A refinement of the gauss-lucas theorem
Autor(a) principal: | |
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Data de Publicação: | 1998 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1090/S0002-9939-98-04381-0 http://hdl.handle.net/11449/65595 |
Resumo: | The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society. |
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Repositório Institucional da UNESP |
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2946 |
spelling |
A refinement of the gauss-lucas theoremNontrivial critical point of a polynomialThe classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.Departamento de CiêNcias de ComputaçÀO E EstatíStica Universidade Estadual Paulista, 15054-000 SãO José, Do Rio Preto, SPDepartamento de CiêNcias de ComputaçÀO E EstatíStica Universidade Estadual Paulista, 15054-000 SãO José, Do Rio Preto, SPUniversidade Estadual Paulista (Unesp)Dimitrov, Dimitar K. [UNESP]2014-05-27T11:19:39Z2014-05-27T11:19:39Z1998-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2065-2070application/pdfhttp://dx.doi.org/10.1090/S0002-9939-98-04381-0Proceedings of the American Mathematical Society, v. 126, n. 7, p. 2065-2070, 1998.0002-9939http://hdl.handle.net/11449/6559510.1090/S0002-9939-98-04381-0WOS:0000746942000252-s2.0-220444408222-s2.0-22044440822.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the American Mathematical Society0.7071,183info:eu-repo/semantics/openAccess2024-01-12T06:25:04Zoai:repositorio.unesp.br:11449/65595Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:45:25.020182Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A refinement of the gauss-lucas theorem |
title |
A refinement of the gauss-lucas theorem |
spellingShingle |
A refinement of the gauss-lucas theorem Dimitrov, Dimitar K. [UNESP] Nontrivial critical point of a polynomial |
title_short |
A refinement of the gauss-lucas theorem |
title_full |
A refinement of the gauss-lucas theorem |
title_fullStr |
A refinement of the gauss-lucas theorem |
title_full_unstemmed |
A refinement of the gauss-lucas theorem |
title_sort |
A refinement of the gauss-lucas theorem |
author |
Dimitrov, Dimitar K. [UNESP] |
author_facet |
Dimitrov, Dimitar K. [UNESP] |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Dimitrov, Dimitar K. [UNESP] |
dc.subject.por.fl_str_mv |
Nontrivial critical point of a polynomial |
topic |
Nontrivial critical point of a polynomial |
description |
The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society. |
publishDate |
1998 |
dc.date.none.fl_str_mv |
1998-12-01 2014-05-27T11:19:39Z 2014-05-27T11:19:39Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1090/S0002-9939-98-04381-0 Proceedings of the American Mathematical Society, v. 126, n. 7, p. 2065-2070, 1998. 0002-9939 http://hdl.handle.net/11449/65595 10.1090/S0002-9939-98-04381-0 WOS:000074694200025 2-s2.0-22044440822 2-s2.0-22044440822.pdf |
url |
http://dx.doi.org/10.1090/S0002-9939-98-04381-0 http://hdl.handle.net/11449/65595 |
identifier_str_mv |
Proceedings of the American Mathematical Society, v. 126, n. 7, p. 2065-2070, 1998. 0002-9939 10.1090/S0002-9939-98-04381-0 WOS:000074694200025 2-s2.0-22044440822 2-s2.0-22044440822.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings of the American Mathematical Society 0.707 1,183 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
2065-2070 application/pdf |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129459429048320 |