The theoretical basis is developed for a technique to fabricate nonaxisymmetric mirrors. Stresses are applied to a mirror blank that would have the effect of elastically deforming a desired surface into a sphere. A sphere is then polished into the blank, and upon release of the applied stress, the spherical surface deforms into the desired one. The method can be applied iteratively, so arbitrar...

We establish a sharp trilinear inequality for the extension operator associated to the paraboloid in R3. Our proof relies on a recent generalisation of the classical Loomis–Whitney inequality.

This paper introduces a novel approach to rendering of highquality shadows in real-time. The contemporary approach to shadow rendering in real-time is shadow maps algorithm. The standard shadow maps suffer from discretization and aliasing due to the limited resolution of the shadow texture. Moreover, omnidirectional lights need additional treatment to work correctly, e.g. with dual-paraboloid s...

The Diffraction coefficient for electromagnetic waves incident obliquely incident on a curved edge formed by perfectly conducting plane surfaces. This diffraction coefficient remains valid in the transition region adjacent to shadow and reflection boundaries where the diffraction coefficients of Keller’s original theory fail. Our method is proposed on Keller’s method of the canonical problem, w...

Abstract. Large Deployable Reflector (LDR) systems are commonly used as mesh reflectors for large aperture space antennas in aerospace applications since they provide affordability while guaranteeing at the same time a high gain and directivity. To improve surface accuracy several methods have been studied, most of which measure distance between cable-net system that forms reflector desired par...

Ten normal adult subjects were tested under a wide range of combinations of stride length and stride frequency. Both longitudinal and vertical accelerations of the body increased with velocity, while stride frequency to stride length ratio (SF/SL) had little effect. The peak-to-peak amplitude of the forward velocity (V) decreased with SF/SL, but at constant SF/SL remained essentially unchanged ...

A formal asymptotic analysis is used to analyze the metastable behavior associated with a nonlocal PDE model describing the upward propagation of a flame-front interface in a vertical channel with a two-dimensional convex cross-section. In a certain asymptotic limit, the flame-front interface assumes a roughly paraboloidal shape whereby the tip of the paraboloid drifts asymptotically exponentia...