Decomposition of L2L^{2}-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential

For $\partial \Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $\mathbb{R}^{d}$ with $d\geq3$, we prove that any field $f\in L^{2} (\partial \Omega ; \mathbb{R}^{d})$ decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of $\mathbb{R}^d\setminus\partial \Omega$. Moreover, this decomposition is orthogonal if and only if $\partial \Omega$ is a sphere. We also show that any $f$ in $L^{2} (\partial \Omega ; \mathbb{R}^{d})$ is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of $\partial \Omega$; we express the corresponding orthogonal projections in terms of layer potentials. When $\partial \Omega$ is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature

Unique reconstruction of simple magnetizations from their magnetic potential

Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such spaces that accommodate constraints suited for applications. In this paper we treat the inverse magnetization problem on a Lipschitz domain with fairly general topology. We characterize the subspace of $L^{2}$-vector fields that causes non-uniqueness, and identify a subspace of harmonic gradients on which the inversion becomes unique. This classification has consequences for applications and we present some of them in the context of geo-sciences. In the second part of the paper, we discuss the space of piecewise constant vector fields. This vector space is too large to make the inversion unique. But as we show, it contains a dense subspace in $L^2$ on which the problem becomes uniquely solvable, i.e., magnetizations from this subspace are uniquely determined by their magnetic potential

SOME CHANGES REQUIRED TO INCREASE THE PUBLIC'S UTILIZATION OF PREVENTIVE DENTISTRY *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65250/1/j.1752-7325.1968.tb03923.x.pd

Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles

Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in angular speed parameter. It is shown that the match applies to any previously known non-rotating fluid source made to rotate slowly for which a zero pressure boundary surface exists. The method is applied to the dust source of Robertson-Walker and in outline to an interior solution due to McVittie describing gravitational collapse. The applicability of the method to additional examples is transparent. The differential angular velocity of the rotating systems is determined and the induced rotation of local inertial frame is exhibited

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.Comment: 6 Pages, Revtex

Kerr-AdS and its Near-horizon Geometry: Perturbations and the Kerr/CFT Correspondence

We investigate linear perturbations of spin-s fields in the Kerr-AdS black hole and in its near-horizon geometry (NHEK-AdS), using the Teukolsky master equation and the Hertz potential. In the NHEK-AdS geometry we solve the associated angular equation numerically and the radial equation exactly. Having these explicit solutions at hand, we search for linear mode instabilities. We do not find any (non-)axisymmetric instabilities with outgoing boundary conditions. This is in agreement with a recent conjecture relating the linearized stability properties of the full geometry with those of its near-horizon geometry. Moreover, we find that the asymptotic behaviour of the metric perturbations in NHEK-AdS violates the fall-off conditions imposed in the formulation of the Kerr/CFT correspondence (the only exception being the axisymmetric sector of perturbations).Comment: 26 pages. 4 figures. v2: references added. matches published versio

EVALUATION OF DENTAL HEALTH EDUCATION IN A SCHOOL DENTAL CARE PROGRAM

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65546/1/j.1752-7325.1978.tb03715.x.pd

Towards a methodology for cluster searching to provide conceptual and contextual "richness" for systematic reviews of complex interventions: case study (CLUSTER)

Background Systematic review methodologies can be harnessed to help researchers to understand and explain how complex interventions may work. Typically, when reviewing complex interventions, a review team will seek to understand the theories that underpin an intervention and the specific context for that intervention. A single published report from a research project does not typically contain this required level of detail. A review team may find it more useful to examine a “study cluster”; a group of related papers that explore and explain various features of a single project and thus supply necessary detail relating to theory and/or context. We sought to conduct a preliminary investigation, from a single case study review, of techniques required to identify a cluster of related research reports, to document the yield from such methods, and to outline a systematic methodology for cluster searching. Methods In a systematic review of community engagement we identified a relevant project – the Gay Men’s Task Force. From a single “key pearl citation” we conducted a series of related searches to find contextually or theoretically proximate documents. We followed up Citations, traced Lead authors, identified Unpublished materials, searched Google Scholar, tracked Theories, undertook ancestry searching for Early examples and followed up Related projects (embodied in the CLUSTER mnemonic). Results Our structured, formalised procedure for cluster searching identified useful reports that are not typically identified from topic-based searches on bibliographic databases. Items previously rejected by an initial sift were subsequently found to inform our understanding of underpinning theory (for example Diffusion of Innovations Theory), context or both. Relevant material included book chapters, a Web-based process evaluation, and peer reviewed reports of projects sharing a common ancestry. We used these reports to understand the context for the intervention and to explore explanations for its relative lack of success. Additional data helped us to challenge simplistic assumptions on the homogeneity of the target population. Conclusions A single case study suggests the potential utility of cluster searching, particularly for reviews that depend on an understanding of context, e.g. realist synthesis. The methodology is transparent, explicit and reproducible. There is no reason to believe that cluster searching is not generalizable to other review topics. Further research should examine the contribution of the methodology beyond improved yield, to the final synthesis and interpretation, possibly by utilizing qualitative sensitivity analysis

Two Sides of the Same Story: Alcohol Use and HIV Risk Taking in South India

This qualitative study examines the role of alcohol in sexual risk among male migrant workers and female sex workers in two South Indian states. Most men reported using alcohol for increased energy and courage prior to their sexual experiences and to reduce feelings of loneliness and isolation. Sex workers, on the other hand, often stated that they avoided alcohol prior to sex in order to stay alert and reduce the risk of violence. Both groups reported that drinking often increased male aggression and reduced condom use. Research is needed to examine the prevalence of these patterns as well as factors associated with sexual risk and violence, in order to develop targeted interventions for these groups. Future risk reduction programs may benefit from addressing safer ways of meeting the needs expressed by the participants. This may include strategies to defuse volatile situations, safe ways of improving the sexual experience, and interventions aimed at alleviating loneliness and isolation for migrants