Existence and uniqueness results for solutions to initial value problems in scales of Banach spaces: a thesis presented in partial fulfilment for the degree of Master of Science in Mathematics at Massey University

This thesis addresses existence and uniqueness of solutions to certain classes of initial-value problems with functional differential equations. The technique of scales of Banach spaces is used. A scale of Banach spaces is a collection of Banach spaces varying on a real parameter. A scale consisting of function spaces can be used to suppress one variable in an initial-value problem in a partial differential equation of two independent variables, therefore enabling local existence and uniqueness of a solution to the problem to be shown with the classical method of successive ap­ proximations from the Picard-Lindelof Theorem of ordinary differential equations. Tuschke's presentation (c.f. [7]) of this technique and a related theorem has been adapted in Chapters 1 and 2. Chapters 3 and 4 present original theorems, stating existence and uniqueness of solutions to more general initial-value problems, having a retarded character

The effects of rhythmic structure on tapping accuracy

Prior investigations of simple rhythms in familiar time signatures have shown the importance of several mechanisms; notably, those related to metricization and grouping. But there has been limited study of complex rhythms, including those in unfamiliar time signatures, such as are found outside mainstream Western music. Here, we investigate how the structures of 91 rhythms with nonisochronous onsets (mostly complex, several in unfamiliar time signatures) influence the accuracy, velocity, and timing of taps made by participants attempting to synchronize with these onsets. The onsets were piano-tone cues sounded at a well-formed subset of isochronous cymbal pulses; the latter occurring every 234 ms. We modelled tapping at both the rhythm level and the pulse level; the latter provides insight into how rhythmic structure makes some cues easier to tap and why incorrect (uncued) taps may occur. In our models, we use a wide variety of quantifications of rhythmic features, several of which are novel and many of which are indicative of underlying mechanisms, strategies, or heuristics. The results show that, for these tricky rhythms, taps are disrupted by unfamiliar period lengths and are guided by crude encodings of each rhythm: the density of rhythmic cues, their circular mean and variance, and recognizing common small patterns and the approximate positions of groups of cues. These lossy encodings are often counterproductive for discriminating between cued and uncued pulses and are quite different to mechanisms—such as metricization and emphasizing group boundaries—thought to guide tapping behaviours in learned and familiar rhythms

Open Notebook Science Challenge: Solubilities of Organic Compounds in Organic Solvents

This book contains the results of the Open Notebook Science Solubility Challenge. All experimental measurements are provided with a link to either the laboratory notebook page where the experiment was carried out or to a literature reference. The Challenge was sponsored by Submeta, Nature and Sigma-Aldrich

Open Notebook Science Challenge: Solubilities of Organic Compounds in Organic Solvents

This book contains the results of the Open Notebook Science Solubility Challenge. All experimental measurements are provided with a link to either the laboratory notebook page where the experiment was carried out or to a literature reference. The Challenge was sponsored by Submeta, Nature and Sigma-Aldrich

Referral pathways for TIA patients avoiding hospital admission : a scoping review

Objective: To identify the features and effects of a pathway for emergency assessment and referral of patients with suspected transient ischaemic attack (TIA) in order to avoid admission to hospital.Design: Scoping review.Data sources: PubMed, CINAHL Web of Science, Scopus.Study selection: Reports of primary research on referral of patients with suspected TIA directly to specialist outpatient services.Data extraction: We screened studies for eligibility and extracted data from relevant studies. Data were analysed to describe setting, assessment and referral processes, treatment, implementation and outcomes.Results: 8 international studies were identified, mostly cohort designs. 4 pathways were used by family doctors and 3 pathways by emergency department physicians. No pathways used by paramedics were found. Referrals were made to specialist clinic either directly or via a 24-hour helpline. Practitioners identified TIA symptoms and risk of further events using a checklist including the ABCD2 tool or clinical assessment. Antiplatelet medication was often given, usually aspirin unless contraindicated. Some patients underwent tests before referral and discharge. 5 studies reported reduced incident of stroke at 90 days, from 6–10% predicted rate to 1.3–2.1% actual rate. Between 44% and 83% of suspected TIA cases in these studies were referred through the pathways.Conclusions: Research literature has focused on assessment and referral by family doctors and ED physicians to reduce hospitalisation of patients with TIA. No pathways for paramedical use were reported. We will use results of this scoping review to inform development of a paramedical referral pathway to be tested in a feasibility trial

The Peculiar Debris Disk of HD 111520 as Resolved by the Gemini Planet Imager

Using the Gemini Planet Imager (GPI), we have resolved the circumstellar debris disk around HD 111520 at a projected range of ~30-100 AU in both total and polarized $H$-band intensity. The disk is seen edge-on at a position angle of ~165$^{\circ}$ along the spine of emission. A slight inclination or asymmetric warping are covariant and alters the interpretation of the observed disk emission. We employ 3 point spread function (PSF) subtraction methods to reduce the stellar glare and instrumental artifacts to confirm that there is a roughly 2:1 brightness asymmetry between the NW and SE extension. This specific feature makes HD 111520 the most extreme examples of asymmetric debris disks observed in scattered light among similar highly inclined systems, such as HD 15115 and HD 106906. We further identify a tentative localized brightness enhancement and scale height enhancement associated with the disk at ~40 AU away from the star on the SE extension. We also find that the fractional polarization rises from 10 to 40% from 0.5" to 0.8" from the star. The combination of large brightness asymmetry and symmetric polarization fraction leads us to believe that an azimuthal dust density variation is causing the observed asymmetry.Comment: 9 pages, 8 Figures, 1 table, Accepted to Ap