Orbifolds, the A, D, E Family of Caustic Singularities, and Gravitational Lensing

We provide a geometric explanation for the existence of magnification relations for the A, D, E family of caustic singularities, which were established in recent work. In particular, it was shown that for families of general mappings between planes exhibiting any of these caustic singularities, and for any non-caustic target point, the total signed magnification of the corresponding pre-images vanishes. As an application to gravitational lensing, it was also shown that, independent of the choice of a lens model, the total signed magnification vanishes for a light source anywhere in the four-image region close to elliptic and hyperbolic umbilic caustics. This is a more global and higher-order analog of the well-known fold and cusp magnification relations. We now extend each of these mappings to weighted projective space, which is a compact orbifold, and show that magnification relations translate into a statement about the behavior of these extended mappings at infinity. This generalizes multi-dimensional residue techniques developed in previous work, and introduces weighted projective space as a new tool in the theory of caustic singularities and gravitational lensing.Comment: 11 page

Autoxidation of lipids in parchment

Historic parchment is a macromolecular material, which is complex due to its natural origin, inhomogeneity of the skin structure, unknown environmental history and potential localised degradation. Most research into its stability has so far focussed on thermal and structural methods of analyses. Using gas chromatographic analysis of the atmosphere surrounding parchment during oxidation, we provide the experimental evidence on the production of volatile aldehydes, which can be the products of lipid autoxidation. Oxidation of parchment with different aldehyde emissions was additionally followed in situ using chemiluminometry and the same techniques were used to evaluate the oxidation of differently delipidised parchment. It was shown that the production of peroxides and the emission of aldehydes from the material decrease with lower lipid content. Building on this evidence, we can conclude that the presence of lipids (either initially present in the skin or resulting from conservation intervention) leads to oxidative degradation of collagen and that the non-destructive analysis of the emission of volatiles could be used as a quick tool for evaluation of parchment stability

The spillover effects of monitoring:A field experiment

Published Online: March 13, 2015We provide field experimental evidence of the effects of monitoring in a context where productivity is multidimensional and only one dimension is monitored and incentivized. We hire students to do a job for us. The job consists of identifying euro coins. We study the direct effects of monitoring and penalizing mistakes on work quality and evaluate spillovers on unmonitored dimensions of productivity (punctuality and theft). We find that monitoring improves work quality only if incentives are harsh, but substantially reduces punctuality irrespectively of the associated incentives. Monitoring does not affect theft, with 10% of participants stealing overall. Our findings are supportive of a reciprocity mechanism, whereby workers retaliate for being distrusted

Submergence of magnetic flux in interaction of sunspot groups

Submergence of magnetic flux is demonstrated in the process of evolution of sunspot groups NOAA 6850 (26 Sep.-07 Oct. 1991) and 7220/22 (06-17 July 1992). In both cases new magnetic flux emerges immediately behind an existing spotgroup. The new flux does not interact with the old one, as can be seen in YOHKOH X-ray images, so no significant flare activity occurs, although umbrae of different magnetic polarity collide. In both cases the quickly forward moving p-spots of the new flux force the submergence of the f-spots of the older region, these being squeezed from two sides between the old and new p-spots. This leads to the disappearance of about 16 1021 Mx of f-polarity in AR 6850. In the case of this region the submerged flux interacts with newly emerging magnetic fields and in the next rotation continues its life as the complex and eruptive AR 6891. In AR 7220/22, spots of both polarities submerge in the intermediate part of the complex between the old leader of AR 7220 and the quickly growing AR 7222, leaving in the next rotation a bipolar-looking group (AR 7248), consisting of two p-polarity spots. So, submergence of magnetic flux due to interaction of old and new activity may play an important role in the decay of sunspot groups

Analysis of airborne Doppler lidar, Doppler radar and tall tower measurements of atmospheric flows in quiescent and stormy weather

The first experiment to combine airborne Doppler Lidar and ground-based dual Doppler Radar measurements of wind to detail the lower tropospheric flows in quiescent and stormy weather was conducted in central Oklahoma during four days in June-July 1981. Data from these unique remote sensing instruments, coupled with data from conventional in-situ facilities, i.e., 500-m meteorological tower, rawinsonde, and surface based sensors, were analyzed to enhance understanding of wind, waves and turbulence. The purposes of the study were to: (1) compare winds mapped by ground-based dual Doppler radars, airborne Doppler lidar, and anemometers on a tower; (2) compare measured atmospheric boundary layer flow with flows predicted by theoretical models; (3) investigate the kinematic structure of air mass boundaries that precede the development of severe storms; and (4) study the kinematic structure of thunderstorm phenomena (downdrafts, gust fronts, etc.) that produce wind shear and turbulence hazardous to aircraft operations. The report consists of three parts: Part 1, Intercomparison of Wind Data from Airborne Lidar, Ground-Based Radars and Instrumented 444 m Tower; Part 2, The Structure of the Convective Atmospheric Boundary Layer as Revealed by Lidar and Doppler Radars; and Part 3, Doppler Lidar Observations in Thunderstorm Environments

Nonlocal lattice fermion models on the 2d torus

Abelian fermion models described by the SLAC action are considered on a finite 2d lattice. It is shown that modification of these models by introducing additional Pauli - Villars regularization supresses nonlocal effects and provides agreement with the continuum results in vectorial U(1) models. In the case of chiral fermions the phase of the determinant differs from the continuum one.Comment: 16 pages, LaTeX, 5 eps figures, uses epsf.sty, rotate.st

Old and New Fields on Super Riemann Surfaces

The ``new fields" or ``superconformal functions" on $N=1$ super Riemann surfaces introduced recently by Rogers and Langer are shown to coincide with the Abelian differentials (plus constants), viewed as a subset of the functions on the associated $N=2$ super Riemann surface. We confirm that, as originally defined, they do not form a super vector space.Comment: 9 pages, LaTex. Published version: minor changes for clarity, two new reference