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.

It is known that, if an equilibrium of a nonlinear system has a stability property when an external input is frozen, then the property is maintained under the input being slowly varying. In this paper, we show that the same stability property is preserved not only under slowly varying input but also under slowlyvarying-average input (which is not actually slowly varying but its ‘average’ is slo...

The Empirical Mode Decomposition (EMD) is a popular algorithm used for the processing of non-linear and non-stationary signals. In this paper we implemented the EMD algorithm and study the use of EMD in broad range of applications for extracting data from the signals. It decomposes the signal into highly varying Intrinsic Mode Functions (IMF) and slowly varying residues. Finally the results are...

We assume that the sequence ck, k ≥ 0, is regularly varying with index −β, β ∈ (1/2, 1) (written as ck ∈ RV−β). This means that ck ∼ k L0(k) as k → ∞, where L0 is slowly varying at infinity (see e.g. [2, Sections 1.4, 1.5] for the definition of slowly varying functions). We shall refer to all such models as long range dependent (LRD) linear processes. In particular, by the Karamata Theorem, the...