Publications

2026

1. 

   A note on the averaging principle for ordinary differential equations depending on the slow time

   Carmen Núñez, Rafael Obaya, and Jorge Rodríguez

   Applied Mathematics Letters, 2026

   Abs DOI

   The work presents a “doubly” nonautonomous version of the averaging principle, applicable to equations that depend on a small parameter ɛ and on (fast) time τ, but also on slow time t=ɛτ. The objectives are to establish optimal conditions on the dependence of the coefficients of the equations on t under which the averaging principle can be extended and to provide good estimates of the distance between the solutions of the initial equation and those of the averaged equation, always with τ varying in intervals of length proportional to 1/ɛ. The applicability of these results is based on the fact that the estimates obtained are uniform with respect to the initial time at which the solutions of both equations coincide.

2025

1. 

   Métodos dinámicos y numéricos de la teoría del promedio con aplicación en problemas de osciladores

   Jorge Rodríguez

   2025

   Abs Website

   This work aims to demonstrate various bounds for the difference between the solution of a system of differential equation where two time-scales are present and its averaged system, using a modern and rigorous approach. The concept of averaging is defined, and properties of KBM functions are analyzed, establishing bounds for the difference between solutions on a time scale of 1/ε. Additionally, UKBM functions are introduced to generalize results to unbounded intervals. The theory of averaging for periodic functions is presented in its classical version, studying a change of variables that transforms the original equation into the averaged one, and generalizing to higher-order approximations. Finally, practical applications are presented, such as the analysis of the Kapitza pendulum and the theoretical basis and implementation of the of stroboscopic averaging numerical methods, which allow for the efficient integration of oscillator problems.

2024

1. 

   Construcción de un pequeño radiotelescopio para la detección de la lı́nea del hidrógeno neutro

   Jorge Rodríguez

   2024

   Abs Website

   This work describes, from basic principles, how to build and operate a radio telescope for detecting the neutral hydrogen line at 21 cm. It covers the design and construction of the antenna, the operation of the electronics, and the subsequent data processing. Finally, it presents the spectra obtained through the described process.

2. 

   Puntos de inflexión de superficies algebraicas, un enfoque moderno del trabajo de Salmon

   Jorge Rodríguez

   2024

   Abs Website

   This work focuses on providing an updated theoretical framework for Clebsch’s calculation, addressing limit cases and formalizing the symbolic method used by Clebsch and Salmon. The symbolic method is formalized using multilinear algebra, properties of determinants in rings are reviewed, and concepts of algebraic geometry are introduced to study inflection points. Finally, a rigorous proof of Clebsch’s calculation is presented to obtain a closed expression for Salmon’s polynomial.