Related papers: Sphere paths in outer space
Orbital solutions for binary or multiple stellar systems that combine astrometry (e.g., position angles and angular separations) with spectroscopy (radial velocities) have important advantages over astrometric-only or spectroscopic-only…
Motion planning is a difficult problem in robot control. The complexity of the problem is directly related to the dimension of the robot's configuration space. While in many theoretical calculations and practical applications the…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…
Astrometry is a powerful technique in astrophysics to measure three-dimensional positions of stars and other astrophysical objects, including exoplanets and the gravitational influence they have on each other. Interferometric astrometry is…
Shape metrics for objects in high dimensions remain sparse. Those that do exist, such as hyper-volume, remain limited to objects that are better understood such as Platonic solids and $n$-Cubes. Further, understanding objects of ill-defined…
We begin by studying the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over the unit sphere in n-dimensions and use this…
We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
In this contribution we summarize recent achievements by our group on the understanding of the structure of the outer Galactic disk, with particular emphasis to the outer disk extent, and the spiral structure beyond the solar circle.
We study $\infty$-modulus on general metric spaces and establish its relation to shortest lengths of paths. This connection was already known for modulus on graphs, but the formulation in metric measure spaces requires more attention to…
The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…
We consider the problem of determining the length of the shortest paths between points on the surfaces of tetrahedra and cubes. Our approach parallels the concept of Alexandrov's star unfolding but focuses on specific polyhedra and uses…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
Off-shell supersymmetry, which restricts sparticles to appear only off-shell, solves the gauge hierarchy problem and unifies the gauge couplings in the usual way. Without introducing any new interactions or exacerbating the naturalness,…
We develop a Morse-Lusternik-Schnirelmann theory for the distance between two points of a smoothly embedded circle in a complete Riemannian manifold. This theory suggests very naturally a definition of width that generalises the classical…
Observations of stellar surfaces - except for the Sun - are hampered by their tiny angular extent, while observed spectral lines are smeared by averaging over the stellar surface, and by stellar rotation. Exoplanet transits can be used to…
Two motions in the galactic plane have been detected and characterized, based on the determination of a common systematic component in Hipparcos catalogue proper motions. The procedure is based only on positions, proper motions and…
Substantial progress in the field of the Local Interstellar Medium has been largely due to recent launches of space missions, mostly in the UV and X-ray domains, but also to ground-based observations, mainly in high resolution spectroscopy.…
The Schwarzschild metric giving the space time due to a spherically symmetric object is derived in the background of the Robertson Walker metric. In other words the two metrics are merged. It is found that under certain conditions the…