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.     

Generalized markushevich bases

Conditions for the embedding of a Banach space as a dense subspace of a continuous function space are studied. Necessary and sufficient conditions for a Banach space to be isomorphic to aP ₁ space are found.     

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.     

Dynamic acceleration effects in explosions of laser-irradiated heteronuclear clusters

Intense, femtosecond irradiation of atomic and molecular clusters can initiate Coulomb explosions, generating particle energies sufficient to drive nuclear fusion. Last and Jortner have proposed, based on particle dynamics simulations, that heteronuclear clusters with a mixture of heavy and light ions will not explode by the simple, equilibrium Coulomb model but that dynamic effects can lead to a boosting of energy of the lighter ejected ions [Phys. Rev. Lett. 87, 033401 (2001)]. We present experimental confirmation of this theoretically predicted ion energy enhancement in methane clusters.     

Excimer laser polymer ablation: twenty years on

Research and development in excimer laser polymer ablation has been actively pursued for some twenty years, driven by interest in the basic science as well as by numerous applications that have emerged for this high-resolution technique for material removal. This paper reviews some of the basic mechanistic aspects of the UV laser–polymer interaction as a prelude to dealing with practical matters related to polymer processing by ablation. Applications in micro-machining and potential areas for future research are briefly covered. Received: 7 October 2002 / Accepted: 8 February 2003 / Published online: 28 May 2003 RID="*" ID="*"Corresponding author. Fax: +44-1482/465-606, E-mail: p.e.dyer@hull.ac.uk     

Theoretical study of rhodium(I) carbene complexes: the structural versatility of phosphino- compared with aminocarbenes

Density functional calculations are reported for complexes of general formula [(carbene)RhClL(2)] featuring model phosphino- and aminocarbenes. Both the cis and trans isomers of the rhodium(I) eta(1)-complexes (1-9) were investigated, and the influence of the rhodium co-ligands (L=ethylene, phosphine, or carbon monoxide) was evaluated. In the case of phosphinocarbenes and carbon monoxide as a ligand, a somewhat unusual coordination mode was observed, in which a significant intramolecular Cl-->C(carbene) interaction is present. The propensity of phosphino- and aminocarbenes to behave as four electron donors was also investigated both structurally and energetically on the related eta(2)-complexes 10-18. These results as a whole emphasize the structural versatility of phosphino- compared with aminocarbene complexes.     

On minimal lengths of expressions of Coxeter group elements as products of reflections

It is shown that the absolute length of a Coxeter group element (i.e. the minimal length of an expression of as a product of reflections) is equal to the minimal number of simple reflections that must be deleted from a fixed reduced expression of so that the resulting product is equal to , the identity element. Also, is the minimal length of a path in the (directed) Bruhat graph from the identity element to , and is determined by the polynomial of Kazhdan and Lusztig.