The Dirichlet space: A Survey

In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we focus mainly on certain function theoretic properties of the Dirichlet space and omit covering the interesting connections between this space and operator theory. The results discussed in this survey show what is known about the Dirichlet space and compares it with the related results for the Hardy space.Comment: 35 pages, typoes corrected, some open problems adde

Preformed metal crowns for decayed primary molar teeth

BackgroundPreformed metal crowns (PMCs) are recommended by the British Society of Paediatric Dentistry (BSPD) for restoring badly broken down primary molar teeth. However, few dental practitioners adopt this technique in clinical practice, citing cost and clinical difficulty as reasons for this. Whilst there is a subjective impression by clinical academics that PMCs provide a more durable restoration than filling materials, there appears to be little evidence within the literature to support this.ObjectivesThe primary aim of this systematic review was to compare clinical outcomes for primary molar teeth restored using PMCs compared to those restored with filling materials.Search methodsThe literature was searched using: the Cochrane Central Register of Controlled Trials (CENTRAL) (The Cochrane Library 2005, Issue 3); MEDLINE (1966 to August 2005); EMBASE (1980 to August 2005); System for Information on Grey Literature in Europe (SIGLE) (1976 to August 2005). Relevant publications' reference lists were reviewed for relevant articles. The most recent search was carried out on 24 August 2005.Selection criteriaRandomised controlled trials (RCTs) that assessed the effectiveness of PMCs compared with filling materials or where there had been no treatment in children with untreated tooth decay in one or more primary molar teeth.Data collection and analysisTwo review authors independently assessed the title and abstracts for each article from the search results to decide whether it was likely to be relevant. Full papers were obtained for relevant articles and all three review authors studied these.Main resultsForty‐seven records were retrieved by the search strategies of which some were duplicates. Of these, 14 studies were scrutinised. No studies met the inclusion criteria and six studies were excluded from the review as they were either retrospective in design or reported as prospective outcomes but not randomised. No data were available for extraction and analysis and therefore, no conclusion could be made as to whether PMCs were more successful than filling materials for restoring primary molar teeth.Authors' conclusionsNo RCTs were available for appraisal. Whilst this technique is recommended by the BSPD for use in clinical practice, the evidence to support this is not strong, consisting mainly of case reports and uncontrolled studies. It is important that the absence of evidence for PMCs is not misinterpreted as evidence for their lack of efficacy.There is a strong need for prospective RCTs comparing PMCs and fillings for managing decayed primary molar teeth. The lower levels of evidence that have been produced, however, have strength in that the clinical outcomes are consistently in favour of PMCs, despite many of the studies placing PMCs on the most damaged of the pair of teeth being analysed

Lecture Notes on Topological Crystalline Insulators

We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like mirror or rotational symmetries. To deduce the topological properties, we use non-Abelian Wilson loops. We also discuss in detail higher-order topological insulators with hinge and corner states, and in particular present interacting bosonic models for the latter class of systems.Comment: Lectures given at the San Sebasti\'an Topological Matter School 2017, published in "Topological Matter. Springer Series in Solid-State Sciences, vol 190. Springer, Cham

A search for variable white dwarfs in large area time domain surveys: a pilot study in SDSS Stripe 82

We present a method to reliably select variable white dwarfs from large area time domain surveys and apply this method in a pilot study to search for pulsating white dwarfs in the Sloan Digital Sky Survey Stripe 82. From a sample 400 high-confidence white dwarf candidates, we identify 24 which show significant variability in their multi-epoch Stripe 82 data. Using colours, we further selected a sample of pulsating white dwarf (ZZ Ceti) candidates and obtained high cadence follow up for six targets. We confirm five of our candidates as cool ZZ Cetis, three of which are new discoveries. Among our 24 candidates we also identify: one eclipsing binary, two magnetic white dwarfs and one pulsating PG1159 star. Finally we discuss the possible causes for the variability detected in the remaining targets. Even with sparse multi-epoch data over the limited area of Stripe 82, we demonstrate that our selection method can successfully identify various types of variable white dwarfs and efficiently select high-confidence ZZ Ceti candidates.Comment: Accepted for publication in MNRAS, 14 pages, 11 figure