Interaction of fullerenes with the concave surfaces of perchloroazatriquinacene

[reaction: see text] Crystal structures of the one-to-one co-crystals of C(60).perchloroazatriquinacene and C(70).perchloroazatriquinacene show that the rigid, chalice-like azatriquinacene packs between completely ordered fullerene molecules with multiple, close Cl...fullerene contacts.     

Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

On the Relation between Curvature,Diameter, and Volume of a Complete Riemannian Manifold

In this note, we prove that if N is a compact totally geodesic submanifold of a complete Riemannian manifold M, g whose sectional curvature K satisfies the relation K ≥ k > 0, then for any point m ∈ M. In the case where dim M = 2, the Gaussian curvature K satisfies the relation K ≥ k ≥ 0, and γ is of length l, we get Vol (M, g) ≤ if k ≠ 0 and Vol (M, g ≤ 2ldiam (M) if k = 0.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 11, pp. 1576–1583, November, 2004.     

Two-atom van der Waals interaction between polarizable/magnetizable atoms near magnetoelectric bodies

The van der Waals potential of two atoms in the presence of an arbitrary arrangement of dispersing and absorbing magnetoelectric bodies is studied. Starting from a polarizable atom placed within a given geometry, its interaction with a second polarizable/magnetizable atom is deduced from its Casimir-Polder interaction with a weakly polarizable/magnetizable test body. The general expressions for the van der Waals potential obtained thusly are illustrated by considering first the case of two atoms in free space, with special emphasis on the interaction between (i) two polarizable atoms and (ii) a polarizable and a magnetizable atom. Furthermore, the influence of magnetoelectric bodies on the van der Waals interaction is studied in detail for the example of two atoms placed near a perfectly reflecting plate or a magnetoelectric half space, respectively. The text was submitted by the authors in English.     

A study of fused silica micro/nano patterning by focused-ion-beam

A dual-beam scanning electron microscopy (SEM)/focused-ion-beam (FIB) system was used to pattern fused silica substrates coated with a 15 nm thin Cr layer. The dimensions of fabricated features together with their surface morphology and profiles were investigated by SEM and atomic force microscopy (AFM). The study demonstrated that with the increase of the ion beam fluence the sputtering rate of the fused silica decreased non-linearly. Also, it was found that initially the sputtering rate increased with the increase of the beam current, after reaching a maximum value, it started decreasing when further beam current increment was performed. Compared with unprocessed areas, the surface finish of the features fabricated by FIB exhibited a significant improvement, and the ion fluence influence on the surface roughness of trenches with low aspect ratios could be considered as negligible. Using a fine beam probe, nano-gratings in the form of grooves with a width down to 54 nm and an aspect ratio higher than three were fabricated. The study showed that FIB machining could be an alternative technology to e-beam lithography for producing fused silica templates for UV nanoimprinting.     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.