The centered hausdorff measure of the Sierpiński gasket

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dc.contributor.authorMera Rivas, María Eugenia
dc.contributor.authorMorán Cabré, Manuel
dc.contributor.authorLlorente Comi, Marta
dc.date.accessioned2024-01-24T09:19:14Z
dc.date.available2024-01-24T09:19:14Z
dc.date.issued2023
dc.description.abstractWe show that the centered Hausdorff measure, Cs(S), with s=log3log2, of the Sierpiński gasket S, is C-computable (continuous-computable), in the sense that its value is the solution of the minimization problem of a continuous function on a compact domain. We also show that Cs(S) is A-computable (algorithmic-computable) in the sense that there is an algorithm that converges to Cs(S), with explicit error bounds. Using this algorithm we show that Cs(S)∼1.0049.en
dc.description.departmentDepto. de Análisis Económico y Economía Cuantitativa
dc.description.facultyFac. de Ciencias Económicas y Empresariales
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.sponsorshipUniversidad Complutense de Madrid
dc.description.statuspub
dc.identifier.citationLlorente, Marta, María Eugenia Mera, y Manuel Morán. «THE CENTERED HAUSDORFF MEASURE OF THE SIERPIŃSKI GASKET». Fractals 31, n.o 09 (enero de 2023): 2350107. https://doi.org/10.1142/S0218348X23501074.
dc.identifier.doi10.1142/s0218348x23501074
dc.identifier.essn1793-6543
dc.identifier.issn0218-348X
dc.identifier.officialurlhttps://doi.org/10.1142/s0218348x23501074
dc.identifier.relatedurlhttps://www.worldscientific.com/worldscinet/fractals
dc.identifier.urihttps://hdl.handle.net/20.500.14352/94973
dc.issue.number9
dc.journal.titleFractals. Complex Geometry, Patterns, and Scaling in Nature and Society
dc.language.isoeng
dc.publisherWorld Scientific
dc.relation.projectIDinfo:eu-repo/grantAgreement/UCM//PR108/20-14
dc.rights.accessRightsopen access
dc.subject.cdu5
dc.subject.keywordSierpiński Gasket
dc.subject.keywordHausdorff Measures
dc.subject.keywordDensity of Measures
dc.subject.keywordComputability of Fractal Measures
dc.subject.ucmCiencias
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmAnálisis matemático
dc.subject.ucmGeometría
dc.subject.ucmAnálisis numérico
dc.subject.unesco12 Matemáticas
dc.subject.unesco1204 Geometría
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleThe centered hausdorff measure of the Sierpiński gasket
dc.title.alternativeLa medida centrada del triángulo de Sierpinski
dc.typejournal article
dc.type.hasVersionAM
dc.volume.number31
dspace.entity.typePublication
relation.isAuthorOfPublication71245121-5334-43ae-92e3-eb84a42790e8
relation.isAuthorOfPublication36e295dc-70b7-4ede-868c-a83357a04413
relation.isAuthorOfPublication3dcd5ee5-5b89-4791-a0c5-0e742ca856ee
relation.isAuthorOfPublication.latestForDiscovery71245121-5334-43ae-92e3-eb84a42790e8

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