Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...

The trajectory planning, which is known as a movement from starting to end point by satisfying the constraints along the path is an essential part of robot motion planning. A common way to create trajectories is to deal with polynomials which have independent coefficients. This paper presents a trajectory formulation as well as a procedure to arrange the suitable trajectories for applications. ...

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. In 2006, Lucas proved that there are rewrite systems that can be shown polynomially terminating by polynomial interpretations with real (algebraic) coefficients, but cannot be shown polynomially ...

Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...

Let Sn denote the full symmetric permutation group of degree n. For each a E e, let (J (a) be the corresponding permutation matrix, i.e., Q(a) = (0 iUU»)' If e is any subgroup of S n, then Q is a faithful representation of e whose c haracter, e, counts the number of fixed points . In trus note, we in vestigate a red uction of fr, the character of the rth Kronecker power of (J . The reduction of...