We consider the problem of …nding the best analytic approximation in Smirnov and Bergman norm to general monomials of the type znzm. We show that in the case of approximation to z in the annulus (and the disk) the best approximation is the same for all values of p. Moreover, the best approximations to z in Smirnov and Bergman spaces characterize disks and annuli.

1.1 Graded associative algebras. A nite Z-grading of an algebra A is a decomposition A = L n i=?n A i such that A i A j A i+j , where A i = 0 for jij > n. From now on a grading means a nite Z-grading. I am interested in associative graded algebras because they arise naturally in study of Lie algebras, although the subject is certainly interesting in its own right. A classiication of gradings of...

Divergence date estimates are central to understand evolutionary processes and depend, in the case of molecular phylogenies, on tests of molecular clocks. Here we propose two non-parametric tests of strict and relaxed molecular clocks built upon a framework that uses the empirical cumulative distribution (ECD) of branch lengths obtained from an ensemble of Bayesian trees and well known non-para...

The averaging method is one of the most powerful methods used to analyse differential equations appearing in the study of nonlinear problems. The idea behind the averaging method is to replace the original equation by an averaged equation with simple structure and close solutions. A large number of practical problems leads to differential equations with discontinuous right-hand sides. In a rigo...

The virtual corrections to the production cross section of a Standard Model Higgs boson are computed up to order α s . Using an effective Lagrangian for the limit Mt → ∞, we evaluate the relevant massless two-loop vertex diagrams by mapping them onto three-loop two-point functions, following a method recently introduced by Baikov and Smirnov [1]. As a result, we find a gauge-invariant contribut...

The calculation of Franck-Condon factors between different one-dimensional Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a very simple program written in Mathematica is compared with other calculations. We show that our results have a similar accuracy as the calculations performed with more sophisticated methods. We d...

In this paper two different consistency testing methods for voxel coloring will be evaluated using voxel coloring algorithm proposed by Seitz & Dyer [1] as a basic tool. The first method is a statistical approach called Kolmogorov-Smirnov distance measure between two color distributions. The second method is a histogram-based consistency method proposed by Stevens & Culbertson [3]. Both of thes...

This contribution deals with the resource allocation in orthogonal frequency division multiplex (OFDM) systems used in the context of cognitive radio. Two main components of the overall system are spectrum sensing using the Kolmogorov-Smirnov significance test and resource (bit) allocation exploiting the results from sensing. The spectrum sensing method performance is firstly evaluated for sign...