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Mathematical methods and theories with interdisciplinary applications are presented in this book. The book chapters are written by eminent scientists and a few of these papers are based on talks which were presented during the International Conference that was held at the Hellenic Military Academy in May 2015. Graduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the book useful to their overall understanding and further research. Each paper discusses possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scattering functions for nonlinear multiobjective optimization, strong and weak convexity of closed sets in a Hilbert space and related subjects.