Derivadas deformadas e aplica??es

Detalhes bibliográficos
Autor(a) principal: Rosa, Wanderson
Data de Publicação: 2019
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Biblioteca Digital de Teses e Dissertações da UFRRJ
Texto Completo: https://tede.ufrrj.br/jspui/handle/jspui/5263
Resumo: In the last decades, several formalisms have been used to describe complex systems. Among them, the fractional calculation and the deformed derivatives can be mentioned. Both showed positive results in the modeling of complex systems. However, the fractional calculation is defined from non-local operators and, therefore, does not satisfy some prop-erties of the usual derivatives; such as the product rule and the chain rule. The deformed derivatives are local operators and are presented as a pre-factor multiplied by a usual derivative. In the case of a deformation in the space of variables, this pre-factor depends on the independent variable and a deformation parameter. If the deformation is in the space of the functions the pre-factor will be dependent on the function being derived and the parameter of deformation. The operators generated in these two cases are dual to each other. The operators generated in the first case have a connection with the Hausdor? derivative, with the mapping in the continuous fractal and satisfy all the basic properties of the derivative. Here, these will be treated as deformed derivatives. The operators generated in the second case will be treated as dual deformed derivatives. In this work will be proposed formalisms of deformed calculation. As a starting point a generalized operator of deformed derivative and two of its particular cases will be taken, as well as the dual forms thereof. Derivatives, integrals, and deformed functions will be proposed, and then deformed variational approaches will be proposed. Finally, applications in both physics and other areas will be proposed from the deformed and deformed dual formalisms of calculation.
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spelling Weberszpil, Jos?CPF: 753.142.407-00Dias, Cl?udia MazzaCPF: 009.112.477-85Vera-Tudella, Carlos Andr?s ReynaHelay?l-Neto, Jos? AbdallaCPF: 118.623.287-06http://lattes.cnpq.br/1720101795275087Rosa, Wanderson2021-11-24T22:54:33Z2019-08-26ROSA, Wanderson. Derivadas deformadas e aplica??es. 2019. 123 f. Disserta??o (Mestrado em Modelagem Matem?tica e Computacional) - Instituto de Ci?ncias Exatas, Universidade Federal Rural do Rio de Janeiro, Serop?dica, 2019.https://tede.ufrrj.br/jspui/handle/jspui/5263In the last decades, several formalisms have been used to describe complex systems. Among them, the fractional calculation and the deformed derivatives can be mentioned. Both showed positive results in the modeling of complex systems. However, the fractional calculation is defined from non-local operators and, therefore, does not satisfy some prop-erties of the usual derivatives; such as the product rule and the chain rule. The deformed derivatives are local operators and are presented as a pre-factor multiplied by a usual derivative. In the case of a deformation in the space of variables, this pre-factor depends on the independent variable and a deformation parameter. If the deformation is in the space of the functions the pre-factor will be dependent on the function being derived and the parameter of deformation. The operators generated in these two cases are dual to each other. The operators generated in the first case have a connection with the Hausdor? derivative, with the mapping in the continuous fractal and satisfy all the basic properties of the derivative. Here, these will be treated as deformed derivatives. The operators generated in the second case will be treated as dual deformed derivatives. In this work will be proposed formalisms of deformed calculation. As a starting point a generalized operator of deformed derivative and two of its particular cases will be taken, as well as the dual forms thereof. Derivatives, integrals, and deformed functions will be proposed, and then deformed variational approaches will be proposed. Finally, applications in both physics and other areas will be proposed from the deformed and deformed dual formalisms of calculation.Nas ?ltimas d?cadas, diversos formalismos foram usados para descrever sistemas complexos. Dentre os quais, podem ser citados o c?lculo fracion?rio e as derivadas defor-madas. Ambos mostraram resultados positivos na modelagem de sistemas complexos. No entanto, o c?lculo fracion?rio ? definido a partir de operadores n?o locais e, portanto, n?o satisfaz algumas propriedades das derivadas usuais; como, por exemplo, a regra do pro-duto e a regra da cadeia. As derivadas deformadas s?o operadores locais e se apresentam como um pr?-fator multiplicado por uma derivada usual. No caso de uma deforma??o no espa?o das vari?veis, este pr?-fator depende da vari?vel independente e de um par?metro de deforma??o. Se a deforma??o for no espa?o das fun??es o pr?-fator ser? dependente da fun??o que est? sendo derivada e do par?metro de deforma??o. Os operadores gerados nesses dois casos s?o duais entre si. Os operadores gerados no primeiro caso tem conex?o com a derivada de Hausdor?, com o mapeamento no fractal continuo e satisfazem todas as propriedades b?sicas de derivada. Aqui, estes ser?o tratados como derivadas deformadas. Os operadores gerados no segundo caso ser?o tratados como derivadas deformadas duais. Neste trabalho ser?o propostos formalismos de c?lculo deformado. Como ponto de par-tida ser? tomado um operador generalizado de derivada deformada e de dois de seus casos particulares, bem como as formas duais dos mesmos. Ser?o propostas derivadas, integrais e fun??es deformadas e ap?s isso ser?o propostas abordagens variacionais deformadas. Por fim, aplica??es tanto em f?sica quanto em outras ?reas ser?o propostas a partir dos formalismos de c?lculo deformado e deformados duais.Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2021-11-24T22:54:33Z No. of bitstreams: 1 2019 - Wanderson Rosa.pdf: 1632619 bytes, checksum: 2f449ffe0f1fb5cb9ee8c5851922648f (MD5)Made available in DSpace on 2021-11-24T22:54:33Z (GMT). No. of bitstreams: 1 2019 - Wanderson Rosa.pdf: 1632619 bytes, checksum: 2f449ffe0f1fb5cb9ee8c5851922648f (MD5) Previous issue date: 2019-08-26CAPES - Coordena??o de Aperfei?oamento de Pessoal de N?vel Superiorapplication/pdfhttps://tede.ufrrj.br/retrieve/67668/2019%20-%20Wanderson%20Rosa.pdf.jpgporUniversidade Federal Rural do Rio de JaneiroPrograma de P?s-Gradua??o em Modelagem Matem?tica e ComputacionalUFRRJBrasilInstituto de Ci?ncias ExatasASANO, C. H.; COLLI, E. C?lculo num?rico-fundamentos e aplica??es. Departamento de Matem?tica Aplicada, IME-USP, 2009. ASSIS, T. A. d. et al. 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Calcolo, Springer, v. 54, n. 3, p. 903?917, 2017.Derivadas DeformadasM?todo Variacional DeformadoDerivadas DuaisDeformed DerivativesDeformed Variational MethodsDual DerivativesCi?ncia da Computa??oMatem?ticaDerivadas deformadas e aplica??esDeformed derivatives and some applicationsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UFRRJinstname:Universidade Federal Rural do Rio de Janeiro (UFRRJ)instacron:UFRRJTHUMBNAIL2019 - Wanderson Rosa.pdf.jpg2019 - Wanderson Rosa.pdf.jpgimage/jpeg3917http://localhost:8080/tede/bitstream/jspui/5263/4/2019+-+Wanderson+Rosa.pdf.jpg1f97bf4d6cb33654bb4f733635d51678MD54TEXT2019 - Wanderson Rosa.pdf.txt2019 - Wanderson Rosa.pdf.txttext/plain185225http://localhost:8080/tede/bitstream/jspui/5263/3/2019+-+Wanderson+Rosa.pdf.txt972609d1f86c35fc0d6a2f6e3ec9ef72MD53ORIGINAL2019 - Wanderson Rosa.pdf2019 - Wanderson Rosa.pdfapplication/pdf1632619http://localhost:8080/tede/bitstream/jspui/5263/2/2019+-+Wanderson+Rosa.pdf2f449ffe0f1fb5cb9ee8c5851922648fMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82089http://localhost:8080/tede/bitstream/jspui/5263/1/license.txt7b5ba3d2445355f386edab96125d42b7MD51jspui/52632021-11-25 02:00:41.862oai:localhost: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Biblioteca Digital de Teses e Dissertaçõeshttps://tede.ufrrj.br/PUBhttps://tede.ufrrj.br/oai/requestbibliot@ufrrj.br||bibliot@ufrrj.bropendoar:2021-11-25T04:00:41Biblioteca Digital de Teses e Dissertações da UFRRJ - Universidade Federal Rural do Rio de Janeiro (UFRRJ)false
dc.title.por.fl_str_mv Derivadas deformadas e aplica??es
dc.title.alternative.eng.fl_str_mv Deformed derivatives and some applications
title Derivadas deformadas e aplica??es
spellingShingle Derivadas deformadas e aplica??es
Rosa, Wanderson
Derivadas Deformadas
M?todo Variacional Deformado
Derivadas Duais
Deformed Derivatives
Deformed Variational Methods
Dual Derivatives
Ci?ncia da Computa??o
Matem?tica
title_short Derivadas deformadas e aplica??es
title_full Derivadas deformadas e aplica??es
title_fullStr Derivadas deformadas e aplica??es
title_full_unstemmed Derivadas deformadas e aplica??es
title_sort Derivadas deformadas e aplica??es
author Rosa, Wanderson
author_facet Rosa, Wanderson
author_role author
dc.contributor.advisor1.fl_str_mv Weberszpil, Jos?
dc.contributor.advisor1ID.fl_str_mv CPF: 753.142.407-00
dc.contributor.advisor-co1.fl_str_mv Dias, Cl?udia Mazza
dc.contributor.advisor-co1ID.fl_str_mv CPF: 009.112.477-85
dc.contributor.referee1.fl_str_mv Vera-Tudella, Carlos Andr?s Reyna
dc.contributor.referee2.fl_str_mv Helay?l-Neto, Jos? Abdalla
dc.contributor.authorID.fl_str_mv CPF: 118.623.287-06
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/1720101795275087
dc.contributor.author.fl_str_mv Rosa, Wanderson
contributor_str_mv Weberszpil, Jos?
Dias, Cl?udia Mazza
Vera-Tudella, Carlos Andr?s Reyna
Helay?l-Neto, Jos? Abdalla
dc.subject.por.fl_str_mv Derivadas Deformadas
M?todo Variacional Deformado
Derivadas Duais
topic Derivadas Deformadas
M?todo Variacional Deformado
Derivadas Duais
Deformed Derivatives
Deformed Variational Methods
Dual Derivatives
Ci?ncia da Computa??o
Matem?tica
dc.subject.eng.fl_str_mv Deformed Derivatives
Deformed Variational Methods
Dual Derivatives
dc.subject.cnpq.fl_str_mv Ci?ncia da Computa??o
Matem?tica
description In the last decades, several formalisms have been used to describe complex systems. Among them, the fractional calculation and the deformed derivatives can be mentioned. Both showed positive results in the modeling of complex systems. However, the fractional calculation is defined from non-local operators and, therefore, does not satisfy some prop-erties of the usual derivatives; such as the product rule and the chain rule. The deformed derivatives are local operators and are presented as a pre-factor multiplied by a usual derivative. In the case of a deformation in the space of variables, this pre-factor depends on the independent variable and a deformation parameter. If the deformation is in the space of the functions the pre-factor will be dependent on the function being derived and the parameter of deformation. The operators generated in these two cases are dual to each other. The operators generated in the first case have a connection with the Hausdor? derivative, with the mapping in the continuous fractal and satisfy all the basic properties of the derivative. Here, these will be treated as deformed derivatives. The operators generated in the second case will be treated as dual deformed derivatives. In this work will be proposed formalisms of deformed calculation. As a starting point a generalized operator of deformed derivative and two of its particular cases will be taken, as well as the dual forms thereof. Derivatives, integrals, and deformed functions will be proposed, and then deformed variational approaches will be proposed. Finally, applications in both physics and other areas will be proposed from the deformed and deformed dual formalisms of calculation.
publishDate 2019
dc.date.issued.fl_str_mv 2019-08-26
dc.date.accessioned.fl_str_mv 2021-11-24T22:54:33Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv ROSA, Wanderson. Derivadas deformadas e aplica??es. 2019. 123 f. Disserta??o (Mestrado em Modelagem Matem?tica e Computacional) - Instituto de Ci?ncias Exatas, Universidade Federal Rural do Rio de Janeiro, Serop?dica, 2019.
dc.identifier.uri.fl_str_mv https://tede.ufrrj.br/jspui/handle/jspui/5263
identifier_str_mv ROSA, Wanderson. Derivadas deformadas e aplica??es. 2019. 123 f. Disserta??o (Mestrado em Modelagem Matem?tica e Computacional) - Instituto de Ci?ncias Exatas, Universidade Federal Rural do Rio de Janeiro, Serop?dica, 2019.
url https://tede.ufrrj.br/jspui/handle/jspui/5263
dc.language.iso.fl_str_mv por
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