Instituto de Matemática

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    A look at generalized degenerate Bernoulli and Euler matrices
    (2023-06-16) Juan Hernández
    In this paper, we consider the generalized degenerate Bernoulli/Euler polynomial matrices and study some algebraic properties for them. In particular, we focus our attention on some matrix-inversion formulae involving these matrices. Furthermore, we provide analytic properties for the so-called generalized degenerate Pascal matrix of the first kind, and some factorizations for the generalized degenerate Euler polynomial matrix.
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    A Note on Soliltary Subgroups of Finite Groups,
    (2016-06-01) Orieta Liriano
    Decimos que un subgrupo H de un grupo finito G es solitario (respectivamente, solitario normal) cuando es un subgrupo (respectivamente, subgrupo normal) de G tal que ningún otro subgrupo (respectivamente, subgrupo normal) de G es isomorfo a H. Se dice que un subgrupo normal N de un grupo G es cociente solitario cuando ningún otro subgrupo normal K de G da un cociente isomorfo a G/N. Mostramos algunos resultados nuevos sobre las propiedades de red de estos subgrupos y su relación con las clases de grupos y presentamos ejemplos que muestran una respuesta negativa a algunas preguntas sobre estos subgrupos.
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    Algebra for the Initial training of Mathematics teachers at Universidad Autónoma of Santo Domingo
    (2018) Aury Rafael Pérez Cuevas
    This report deals with one of the problems that arise in the initial formation of Mathematics teachers at the Universidad Autónoma of Santo Domingo. Its main purpose is to characterize the educational process of Linear Algebra by making with emphasis on solving problems. The methods used were the historical-logical and the analysis-synthesis. Finally, the principal result was the accuracy of different theoretical approaches and the evolutionary stages of that process.
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    Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
    (2024-04-03) Carlos Féliz Sánchez
    Given a sequence of orthogonal polynomials {𝐿𝑛}∞𝑛=0, orthogonal with respect to a positive Borel 𝜈 measure supported on ℝ+, let {𝑄𝑛}∞𝑛=0 be the the sequence of orthogonal polynomials with respect to the modified measure 𝑟(𝑥)𝑑𝜈(𝑥), where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula 𝑄(𝑑)𝑛(𝑧)𝐿(𝑑)𝑛(𝑧)⇉𝑛∏𝑁1𝑘=1(𝑎𝑘√+𝑖𝑧√+𝑎𝑘√)𝐴𝑘∏𝑁2𝑗=1(𝑧√+𝑏𝑗√𝑏𝑗√+𝑖)𝐵𝑗, on compact subsets of ℂ∖ℝ+, where 𝑎𝑘 and 𝑏𝑗 are the zeros and poles of r, and the 𝐴𝑘, 𝐵𝑗 are their respective multiplicities.
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    Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself
    (2023-06-15) Elaine Segura
    In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results.
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    Behind Jarratt’s Steps: Is Jarratt’s Scheme the best version of itself?
    (2023-06-15) Elaine Segura
    In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results.
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    Combined matrices and conditioning
    (2021-08-12) Máximo Santana
    In this work, we study a lower bound of the condition number of a matrix by its combined matrix. In particular, we construct a special combined matrix in such a way that the sums of its columns are lower bounds of the condition number of the matrix. Cases for special matrices as unitary matrices are considered.
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    Combined matrices and conditioning, en la revista Applied Mathematics and Computation
    (2022-06-01) Máximo Santana
    In this work, we study a lower bound of the condition number of a matrix by its combined matrix. In particular, we construct a special combined matrix in such a way that the sums of its columns are lower bounds of the condition number of the matrix. Cases for special matrices as unitary matrices are considered.
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    Combined Matrices of Sign Regular Matrices,
    (2016-06) Máximo Santana
    La matriz combinada de una matriz no singular A es el producto Hadamard (entrada sabia) . Dado que cada fila y columna suma de es igual a uno, la matriz combinada es doblemente estocástica cuando no es negativa. En este trabajo, estudiamos la no agresividad de la matriz combinada de matrices regulares de signos, en función de su firma. En particular, algunas coordenadas de la firma ε de A desempeñar un papel crucial en la determinación de si o no no es negativo.
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    Combined matrix of diagonally equipotent matrices
    (2023-09-12) Máximo Santana
    Let (𝐴)=𝐴∘𝐴−𝑇 be the combined matrix of an invertible matrix 𝐴, where ∘ means the Hadamard product of matrices. In this work, we study the combined matrix of a nonsingular matrix, which is an 𝐻 -matrix whose comparison matrix is singular. In particular, we focus on (𝐴) when 𝐴 is diagonally equipotent, and we study whether(𝐴) is an 𝐻 -matrix and to which class it belongs. Moreover, we give some properties on the diagonal dominance of these matrices and on their comparison matrices.
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    Combined matrix of diagonally equipotent matrices
    (2023-12-23) Máximo Santana
    Let be the combined matrix of an invertible matrix A, where means the Hadamard product of matrices. In this work, we study the combined matrix of a nonsingular matrix, which is an H -matrix whose comparison matrix is singular. In particular, we focus on C (A) when A is diagonally equipotent, and we study whether C (A) is an H -matrix and to which class it belongs. Moreover, we give some properties on the diagonal dominance of these matrices and on their comparison matrices."
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    Conceptualización didáctica del desarrollo de la competencia modelar problemas de programación lineal en las carreras de ingeniería
    (2019-03-29) Juan Antonio Manzueta
    Los estudios en el área de la programación lineal han proliferado en la última década; no obstante, se denotan insuficiencias en el tratamiento didáctico de la modelación matemática en las carreras de ingeniería, lo que limita el desempeño de los estudiantes en la solución de problemas y sus aplicaciones. En respuesta a lo anterior se elaboró una conceptualización didáctica de desarrollo de la competencia modelar problemas de programación lineal desde el proceso de enseñanza-aprendizaje de las carreras de Ingeniería. De ese modo dicha elaboración sirve para develar la estructura de desarrollo de dicha competencia, sus desempeños y evidencias; así como de la lógica de su desarrollo connotándose la orientación hacia los precedentes generales de la modelación matemática, la contextualización didáctica de la modelación de problemas de programación lineal y de valoración didáctica de los desempeños, de cuya sinergia resulta la aprehensión sistematizada de dicho proceso, la cual expresa la esencia didáctica que condiciona y legitima el significado intrínseco y peculiar de la programación lineal. Para la elaboración del artículo fueron utilizados esencialmente métodos y técnicas de carácter teórico como el análisis-síntesis, la inducción-deducción y la concreción-abstracción, característicos de este tipo de estudio.
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    Convergence and stability of a new parametric class of iterative processes for nonlinear systems
    (2023-03-16) Antmel Rodríguez
    In this manuscript, we carry out a study on the generalization of a known family of multipoint scalar iterative processes for approximating the solutions of nonlinear systems. The convergence analysis of the proposed class under various smooth conditions is provided. We also study the stability of this family, analyzing the fixed and critical points of the rational operator resulting from applying the family on low-degree polynomials, as well as the basins of attraction and the orbits (periodic or not) that these points produce. This dynamical study also allows us to observe which members of the family are more stable and which have chaotic behavior. Graphical analyses of dynamical planes, parameter line and bifurcation planes are also studied. Numerical tests are performed on different nonlinear systems for checking the theoretical results and to compare the proposed schemes with other known ones.
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    Convergence and Stability of a New Parametric Class of Iterative Processes for Nonlinear Systems
    (2023-03-16) Antmel Rodríguez
    In this manuscript, we carry out a study on the generalization of a known family of multipoint scalar iterative processes for approximating the solutions of nonlinear systems. The convergence analysis of the proposed class under various smooth conditions is provided. We also study the stability of this family, analyzing the fixed and critical points of the rational operator resulting from applying the family on low-degree polynomials, as well as the basins of attraction and the orbits (periodic or not) that these points produce. This dynamical study also allows us to observe which members of the family are more stable and which have chaotic behavior. Graphical analyses of dynamical planes, parameter line and bifurcation planes are also studied. Numerical tests are performed on different nonlinear systems for checking the theoretical results and to compare the proposed schemes with other known ones.
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    Darboux transformations for orthogonal differential systems and differential Galois theory
    (2023-03-31) Primitivo Acosta
    Darboux developed an ingenious algebraic mechanism to construct infinite chains of “integrable’’ second-order differential equations as well as their solutions. After a surprisingly long time, Darboux’s results were rediscovered and applied in many frameworks, for instance in quantum mechanics (where they provide useful tools for supersymmetric quantum mechanics), in soliton theory, Lax pairs and many other fields involving hierarchies of equations. In this paper, we propose a method which allows us to generalize the Darboux transformations algorithmically for tensor product constructions on linear differential equations or systems. We obtain explicit Darboux transformations for third-order orthogonal systems (so(3,CK) systems) as well as a framework to extend Darboux transformations to any symmetric power of SL(2,C) -systems. We introduce SUSY toy models for these tensor products, giving as an illustration the analysis of some shape invariant potentials. All results in this paper have been implemented and tested in the computer algebra system Maple.
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    Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
    (2023) Primitivo Acosta
    Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprisingly long time, Darboux's results were rediscovered and applied in many frameworks, for instance in quantum mechanics (where they provide useful tools for supersymmetric quantum mechanics), in soliton theory, Lax pairs and many other fields involving hierarchies of equations. In this paper, we propose a method which allows us to generalize the Darboux transformations algorithmically for tensor product constructions on linear differential equations or systems. We obtain explicit Darboux transformations for third-order orthogonal systems (so(3,CK) systems) as well as a framework to extend Darboux transformations to any symmetric power of SL(2,C) -systems. We introduce SUSY toy models for these tensor products, giving as an illustration the analysis of some shape invariant potentials. All results in this paper have been implemented and tested in the computer algebra system Maple.
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    Desarrollo profesional del docente universitario de matemática en la República Dominicana
    (2022-10-28) Alicia Virginia Martín S.; Carmen Evarista Matías
    Objetivo: El artículo expone una síntesis del modelo teórico aportado para dirigir el proceso de desarrollo profesional de los docentes universitarios que imparten Matemática en República Dominicana. Métodos: Se empleó la revisión documental, los estudios lógicos e históricos y la modelación. Resultado: Se conformó un modelo teórico como marco de referencia para la dirección del desarrollo profesional del docente universitario que imparte Matemática y una estrategia pedagógica estructurada en tres fases que posibilita la concreción en la práctica de la propuesta teórica. Transformación, ISSN: 2077-2955, RNPS: 098, enero-abril 2023, 19 (1), 195-214 Universidad de Camagüey “Ignacio Agramonte Loynaz” 196 Conclusión: El modelo teórico y la estrategia pedagógica que viabiliza la dirección del desarrollo profesional, permiten garantizar transformaciones pertinentes y de calidad, acorde con las exigencias de la sociedad.
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    Desarrollo profesional del docente universitario de Matemática en la República Dominicana
    (2023) Alicia Virginia Martín; Carmen Evarista Matías
    "Objetivo: El artículo expone una síntesis del modelo teórico aportado para dirigir el proceso de desarrollo profesional de los docentes universitarios que imparten Matemática en República Dominicana. Métodos: Se empleó la revisión documental, los estudios lógicos e históricos y la modelación. Resultado: Se conformó un modelo teórico como marco de referencia para la dirección del desarrollo profesional del docente universitario que imparte Matemática y una estrategia pedagógica estructurada en tres fases que posibilita la concreción en la práctica de la propuesta teórica. Transformación, ISSN: 2077-2955, RNPS: 2098, enero-abril 2023, 19 (1), 195-214 Universidad de Camagüey “Ignacio Agramonte Loynaz” 196 Conclusión: El modelo teórico y la estrategia pedagógica que viabiliza la dirección del desarrollo profesional, permiten garantizar transformaciones pertinentes y de calidad, acorde con las exigencias de la sociedad"
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    Design and dynamical behavior of a fourth order family of iterative methods for solving nonlinear equations
    (2024-02-28) Arleen Ledesma Collado
    In this paper, a new fourth-order family of iterative schemes for solving nonlinear equations has been proposed. This class is parameter-dependent and its numerical performance depends on the value of this free parameter. For studying the stability of this class, the rational function resulting from applying the iterative expression to a low degree polynomial was analyzed. The dynamics of this rational function allowed us to better understand the performance of the iterative methods of the class. In addition, the critical points have been calculated and the parameter spaces and dynamical planes have been presented, in order to determine the regions with stable and unstable behavior. Finally, some parameter values within and outside the stability region were chosen. The performance of these methods in the numerical section have confirmed not only the theoretical order of convergence, but also their stability. Therefore, the robustness and wideness of the attraction basins have been deduced from these numerical tests, as well as comparisons with other existing methods of the same order of convergence.
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    Design and dynamical behavior of a fourth order family of iterative methods for solving nonlinear equations
    (2024) Arleen Ledesma Collado
    In this paper, a new fourth-order family of iterative schemes for solving nonlinear equations has been proposed. This class is parameter-dependent and its numerical performance depends on the value of this free parameter. For studying the stability of this class, the rational function resulting from applying the iterative expression to a low degree polynomial was analyzed. The dynamics of this rational function allowed us to better understand the performance of the iterative methods of the class. In addition, the critical points have been calculated and the parameter spaces and dynamical planes have been presented, in order to determine the regions with stable and unstable behavior. Finally, some parameter values within and outside the stability region were chosen. The performance of these methods in the numerical section have confirmed not only the theoretical order of convergence, but also their stability. Therefore, the robustness and wideness of the attraction basins have been deduced from these numerical tests, as well as comparisons with other existing methods of the same order of convergence.