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.     

A generalization of certain homological functors

Summary By a natural process of relativization groups Extⁿ(A, φ), π_n(A, φ) are defined in any abelian category with sufficient injectives and projectives. Functoriality in φ i spro. ved and excision properties are established; and the groups are shown to behave well under suspension. The technique involves an interplay of different mapping-cone constructions In memory of Guido Castelnuovo, on the occasion of the first centenary of his birth.     

Ground-state inversion method applied to calculation of molecular photoionization cross-sections by atomic extrapolation: Interference effects at low energies

The ground-state inversion method, which we have previously developed for the calculation of atomic cross-sections [ 29 ], is applied to the calculation of molecular photoionization cross-sections. These are obtained as a weighted sum of atomic subshell cross-sections plus multi-centre interference terms. The atomic cross-sections are calculated directly for the atomic functions which when summed over centre and symmetry yield the molecular orbital wave function. The use of the ground-state inversion method for this allows the effect of the molecular environment on the atomic cross-sections to be calculated. Multi-centre terms are estimated on the basis of an effective plane-wave expression for this contribution to the total cross-section. Finally the method is applied to the range of photon energies from 0 to 44 eV where atomic extrapolation procedures have not previously been tested. Results obtained for H₂, N₂ and CO show good agreement with experiment, particularly when interference effects and effects of the molecular environment on the atomic cross-sections are included. The accuracy is very much better than that of previous plane-wave and orthogonalized plane-wave methods, and can stand comparison with that of recent more sophisticated approaches. It is a feature of the method that calculation of cross-sections either of atoms or of large molecules requires very little computer time, provided that good quality wave functions are available, and it is then of considerable potential practical interest for photoelectron spectroscopy.