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...

in his recognition of being and achievement of truth, man has two instruments in his constitution and two ways before him: intellect and heart; reasoning and intuition. some have opted the way of reasoning and underestimated intuition because of its lack of reasoning, and some have preferred intuition over reasoning because of its being presential (intuitive). with their research on philosophy ...

The study of the convergence to equilibrium of solutions to FokkerPlanck type equations with linear diffusion and super-linear drift leads in a natural way to a minimization problem for an energy functional (entropy) which relies on a sub-linear convex function. In many cases, conditions linked both to the non-linearity of the drift and to the space dimension allow the equilibrium to have a sin...

It is shown that a large class of solutions in two-degree-of-freedom Hamiltonian systems of billiard type can be described by slowly varying one-degree-of-freedom Hamiltonian systems. Under some non-degeneracy conditions such systems are found to possess a large set of quasiperiodic solutions filling out two dimensional tori, which correspond to caustics in the classical billiard. This provides...

Cognitive jammers are able to deploy advanced strategies that degrade the performance of cognitive radio user communications. In this paper, we study the problem of power allocation in cognitive radio user and jammer games, over parallel Gaussian channels. We model the interaction between a communicator (a transmitter-receiver pair) and a jammer using zero-sum games with continuous action sets;...

The notion of center of mass for an isolated system has been previously encoded in the definition of the so called nice sections. In this article we present a generalization of the proof of existence of solutions to the linearized equation for nice sections, and formalize a local existence proof of nice sections relaxing the radiation condition. We report on the differentiable and non-self-cros...

In the present paper we consider one class of zero-sum games with discontinuous payoffs which may have no solutions in the sets of pure or mixed strategies. We show that, however, the solution always exists in the set of so-called R-mixed strategies which are the elements of the space R of distributions with discontinuous test functions. The advantages of the new space of distributions (in comp...