Related papers: Generalizations of the shadow problem
We study the simplex method over polyhedra satisfying certain "discrete curvature" lower bounds, which enforce that the boundary always meets vertices at sharp angles. Motivated by linear programs with totally unimodular constraint…
A shadowed polyhedron is a simple polyhedron equipped with half integers on regions, called gleams, which represents a compact, oriented, smooth 4-manifold. The polyhedron is embedded in the 4-manifold and it is called a shadow of that…
Recently Ovsienko and Tabachnikov considered extensions of Somos and Gale-Robinson sequences, defined over the algebra of dual numbers. Ovsienko used the same idea to construct so-called shadow sequences derived from other nonlinear…
We consider overdetermined problems of Serrin's type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence…
We investigate the shadow properties of a wide class of spacetimes arising from different parameter regimes of the generalized Hayward metric, characterized by two independent parameters $(\sigma, \kappa)$ (Phys. Rev. D 106, 044028). This…
We deal with dynamical systems on complex lattices possessing chains of non-transversal heteroclinic connections between several periodic orbits. The systems we consider are inspired by the so-called \emph{toy model systems} (TMS) used to…
Our purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on simple polyhedra and discuss this problem combinatorially. We consider a shadowed polyhedron $X$ and a simple polyhedron $X_0$ that is…
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the…
In this work, we generalize Sacks-Uhlenbeck's existence result for harmonic spheres, constructing for $n \ge 2$, regular, non-trivial, $n$-harmonic $n$-spheres into suitable target manifolds. We obtain an infinite family of new…
We show that the diagonal light-like solution with 16 supersymmetries in eleven-dimensional supergravity derived in our previous paper (hep-th/0509173) can be generalised to non-diagonal solutions preserving the same number of…
We prove the subsolution theorem for the complex Hessian equations in a smoothly bounded strongly $m$-pseudoconvex domain, $1 < m < n$, in $\bC^n$.
Conditions, related to the so-called bending problem are considered for hypersurfaces of a pseudo-Euclidean space. Corresponding theorems are proved.
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
Previous works on black hole shadows have been primarily focused on studying shadows in asymptotically flat and anti-de Sitter space times. In the present work, we find general expressions for asymptotically de Sitter black hole shadow as…
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…
We present a new result about the shadowing of nontransversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with several examples. As an application we discuss this mechanism in…
We provide infinitely many solutions of a Dirichlet problem on balls.
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
Several classes of solutions of the generalized Weierstrass system, which induces constant mean curvature surfaces into four-dimensional Euclidean space are constructed. A gauge transformation allows us to simplify the system considered and…
A compact object illuminated by background radiation produces a dark silhouette. The edge of the silhouette or shadow (alternatively, the apparent boundary or the critical curve) is commonly determined by the presence of the photon sphere…