The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis −∞ < E < ∞ instead of being bounded from below 0 ≤ E < ∞ (“Fer...

This paper develops a supervised dimensionality reduction method, Lorentzian Discriminant Projection (LDP), for discriminant analysis and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and ...

The transverse magnetoresistance (MR) hysteresis loops of a magnetically ordered Corbino disk have been studied in the temperature range 300–2 K an external magnetic field with induction up to 1 T oriented plane (ϕ = 0°) and perpendicularly its 90°). is made thin permalloy film obtained on insulating sitall substrate by ion-beam sputtering. Independently measurement geometry, dependences MR wea...

‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of t...

In this paper, we consider the Lorentzian approximations of rigid motions Minkowski plane E L 2 1,1 . By using method approximations, define notions intrinsic curvature for regular curves, geodesic curves...

In this work, we firstly introduce notions of principal directed curves and donor which are associated a Frenet curve in the dual Lorentzian space D 3 1 D13 . We give some relations between curvature torsion curve. show that general helix is plane obtain equation by using position vector Then circle $\mathbb{D}^{2}$ or hyperbola $\mathbb{D}_{1}^{2}$ slant $\mathbb{D}_{1}^{3}$ helix, respectivel...