The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carathéodory, the Keenan School, Lieb and Yngvason, and the present authors. An improvement of the latter method is then presented. Seven basic axioms are employed: three Postulates, which are considered as having a quite general validity, and four Assumptions, which iden...

We investigate the possibility of designing phononic crystal-based devices for telecommunication applications using materials commonly employed in microfabrication. We focus our attention on a phononic crystal made of a square array of cylindrical holes drilled in an active piezoelectric PZT5A matrix. Two different structures are considered, namely, a freestanding phononic crystal plate and a p...

Transmission of acoustic waves in two-dimensional binary solid/solid composite media composed of arrays of Duralumin cylindrical inclusions embedded in an epoxy resin matrix is studied. The experimental transmission spectrum and theoretical band structure of two periodic arrays of cylinders organized on a square lattice and on a centred rectangular network are reported. Absolute gaps extending ...

neither the ash‘arites nor kierkegaard’s systems of theology are anti-rational, for kierkegaard regards the contradiction present in the object of faith as absolute rather than logical, suggesting thereby the existential dialectics for understanding this contradiction instead of resolving it. the ash‘arites also hold that one can understand the existence of god through absolute reason, or reaso...

Long after its alleged demise, phlogiston was still presented, discussed and defended by leading chemists. Even some of the leading proponents of the new chemistry admitted its 'absolute existence'. We demonstrate that what was defended under the title 'phlogiston' was no longer a particular hypothesis about combustion and respiration. Rather, it was a set of ontological and epistemological ass...

The space L(0, 1) has a natural Riemannian structure on the basis of which we introduce an L(0, 1)–infinite dimensional torus T. For a class of Hamiltonians defined on its cotangent bundle we establish existence of a viscosity solution for the cell problem on T or, equivalently, we prove a Weak KAM theorem. As an application, we obtain existence of absolute action-minimizing solutions of prescr...

For a series of randomly discounted terms we give an integral criterion to distinguish between almost-sure absolute convergence and divergence in probability to 1, these being the only possible forms of asymptotic behaviour. This solves the existence problem for a one-dimensional perpetuity that remains from a 1979 study by Vervaat, and yields a complete characterization of the existence of dis...

Neither the Ash‘arites nor Kierkegaard’s systems of theology are anti-rational, for Kierkegaard regards the contradiction present in the object of faith as absolute rather than logical, suggesting thereby the existential dialectics for understanding this contradiction instead of resolving it. The Ash‘arites also hold that one can understand the existence of God through absolute reason, or reaso...

Abstract. We propose a mathematical framework to effectively study lattice materials with periodic and non-periodic structures over entire spaces in one, two, and three dimensions. The existence and uniqueness of solutions for periodic lattice problems with absolute terms are proved in discrete Sobolev spaces. By Fourier transform discrete lattice problems are converted to semi-discrete problem...