A model of anaerobic digestion for biogas production using abel equations
Mathematical models for biogas production are studied due to their importance in the use of control and optimization of renewable resources and clean energy. In this paper, we combine two algebraic methods to obtain solutions of Abel equation of first kind that arises from a mathematical model to bi...
- Autores:
-
Acosta-Humánez, Primitivo B.
Machado Higuera, Maximiliano
Sinitsyn, Alexander V.
- Tipo de recurso:
- Fecha de publicación:
- 2017
- Institución:
- Universidad Simón Bolívar
- Repositorio:
- Repositorio Digital USB
- Idioma:
- eng
- OAI Identifier:
- oai:bonga.unisimon.edu.co:20.500.12442/1895
- Acceso en línea:
- http://hdl.handle.net/20.500.12442/1895
- Palabra clave:
- Abel equation
Biogas
Differential equations
Hamiltonian algebrization
Liouvillian solutions
- Rights
- License
- licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional
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A model of anaerobic digestion for biogas production using abel equations |
| title |
A model of anaerobic digestion for biogas production using abel equations |
| spellingShingle |
A model of anaerobic digestion for biogas production using abel equations Abel equation Biogas Differential equations Hamiltonian algebrization Liouvillian solutions |
| title_short |
A model of anaerobic digestion for biogas production using abel equations |
| title_full |
A model of anaerobic digestion for biogas production using abel equations |
| title_fullStr |
A model of anaerobic digestion for biogas production using abel equations |
| title_full_unstemmed |
A model of anaerobic digestion for biogas production using abel equations |
| title_sort |
A model of anaerobic digestion for biogas production using abel equations |
| dc.creator.fl_str_mv |
Acosta-Humánez, Primitivo B. Machado Higuera, Maximiliano Sinitsyn, Alexander V. |
| dc.contributor.author.none.fl_str_mv |
Acosta-Humánez, Primitivo B. Machado Higuera, Maximiliano Sinitsyn, Alexander V. |
| dc.subject.eng.fl_str_mv |
Abel equation Biogas Differential equations Hamiltonian algebrization Liouvillian solutions |
| topic |
Abel equation Biogas Differential equations Hamiltonian algebrization Liouvillian solutions |
| description |
Mathematical models for biogas production are studied due to their importance in the use of control and optimization of renewable resources and clean energy. In this paper, we combine two algebraic methods to obtain solutions of Abel equation of first kind that arises from a mathematical model to biogas production formulated in France on 2001. The aim of this paper is to obtain Liouvillian solutions of Abel’s equations through Hamiltonian algebrization. As an illustration, we present graphics of solutions for Abel equations and solutions for Abel equations in algebraic form. |
| publishDate |
2017 |
| dc.date.issued.none.fl_str_mv |
2017 |
| dc.date.accessioned.none.fl_str_mv |
2018-03-21T22:24:38Z |
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2018-03-21T22:24:38Z |
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article |
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http://purl.org/coar/resource_type/c_6501 |
| dc.identifier.issn.none.fl_str_mv |
09720871 |
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http://hdl.handle.net/20.500.12442/1895 |
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09720871 |
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http://hdl.handle.net/20.500.12442/1895 |
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eng |
| language |
eng |
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http://purl.org/coar/access_right/c_abf2 |
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licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional |
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licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
| dc.publisher.eng.fl_str_mv |
Pushpa Publishing House |
| dc.source.eng.fl_str_mv |
Revista Far East Journal of Mathematical Sciences (FJMS) |
| dc.source.none.fl_str_mv |
Vol. 101, No. 6 (2017) |
| institution |
Universidad Simón Bolívar |
| dc.source.uri.eng.fl_str_mv |
https://www.researchgate.net/profile/A_Sinitsyn/publication/305809139_A_model_of_anaerobic_digestion_for_biogas_production_using_Abel_equations/links/57a2a91308aeb1604835f5e2/A-model-of-anaerobic-digestion-for-biogas-production-using-Abel-equations.pdf |
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licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Acosta-Humánez, Primitivo B.9439add6-3451-4b3f-b187-8b8ba4133fcd-1Machado Higuera, Maximiliano4beccbb8-8422-4314-b701-7207a1114c41-1Sinitsyn, Alexander V.732aa30b-d289-49d3-9b0e-f1b8933ba8b2-12018-03-21T22:24:38Z2018-03-21T22:24:38Z201709720871http://hdl.handle.net/20.500.12442/1895Mathematical models for biogas production are studied due to their importance in the use of control and optimization of renewable resources and clean energy. In this paper, we combine two algebraic methods to obtain solutions of Abel equation of first kind that arises from a mathematical model to biogas production formulated in France on 2001. The aim of this paper is to obtain Liouvillian solutions of Abel’s equations through Hamiltonian algebrization. As an illustration, we present graphics of solutions for Abel equations and solutions for Abel equations in algebraic form.engPushpa Publishing HouseRevista Far East Journal of Mathematical Sciences (FJMS)Vol. 101, No. 6 (2017)https://www.researchgate.net/profile/A_Sinitsyn/publication/305809139_A_model_of_anaerobic_digestion_for_biogas_production_using_Abel_equations/links/57a2a91308aeb1604835f5e2/A-model-of-anaerobic-digestion-for-biogas-production-using-Abel-equations.pdfAbel equationBiogasDifferential equationsHamiltonian algebrizationLiouvillian solutionsA model of anaerobic digestion for biogas production using abel equationsarticlehttp://purl.org/coar/resource_type/c_6501P. B. Acosta-Humánez, Galoisian Approach to Supersymmetric Quantum Mechanics: The Integrability Analysis of the Schrödinger Equation by Means of Differential Galois Theory, VDM Verlag Dr. Müller, 2010, 128 pp.P. B. Acosta-Humánez, Nonautonomous Hamiltonian systems and Morales-Ramis theory I. The case ¨x = f (x, t), SIAM J. Appl. Dyn. Syst. 8 (2009), 279-297. DOI:10.1137/080730329.P. B. Acosta-Humánez, J. T. Lázaro, J. Morales-Ruiz and Ch. Pantazi, On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory, Discrete and Continuous Dynamical Systems - Series A (DCDS-A) 35 (2015), 1767-1800. http://dx.doi.org/10.3934/dcds.2015.35.1767.P. B. Acosta-Humánez, J. J. Morales-Ruiz and J.-A. Weil, Galoisian approach to integrability of Schrödinger equation, Rep. Math. Phys. 67 (2011), 305-374. DOI:10.1016/S0034-4877(11)60019-0.P. B. Acosta-Humánez and E. Suazo, Liouvillian propagators, Riccati equation and differential Galois theory, Journal of Physics A: Mathematical and Theoretical 46 (2013), 455203. DOI:10.1088/1751-8113/46/45/455203.B. Benyahia, T. Sari, B. Cherki and J. Harmand, Bifurcation and stability analysis of a two step model for monitoring anaerobic digestion processes, Journal of Process Control 22(6) (2012), 1008-1019. DOI:10.1016/j.jprocont.2012.04.012.O. Bernard, Z. Hadj-Sadok, D. Dochain, A. Genovesi and J. Steyer, Dynamical model development and parameter identification for an anaerobic wastewater treatment process, Biotechnology and Bioengineering 75(4) (2001), 424-438. DOI:10.1002/bit.10036.F. Mariet, O. Bernard, M. Ras, L. Lardon and J. Steyer, Modeling anaerobic digestion of microalgae using ADM1, Bioresource Technology 102(13) (2011), 6823-6829. DOI:10.1016/j.biortech.2011.04.015.M. Machado Higuera and A. V. Sinitsyn, Existence of lower and upper solutions in reverse order with respect to a variable in a model of acidogenesis to anaerobic digestion, Bulletin of the South Ural State University, Ser. Mathematical Modelling, Programming and Computer Software 8(2) (2015), 55-68. DOI:10.14529/mmp150205.E. Salinas, R. Muñoz, J. Sosa and B. López, Analysis to the solutions of Abel’s differential equations of the first kind under transformation y = u(x) z(x) + v(x), Appl. Math. Sci. 7(41-44) (2013), 2075-2092. DOI:10.12988/ams.B. Sialve, N. Bernet and O. Bernard, Anaerobic digestion of microalgae as a necessary step to make microalgal biodiesel sustainable, Biotechnology Advances 27(4) (2009), 409-416. DOI:10.1016/j.biotechadv.2009.03.001.M. Machado Higuera, Existencia de super y sub soluciones, estabilidad y bifurcación para un modelo matemático de digestión anaerobia para la producción de biogás, Thesis (Ph.D.), Universidad Veracruzana de México, Xalapa, 2015, 124 pp.LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bonga.unisimon.edu.co/bitstreams/9d47ee91-cce0-4e72-8804-be1ba09e0ebf/download8a4605be74aa9ea9d79846c1fba20a33MD5220.500.12442/1895oai:bonga.unisimon.edu.co:20.500.12442/18952019-04-11 21:51:32.63metadata.onlyhttps://bonga.unisimon.edu.coDSpace UniSimonbibliotecas@biteca.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 |