https://revistas.unitru.edu.pe/index.php/SSMM/issue/feedSelecciones Matemáticas2025-07-26T15:43:48+00:00Dr. Obidio Rubio Mercedesorubio@unitru.edu.peOpen Journal Systems<p>Revista Científica do Departamento Acadêmico de Matemática da <span style="text-decoration: underline;"><a href="http://www.unitru.edu.pe/" target="_blank" rel="noopener">Universidad Nacional de Trujillo</a>.</span> A revista tem como <strong>objetivo</strong> publicar e divulgar os resultados de pesquisas <strong>originais</strong> e inéditas na área de Matemática Pura e Matemática Aplicada.</p> <p>"<strong>Selecciones Matemáticas</strong>" é uma <strong>Revista de Acesso Aberto.</strong></p> <p><strong>ISSN-e: 2411-1783,</strong></p> <p><strong> DOI: 10.17268 / Sel.mat</strong></p> <p><strong>Nome curto: Sel. Mat. <img src="https://revistas.unitru.edu.pe/public/site/images/admrevffmm/Open_Acces.png" alt="" /></strong></p> <p><strong>------------------------------------------------------------------------------------------------------------------------------------------------------------</strong></p>https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6638Sistemas Dinámicos Discretos en Economía: Un estudio de Ecuaciones en Diferencias Lineales y Modelos No Lineales con Expectativas Ingenuas y Adaptativas2025-07-25T21:50:21+00:00Jose Luis Matos Tejadajmatos@unitru.edu.pe<p>En este trabajo se investigó la dinámica de los mercados mediante un modelo económico discreto de oferta y demanda. En una primera etapa, se analiza el caso lineal con expectativas ingenuas o estáticas, determinando analíticamente las condiciones de estabilidad que conducen a diferentes comportamientos del sistema: convergencia al equilibrio, oscilaciones periódicas o divergencia.</p> <p>Esto se realiza a través del estudio de los puntos fijos y de la dinámica tipo telaraña. Posteriormente, el análisis se amplía al caso no lineal con expectativas adaptativas, donde se identifica que la interacción entre la no linealidad de la oferta y el proceso de formación de expectativas puede generar comportamientos complejos. Los resultados muestran cómo la variación del parámetro de no linealidad induce bifurcaciones, observables en las series temporales. El estudio ofrece un marco analítico integral que vincula las propiedades matemáticas con fenómenos económicos observables, brindando herramientas útiles para predecir y gestionar la estabilidad en mercados reales, con aplicaciones directas en la formulación de políticas económicas y la gestión de riesgos financieros.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6639Fatou’s Theorem; its contribution to harmonic analysis2025-07-25T22:02:34+00:00Alejandro Ortiz Fernándezjortiz@pucp.edu.pe<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6640Applied mathematics, its importance in developing it in Peru2025-07-26T01:28:45+00:00Alejandro Ortiz Fernándezjortiz@pucp.edu.pe<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6641On pullback attractors in non-autonomous dynamical systems2025-07-26T01:50:05+00:00Carlos Felipe Vidarte Chavezp880300324@unitru.edu.pe<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6616Integration of Monomials over the Unit Sphere and Unit Ball in Rn2025-07-24T03:26:02+00:00Calixto P. Calderóncalixtopcalderon@gmail.comAlberto Torchinskytorchins@iu.edu<p>We compute the integral of monomials of the form x^2β over the unit sphere and the unit ball in R^n where β = (β1, . . . , βn) is a multi–index with real components βk > −1/2, 1 ≤ k ≤ n, and discuss their asymptotic behavior as some, or all, βk → ∞. This allows for the evaluation of integrals involving circular and hyperbolic trigonometric functions over the unit sphere and the unit ball in Rn. We also consider the Fourier transform of monomials xα restricted to the unit sphere in Rn, where the multi–indices α have integer components, and discuss their behaviour at the origin.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6642Euclidean space perturbed by a constant vector field and its relation to a Zermelo navigation problem2025-07-26T15:22:20+00:00Dik D. Lujerio Garciadlujeriog@unasam.edu.peNewton M. Solórzano Cháveznmayer159@gmail.comMarck A. Molina Moralesmmolinam@unasam.edu.peBibiano M. Cerna Maguiñabcernam@unasam.edu.pe<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6617Surfaces with mean of the hyperbolic curvature radii of double harmonic type2025-07-24T14:26:10+00:00Armando M. V. Corroavcorro@gmail.comCarlos M. C. Riveroscarlos@mat.unb.brRaquel P. de Aráujoraquel.araujo@ifgoiano.edu.br<p>In this paper, we define surfaces with mean of the hyperbolic curvature radii of double harmonic type (in short DHRMC-surfaces) in the hyperbolic space, these surfaces include the generalized Weingarten surfaces of the harmonic type (HGW-surfaces). We give a characterization of DHRMCsurfaces.</p> <p>Given a real function, we will present a family of DHRMC-surfaces that depend on two holomorphic functions. Moreover, we classify the DHRMC-surfaces of rotation.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6618Traveling waves in a delayed reaction-diffusion SVIR epidemic model with generalized incidence function and imperfect vaccination2025-07-24T14:49:44+00:00Rassim Darazirarrassimrassim269@gmail.com<p>This paper is concerned with traveling wave solutions for a delayed reaction-diffusion SVIR epidemic model that includes both general incidence function and imperfect vaccination. In the model, the spread of infection in space is explicitly taken into account by using a heterogeneous environment; it takes into consideration the delay in immune response and inefficiency in vaccinations. The analysis carried out below shows that the basic reproduction number Ro will be a critical value for determining the existence of traveling waves. More precisely, when Ro > 1 there exists a minimal wave speed ρ* > 0 such that the system admits nontrivial traveling wave solutions for ρ ≥ ρ* whereas no such solutions exist for ρ < ρ*. On the other hand, if Ro ≤ 1, there are no traveling wave solutions. The introduction of delays and imperfect vaccination adds richness and complexity to the dynamics, such as possible wave speed adjustments and pattern formations, which are hallmarks of complex systems. This work develops a theoretical framework that shall guide the understanding of how delays, spatial spread, and control measures interact in epidemic systems and offers insights applicable to real-world infectious disease dynamics. Numerical simulations for some typical nonlinear incidence functions are given in the last to illustrate the existence of traveling waves.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6619Some Variants of Wayment's Mean Value Theorem for Integrals2025-07-24T15:02:09+00:00German Lozada-Cruzgerman.lozada@unesp.br<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6621Análisis matemático de un modelo eco-epidemiológico con efecto de retroalimentación y refugio en la presa2025-07-24T17:06:33+00:00Neisser Pino Romeroneisser.pino@unmsm.edu.peRoxana López-Cruzrlopezc@unmsm.edu.pe<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6623A note on Mehler's formula2025-07-24T20:28:17+00:00Alessandri Canchoa Quispecanchoa@lamolina.edu.peSergio Camizsergio@camiz.itEladio Ocañaeocana@imca.edu.pe<p>In this paper we propose an original proof of Mehler expansion of the Gaussian distribution in terms of probabilistic Hermite polynomials.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6624A note about a Morse's conjecture2025-07-24T20:40:46+00:00Walter T. Huaraca Vargaswalterhv@ufv.br<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6625Tangential intersection curves of two surfaces in the three-dimensional Lorentz-Minkowski space2025-07-24T20:51:20+00:00Osmar Alessioosmar.alessio@uftm.edu.brLuiz Augusto Ramos Cintra Netolarcintraneto@gmail.com<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6626On the structure of the fundamental étale group of normal schemes2025-07-24T21:07:10+00:00Ronald Jesús Mas Huamánrmash@uni.edu.pe<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6629The energy allocation toward life-history functions: Link between the individual and population levels2025-07-25T01:05:23+00:00Víctor Saldaña-Núñezvictor.saldana@uautonoma.clAlex Altamirano-Fernándezaaltamirano@ucm.clRanghely Hernández-Castañedaranghely.hernandez@alumnos.ucm.clRodrigo Gutiérrezrgutierreza@ucm.cl<p>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.</p> <p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6630Eigen-concepts in the multiplicative linear algebra context 2025-07-25T01:31:47+00:00Fernando Córdova-Lepefcordova@ucm.clFranco Lara-Muñozfranco.lara@alumnos.ucm.clRanghely Hernández-Castañedaranghely.hernandez@alumnos.ucm.clRodrigo Gutiérrezrgutierreza@ucm.cl<p>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.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025 https://revistas.unitru.edu.pe/index.php/SSMM/article/view/6637Tangencias para Funcoes Potencia de Expoente Inteiro2025-07-25T21:35:15+00:00Cairo Henrique Vaz Cotrimcairo.h.vaz@usp.brLaredo Rennan Pereira Santoslaredo.santos@ifg.edu.br<p>Considerando uma funcao potencia f(x) = x^n com expoente n inteiro positivo, mostramos que, para cada um de seus pontos, existe uma única funcao polinomial de grau n − 1 que a tangencia neste ponto. Semelhantemente, verificamos que toda funcao potencia h(x) = x^k, com expoente k inteiro negativo, é tangente, em cada um de seus pontos, a uma funcao da forma l(x) =Suma: a^t.x^t, com expoentes t inteiros entre k + 1 e −1.</p>2025-07-26T00:00:00+00:00Copyright (c) 2025