Selecciones Matemáticas
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description: Journal of the Academic department of Mathematics of the National University of Trujillo. The purpose of the journal is to publish the results of original and unpublished research in the field of Mathematics and Applied Mathematics. "Selecciones Matemáticas" is an Open Access Journal. ISSN-e: 2411 - 1783 DOI: 10.17268/Sel.mat Short title: Sel.Mat. ----------------------------------------------------------------------------------------------------------------------------------------------------------
publisher: National University of Trujillo - Academic Department of Mathematics
language: en
publication name: Selecciones Matemáticas
issn: 2411-1783
copyright: The authors who publish in this journal accept the following conditions: 1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine. 2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal. 3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
items: Centenary of the first predator-prey model. Revision, modifications and challenges of this fundamental ecological interrelationship
items: Some Results for Generalized Local Homology Modules
items: Euler-Rodrigues Rotation for computes the tangent vector and curvature vector of the intersection curve of two surface in 3D Lorentz-Minkowski space
items: On a special class of hypersurfaces in R5
items: Curves with Prescribed Curvature and Associated Surfaces
items: Numerical simulation for shell deformation using the Naghdi and Koiter models
items: Mathematical Modeling and Numerical Simulation for the Design of Agricultural Irrigation Channels with Bend Failures
items: Kinetic evaluation of the Arrhenius equation for artificial ageing of polymers
items: Control and Communication in Dialogue: Controllability, Observability, and Bang–Bang Dynamics
items: Stochastic Analysis on Efficiency Vaccination in a SIR Model
items: Refuge use by prey dependent on the number of predators in a Gause-type model
items: Mutualism as a stabilizing effect on the population densities of two interacting species
items: Perturbation of a biological control model of malaria considering species competition
items: Well-posedness for a Third-Order PDE with Dissipation
items: Analysis and numerical simulation of a parabolic equation with non-local terms
items: Numerical Modeling and Simulations for an Ocean Circulation Model of the Southern Pacific
items: Euclidean space perturbed by a constant vector field and its relation to a Zermelo navigation problem
items: On pullback attractors in non-autonomous dynamical systems
items: Applied mathematics, its importance in developing it in Peru
items: Fatou’s Theorem; its contribution to harmonic analysis
items: Discrete Dynamic Systems in Economics: A Study of Linear Difference Equations and Nonlinear Models with Naive and Adaptive Expectations
items: Tangencies for Power Functions with Integer Exponent
items: Eigen-concepts in the multiplicative linear algebra context
items: The energy allocation toward life-history functions: Link between the individual and population levels
items: On the structure of the fundamental étale group of normal schemes
items: Tangential intersection curves of two surfaces in the three-dimensional Lorentz-Minkowski space
items: A note about a Morse's conjecture
items: A note on Mehler's formula
items: A mathematical analysis of an eco-epidemiological model with prey-feedback effect and prey-refuge
items: Some Variants of Wayment's Mean Value Theorem for Integrals

Centenary of the first predator-prey model. Revision, modifications and challenges of this fundamental ecological interrelationship
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description: For many applied mathematicians, and especially for biomathematicians, the first model proposed by the Italian mathematician Vito Volterra in 1926 is well known, describing for the first time the relationship between a predator and its prey. This model coincided with a similar system, on chemical reactions, proposed by the physicist-chemist Alfred J. Lotka years earlier. Since then, and with an epidemic character, variations, modifications, and the incorporation of new phenomena or ecological principles have been formulated to ”make more realistic” the foundations and studies on this fundamental interaction between two species of living beings. In this work, we will give a brief description of the historical context of this seminal model, emphasizing its main properties; then we will add specific modifications, briefly outlining properties of some of them.
subject: Review
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creator: Eduardo González-Olivares
creator: Alejandro Rojas-Palma
creator: Marcelo Eduardo Alberto
creator: Francisco J. Reyes-Bahamon
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 475
ending page: 490
doi: 10.17268/sel.mat.2025.02.16

Some Results for Generalized Local Homology Modules
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description: We prove some results on the finiteness of co-associated primes of generalized local homology modules inspired by the conjecture of Grothendieck and the question of Huneke. We also show equivalent properties of minimax local homology modules. Here, we get applications for the generalized local homology module, in a general theory of modules.
subject: Communications
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creator: Carlos Henrique Tognon
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 469
ending page: 474
doi: 10.17268/sel.mat.2025.02.15

Euler-Rodrigues Rotation for computes the tangent vector and curvature vector of the intersection curve of two surface in 3D Lorentz-Minkowski space
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description: We present method computes the tangent and curvature vector of the intersection curve of two surface, parametric/implicit or implicit/implicit, in Lorentz-Minkowski space E3, by applying a Euler-Rodrigues rotation to a vector projected onto the tangent space. The axis of rotation is the normal vector of the surface (the surfaces can be timelike, spacelike or lightlike), therefore three types of rotations, since the normal vectors can be: spacelike, lightlike, or timelike.
subject: Articles
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creator: Osmar Aléssio
creator: Luiz Augusto Ramos Cintra Neto
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 439
ending page: 468
doi: 10.17268/sel.mat.2025.02.14

On a special class of hypersurfaces in R5
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description: In this paper we study hypersurfaces in R5 parametrized by lines of curvature, with four distinct principal curvatures and with Laplace invariants mji = mki = mli = 0, mjik ̸= 0, mjkl ̸= 0, mljk ̸= 0, Tijkl ̸= 0 for i, j, k, l distinct fixed indices. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. Moreover, we show that these vector valued functions are invariant under inversions and homotheties. We observe that this class of hypersurfaces cannot have constant Mobius curvature.
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creator: Carlos M. C. Riveros
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 423
ending page: 438
doi: 10.17268/sel.mat.2025.02.13

Curves with Prescribed Curvature and Associated Surfaces
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description: In this work, we study surfaces with a canonical principal direction (CPD surfaces) under the simultaneous prescription of two extrinsic geometric invariants: one principal curvature and the support function. Based on these prescriptions, we reformulate the first and second fundamental forms, which enables us to construct explicit examples of such surfaces. Finally, we show that when the curvature of the profile curve is constant, that is, when one of the principal curvatures is constant, the corresponding CPD surface is a tubular surface.
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creator: Armando M. V. Corro
creator: Marcelo Lopes Ferro
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 413
ending page: 422
doi: 10.17268/sel.mat.2025.02.12

Numerical simulation for shell deformation using the Naghdi and Koiter models
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description: In this research work, shell deformations generated by surface forces acting on the shell are described and simulated. The Naghdi and Koiter models are used to describe shell deformations. A weak formulation for the model is obtained, and some results on the existence of solutions are presented. The finite element method is then used to obtain the deformations. In addition, simulations of shell deformations are shown for the case of sectional curvature k = 0.
subject: Articles
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creator: José Luis Ponte Bejarano
creator: Juan Carlos Ponte Bejarano
creator: Alexis Rodriguez Carranza
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 396
ending page: 412
doi: 10.17268/sel.mat.2025.02.11

Mathematical Modeling and Numerical Simulation for the Design of Agricultural Irrigation Channels with Bend Failures
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description: This work analyzes water flows in open irrigation channels with bend failures. To improve this failure, a mathematical model based on elliptic equations is proposed, which is solved by applying the SchwarzChristoffel transformation in complex analysis. Given its complex geometry, and with the desire to improve the structural curve of the channel, a numerical method is employed for adaptive mesh generation, based on conformal mapping via the Schwarz-Christoffel transformation. This allows for the obtaining of orthogonal meshes adapted to the geometry of the bends. The fundamental part of this study lies in the detailed simulation of the flow in the channel bends and in the evaluation of the bend’s geometric configuration and the improvement technique for hydraulic efficiency of the channel, ultimately aiming to enhance its hydraulic performance. The results obtained will be contrasted with the data found in Google Earth satellite imagery and numerical analysis, using devices such as drones to discuss the results and draw useful conclusions for the design of irrigation channels with bend failures.
subject: Articles
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creator: Brillith Rudas
creator: Irla Mantilla
creator: David Campos
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 383
ending page: 395
doi: 10.17268/sel.mat.2025.02.10

Kinetic evaluation of the Arrhenius equation for artificial ageing of polymers
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description: Artificial ageing of polymers is a crucial and complex issue, especially considering that critical infrastructures such as nuclear power plants have lifespans varying from 40 to 60 years or even longer. Controlled artificial ageing allows the evaluation of polymer lifetimes while ensuring that their properties are preserved. However, a unified and validated methodology for artificially ageing polymers is still lacking. One of the most extended methodologies for the artificial ageing of polymers is the Arrhenius methodology. This methodology is based on the application of the Arrhenius equation, which is extensively applied in the study of thermal decomposition reactions. Nevertheless, the Arrhenius methodology requires the estimation of activation energy, and the lack of a unified method introduces variability in results obtained using different methods. Furthermore, the Arrhenius ageing methodology assumes that the kinetic parameters do not change during ageing, meaning that aged and non-aged materials should exhibit the same activation energy. The present work aims to analyse the hypothesis of unvariable activation energy during ageing. This was investigated using both new and artificially aged PVC samples, evaluating the activation energy through various mathematical models based on thermogravimetric analysis.
subject: Articles
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creator: David Lázaro
creator: María González-Alvear
creator: Eugenia Morgado
creator: Miguel Á. Jiménez
creator: Angel Cobo
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 375
ending page: 382
doi: 10.17268/sel.mat.2025.02.09

Control and Communication in Dialogue: Controllability, Observability, and Bang–Bang Dynamics
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description: This work interprets human conversation as a controllable and observable dynamical system. Each interlocutor influences the discursive state of the other, allowing the interaction to be modeled by differential equations. Using results from control theory, we consider a convex and compact space as admissible interactions, with extreme points corresponding to bang–bang interventions such as interruptions or emphatic statements. We validate the model through numerical simulations and synchrony metrics, showing that conversational symmetry improves stability and consensus, asymmetry produces biased equilibria, and temporal variations in coupling generate transient desynchronization followed by recovery, analogous to conflict and reconciliation phases in dialogue.
subject: Articles
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creator: Lisseth Navarrete Vaca
creator: Cristhian Núñez Ramos
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 365
ending page: 374
doi: 10.17268/sel.mat.2025.02.08

Stochastic Analysis on Efficiency Vaccination in a SIR Model
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description: In this paper, we model the stochastic effect of vaccination on an epidemic which like epimdemic model, it can be susceptible to environmental changes. This study is carried out using a SIR model in which population remain susceptible after having been vaccinated. One important point of our research is that we apply a whit noise on recuperate rate of the infected individuals. Further, we show some stability results and some numerical simulations.
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creator: Carlos Granados
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 356
ending page: 364
doi: 10.17268/sel.mat.2025.02.07

Refuge use by prey dependent on the number of predators in a Gause-type model
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description: This paper deals with a continuous-time predator-prey model of Gause-type considering the use of a physical refuge by a fraction of the prey population. The fraction of hidden prey is assumed to be dependent on the presence of predators in the environment. The conditions for the existence of equilibrium points and their local stability are established. According to these results, the extinction of both species is not possible, and they coexist over the long term. We conclude that the dynamics of the studied model are very similar to the model that does not consider prey refuge. However, this cannot be stated if another function is used to describe this anti-predator behavior.
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creator: Virginia Belén Gallar
creator: Alejandro Rojas-Palma
creator: Marcelo Eduardo Alberto
creator: Eduardo González-Olivares
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 344
ending page: 355
doi: 10.17268/sel.mat.2025.02.06

Mutualism as a stabilizing effect on the population densities of two interacting species
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description: Mathematical models are a very useful tool to understand, describe or predict the population dynamics of species interacting. Ecologists and mathematicians have extensively studied the predator-prey, victim-exploiter, competition and mutualistic relationships. However, mutualism between species has not received the same attention as the other ecological interactions. In this work, we exclude periodic solutions of three types of systems by the construction of Dulac functions. These systems can be used to describe the population dynamics of mutualistic species. The system type I includes a wide variety of mutualistic models in which both the intrinsic rate of increase and the carrying capacity of each species increase by the interaction between species. In particular, the system type I can be applied to exclude periodic solutions of models with conditioned interactions such that mutualism occurs at low population densities and competition occurs at high population densities. The system type II includes mutualistic models that describe a consumer-resources interaction. In these models, it is assumed that the net change of benefitscosts due to the interaction depends on the densities of the recipient species and the partner one. The system type III describes mutualistic models in which the per capita growth rate of each species is affected by a weak Allee effect. We also apply the results of this work to models mentioned in a historical list of mutualistic models provided in [1]. From the results obtained, we conclude that mutualism leads to the exclusion of periodic behaviors in the population dynamics of interacting species. Therefore, the population densities of the mutualistic species converge to an equilibrium point. Then, when the population densities oscillate, the oscillatory behaviors are transient. These results are relevant since the dynamics of mutualistic species has not been deeply characterized and the discussion about the existence of sustained oscillato…
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creator: Osvaldo Osuna
creator: Brenda Tapia-Santos
creator: Geiser Villavicencio-Pulido
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 326
ending page: 343
doi: 10.17268/sel.mat.2025.02.05

Perturbation of a biological control model of malaria considering species competition
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description: This work studies a mathematical model describing the transmission dynamics of malaria, incorporating intraspecific competition in human and mosquito populations, and biological control through larvivorous fish. We prove the existence of a compact attracting set for the proposed system of differential equations. Through stability analysis, we characterize the disease-free and endemic equilibrium points, determining epidemiologically relevant thresholds. The basic reproduction number (R0) is a key parameter: when R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable, whereas for R0 > 1, a stable endemic equilibrium emerges. Numerical simulations validate the theoretical results and reveal the regulatory effect of intraspecific competition on disease prevalence. Finally, we generalize previous models by incorporating competitive interactions and vector management strategies.
subject: Articles
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creator: Marco Antonio Tamariz Milla
creator: Roxana López-Cruz
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 309
ending page: 325
doi: 10.17268/sel.mat.2025.02.04

Well-posedness for a Third-Order PDE with Dissipation
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description: In this work, we prove that the Cauchy problem associated with a third-order equation with dissipation in periodic Sobolev spaces admits a unique solution. We also show that the solution depends continuously on the initial data. Our approach combines both an intuitive method, based on Fourier theory, and a more abstract framework using semigroup theory. Furthermore, by employing an alternative method, we demonstrate the uniqueness of the solution through its dissipative nature, drawing inspiration from the contributions of Iorio [1] and Santiago [2]. To deepen and enrich our study, we investigate the infinite dimensional space in which differentiability occurs and its connection to the initial data. Finally, we extend our results to equations of arbitrary nth order.
subject: Articles
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creator: Yolanda Silvia Santiago Ayala
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 288
ending page: 308
doi: 10.17268/sel.mat.2025.02.03

Analysis and numerical simulation of a parabolic equation with non-local terms
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description: In this work, we investigate the existence and uniqueness of global strong solutions, as well as the exponential decay of these solutions in bounded domains, for an initial-boundary value problem associated with parabolic equations involving nonlocal terms. The theoretical results are complemented by numerical simulations obtained using the finite element method for the spatial variable and the finite difference method for the temporal variable.
subject: Articles
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creator: Juan Pablo Límaco
creator: Pitagoras P. de Carvalho
creator: Mauro A. Rincon
creator: Juan L. Ferrel
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 273
ending page: 287
doi: 10.17268/sel.mat.2025.02.02

Numerical Modeling and Simulations for an Ocean Circulation Model of the Southern Pacific
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description: In this work, we consider the primitive equations of an ocean circulation model for the southern pacific, which consists of the time-dependent Navier-Stokes equations in the β-plane coupled with the temperature transport equation. Specifically, the full three-dimensional equations are adopted and formulated as a monolithic system of nonstationary, nonlinear, coupled partial differential equations. The El Nino phenomenon is simulated by the action of given wind stresses on the ocean surface. We present an approximation scheme with Crank-Nicolson finite differences in time, and in space we take inf-sup stable Galerkin finite elements for the Navier-Stokes part and bilinear elements for the temperature. We solve the resulting, nonlinear monolithic discrete system by Newton's method. Numerical experiments with realistic geometry and material data are conducted, which show the practicability of our approach.
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creator: Thomas Hartmann
creator: Ernst P. Stephan
creator: Thomas Wick
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-12-27
publication date: 2025-12-27
starting page: 261
ending page: 272
doi: 10.17268/sel.mat.2025.02.01

Euclidean space perturbed by a constant vector field and its relation to a Zermelo navigation problem
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description: In this work, the authors perturb the Euclidean plane with a constant vector field of the form W = (0, ε) with 0 ≤ ε < 1, which can be interpreted as wind currents affecting the movement of ships in a constant unidirectional way. It is observed that the resulting perturbed norm, called the ε-Euclidean metric, which is non-reversible, is a Finsler metric. In this way, a new non-Euclidean geometry is introduced. With this, the ε-Euclidean distance is induced and defined. This new way of measuring point-to-point distances can be interpreted, physically, as optimal travel time. Due to the non-reversibility of the ε-Euclidean metric, two types of circumferences are defined and characterized. Distance formulas (or optimal travel time) from point to line, from line to point, and from line to line are obtained, as well as a geometric construction technique for obtaining the distance from a point to a parabola, which can be adapted to other curves that simulate the Edge of a beach. Examples and graphs are presented for a better understanding of the work.
subject: Articles
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creator: Dik D. Lujerio Garcia
creator: Newton M. Solórzano Chávez
creator: Marck A. Molina Morales
creator: Bibiano M. Cerna Maguiña
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 15
ending page: 32
doi: 10.17268/sel.mat.2025.01.02

On pullback attractors in non-autonomous dynamical systems
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description: The theory of pullback attractors constitutes an important tool to interpret the dynamics of physical, biological or engineering phenomena, as it addresses the study of the asymptotic behavior of nonautonomous dynamic systems, where differential equations explicitly depend on time. The objective of this article seeks to synthesize recent advances, present some general techniques such as the energy estimations or asymptotic compactness. This work stick out the importance of pullback attractors to model systems with variable coefficients, memory, delays or in non-cylindrical domains and also points out some challenges such as extension to stochastic systems or complex geometries.
subject: Review
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creator: Carlos Felipe Vidarte Chavez
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 243
ending page: 260
doi: 10.17268/sel.mat.2025.01.17

Applied mathematics, its importance in developing it in Peru
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description: The objective of this article is to contribute with some ideas and proposals with the purpose of further developing the study and research in our country of this area of mathematics, given the historical background of how, thanks to it, many countries have achieved their technological development and in this way with the well-being of the respective society.
subject: Review
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creator: Alejandro Ortiz Fernández
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 218
ending page: 242
doi: 10.17268/sel.mat.2025.01.16

Fatou’s Theorem; its contribution to harmonic analysis
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description: The objective of this article is to see how Fatou’s theorem, given at the beginning of the 20th century, motivated new developments in harmonic analysis and partial differential equations in the second half of that century. In this writing we give a brief tour of some of the contributions given by distinguished analysis and in this way our interest is to make such progress known in Peru and thus contribute to the development of this beautiful branch of mathematical analysis, which we believe is almost unknown in our country. In particular we have paid some attention to the work of Jerison - Kenig [1] because such work contains an overview that helps meet our objective.
subject: Review
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creator: Alejandro Ortiz Fernández
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 186
ending page: 217
doi: 10.17268/sel.mat.2025.01.15

Discrete Dynamic Systems in Economics: A Study of Linear Difference Equations and Nonlinear Models with Naive and Adaptive Expectations
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description: This study investigates market dynamics using a discrete economic model of supply and demand. Initially, the linear case with naïve or static expectations is analyzed, and the stability conditions that lead to different system behaviors, such as convergence to equilibrium, periodic oscillations, or divergence, are determined analytically through the study of fixed points and cobweb dynamics. Subsequently, the analysis is extended to the nonlinear case with adaptive expectations, where the interaction between supply nonlinearity and the expectation formation process is found to generate complex behaviors. The results show how variations in the nonlinearity parameter induce bifurcations observable in time series. The study provides a comprehensive analytical framework that links mathematical properties with observable economic phenomena, offering tools to predict and manage stability in real markets, with direct applications in economic policy and financial risk management.
subject: Review
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creator: Jose Luis Matos Tejada
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 162
ending page: 185
doi: 10.17268/sel.mat.2025.01.14

Tangencies for Power Functions with Integer Exponent
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description: Considering a power function f(x) = x^n with exponent n as a positive integer, we show that, at each of its points, there exists a unique polynomial function of degree n − 1 that is tangent to it at that point. Similarly, we verify that every power function h(x) = x^k with exponent k as a negative integer is tangent, at each of its points, to a function of the form l(x) =Sa^t.x^t, where the exponents t are integers between k + 1 and −1.
subject: Communications
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creator: Cairo Henrique Vaz Cotrim
creator: Laredo Rennan Pereira Santos
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 155
ending page: 161
doi: 10.17268/sel.mat.2025.01.13

Eigen-concepts in the multiplicative linear algebra context
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description: The concept of eigenvalues is associated with the linearity one, through the structure of vectorial space. The multiplicative linear algebra is a structure in which an expression such as x^3y^2 can be considered a linear combination of variables x and y. This article is reserved to show the corresponding analogues for an Eigenvalue Theory. We exemplify its applications by introducing a connection with the analysis of a nonlinear dynamical system in the standard sense, although a linear recurrence in the multiplicative one.
subject: Articles
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creator: Fernando Córdova-Lepe
creator: Franco Lara-Muñoz
creator: Ranghely Hernández-Castañeda
creator: Rodrigo Gutiérrez
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 142
ending page: 154
doi: 10.17268/sel.mat.2025.01.12

The energy allocation toward life-history functions: Link between the individual and population levels
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description: The population dynamics of organisms are strongly influenced by life-history strategies that result from the optimal allocation of energy to vital functions such as growth, reproduction, and survival. These strategies, characterized by phenotypic traits, emerge as evolutionary adaptations to specific ecological conditions and define functional trade-offs relevant facing biotic and abiotic pressures. The aim of this study is to examine the link between life history and population dynamics from a bioenergetic perspective, articulating individual and population-level processes through mathematical models that capture adaptive decisions in simulated environments described in terms of constant, decreasing, and periodic resource availability over time. Using a discrete-time mathematical model with two state variables, internal energy and survival probability, energy allocation toward reproduction and foraging is incorporated in order to determine the optimal strategy that maximizes the net reproductive rate. To solve this control problem, Pontryagin’s maximum principle is applied, using the forward–backward method to obtain optimal trajectories of allocation, energy, and survival. These trajectories are analyzed with respect to relevant physiological parameters under different scenarios of resource availability, thereby allowing the exploration of how environmental conditions influence the bioenergetic decisions of organisms.
subject: Articles
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creator: Víctor Saldaña-Núñez
creator: Alex Altamirano-Fernández
creator: Ranghely Hernández-Castañeda
creator: Rodrigo Gutiérrez
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 132
ending page: 141
doi: 10.17268/sel.mat.2025.01.11

On the structure of the fundamental étale group of normal schemes
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description: The étale fundamental group is a central tool in algebraic geometry that generalizes the topological fundamental group to the context of schemes. In this article, we explore its behavior for normal schemes, highlighting its relationship to arithmetic and geometric invariants.
subject: Articles
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creator: Ronald Jesús Mas Huamán
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 123
ending page: 131
doi: 10.17268/sel.mat.2025.01.10

Tangential intersection curves of two surfaces in the three-dimensional Lorentz-Minkowski space
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description: We present algorithms for computing the differential geometry properties of tangential intersection curves of two surfaces in the three-dimensional Lorentz-Minkowski space E31 . We compute the tangent vector of tangential intersection curves of two surfaces parametric, where the surfaces can be: spacelike, timelike, or lightlike. The first method computed the tangent vector using the equality of the projection of the second derivative vector onto the normal vector and second method computes the tangent vector by applying a rotation to a vector projected onto the tangent space, where the axis of rotation is the normal vector of the surface. In Minkowski space, there are three types of rotations, since the normal vectors can be: spacelike, lightlike, or timelike.
subject: Articles
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creator: Osmar Alessio
creator: Luiz Augusto Ramos Cintra Neto
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 97
ending page: 122
doi: 10.17268/sel.mat.2025.01.09

A note about a Morse's conjecture
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description: In dynamical systems it is known that metrically transitive systems are topologically transitive. M. Morse in 1946 ([1]) conjectured that if the dynamical system has some degree of regularity, then the converse is true. In this article, we will study the Morse conjecture for R2-actions on three-dimensional manifolds and prove the following two results: The conjecture is false if we do not impose restrictions on the singular set and we will prove that The Morse’s Conjecture is valid for locally free actions.
subject: Articles
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creator: Walter T. Huaraca Vargas
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 90
ending page: 96
doi: 10.17268/sel.mat.2025.01.08

A note on Mehler's formula
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description: In this paper we propose an original proof of Mehler expansion of the Gaussian distribution in terms of probabilistic Hermite polynomials.
subject: Articles
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creator: Alessandri Canchoa Quispe
creator: Sergio Camiz
creator: Eladio Ocaña
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 86
ending page: 89
doi: 10.17268/sel.mat.2025.01.07

A mathematical analysis of an eco-epidemiological model with prey-feedback effect and prey-refuge
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description: This study investigates an eco-epidemiological model incorporating feedback mechanisms and prey refuge, formulated as a system of nonlinear ordinary differential equations. The model describes interactions among susceptible prey, infected prey, and predators, including disease transmisión and nonlinear predation effects. We establish the existence, uniqueness, and positivity of solutions, and analyze their boundedness within a biologically feasible region. Local stability of equilibria is studied via linearization, while global stability is proven using Lyapunov functions. Numerical simulations complement the analytical results, demonstrating how key parameters affect the system’s long-term dynamics.
subject: Articles
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creator: Neisser Pino Romero
creator: Roxana López-Cruz
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 67
ending page: 85
doi: 10.17268/sel.mat.2025.01.06

Some Variants of Wayment's Mean Value Theorem for Integrals
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description: This note deals with some variants of Wayment’s Mean Value Theorem for integrals. Our approach is rather elementary and does not use advanced techniques from analysis. The simple auxiliary functions were used to prove the results.
subject: Articles
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creator: German Lozada-Cruz
rights: Copyright (c) 2025 https://creativecommons.org/licenses/by/4.0
date: 2025-07-26
publication date: 2025-07-26
starting page: 62
ending page: 66
doi: 10.17268/sel.mat.2025.01.05