Related papers: Gale transform of a starshaped sphere
Galaxies are key objects for the study of cosmology, the life cycle of matter, and stellar evolution. X-ray observations have given us a new key window into these building blocks of the Universe, that allows us to investigate their hot…
The spaces of flattenings of a simplicial sphere played a key role in the study of existence and uniqueness of differentiable structures on a simplicial sphere. In this paper, we will establish that the spaces of flattenings of some…
Radiative energy transfer between closely spaced bodies is known to be significantly larger than that predicted by classical radiative transfer because of tunneling due to evanescent waves. Theoretical analysis of near--field radiative…
Topology and geometry are deeply intertwined in the study of surfaces, though their interaction manifests differently in smooth and discrete settings. In the smooth category, a classical result asserts that any closed smooth surface…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
Gravitational lensing refers to the deflection of light by the gravity of celestial bodies, often predominantly composed of dark matter. Seen through a gravitational lens, the images of distant galaxies appear distorted. In this paper we…
In this article we have studied the structure of hypothetical two-dimensional polytropic stars. Considering some academic interest, we have developed a formalism to investigate some of the gross properties of such stellar objects. However,…
After the surface theory of M\"obius geometry, this study concerns a pair of conformally immersed surfaces in $n$-sphere. Two new invariants $\theta$ and $\rho$ associated with them are introduced as well as the notion of touch and…
Definition of generalized normal form for a system of ODEs corresponding to an infinitesimal symplectic or contact transformation near a singular point, with an arbitrary polynomial unperturbed part, and a method of its finding are…
We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial…
Using a perturbative approach we solve stellar structure equations for low-density (solar-type) stars whose interior is described with a polytropic equation of state in scenarios involving a subset of modified gravity theories. Rather than…
Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…
Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp. 33-54,…
The orbit graph of a k-orbit polytope is a graph on k nodes that shows how the flag orbits are related by flag adjacency. Using orbit graphs, we classify k-orbit polytopes and determine when a k-orbit polytope is i-transitive. We then…
We demonstrate that for several of the gravitational lens models used to describe galaxies, there exists a quantity we dub the magnification invariant, equaling the sum of the signed magnifications of the images, that is a constant when the…
We obtain new inversion formulas for the Funk type transforms of two kinds associated to spherical sections by hyperplanes passing through a common point $A$ which lies inside the n-dimensional unit sphere or on the sphere itself.…
For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are…
The present work represents a step to deal with stellar structure using a pure geometric approach. A geometric field theory is used to construct a model for a spherically symmetric configuration. The model obtained can be considered as a…
A simple example of an $n$-dimensional admissible complex of planes is given for the overdetermined $k$-plane transform in $\mathbb{R}^n$. For the corresponding restricted $k$-plane transform sharp existence conditions are obtained and…
This papers presents a novel quantised transform (the Sinclair-Town or ST transform for short) that subsumes the rolls of both edge-detector, MSER style region detector and corner detector. The transform is similar to the $unsharp$…