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I show that the precession of the orbit of Mercury and the deflection of starlight by the Sun are effects of special relativity alone when the gravitational field of a particle is treated in the same way as the electric field of a charged…
Light refracted by the planet's atmosphere is usually ignored in analysis of planetary transits. Here we show that refraction can add shoulders to the transit light curve, i.e., an increase in the observed flux, mostly just before and after…
In this letter we identify similarities amongst sunspots and terrestrial vortices. The dark appearance of the central part of any sunspot is currently justified by an anticipated cooling effect experienced by the ionized gas. However, it…
We argue that at low-energies, typical of the resonance region, the contribution from direct-channel exotic trajectories replaces the Pomeron exchange, typical of high energies. A dual model realizing this idea is suggested. While at high…
An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in…
We shall prove that the Poisson deformation functor of an affine (singular) symplectic variety is unobstructed. As a corollary, we prove the following result. Theorem: For an affine symplectic variety $X$ with a good $C^*$-action (where its…
We consider random flights in $\mathbb{R}^d$ reflecting on the surface of a sphere $\mathbb{S}^{d-1}_R,$ with center at the origin and with radius $R,$ where reflection is performed by means of circular inversion. Random flights studied in…
It is shown that the Sun can become partially transparent to high energy photons in the presence of a pseudo-scalar. In particular, if the axion interpretation of the PVLAS result were true then up to 2% of GeV energy gamma rays might pass…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
A critical review of experimental studies of the so-called 'slow light' arising due to anomalously high steepness of the refractive index dispersion under conditions of electromagnetically induced transparency or coherent population…
Non-line-of-sight (NLOS) imaging has recently attracted a lot of interest from the scientific community. The goal of this paper is to provide the basis for a comprehensive mathematical framework for NLOS imaging that is directly derived…
In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are…
We study a detection problem in the following setting: On the one-dimensional integer lattice, at time zero, place nodes on each site independently with probability $\rho \in [0,1)$ and let them evolve as a simple symmetric exclusion…
After a brief description of the basic principle of a photon collider, we summarize the physics potential of such a facility at high energies. Unique opportunities are provided in supersymmetric theories for the discovery of heavy scalar…
The question is considered about possibility of overcoming diffraction limit at device, named superlens. This device is a flat slab, executed from material with index of refraction n,equal n=-1. It is shown, what this device really can…
We demonstrate spectroscopy of incoherent light with sub-diffraction resolution. In a proof-of-principle experiment we analyze the spectrum of a pair of incoherent point-like sources whose separation is below the diffraction limit. The two…
A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly…
We prove a gravitational lensing theorem: the magnification of a source of uniform brightness by a foreground spherical lens is mu =1+pi(2R_E^2-R_L^2)/A, where A is the area of the source and R_E and R_L are the Einstein radius and size of…
We present an elementary analysis of the effects on light reflected from a uniformly moving mirror by using the photon picture of light and the conservation laws for energy and momentum of the system photon-mirror. Such a dynamical approach…
A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a…