Related papers: Caustics by Refraction of Circles and Lines
The late infall of cold dark matter onto our galaxy produces discrete flows and caustics in its halo. The recently discovered ring of stars near galactocentric distance 20 kpc and a series of sharp rises in the Milky Way rotation curve are…
In this work we present an analogue of the inverse scattering for Canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the…
In this note, we will consider two classical volume problems related to elliptic integrals. The first problem has a neat formula by means of elliptic integrals. We remade it with details. In the second problem, we found a messy formula. On…
We extend the work of Mishchenko et al. (2000) regarding the exact results of the polarization effect, using the theory of Amic et al. (1997) to derive a model prediction for the polarization coherent opposition effect at small angles. Our…
A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In…
Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…
We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…
Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint.…
We present recent evolutions of the detailed opacity code SCO-RCG which combines statistical modelings of levels and lines with fine-structure calculations. The code now includes the Partially-Resolved-Transition-Array model, which allows…
Gravitational lensing magnification is maximal around caustics. At these source locations, an incoming wave from a point source would formally experience an infinite amplification in the high-frequency or geometric optics limit. This…
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest…
It is shown that the infall of collisionless dark matter onto isolated galaxies produces a series of caustic rings in the halo dark matter distribution. The properties of these caustics are investigated. The density profile of the caustic…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
The study of relativistic Coulomb systems in velocity space is prompted by the fact that the study of Newtonian Kepler/Coulomb systems in velocity space, although less familiar than the analytic solutions in ordinary space, provides a much…
Microlensings events are predicted for the light coming from cosmological sources. In addition to the microlensing due to gravitation lensing, microlensing produced also by refraction of light due to either ionized, or not, gas clouds can…
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
A reflection principle for Corson compacta holds in the forcing extension obtained by Levy-collapsing a supercompact cardinal to~$\aleph_2$. In this model, a compact Hausdorff space is Corson if and only if all of its continuous images of…
In this paper we study the inversion in an ellipse and some properties, which generalizes the classical inversion with respect to a circle. We also study the inversion in an ellipse of lines, ellipses and other curves. Finally, we…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…