Casimir Effect in Hyperbolic Polygons

We derive a trace formula for the spectra of quantum mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two dimensional hyperboloid. Using this trace formula and the point splitting regularization method we calculate the Casimir energy for a scalar fields in such domains. The dependence of the vacuum energy on the number of vertexes is established.Comment: Latex, 1

A Rapid Assessment Scorecard to Identify Informal Settlements at Higher Maternal and Child Health Risk in Mumbai

The communities who live in urban informal settlements are diverse, as are their environmental conditions. Characteristics include inadequate access to safe water and sanitation, poor quality of housing, overcrowding, and insecure residential status. Interventions to improve health should be equity-driven and target those at higher risk, but it is not clear how to prioritise informal settlements for health action. In implementing a maternal and child health programme in Mumbai, India, we had conducted a detailed vulnerability assessment which, though important, was time-consuming and may have included collection of redundant information. Subsequent data collection allowed us to examine three issues: whether community environmental characteristics were associated with maternal and newborn healthcare and outcomes; whether it was possible to develop a triage scorecard to rank the health vulnerability of informal settlements based on a few rapidly observable characteristics; and whether the scorecard might be useful for future prioritisation. The City Initiative for Newborn Health documented births in 48 urban slum areas over 2 years. Information was collected on maternal and newborn care and mortality, and also on household and community environment. We selected three outcomes—less than three antenatal care visits, home delivery, and neonatal mortality—and used logistic regression and classification and regression tree analysis to test their association with rapidly observable environmental characteristics. We developed a simple triage scorecard and tested its utility as a means of assessing maternal and newborn health risk. In analyses on a sample of 10,754 births, we found associations of health vulnerability with inadequate access to water, toilets, and electricity; non-durable housing; hazardous location; and rental tenancy. A simple scorecard based on these had limited sensitivity and positive predictive value, but relatively high specificity and negative predictive value. The scorecard needs further testing in a range of urban contexts, but we intend to use it to identify informal settlements in particular need of family health interventions in a subsequent program

Ground motion measurements at the LBL Light Source site, the Bevatron and at SLAC

This report describes the technique for measuring ground motion at the site of the 1.0 to 2.0 GeV Synchrotron Radiation Facility which was known as the Advanced Light Source (in 1983 when the measurements were taken). The results of ground motion measurements at the Light Source site at Building 6 at LBL are presented. As comparison, ground motion measurements were made at the Byerly Tunnel, the Bevatron, Blackberry Canyon, and SLAC at the Spear Ring. Ground Motion at the Light Source site was measured in a band from 4 to 100 Hz. The measured noise is primarily local in origin and is not easily transported through LBL soils. The background ground motion is for the most part less than 0.1 microns. Localized truck traffic near Building 6 and the operation of the cranes in the building can result in local ground motions of a micron or more for short periods of time. The background motion at Building 6 is between 1 and 2 orders of magnitude higher than ground motion in a quiet seismic tunnel, which is representative of quiet sites worldwide. The magnitude of the ground motions at SLAC and the Bevatron are comparable to ground motions measured at the Building 6 Light Source site. However, the frequency signature of each site is very different

Constraints on the CMB temperature redshift dependence from SZ and distance measurements

The relation between redshift and the CMB temperature, $T_{CMB}(z)=T_0(1+z)$ is a key prediction of standard cosmology, but is violated in many non-standard models. Constraining possible deviations to this law is an effective way to test the $\Lambda$CDM paradigm and search for hints of new physics. We present state-of-the-art constraints, using both direct and indirect measurements. In particular, we point out that in models where photons can be created or destroyed, not only does the temperature-redshift relation change, but so does the distance duality relation, and these departures from the standard behaviour are related, providing us with an opportunity to improve constraints. We show that current datasets limit possible deviations of the form $T_{CMB}(z)=T_0(1+z)^{1-\beta}$ to be $\beta=0.004\pm0.016$ up to a redshift $z\sim 3$. We also discuss how, with the next generation of space and ground-based experiments, these constraints can be improved by more than one order of magnitude.Comment: 27 pages, 11 figure

Relativistic Kramers-Pasternack Recurrence Relations

Recently we have evaluated the matrix elements $$,$where$O$$={1,\beta, i\mathbf{\alpha n}\beta} $are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, in terms of generalized hypergeometric functions$_{3}F_{2}(1) $ for all suitable powers and established two sets of Pasternack-type matrix identities for these integrals. The corresponding Kramers--Pasternack three-term vector recurrence relations are derived here.Comment: 12 pages, no figures Will appear as it is in Journal of Physics B: Atomic, Molecular and Optical Physics, Special Issue on Hight Presicion Atomic Physic

On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.Comment: 47 pages, 5 figures. v2: See end of introduction for an important note adde

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers