Physical Mathematics

Lucas numbers, a lesser-known counterpart to the Fibonacci sequence, exhibit fascinating properties and relationships within the realm of number theory. This paper delves into their coefficients, elucidating the underlying mathematical significance of these values. By exploring the connections between Lucas numbers and various mathematical concepts, including prime numbers, golden ratio and recursive sequences, we uncover deeper insights into their nature and applications. Through analytical methods and mathematical reasoning, we unveil the hidden patterns and structures embedded within Lucas numbers, shedding light on their profound significance in the landscape of mathematics.

Periodic solutions are a cornerstone of dynamical systems, appearing in diverse fields from physics to biology. This abstract explores the essence of periodic solutions, emphasizing the role of persistence in oscillation phenomena. It delves into the underlying principles governing the stability and existence of periodic solutions, elucidating their significance in understanding the behavior of complex systems. Through a synthesis of theoretical insights and practical examples, this abstract illuminates the enduring allure and profound implications of periodic solutions in the realm of dynamical systems theory.

Functionally graded (FG) sandwich structures have garnered significant attention due to their potential in lightweight engineering applications. Porosity, a common feature in many materials, plays a crucial role in determining the mechanical behavior of these structures. This article aims to analyze the influence of various porosity models on the mechanical properties of FG sandwich plates. Through a comprehensive review and comparison of different porosity models, insights into their effects on stiffness, strength and failure modes of FG sandwich plates are presented. The findings contribute to the understanding of material design and optimization for advanced engineering applications.

This study presents a novel approach to optimizing bioventing processes through the development of a comprehensive three-dimensional mathematical model. Bioventing, a widely used remediation technique for soil and groundwater contaminated with petroleum hydrocarbons, relies on the stimulation of indigenous microbial populations to degrade contaminants. However, its efficacy is often limited by various factors, including the heterogeneity of subsurface conditions. To address this challenge, our model integrates key parameters such as soil properties, airflow dynamics, microbial activity and contaminant transport in a three-dimensional framework. Through rigorous calibration and validation against experimental data, the model offers a robust tool for predicting and optimizing bioventing performance under diverse environmental conditions. Implementation of this model can enhance the efficiency and cost-effectiveness of bioventing as a sustainable remediation strategy for contaminated sites.