Related papers: Hyperbolic type distances in starlike domains
It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such…
Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase…
Observations have repeatedly confirmed the presence of large-scale peculiar motions in the universe, commonly referred to as ``bulk flows''. These are vast regions of the observable universe, typically spanning scales of several hundred…
We construct the hyperbolic and trigonometric solutions to the star-star relation via the gauge/YBE correspondence by using the three-dimensional lens partition function and superconformal index for a certain N=2 supersymmetric gauge dual…
In this paper we consider ordinary derivative of universal covering mappings $f$ of hyperbolic regions $D$ in the complex plane. We obtain sharp bounds for the ratio $|f'(z)|/{\rm dist}(f(z),\partial f(D))$ in terms of the hyperbolic…
In this paper we express the Minkowski dimension of spiral trajectories near hyperbolic saddles and semi-hyperbolic singularities in terms of the Minkowski dimension of intersections of such spirals with transversals near these…
We construct $C^2$-robust homoclinic and heterodimensional tangencies of large codimension inside transitive partially hyperbolic sets.
Based on axi-symmetric hydrodynamical simulations and 3D reconstructions with Shape, we investigate the kinematic signatures of deviations from homologous ("Hubble-type") outflows in some typical shapes of planetary nebulae. We find that,…
We study the distribution of angular positions and angular separations of unbound hypervelocity stars (HVSs). HVSs are spatially anisotropic at the 3-sigma level. The spatial anisotropy is significant in Galactic longitude, not in latitude,…
We construct a hyperbolic three-manifold with trivial finite type invariants up to a given degree.
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the…
We study the form of the luminosity distance as a function of redshift in the presence of large scale inhomogeneities, with sizes of order 10 Mpc or larger. We approximate the Universe through the Swiss-cheese model, with each spherical…
Optical band images of distant (z > 0.5) galaxies, such as those of the Hubble Deep Field, record light from the rest-frame vacuum ultraviolet (< 3000 A). Because the appearance of a galaxy is a very strong function of wavelength, and…
We study one-dimensional linear hyperbolic systems with $L^{\infty}$-coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of…
In this paper, we introduce the notion of "geodesic cover" for Fuchsian groups, which summons copies of fundamental polygons in the hyperbolic plane to cover pairs of representatives realizing distances in the corresponding hyperbolic…
Recent fully non-linear simulations of ultracompact spherically symmetric boson stars have presented evidence for their long-term stability. All observed dynamics could be mainly attributed to the fundamental radial mode. In this work, we…
We consider the ultrahyperbolic equation in the Euclidean space. The behavior at the infinity of a certain class of solutions is studied. We examine the issue of existence of solutions to the scattering problem: for a given asymptotics at…
In the spirit of Otal and Croke, we prove that a negatively-curved asymptotically hyperbolic surface is boundary distance rigid, where the distance between two points on the boundary at infinity is defined by a renormalized quantity.
After having investigated the real conic sections and their isoptic curves in the hyperbolic plane $\bH^2$ we consider the problem of the isoptic curves of generalized conic sections in the extended hyperbolic plane. This topic is widely…
Accurate astronomical distance determination is crucial for all fields in astrophysics, from Galactic to cosmological scales. Despite, or perhaps because of, significant efforts to determine accurate distances, using a wide range of…