Related papers: Sphere paths in outer space
It is known that the shape of a planet (oblateness, rings, etc.) slightly modifies the shape of the transit light curve. The forthcoming space missions (Corot, Kepler), able to detect the transit of Earth-like planets, could a fortiori also…
We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs.
We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of…
The motion of Mercury using numerical methods in the framework of a model including only the non-relativistic Newtonian gravitational interactions of the solar system, 9 planets in translation (including Pluto) around the sun has been…
Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Mathematically, a shape can be modeled as an un-parameterized immersed sub-manifold, which is the notion of shape used here. Endowing shape…
A graph is outerplanar if it can be embedded in a plane such that all vertices lie on its outer face. The outerplanar Tur\'{a}n number of a given graph $H$, denoted by ${\rm ex}_{\mathcal{OP}}(n,H)$, is the maximum number of edges over all…
In this contribution we investigate the Schr\"ordinger equation associated to the Laplacian on the sphere in the form of sharp Strichartz estimates. We will provided simple proofs for our main theorems using purely the $L^2\rightarrow L^p$…
For a Riemannian manifold $M^{n+1}$ and a compact domain $\Omega \subset M^{n+1}$ bounded by a hypersurface $\partial \Omega$ with normal curvature bounded below, estimates are obtained in terms of the distance from $O$ to $\partial \Omega$…
Atmospheric spectroscopy provides a window into the properties of exoplanets. However, the physical interpretation of retrieved data and its implications for the internal properties of exoplanets remains nebulous. This letter addresses…
The Hipparcos Intermediate Astrometric Data have been used lately to estimate the inclination of the orbital plane of candidate extrasolar planets. Whereas most of these investigations derive almost face-on orbits, we show that the…
We study hyper-spheres, spheres and circles, with respect to an indefinite metric, in a tangent space on a 4-dimensional differentiable manifold. The manifold is equipped with a positive definite metric and an additional tensor structure of…
We consider the area of spheres centered at the distinguished point in the Brownian plane. As a function of the radius, the resulting process has continuously differentiable sample paths. Furthermore, the pair consisting of the process and…
A method of a non-stationary description of tunneling of a particle through the one-dimensional and spherically symmetric rectangular barriers on the basis of analisis of multiple internal reflections of wave packets in relation on the…
Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
We use the trimming transformations to study the tight span of a metric space.
We investigate the effect of spiral structure on the Galactic disk as viewed by pencil beams centered on the Sun, relevant to upcoming surveys such as ARGOS, SEGUE, and GAIA. We create synthetic Galactic maps which we call Pencil Beam Maps…
This paper deals with projective shape analysis, which is a study of finite configurations of points modulo projective transformations. The topic has various applications in machine vision. We introduce a convenient projective shape space,…
Making use of Murakami's classification of outer involutions in a Lie algebra and following the Morse-theoretic approach to harmonic two-spheres in Lie groups introduced by Burstall and Guest, we obtain a new classification of harmonic…
Sphere recognition is known to be undecidable in dimensions five and beyond, and no polynomial time method is known in dimensions three and four. Here we report on positive and negative computational results with the goal to explore the…