The contributions in this volume aim to deepen
understanding of some of the current research problems and theories in
modern topics such as calculus of variations, optimization theory, complex
analysis, real analysis, differential equations, and
geometry. Applications to these areas of mathematics are presented within
the broad spectrum of research in Engineering Science with
particular emphasis on equilibrium problems, complexity in numerical
optimization, dynamical systems, non-smooth optimization, complex network
analysis, statistical models and data mining, and energy systems. Additional
emphasis is given to interdisciplinary research, although subjects are treated
in a unified and self-contained manner. The presentation of methods, theory and
applications makes this tribute an invaluable reference for teachers,
researchers, and other professionals interested in pure and applied
research, philosophy of mathematics, and mathematics education. Some
review papers published in this volume will be particularly useful for a
broader audience of readers as well as for graduate students who search for the
latest information.



Constantin
Caratheodory's wide-ranging influence in the international mathematical
community was seen during the first Fields Medals awards at the International
Congress of Mathematicians, Oslo, 1936. Two medals were awarded, one to Lars V.
Ahlfors and one to Jesse Douglass. It was Caratheodory who presented both their
works during the opening of the International Congress. This volume contains
significant papers in Science and Engineering dedicated to the memory of
Constantin Caratheodory and the spirit of his mathematical influence.