Light rays having extreme points with the same spatial coordinates

Viewpoint: Extreme X Rays Probe Extreme Matter

Extreme X Rays Probe Extreme Matter

It takes a strong electric field to ionize atoms or ions in the creation of plasmas. These fields can be generated in lightning bolts (electric discharges), neon light bulbs, at the focus of a laser, and in the path of particle beams. It is perhaps less obvious that plasma itself can also have sufficiently strong fields within it to further ionize ions, since one might expect equal amounts of p...

Narrowing light rays with mirrors

Pach raised the question of whether a match lit in a nite forest of disjoint circular mirror trees necessarily sends light to innnity CFG90]. In other words, can one trap light rays from a point source with such mirrors? This remains an unsolved problem. We pose related mirror trapping questions. Can one trap light with arbitrarily curved mirrors? Here the answer is yes. Can one trap light with...

Riemannian metrics having the same geodesics with Berwald metrics

In Theorem 1, we generalize the results of Szabó [Sz1, Sz2] for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F . Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwa...

Cosmic Rays at Extreme Energies

Interest in extremely high energy cosmic rays has increased rapidly in the last decade. More important perhaps is that that interest now extends well beyond the \usual suspects" to include members of the wider astrophysics and high energy physics communities. Factors which have contributed to this development include: a keener appreciation of the diiculties associated with cosmic ray production...