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...

Urine samples must be acidified if accurate calcium analyses are to be obtained (1). In many institutions the nursing staff is not permitted to dispense the strong acids traditionally used to decrease the pH of urine, so that the acid must be transferred into the collection vessels in the clinical laboratory. To avoid the dangerous practice of using a caustic liquid acid as a preservative, we h...

We propose an original method for determining suitable refracting profiles between two media to solve two related problems: to produce a given wave front from a single point source after refraction at the refracting profile, and to focus a given wave front in a fixed point. These profiles are obtained as envelopes of specific families of Cartesian ovals. We study the singularities of these prof...

We describe a technique for measuring the surface profile of a radio telescope with a fast paraboloidal primary. The technique uses a sensor, at the center of curvature of the primary, consisting of a millimeter-wave source and an array of receivers to measure the field in the caustic. The sensor is mounted on the telescope enclosure and it moves with the telescope, so the measurements can be u...

Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has a caustic, which can be either a confocal ellipse or a confocal hyperbola. Resonant caustics —the ones whose tangent trajectories are closed polygons— are d...

The caustic or Gaviola test, used for testing aspheric mirrors, has been studied with reference to the research of Schroader ["The caustic test," in Amateur Telescope Making III, A. G. Ingalls, ed. (Kingsport Press, Kingsport, Tenn., 1953), pp. 429-456]. It is shown that the two central formulas, which are used to determine the mirror quality, give significant errors for the large-diameter, sho...

Waves propagating in a medium with highly variable refractive index tend to focus forming caustics. The energy content of the waveeeld in the vicinity of a caustic is higher than that of the ambient eld away from the caustic. Consequently, waves scattering from heterogeneities located near caustics have more energy than a eld scattering a little further away from the caustic. For a suitable cho...