/eng/zvmmf/v47/i8/p1413
  • This publication is cited in the following 7 articles:
    1. V. G. Nazarov, “Vybor optimalnykh znachenii energii izlucheniya v zadache nakhozhdeniya khimicheskogo sostava sredy”, Matem. modelirovanie, 30:1 (2018), 91–102  mathnet  elib
    2. V. G. Nazarov, “Metod singulyarnogo razlozheniya matritsy v zadache nakhozhdeniya khimicheskogo sostava sredy”, Sib. elektron. matem. izv., 14 (2017), 821–837  mathnet  crossref
    3. Mikhail Guzev, Vasilii Nazarov, Igor Prokhorov, “Modelling of Material Composition in X-Ray Diagnostics”, AMM, 749 (2015), 116  crossref
    4. V. G. Nazarov, “Opredelenie khimicheskogo sostava neodnorodnogo tela metodom multienergeticheskoi radiografii”, Sib. zhurn. industr. matem., 13:1 (2010), 72–83  mathnet
    5. V. V. Vasin, V. N. Dubinin, V. G. Romanov, “Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke””, Sib. elektron. matem. izv., 5 (2008), 427–439  mathnet  elib
    6. A. E. Kovtanyuk, V. M. Mun, V. G. Nazarov, I. V. Prokhorov, I. P. Yarovenko, “Zadachi rentgenovskoi i opticheskoi tomografii [Itogovyi nauchnyi otchet po mezhdistsiplinarnomu integratsionnomu proektu SO RAN: “Razrabotka teorii i vychislitelnoi tekhnologii resheniya obratnykh i ekstremalnykh zadach s prilozheniem v matematicheskoi fizike i gravimagnitorazvedke”]”, Sib. elektron. matem. izv., 5 (2008), 483–498  mathnet  mathscinet
    7. S. A. Nazarov, “On the concentration of the point spectrum on the continuous one in problems of the linearized theory of water-waves”, J. Math. Sci. (N. Y.), 152:5 (2008), 674–689  mathnet  crossref  mathscinet  scopus
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