On a generalization of a theorem of Lyapunov

A constructive and simple proof is given of a generalization of a result of Lyapunov on the convexity of the range of vector measure.     

Bound-to-bound and bound-to-free yellow emission of ion-implanted zinc telluride

Broad structureless emission bands centred near 580 nm have been observed in the low temperature cathodoluminescence emission spectra of zinc telluride single crystals implanted with zinc, argon or aluminum ions. Time-resolved spectroscopy measurements and measurements of the emission intensities as a function of sample temperature and of temperature of post-implantation isochronal annealing show that one yellow band occurs in both ZnTe : Zn and ZnTe : Ar and results from bound-to-free recombination involving an intrinsic donor level, probably due to a V_Te defect. In addition, there is a second yellow band present in ZnTe : A1 which is due to donor-acceptor pair recombination with the donors and acceptors identified with Al_Zn and V_ZnAl_Zn respectively.     

Characterization of luminescence centres in neodymium implanted zinc sulphide

Analysis of the cathodoluminescence emission spectra of neodymium implanted cubic single crystal ZnS as a function of post-implantation annealing temperature has enabled groups of emission lines to be identified as originating from transitions within particular luminescence centres. For each group of lines the wavelength separations yield energy splittings characteristic of the crystal field at the luminescence centre. Comparison of these splittings with values calculated by crystal field theory on the basis of a point charge model, with due regard to possible sites of cubic symmetry in ZnS, has allowed two luminescence centres (A and B) to be identified.Centre A, which exists at low annealing temperatures, consists of a Nd³⁺ ion situated interstitially with 4 tetrahedrally disposed nearest neighbour S^2? ions. At higher annealing temperatures the emissions from centre A were found to decline giving way to those of centre B, which analysis shows to be a Nd³⁺ ion situated on a zinc substitutional site.     

Neutron spectra at 0° from (p,n) reactions on 9Be, 12C,and 27Al at 647 and 800 MeV

The measured cross sections show a narrow high-energy peak (20–30 MeV/cFWHM) and a broad bump at lower momenta associated with pion production. Comparison is made to an intranuclear cascade calculation.     

Implantation of ytterbium ions into group II-VI compounds

50 keV ytterbium ions have been implanted into ZnS, CdS, ZnSe, CdTe, CdSe and ZnTe and, after subsequent annealing treatments of varying degree, the cathodoluminescence emission spectra produced by 10 keV or 100 keV electron excitation have been studied.     

On the Hamilton‐Waterloo Problem for Bipartite 2‐Factors

Given two 2‐regular graphs F₁ and F₂, both of order n, the Hamilton‐Waterloo Problem for F₁ and F₂ asks for a factorization of the complete graph into α₁ copies of F₁, α₂ copies of F₂, and a 1‐factor if n is even, for all nonnegative integers α₁ and α₂ satisfying . We settle the Hamilton‐Waterloo Problem for all bipartite 2‐regular graphs F₁ and F₂ where F₁ can be obtained from F₂ by replacing each cycle with a bipartite 2‐regular graph of the same order.     

Obstructions to lifting automorphisms of free algebras

ABSTRACT

A monomial basis and a filtration of subalgebras for the universal enveloping algebra 𝔘(𝔤 _l ) of a complex simple Lie algebra 𝔤 _l of type A _l is given in this note. In particular, a new multiplicity formula for the Weyl module V(λ) of 𝔘(𝔤 _l ) is obtained in this note.     

Metal‐nanoparticle plasmonics

The rapid emergence of nanoplasmonics as a novel technology has been driven by recent progress in the fabrication, characterization, and understanding of metal‐nanoparticle systems. In this review, we highlight some of the key advances in each of these areas. We emphasize the basic physical understanding and experimental techniques that will enable a new generation of applications in nano‐optics.