Simultaneous core partitions with nontrivial common divisor

Acknowledgements Part of this work was done at the Centre Interfacultaire Bernoulli (CIB), in the École Polytechnique Fédérale de Lausanne (Switzerland), during the Semester Local Representation Theory and Simple Groups. The first two authors are grateful to the CIB for their financial and logistical support. The first author also acknowledges financial support from the Engineering and Physical Sciences Research Council grant Combinatorial Representation Theory EP/M019292/1. The second author was supported by 586 PSC-TRADA-46-493 and thanks George Andrews who supported a visit to Penn State where this research began. The second author also thanks Christopher R. H. Hanusa for helpful conversations on diagrams and references, and notes that some diagrams were made using the ytab package. All of the authors thank the anonymous referee for the careful reading and detailed and helpful suggestions.Peer reviewedPostprin

Liquid crystals from poly(4,4'-methoxybiphenylyl methacrylate)

Side-chain liquid crystalline poly(4,4'-biphenylyl methacrylate) was studied by X-ray diffraction. Three smectic phases were described using a ribbon-like structural model for the polymer chain. In the smectic SP phase, ribbons lie flat on their sides to form layers with a spacing equal to the thickness of the ribbons. In the smectic SA phase, the ribbons stand upright giving layers with a thickness corresponding to the length of one extended monomeric unit. In the ordered smectic So phase, the layer thickness also corresponds to one extended repeat unit, and the pendant groups are arranged according to a two-dimensional oblique lattice. The Schlieren texture observed in the SP phase was analysed in terms of symmetry.Les phases liquides cristallines d'un poly(methacrylate) de 4,4'-biphénylyle ont été étudiées par diffraction des rayons X. Trois phases smectiques ont été décrites à l'aide d'un même modèle de chaîne macromoléculaire sous forme de ruban. Dans la phase smectique Sp, les rubans sont disposés à plat dans des couches avec un espacement égal à l'épaisseur des rubans. Dans la phase smectique SA, les rubans sont arrangés en simples couches avec un espacement égal à la largeur des rubans. Dans la phase smectique ordonnée So, les rubans sont arrangés comme dans la phase SA mais avec les groupes mésogènes assemblés suivant un réseau bidimensionnel oblique. La texture de type Schlieren observée pour la phase Sp a été analysée en termes de symétrie

Abelian BF theory and Turaev-Viro invariant

The U(1) BF Quantum Field Theory is revisited in the light of Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition function is related to the BF one and how the latter on its turn coincides with an abelian Turaev-Viro invariant. Significant differences compared to the non-abelian case are highlighted.Comment: 47 pages and 6 figure

Is there a common water-activity limit for the three domains of life?

Archaea and Bacteria constitute a majority of life systems on Earth but have long been considered inferior to Eukarya in terms of solute tolerance. Whereas the most halophilic prokaryotes are known for an ability to multiply at saturated NaCl (water activity (a w) 0.755) some xerophilic fungi can germinate, usually at high-sugar concentrations, at values as low as 0.650-0.605 a w. Here, we present evidence that halophilic prokayotes can grow down to water activities of <0.755 for Halanaerobium lacusrosei (0.748), Halobacterium strain 004.1 (0.728), Halobacterium sp. NRC-1 and Halococcus morrhuae (0.717), Haloquadratum walsbyi (0.709), Halococcus salifodinae (0.693), Halobacterium noricense (0.687), Natrinema pallidum (0.681) and haloarchaeal strains GN-2 and GN-5 (0.635 a w). Furthermore, extrapolation of growth curves (prone to giving conservative estimates) indicated theoretical minima down to 0.611 a w for extreme, obligately halophilic Archaea and Bacteria. These were compared with minima for the most solute-tolerant Bacteria in high-sugar (or other non-saline) media (Mycobacterium spp., Tetragenococcus halophilus, Saccharibacter floricola, Staphylococcus aureus and so on) and eukaryotic microbes in saline (Wallemia spp., Basipetospora halophila, Dunaliella spp. and so on) and high-sugar substrates (for example, Xeromyces bisporus, Zygosaccharomyces rouxii, Aspergillus and Eurotium spp.). We also manipulated the balance of chaotropic and kosmotropic stressors for the extreme, xerophilic fungi Aspergillus penicilloides and X. bisporus and, via this approach, their established water-activity limits for mycelial growth (∼0.65) were reduced to 0.640. Furthermore, extrapolations indicated theoretical limits of 0.632 and 0.636 a w for A. penicilloides and X. bisporus, respectively. Collectively, these findings suggest that there is a common water-activity limit that is determined by physicochemical constraints for the three domains of life

Cultivation of Halophilic Hydrocarbon Degraders

Few extremely halophilic hydrocarbon-degrading microbes have been grown in pure culture, and so in this chapter we outline some of the strategies that have been successfully adopted, with primary consideration to enhancing the bioavailability of hydrocarbons at high salinity. A minimal medium is presented, but it should be considered only as a starting point, and adapted to reflect the salt composition of the environment. General strategies for growing previously uncultivated microbes are briefly reviewed, and the approaches used to add hydrocarbons to media are also considered. In order to increase the chances of cultivating halophilic hydrocarbon degraders, we suggest that the growth medium is prepared or supplemented with brine from the environment under study

Prokaryotic hydrocarbon degraders

Hydrocarbons have been part of the biosphere for millions of years, and a diverse group of prokaryotes has evolved to use them as a source of carbon and energy. To date, all the formally defined genera are eubacterial, in 7 of the 24 major phyla currently recognized (Tree of Life, 2009); principally in the Actinobacteria, the Bacteroidetes, the Firmicutes, and the Proteobacteria. Some Cyanobacteria have been shown to degrade hydrocarbons on a limited scale, but whether this is of any ecological significance remains to be seen ? it is likely that all aerobic organisms show some basal metabolism of hydrocarbons by nonspecific oxygenases, and similar ?universal? metabolism may occur in anaerobes. More recently, some thermophilic, acidophilic methanotrophs from the phylum Verrucomicrobia have also been isolated (Chapter 26, Vol. 3, Part 1); we may expect more diversity as research proceeds. There have been publications indicating that halophilic archaea are significant hydrocarbon-degraders in some environments, but these have not yet been rigorously, or formally, described

Smectic E side-chain liquid crystalline poly(methacrylates)

A homologous series of three side-chain liquid crystalline poly(methacrylates) with 4'methoxybiphenylyl pendant mesogenic groups and oligo(ethylene-oxide) flexible spacers has been studied by X-ray diffraction. These polymers were shown to form a single layered smectic E structure, which has been analysed in terms of polymer chain conformation. The pendant groups were found to all hang on the same side of the polymer backbone to form ribbons, which are assembled side by side with an alternating up and down orientation of the pendant groups.Une série homologue de trois poly(méthacrylates) liquides cristallins à groupes mésogènes latéraux a été étudiée par diffraction des rayons X. Les groupes mésogènes constitués par des groupes 4'méthoxybiphénylyle étaient reliés au squelette macromoléculaire par des espaceurs souples de nature oligooxyéthyléniques. La structure smectique E monocouche de ces polymères a été analysée en termes de conformations du squelette macromoléculaire. Les groupes latéraux sont tous situés du même côté par rapport à la chaîne principale, et conduisent à des éléments de structure ayant la forme de rubans. Les rubans sont assemblés côte à côte avec les groupes mésogènes pointant alternativement vers le haut et vers le bas