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Nonextensive statistical mechanics has been a source of investigation in mathematical structures such as deformed algebraic structures. In this work, we present some consequences of $q$-operations on the construction of $q$-numbers for all numerical sets. Based on such a construction, we present a new product that distributes over the $q$-sum. Finally, we present different patterns of $q$-Pascals triangles, based on $q$-sum, whose elements are $q$-numbers.
We study the thermodynamics of metals by applying q-deformed algebras. We shall mainly focus our attention on q-deformed Sommerfeld parameter as a function of q-deformed electronic specific heat. The results revealed that q-deformation acts as a fact
We study the coherent state and two-mode squeezed state in the q-deformed Pegg-Barnett(PB) formalism. We show that when the truncation of the Fock space S is large enough, the phase properties of the q-deformed PB coherent state approach that of the
We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a $q$-analogue of a real. The construction is based on the notion of $q$-deformed rational number introduced in arXiv:1812.00170. Exte
We examine time dependent Schru007fodinger equation with oscillating boundary condition. More specifically, we use separation of variable technique to construct time dependent rationally extended Pu007foschl-Teller potential (whose solutions are give
In this paper, classical small perturbations against a stationary solution of the nonlinear Schrodinger equation with the general form of nonlinearity are examined. It is shown that in order to obtain correct (in particular, conserved over time) nonz