The Hodge equations for 1-forms are studied on Beltrami’s projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for weakly harmonic 1-fields, changing type on the unit circle, is derived under Dirichlet conditions imposed on the non-characteristic portion of the boundary. A sim...

We analyze the optical caustic produced by light refracted at the curved meniscus surrounding a cylindrical rod standing partially out of a liquid-filled container. When the rod is tilted from the vertical or when light is diagonally incident, the caustic is a four-cusped astroid with two of its cusps obscured by the rod's shadow. If a portion of the flat end of the rod is raised above the wate...

Underwater, natural illumination typically varies strongly temporally and spatially. The reason is that waves on the water surface refract light into the water in a spatiotemporally varying manner. The resulting underwater illumination field forms a caustic network and is known as flicker. This work shows that caustics can be useful for stereoscopic vision, naturally leading to range mapping of...

The case is reported of a young ex-nurse with severe inflammation in the distal colon, extending 15 cm proximally from the anus, due to the self-instillation of a noxious substance, namely, caustic soda. She escaped detection over a period of months. The result was extensive inflammatory change in the terminal 15 cm of the large bowel, with gross macroscopic, histological and radiological abnor...

Introduction. Ingestion of corrosive substances may lead to stricture formation in esophagus as a late complication. Full thickness injury seems to exterminate tissue stem cells of esophagus. Mesenchymal stem cells (MSCs) can differentiate into specific cell lineages and have the capacity of homing in sites of injury. Aim and Methods. We aimed to investigate the efficacy of MSC transplantation,...

Severe caustic injury to the gastrointestinal tract carries a high risk of luminal strictures. The aim of this retrospective study was to identify predicting factors for progress of caustic injury to gastric outlet obstruction (GOO) and esophageal strictures (ES), using modified endoscopic mucosal injury grading scale. We retrospectively reviewed medical records of patients with caustic injurie...

Irregularities in the perimeter of a water droplet adhering to a vertical pane of glass cause perturbations in the curvature of the droplet surface. When laser light passes through such a droplet, the perturbations produce a far field refraction caustic, which is a section of the caustic known as the parabolic umbilic in the catastrophe theory classification. As the water evaporates and the dro...

In this Letter, we propose a general real-space method for the generation of nonparaxial accelerating beams with arbitrary predefined convex trajectories. Our results lead to closed-form expressions for the required phase at the input plane. We present such closed-form results for a variety of caustic curves: beside circular, elliptic, and parabolic, we find for the first time general power-law...

A method to design Ronchi-Hartmann screens for improved alignment in the testing of fast plano-convex spherical lenses is presented. We design null screens that produce aligned straight fringes for observed patterns. The designs of these null screens are based on knowledge of the caustic by refraction. A qualitative test for a lens is presented.

background: the incidence of caustic ingestion injuries in developed countries has been decreasing, while it still remains a great concern in developing countries including iran. in this study we focused on alkali esophageal injuries in children which occur frequently in southern iran, due to both, unsafe products and unfamiliarity of families with the alkali consumption hazards. methods : in a...