Featured Books

Order Relations for the Cryptanalysis of Substitution Ciphers on
the Basis of Linguistic Data Structures as an Optimal Strategy

In order to analyze the solution behavior of general substitution ciphers for cryptanalysis, for the first time this book utilizes the methods of set optimization. The book investigates how to proceed optimally in a specific case. Linguistic data structures, such as the frequencies of the different letters, bigrams and trigrams, are divided into sets and described by order relations appropriate to the German and English languages. In the context of cryptanalysis this allows new solutions of existing models within the scope of set-valued order relations. This approach leads to an optimal strategy.

Compensation Payments for Aircraft Noise in an Urban Building Conflict Situation on the Basis of a Set-Valued Conjugate Duality

This book investigates compensation payments to property owners for aircraft noise in urban conflict situations in the region surrounding the airport for the first time on the basis of a set-valued conjugate duality. This optimal perturbation approach serves as justification for the realization of variable results. This "dual" socio-economy indicates the action strategy of different interest groups. Linear point sets as a new optimum set varying according to socio-economic properties and a payment function are therefore well substantiated.

Laplacian Eigenstructure of the Equilateral Triangle

"... The present book narrates this mathematical journey by providing a complete and self-contained treatment of the eigenstructure of the Laplacian on an equilateral triangle. The historical context and practical significance of the problem is carefully traced. The separate cases of Dirichlet, Neumann, radiation, absorbing and impedance boundary conditions are individually and exhaustively treated with the Dirichlet and Neumann cases also extended from the continuous to the discrete Laplacian. Corresponding results for the Sturm-Liouville boundary value problem under an impedance boundary condition are reviewed and applied to the parallel plate waveguide. Polygons with trigonometric eigenfunctions receive comprehensive study. Application to modal degeneracy in equilateral triangular waveguides has also been included."

Laplacian Eigenstructure of the Equilateral Triangle
BOOK REVIEW by Philip J. Davis
Celebrating Equilateralism, SIAM News, Volume 45, Number 1, January/February 2012

"... Contributor of a substantial addition to the literature of triangle geometry, Brian J. McCartin of Kettering University, a prize-winning author, has fallen in love with the equilateral triangle. Even as mathematician Lewis Carroll had his Snark pursued with “forks and hope,” McCartin has pursued the equilateral triangle with a fine-tooth comb supported by an eagle eye. He has tracked down the multiple personality of the equilateral triangle as it appears in history, design; in theorems of plane geometry; in applications, games, recreational mathematics, competitions (e.g., the Olympiads); and in popular culture."