We show that a connection between the generalized entropy and theory of quantum groups,
recently pointed out by Tsallis [Phys. Lett. A 195 (1994) 329], can naturally be understood in …

We formulate generalized uncertainty relations in a crystal-like universe—a “world crystal”—
whose lattice spacing is of the order of Planck length. In the particular case when energies …

In the past decade there has been an extemely rapid growth in the interest and development
of quantum group theory. This book provides students and researchers with a practical …

A translation operator is introduced to describe the quantum dynamics of a position-
dependent mass particle in a null or constant potential. From this operator, we obtain a …

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry.
Any differential algebra on a discrete set can be regarded as a ''reduction''of the ''universal …

Two different formalisms have been recently developed for nonextensive physics, namely
the generalized statistical mechanics and thermodynamics (characterized by q≠ 1) and the …

We develop differential calculus and gauge theory on a finite set G. An elegant formulation is
obtained when G is supplied with a group structure and in particular for a cyclic group …

We propose that the phonons in 4 He obey aq deformation of the Heisenberg algebra and
we give an algebraic interpretation for the polynomial expansion of the small momenta …

We present an algorithm for solving unconstrained optimization problems based on the q-
gradient vector. The main idea used in the algorithm construction is the approximation of the …

The modifications that must be introduced within the framework of standard, classical N-
body statistical mechanics techniques, in order to deal with the recently proposed …