We propose that local Lorentz invariance is spontaneously violated at high energies, due to a nonvanishing vacuum expectation value of a vector field φμ, as a possible explanation of the observation of ultra-high energy cosmic rays with an energy above the GZK cutoff. Certain consequences of spontaneous breaking of Lorentz invariance in cosmology are discussed.

The question of the existence of order in two-dimensional isotropic dipolar Heisen-berg antiferromagnets is studied. It is shown that the dipolar interaction leads to a gap in the spin-wave energy and a nonvanishing order parameter. The resulting finite Néel-temperature is calculated for a square lattice by means of linear spin-wave theory.

We give a reduction of the conjecture that for terminal projective threefolds whose anticanonical divisors are nef, the second Chern classes are pseudo-effective. On the other hand, some effective nonvanishing results are obtained as applications of the pseudo-effectivity of the second Chern classes.

A universe consisting of two interacting perfect fluids with the same 4-velocity is considered. A heuristic mean free time argument is used to show that the system as a whole cannot be perfect as well but neccessarily implies a nonvanishing bulk viscosity. A new formula for the latter is derived and compared with corresponding results of radiative hydrodynamics.

An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characte...

The problem of zeroing the output in an arbitrary linear continuous-time system S(A, B, C, D) with a nonvanishing transfer function is discussed and necessary conditions for output-zeroing inputs are formulated. All possible real-valued inputs and real initial conditions which produce the identically zero system response are characterized. Strictly proper and proper systems are discussed separa...

We introduce the notion of a mock tridiagonal system. This is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain nonvanishing condition. We show how mock tridiagonal systems can be used to construct tridiagonal systems that meet certain specifications. This paper is part of our ongoing project to classify the tridiagonal systems up to isomor...

We study the linear response spin Hall conductivity of a two-dimensional electron gas (2DEG) in the presence of the Rashba spin-orbit interaction in the diffusive transport regime. When defect scattering is modeled by isotropic short-range potential scatterers the spin Hall conductivity vanishes due to the vertex correction. A nonvanishing spin Hall effect may be recovered for dominantly forwar...