BOSCH PÉREZ, PAUL JESÚS

Preferred name
BOSCH PÉREZ, PAUL JESÚS
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Email
pbosch@udd.cl
ORCID
0000-0001-5194-4173
Scopus Author ID
8630247500
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    Jensen-type inequalities for <i>m</i>-convex functions
    (2022)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Yamilet Quintana
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work, we prove some new Jensen-type inequalities for <jats:italic>m</jats:italic>-convex functions and apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.
      2Scopus© Citations 16
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    Total Outer-Independent Domination Number: Bounds and Algorithms
    (MDPI AG, 2025-03-10)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Ernesto Parra Inza
    ;
    Ismael Rios Villamar
    ;
    José Luis Sánchez-Santiesteban
    In graph theory, the study of domination sets has garnered significant interest due to its applications in network design and analysis. Consider a graph G(V,E); a subset of its vertices is a total dominating set (TDS) if, for each x∈V(G), there exists an edge in E(G) connecting x to at least one vertex within this subset. If the subgraph induced by the vertices outside the TDS has no edges, the set is called a total outer-independent dominating set (TOIDS). The total outer-independent domination number, denoted as γtoi(G), represents the smallest cardinality of such a set. Deciding if a given graph has a TOIDS with at most r vertices is an NP-complete problem. This study introduces new lower and upper bounds for γtoi(G) and presents an exact solution approach using integer linear programming (ILP). Additionally, we develop a heuristic and a procedure to efficiently obtain minimal TOIDS.
      3
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    A general version of Milne-type inequalities
    (Springer Science and Business Media LLC, 2026-03-31)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
      3
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    On the Inverse Degree Polynomial
    (2019)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José Manuel Rodríguez
    ;
    Omar Rosario
    ;
    José María Sigarreta
    <jats:p>Using the symmetry property of the inverse degree index, in this paper, we obtain several mathematical relations of the inverse degree polynomial, and we show that some properties of graphs, such as the cardinality of the set of vertices and edges, or the cyclomatic number, can be deduced from their inverse degree polynomials.</jats:p>
      12
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    Dirichlet Type Problem for 2D Quaternionic Time-Harmonic Maxwell System in Fractal Domains
    (2020)
    Yudier Peña Pérez
    ;
    Ricardo Abreu Blaya
    ;
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Juan Bory Reyes
    <jats:p>We investigate an electromagnetic Dirichlet type problem for the 2D quaternionic time-harmonic Maxwell system over a great generality of fractal closed type curves, which bound Jordan domains in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>. The study deals with a novel approach of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>h</mml:mi></mml:math>-summability condition for the curves, which would be extremely irregular and deserve to be considered fractals. Our technique of proofs is based on the intimate relations between solutions of time-harmonic Maxwell system and those of the Dirac equation through some nonlinear equations, when both cases are reformulated in quaternionic forms.</jats:p>
      3Scopus© Citations 2
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    Generalized inequalities involving fractional operators of the Riemann-Liouville type
    (2021)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    Héctor J. Carmenate
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    In this paper, we present a general formulation of the well-known fractional drifts of Riemann-Liouville type. We state the main properties of these integral operators. Besides, we study Ostrowski, Székely-Clark-Entringer and Hermite-Hadamard-Fejér inequalities involving these general fractional operators.
      1  2Scopus© Citations 12
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      6  1
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    On new Milne-type inequalities and applications
    (2023)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez
    ;
    José M. Sigarreta
    Inequalities play a major role in pure and applied mathematics. In particular, the inequality plays an important role in the study of Rosseland’s integral for the stellar absorption. In this paper we obtain new Milne-type inequalities, and we apply them to the generalized Riemann–Liouville-type integral operators, which include most of the known Riemann–Liouville integral operators.
      18  1Scopus© Citations 23
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    On Jensen-type inequalities for harmonic convex functions
    (Element d.o.o., 2024)
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    José M. Rodríguez-García
    ;
    José M. Sigarreta
      2Scopus© Citations 4
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    A New Genetic Algorithm Encoding for Coalition Structure Generation Problems
    (2020)
    Juan Pablo Contreras
    ;
    BOSCH PÉREZ, PAUL JESÚS  
    ;
    VARAS VALDÉS, MAURICIO ANDRÉS  
    ;
    Franco Basso
    Genetic algorithms have proved to be a useful improvement heuristic for tackling several combinatorial problems, including the coalition structure generation problem. In this case, the focus lies on selecting the best partition from a discrete set. A relevant issue when designing a Genetic algorithm for coalition structure generation problems is to choose a proper genetic encoding that enables an efficient computational implementation. In this paper, we present a novel hybrid encoding, and we compare its performance against several genetic encoding proposed in the literature. We show that even in difficult instances of the coalition structure generation problem, the proposed approach is a competitive alternative to obtaining good quality solutions in reasonable computing times. Furthermore, we also show that the encoding relevance increases as the number of players increases.
    Scopus© Citations 12  1