ON SLOWLY VARYING STOKES WAVES by VINCENT HWA-HING CHU In this thesis investigations are made on the theory of a train of slowly modulated gravity waves propagating over uneven bottom topography. The primary object is to study the interplay of amplitude dispersion the frequency dispersion in waves on the surface of water where the depth is not too shallow compared to a typical wave length. The ...

This paper is a sequel to both Ash, Erd1⁄2os and Rubel [AER], on very slowly varying functions, and [BOst1], on foundations of regular variation. We show that generalizations of the Ash-Erd1⁄2os-Rubel approach –imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property – lead naturally to the main result of regular variation, th...

We shall denote the set of all regularly varying functions by R. We shall also denote by L the set of slowly slowly varying (or slowly oscillating) functions, namely those functions in R for which the index ρ = 0. It is easy to show that if h ∈ R, then there exists L ∈ L such that h(x) = xL(x), with ρ being the index of h. Slowly varying functions arise naturally in many branches of number theo...