This compilation contains seven chapters, each detailing a particular advancement in mathematics research. Chapter One presents labeled paths as methods for encryption and decryption. Chapter Two presents the possibilities of risk assessment and management assistance built around Bayesian tools. Chapter Three analyzes in detail the Lie point symmetries of the second-order scalar ordinary differential equations appearing in the Painlevé-Gambier classification. Chapter Four focuses on the application of Adomian decomposition method (ADM) for solving singular and non-singular ordinary and partial differential equations with initial and boundary conditions. Chapter Five describes the structure of compact global attractor (Levinson center) for monotone Bohr/Levitan almost periodic dynamical systems. Chapter Six presents the mathematical modeling from the PI model of three real segments derived from the electric power network of two concessionaires located in the city of Ijuí, Brazil. Finally, Chapter Seven presents a study of the mathematical aspects of the theory of error-detecting/correcting codes based on coding theory.