Let f be a non-negative function on R, which is radially monotone (0 < f ↓ r). For 1 < p < ∞, g ≥ 0 and v a weight function, an equivalent expression for sup f↓r ∫ Rn fg (∫ Rn f pv ) 1 p is proved as a generalization of the usual Sawyer duality principle. Some applications involving boundedness of certain integral operators are also given.

In this paper, the analysis is focused on single-time optimal control problems based on simple integral cost functionals from Lagrangians whose order is smaller than the higher order of ODEs constraints. The basic topics of our theory include: variational differential systems, adjoint differential systems, Legendrian duality, single-time maximum principle. The main original results refer to the...

In 1991 Claus Emmeche and I suggested that ‘the chain of events which sets life apart from non-life.... needs at least two codes: one code for action (behaviour) and one code for memory—the very first of these codes necessarily must be analog and the second very probably must be digital.’ This principle of code-duality played a major role in our initial ideas on biosemiotics. The paper looks ba...

We propose and study WCh-branes of M-theory and type IIA theory on backgrounds that are related by Hopf T-duality. The dynamics of these branes, with a reasonable degree of gauge symmetry, is reduced to that for particles that evolve somewhere along elastic worldlines. This constitutes an interesting holographic principle that allows us to determine moduli spaces of soliton solutions for WCh-br...

A discrete-time linear optimal control problem with given initial and terminal times, state-control constraints, and variable end points is set forth. Corresponding to this primal control problem, or maximization problem, is a dual linear control problem, or minimization problem. The fundamental properties of duality are stated. A dual maximum principle is proved with the aid of the duality the...

De Vrijer has presented a proof of the finite developments theorem which, in addition to showing that all developments are finite, gives an effective reduction strategy computing longest developments as well as a simple formula computing their length. We show that by applying a rather simple and intuitive principle of duality to de Vrijer’s approach one arrives at a proof that some developments...