Departamento de Matematicas

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http://repositorioabierto.uantof.cl/handle/uantof/222

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    Geogebra in the visualization of integrating factors in non-exact differential equations
    (2024) Jorge Olivares; P. Martin; E. Valero
    In the present work, integrating factors used in the solution of non-exact differential equations will be shown with general examples through software application of dynamic geometry GeoGebra. Now these applets are part of theteaching support material in the eigineering careers of the University of Antofagasta on 2020.
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    GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations
    (2024) Nicolás Murúa; Aníbal Coronel; Alex Tello; Stefan Berres; Fernando Huancas
    In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently.
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    New Spectral Results for Laplacian Harary Matrix and the HararyLaplacian-Energy-like Applying a Matrix Order Reduction
    (2024) Luis Medina; Jonnathan Rodríguez; Macarena Trigo
    In this paper, we introduce the concepts of Harary Laplacian-energy-like for a simple undirected and connected graph Gwith ordern. We also establish novel matrix results in this regard.Furthermore, by employing matrix order reduction techniques, we derive upper and lower bounds utilizing existing graph invariants and vertex connectivity. Finally, we characterize the graphs that achieve the aforementioned bounds by considering the generalized join operation of graphs.
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    Observational cross-sectional study of Trichomonas tenax in patients with periodontal disease attending a Chilean university dental clinic
    (2019) Casandra Bracamonte Wolf; Patricio R. Orrego; Christian Muñoz; Daniel Herrera; Joel Bravo; Jorge Gonzalez; Héctor Varela; Alejandro Catalán; Jorge E. Araya
    Background: The oral flagellated protozoan Trichomonas tenax has been associated with patients with periodontal disease. However, no recent studies have been conducted on the prevalence of T. tenax in Chile. The aim of this study was to determine the presence of T. tenax in patients with periodontal disease, admitted to the Dental Clinic of the University of Antofagasta, Chile, through Polymerase Chain Reaction (PCR) amplification of the beta-tubulin gene. Methods: An observational, cross-sectional study was conducted on 50 patients diagnosed with periodontal disease, 20 of them with gingivitis and 30 with periodontitis. T. tenax was identified by PCR amplification of the beta-tubulin gene. Associations between the protozoan and periodontal disease or the presence of risk factors to establish T. tenax infection were determined using the chi-square test and binary logistic regression analysis. Results: T. tenax was present in 28 out of 50 (56%) of patients with periodontal disease, and was more prevalent when associated with periodontitis (21 out of 30; 70%) than dental plaque-induced gingivitis (7 out of 20; 35%). Non-statistically-significant associations were observed between the presence of T. tenax and age, gender, smoking habit or diabetes. Statistically significant associations were observed between the presence of T. tenax and periodontal disease, and between T. tenax and the Periodontal Screening and Recording (PSR) index. Conclusion: T. tenax showed a high presence in patients with progressive states of periodontal diseases. Consequently, T. tenax detection is strongly recommended in patients with periodontal disease diagnosis and with a PSR index greater than 3.
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    Realization of Extremal Spectral Data by Pentadiagonal Matrices
    (2024) Hubert Pickmann-Soto; Susana Arela-Pérez; Charlie Lozano; Hans Nina
    In this paper, we address the extremal inverse eigenvalue problem for pentadiagonal matri-ces. We provide sufficient conditions for their existence and realizability through new constructions that consider spectral data of its leading principal submatrices. Finally, we present some examples generated from the algorithmic procedures derived from our results.
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    Semigroup theory and nite element method applied to a non-linear dissipative wave equation
    (2024) Gino Chavez; Luis Cortes Vega; Adrián Sotomayor
    We study the wave equation with a non-linear dissipative term associated to a bidimensional membrane with xed boundary. We use the semigroup theory to consider the existence and uniqueness of solutions to the problem and we implement the nite element method to analyse the vibrating evolutionary equation. In particular we use Comsol Multiphysics software with a rectangular mesh to analyze the corresponding evolutionary system. We mention that this system can appear, for example, in the diaphragm of a centrifugal pump in mining processes.