By a highly–oscillating function we mean one with large number of local maxima and minima over some interval. The computation of integrals of highly–oscillating functions is one of the most important issues in numerical analysis since such integrals abound in applications in many branches of mathematics as well as in other sciences, e.g., quantum physics, fluid mechanics, electromagnetics, etc....

Acknowledgements: I would like to thank E. Sonnendrücker for the stimulating discussions we had together and from which the problem treated in this paper emerged. Abstract: we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms. Each of those terms writes as an oscillating operator acting on ...

An 'oscillating' version of Brownian motion is defined and studied. 'Ordinary' Brownian motion and 'reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is establis...

a noninteracting quantum-dot arrays side coupled to a quantum wire is studied. transport through the quantum wire is investigated by using a noninteracting anderson tunneling hamiltonian. the conductance at zero temperature develops an oscillating band with resonances and antiresonances due to constructive and destructive interference in the ballistic channel, respectively. moreover, we have fo...

Microbially mediated reduction–oxidation (redox) reactions are often invoked as being the mechanisms by which redox state influences the degradation of sedimentary organic matter (OM) in the marine environment. To evaluate the effects of elevated, oscillating and reduced redox potentials on the fate of primarily aged, mineral-adsorbed OM contained in continental shelf sediments, we used microbi...

A viscometer for bedside blood measurements was developed, consisting of an oscillating resonator probe mounted directly into a disposable vacutainer tube for blood withdrawal. It was tested in vitro on blood samples with variable hematocrits (20-60%), increasing fibrinogen concentrations (0-20 g/l), increasing concentrations of an admixed radiographic contrast medium and erythrocyte suspension...