相关论文: Generalized convex sets and shadows problem
Black hole (BH) shadows in dynamical binary BHs (BBHs) have been produced via ray-tracing techniques on top of expensive fully non-linear numerical relativity simulations. We show that the main features of these shadows are captured by a…
The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of the Edelman-Jamison problem is equivalent to the well known…
In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set.
Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let $X$…
We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this…
In this paper we study convex subcomplexes of spherical buildings. We pay special attention to fixed point sets of type-preserving isometries of spherical buildings. This sets are also convex subcomplexes of the natural polyhedral structure…
We study properties of the convex hull of a set $S$ described by quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take a nonnegative linear combinations of the defining inequalities of $S$. We call such…
Shadows are common aspect of images and when left undetected can hinder scene understanding and visual processing. We propose a simple yet effective approach based on reflectance to detect shadows from single image. An image is first…
We develop a compactness result near the boundary for families of locally convex immersions. We also develop a mod 2 degree theory for immersion of constant (and prescribed) Gaussian curvature with prescribed boundary. These are then used…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
In previous papers we define certain Lagrangian shadows of ample divisors in algebraic varieties. In the present brief note an existence condition is discussed for these Lagrangian shadows.
By a recent result obtained by R. Howlett and the author considerable progress has been made towards a complete solution of the isomorphism problem for Coxeter groups. In this paper we give a survey on the isomorphism problem and explain in…
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are…
The still-unsolved problem of determining the set of eigenvalues realized by $n$-by-$n$ doubly stochastic matrices, those matrices with row sums and column sums equal to $1$, has attracted much attention in the last century. This problem is…
The existence of extremely dark and compact astronomical bodies is by now a well established observational fact. On the other hand, classical General Relativity predicts the existence of black holes which fit very well with the…
In this paper we look for the convex hull of a set using the geometric evolution by minimal curvature of a hypersurface that surrounds the set. To find the convex hull, we study the large time behavior of solutions to an obstacle problem…
We introduce a method for analyzing the convex hull of a set in non-positively curved piecewise Euclidean polygonal complexes and we apply this method to prove that, with the usual action of Fm x Zn on the metric product of the Cayley graph…
Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar…
We investigate the shadow of an exact black hole solution of Einstein's equations recently proposed by Cardoso et al., to describe a supermassive black hole immersed in a dark matter halo. We analyze and discuss the light rings and the…
Given a finite set of lattice points, we compare its sumsets and lattice points in its dilated convex hulls. Both of these are known to grow as polynomials. Generally, the former are subsets of the latter. In this paper, we will see that…