Abstract The well-known $$\mathcal {E}$$ E -set introduced by Hayman in 1960 is a countable collection of Euclidean discs the complex plane, whose subtending angles at origin have finite sum. An important special case an known as R -set, for which sum diameters finite. These sets appear numerous papers theori...

driver fatigue may impose the risk of crashes and is a leading cause of death in transportation industry. this study aimed to detect driver cognitive fatigue based on changes in eeg frequency bands in non-professional drivers during a simulated driving task. in a descriptive-analytical study, 12 healthy male car drivers took part in a two hour driving session on a simulated monotonous road, whi...

Single nucleotide polymorphism (SNP) data can be used for parameter estimation via maximum likelihood methods as long as the way in which the SNPs were determined is known, so that an appropriate likelihood formula can be constructed. We present such likelihoods for several sampling methods. As a test of these approaches, we consider use of SNPs to estimate the parameter Theta = 4N(e)micro (the...

The “Theta method” of forecasting performed particularly well in the M3competition and is therefore of interest to forecast practitioners. The original description of the method given by Assimakopoulos and Nikolopoulos (2000) involves several pages of algebraic manipulation. We show that the method can be expressed much more simply and that the forecasts obtained are equivalent to simple expone...

The primitive cohomology of the theta divisor of a principally polarized abelian variety of dimension g contains a Hodge structure of level g− 3 which we call the primal cohomology. The Hodge conjecture predicts that this is contained in the image, under the Abel-Jacobi map, of the cohomology of a family of curves in the theta divisor. In this paper we use the Prym map to show that this version...

It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...

OBJECTIVE We examined whether the method of event-related (de-)synchronization (ERD/ERS) revealed differential effects of selective attention and working memory load in children (8-11 years) with pervasive developmental disorder - not otherwise specified (PDD-NOS) or attention-deficit/hyperactivity disorder (ADHD). METHODS Fifteen healthy controls and three equally large groups of children wi...