The three-dimensional Heisenberg group H3 has three left-invariant Lorentz metrics g1 , g2 and g3 as in [R92] . They are not isometric each other. In this paper, we characterize the left-invariant Lorentzian metric g1 as a Lorentz Ricci soliton. This Ricci soliton g1 is a shrinking non-gradient Ricci soliton. Likewise we prove that the isometry group of flat Euclid plane E(2) has Lorentz Ricci ...

We find 14 reflections in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that these 14 reflections generate the automorphism group of L. We find evidence that these reflections behave like the simple roots and the vector fixed by the diagram automorphisms behaves like the ...

Abstract We consider an inverse boundary value problem for a semilinear wave equation on time-dependent Lorentzian manifold with time-like boundary. The coefficients of the nonlinear terms can be recovered in interior from knowledge Neumann-to-Dirichlet map. Either distorted plane waves or Gaussian beams used to derive uniqueness.

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

We study aspects of the interaction between a D–brane and an anti-D–brane in the maximally supersymmetric plane wave background of type IIB superstring theory, which is equipped with a mass parameter μ. An early such study in flat spacetime (μ = 0) served to sharpen intuition about D–brane interactions, showing in particular the key role of the “stringy halo” that surrounds a D–brane. The halo ...

We consider the semilinear wave equation □gu+au4=0, a≠0, on a Lorentzian manifold (M, g) with timelike boundary. show that from knowledge of Dirichlet-to-Neumann map one can recover metric g and coefficient up to natural obstructions. Our proof rests analysis interaction distorted plane waves together scattering control argument, as well Gaussian beam solutions.

Understanding vanishing transmission in Fano resonances quantum systems and metamaterials, ultralow disordered media is key to elucidating optical interactions. Using analytic theory numerical simulations, we discover the topological structure motion under deformation of zeros complex energy plane. We demonstrate can be controlled create ultranarrow Lorentzian lines spectra time diverging rates...

2014 A study of the proton nuclear relaxation of crystalline thiophene has been undertaken. Our results demonstrate that, in both the stable and the metastable phase sequences, the in-plane molecular reorientation does not have a single correlation time. This non Lorentzian nuclear relaxation is discussed in terms of a distribution of correlation times and in terms of the mathematically equival...

We present a planar design of a metamaterial exhibiting electromagnetically induced transparency that is amenable to experimental verification in the microwave frequency band. The design is based on the coupling of a split-ring resonator with a cut-wire in the same plane. We investigate the sensitivity of the parameters of the transmission window on the coupling strength and on the circuit elem...

For two diierent integral forms K of the exceptional Jordan algebra we show that Aut K is generated by octave reeections. These providègeometric' examples of discrete reeection groups acting with nite covolume on the octave (or Cayley) hyperbolic plane O H 2 , the exceptional rank one symmetric space. (The isometry group of the plane is the exceptional Lie group F 4(?20) .) Our groups are deene...