This paper presents an efficient method to solve a large body scattering problem, viz. a paraboloid reflector antenna system, with only partial circular symmetry. The asymmetry in the system is introduced by two factors, viz. the microstrip feed and an inhomogeneous radome. The paper presents a novel approach, based on the equivalence and reciprocity principles and the “equiv­ alent” aperture t...

X iv :m at h/ 02 10 08 4v 2 [ m at h. C A ] 1 3 D ec 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon ...

In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to bui...

A “Wick rotation” is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space for the noncommutative algebra can be completed to a Hilbert space, where multiplication is not continuous. A method of constructing noncommutative analogues of ...

The tightness of the bounding volume is often difficult to adjust to suit different applications. In this paper, we present a technique to derive a tunable bounding volume for elliptic paraboloids, where the tightness can easily be controlled and altered at several levels. Our technique develops such a tunable bounding volume through the optimization process. Bounding volumes thus developed con...

This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Ga...

In lecture 8 we have formulated the condition of static equilibrium of bodies and structures by studying a small change (variation) of the total potential energy. The system was said to be in equilibrium if the first variation of the total potential energy vanishes. The analysis did not say anything about the stability of equilibrium. The present lecture will give an answer to that question by ...

For Augmented Reality using a pair of transparent 3D glasses, a precise and fast method for head tracking is required, to determine the user’s position and direction of gaze in all six degrees of freedom. The methods currently available require expensive external sensors and have small working areas and/or other limitations. We propose a method that uses a panoramic camera that is mounted direc...

A series of dinuclear complexes of a pseudocalixarene macrocycle H6L containing two 2,2'-methylenediphenol groups have been synthesised and structurally characterised. Using divalent metal ions, complexes containing a common hyperbolic paraboloid (saddle) M2(H4L)2+ core are formed. The structure is controlled by two strong O-H-O interactions resulting from metal ion-promoted monodeprotonation o...