Boundary version of a twin region convergence theorem for continued fractions

AbstractThe starting point of the present paper is a result by Thron (1959) on twin convergence regions, dealing with continued fractions K(cn2/1), where |c2m-1| ⩽ ρ <1 and |c2m±i| ⩾ρ. In the present paper these regions are replaced by their boundaries, and the sets of continued fraction values are determined

Some univalent compositions of polynomials with univalent functions

Abstract. Let S denote the family of functions f, holomorphic and univalent in the open unit disk U, and normalized by f(0) = 0, f'(0) = 1

Monotonicity of CF-coefficients in Gauss-fractions

AbstractMonotonicity properties of coefficients in S-fraction expansions are often very useful in the computation of truncation error bounds for approximate function values. For hypergeometric functions F12 with parameters such that the C-fraction expansion is an S-fraction, it turns out that the CF-coefficients essentially always have those properties. This is proved in the present paper

Rhythmic movements and moveable rhythms : syntheses of expressive timing by means of rhythmic frequency modulation

dr.art.dr.art

Synthesis of asymmetric movement trajectories in timed rhythmic behaviour by means of frequency modulation

Results from different empirical investigations on gestural aspects of timed rhythmic movements indicate that the production of asymmetric movement trajectories is a feature that seems to be a common characteristic of various performances of repetitive rhythmic patterns. The behavioural or neural origin of these asymmetrical trajectories is, however, not identified. In the present study we outline a theoretical model that is capable of producing syntheses of asymmetric movement trajectories documented in empirical investigations by Balasubramaniam, Wing, and Daffertshofer (2004). Characteristic qualities of the extension/ flexion profiles in the observed asymmetric trajectories are reproduced, and we conduct an experiment similar to Balasubramaniam et al. (ibid.) to show that the empirically documented movement trajectories and our modelled approximations share the same spectral components. The model is based on an application of frequency modulated movements, and a theoretical interpretation offered by the model is to view paced rhythmic movements as a result of an unpaced movement being “stretched” and “compressed”, caused by the presence of a metronome. We discuss our model construction within the framework of event-based and emergent timing, and argue that a change between these timing modes might be reflected by the strength of the modulation in our model