The fuzzy entropy h(T) of a dynamical system has been introduced in [5] (see also [1, 3, 8, 10]). Generalizing the notion of a fuzzy partition Mesiar and Rybarik have studied the p-entropy (see [7, 10, 11]) based on the Pap y-calculus ([9]). The notion is based on an increasing bijective function g : [0,oo] —> [0, oo], such that #(0) = 0 and #(1) = 1. The choice g(x) = x leads to the fuzzy entr...

Using a variational formulation, we derive the Kirkwood superposition approximation for systems at equilibrium in the thermodynamic limit. We define the entropy of the triplet correlation function and show that the Kirkwood closure brings the entropy to its maximal value. This approach leads to a different interpretation for the Kirkwood closure relation, usually explained by probabilistic cons...

Two cellular automata are strongly conjugate if there exists a shiftcommuting conjugacy between them. We prove that the following two sets of pairs (F,G) of one-dimensional one-sided cellular automata over a full shift are recursively inseparable: (i) pairs where F has strictly larger topological entropy than G, and (ii) pairs that are strongly conjugate and have zero topological entropy. Becau...

We., generalize the c~:mcept of perfect graphs in terms of additivity of a functional called graph entropy. The latter is an information theoretic functional on a graph G with a probability distribution P on its vertex set. For any fixed P it is .sub-additive with respect to graE._h union. The entropy of the complete graph equals the sum of those of G and its complement G iff G is perfect. We '...

It is well known that if G is a countable amenable group and G y (Y ,ν) factors onto G y (X ,μ), then the entropy of the first action must be at least the entropy of the second action. In particular, if G y (X ,μ) has infinite entropy, then the action G y (Y ,ν) does not admit any finite generating partition. On the other hand, we prove that if G is a countable nonamenable group then there exis...

Spatially homogeneous batch reactor systems are characterized by the simultaneous presence of a wide range of time scales. When the dynamics of such reactive systems develop very-slow and very-fast time scales separated by a range of active time scales, with large gaps in the fast/active and slow/active time scales, then it is possible to achieve multi-scale adaptive model reduction along-with ...

where B(x,R) is the ball of radius R around a fixed point x in the universal cover X. (For noncompact M , see Section 6.2.) The number h(g) is independent of the choice of x, and equals the topological entropy of the geodesic flow on (M, g) when the curvature K(g) satisfies K(g) ≤ 0 (see [Ma]). Note that while the volume Vol(M, g) is not invariant under scaling the metric g, the normalized entropy

A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) ? h( f ). In this pap...

The interaction of Fe2+ ion with Pyrazole was theoretically studied by Gussian 03, software at HF/(LanL2DZ+6-31G) and HF/ (LanL2DZ+6-31G (d)) levels in gas phase and solution. In this study acompartion between optimized structures of Pyrazole molecule in aspect of thermodynamicparameters such as enthalpy (H°), Gibbs free energy (G°) and entropy (S°) in presence of metallic ion(Fe2+), was perfor...