Some bounds for the effective multiplication factor

The effective multiplication factor (keff) is the dominant eigenvalue for the stationary linear particle transport problem. Using positivity, global balance and a general duality formula bounds for the keff are derived in terms of the reactivity of the medium, perturbation of cross-sections and change of the size of the domain and/or its surface albedo. A different bound is also obtained with the help of a local keff value that is solution of an adjoint source problem.