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A non-perturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. The theoretical formalism yields a…
Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…
A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with the wave and whether gravitational energy transfer is null.
A perfect cuboid is a rectangular parallelepiped with integer edges, integer face diagonals, and integer space diagonal. Such cuboids have not yet been found, but nor has their existence been disproved. Perfect cuboids are described by a…
We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell's theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple…
A systematic analysis of matched layers is undertaken with special attention to better understand the remarkable method of B\'erenger. We prove that the B\'erenger and closely related layers define well posed transmission problems in great…
Maxwell's equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell's equations into evolution equations and constraints, we derive the characteristic equation and we…
Solutions to the complementarity problem constructed in [1], generally, possess non-zero total charge. In natural sciences, bodies possessing non-zero total charge (ions and similar object) are considered as specific objects. Bodies…
A planewave incident on an active etalon with net roundtrip gain may be expected to diverge in field amplitude, yet Maxwell's equations admit only a convergent solution. By examining a Gaussian beam obliquely incident on such a cavity, we…
Let $X$ be an integral affine or projective scheme of finite presentation over a perfect field. We prove that $X$ admits a resolution, that is, there exists a smooth scheme $\widetilde X$ and a projective birational morphism from…
We derive sharp regularity for viscosity solutions of an inhomogeneous infinity Laplace equation across the free boundary, when the right hand side does not change sign and satisfies a certain growth condition. We prove geometric regularity…
Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this…
Although remarkable progress has been made, existing methods for enhancing underexposed photos tend to produce visually unpleasing results due to the existence of visual artifacts (e.g., color distortion, loss of details and uneven…
This work reports the incompatibility of the Stokes relation for time reversibility of wave's propagation and the usage of complex atomic form-factor in diffraction theories. The implications behind a diffraction theory that obeys the…
All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld…
A new class of solutions to the coupled, spherically symmetric Einstein-Maxwell equations for a compact material source is constructed. Some of these solutions can be made to satisfy a number of requirements for being physically relevant,…
We show that localized (non-evanescent) solutions to Maxwell equations exist, which propagate without distortion along normal waveguides with Superluminal speed.
This paper presents a point-wise divergence-free projection method for numerical approximations of photonic quasicrystals problems. The original three-dimensional quasiperiodic Maxwell's system is transformed into a periodic one in higher…
A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. Its existence is equivalent to the existence of a perfect cuboid with all…
Non-polynomial Baxterized solutions of reflection equations associated with affine Hecke and affine Birman-Murakami-Wenzl algebras are found. Relations to integrable spin chain models with nontrivial boundary conditions are discussed.