Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness
ABSTRACT: The trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the point view of the theory of Differential Algebra. In particular, by Morales-Ramis theory it is possible to analyze...
- Autores:
-
Giraldo Salazar, Hernán Alonso
Piedrahíta Escobar, Carlos Cesar
Acosta Humánez, Primitivo Belén
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2016
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/44292
- Acceso en línea:
- https://hdl.handle.net/10495/44292
- Palabra clave:
- Teoría de Galois
Galois theory
Ecuaciones
Equations
Sismología
Seismology
Geofísica
Geophysics
Sistemas de Hamilton
Hamiltonian systems
Ecuación de Eikonal
Ecuación de Helmholtz
Aproximación de alta frecuencia
Teoría de Morales Ramis
Teoría de rayos
- Rights
- openAccess
- License
- https://creativecommons.org/licenses/by-nc-sa/4.0/
| id |
UDEA2_d162590ca52b6e258e21d720ed1f9f85 |
|---|---|
| oai_identifier_str |
oai:bibliotecadigital.udea.edu.co:10495/44292 |
| network_acronym_str |
UDEA2 |
| network_name_str |
Repositorio UdeA |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| title |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| spellingShingle |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness Teoría de Galois Galois theory Ecuaciones Equations Sismología Seismology Geofísica Geophysics Sistemas de Hamilton Hamiltonian systems Ecuación de Eikonal Ecuación de Helmholtz Aproximación de alta frecuencia Teoría de Morales Ramis Teoría de rayos |
| title_short |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| title_full |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| title_fullStr |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| title_full_unstemmed |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| title_sort |
Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of Slowness |
| dc.creator.fl_str_mv |
Giraldo Salazar, Hernán Alonso Piedrahíta Escobar, Carlos Cesar Acosta Humánez, Primitivo Belén |
| dc.contributor.author.none.fl_str_mv |
Giraldo Salazar, Hernán Alonso Piedrahíta Escobar, Carlos Cesar Acosta Humánez, Primitivo Belén |
| dc.contributor.researchgroup.spa.fl_str_mv |
Álgebra, Teoría de Números y Aplicaciones: ERM Álgebra U de A |
| dc.subject.lemb.none.fl_str_mv |
Teoría de Galois Galois theory Ecuaciones Equations Sismología Seismology Geofísica Geophysics Sistemas de Hamilton Hamiltonian systems |
| topic |
Teoría de Galois Galois theory Ecuaciones Equations Sismología Seismology Geofísica Geophysics Sistemas de Hamilton Hamiltonian systems Ecuación de Eikonal Ecuación de Helmholtz Aproximación de alta frecuencia Teoría de Morales Ramis Teoría de rayos |
| dc.subject.proposal.spa.fl_str_mv |
Ecuación de Eikonal Ecuación de Helmholtz Aproximación de alta frecuencia Teoría de Morales Ramis Teoría de rayos |
| description |
ABSTRACT: The trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the point view of the theory of Differential Algebra. In particular, by Morales-Ramis theory it is possible to analyze inte- grable Hamiltonian systems through the abelian structure of their variational equations. In this paper we obtain the abelian differential Galois groups and the representation of the quiver, that allow us to obtain such abelian differential Galois groups, for some seismic models with constant Hessian of square of slowness, proposed in [20], which are equivalent to linear Hamiltonian systems with three uncoupled harmonic oscillators. |
| publishDate |
2016 |
| dc.date.issued.none.fl_str_mv |
2016 |
| dc.date.accessioned.none.fl_str_mv |
2025-01-21T20:01:08Z |
| dc.date.available.none.fl_str_mv |
2025-01-21T20:01:08Z |
| dc.type.spa.fl_str_mv |
Artículo de investigación |
| dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.redcol.spa.fl_str_mv |
https://purl.org/redcol/resource_type/ART |
| dc.type.coarversion.spa.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| format |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| status_str |
publishedVersion |
| dc.identifier.issn.none.fl_str_mv |
0972-0871 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/10495/44292 |
| dc.identifier.eissn.none.fl_str_mv |
0971-4332 |
| identifier_str_mv |
0972-0871 0971-4332 |
| url |
https://hdl.handle.net/10495/44292 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.citationendpage.spa.fl_str_mv |
15 |
| dc.relation.citationstartpage.spa.fl_str_mv |
1 |
| dc.relation.citationvolume.spa.fl_str_mv |
102 |
| dc.relation.ispartofjournal.spa.fl_str_mv |
Far East Journal of Mathematical Sciences |
| dc.rights.uri.spa.fl_str_mv |
https://creativecommons.org/licenses/by-nc-sa/4.0/ |
| dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-sa/2.5/co/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.coar.spa.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/4.0/ http://creativecommons.org/licenses/by-nc-sa/2.5/co/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.spa.fl_str_mv |
15 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Universidad de Allahabad |
| dc.publisher.place.spa.fl_str_mv |
Allahabad, India |
| institution |
Universidad de Antioquia |
| bitstream.url.fl_str_mv |
https://bibliotecadigital.udea.edu.co/bitstreams/52285722-023a-4986-927e-a8ac64f3fb87/download https://bibliotecadigital.udea.edu.co/bitstreams/06d3d3f0-2a90-442f-9d6d-7a19371887d1/download https://bibliotecadigital.udea.edu.co/bitstreams/52a1c048-e78b-40f8-ab3b-3e8b02d71994/download https://bibliotecadigital.udea.edu.co/bitstreams/01874f3e-b220-4cde-a833-9b4b3b5eab64/download https://bibliotecadigital.udea.edu.co/bitstreams/2f2136a1-5709-4c9e-8126-2a30fae81177/download |
| bitstream.checksum.fl_str_mv |
7cefbb017e445a31ba394b7571d797ec e2060682c9c70d4d30c83c51448f4eed 8a4605be74aa9ea9d79846c1fba20a33 ed7f080a381c330a66db038ae330de80 7c47fd1cd8e98bd589cca9835a76b189 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional de la Universidad de Antioquia |
| repository.mail.fl_str_mv |
aplicacionbibliotecadigitalbiblioteca@udea.edu.co |
| _version_ |
1851052303875833856 |
| spelling |
Giraldo Salazar, Hernán AlonsoPiedrahíta Escobar, Carlos CesarAcosta Humánez, Primitivo BelénÁlgebra, Teoría de Números y Aplicaciones: ERMÁlgebra U de A2025-01-21T20:01:08Z2025-01-21T20:01:08Z20160972-0871https://hdl.handle.net/10495/442920971-4332ABSTRACT: The trajectory of energy is modeled by the solution of the Eikonal equation, which can be solved by solving a Hamiltonian system. This system is amenable of treatment from the point view of the theory of Differential Algebra. In particular, by Morales-Ramis theory it is possible to analyze inte- grable Hamiltonian systems through the abelian structure of their variational equations. In this paper we obtain the abelian differential Galois groups and the representation of the quiver, that allow us to obtain such abelian differential Galois groups, for some seismic models with constant Hessian of square of slowness, proposed in [20], which are equivalent to linear Hamiltonian systems with three uncoupled harmonic oscillators.Universidad de Antioquia. Vicerrectoría de investigación. Comité para el Desarrollo de la Investigación - CODIColombia. Ministerio de Ciencia, Tecnología e Innovación - MinCienciasCOL0017217COL008689615 páginasapplication/pdfengUniversidad de AllahabadAllahabad, Indiahttps://creativecommons.org/licenses/by-nc-sa/4.0/http://creativecommons.org/licenses/by-nc-sa/2.5/co/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Differential Galois Groups and Representation of Quivers for Seismic Models with Constant Hessian of Square of SlownessArtículo de investigaciónhttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionTeoría de GaloisGalois theoryEcuacionesEquationsSismologíaSeismologyGeofísicaGeophysicsSistemas de HamiltonHamiltonian systemsEcuación de EikonalEcuación de HelmholtzAproximación de alta frecuenciaTeoría de Morales RamisTeoría de rayos151102Far East Journal of Mathematical SciencesEstrategia de Sostenibilidad 2016-20170266-2013RoR:03bp5hc83RoR:03fd5ne08PublicationORIGINALGiraldoHernan_2017_Differential_Galois_Representation.pdfGiraldoHernan_2017_Differential_Galois_Representation.pdfArtículo de investigaciónapplication/pdf229797https://bibliotecadigital.udea.edu.co/bitstreams/52285722-023a-4986-927e-a8ac64f3fb87/download7cefbb017e445a31ba394b7571d797ecMD51trueAnonymousREADCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81051https://bibliotecadigital.udea.edu.co/bitstreams/06d3d3f0-2a90-442f-9d6d-7a19371887d1/downloade2060682c9c70d4d30c83c51448f4eedMD52falseAnonymousREADLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstreams/52a1c048-e78b-40f8-ab3b-3e8b02d71994/download8a4605be74aa9ea9d79846c1fba20a33MD53falseAnonymousREADTEXTGiraldoHernan_2017_Differential_Galois_Representation.pdf.txtGiraldoHernan_2017_Differential_Galois_Representation.pdf.txtExtracted texttext/plain41444https://bibliotecadigital.udea.edu.co/bitstreams/01874f3e-b220-4cde-a833-9b4b3b5eab64/downloaded7f080a381c330a66db038ae330de80MD54falseAnonymousREADTHUMBNAILGiraldoHernan_2017_Differential_Galois_Representation.pdf.jpgGiraldoHernan_2017_Differential_Galois_Representation.pdf.jpgGenerated Thumbnailimage/jpeg9228https://bibliotecadigital.udea.edu.co/bitstreams/2f2136a1-5709-4c9e-8126-2a30fae81177/download7c47fd1cd8e98bd589cca9835a76b189MD55falseAnonymousREAD10495/44292oai:bibliotecadigital.udea.edu.co:10495/442922025-03-26 20:13:59.488https://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://bibliotecadigital.udea.edu.coRepositorio Institucional de la Universidad de Antioquiaaplicacionbibliotecadigitalbiblioteca@udea.edu.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 |