The Maxwell and Maxwell-de Rham equations can be solved exactly to first order in an external gravitational field. The gravitational background induces phases in the wave functions of spin-1 particles. These phases yield the optics of the particles without requiring any thin lens approximation.

G. Papini G. Scarpetta A. Feoli G. Lambiase

A new relativistic invariant version of nonlinear Maxwell equations is offerred. Some properties of these equations are considered.

G. A. Kotel'nikov

Maxwell's fish eye has been known to be a perfect lens within the validity range of ray optics since 1854. Solving Maxwell's equations we show that the fish-eye lens in three dimensions has unlimited resolution for electromagnetic waves.

Ulf Leonhardt Thomas G. Philbin

Exact time-dependent solutions of Maxwell's equations in Maxwell's fish eye show that perfect imaging is not an artifact of a drain at the image, although a drain is required for subwavelength resolution.

Ulf Leonhardt Thomas G. Philbin

We define scoring metrics on separable metric spaces and show that they are always no coarser than the metrics from which they spring.

Kerry M. Soileau

We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.

Kerry M. Soileau

In this paper we give a definition of cyclic orthonormal generators (cogs) in R^N. We give a general canonical form for their expression. Further, we give an explicit formula for computing the canonical form of any given cog.

Kerry M. Soileau

In this paper we show how to approximate ("learn") a function f, where X and Y are metric spaces.

Kerry M. Soileau

We introduce the concept of a consistency space. The idea of the consistency space is motivated by the question, Given only the collection of sets of sentences which are logically consistent, is it possible to reconstruct their lattice structure?

Kerry M. Soileau

The Collatz conjecture implies that an iterated function sequence under a certain linear operator, beginning with a certain complex valued function, must converge to a certain complex function.

Kerry M. Soileau