Standard

Structure and differential properties of 2D tensor fields of small ranks. / Polyakova, A.; Derevtsov, E.

в: Eurasian Journal of Mathematical and Computer Applications, Том 13, № 2, 5, 30.06.2025, стр. 62-74.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Polyakova, A & Derevtsov, E 2025, 'Structure and differential properties of 2D tensor fields of small ranks', Eurasian Journal of Mathematical and Computer Applications, Том. 13, № 2, 5, стр. 62-74. https://doi.org/10.32523/2306-6172-2025-13-2-62-74

APA

Polyakova, A., & Derevtsov, E. (2025). Structure and differential properties of 2D tensor fields of small ranks. Eurasian Journal of Mathematical and Computer Applications, 13(2), 62-74. [5]. https://doi.org/10.32523/2306-6172-2025-13-2-62-74

Vancouver

Polyakova A, Derevtsov E. Structure and differential properties of 2D tensor fields of small ranks. Eurasian Journal of Mathematical and Computer Applications. 2025 июнь 30;13(2):62-74. 5. doi: 10.32523/2306-6172-2025-13-2-62-74

Author

Polyakova, A. ; Derevtsov, E. / Structure and differential properties of 2D tensor fields of small ranks. в: Eurasian Journal of Mathematical and Computer Applications. 2025 ; Том 13, № 2. стр. 62-74.

BibTeX

@article{098a3f9b49a44618914f8bfa49e778f4,
title = "Structure and differential properties of 2D tensor fields of small ranks",
abstract = "The Radon transform generates many other integral transforms in integral geometry and tensor tomography. Together with complicated geometrical objects, the weighted ray and Radon transforms arise. Usually symmetric tensor fields are considered as the object should be reconstructed. We consider complete, symmetric and difference non-symmetric tensor fields of small ranks as the objects for applications in integral geometry and tensor tomography. The structure and differential properties of such fields are investigated. We establish a decomposition theorem for a complete tensor field, properties and attributes of solenoidal and potential fields.",
keywords = "tensor field, gradient, divergence, symmetric tensor field, potential field, solenoidal field",
author = "A. Polyakova and E. Derevtsov",
note = "The work was financially supported by the Russian Scientific Foundation (RSF), project No. 24-21-00200.",
year = "2025",
month = jun,
day = "30",
doi = "10.32523/2306-6172-2025-13-2-62-74",
language = "English",
volume = "13",
pages = "62--74",
journal = "Eurasian Journal of Mathematical and Computer Applications",
issn = "2306-6172",
publisher = "L. N. Gumilyov Eurasian National University",
number = "2",

}

RIS

TY - JOUR

T1 - Structure and differential properties of 2D tensor fields of small ranks

AU - Polyakova, A.

AU - Derevtsov, E.

N1 - The work was financially supported by the Russian Scientific Foundation (RSF), project No. 24-21-00200.

PY - 2025/6/30

Y1 - 2025/6/30

N2 - The Radon transform generates many other integral transforms in integral geometry and tensor tomography. Together with complicated geometrical objects, the weighted ray and Radon transforms arise. Usually symmetric tensor fields are considered as the object should be reconstructed. We consider complete, symmetric and difference non-symmetric tensor fields of small ranks as the objects for applications in integral geometry and tensor tomography. The structure and differential properties of such fields are investigated. We establish a decomposition theorem for a complete tensor field, properties and attributes of solenoidal and potential fields.

AB - The Radon transform generates many other integral transforms in integral geometry and tensor tomography. Together with complicated geometrical objects, the weighted ray and Radon transforms arise. Usually symmetric tensor fields are considered as the object should be reconstructed. We consider complete, symmetric and difference non-symmetric tensor fields of small ranks as the objects for applications in integral geometry and tensor tomography. The structure and differential properties of such fields are investigated. We establish a decomposition theorem for a complete tensor field, properties and attributes of solenoidal and potential fields.

KW - tensor field

KW - gradient

KW - divergence

KW - symmetric tensor field

KW - potential field

KW - solenoidal field

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105015179013&origin=inward

UR - https://www.mendeley.com/catalogue/f6ba793c-646f-35f3-9bc7-d2c0bfdbfa2c/

U2 - 10.32523/2306-6172-2025-13-2-62-74

DO - 10.32523/2306-6172-2025-13-2-62-74

M3 - Article

VL - 13

SP - 62

EP - 74

JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

SN - 2306-6172

IS - 2

M1 - 5

ER -

ID: 69360889