On a characterization of directed divergence

Shannon's entropy was characterized by many authors by assuming different sets of postulates. One other measure associated with Shannon's entropy is directed divergence or information gain. In this paper, a characterization theorem for the measure directed divergence is given by assuming intuitively reasonable postulates and with the help of functional equations

Enumeration of almost cubic maps

AbstractThis paper deals with the enumeration of rooted planar maps in which the root vertex is of arbitrary valence and all other vertices are trivalent. A formula, in explicit form, is given and closed form expressions are given for several cases of interest. Some interesting summation formulae are also obtained towards the end of the paper

Consequences of temperature fluctuations in observables measured in high energy collisions

We review the consequences of intrinsic, nonstatistical temperature fluctuations as seen in observables measured in high energy collisions. We do this from the point of view of nonextensive statistics and Tsallis distributions. Particular attention is paid to multiplicity fluctuations as a first consequence of temperature fluctuations, to the equivalence of temperature and volume fluctuations, to the generalized thermodynamic fluctuations relations allowing us to compare fluctuations observed in different parts of phase space, and to the problem of the relation between Tsallis entropy and Tsallis distributions. We also discuss the possible influence of conservation laws on these distributions and provide some examples of how one can get them without considering temperature fluctuations.Comment: Revised version of the invited contribution to The European Physical Journal A (Hadrons and Nuclei) topical issue about 'Relativistic Hydro- and Thermodynamics in Nuclear Physics' guest eds. Tamas S. Biro, Gergely G. Barnafoldi and Peter Va

A directed-divergence function of type β

A new concept of directed-divergence function of type β is introduced in this paper. This concept is used in obtaining a directed-divergence of type β which generalizes Kullback's directed-divergence and has a relation with RÉnyi's information-gain of order β. This relation can be used to give another characterization of information-gain of order β. A characterization theorem for the directed-divergence of type β is proved with the help of a functional equation