Classical (Birkhoff) billiards with full 1-parameter families of periodic orbits are considered. It is shown that construction of a convex billiard with a “rational” caustic (i.e. carrying only periodic orbits ) can be reformulated as the problem of finding a closed curve tangent to a non-integrable distribution on a manifold. The properties of this distribution are described as well as the con...

Supervising Section Editor: Rick A McPheeters, DO Submission history: Submitted January 08, 2012; Revision received March 26, 2012; Accepted April 02, 2012 Full text available through open access at http://escholarship.org/uc/uciem_westjem DOI: 10.5811/westjem.2012.4.11734 [West J Emerg Med. 2012;13(5):426-428.] Matthew Hanson, MD John William Hafner, MD, MPH University of Illinois College of M...

approximately 20% of caustic ingestions result in some degree of esophageal injury. alkaline materials are the most frequent corrosive materials ingested.     the physical form and ph of ingested materials play a critical role in the site and type of gastrointestinal injury (ph > 12 or ph < 1.5, crystalline drain cleaners). unlike alkaline solutions, strong acids are bitter, burn on contact and...

A growing era of alternative medicine is upon us. All who practice medicine have a small population of patients who eschew Western medicine and prefer alternative approaches, including botanical remedies, to treat their medical problems. Many alternative practitioners advertise and sell products on the Internet. Indeed, this trend now includes a growing number of topical treatments for skin can...

The lensing properties of the Plummer model with a central point mass and external shear are derived, including the image multiplicities, critical curves and caustics. This provides a simple model for a flattened galaxy with a central supermassive black hole. For the Plummer model with black hole, the maximum number of images is 4, provided the black hole mass is less than an upper bound which ...

In a number of previous papers of the first and third authors, caustics, cut-loci, spheres, and wave fronts of a system of sub-Riemannian geodesics emanating from a point q0 were studied. It turns out that only certain special arrangements of classical Lagrangian and Legendrian singularities occur outside q0. As a consequence of this, for instance, the generic caustic is a globally stable objec...

Development of environmentally benign approaches to remediation of metal-contaminated soils and sewage sludges are needed to replace currently used techniques of either landfilling or metal extraction using caustic or toxic agents. We report results from four application technologies that use a metal-chelating biosurfactant, rhamnolipid, for removal of metals or metal-associated toxicity from m...

1801, amputated the cervix uteri, and repeated the operation with success on several subsequent occasions. His example has been followed by Dupuvtren, Ilecamier, Hervez de Chegoin, Cazenave, Strachan, Huenier, Simpson, Langenbeck, Scanzoni, and others ; but above all, Lisfranc, in Franco, tried to bring the operation into repute by adopting 110 other kind of proceeding. Dr. Amnssat (senior) on ...

We study the geometry of the event horizon of a spacetime in which a small compact object plunges into a large Schwarzschild black hole. We first use the Regge-Wheeler and Zerilli formalisms to calculate the metric perturbations induced by this small compact object, then find the new event horizon by propagating null geodesics near the unperturbed horizon. A caustic is shown to exist before the...