The Angular Radial Edge Histogram (AREH) extends prior work on a compact image representation based on geometric distributions of edge pixels. Histograms of edge pixels are computed along the dimensions of angle and radius. Fourier transform is applied to accommodate rotation invariance. It achieves invariance for scale variation, in-plane rotation, and translation. By using a grid-based approa...

2 Exercise. Prove it. ◦ In fact, as sophisticates can show you, on a complex space a linear operator which preserves all norms will also preserve all inner products. But the key thing is to remember is that a unitary operator preserves all inner products (and therefore all norms). • This is analogous to the fact that translations and rotations in ordinary three-dimensional space preserve distan...

Starting from the simplest possible building blocks—a ket, a bra, a time-reversed ket, and a time-reversed bra— a diagrammatic formalism is developed for angular momentum coupling problems. The formalism comprises Clebsch–Gordan coefficients as well as 3jm-symbols. The idea of constructing invariants (internal lines) by contracting contragredient pairs of quantities is emphasized throughout. Th...

Equal channel angular Pressing (ECAP) is an innovative technique for developing ultrafine-grained microstructures first developed by Segal et al in 1981 in the former Soviet Union. The ECAP method consists of two channels that intersect at an angle, generally comprised between 90◦ and 135◦ . The deformation is produced by shear as the billet is extruded through the channels. One of the geometri...

The paper deals with the problem of angular vibration measurements in time history of rotation angle, angular velocity or angular acceleration. The source of information about angular vibrations is an encoder producing an impulse signal. It is supposed that the impulse frequency is changed proportionally to the rotational frequency. A time record of an impulse signal is transformed to an analyt...

We demonstrate the optical orbital angular momentum conservation during the transfer process from subwavelength plasmonic vortex lens (PVLs) to light and the generating process of surface plasmon polaritons (SPPs). Illuminating plasmonic vortex lenses with beams carrying optical orbital angular momentum, the SP vortices with orbital angular momentum were generated and inherit the optical angula...

One of the key ideas in describing the multiparticle production at high energies in the perturbative QCD is the angular ordering in successive soft-gluon emission. We analyse the angular distribution of particles in a jet, and investigate the corrections to the angular ordering. At a small angle from the jet direction, the angular ordering is exact at the next-to-leading order. At a large angle...

A circularly polarized paraxial Gaussian laser beam carries ±h̄ angular momentum per photon as spin, with zero orbital angular momentum. Focusing the beam with a rotationally symmetric lens cannot change this angular momentum flux, yet the focused beam must have spin |Sz | < h̄ per photon. The remainder of the original spin is converted to orbital angular momentum, manifesting itself as a longitu...