Matemáticas
URI permanente para esta colecciónhttp://hdl.handle.net/11349/48
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Ítem Integrales de Henstock-Kurzweil, espacios de Sobolev y algunas aplicacionesBlanco Cano, Sebastian Camilo; Ramos Fernández, Julio CésarIn this paper a study of the most relevant properties of the HK integral and of the HK-Sobolev spaces defined in the recent paper by Pérez-Becerra et al. It is shown that the definite integral for functions in these spaces fulfills the same characteristics as Riemann-integrable functions, such as, for example, a fundamental theorem of calculus and a formula for integration by parts. Then, the existence and uniqueness of solutions for a boundary value problem in these spaces is proved.Ítem Superficies mínimasBogotá Mora, Maicol Stiven; Sanjuan Cuellar, Alvaro ArturoIn the present work, we will study some basic properties of the minimum surfaces in R^3, through concepts of geometry, variational calculus, and complex variables among others. In this way, we will make a brief introduction to the classical theory of minimal surfaces, in particular, what is related to the Enneper-Weierstrass Representation Theorem and the Bjorling problem.Ítem Un problema de demografía modelado por una ecuación de Mckendrick - Von FoersterLeón Hernández, Manuel Andrey; Nieto Huertas, Danna Katherine; Sanjuán Cuellar, Álvaro Arturo; Sanjuán Cuellar, Álvaro Arturo [0000-0002-0309-8299]In this monograph we will study an age-structured model of poblational dynamic that arises in the papers of McKendrick retaken by Von Foester. In this model we have a function of age distribution, the mortality rate and the offspring rate of the population. The most interesting thing about this model is its boundary condition because it's depending on the unknown solution. Under certain conditions the model could be solved through the method of the characteristics. This will take us to consider the border condition as a Non-homogenous Volterra integral equation called renewal equation. We will show that Volterra integral equation has an only solution and we will study it throughout approaches using Neumman series, to apply it and obtain the age structure for the population according to the renewal equation.Ítem Construcción funcional de SadowskyRíos Cristancho, José David; Ovalle Velandia, María Valentina; Sanjuan Cuellar, Alvaro ArturoIn this work we will study that thin rectangular strips defined as configurations that minimize the energy of the Sadowsky functional for narrow elastic strips that are developable, are prone to build spherical shapes. in the sense that the forceless solutions lie on a sphere. This has implications for ribbon-shaped objects. We also address the relationship that the Sadowsky functional has with the principal curvatureÍtem Implementación de algunos modelos analíticos y estadísticos para la validación del correcto reporte de información en cuentas maestrasSánchez Rodríguez, Natalia; Villarraga Poveda, Luis FernandoThis degree work will focus on the illustration of the internship developed during the period 2022 − 1, in the Master Accounts team belonging to group 028 of the Subdirectorate of Support for territorial fiscal consolidation of the General Directorate of Fiscal Support (DAF) of the Ministry of Finance and Public Credit. Where the focus was oriented towards the structuring of the new banking information reporting system for Master Accounts and Master Paying Accounts; and also to the review of reprocessing documents of Master Paying Accounts.Ítem Modelos de mezclas Gaussianas como clasificadores en el contexto de machine learningMartinez Castillo, Daniel Stiven; Másmela Caita, Luis AlejandroIn this document I study of Gaussian mixture models. Specifically, an analysis of its mathematical structure, its interpretation and a classic method of estimating its parameters, the Expectation-Maximization algorithm known in the literature by its acronym as EM algorithm. The theory presented is illustrated through the use of the data set "Rice_MSC_Dataset", for this, the "mclust" package is implemented in the R software.