Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is...

A class of boundary value problems arising in the study of scattering of surface water waves by barriers, under the assumption of the linearized theory, is reduced to singular integral equations of the first kind, involving only ”weakly singular” kernels. The unified treatment presented here is observed to be most suitable to handle the class of scattering problems under consideration and it is...