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On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields. / Derevtsov, E. Yu.

In: Journal of Applied and Industrial Mathematics, Vol. 14, No. 2, 01.05.2020, p. 256-264.

Research output: Contribution to journal › Article › peer-review

Harvard

Derevtsov, EY 2020, 'On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields', Journal of Applied and Industrial Mathematics, vol. 14, no. 2, pp. 256-264. https://doi.org/10.1134/S1990478920020052

APA

Derevtsov, E. Y. (2020). On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields. Journal of Applied and Industrial Mathematics, 14(2), 256-264. https://doi.org/10.1134/S1990478920020052

Vancouver

Derevtsov EY. On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields. Journal of Applied and Industrial Mathematics. 2020 May 1;14(2):256-264. doi: 10.1134/S1990478920020052

Author

Derevtsov, E. Yu. / On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields. In: Journal of Applied and Industrial Mathematics. 2020 ; Vol. 14, No. 2. pp. 256-264.

BibTeX

@article{c604d2ee321841d3b6926d30961e4767,
title = "On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields",
abstract = "Under consideration are the operators of angular moments which map the values ofgeneralized attenuated ray transforms (ART) into the set of symmetric p-tensor fields. The differential relations between thevalues of ARTs of various orders, acting on stationary or dynamic source distributionsf, serve as the basis for establishing the differentialconnections between the tensor fields of angular moments of various orders k and ranks p. The particular cases are indicated allowing us toobtain some previously known results. Connections of the ARTs of order k with the problems of tomography and integralgeometry as well as the established properties and connections between ARTs and angularmoments can be useful as additional information when constructing the iterative algorithms forsolving the problems of dynamic refraction tensor tomography.",
keywords = "attenuated ray transform, back projection, operator of angular moment, tensor field, transport equation",
author = "Derevtsov, {E. Yu}",
year = "2020",
month = may,
day = "1",
doi = "10.1134/S1990478920020052",
language = "English",
volume = "14",
pages = "256--264",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - On the Angular Moment Operators of Attenuated Ray Transforms of Scalar 3D-Fields

AU - Derevtsov, E. Yu

PY - 2020/5/1

Y1 - 2020/5/1

N2 - Under consideration are the operators of angular moments which map the values ofgeneralized attenuated ray transforms (ART) into the set of symmetric p-tensor fields. The differential relations between thevalues of ARTs of various orders, acting on stationary or dynamic source distributionsf, serve as the basis for establishing the differentialconnections between the tensor fields of angular moments of various orders k and ranks p. The particular cases are indicated allowing us toobtain some previously known results. Connections of the ARTs of order k with the problems of tomography and integralgeometry as well as the established properties and connections between ARTs and angularmoments can be useful as additional information when constructing the iterative algorithms forsolving the problems of dynamic refraction tensor tomography.

AB - Under consideration are the operators of angular moments which map the values ofgeneralized attenuated ray transforms (ART) into the set of symmetric p-tensor fields. The differential relations between thevalues of ARTs of various orders, acting on stationary or dynamic source distributionsf, serve as the basis for establishing the differentialconnections between the tensor fields of angular moments of various orders k and ranks p. The particular cases are indicated allowing us toobtain some previously known results. Connections of the ARTs of order k with the problems of tomography and integralgeometry as well as the established properties and connections between ARTs and angularmoments can be useful as additional information when constructing the iterative algorithms forsolving the problems of dynamic refraction tensor tomography.

KW - attenuated ray transform

KW - back projection

KW - operator of angular moment

KW - tensor field

KW - transport equation

UR - http://www.scopus.com/inward/record.url?scp=85087774468&partnerID=8YFLogxK

U2 - 10.1134/S1990478920020052

DO - 10.1134/S1990478920020052

M3 - Article

AN - SCOPUS:85087774468

VL - 14

SP - 256

EP - 264

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 24753028