Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization classical and quantum information processing. The ability implementing any n-dimensional unitary signal transformation by using reconfigurable optical hardware has recently led to pioneering concept programmable processor, whose basic building block (BB) must be correct...

We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi exactly system is studied which provides a direct counterpart of the Lamé equation.

We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N = 4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an overall phase. We carry on by diago-nalising it and obtain Bethe equations for periodic states. This proves an earlier proposal for the asymptotic Bethe equ...

the matrix functions appear in several applications in engineering and sciences. the computation of these functions almost involved complicated theory. thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. the aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. more...