Remarks on canonical commutation relations
On peculiarity of the case among the -state Ising-like models.
On deformations of finite operator calculus of Rota
The author develops a -analogue of Rota’s finite operator calculus in enumerative combinatorics.
Clifford and Grassmann like algebra
On the meaning of Bell's inequalities violation
Critical curves in nonstandard Potts models
Calculation of the free energy in a simple model
Algebraic properties of the 3-state vector Potts model
Further remarks on extended umbral calculus
The paper deals with extensions of the finite operator calculus of G.-C. Rota called -extensions which give a framework for corresponding quantum group investigations. This also covers the instance of the well-known -analogue of umbral calculus. The article also contains glossaries of the most important terms and notations used by Ward, Viskov, Markowsky and Roman on one side and the Rota-oriented notations on the other side.
More on deformed oscillator algebras and extended umbral calculus
This paper deals with calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily -extendable. The particular case is known to be relevant for quantum group investigations. It is shown here that such umbral calculus leads to infinitely many new -deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of umbral and calculus in which new families of extensions...
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