Andrews–Gordon type identities from combinations of Virasoro characters

For p∈{3,4} and all p′>p, with p′ coprime to p, we obtain fermionic expressions for the combination χ _1,s ^p,p′+q ^Δ χ _p−1,s ^p,p′ of Virasoro (W ₂) characters for various values of s, and particular choices of Δ. Equating these expressions with known product expressions, we obtain q-series identities which are akin to the Andrews–Gordon identities. For p=3, these identities were conjectured by Bytsko. For p=4, we obtain identities whose form is a variation on that of the p=3 cases. These identities appear to be new. The case (p,p′)=(3,14) is particularly interesting because it relates not only to W ₂, but also to W ₃ characters, and offers W ₃ analogues of the original Andrews–Gordon identities. Our fermionic expressions for these characters differ from those of Andrews et al. which involve Gaussian polynomials. BF is partially supported by grant number RFBR 05-01-01007, and OF by the Australian Research Council (ARC).     

Sequential change-point detection for mixing random sequences under composite hypotheses

The problem of sequential detection of a change-point in the density function of one-dimensional distribution of observations from a mixing random sequence is considered when both before and after a change-point this density function belongs to a certain family of distributions, i.e. in the situation of composite hypotheses. A new quality criterion for change-point detection is proposed. The asymptotic a priori lower bound for this criterion is proved for wide class of methods of change-point detection. An asymptotically optimal method of change-point detection is proposed for which this lower bound is attained asymptotically. In particular, for the case of a simple hypothesis before a change-point, this method coincides with the generalized cumulative sums (CUSUM) method.      

Initial oxidation of duplex stainless steel

Three different techniques were used to produce thin oxide layers on polished and sputter-cleaned duplex stainless-steel samples. These samples were exposed to 10⁻⁵ mbar of pure oxygen inside the vacuum chamber, exposed to ambient conditions for 24 h, and plasma oxidized. The oxide layers thus produced were analysed using XPS depth profiling in order to determine the oxide layers’ compositions with depth. We found that all the techniques produce oxide layers with different traces of metallic components and with the maximum concentration of chromium oxide shifted towards the oxide-layer-bulk-metal interface. A common characteristic of all the oxide layers investigated is a double-oxide stratification, with regions closer to the surface exhibiting higher concentrations of iron oxide and those more in-depth exhibiting higher concentrations of chromium oxide. A simple non-destructive Thickogram procedure was used to corroborate the thickness estimates for the thinnest oxide layers.     

Etudes par spectroscopie dans l'ultra-violet et le visible, du fullerène C60 en solution dans le n-hexane ou adsorbé sur des solides diélectriques

Ultraviolet and visible spectroscopy studies of the fullerene C₆₀ melted in n-hexane or adsorbed on dielectric solids. Experiments of spectroscopy have been carried out, between the far ultraviolet and the near infrared, with pure C₆₀ or containing endohedral complexes rare gas atom-C₆₀, melted in n-hexane, and also pure C₆₀ adsorbed on surfaces of solids.Several phenomena have been observed: 1. a charge transfer due to the influence of interactions between the molecules of C₆₀ and surfaces of solids, yielding new transitions observed in the far ultraviolet ; and interpreted as super excited states of Rydberg type; 1.1. red and blue shifts for some transitions of adsorbed C₆₀, interpreted on the basis of attractive, or turned repulsive, dispersion forces; 1.1.1. emission processes for several transitions of adsorbed C₆₀, explained on the basis of a resonant coupling between these transitions and modes of the surface plasmon induced by the collective excitations of the C₆₀ molecule; this kind of process might be drawn to the Faraday instability in acoustics.     

Minimum perimeter rectangles that enclose congruent non-overlapping circles

We use computational experiments to find the rectangles of minimum perimeter into which a given number, n, of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings found, the circles form the usual regular square-grid or hexagonal patterns or their hybrids. However, for most values of n in the tested range n≤5000, e.g., for n=7,13,17,21,22,26,31,37,38,41,43,…,4997,4998,4999,5000, we prove that the optimum cannot possibly be achieved by such regular arrangements. Usually, the irregularities in the best packings found for such n are small, localized modifications to regular patterns; those irregularities are usually easy to predict. Yet for some such irregular n, the best packings found show substantial, extended irregularities which we did not anticipate. In the range we explored carefully, the optimal packings were substantially irregular only for n of the form n=k(k+1)+1, k=3,4,5,6,7, i.e. for n=13,21,31,43, and 57. Also, we prove that the height-to-width ratio of rectangles of minimum perimeter containing packings of n congruent circles tends to 1 as n→∞.     

Nonlinear phenomena in degenerate quantum gases

In this introductory survey, we give an overview of the main physical problems and corresponding themes of research addressed in this Special Issue. We also briefly discuss some avenues of potential interest for future research in degenerate quantum gases.     

The structure of hormaomycin and one of its all-peptide aza-analogues in solution: syntheses and biological activities of new hormaomycin analogues

Four new aza-analogues of hormaomycin 1, a secondary metabolite with interesting biological activities produced by Streptomyces griseoflavus, were synthesized and subjected to preliminary tests of their antibiotic activity to provide new insights into the structure-activity relationship studies of this class of compounds. The solution structures of hormaomycin 1 and its aza-analogue 2 a were determined by NMR spectroscopy. The data exhibited a reasonably rigid conformation for both molecules, stabilized by stacking interactions between the aromatic moieties attached to the ring and the side chain. According to NMR-spectral data the aza-analogue epi-2 a has a rather different conformation and indeed shows no antibacterial activity whatsoever.