This volume contains eight chapters that detail advances in mathematics research. Chapter One discusses the development and analysis of heuristic and metaheuristic methods for solving optimization problems of cutting and packing. Chapter Two details virial energy components, extreme physical information, and property flows in communication networks. Chapter Three explores two functions of molecular information systems, consecutive (cascade) and simultaneous (combination). Chapter Four considers the expressions of a digital-to-analog piezo converter-actuator using the equations of reverse piezo effect and the ordinary linear differential equation of the second order. Chapter Five discusses large regression modeling under Lp-Norm loss function. Chapter Six explains cyclic evolutions in nonrelativistic quantum mechanics and geometric phases. Chapter Seven investigates the HIV/AIDS epidemic model using stability and Lie symmetry analysis. Lastly, Chapter Eight examines a SIRD (Susceptible, Infected, Recovered,Dead) epidemic model via the lens of Lie symmetry analysis.