Estudio de la Isotopología de Tsagas-Sourlas-Santilli

Since his original proposal of 1978 to study Lie-isotopic and Lie-admissible liftings of conventional, local-differential Hamiltonian formulations of point particles, the physicist R. M. Santilli suggested the contribution of a new topology as the mathematical foundations for the representation of e...

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Autores: Falcón Ganfornina, Raúl Manuel, Núñez Valdés, Juan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2003
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/69117
Acceso en línea:https://hdl.handle.net/11441/69117
Access Level:acceso abierto
Palabra clave:Isotería de Santilli
Isotopía
Isotopología
Isocontinuidad
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spelling Estudio de la Isotopología de Tsagas-Sourlas-SantilliFalcón Ganfornina, Raúl ManuelNúñez Valdés, JuanIsotería de SantilliIsotopíaIsotopologíaIsocontinuidadSince his original proposal of 1978 to study Lie-isotopic and Lie-admissible liftings of conventional, local-differential Hamiltonian formulations of point particles, the physicist R. M. Santilli suggested the contribution of a new topology as the mathematical foundations for the representation of extended, nonspherical and deformable particles with conventional local-differential interaction plus new nonlocal-integral interation as occurring, for instance, in molecular valence bonds. A first isotopic lifting of the conventional continuity was introduced by the physicist J. V. Kadeisvili in 1992. In 1993 the mathematicians G. T. Tsagas and D. S. Sourlas built the topology proposed by Santilli within the context of isotopic mathematics defined over fields of conventional numbers. In the same year, Santilli constructed the fields isonumbers, namely numbers with a positive-definite but otherwise arbitrary multiplicative unit. As a necesary condition to achieve invariance of isotopic formulations under the action of their own time evolution group, Santilli extended in 1996 the topology of Tsagas and Sourlas to isofields whose unit is a sufficiently smooth and positive definite, but arbitrary integro-differential expression representing extended particles with local-differential and nonlocal-integral interations. This memoir is dedicated to the aparently first, comprehensive mathematical study and generalization of the Tsagas-Sourlas-Santilli isotopology and includes: a generalization of the Kadeisvili's isocontinuity; the identification of the broadest possible isofields and isomanifolds; the systematic study of the broadest possible isotopology; and other topics. It is hoped that the isotopology emerging from this study does indeed fulfill Santilli's original suggestion of constituting the foundations of mathematical, physical and chemical studies on isotopic representations of extended, nonspherical and deformable particles with local-differential and nonlocal-integral interactions.En 1993, Tsagas y Sourlas definieron una isotopología en el caso en el que la proyección de un levantado isotópico de los números reales en el nivel convencional no coincida con dicho conjunto, es decir, en el caso en que se está trabajando con un isocuerpo de los denominado por Santilli de primer tipo. el propio Santilli también trató, en 1996, el caso de una isotopología para los llamados isocuerpos de segundo tipo. El objetivo principal de este artículo es profundizar en el estudio de esta segunda construcción, teniendo en cuenta los trabajados mencionados anteriormente de Tsagas, Sourlas y Santilli. Hemos optado para ello por definir un isoorden en el isocuerpo construido y realizar una generalización de la isocontinuidad de Kadeisvili para icuerpos de segundo tipo.Hadronic PressMatemática Aplicada IGeometría y Topología2003info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/69117reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)EspañolAlgebras, Groups and Geometries, 20 (1), 1-100.info:eu-repo/semantics/openAccessoai:idus.us.es:11441/691172026-06-17T12:51:07Z
dc.title.none.fl_str_mv Estudio de la Isotopología de Tsagas-Sourlas-Santilli
title Estudio de la Isotopología de Tsagas-Sourlas-Santilli
spellingShingle Estudio de la Isotopología de Tsagas-Sourlas-Santilli
Falcón Ganfornina, Raúl Manuel
Isotería de Santilli
Isotopía
Isotopología
Isocontinuidad
title_short Estudio de la Isotopología de Tsagas-Sourlas-Santilli
title_full Estudio de la Isotopología de Tsagas-Sourlas-Santilli
title_fullStr Estudio de la Isotopología de Tsagas-Sourlas-Santilli
title_full_unstemmed Estudio de la Isotopología de Tsagas-Sourlas-Santilli
title_sort Estudio de la Isotopología de Tsagas-Sourlas-Santilli
dc.creator.none.fl_str_mv Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
author Falcón Ganfornina, Raúl Manuel
author_facet Falcón Ganfornina, Raúl Manuel
Núñez Valdés, Juan
author_role author
author2 Núñez Valdés, Juan
author2_role author
dc.contributor.none.fl_str_mv Matemática Aplicada I
Geometría y Topología
dc.subject.none.fl_str_mv Isotería de Santilli
Isotopía
Isotopología
Isocontinuidad
topic Isotería de Santilli
Isotopía
Isotopología
Isocontinuidad
description Since his original proposal of 1978 to study Lie-isotopic and Lie-admissible liftings of conventional, local-differential Hamiltonian formulations of point particles, the physicist R. M. Santilli suggested the contribution of a new topology as the mathematical foundations for the representation of extended, nonspherical and deformable particles with conventional local-differential interaction plus new nonlocal-integral interation as occurring, for instance, in molecular valence bonds. A first isotopic lifting of the conventional continuity was introduced by the physicist J. V. Kadeisvili in 1992. In 1993 the mathematicians G. T. Tsagas and D. S. Sourlas built the topology proposed by Santilli within the context of isotopic mathematics defined over fields of conventional numbers. In the same year, Santilli constructed the fields isonumbers, namely numbers with a positive-definite but otherwise arbitrary multiplicative unit. As a necesary condition to achieve invariance of isotopic formulations under the action of their own time evolution group, Santilli extended in 1996 the topology of Tsagas and Sourlas to isofields whose unit is a sufficiently smooth and positive definite, but arbitrary integro-differential expression representing extended particles with local-differential and nonlocal-integral interations. This memoir is dedicated to the aparently first, comprehensive mathematical study and generalization of the Tsagas-Sourlas-Santilli isotopology and includes: a generalization of the Kadeisvili's isocontinuity; the identification of the broadest possible isofields and isomanifolds; the systematic study of the broadest possible isotopology; and other topics. It is hoped that the isotopology emerging from this study does indeed fulfill Santilli's original suggestion of constituting the foundations of mathematical, physical and chemical studies on isotopic representations of extended, nonspherical and deformable particles with local-differential and nonlocal-integral interactions.
publishDate 2003
dc.date.none.fl_str_mv 2003
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/69117
url https://hdl.handle.net/11441/69117
dc.language.none.fl_str_mv Español
language_invalid_str_mv Español
dc.relation.none.fl_str_mv Algebras, Groups and Geometries, 20 (1), 1-100.
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Hadronic Press
publisher.none.fl_str_mv Hadronic Press
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
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