Generalized Rotation numbers

A rooted graph is a pair (G,x), where G is a simple undirected graph and x ∈ V(G). If G is rooted at x, its kth rotation number h_k (G,x) is the minimum number of edges in a graph F of order |G| + k such that for every v ∈ V(F) we can find a copy of G in F with the root vertex x at v. When k = 0, this definition reduces to that of the rotation number h(G,x), which was introduced in [“On Rotation Numbers for Complete Bipartite Graphs,” University of Victoria, Department of Mathematics Report No. DM-186-IR (1979)] by E.J. Cockayne and P.J. Lorimer and subsequently calculated for complete multipartite graphs. In this paper, we estimate the kth rotation number for complete bipartite graphs G with root x in the larger vertex class, thereby generalizing results of B. Bollobás and E.J. Cockayne [“More Rotation Numbers for Complete Bipartite Graphs,” Journal of Graph Theory, Vol. 6 (1982), pp. 403–411], J. Haviland [“Cliques and Independent Sets,” Ph. D. thesis, University of Cambridge (1989)], and J. Haviland and A. Thomason [“Rotation Numbers for Complete Bipartite Graphs,” Journal of Graph Theory, Vol. 16 (1992), pp. 61–71]. © 1993 John Wiley & Sons, Inc.     

A potent and highly selective sulfotransferase inhibitor

In the present work, we have used a newly developed, fluorescence-based assay to screen a library of >30 000 compounds as potential beta-arylsulfotransferase-IV inhibitors. A total of 11 inhibitors were discovered. Most of the compounds discovered showed low micromolar inhibition, but one of the compounds showed potent inhibition (Ki = 96 nM). The most potent of these inhibitors was tested against a variety of other purine binding enzymes and showed remarkable specificity.     

Exploration of the ultimate patterning potential achievable with high resolution focused ion beams

Controlled and reproducible fabrication of nano-structured materials will be one of the main industrial challenges in the next few years. We have recently proposed exploitation of the nano-structuring potential of a high resolution Focused Ion Beam Tool, to overcome basic limitations of current nano-fabrication techniques. The aim of this article is to present some new routes for material patterning, which benefit from ion-induced local property modifications or damage. In the experiments we describe hereafter an ultra-sharp pencil of 30 keV gallium ions is used to tailor the characteristics of several materials at a scale of a few nanometres. The experimental results are then compared to simulations. First, we simulate the control of collisional defects generated in a thin magnetic layer under FIB irradiation. The results explain the stable magnetic structures we have obtained experimentally. This was achieved with a low surface ion dose (10¹² to 10¹⁴ ions/cm²). In addition we have explored the promising direction of Bottom-up or self-organization processes using a FIB instrument. We have defined artificial surface defects. These defects created by the impact of an 8-nm FWHM probe were used to pin the diffusion and to organize nanometre-sized gold clusters on a graphite surface. PACS 79.20.Rf; 81.07.-b     

Charged particle multiplicity distributions ine + e − annihilation at 29 GeV: a comparison with hadronic data

The charged particle multiplicity distributions for two-jet events ine ⁺ e ^? annihilation at 29 GeV have been measured using the High Resolution Spectrometer at PEP. A Poisson distribution describes the data for both the complete event and for the single jets. In addition, no correlation is observed between the multiplicities in the two jets of an event. For fixed values of the prong number of the complete event, the multiplicity sharing between the two jets is in good agreement with a binomial distribution. The rapidity gap distribution is exponential with a slope equal to the mean rapidity density. These observations, which are consistent with a picture of independent emission of single particles, are contrasted to the results from soft hadronic collisions and conclusions are drawn about the nature of clusters.