Pro Mathematica
Permanent URI for this communityhttp://54.81.141.168/handle/123456789/182659
e-ISSN: 2305-2430
La revista PRO MATHEMATICA, fundada en el año 1987, es una publicación del Departamento de Ciencias, Sección Matemáticas, de la Pontificia Universidad Católica del Perú, PUCP. Esta revista acoge artículos de investigación de alto estándar tanto en exposición como en contenido sea en matemáticas puras, matemáticas aplicadas o estadística. Anualmente se edita un volumen compuesto de dos números. Todos los artículos pasan por riguroso proceso de arbitraje. PRO MATHEMATICA se encuentra actualmente indexada en el catálogo Latindex. Desde el año 2014 la distribución será exclusivamente electrónica.
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Item Metadata only Meromorphic functions on germs of surfaces along a rational curve(Pontificia Universidad Católica del Perú, 2023-12-29) Falla Luza, MaycolWe give examples of germs of surfaces containing a rational curve with positive self-intersection and with zero, one or two independent meromorphic functions.Item Metadata only Categoría de una aplicación y análisis no lineal(Pontificia Universidad Católica del Perú, 2023-12-29) Ipanaque Zapata, Cesar A.A classic problem in analysis is to solve nonlinear equations of the form F (x) = 0, where F : Dn → Rm is a continuous map of the closed unit disk Dn ⊂ Rn in Rm. A topological technique, which exists in the literature, for the existence of solutions of nonlinear equations is the topological degree theory. In this work, we will use the category of a map theory to solve the problem of existence of solutions of nonlinear equations. This theory, as we will show in this work, provides an alternative topological technique to study nonlinear equations.Item Metadata only Solución de sistemas lineales singulares basada en minimización(Pontificia Universidad Católica del Perú, 2023-12-29) Casavilca, Juan E.This article introduces a new concept of solution of a linear singular system (descriptor system), based on minimization. It is shown that, by imposing a hypothesis on the matrices of the descriptor system, the minimization-based solution exists and is unique for any initial condition. In particular, if the initial condition is consistent, then the minimization-based solution is equal to the classical solution. Also in this work, a numerical example is given in order to analyze the minimization-based solutions for different initial conditions.Item Metadata only On a class of predator-prey models of Gause type with Allee effect and a square-root functional response(Pontificia Universidad Católica del Perú, 2022-08-31) Puchuri, Liliana; Bueno, OrestesA predator-prey model of Gause type is an extension of the classical Lotka-Volterra predator-prey model. In this work, we study a predator-prey model of Gause type, where the prey growth rate is subject to an Allee effect and the action of the predator over the prey is given by a square-root functional response, which is non-differentiable at the y-axis. This kind of functional response appropriately models systems in which the prey have a strong herd structure, as the predators mostly interact with the prey on the boundary of the herd. Because of the square root term in the functional response, studying the behavior of the solutions near the origin is more subtle and interesting than other standard models.Our study is divided into two parts: the local classification of the equilibrium points, and the behavior of the solutions in certain invariant set when the model has a strong Allee effect. In one our main results we prove, for a wide choice of parameters, that the solutions in certain invariant set approach to the y-axis. Moreover, for a certain choice of parameters, we show the existence of a separatrix curve dividing the invariant set in two regions, where in one region any solution approaches the y-axis and in the other there is a globally asymptotically stable equilibrium point. We also give conditions on the parameters to ensure the existence of a center-type equilibrium, and show the existence of a Hopf bifurcation.Item Metadata only Singular traces of an integral operator related to the Riemann Hypothesis(Pontificia Universidad Católica del Perú, 2022-08-31) Sotelo-Pejerrey, AlfredoNo presenta resumenItem Metadata only A remark on the Tjurina and Milnor numbers of a foliation of second type(Pontificia Universidad Católica del Perú, 2022-08-31) Fernández Sánchez, Percy; García, Evelia R.; Saravia Molina, NancyWe present a relation between the Tjurina and Milnor numbers of a holomorphic foliation of secont type and the Tjurina and Milnor numbers of its union of separatrices when this last one is holomorphic.Item Metadata only Hyperbolic groups with few linear representations(Pontificia Universidad Católica del Perú, 2022-08-31) Vargas Pallete, FrancoIn this paper we are going to develop an unpublished argument of William Thurston that shows the existence of hyperbolic groups with no non-trivial representations to linear groups over any ring, for a given dimension. His approach studies the space of representations of any non-elementary hyperbolic group G to conclude that there is a hyperbolic quotient with such property.Item Metadata only Trenes de ondas en habitats periódicos en un modelo del tipo kolmogorov(Pontificia Universidad Católica del Perú, 2000) Cavani, MarioEn el presente trabajo se considera un sistema de reacción y difusión que representa un modelo depredador-presa de tipo Kolmogorov, y se supone que las especies difunden, de acuerdo a la Ley de Fick, en un espacio unidimensional. Utilizando el método de Liapunov-Schmidt se demuestra que, bajo ciertas condiciones sobre los parámetros, el sistema presenta soluciones en la forma de trenes de ondas cuando el punto de equilibrio de coordenadas positivas pierde estabilidad.Item Metadata only Evolutionary games in finite populations(Pontificia Universidad Católica del Perú, 2006) Rivasplata Zevallos, Omar; Rychtar, Jan; Sykes, ChristianThe classical replicator dynamics for evolutionary games in infinite populations formulated by Taylor and Jonker is invariant when all the payoff values are shifted by a constant. We demonstrate that this is not the case in finite populations. We show that both deterministic and stochastic evolutionary game dynamics based on the original model of Taylor and Jonker depend on the actual payoff values. We present a variant of Maynard Smith 's evolutionary stability criteria for finite populations that are large ( and possibly of unknown size). We give a full description for the case of a two strategy game. Our main contribution is a statement that an evolutionarily stable strategy as originally defined by M aynard Smith still works for large populations provided that it does well against itself.Item Metadata only Dinámica de la composición polinomios de la forma zd + cn(Pontificia Universidad Católica del Perú, 2021-02-01) Sánchez, SamirEn este trabajo estudiamos sucesiones de polinomios que se encuentran en P={(fn) :fn(z) =zd+cn, con (cn) sucesión en C}. Dada una secuencia (fn)∈ P, escribimos Fn para denotar la composición fn◦ ··· ◦f1. Clasificamos las sucesiones de polinomios (fn) según el comportamiento asintótico de (Fn) y caracterizamos dicha clasificación según el comportamiento de la sucesión (cn). Generalizamos resultados de Buger y Bruck y realizamos una comparación entre la teoría clásica de iteraciones y nuestro enfoque. Buscamos cuáles resultados se preservan para cualquier tipo de secuencia (fn) y en otros casos formulamos condiciones necesarias para que ellos se mantengan.