Related papers: Generic Spectrahedral Shadows
The Schur-Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semidefinite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the…
We provide convergent hierarchies for the cone C of copositive matrices and its dual, the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner)…
General relativity (GR) passed many astronomical tests but in majority of them GR predictions have been tested in a weak gravitational field approximation. Around 50 years ago a shadow has been introduced by J. Bardeen as a purely…
The spherical symmetry Black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions of whether a dynamical horizon forms…
A toric polyhedron is a reduced closed subscheme of a toric variety that are partial unions of the orbits of the torus action. We prove vanishing theorems for toric polyhedra. We also give a proof of the $E_1$-degeneration of Hodge to de…
We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an…
A pseudo-triangle is a simple polygon with three convex vertices, and a pseudo-triangulation is a face-to-face tiling of a planar region into pseudo-triangles. Pseudo-triangulations appear as data structures in computational geometry, as…
We discuss various questions which arise when one considers the central projection of three dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that…
We develop a perturbation theory for surfaces confining photons and massive particles in static spherically symmetric spacetimes in terms of two parameters: the mass-to-energy ratio and the deviation of metric functions from a given form,…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
We study dimensions of the faces of the cone of nonnegative polynomials and the cone of sums of squares; we show that there are dimensional differences between corresponding faces of these cones. These dimensional gaps occur in all cases…
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture…
We define a family of spacetimes representing isolated black holes exhibiting remarkable universal properties which are natural generalizations from stationary spacetimes. They admit a well defined notion of surface gravity k_H. This…
Projection matrices are necessary for a large portion of rendering computer graphics. There are primarily two different types of projection matrices -- perspective and orthographic -- which are used frequently, and are traditionally treated…
In light of the Event Horizon Telescope (EHT) images of the supermassive black holes $\textrm{Sgr A}^\star$ and $\textrm{M87}^\star$, we explore a potential supersymmetry suspicion within the observational data. Specifically, we investigate…
In this paper we show that generic continuous Lebesgue measure preserving circle maps have the s-limit shadowing property. In addition we obtain that s-limit shadowing is a generic property also for continuous circle maps. In particular,…
Shadowing is a quantum phenomenon leading to a non-additivity of electroweak cross sections on nucleons bound in a nucleus. It occurs due to destructive interference of amplitudes on different nucleons. Although the current experimental…
In this work, we consider two recently introduced novel regular black hole solutions and investigate the circular null geodesics to find the connection between the photon sphere, the horizon and the black hole shadow radii. We also study…
For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the…
We study the structure of $C^1$-interiors of sets of smooth vector fields with various properties of shadowing of pseudotrajectories. It is shown for which classes of reparametrizations of shadowing trajectories the corresponding interiors…