The thermodynamic functions such as enthalpy (H), Gibbs free energy (G) and entropy (S) ofPyrazole was theoretically studied at 5 different temperatures 25, 30, 35, 40 and 45°C by usingGussian o3, software. First, the structural optimization of isolated Pyrazole was done in the gas phaseby appling the Density Functional Theory (B3LYP) level with 3-21G, 6-31G and 6-31+G(d) basissets. Moreover, v...

The information entropy, as a measurement of the average amount of information contained in an information system, is used in the classification of objects and the analysis of information systems. The information entropy of a partition is non-increasing when the partition is refined, and is related to rough sets by Wong and Ziarko. The partitions and information entropy have some graph-theoreti...

For a topological dynamical system (X, f), consisting of a continuous map f : X → X, and a (not necessarily compact) set Z ⊂ X, Bowen [2] defined a dimension-like version of entropy, hX(f, Z). In the same work, he introduced a notion of entropyconjugacy for pairs of invertible compact systems: the systems (X, f) and (Y, g) are entropy-conjugate if there exist invariant Borel sets X ′ ⊂ X and Y ...

This paper deals with the problem of finding the range of entropy values resulting from actions of discrete amenable groups by automorphisms of compact abelian groups. When the acting group G is locally normal, we obtain an entropy formula and show that the full range of entropy values [0,∞] occurs for actions of G. We consider related entropy range problems, give sufficient conditions for zero...

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...

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...

Let FG(P ) be a functional defined on the set of all the probability distributions on the vertex set of a graph G. We say that G is symmetric with respect to FG(P ) if the uniform distribution on V (G) maximizes FG(P ). Using the combinatorial definition of the entropy of a graph in terms of its vertex packing polytope and the relationship between the graph entropy and fractional chromatic numb...

For an ergodic p.m.p. action G y (X,μ) of a countable group G, we define the Rokhlin entropy hRok G (X,μ) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov– Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Un...

Let (G,μ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A μ-random walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the random walk first hits Γ. We prove that the Furstenberg entropy of a (G,μ)-stationary space, with respect to the...

We study properties of graph colorings that minimize the quantity of color information with respect to a given probability distribution P on the vertices of the graph. The minimum entropy of any coloring of such a probabilistic graph (G,P ) is the chromatic entropy Hχ(G,P ). Applications of the chromatic entropy are found in data compression with side information at the receiver and digital ima...