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A morph between two straight-line planar drawings of the same graph is a continuous transformation from the first to the second drawing such that planarity is preserved at all times. Each step of the morph moves each vertex at constant…
We consider the lateral shift of a light beam reflecting from a dielectric slab backed by a metal. It is found that the lateral shift of the reflected beam can be negative while the intensity of reflected beam is almost equal to the…
It was shown by Seaman that if a compact, oriented 4-dimensional riemannian manifold (M, g) of positive sectional curvature admits a harmonic 2-form of constant length, its intersection form is definite and such a harmonic form is unique up…
In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of…
The array of micro-prisms was described by model of multi-period blazed gratings consisting of triangular apertures. The origins of hexagram-shaped diffraction patterns were interpreted based on multiple-beam interference and diffraction…
In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. Based on a dynamic correction of the incident…
A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one…
We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
Face analysis is a core part of computer vision, in which remarkable progress has been observed in the past decades. Current methods achieve recognition and tracking with invariance to fundamental modes of variation such as illumination, 3D…
Calabi-Yau manifolds are important objects in algebraic geometry and in theoretical physics. A hypothesis of mirror symmetry is that Calabi-Yau manifolds of dimension 3 come in pairs, with the Hodge numbers of one manifold mirroring the…
Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We…
We investigate here the deformations of Berglund H\"ubsch loop and chain mirrors where the original manifolds are defined in the same weighted projective space. We show that the deformations are equivalent by two methods. First, we map…
We first derive the round-trip Jones matrix for double passage through a reciprocal optical medium by means of reflection off a plane mirror that could be optically anisotropic. We then show that if a medium with only linear birefringence…
A billiard is a dynamical system in which a particle alternates between motion in a straight line and specular reflection from a boundary. For billiards in non-convex areas bounded by segments of confocal quadrics are studied. The topology…
Here we are concerned with a special issue of billiard invisibility, where a bounded set with a piecewise smooth boundary in Euclidean space is identified with a body with mirror surface, and the billiard in the complement of the set is…
Following Hausel-Hitchin, we investigate core Lagrangians and upward flows in Hilbert schemes of points on elliptic surfaces. We compute the scheme-theoretic multiplicities of core Lagrangians, as well as the equivariant multiplicities of…
We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far field images of several Gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images…
A programming library was developed, based on Stratton-Chu diffraction integrals for calculating reflected optical fields. Dipole-type focusing schemes with tunable number of beams and mirror placements were studied, considering the…
In the diffraction pattern produced by a half-plane sharp edge when it obstructs the passage of a laser beam, two characteristic regions are noticeable. There is a central region, where it can be noticed the diffraction of laser light in…