Quantum doubles from a class of noncocommutative weak Hopf algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products is constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterizations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained. (C) 2004 American Institute of Physics.

Geochemistry of late Archaean stromatolites from Zimbabwe: evidence for microbial life in restricted epicontinental seas

We report comprehensive trace element and Sr-isotope data for microbial carbonates from the Archaean Mushandike limestone, Masvingo Greenstone Belt, Zimbabwe. The stromatolites have very coherent REE + Y patterns and share the essential shale-normalised characteristics of other Archaean marine precipitates (positive La and Gd anomalies, absence of a negative Cc anomaly and a strongly superchondritic Y/Ho ratio). Mixing models constrain the maximum amount of shale contamination to 0.25-1% and calculated detritus-free carbonate REE + Y systematics require precipitation from seawater. In terms of light-REE over heavy-REE depletion, however, the studied samples are very different from all other known Archaean marine precipitates. In shale-normalised plots, the Mushandike samples yield a negative slope. A very restricted, regional input source of the dissolved load is indicated because normalisation with locally occurring tonalite gneiss REE + Y data yields a pattern closely resembling typical shale-normalised Archaean marine chemical sediments. The disappearance of a negative Eu anomaly when patterns are normalised with local tonalite gneiss strengthens this interpretation. Sr-isotope ratios are strongly correlated with trace element contents and ratios, which explains the modest scatter in Sr-isotope ratios as representing (minor) clastic contamination. Importantly, even the least contaminated samples have very radiogenic initial Sr-87/Sr-86 ratios (0.7184) implying Sr input from an ancient high Rb/Sr source, such as the early Archaean gneisses of south-central Zimbabwe. A local ancient (3.5-3.8 Ga) source is also indicated by previously published Pb-isotope datasets for the Mushandike stromatolites. This is entirely compatible with the occurrence of 3.7-3.8 Ga zircons in quartzites and metapelites from comparably old greenstone belts within less than 150 km of the studied locality. Comparison of the Pb-isotope ratios of the Mushandike stromatolites with 2.7 and 2.6 Ga old stromatolites from the neighbouring, Belingwe Greenstone Belt demonstrates differences in initial isotope composition that relate to the extent of exchange with the open ocean. The development of numerous basins on old continental crust, with water masses variably restricted from the open ocean. suggests a lack of strong vertical topography on this late Archaean craton. (C) 2004 Elsevier B.V. All rights reserved.

The genetic structure of Australian populations of Mycosphaerella musicola suggests restricted gene flow at the continental scale

Mycosphaerello musicolo causes Sigatoka disease of banana and is endemic to Australia. The population genetic structure of M. musicola in Australia was examined by applying single-copy restriction fragment length polymorphism probes to hierarchically sampled populations collected along the Australian cast coast. The 363 isolates studied were from 16 plantations at 12 sites in four different regions, and comprised 11 populations. These populations displayed moderate levels of gene diversity (H = 0.142 to 0.369) and similar levels of genotypic richness and evenness. Populations were dominated by unique genotypes, but isolates sharing the same genotype (putative clones) were detected. Genotype distribution was highly localized within each population, and the majority of putative clones were detected for isolates sampled from different sporodochia in the same lesion or different lesions on a plant. Multilocus gametic disequilibrium tests provided further evidence of a degree of clonality within the populations at the plant scale. A complex pattern of population differentiation was detected for M. musicola in Australia. Populations sampled from plantations outside the two major production areas were genetically very different to all other populations. Differentiation was much lower between populations of the two major production areas, despite their geographic separation of over 1,000 km. These results suggest low gene flow at the continental scale due to limited spore dispersal and the movement of infected plant material.

Eigenvalues of Casimir invariants for Uq[osp(m|n)]

For each quantum superalgebra U-q[osp(m parallel to n)] with m > 2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated. (c) 2005 American Institute of Physics.

Embedding a restricted class of partial K-4-designs

Given a partial K-4-design (X, P), if x is an element of X is a vertex which occurs in exactly one block of P, then call x a free vertex. In this paper, a technique is described for obtaining a cubic embedding of any partial K-4-design with the property that every block in the partial design contains at least two free vertices.

Entanglement under restricted operations: Analogy to mixed-state entanglement

We show that the classification of bipartite pure entangled states when local quantum operations are restricted yields a structure that is analogous in many respects to that of mixed-state entanglement. Specifically, we develop this analogy by restricting operations through local superselection rules, and show that such exotic phenomena as bound entanglement and activation arise using pure states in this setting. This analogy aids in resolving several conceptual puzzles in the study of entanglement under restricted operations. In particular, we demonstrate that several types of quantum optical states that possess confusing entanglement properties are analogous to bound entangled states. Also, the classification of pure-state entanglement under restricted operations can be much simpler than for mixed-state entanglement. For instance, in the case of local Abelian superselection rules all questions concerning distillability can be resolved.

Restricted mating dispersal and strong breeding group structure in a mid-sized marsupial mammal (Petrogale penicillata)

Ecological genetic studies have demonstrated that spatial patterns of mating dispersal, the dispersal of gametes through mating behaviour, can facilitate inbreeding avoidance and strongly influence the structure of populations, particularly in highly philopatric species. Elements of breeding group dynamics, such as strong structuring and sex-biased dispersal among groups, can also minimize inbreeding and positively influence levels of genetic diversity within populations. Rock-wallabies are highly philopatric mid-sized mammals whose strong dependence on rocky terrain has resulted in series of discreet, small colonies in the landscape. Populations show no signs of inbreeding and maintain high levels of genetic diversity despite strong patterns of limited gene flow within and among colonies. We used this species to investigate the importance of mating dispersal and breeding group structure to inbreeding avoidance within a 'small' population. We examined the spatial patterns of mating dispersal, the extent of kinship within breeding groups, and the degree of relatedness among brush-tailed rock-wallaby breeding pairs within a colony in southeast Queensland. Parentage data revealed remarkably restricted mating dispersal and strong breeding group structuring for a mid-sized mammal. Breeding groups showed significant levels of female kinship with evidence of male dispersal among groups. We found no evidence for inbreeding avoidance through mate choice; however, anecdotal data suggest the importance of life history traits to inbreeding avoidance between first-degree relatives. We suggest that the restricted pattern of mating dispersal and strong breeding group structuring facilitates inbreeding avoidance within colonies. These results provide insight into the population structure and maintenance of genetic diversity within colonies of the threatened brush-tailed rock-wallaby.

Varieties of algebras arising from K-perfect m-cycle systems

A class of algebras forms a variety if it is characterised by a collection of identities. There is a well-known method, often called the standard construction, which gives rise to algebras from m-cycle systems. It is known that the algebras arising from {1}-perfect m-cycle systems form a variety for m is an element of {3, 5} only, and that the algebras arising from {1, 2}-perfect m-cycle systems form a variety for m is an element of {3, 5, 7} only. Here we give, for any set K of positive integers, necessary and sufficient conditions under which the algebras arising from K-perfect m-cycle systems form a variety. (c) 2006 Elsevier B.V. All rights reserved.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.