A note concerning the chromatic index of multigraphs

We improve an upper bound for the chromatic index of a multigraph due to Andersen and Gol'dberg. As a corollary we deduce that if no two edges of multiplicity at least two in G are adjacent, then χ′(G) ? Δ(G) + 1. In addition we generalize results concerning the structure of critical graphs due to Vizing and to Chetwynd and Hilton.     

Far infrared measurements of bulk and surface phonons in GaAs/AlAs superlattices

We have used far-infrared oblique-incidence reflection spectroscopy to study bulk phonon polaritons, and attenuated total reflection (ATR) spectroscopy to study surface phonon polaritons, in long-period GaAs/Al_xGa_1–xAs and short-period GaAs/AlAs superlattices. Results on the former are in good agreement with an effective-medium bulk-slab model of the dielectric tensor of the superlattice; results on the latter are analysed in terms of a model that contains dielectric-tensor contributions from the confined optic phonons.     

Doubly diagonal orthogonal latin squares

A pair of doubly diagonal orthogonal latin squares of order n, DDOLS(n), is a pair of orthogonal latin squares of order n with the property that each square has a transversal on both the front diagonal (the cells {(i, i):1?i?n}) and the back diagonal (the cells {(i, n + 1?i): 1?i?n}). We show that for all n except n = 2, 3, 6, 10, 12, 14, 15, 18 and 26, there exists a pair of DDOLS(n). Obbviously these do not exist when n = 2, 3 and 6.     

Hamiltonian decompositions of complete graphs

It is well known that K_{2n + 1} can be decomposed into n edge-disjoint Hamilton cycles. A novel method for constructing Hamiltonian decompositions of K_{2n + 1} is given and a procedure for obtaining all Hamiltonian decompositions of of K_{2n + 1} is outlined. This method is applied to find a necessary and sufficient condition for a decomposition of the edge set of K_r (r ≤ 2n) into n classes, each class consisting of disjoint paths to be extendible to a Hamiltonian decomposition of K_{2n + 1} so that each of the classes forms part of a Hamilton cycle.     

High-average-power Nd:YAG planar waveguide laser that is face pumped by 10 laser diode bars

A planar waveguide Nd:YAG laser is pumped with 430 W of power from 10 laser diode bars to produce a multimode output power of 150 W at an optical efficiency of 35%. Use of a hybrid resonator of the positive-branch confocal unstable type for the lateral axis and of one of the near-case I waveguide type for the transverse axis increased the laser brightness by a factor of ~26 with only 12% less power than in the multimode case.     

Optical orientation and femtosecond relaxation of spin-polarized holes in GaAs

Optical orientation of spin-polarized heavy and light holes followed by relaxation to other valence subband states has been observed unambiguously in undoped bulk GaAs in spite of the extremely short spin relaxation time. The measured relaxation time for the heavy holes is 110 fs +/-10%. The results are relevant for applications such as interpretation of spin-polarized transport in semiconductors as well as the assessment of feasibility of hole-based spin-transport devices which relies on precise knowledge of the hole-spin relaxation time.     

Carbon-13 NMR of polycyclic aromatic compounds. 1—Methoxybenz[a]anthracene-7, 12-diones

Benz[a]anthracene-7, 12-dione, eight monomethoxybenz[a]anthracene-7, 12-diones and two dimethoxybenz[a]anthracene-7, 12-diones were analyzed by ¹³C and ¹H NMR. All ¹³C and ¹H resonances have been assigned. Substituent effects on the ¹³C chemical shifts are discussed.     

Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering

We demonstrate that emission-induced self-organization of two-level atoms can effect strong damping of the sample's center-of-mass motion. When illuminated by far-detuned light, cold cesium atoms assemble into a density grating that efficiently diffracts the incident light into an optical resonator. We observe random phase jumps of pi in the emitted light, confirming spontaneous symmetry breaking in the atomic self-organization. The Bragg diffraction results in a collective friction force with center-of-mass deceleration up to 1000 m/s(2) that is effective even for an open atomic transition.