The radio rays are reflected from the parabolic surface and concentrated at the focus. This focusing and amplification property of parabolic reflectors is also used for solar heating and generating solar …

Take a closed orbit, and get a parabolic subgroup P1 as before, by looking at some isotropy. If P1 = G, mod out by another 1-D subspace corresponding to a point in the isotropy.

The idea is to use the parabolic weak maximum principle for bounded domains. But since we want to estimate the supremum of the function by the supremum on the bottom part of the parabolic cylinder …

Instead of y, time t may be the second independent variable. If B2 4AC = 0, then the PDE is parabolic (heat). If B2 4AC > 0, then the PDE is hyperbolic (wave). If B2 4AC < 0, then the PDE is elliptic …

1. Parabolic Subgroups ubgroups of GLn(C). Before we go on to discuss the specific case of GLn(C) we describe parabolic sub roups of any group. To begin we refresh our memories on solvable groups. …

Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hyper-surface type CR …

1. Introduction the positive system of roots k (P0; S) for a maximal split k-tor s S P0. A parabolic k-subgroup of G is called standard if it contains P0. We have seen that each G(k)-conjugacy class of …