On increase of calculation accuracy at the problem of determining the chemical
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 219-232.

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In work the problem of a finding of a chemical composition of a homogeneous medium by a method of collimated multiple X-ray irradiation is considered. The question on possibility of increase of accuracy of the solution is thus studied by carrying out of several series of repeated measurements of passing radiation. It is shown that under some natural assumptions on measurement errors of passing radiation, the solution errors tend to zero with growth of number of the measurements fulfilled. Results of the calculations executed for concrete substance are shown by way of illustration.
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V. G. Nazarov. On increase of calculation accuracy at the problem of determining the chemical. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 219-232. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a10/

[1] Sergei Osipov, Sergei Chakhlov, Andrey Batranin, Oleg Osipov, Van Bak Trinh, Juriy Kytmanov, “Theoretical study of a simplified implementation model of a dual-energy technique for computed tomography”, NDT and E International, 98 (2018), 63–69 | DOI

[2] S. P. Osipov, V. A. Udod, Yanzhao Wang, “Identification of Materials in X-Ray Inspections of Objects by the Dual-Energy Method”, Russian Journal of Nondestructive Testing, 53 (8) (2017), 568–587 | DOI

[3] V. A. Klimenov, S. P. Osipov, A. K. Temnik, “Identifikatsiya veschestva ob'ekta kontrolya metodom dualnykh energii”, Defektoskopiya, 11 (2013), 40–50

[4] V. G. Nazarov, “Metod singulyarnogo razlozheniya matritsy v zadache nakhozhdeniya khimicheskogo sostava sredy”, Sibirskie elektronnye matematicheskie izvestiya, 14 (2017), 821–837 | MR | Zbl

[5] V. G. Nazarov, “Vybor optimalnykh znachenii energii izlucheniya v zadache nakhozhdeniya khimicheskogo sostava sredy”, Matematicheskoe modelirovanie, 30 (2018), 91–102 | Zbl

[6] D. S. Anikonov, A. E. Kovtanyuk, I. V. Prokhorov, Ispolzovanie uravneniya perenosa v tomografii, Logos, M., 2000

[7] D. S. Anikonov, A. E. Kovtanyuk, I. V. Prokhorov, Transport Equation and Tomography, VSP, Utrecht-Boston, 2002 | MR | Zbl

[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, Preprint NISTIR-5632, Nat. Inst. of Standard and Technology, Gaithersburg, 1995

[9] M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, 2005 http://www.physics.nist.gov/xcom

[10] S. K. Godunov, A. G. Antonov, O. P. Kirilyuk, V. I. Kostin, Garantirovannaya tochnost resheniya sistem lineinykh uravnenii v evklidovykh prostranstvakh, Nauka. Sib. otd-nie, Novosibirsk, 1988

[11] Dzh. Forsait, M. Malkolm, K. Mouler, Mashinnye metody matematicheskikh vychislenii, Mir, M., 1980

[12] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988 | MR