相关论文: A lower bound of the distance between two elliptic…
We present new families of bound, closed, nonelliptical orbits that are supported by various spherical potentials in clear contradiction to Newton's and Bertrand's theorems. We calculate analytically some typical closed orbits of…
Different sequences of ellipsoids are represented on the ellipticity-rotation plane. The rotation parameter is defined as the ratio of kinetic energy related to the mean tangential equatorial velocity component to kinetic energy related to…
Consider the action of a connected complex reductive group on a finite-dimensional vector space. A fundamental result in invariant theory states that the orbit closure of a vector v is separated from the origin if and only if some…
We consider spherically symmetric black holes with minimally coupled scalar fields and concentrate our attention on asymptotically flat self-gravitating configurations having the event horizons located at radii much smaller than $2m$. We…
As a comet, asteroid or planet approaches its parent star, the orbit changes shape due to the curvature of spacetime. For comets in particular, the deviation at the pericentre may noticeably change their ephemerides and affect the dynamics…
An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for…
Multi-planetary systems detected by the Kepler mission present an excess of planets close to first-order mean-motion resonances (2:1 and 3:2) but with a period ratio slightly higher than the resonant value. Several mechanisms have been…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements…
The concept of sphere of influence of a planet is useful in both the context of impact monitoring of asteroids with the Earth and of the design of interplanetary trajectories for spacecrafts. After reviewing the classical results, we…
In this article, the minimum distance of the dual $C^{\bot}$ of a functional code $C$ on an arbitrary dimensional variety $X$ over a finite field $\F_q$ is studied. The approach consists in finding minimal configurations of points on $X$…
Many multiple-planet systems have been found by the Kepler transit survey and various radial velocity (RV) surveys. Kepler planets show an asymmetric feature, namely, there are small but significant deficits/excesses of planet pairs with…
This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground…
The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 ; or over even degree…
A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…
We obtain a substantially improved lower bound for the minimum overlap problem asked by Erd\H{o}s. Our approach uses elementary Fourier analysis to translate the problem to a convex optimization program.
Dark matter is the generally accepted paradigm in astrophysics and cosmology as a solution to the higher rate of rotation in galaxies, among many other reasons. But since there are still some problems encountered by the standard dark matter…
This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated…
In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds…
We obtain an upper bound on the lowest magnetic Neumann eigenvalue of a bounded, convex, smooth, planar domain with moderate intensity of the homogeneous magnetic field. This bound is given as a product of a purely geometric factor…