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 this study, time-delayed stochastic dynamical systems of linear and nonlinear equations are discussed. The existence uniqueness the semilinear time-delay system in finite dimensional space is investigated. Introducing delay Gramian matrix, we establish some sufficient necessary conditions for relative approximate controllability systems. addition, by applying Banach fixed point theorem, diff...

in the present work, dft calculations are employed to obtain the optimized structures of 4-acyl pyrazolone tautomers (19 tautomers) using b3lyp/6-311++g** calculations. inaddition, molecular parameters, ir frequencies and relative energies are extracted for alltautomers. the existence of aromatic ring, keto tautomer (versus enol tautomer), n-h bond(versus c-h bond) and c=n double bond (versus n...

modern scientific cosmology, having grounded itself in materialism, rebuts any theocentric explanation of the world as unnecessary and irrational. stephan hawking, being a prominent figure in this field, seeks to demonstrate that the world has come to existence by chance or necessity through an antitheistic argument based on big bang theory. regarding the metaphysical dimensions of the discours...

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...