A Representation of Weyl-Heisenberg Lie Algebra in the Quaternionic Setting

Using a left multiplication defined on a right quaternionic Hilbert space, linear self-adjoint momentum operators on a right quaternionic Hilbert space are defined in complete analogy with their complex counterpart. With the aid of the so-obtained position and momentum operators, we study the Heisenberg uncertainty principle on the whole set of quaternions and on a quaternionic slice, namely on a copy of the complex plane inside the quaternions. For the quaternionic harmonic oscillator, the uncertainty relation is shown to saturate on a neighborhood of the origin in the case we consider the whole set of quaternions, while it is saturated on the whole slice in the case we take the slice-wise approach. In analogy with the complex Weyl-Heisenberg Lie algebra, Lie algebraic structures are developed for the quaternionic case. Finally, we introduce a quaternionic displacement operator which is square integrable, irreducible and unitary, and we study its properties.Comment: to appear in Annals of Physic

Performance of Port Facilities During the Northridge Earthquake

During the January 17, 1994, Northridge earthquake, two of the Port of Los Angeles\u27 facilities called Berths 121-126 and Pier 300 sustained moderate damage. Lateral displacement of dikes up to five inches and liquefaction of hydraulic fills were observed. Several geotechnical analyses from simplified SPT -based method to sophisticated fully-coupled analyses are presented. Observed lateral displacements are predicted reasonably well by the fully-coupled analysis procedure and an intermediate analysis procedure which incorporates some results from a fully-coupled analysis in to a simplified Newmark-type deformation analysis. The potential for higher pore pressure generation underneath the dike compared to a level ground is also discussed