Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra
UDC 517.5 Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field...
Gespeichert in:
| Datum: | 2025 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2025
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7982 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512838486851584 |
|---|---|
| author | Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo |
| author_facet | Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo |
| author_sort | Díaz-Marín, Homero G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-08-09T14:51:15Z |
| description | UDC 517.5
Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field $\varphi$ with respect to which the components of all functions $\mathcal L\circ\varphi$ are solutions, where $\mathcal L$ is differentiable in a sense of Lorch with respect to $\mathbb A.$ If we consider the 3D cyclic algebra and a suitable 3D affine map $\varphi,$ then we get families of solutions for the Laplace equation with three independent variables. |
| doi_str_mv | 10.3842/umzh.v76i11.7982 |
| first_indexed | 2026-03-24T03:35:09Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7982 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:35:09Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-79822025-08-09T14:51:15Z Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo Functions of hypercomplex variables, Laplace operator, Solenoidal vector fields, Calculus over algebras, Differentiation theory. UDC 517.5 Given a PDE, in [E. López-González, E. A. Martínez-García, R.~Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)], the authors proposed a method for the construction of solutions by considering an associative real algebra $\mathbb A$ and a suitable affine vector field $\varphi$ with respect to which the components of all functions $\mathcal L\circ\varphi$ are solutions, where $\mathcal L$ is differentiable in a sense of Lorch with respect to $\mathbb A.$ If we consider the 3D cyclic algebra and a suitable 3D affine map $\varphi,$ then we get families of solutions for the Laplace equation with three independent variables. УДК 517.5 Потенціали для соленоїдних полів з використанням тривимірної $\varphi$-гармонічної циклічної алгебри Для заданого диференціального рівняння з частинними похідними в статті [E. López-González, E. A. Martínez-García, R. Torres-Córdoba, Chaos, Solitons and Fractals, 73, Article 113757 (2023)] запропоновано метод побудови розв'язків шляхом розгляду асоціативної дійсної алгебри $\mathbb A$ та відповідного афінного векторного поля $\varphi,$ щодо якого компоненти всіх функцій $\mathcal L\circ\varphi$ є розв'язками, де функція $\mathcal L$ диференційовна в сенсі Лорха щодо $\mathbb A.$ Розглядаючи тривимірну циклічну алгебру та відповідне тривимірне афінне відображення $\varphi,$ ми отримуємо сім'ї розв'язків рівняння Лапласа з трьома незалежними змінними. Institute of Mathematics, NAS of Ukraine 2025-08-06 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7982 10.3842/umzh.v76i11.7982 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 11 (2024); 1584 - 1601 Український математичний журнал; Том 76 № 11 (2024); 1584 - 1601 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7982/10278 Copyright (c) 2024 HOMERO DÍAZ-MARÍN, Elifalet López-González, Osvaldo Osuna |
| spellingShingle | Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo Díaz-Marín, Homero G. López-González, Elifalet Osuna, Osvaldo Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title | Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title_alt | Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title_full | Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title_fullStr | Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title_full_unstemmed | Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title_short | Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| title_sort | potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra |
| topic_facet | Functions of hypercomplex variables Laplace operator Solenoidal vector fields Calculus over algebras Differentiation theory. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7982 |
| work_keys_str_mv | AT diazmarinhomerog potentialsforsolenoidalfieldsusingthethreedimensionalvarphiharmoniccyclicalgebra AT lopezgonzalezelifalet potentialsforsolenoidalfieldsusingthethreedimensionalvarphiharmoniccyclicalgebra AT osunaosvaldo potentialsforsolenoidalfieldsusingthethreedimensionalvarphiharmoniccyclicalgebra AT diazmarinhomerog potentialsforsolenoidalfieldsusingthethreedimensionalvarphiharmoniccyclicalgebra AT lopezgonzalezelifalet potentialsforsolenoidalfieldsusingthethreedimensionalvarphiharmoniccyclicalgebra AT osunaosvaldo potentialsforsolenoidalfieldsusingthethreedimensionalvarphiharmoniccyclicalgebra |