In this work we define a stochastic adding machine associated to a quadratic base $(F_n)_{n \geq 0}$ formed by recurrent sequences of order 2. We obtain a Markov chain with states in $\mathbb{Z}^+$ and we prove that the spectrum of the transition operator associated to this Markov chain is connected to the filled Julia sets for a class of endomorphisms in $\mathbb{C}^2$ of which we study topological properties.

Modelo básico epidemiológico SIR para el COVID-19: caso las Regiones del Perú

Medidas de robustez y estabilidad para problemas de scheduling con incertidumbre: Una revisión del estado del arte

This paper presents an improved approach to measuring monetary poverty using a fuzzy methodology, specifically the recent model proposed by Belhadj and Bounani (2023). Using data from the National Household Survey for the province of Trujillo, La Libertad, Peru, the study demonstrates that this method provides a more detailed and continuous assessment of monetary poverty levels than traditional binary classifications. The fuzzy framework captures the intensity of deprivation experienced by individuals or households by assigning different degrees of membership to each poverty indicator, allowing the identification of intermediate situations that conventional methods typically ignore. The results reveal the existence of individuals or households that are not officially categorized as poor but exhibit deprivation patterns similar to those of the poor population. Identifying these vulnerable groups is essential for designing more inclusive and effective public policies, as it helps populations at risk of falling into poverty and supports a more precise targeting of social programs. Overall, the fuzzy approach offers a more sensitive and realistic representation of poverty dynamics in the study area, providing valuable information for decision-makers seeking to improve poverty-reduction strategies.

This paper applies the updated fuzzy model proposed by Belhadj and Bounani in 2023 to microdata from the National Household Survey (ENAHO) for the province of Trujillo, La Libertad, Peru, to measure monetary poverty. The study demonstrates that this framework offers a more detailed, continuous assessment of poverty levels than traditional binary classifications. By assigning degrees of deprivation to various poverty indicators, the fuzzy approach captures the full intensity of deprivation, uncovering intermediate socioeconomic states that conventional methods systematically overlook. While the official binary classification by INEI categorizes 94.62% of Trujillo’s population as “non-poor,” the fuzzy methodology reveals that only 22.18% experience complete non-deprivation. Crucially, it exposes that 49.94% of the population resides in a state of “mild poverty”—a highly vulnerable segment rendered invisible by standard metrics. District-level disaggregation highlights sharp territorial disparities, ranging from severe structural vulnerability in Florencia de Mora (Fuzzy Poverty Index = 0.428) to consolidated stability in Víctor Larco Herrera (0.288). Ultimately, the fuzzy approach provides a more nuanced and realistic representation of poverty dynamics. This offers crucial insights for policymakers designing targeted poverty-reduction interventions.