Contributions in Mathematics and Engineering

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This volume deepens the understanding of current research problems and theories in modern mathematics, including calculus of variations, optimization theory, complex analysis, real analysis, differential equations, and geometry. It presents applications within the broad spectrum of Engineering Science, emphasizing equilibrium problems, complexity in numerical optimization, dynamical systems, non-smooth optimization, complex network analysis, statistical models, data mining, and energy systems. Interdisciplinary research is highlighted, with subjects treated in a unified and self-contained manner. The methods, theory, and applications presented make this tribute an invaluable reference for teachers, researchers, and professionals interested in pure and applied research, the philosophy of mathematics, and mathematics education. Review papers included will be particularly beneficial for a broader audience and graduate students seeking the latest information. The influence of Constantin Carathéodory in the international mathematical community is acknowledged, notably during the first Fields Medals awards at the International Congress of Mathematicians in Oslo, 1936, where he presented the works of Lars V. Ahlfors and Jesse Douglass. This volume contains significant papers in Science and Engineering dedicated to Carathéodory's memory and his mathematical legacy.