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

Food Insecurity Among Homeless and Marginally Housed Individuals Living with HIV/AIDS in San Francisco

Food insecurity is a risk factor for both HIV transmission and worse HIV clinical outcomes. We examined the prevalence of and factors associated with food insecurity among homeless and marginally housed HIV-infected individuals in San Francisco recruited from the Research on Access to Care in the Homeless Cohort. We used multiple logistic regression to determine socio-demographic and behavioral factors associated with food insecurity, which was measured using the Household Food Insecurity Access Scale. Among 250 participants, over half (53.6%) were food insecure. Higher odds of food insecurity was associated with being white, low CD4 counts, recent crack use, lack of health insurance, and worse physical and mental health. Food insecurity is highly prevalent among HIV-infected marginally housed individuals in San Francisco, and is associated with poor physical and mental health and poor social functioning. Screening for and addressing food insecurity should be a critical component of HIV prevention and treatment programs

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

Explaining Variability in Caries Experience Using an Ecological Model

A model including diet, oral hygiene, and dental treatment and three ecological levels was tested to study variability in caries experience. Analysis produced a rank order of explanation for the ecological variables: (1) community, (2) family, (3) individual. The treatment factor contributed more to oral condition than oral hygiene or diet within each ecological level.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67939/2/10.1177_00220345740530030701.pd

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

Second order gauge invariant gravitational perturbations of a Kerr black hole

We investigate higher than the first order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar $\psi_4,$ representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order gauge (coordinates) and tetrad invariant waveform, $\psi_I$, by explicit construction. This waveform is formed by the second order piece of $\psi_4$ plus a term, quadratic in first order perturbations, chosen to make $\psi_I$ totally invariant and to have the appropriate behavior in an asymptotically flat gauge. $\psi_I$ fulfills a single wave equation of the form ${\cal T}\psi_I=S,$ where ${\cal T}$ is the same wave operator as for first order perturbations and $S$ is a source term build up out of (known to this level) first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy and momentum radiated and wave extraction for direct comparison with full numerical approaches to solve Einstein equations.Comment: 19 pages, REVTEX. Some misprints corrected and changes to improve presentation. Version to appear in PR

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

The SPORTSMART study: a pilot randomised controlled trial of sexually transmitted infection screening interventions targeting men in football club settings

Background: Uptake of chlamydia screening by men in England has been substantially lower than by women. Non-traditional settings such as sports clubs offer opportunities to widen access. Involving people who are not medically trained to promote screening could optimise acceptability. Methods: We developed two interventions to explore the acceptability and feasibility of urine-based sexually transmitted infection (STI) screening interventions targeting men in football clubs. We tested these interventions in a pilot cluster randomised control trial. Six clubs were randomly allocated, two to each of three trial arms: team captain-led and poster STI screening promotion; sexual health adviser-led and poster STI screening promotion; and poster-only STI screening promotion (control/comparator). Primary outcome was test uptake. Results: Across the three arms, 153 men participated in the trial and 90 accepted the offer of screening (59%, 95% CI 35% to 79%). Acceptance rates were broadly comparable across the arms: captain-led: 28/56 (50%); health professional-led: 31/46 (67%); and control: 31/51 (61%). However, rates varied appreciably by club, precluding formal comparison of arms. No infections were identified. Process evaluation confirmed that interventions were delivered in a standardised way but the control arm was unintentionally ‘enhanced’ by some team captains actively publicising screening events. Conclusions: Compared with other UK-based community screening models, uptake was high but gaining access to clubs was not always easy. Use of sexual health advisers and team captains to promote screening did not appear to confer additional benefit over a poster-promoted approach. Although the interventions show potential, the broader implications of this strategy for UK male STI screening policy require further investigation