Related papers: Some properties of rectangle and a random point
We construct time dependent random fields on the sphere through coordinates change and subordination and we study the associated angular power spectrum. Some of this random fields arise naturally as solutions of partial differential…
The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic of a stationary random closed set intersected with a fixed observation window. We formulate this result in the setting of sets…
The effect of random shooting of particles is considered on the basis of solution of the Schrodinger equation and in terms of the Wigner function. Two-particles description shows, in particular, that initial correlation leads to high…
We investigate the correspondence between the decay of correlation in classical system, governed by Ruelle--Pollicott resonances, and the properties of the corresponding quantum system. For this purpose we construct classical systems with…
We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special…
In this work we review and further develop the controversial concept of "classical entanglement" in optical beams. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several…
Motivated by circle graphs, and the enumeration of Euler circuits, we define a one-variable ``interlace polynomial'' for any graph. The polynomial satisfies a beautiful and unexpected reduction relation, quite different from the cut and…
Within classical optics, one may add microscopic "roughness" to a macroscopically flat mirror so that parallel rays of a given angle are reflected at different outgoing angles. Taking the limit (as the roughness becomes increasingly…
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio of its six intersection points with neighboring circles is equal to -1.…
In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…
Non-Euclidean triangle centers can be described using homogeneous coordinates that are proportional to the generalized sines of the directed distances of a given center from the edges of the reference triangle. Identical homogeneous…
In this article we exploit the fact that the special relativistic formula which relates the energy and the 3-momentum of an elementary particle with its rest mass, resembles the pythagorean theorem for right triangles. Using such triangles,…
We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
Circles through the Brocard points (Omega circles) share nearly all the properties of circles through the orthocentre including the fact that key triangles inscribed in them are indirectly similar to triangles inscribed in the circumcircle.…
Nonrelativistic equation of particle with a spin for the Lagrangian on a nonassociative algebra is obtained. It is shown that in this model arises Riemann-Cartan space. In the case of central symmetry in addition to the pseudo-curvature…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
The identity of classical motion is established for two physically different models, one of which is the relativistic particle with torsion, whose action contains higher derivatives and which is the effective system for the statistically…
Coherent states with large amplitudes are traditionally thought of as the best quantum mechanical approximation of classical behavior. Here we argue that, far from being classical, coherent state are in fact highly entangled. We demonstrate…