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Generalización de notación asintótica vía filtros

dc.contributor.advisorSalas Brown, Margot del Valle
dc.creatorLópez Chacón, Ana Valentina
dc.creator.degreeProfesional en Matemáticas Aplicadas y Ciencias de la Computación
dc.creator.degreetypeFull time
dc.descriptionEn este documento, proporcionamos una generalización de la notación asintótica mediante la estructura topológica conocida como filtro. Presentamos algunas propiedades relevantes, como reflexividad, simetría y transitividad, junto con ejemplos adecuados para exhibir el amplio alcance de esta nueva noción. Además, se demuestra que la definición habitual de notaciones asintóticas implica la generalizada por filtros, y presentamos diferentes ejemplos para asegurar que la afirmación recíproca no es válida. Además, proponemos una caracterización de las notaciones asintóticas usuales en términos de filtros. Finalmente, establecemos una relación entre sucesiones acotadas o convergentes a cero y notaciones asintóticas en filtros, que nos permiten determinar algunas propiedades de los temas tratados en este estudio
dc.description.abstractWithin this document, we provide a generalization of asymptotic notation by the topological structure known as a filter. We present a few relevant properties, such as reflexivity, symmetry, and transitivity, along with suitable examples to exhibit the wide reach of this new notion. Additionally, it is shown that the usual definition of asymptotic notations implies the one generalized by filters, and we present different examples in order to ensure that the reciprocal statement is not valid. Furthermore, we propose a characterization of the usual asymptotic notations in terms of filters. Finally, we established a relationship between bounded or vanishing sequences and asymptotic notations in filters, which allowed us to determine some properties of the subjects discussed in this study
dc.format.extent64 pp
dc.publisherUniversidad del Rosario
dc.publisher.departmentEscuela de Ingeniería, Ciencia y Tecnología
dc.publisher.programPrograma de Matemáticas Aplicadas y Ciencias de la Computación - MACC
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 International*
dc.rights.accesoAbierto (Texto Completo)
dc.source.bibliographicCitationAkin, E. (1997). Recurrence in topological dynamics. Furstenberg families and Ellis actions, The University Series in Mathematics, Plenum Press, New York, 1997.
dc.source.bibliographicCitationAkomolafe, D. T. Nwanz, N. M. (2021). Deployment of an efficient algorithm for searching motor vehicle database, Asian Journal of Advances in Research, 18-26.
dc.source.bibliographicCitationBenzmüller, C. Fuenmayor, D. (2019). Computer-supported Analysis of Positiive Properties, Ultrafilters and Modal Collapse in Variants of Gödel’s Ontological Argument. Bulletin of the Section of Logic, 49(2), 127-148.
dc.source.bibliographicCitationBernstein, A. R. (1970). A new kind of compactness for topological spaces, Fund. Math. 66, 185-193.
dc.source.bibliographicCitationBourbaki, N. (1966). Elements of Mathematics, General Topology, Part I, AddisonWesley Pub. Co.
dc.source.bibliographicCitationBrassard, G. (1985). Crusade for a better notation, ACM SIGACT News, vol. 17, no. 1, pp. 60–64.
dc.source.bibliographicCitationCartan, H. (1937). Théorie des filtres. Rend, 205, 595-598.
dc.source.bibliographicCitationCartan, H. (1937). Filters et ultrafilters, Compt. Rend, 205, 777-779.
dc.source.bibliographicCitationConnor, J. Kline, J. (1996). On statistical limit points and the consistency of statistical convergence. Journal of mathematical analysis and applications, 197(2), 392-399.
dc.source.bibliographicCitationCormen, T. H. Leiserson, C. E. Rivest, R. L. Stein, C. (2009). Introduction to algorithms. MIT press.
dc.source.bibliographicCitationEhrig, H. Herrlich, H. Kreowski, H. J. Preuß, G. (Eds.). (1989). Categorical methods in computer science: with aspects from topology (Vol. 393). Springer Science Business Media.
dc.source.bibliographicCitationFolea, R. Slusanschi, E. I. (2021). A new metric for evaluating the performance and complexity of computer programs: A new approach to the traditional ways of measuring the complexity of algorithms and estimating running times. In 2021 23rd International Conference on Control Systems and Computer Science (CSCS) (pp. 157-164). IEEE.
dc.source.bibliographicCitationFrolík, Z. (1967). Sums of ultrafilters, Bull. Amer. Math. Soc. 73 , 87-91.
dc.source.bibliographicCitationFurstenberg, H. (1981). Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press.
dc.source.bibliographicCitationGoldreich, O. (2008). Computational complexity: a conceptual perspective. ACM Sigact News, 39(3), 35-39.
dc.source.bibliographicCitationGuevara, A. Sanabria, J. Rosas, E. (2020). SI-convergence of sequences. Trans. A. Razmadze Math. Inst, 174(1), 75-81.
dc.source.bibliographicCitationKostyrko, P. Šalát, T. Wilczyński, W. (2000). I-convergence∗. Real analysis exchange, 669-685.
dc.source.bibliographicCitationKuratowski, K. (1933). Topologies I. Warszawa
dc.source.bibliographicCitationMogos, A. H. Florea, A. M. (2010). A method to compare two complexity functions using complexity classes. University"Politehnica.of Bucharest Scientific Bulletin, Series A: Applied Mathematics and Physics, 72(2), 69-84.
dc.source.bibliographicCitationMogoş, A. H. Mogoş, B. Florea, A. M. (2015). A new asymptotic notation: Weak Theta. Mathematical Problems in Engineering.
dc.source.bibliographicCitationLim, T. S. Loh, W. Y. Shih, Y. S. (2000). A comparison of prediction accuracy, complexity, and training time of thirty-three old and new classification algorithms. Machine learning, 40(3), 203-228.
dc.source.bibliographicCitationRamesh, V. P. Gowtham, R. (2017). Asymptotic notations and its applications, Ramanujan Math. Soc., Math. News, 28 (4) , 10–16.
dc.source.bibliographicCitationRussell, S. J. (2010). Artificial intelligence a modern approach. Pearson Education, Inc.
dc.source.bibliographicCitationThomas, C. Leiserson, C. E. Stein, C. (2009). Introduction to Algorithms, 3rd.
dc.source.bibliographicCitationVan Leeuwen, J. (1991). Handbook of theoretical computer science (vol. A) algorithms and complexity. Mit Press.
dc.source.instnameinstname:Universidad del Rosario
dc.source.reponamereponame:Repositorio Institucional EdocUR
dc.subjectNotación asintótica
dc.subjectEspacio topológico
dc.subjectSucesión convergente
dc.subjectSucesión acotada
dc.subject.keywordAsymptotic notation
dc.subject.keywordTopological space
dc.subject.keywordConvergent sequence
dc.subject.keywordBounded sequence
dc.titleGeneralización de notación asintótica vía filtros
dc.title.TranslatedTitleGeneralization of asymptotic notation via filters
dc.type.documentTrabajo de grado
dc.type.spaTrabajo de grado
local.department.reportEscuela de Ingeniería, Ciencia y Tecnología
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