A natural approach for solving large, high-frequency scattering problems is to augment a numerical (simulated) solution with the notion that light travels as rays. This combines the robustness of numerical methods, where every detail of the problem is modeled in the computer, with the quick timeto-solution characteristic of ray models. The resulting algorithms have potential to reduce overall c...

We consider K-interpolation spaces involving slowly varying functions, and derive necessary sufficient conditions for a Holmstedt-type formula to be held in the limiting case θ 0 = 1 ∈ { , } $\theta _0=\theta _1\in \lbrace 0,1\rbrace$ . also study ( ) (0,1)$ Applications are given Lorentz–Karamata spaces, generalized gamma Besov spaces.

Asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors is studied. It is shown that the asymptotic distribution may belong to one of four types depending on the relative rates of growth of the regressors. The paper expands and corrects recent results by P.C.B.Phillips (2007).

This paper proves the Baum–Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions. The proof exploits some properties slowly varying functions and de Bruijn conjugates, uses techniques developed by Rio (1995) to avoid using maximal type inequalities.