The following result is proved: Let R be a 2-torsion free semiprime ring, and let T : R → R be an additive mapping, related to a surjective homomorphism θ : R → R, such that 2T (x2) = T (x)θ(x) + θ(x)T (x) for all x ∈ R. Then T is both a left and a right θ-centralizer.

Bursts of coherent synchrotron radiation at far-infrared and millimeter wavelengths have been observed at several storage rings. A microbunching instability has been proposed as the source for the bursts but the mechanism has yet to be elucidated. We provide the first evidence that the bursts are due to a microbunching instability driven by the emission of synchrotron radiation in the bunch. Ob...

We demonstrate, by coherent driving two uncoupled rings in same direction, that the effective photon circulating time in the dual-ring modulator is reduced, with increased modulation quality. The inter-ring detuning-dependent photon dynamics, Q factor, extinction ratio, and optical modulation amplitude of two cascaded silicon ring resonators are studied and compared with that of a single-ring m...

Bursts of coherent synchrotron radiation at far-infrared and millimeter wavelengths have been observed at several storage rings. A microbunching instability has been proposed as the source for the bursts. However, the microbunching mechanism has yet to be elucidated. We provide the first evidence that the bursts are due to a microbunching instability driven by the emission of synchrotron radiat...

Most studies of Coherent Synchrotron Radiation (CSR) have only considered the radiation from independent dipole magnets. However, in the damping rings of future linear colliders, a large fraction of the radiation power will be emitted in damping wigglers. In this paper, the longitudinal wakefield and impedance due to CSR in a wiggler are derived in the limit of a large wiggler parameter K. Afte...

We show how Newton’s rings manifest themselves in near-field scanning optical microscopy and discuss how this effect can be used with topographic imaging to measure correlated roughness of thin films. In conventional optics, transmission through a thin nonabsorbing film depends on film thickness when multiple reflections from the film boundaries are coherent. Measurements and modeling of the tr...

We consider phase-coherent transport through ballistic and diffusive two-dimensional hole systems based on the Kohn-Luttinger Hamiltonian. We show that intrinsic heavy-hole-light-hole coupling gives rise to clear-cut signatures of an associated Berry phase in the weak localization which renders the magnetoconductance profile distinctly different from electron transport. Nonuniversal classical c...

We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves over a semi-separated noetherian scheme, generalising complete flat resolutions over a ring. By studying these complexes as objects of the pure derived category of flat sheaves we extend several results about totally acyclic complexes of projective modules to schemes; for example, we prove that a scheme is Goren...