A non-relativistic Fokker-Planck equation for the electron distribution function is formulated incorporating the effects of stochastic acceleration by whistlermode waves and Coulomb collisions. The stationary solution f to the equation, subject to a zero-flux boundary condition, is found to be a generalized Lorentzian (or kappa) distribution, which satisfies f ∝ v for large velocity v, where κ ...

A stationary space-time (M,g) is a 4-manifold M with a smooth Lorentzian metric g, of signature (−,+,+,+), which has a smooth 1-parameter group G ≈ R of isometries whose orbits are time-like curves in M . We assume throughout the paper that M is a chronological space-time, i.e. M admits no closed time-like curves, c.f. §1.1 for further discussion. Let S be the orbit space of the action G. Then ...

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.

We describe the space of isometric immersions from the Lorentz plane L into the anti-de Sitter 3-space H31, and solve several open problems of this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from the above result a description of the space of Lorentzian flat tori isometrically immersed in H31 in terms of pairs of closed curves with wave front singularities in the hyperbo...

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...