Doctor of Philosophy / Department of Mathematics / Charles N. Moore / The main focus of this work is to study the classical Calder\'n-Zygmund theory and its recent developments. An attempt has been made to study some of its theory in more generality in the context of a nonhomogeneous space equipped with a measure which is not necessarily doubling. We establish a Hedberg type inequality associated to a non-doubling measure which connects two famous theorems of Harmonic Analysis-the Hardy-Littlewood-Weiner maximal theorem and the Hardy-Sobolev integral theorem. Hedberg inequalities give pointwise estimates of the Riesz potentials in terms of an appropriate maximal function. We also establish a good lambda inequality relating the distribution function of the Riesz potential and the fractional maximal function in $(\rn, d\mu)$, where $\mu$ is a positive Radon measure which is not necessarily doubling. Finally, we also derive potential inequalities as an application.

Radioactive decay of nuclei via emission of ??-particles is studied using three different theoretical approaches, viz: the quasi-bound state wavefunction approach (QSWA), the superasymmetric ??ssion model (SAFM) and the semiclassical approximation (QCA). The half-lives of the radioactive nuclei, calculated using these methods, are compared with each other and with available experimental data. The resonance wavefunction is obtained by numerically integrating the Schrödinger equation with outgoing boundary conditions. The sensitivity of the calculated decay widths to two particular parameter sets of the Woods-Saxon (WS) optical potentials are studied. Double folding (DF) model calculations to obtain the bare ??-nucleus potential have been carried out with the Reid M3Y effective nucleon-nucleon (NN) interactions. The exchange part of the interaction was taken to be of zero-range pseudo-potential and the density dependence of the NN interaction is accounted for. The effectiveness of the method is demonstrated using both even-even and odd-mass spherical nuclei. / Physics / MSC (PHYSICS)

Research suggests hypertension is associated with reduced somatosensory perception. Further, natural fluctuations in blood pressure (BP) across the cardiac cycle have been shown to modulate nociceptive responding, pain and tactile sensitivity, suggesting that arterial baroreceptors may be important moderators of somatosensation. This thesis further examined the influence of natural fluctuations in BP, and thus baroreceptor activity, across the cardiac cycle on electrocutaneous pain and tactile sensory thresholds and pain-related evoked potentials (PREPs) in normotensive individuals. Study 1 found pain thresholds were higher, i.e. pain was reduced, during systole compared to diastole. Further analysis revealed only participants with low-normal systolic BP displayed this cardiac cycle modulation, suggesting tonic BP may moderate cardiac cycle-related pain modulation. In the second study, tactile sensory thresholds did not vary across the cardiac cycle. However, when participants were split into high-normal and low-normal BP groups, interactions between BP and tactile sensory thresholds across the cardiac cycle were revealed. This finding suggests tonic BP may be an important factor determining the cardiac cycle modulation of tactile sensation. Study 3 found no variation in the N2 or P2 peak amplitudes, or N2-P2 peak-to-peak amplitudes across the cardiac cycle at scalp recording sites Cz, C3, or C4. Furthermore, BP median split analyses revealed no BP Group or interaction effect. As previous work reported a systolic dampening of PREPs, these data suggest the cardiac cycle-related modulation of PREPs may not be as robust as other measures of pain such as the nociceptive flexion reflex. Study 4 reported, in line with Study 3, no cardiac cycle related modulation of PREPs following stimulation of the right and left hands. However, a Hand x Scalp Electrode Site x Interval interaction was revealed for N2 peak amplitudes. These data suggest that the combination of side of stimulation and scalp recording site may be important in determining the patterning of PREPs across the cardiac cycle. Taken together, the findings of these studies suggest that pain perception, and to a lesser extent tactile sensation, are influenced by natural variations in BP across the cardiac cycle. However, modulation appears dependent on tonic BP. Conversely, pain-related brain activity across the cardiac cycle was not affected by tonic BP, but may be influenced by the combination of stimulation and recording sites.

No description available.

Statistical learning (SL) is believed to be a mechanism that enables successful language acquisition. Language acquisition in turn is heavily influenced by environmental factors such as socioeconomic status (SES). However, it is unknown to what extent SL abilities interact with SES in affecting language outcomes. To examine this potential interaction, we measured event-related potentials (ERPs) in 38 children aged 7-12 while performing a visual SL task consisting of a sequence of stimuli that contained covert statistical probabilities that predicted a target stimulus. Hierarchical regression results indicated that SL ability moderated the relationship between SES (average of both caregiver’s education level) and language scores (grammar, and marginally with receptive vocabulary). For children with high SL ability, SES had a weaker effect on language compared to children with low SL ability, suggesting that having good SL abilities could help ameliorate the disadvantages associated with being raised in a family with lower SES.

Thesis (PhD (Physics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The aim of this thesis is threefold. Firstly, I give an overview of non-commutative quan- tum mechanics and build up a description of non-commutative piecewise constant poten- tial wells in this context. Secondly, I look at some of the stationary properties of a finite non-commutative well using the mathematical tools laid out in the first part. Lastly, I in- vestigate how non-commutativity affects the tunneling rate through a barrier. Throughout this work I give the normal commutative descriptions and results for comparsion. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is drievoudig. Eerstens gee ek ’n oorsig van niekommutatiewe kwantummeganika en bou daarmee ’n beskrywing van niekommutatiewe deelswyskon- stante potensiaal putte op. Tweedens kyk ek na ’n paar van die stasionˆere eienskappe van ’n eindige niekommutatiewe potensiaal put deur die wiskunde te gebruik wat in die eerste deel uiteengesit is. Laastens ondersoek ek hoe niekommutatiwiteit die spoed van tonneling deur ’n potensiaal wal be¨ınvloed. Dwarsdeur die hierdie hele tesis gee ek die normale kommutatiewe beskrywings en resultate vir maklike vergelyking.

The work in this thesis is concerned with examining the retinal and cortical contributions to human trichromatic colour vision. Chromatic processing at the cortex level was examined using visual evoked potentials (VEPs). These responses were elicited by chromatic spot stimuli, which were manipulated in order to selectively activate the chromatic processing system. Chromatic processing at the retinal level was examined using the electroretinograms (ERGs) for which cone isolating stimuli were used to assess the nature of L and M cone inputs to cone-opponent mechanisms. The results from the VEP experiments suggest VEP morphology is dependent upon 1) chromatic and or luminance contrast content of the stimulus, 2) stimulus size, and 3) extent to which the chromatic stimulus activates either the L/M or S/(L+M) opponent mechanism. The experiments indicate that chromatic stimulation is indexed by large N1 component and small offset responses. Optimal stimulus size for chromatic isolation is 2-4 ° along L/M axes and 6° along S/(L+M) axis. From the ERG experiments, It has been shown that the low (12Hz) and high (30Hz) temporal frequency flickering stimuli can isolate the chromatic and luminance processing mechanisms in the retina. For low temporal frequency ERGs, the L:M ratio was close to unity and L/M phase difference was close to 180°. For high temporal frequency ERGs, the L:M ratio was more than unity and L/M phase difference was close to 90°. In addition to this, the variation in L:M ratio across the retinal eccentricity was also examined. These results suggest, for the chromatic processing, L:M ratio is close to unity independent of retinal eccentricity and individuals. For the luminance processing, L:M ratio is more than unity and depends upon the region of the retina being stimulated. These findings indicate the maintenance of cone selective input for the chromatic processing across the human retina.

In this thesis, we establish an analog of the Paley-Wiener Theorem for the ZS-AKNS scattering transform on a set of real potentials. We also demonstrate one application of our techniques to the study of an inverse spectral problem for a half-line Miura potential Schroedinger equation.

Individual differences in learning with a focus on neuropsychologic anomalies underlying learning strategies has been receiving attention in recent years. As a result, interest has increased in quantifying and analyzing cognitive behavior more directly. One of the tools that measures brain activity directly is the evoked potential (EP). This study investigated the EP recorded from the brainstem region, often referred to as brainstem auditory evoked response (BAER). The importance of BAERs in detecting pathology in the brainstem has been well documented. BAERs have also been advocated as an important tool in the electrophysiological assessment of children's brainstem function relative to learning disorders. BAER latencies were recorded, therefore, from a small group of average children and studied in relation to the BAER stability overtime. Intra-individual differences were compared to between-subject differences. So little BAER research has been performed with children that more studies are needed just to clarify normal variability of BAER parameters. The present investigation studied intra-individual differences in the stability of BAER latencies over time in young subjects with normal hearing, for comparing with and contrasting to previous results from a study using an adult sample. BAER latencies were recorded for left, right, and binaural ear presentations. A coefficient of stability (CS) was calculated for each peak, for each ear over time. ANOVA results showed significance for peak and peak by ear interaction. Several BAER parameters were examined within-subjects that may not be revealed in studies between-subjects. Profiles for intra-aural differences over time showed individual differences in the stability of the BAER. Although there appeared to be a trend toward inter-ear differences the differences did not reach significance. The profiles indicated considerable intra-aural pattern replicability, and a trend toward increase in stability over time. The results supported a need for future research on laterality studies, more age specific normative data and correlational studies in relation to individual cognitive differences.

The present dissertation aims to evaluate the phenomenon of visual masking as a tool for studying visual awareness focusing on two-alternative forced choice (2AFC) discrimination tasks. Two existing theories of masking - Bachmann's (1984) perceptual retouch theory and Marcel's (1983) recovery theory - are discussed along with the global neuronal workspace theory of awareness (Baars. 1989; Dehaene, Kerszberg, & Changeux, 1998). Performance accuracy on Semantic discrimination is compared to that on Orthographic discrimination as an indication of a potential difference between semantic and orthographic processing of masked word stimuli presented for 40 ms and 50 ms. This is further compared to an e-detection task previously used as an indicator of awareness in some masked priming experiments. Together, these tasks are further evaluated in terms of their relationship with participants' subjective reports collected in the form of confidence ratings. The implications and predictions drawn from the theories of masking and visual awareness as well as the notion of partial awareness (Kouider & Dupoux, 2001) are assessed taking into account the data obtained in the current experiments.The relevance of these data for masked priming is determined by performing a comparison between 2AFC discrimination and detection tasks, and the lexical decision task. An ERP study is also presented, in which Semantic and Orthographic discrimination as well as e-detection are paired with confidence ratings and electrophysiological recordings in search of an ERP component that can be correlated with both subjective (confidence) and objective (performance) measures of awareness. A binding account of visual awareness with special attention paid to visual masking is proposed and compared to the three existing theories.