Geodesic
Problem of partial identification of unknown medium
Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 1, pp. 43-62 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper deals with the problem of partial identification of an unknown medium chemical composition by the method of repeated scanning of this medium by collimated x-ray flux. A mathematical model for the problem of identification is formulated and its comparison with the task of finding the chemical composition of the medium carried out. A method for solving the problem of identification is based on the construction of a special function, called the indicator of distinguishability of substances. By way of illustration, results of calculations performed for various specific groups of chemical elements are presented. 
@article{DVMG_2019_19_1_a6,
     author = {V. G. Nazarov},
     title = {Problem of partial identification of unknown medium},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {43--62},
     year = {2019},
     volume = {19},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2019_19_1_a6/}
}
TY  - JOUR
AU  - V. G. Nazarov
TI  - Problem of partial identification of unknown medium
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2019
SP  - 43
EP  - 62
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DVMG_2019_19_1_a6/
LA  - ru
ID  - DVMG_2019_19_1_a6
ER  - 
%0 Journal Article
%A V. G. Nazarov
%T Problem of partial identification of unknown medium
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2019
%P 43-62
%V 19
%N 1
%U http://geodesic.mathdoc.fr/item/DVMG_2019_19_1_a6/
%G ru
%F DVMG_2019_19_1_a6
V. G. Nazarov. Problem of partial identification of unknown medium. Dalʹnevostočnyj matematičeskij žurnal, Tome 19 (2019) no. 1, pp. 43-62. http://geodesic.mathdoc.fr/item/DVMG_2019_19_1_a6/

[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] 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

[5] 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

[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] V. G. Nazarov, “O povyshenii tochnosti vychislenii v zadache nakhozhdeniya khimicheskogo sostava sredy”, Dalnevostochnyi matematicheskii zhurnal, 18:2 (2018), 219–232 | MR | Zbl

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

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

[11] 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

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

[13] D. S. Anikonov, “Integro-differential heterogeneity indicator in tomography problem”, J.Inv.Ill-Posed Problems, 7:1 (1999), 17–59 | DOI | MR | Zbl

[14] A. I. Volkov, I. V. Zharskii, Bolshoi khimicheskii spravochnik, Sovremennaya shkola, Minsk, 2005