In this work we show an error estimate for a first order Gaussian beam at fold caustic, approximating time-harmonic waves governed by the Helmholtz equation. For caustic that study exact solution can be constructed using Airy functions and there are explicit formulae parameters. Via precise comparisons pointwise on is of O ( k − 5 / 6 ) where wave number in Helmholtz.

Acute esophageal necrosis, commonly referred to as "black esophagus" or "acute necrotizing esophagitis", is a rare clinical disorder with an unclear etiology. The definition excludes patients with a history of recent caustic ingestion. Oesophageal necrosis can be diagnosed at endoscopy by the presence of black necroting appearing oesophagus. Contrary to the caustic oesophagitis whose treatment ...

Caustics are captivating light patterns created by materials bundling or diverting light by refraction or reflection. We know caustics as random side effects, appearing, for example, at the bottom of a swimming pool. In this paper we show that it is possible to control caustic patterns to form almost any desired shape by optimizing the geometry of the reflective or refractive surface generating...

In this paper, we describe the global structure of webs in codimension one, and study in particular their singularities (the caustic). We define and study different concepts which have no interest locally near regular points, such as the type, the reducibility, the quasi-smoothness, the CIproperty (complete intersection), the dicriticity.... As an example of application, we explain how the alge...

Caustic esophageal strictures still represent a challenge to endoscopist. Standard treatment is regular esophageal dilatation until the resolution of dysphagia. Caustic strictures require dilations more frequently for a positive clinical response [1]. Increasingly frequent dilation may become a selfdefeating cycle in refractory stricture as recurrent trauma to the mucosa, enhance scar formation...