We study compositional inverses of permutation polynomials, complete map-pings, mutually orthogonal Latin squares, and bent vectorial functions. Recently it was obtained in [33] the compositional inverses of linearized permutation binomials over finite fields. It was also noted in [29] that computing inverses of bijections of subspaces have applications in determining the compositional inverses...

We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe A is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.