A collection of presentations from a conference held in April 2011 at the Hellenic Army Academy, this book covers various mathematical methods that might be employed in advanced military applications.

The book’s 15 distinct papers are grouped in seven parts. Part 1 is a general introduction describing the role of technological initiatives in the history of war and the significance of graduate programs at military universities.

Part 2 focuses on operations research as it applies to military applications. The first paper considers the evaluation of network connectivity by identifying the subsets of critical elements, such as nodes, arcs, paths, clusters, cliques, and so on. Besides the apparent connotation for the robustness of military undertakings, this problem is important for such fields as neuroscience, biology, and genetics. The second paper is devoted to an interesting methodology for satellite engagement with mobile targets, designed to estimate the probability of locating a target as a function of time, when the moment it was stopped is unknown.

Part 3 deals with signal processing. The first paper, “Solving an Electromagnetic Scattering Problem in Chiral Media,” focuses on an intensively studied topic in electromagnetic theory concerning the scattering of time-harmonic waves by 3D chiral obstacles. The second paper, “Orthonormality in Interpolation Schemes for Reconstructing Signals,” considers efficient approximants to highly nonsmooth periodic signals using real parts of rational functions, similar to the Padé approach.

Part 4 explores scientific computing. The first paper, “Computer Graphics Techniques in Military Applications,” considers the determination of intersection points on plane curves, a procedure that has many applications, including trajectory tracing. Classical methods for solving this problem take O(n4) operations. The authors claim to reduce this number by an order of magnitude. The second paper, “Numerical Optimization for the Length Problem,” is aimed at the investigation of the length problem for normalized orthogonal matrices, with the goal of verifying certain complicated mathematical relationships.

Part 5 concerns combat models. The first paper investigates adaptive policies for sequential sampling from k independent statistical populations with unknown distributions having a constraint on the sampling cost. The second paper expands the renowned Lanchester Combat Model with a feature for reinforcement. The third paper considers land warfare in terms of complexity developments, including major related concepts such as cellular automata, genetic algorithms, and swarms. The work summarizes the research results that identify the basic features of complex adaptive systems in relation to the fundamental processes of war, particularly land combat.

Part 6 presents topics associated with satellite remote sensing. In the paper “Wavelet Transform in Remote Sensing with Implementation in Edge Detection and Noise Reduction,” the treatment of this subject is preceded with an overview of wavelet properties. Another paper, “Optimal Orbital Coverage of Theater Operations and Targets,” concentrates on the use of satellites as tactical tools to support small region operations. This study examines the optimization of orbit parameters for optimum coverage of a theater target. Tactical satellites may serve other missions besides visible imaging for communications or surveillance.

Part 7 demonstrates applications for coding and statistical modeling. The first paper, “A Bird’s-Eye View of Modern Symmetric Cryptography from Combinatorial Designs,” summarizes results in modern symmetric (private-key) cryptography employing special classes of combinatorial designs. The second paper, “On the Weak Convergence of an Empirical Estimator of the Discrete-Time Semi-Markov Kernel,” presents an application analysis of the properties of discrete-time semi-Markov processes. The third paper, “Analysis Methods for Unreplicated Factorial Experiments,” addresses the problem of unreplicated factorial designs, which are widely used in engineering and military trials when only a limited number of experimental runs is available.

The presented topics cover a wide range of applications in various human enterprises, of which military technology is just a significant example. The book would definitely be of interest to a variety of specialists.