Boundedness of maximal operators and oscillation of functions in metric measure spaces

In this dissertation the action of maximal operators and the properties of oscillating functions are studied in the context of doubling measure spaces. The work consists of four articles, in which boundedness of maximal operators is studied in several function spaces and different aspects of the oscillation of functions are considered. In particular, new characterizations for the BMO and the weak L∞ are obtained

John-Nirenberg lemmas for a doubling measure

We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderon-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.Comment: 17 pages, some typos correcte

Modal Locking Between Vocal Fold Oscillations and Vocal Tract Acoustics

During voiced speech, vocal folds interact with the vocal tract acoustics. The resulting glottal source-resonator coupling has been observed using mathematical and physical models as well as in in vivo phonation. We propose a computational time-domain model of the full speech apparatus that contains a feedback mechanism from the vocal tract acoustics to the vocal fold oscillations. It is based on numerical solution of ordinary and partial differential equations defined on vocal tract geometries that have been obtained by magnetic resonance imaging. The model is used to simulate rising and falling pitch glides of [alpha, i] in the fundamental frequency (f(o)) interval [145 Hz, 315 Hz]. The interval contains the first vocal tract resonance f(R1) and the first formant F-1 of [i] as well as the fractions of the first resonance f(R1)/5, f(R1)/4, and f(R1)/3 of [alpha]. The glide simulations reveal a locking pattern in the f(o) trajectory approximately at f(R1) of [i]. The resonance fractions of [alpha] produce perturbations in the pressure signal at the lips but no locking.Peer reviewe

Behavioral and subcortical signatures of musical expertise in Mandarin Chinese speakers

Both musical training and native language have been shown to have experience-based plastic effects on auditory processing. However, the combined effects within individuals are unclear. Recent research suggests that musical training and tone language speaking are not clearly additive in their effects on processing of auditory features and that there may be a disconnect between perceptual and neural signatures of auditory feature processing. The literature has only recently begun to investigate the effects of musical expertise on basic auditory processing for different linguistic groups. This work provides a profile of primary auditory feature discrimination for Mandarin speaking musicians and nonmusicians. The musicians showed enhanced perceptual discrimination for both frequency and duration as well as enhanced duration discrimination in a multifeature discrimination task, compared to nonmusicians. However, there were no differences between the groups in duration processing of nonspeech sounds at a subcortical level or in subcortical frequency representation of a nonnative tone contour, for f(o) or for the first or second formant region. The results indicate that musical expertise provides a cognitive, but not subcortical, advantage in a population of Mandarin speakers.Peer reviewe