Specificity of 17 beta-oestradiol and benzo[a] pyrene oxidation by polymorphic human cytochrome P4501B1 variants substituted at residues 48, 119 and 432

1. Eight human cytochrome P4501B1 (CYP1B1) allelic variants, namely Arg(48)Ala(119)Leu(432), Arg(48)Ala(119)Val(432), Gly(48)Ala(119)Leu(432), Gly(48)Ala(119)Val(432), Arg(48)Ser(119)Leu(432), Arg(48)Ser(119)Val(432), Gly(48)Ser(119)Leu(432) and Gly(48)Ser(119)Val(432) (all with Asn(453)), were expressed in Escherichia coli together with human NADPH-P450 reductase and their catalytic specificities towards oxidation of 17 beta -oestradiol and benzo[a]pyrene were determined. 2. All of the CYP1B1 variants expressed in bacterial membranes showed Fe2+. CO versus Fe2+ difference spectra with wavelength maxima at 446 nm and they reacted with antibodies raised against recombinant human CYP1B1 in immunoblots. The ratio of expression of the reductase to CYP1B1 in these eight preparations ranged from 0.2 to 0.5. 3. CYP1B1 Arg(48) variants tended to have higher activities for 17 beta -oestradiol 4-hydroxylation than Gly(48) variants, although there were no significant variations in 17 beta -oestradiol 2-hydroxylation activity in these eight CYP1B1 variants. Interestingly, ratios of formation of 17 beta -oestradiol 4-hydroxylation to 2-hydroxylation by these CYP1B1 variants were higher in all of the Val(432) forms than the corresponding Leu(432) forms. 4. In contrast, Leu(432) forms of CYP1B1 showed higher rates of oxidation of benzo[a]pyrene (to the 7, 8-dihydoxy-7,8-dihydrodiol in the presence of epoxide hydrolase) than did the Val(432) forms. 5. These results suggest that polymorphic human CYP1B1 variants may cause some altered catalytic specificity with 17 beta -oestradiol and benzo[a]pyrene and may influence susceptibilities of individuals towards endogenous and exogenous carcinogens.

Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Elliptic Gaudin models and elliptic KZ equations

The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Entangled subspaces and quantum symmetries

Entanglement is defined for each vector subspace of the tensor product of two finite-dimensional Hilbert spaces, by applying the notion of operator entanglement to the projection operator onto that subspace. The operator Schmidt decomposition of the projection operator defines a string of Schmidt coefficients for each subspace, and this string is assumed to characterize its entanglement, so that a first subspace is more entangled than a second, if the Schmidt string of the second majorizes the Schmidt string of the first. The idea is applied to the antisymmetric and symmetric tensor products of a finite-dimensional Hilbert space with itself, and also to the tensor product of an angular momentum j with a spin 1/2. When adapted to the subspaces of states of the nonrelativistic hydrogen atom with definite total angular momentum (orbital plus spin), within the space of bound states with a given total energy, this leads to a complete ordering of those subspaces by their Schmidt strings.

Pseudo memory effects, majorization and entropy in quantum random walks

A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial distribution. In a classical walk, entropy increase can be regarded as a consequence of the majorization ordering of successive distributions. The Lorenz curves of successive distributions for a symmetric quantum walk reveal no majorization ordering in general. Nevertheless, entropy can increase, and computer experiments show that it does so on average. Varying the stages at which the quantum coin system is traced out leads to new quantum walks, including a symmetric walk for which majorization ordering is valid but the spreading rate exceeds that of the usual symmetric quantum walk.

Radiocarbon in tropical tree rings during the Little Ice Age

Cross-dated tree-ring cores (Pinus merkusii) from north-central Thailand, spanning AD 1620-1780, were used to investigate atmospheric C-14 for the tropics during the latter part of the Little Ice Age. In addition, a cross-dated section of Huon pine from western Tasmania, covering the same period of time, was investigated. A total of 16 pairs of decadal samples were extracted to alpha-cellulose for AMS C-14 analysis using the ANTARES facility at ANSTO. The C-14 results from Thailand follow the trend of the southern hemisphere, rather than that of the northern hemisphere. This is a surprising result, and we infer that atmospheric C-14 for north-central Thailand, at 17degrees N, was strongly influenced by the entrainment of southern hemisphere air parcels during the southwest Asian monsoon, when the Inter-Tropical Convergence Zone moves to the north of our sampling site. Such atmospheric transport and mixing are therefore considered to be one of the principal mechanisms for regional C-14 offsets. (C) 2004 Elsevier B.V. All rights reserved.

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.