Matemática

URI permanente para esta colección

https://hdl.handle.net/10669/15621

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Examinando Matemática por Tipo "artículo original"

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  • Miniatura
    Ítem
    Geometric goodness of fit measure to detect patterns in data point clouds
    (2022-06-23) Hernández Alvarado, Alberto José; Solís Chacón, Maikol
    In this work, we derive a geometric goodness-of-fit index similar to R2 using geomet- ric data analysis techniques. We build the alpha shape complex from the data-cloud projected onto each variable and estimate the area of the complex and its domain. We create an index that measures the difference of area between the alpha shape and the smallest squared window of observation containing the data. By applying ideas similar to those found in the closest neighbor distribution and empty space distribu- tion functions, we can establish when the characterizing geometric features of the point set emerge. This allows for a more precise application for our index. We pro- vide some examples with anomalous patterns to show how our algorithm performs.
  • Miniatura
    Ítem
    Minimum depth of factorization algebra extensions
    (2023) Hernández Alvarado, Alberto José
    In this paper we study the minimum depth of a subalgebra embedded in a factorization algebra, and outline how subring depth, in this context, is related to module depth of the regular left module representation of the given subalgebra, within the appropriate module ring. As a consequence, we produce specific results for subring depth of a Hopf subalgebra in its Drinfel'd double. Moreover we study a necessary and sufficient condition for normality of a Hopf algebra within a double cross product context, which is equivalent to depth 2, as it is well known by a result of Kadison. Using the sufficient condition, we then prove some results regarding minimum depth 2 for Drinfel'd double Hopf subalgebra pairs, particularly in the case of finite group algebras. Finally, we provide formulas for the centralizer of a normal Hopf subalgebra in a double cross product scenario.