Intertwined Hamiltonians in Two Dimensional Curved Spaces

The problem of intertwined Hamiltonians in two dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane,Minkowski plane, Poincar{\' e} half plane ($AdS_2$), de Sitter Plane ($dS_2$), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems of considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum are like the spectrum of a free particle.Comment: To appear in Annals of Physic

Warped Entanglement Entropy

We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS$_3$ spacetimes with an SL(2,R) x U(1) isometry. We begin by applying the proposal to locally AdS$_3$ backgrounds which are written as a real-line fibration over AdS$_2$. We then perturb away from this geometry by considering a warping parameter $a=1+\delta$ to get an asymptotically warped AdS$_3$ spacetime and compute the dual entanglement entropy perturbatively in $\delta$. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in $\delta$ and takes the universal form appropriate for two-dimensional CFTs. The warping-dependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal two-dimensional CFT answers, with the left-moving and right-moving temperatures appearing appropriately in the result.Comment: 25 pages plus appendices; v2 references added, discussions clarified and equations sharpene

Topological Symmetries

We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and (2,1). This leads to a novel derivation of the algebras of supersymmetry and $p=2$ parasupersummetry.Comment: Plain LaTeX Ref: Mod. Phys. Lett. A 15, 175-184 (2000

A review of CAD/CAM use in dentistry (part II): Comparison of intraoral digital scanners used in restorative dentistry

Introduction: Intraoral imaging technology has become one of the most exciting new fields in dentistry. Three-dimensional scanning of the oral cavity is used in many dental procedures such as restorative dentistry and orthodontics. To date, a number of intraoral scanners have been developed for restorative dentistry throughout the world, and many researchers and manufacturers seek the design and development of new digital devices. Only some of these devices are currently available on the market and some others are being clinically tested. All existing intraoral scanners try to overcome the drawbacks of traditional impression processes. The aim of the present article is to provide an extensive evaluation of intraoral scanners in restorative dentistry, with special attention to their assessment principles, characteristics and performance. Review report: This review article was prepared by scientific searching in electronic sources of Pubmed and ISI Web of Science in connection with articles published in English until 2014, and with these key words: intraoral scanners and digital impression. Conclusion: Over the years there have been major advances in digital scanning systems, and a variety of digital systems have been introduced that enable the dentist to select different intraoral reconstruction methods in the extraoral environment. The ultimate goal of dentists is to provide accurate and efficient dental restorations for the patient, while maintaining patient comfort during the impression process. High-resolution dental optical scanners will enable the operator to provide high-quality restorations. With digital impression techniques, the number of operators and material variables will decrease, making restoration fabrication processes more predictable and easier

Holographic RG-flows and Boundary CFTs

Solutions of $(d+1)$-dimensional gravity coupled to a scalar field are obtained, which holographically realize interface and boundary CFTs. The solution utilizes a Janus-like $\mathrm{AdS}_d$ slicing ansatz and corresponds to a deformation of the CFT by a spatially-dependent coupling of a relevant operator. The BCFT solutions are singular in the bulk, but physical quantities such as the holographic entanglement entropy can be calculated.Comment: 26 pages, 11 figure

Virtual patient design : exploring what works and why : a grounded theory study

Objectives: Virtual patients (VPs) are online representations of clinical cases used in medical education. Widely adopted, they are well placed to teach clinical reasoning skills. International technology standards mean VPs can be created, shared and repurposed between institutions. A systematic review has highlighted the lack of evidence to support which of the numerous VP designs may be effective, and why. We set out to research the influence of VP design on medical undergraduates. Methods: This is a grounded theory study into the influence of VP design on undergraduate medical students. Following a review of the literature and publicly available VP cases, we identified important design properties. We integrated them into two substantial VPs produced for this research. Using purposeful iterative sampling, 46 medical undergraduates were recruited to participate in six focus groups. Participants completed both VPs, an evaluation and a 1-hour focus group discussion. These were digitally recorded, transcribed and analysed using grounded theory, supported by computer-assisted analysis. Following open, axial and selective coding, we produced a theoretical model describing how students learn from VPs. Results: We identified a central core phenomenon designated ‘learning from the VP’. This had four categories: VP Construction; External Preconditions; Student–VP Interaction, and Consequences. From these, we constructed a three-layer model describing the interactions of students with VPs. The inner layer consists of the student's cognitive and behavioural preconditions prior to sitting a case. The middle layer considers the VP as an ‘encoded object’, an e-learning artefact and as a ‘constructed activity’, with associated pedagogic and organisational elements. The outer layer describes cognitive and behavioural change. Conclusions: This is the first grounded theory study to explore VP design. This original research has produced a model which enhances understanding of how and why the delivery and design of VPs influence learning. The model may be of practical use to authors, institutions and researchers