We consider the asymptotic behavior of solutions to nonlinear partial differential equations in the limit of short wavelength. For initial data which cause focusing at one point, we highlight critical indexes as far as the influence of the nonlinearity in the neighborhood of the caustic is concerned. Our results generalize some previous ones proved by the first author in the case of nonlinear S...

A quasilinear system of elliptic-hyperbolic partial differential equations arising from the uniformly asymptotic approximation of solutions to the Helmholtz equation is discussed. These equations produce a model for high-frequency waves which is stable on both sides of a smooth, convex caustic. We prove the existence of strong solutions to a class of inhomogeneous boundary-value problems for an...

Benjamin Rush, MD (1745-1813), was not only the most well known physician in 18th-century America, he was also a patriot, philosopher, author, lecturer, fervent evangelist, politician, and dedicated social reformer. He was unshakable in his convictions, as well as self-righteous, caustic, satirical, humorless, and polemical. Unquestionably brilliant, he graduated from what later became Princeto...

We prove the existence of strong solutions to a class of inhomogeneous boundary-value problems for an elliptic-hyperbolic equation. The equation is an arbitrarily small lower-order perturbation of an equation that arises in the linearization of an approximate model for high-frequency waves near a caustic. The domain boundary is allowed to extend into both the elliptic and hyperbolic regions of ...

The four bright images of the gravitationally lensed quasar Q2237+0305 are being monitored from the ground (eg. OGLE collaboration, Apache Point Observatory) in the hope of observing a high magnification event (HME). Over the past three seasons (1997-1999) the OGLE collaboration has produced microlensing light-curves with unprecedented coverage. These demonstrate smooth, independent (therefore ...

Introduction: Potassium Permanganate (KMnO4) is an uncommon cause of caustic ingestion in teenagers and adults; only case reports are found the recent literature. At Ngwelezana Hospital South Africa, KMnO4 not indication for admission. readily available as used most households recommended medicinal purposes by traditional health practitioners. Aim: To ascertain reasons ingestion, extent severit...

Four of nine exoplanets found by microlensing were detected by the resonant caustic, which represents the merging of the planetary and central caustics at the position when the projected separation of a host star and a bounded planet is s ∼ 1. One of the resonant caustic lensing events, OGLE-2005-BLG-169, was a caustic-crossing highmagnification event with Amax ∼ 800 and the source star was muc...

Ingested corrosive agents produce oropharyngeal and gastroesophageal injuries ranging from minor burns to severe necrosis, depending on the agent amount, concentration, and duration of exposure. The aim of this study was to present our patients with corrosive ingestion retrospectively. Four hundred seventy-three children younger than 16 years of age (mean age, 3.7+/-0.1 years) who were admitted...