We prove Ostrowski inequalities (regular and weighted cases) on time scales and thus unify and extend corresponding continuous and discrete versions from the literature. We also apply our results to the quantum calculus case.

Linear and nonlinear Hamiltonian systems are studied on time scales . We unify symplectic flow properties of discrete and continuous Hamiltonian systems. A chain rule which unifies discrete and continuous settings is presented for our so-called alpha derivatives on generalized time scales. This chain rule allows transformation of linear Hamiltonian systems on time scales under simultaneous chan...

A study of ion sculpting dynamics in SiO2 and SiN using periodically pulsed ion beams reveals material transport that depends strongly on the time structure of the pulsed beams. It is found that significant nanoscale matter transport can occur over second long time scales after the ion beam has been extinguished. A simple phenomenological model described the dynamics of ion beam sculpting in te...

While the functions in (1.1) do not have ordinary derivatives at t = 0, they have symmetric derivatives: f s (0) = g (0) = h (0) = 0. For a deeper understanding of the symmetric derivative and its properties, we refer the reader to the specialized monograph [8]. Here we note that the symmetric quotient (f (t+ h)− f (t− h)) /(2h) has, in general, better convergence properties than the ordinary d...

where A ( < ) is analytic in the small parameter e . Our basic result is a uniform asymptotic approximation to exp A ( e ) r that we obtain under a certain multiple semistability condition. This asymptotic approximation gives a complete multiple time scale decomposition of the above system and specifies a set of reduced order models valid at each time scale. Our contribution is threefold. 1...

Integrable systems are usually given in terms of functions of continuous variables (on R), in terms of functions of discrete variables (on Z), and recently in terms of functions of q-variables (on Kq). We formulate the Gel’fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yie...

This paper studies the role of ‡uctuations in the aggregate price-earning ratio at di¤erent time scales for predicting stock returns and explore the channels through which returns are predicted. Using U.S. quarterly and international monthly data, we …nd that cycles in the price-earning ratio are strong and better predictors of future returns at short and intermediate horizons than the aggregat...