On the complexity of partitioning graphs into connected subgraphs

This paper is mainly concerned with the computational complexity of determining whether or not the vertices of a graph can be partitioned into equal sized subsets so that each subset induces a particular type of graph. Many of the NP-completeness results are for planar graphs. These are proved using a planar version of 3-dimensional matching.     

Interference effects in 157 nm laser ablated cones in polycarbonate and application to spatial coherence measurement

Conical structures formed in 157 nm laser-ablated polycarbonate exhibit a well-defined fringe structure with a period of a few 100 nm surrounding the cone base. Experiments and modelling studies of the interference produced by these micro-conical mirrors are shown to provide a means of measuring the spatial coherence of the highly multi-mode 157 nm laser.     

Embeddings of root systems I: Root systems over commutative rings

This paper gives examples of embeddings of root systems of Coxeter groups, including sporadic embeddings of standard real root systems in other standard real root systems, and, for a general Coxeter group, an embedding of its universal symmetric root system over commutative rings into the standard real root system of a simply laced Coxeter group.     

Monitoring the effect of ultrafast deactivation of the electronic excited states of DNA bases and polynucleotides following 267 nm laser excitation using picosecond time-resolved infrared spectroscopy

In this paper we demonstrate the use of picosecond time-resolved infrared spectroscopy (ps-TRIR) to monitor the early structural dynamics of DNA bases and polydeoxynucleotides following UV excitation in solution.     

Probabilistic analysis of the generalised assignment problem

We analyse thegeneralised assignment problem under the assumption that all coefficients are drawn uniformly and independently from [0, 1]. We show that such problems can be solved exactly with high probability, in a well-defined sense. The results are closely related to earlier work of Lueker, Goldberg and Marchetti-Spaccamela and ourselves.Supported by NATO grant RG0088/89.Supported by NSF grant CCR-8900112 and NATO grant RG0088/89.     

Synthesis and carbon-13 nuclear magnetic resonance spectroscopy of 5,6-dihydro-2-methyl-1,4-oxathiin,trans-tetrahydro-1,4-benzoxathiin, 1,4-tetrahydro-[9,10]benzoxathiin,the 4-oxides, 4,4-dioxides and related acyclic compounds

The results of a ¹³C NMR spectral investigation involving 5,6-dihydro-1,4-oxathiins, 1,4-tetrahydro[9,10]benzoxathiin, trans-tetrahydro-1,4-benzoxathiin, and the corresponding sulfoxides and sulfones are reported. An interpretation involving a dipolar structure with (2p→2p)π conjugation as opposed to (2p→3d)π interactions with the vinyloxy sulfides seems consistent with trends in the ¹³C NMR shifts. For the sulfoxides and sulfones, the substitutent-induced chemical shift (SCS) effects at the β vinylic carbons (βSO and βSO₂ effects) are considerably less than those at sp³ carbons. The γSO and γSO₂ values at the sp²γ carbons indicate deshielding, in contrast to the shielding at the sp³ carbons.