In 2004 Rosas and Sagan asked whether there was a way to define basis in the algebra of symmetric functions noncommuting variables, NCSym, having properties analogous classical Schur functions. This because they had constructed partial such set that not basis. We answer their question by defining variables using noncommutative analogue Jacobi-Trudi determinant. Our NCSym map under commutation, ...

Some fixed and coincidence point theorems for R-weakly commuting mappings are obtained. Our results generalize some recent results of Daffer and Kaneko [2] and many of the others. AMS Mathematics Subject Classification (2000): 54H25

Quantum teleportation is possible because entanglement allows a definition of precise correlations between the noncommuting properties of a local system and corresponding noncommuting properties of a remote system. In this paper, the exact causality achieved by maximal entanglement is analyzed and the results are applied to the transfer of effects acting on the entanglement distribution channel...

In [12], Stanley associated with a graph G a symmetric function XG which reduces to G’s chromatic polynomial XG(n) under a certain specialization of variables. He then proved various theorems generalizing results about XG(n), as well as new ones that cannot be interpreted on the level of the chromatic polynomial. Unfortunately, XG does not satisfy a Deletion-Contraction Law which makes it diffi...