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 ...

Solutions u(x) to the class of inhomogeneous nonlinear ordinary differential equations taking form for parameter α are studied. The problem is defined on x line with decay both solution and imposed forcing f(x) as |x| → ∞. rate important has a strong influence structure space. Three particular forcings examined primarily: rectilinear top-hat, Gaussian, Lorentzian, latter two exhibiting exponent...

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...

A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the so-called κ distribution frequently found in collisionless turbulent systems like space plasmas. We show that this distribution function satisfies a generalised H...

We utilize the travelling-wave Ansatz to obtain novel analytical solutions linear diffusion–reaction equation. The reaction term is a function of time and space simultaneously, firstly in Lorentzian form secondly cosine form. new contain Heun functions first case Mathieu for second case, therefore are highly nontrivial. use these test some non-conventional explicit stable numerical methods agai...