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A nanoscale dendrimer-based Fe24 cluster: synthesis and molecular self-assembly

We report the synthesis, characterisation and self-assembly of a nanoscopic Fe24 cluster using an organic dendrimer as a molecular substrate for building up well-defined molecular nanostructures.     

Constraining hadronic superfluidity with neutron star precession

I show that the standard picture of the neutron star core containing coexisting neutron and proton superfluids, with the proton component forming a type II superconductor threaded by flux tubes, is inconsistent with observations of long-period (approximately 1 yr) precession in isolated pulsars. I conclude that either the two superfluids coexist nowhere in the stellar core, or the core is a type I superconductor rather than type II. Either possibility would have interesting implications for neutron star cooling and theories of spin jumps (glitches).     

Acid-promoted Prins cyclizations of enol ethers to form tetrahydropyrans

Trifluoroacetic acid efficiently catalyzes Prins cyclizations of enol ethers 8 to provide tetrahydropyrans 9 and 10. These tetrahydropyrans are isolated with combined yields of 42-85% and stereoselectivities at C(4) ranging from 95:5 to 50:50 depending on the nature of the substituent R. Unique byproducts of these cyclizations that reveal the presence of underlying equilibria have been isolated and identified. [reaction: see text]     

Randomised circular means of Fourier transforms of measures

We explore decay estimates for circular means of the Fourier transform of a measure on in terms of its -dimensional energy. We find new upper bounds for the decay exponent. We also prove sharp estimates for a certain family of randomised versions of this problem.

     

GO-spaces with -closed discrete dense subsets

In this paper we study the question ``When does a perfect generalized ordered space have a -closed-discrete dense subset?' and we characterize such spaces in terms of their subspace structure, -mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a -closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.

     

Hausdorff means and moment sequences

We prove Schur’s theorem on the complete symmetric functions by using Hausdorff means. This approach leads to a more general result and to some new properties of moment sequences.     

The Art of Course Planning: Soft O.R. in Action

This article is a case study described from two viewpoints: that of an analyst and that of a ‘decision-maker’. It describes the use of two ‘soft O.R.’ methods in helping the members of a university O.R. group to plan revisions to a postgraduate Diploma course, resulting in the implementation of an improved course. One author conducted the exercise while the other was a member of the client group. Given that case studies are usually written by the analyst alone, it is hoped that a client's eye-view will be useful as feedback for practitioners and can also introduce some of the concepts and terminology of soft O.R. to those engaged in more mathematical O.R. activities.