Optimal radiation energies finding at the problem of determining the chemical composition of a medium
Matematičeskoe modelirovanie, Tome 30 (2018) no. 1, pp. 91-102.

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Within the bounds of the problem of the chemical composition finding of a homogeneous medium by multi-energy radiography a task of choosing the best X-ray energies is considered. A mathematical model of the problem has been formulated and a method of its solution has been advanced. The method consists in finding such a set of radiation energy, in which the condition number of some matrix is minimized. The studies for several groups of substances have been carried out. Several examples of the problem solutions for media of different chemical composition are presented.
Mots-clés : radiation transport equation
Keywords: X-ray radiography, determining chemical composition of medium.
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V. G. Nazarov. Optimal radiation energies finding at the problem of determining the chemical composition of a medium. Matematičeskoe modelirovanie, Tome 30 (2018) no. 1, pp. 91-102. http://geodesic.mathdoc.fr/item/MM_2018_30_1_a7/

[1] S.V. Naidenov, V.D. Ryzhykov, “Ob opredelenii sostava metodom multienergeticheskoi radiografii”, Pisma v ZHTF, 28:9 (2002), 6–13

[2] S.P. Osipov, A.K. Temnik, S.V. Chakhlov, “Vliianie fizicheskikh faktorov na kachestvo identifikatsii veshchestv obiektov kontrolia vysokoenergeticheskim metodom dualnykh energii”, Defektoskopiia, 2014, no. 8, 69–77

[3] V.M. Fedoseev, Rentgenovskiy sposob obnaruzheniia veshchestva po znacheniiu ego effectivnogo atomnogo nomera, Patent RF No 2095795, 1997, Bull. No 16, 2002.06.10

[4] V.G. Nazarov, “Opredelenie khimicheskogo sostava i struktury neodnorodnoi sredy metodom rentgenovskoi tomografii”, ZhVMiMF, 47:8 (2007), 1413–1422 | MR

[5] A.E. Kovtanyuk, V.G. Nazarov, I.V. Prokhorov, I.P. Yarovenko, Sposob identifikatsii materialov putem mnogokratnogo radiograficheskogo oblucheniya, Patent RF No 2426102. 10.08.2011. Byull. No 22

[6] V.G. Nazarov, “Opredelenie khimicheskogo sostava neodnorodnogo tela metodom multienergeticheskoi radiografii”, SibZhIM, XIII:1(41) (2010), 72–83 ; V.G. Nazarov, “Determining the Chemical Composition of an Inhomogeneous Body by Multi-Energy Rsdiography”, Journal of Applied and Industrial Mathematics, 5:2 (2011), 1–12 | MR | Zbl | DOI

[7] A.S. Kurilik, Opredelenie atomnogo nomera veshchestva obiektov po oslableniiu puchkov fotonov s energiiami do 10 MeV, Dissertatsiia na soiskanie uchenoi stepeni kandidata fiz.-mat. nauk, NIIIaF MGU, 2014, 111 pp.

[8] J.H. Hubbell, S.M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy Absorption Coefficients 1 KeV to 20 MeV for Elements Z=1 to 92 and 48 Additional Substances of Dosimetric Interest, NISTIR 5632, 1995

[9] M.J. Berger, J.H. Hubbell, S.M. Seltzer, J. Chang, J.S. Coursey, R. Sukumar, D.S. Zucker, K. Olsen, NIST Standard Reference Database 8 (XGAM), http://physics.nist.gov/PhysRefData/Elements/index.html

[10] N.F. Losev, A.N. Smagunova, Osnovy rentgenospektralnogo fluorestsentnogo analiza, Khimiia, M., 1982, 208 pp.

[11] R. Chierniak, X-Ray Computed Tomography in Biomedical Engineering, Springer Verlag London Limited, 2011, xii+319 pp.

[12] P. Lankaster, Theory of matrices, Academic Press, New York–London, 1969 | MR | MR

[13] N.M. Andriushevskii, Analiz ustoichivosti reshenii system lineinykh algebraicheskikh uravnenii, Uchebnoe posobie, Izdatelskii otdel fakulteta VMiK MGU im. M.V. Lomonosova; MAKS Press, 2008, 71 pp.

[14] I.L. Knuniants (gl. red.) i dr., Khimicheskaia entsiklopediia, v. 5t, Sovetskaia entsiklopediia, M., 1988

[15] A.I. Volkov, I.M. Zharskii, Bolshoy ximicheskii spravochnik, Sovremennaia shkola, Minsk, 2005, 608 pp.

[16] N.V. Koronovskii, “Gidrotermalnye obrazovaniia v okeanakh”, Sorosovskii obrazovatelnyi zhurnal, 1999, no. 10, 55–62

[17] A. N. Tikhonov, V. Ia. Arsenin, Metody resheniia nekorrektnykh zadach, Nauka, M., 1979, 285 pp. | MR