Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems

Exact space invariant illumination for partially coherent imaging systems.

What we believe to be a new illumination scheme that achieves space invariance and permits analytical determination of the image intensity distribution is proposed for partially coherent imaging systems. No additional lenses are needed for phase correction in front of the object and no restriction on illumination coherence is required. Conditions on the axial placement of the condenser with res...

Counting Solutions to Polynomial Systems via Reductions

This paper provides both positive and negative results for counting solutions to systems of polynomial equations over a finite field. The general idea is to try to reduce the problem to counting solutions to a single polynomial, where the task is easier. In both cases, simple methods are utilized that we expect will have wider applicability (far beyond algebra). First, we give an efficient dete...

Exact solutions for impulsive gravitational waves∗

All impulsive waves (with no tails) in vacuum backgrounds of constant curvature (i.e. Minkowski, de Sitter and anti-de Sitter) are classified according to whether they are expanding or non-expanding. It is demonstrated that the expanding waves may, in some sense, be regarded as impulsive limits of Robinson–Trautman type N solutions.

Blind phase retrieval for aberrated linear shift- invariant imaging systems

New exact solutions for polynomial oscillators in large dimensions

We study the family of polynomial potentials (with up to 2q “anharmonic” couplings) which possess the wave functions proportional to a polynomial of degree N . We reveal that the usual (so called quasi-exact) implicit formula for their energies and couplings (= roots of the q coupled N−dimensional secular determinants) becomes solvable in closed form at the large spatial dimensions D → ∞. This ...