This paper provides an updated efficiency analysis of the LightForce space debris collision avoidance scheme. LightForce aims to prevent collisions on warning by utilizing photon pressure from ground based, commercial off the shelf lasers. Past research has shown that a few ground-based systems consisting of 10 kW class lasers directed by 1.5 m telescopes with adaptive optics could lower the ex...

abstract in this paper, we study the generalized order- jacobsthal sequences modulo for and the generalized order-k jacobsthal-padovan sequence modulo for . also, we define the generalized order-k jacobsthal orbit of a k-generator group for and the generalized order-k jacobsthal-padovan orbit a k-generator group for . furthermore, we obtain the lengths of the periods of the generalized order-3 ...

We review the Skyrme interaction as first used by Vautherin and Brink in the Hartree-Fock (HF) formalism to construct the energy density functional and more specifically, the two-body spin-orbit term. Problems with this term were already pointed out by Skyrme himself and have been discussed in the past years by other authors. We present examples where existing Skyrme parametrizations are unable...

Modern machine learning problems typically have multiple criteria, but there is currently no systematic mathematical theory to guide the design of formulations and exploration of alternatives. Homotopy methods are a promising approach to characterize solution spaces by smoothly tracking solutions from one formulation (typically an “easy” problem) to another (typically a “hard” problem). New res...

The existing robust narrowband beamformers based on probability-constrained optimization have an excellent performance as compared to several state-of-the-art robust beamforming algorithms. However, they always assume that the steering vector errors are small enough. Without this assumption, we extend the probability-constrained approach to a wideband beamformer. In addition, a novel robust wid...

Context. The potentially hazardous asteroid (99942) Apophis, previously designated 2004 MN4, is emblematic of the study of asteroids that could impact the Earth in the near future. Orbit monitoring and error propagation analysis are mandatory to predict the probability of an impact and, furthermore, its possible mitigation. Several aspects for this prediction have to be investigated, in particu...

We study driven by an external electric field quantum orbital and spin dynamics of electron in a one-dimensional double quantum dot with spin-orbit coupling. Two types of external perturbation are considered: a periodic field at the Zeeman frequency and a single half-period pulse. Spin-orbit coupling leads to a nontrivial evolution in the spin and orbital channels and to a strongly spin- depend...

For each group G having an infinite normal subgroup with the relative property (T) (e.g. G = H ×K, with H infinite with property (T) and K arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G) × Λ. We deduce that G has uncountably many non stabl...

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with in...

For each group G having an infinite normal subgroup with the relative property (T) (for instance groups of the form G = H ×K, where H is infinite with property (T) and K is arbitrary) and each countable abelian group Λ we construct free ergodic measure-preserving actions σΛ of G on the probability space such that the 1’st cohomology group of σΛ, H (σΛ, G), is equal to Char(G)×Λ. We deduce that ...