Ladder operator for the one-dimensional Hubbard model

The one-dimensional Hubbard model is integrable in the sense that it has an infinite family of conserved currents. We explicitly construct a ladder operator which can be used to iteratively generate all of the conserved current operators. This construction is different from that used for Lorentz invariant systems such as the Heisenberg model. The Hubbard model is not Lorentz invariant, due to the separation of spin and charge excitations. The ladder operator is obtained by a very general formalism which is applicable to any model that can be derived from a solution of the Yang-Baxter equation.

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.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

The structure of quantum Lie algebras for the classical series, B-l, C-l and D-l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q = 1. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint --> adjoint We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B-l, C-l and D-l. In the quantum case the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.

Eigenvalues of Casimir operators for gl(m/infinity)

A full set of Casimir operators for the Lie superalgebra gl(m/infinity) is constructed and shown to be well defined in the category O-FS generated by the highest-weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from gl(m/infinity) are also determined.

Structure-activity studies of conantokins as human N-methyl-D-aspartate receptor modulators

The activities of conantokin-G (con-G), conantokin-T (con-T), and several novel analogues have been studied using polyamine enhancement of [H-3]MK-801 binding to human glutamate-N-methyl-D-aspartate (NMDA) receptors, and their structures have been examined using CD and H-1 NMR spectroscopy. The potencies of con-G[A7], con-G, and con-T as noncompetitive inhibitors of spermine-enhanced [H-3]MK-801 binding to NMDA receptor obtained from human brain tissue are similar to those obtained using rat brain tissue. The secondary structure and activity of con-G are found to be highly sensitive to amino acid substitution and modification. NMR chemical shift data indicate that con-G, con-G[D8,D17], and con-G[A7] have similar conformations in the presence of Ca2+. This consists of a helix for residues 2-16, which is kinked in the vicinity of Gla10. This is confirmed by 3D structure calculations on con-G[A7]. Restraining this helix in a linear form (i.e., con-G[A7,E10-K13]) results in a minor reduction in potency. Incorporation of a 7-10 salt-bridge replacement (con-G[K7-E10]) prevents helix formation in aqueous solution and produces a peptide with low potency. Peptides with the Leu5-Tyr5 substitution also have low potencies (con-G[Y5,A7] and con-G[Y5,K7]) indicating that Leu5 in con-G is important for full antagonist behavior. We have also shown that the Gla-Ala7 substitution increases potency, whereas the Gla-Lys7 substitution has no effect. Con-G and con-G[K7] both exhibit selectivity between NMDA subtypes from mid-frontal and superior temporal gyri, but not between sensorimotor and mid-frontal gyri. Asn8 and/or Asn17 appear to be important for the ability of con-G to function as an inhibitor of polyamine-stimulated [3H]MK-801 binding, but not in maintaining secondary structure. The presence of Ca2+ does not increase the potencies of con-G and con-T for NMDA receptors but does stabilize the helical structures of con-G, con-G[D8,D17], and, to a lesser extent, con-G[A7]. The NMR data support the existence of at least two independent Ca2+-chelating sites in con-G, one involving Gla7 and possibly Gla3 and the other likely to involve Gla10 and/or Gla14.

Amphilactams A-D: Novel nematocides from southern Australian marine sponges of the genus Amphimedon

Bioassay-directed fractionation of the ethanol extracts of two Amphimedon spp. collected during trawling operations in the Great Australian Eight yielded four new macrocyclic lactone/lactams, amphilactams A-D (1-4). The amphilactams possess potent in vitro nematocidal properties, and their structures were assigned on the basis of detailed spectroscopic analysis and comparison with synthetic model compounds. The amphilactams feature both carbon skeletons and an enamino lactone/lactam moiety unprecedented in the natural products literature.

Nuapapuin A and sigmosceptrellins D and E: New norterpene cyclic peroxides from a southern Australian marine sponge, Sigmosceptrella sp.

A Sigmosceptrella sp. from the Great Australian Eight, Australia, has yielded the new norditerpene cyclic peroxide, nuapapuin A (2a), and the norsesterterpene cyclic peroxide sigmosceptrellin D (3a), characterized as the corresponding methyl esters 2b and 3b. The crude methylated sponge extract also yielded the new norsesterterpene cyclic peroxide sigmosceptrellin E methyl ester (4). Relative stereochemistry about C2, C3, and C6 was assigned by established empirical rules and absolute stereochemistry by the advanced Mosher procedure. A plausible biosynthetic pathway has been proposed that rationalizes key transformations in the biosynthesis of all known norterpene cyclic peroxides and related norterpene ketones, dienes and sigmosceptrins.

Interaction of zinc(II) with the cyclic octapeptides, cyclo[Ile(Oxn)-D-Val(Thz)](2) and ascidiacyclamide, a cyclic peptide from Lissoclinum patella

The interactions between zinc salts and the naturally occurring cyclic octapeptide ascidiacyclamide in methanol, as well as a synthetic analogue cyclo[Ile(Oxn)-D-Val(Thz)](2), were monitored by H-1 NMR and CD spectroscopy. Three zinc complexes were identified, their relative amounts depending on the nature of the anion (perchlorate, triflate or chloride) and the presence or absence of base. Binding constants for two of the zinc species were calculated from CD or H-1 NMR spectra, [Zn(L - H)](+) (KZn(L-H) = [Zn(L - H)(+)]/[Zn2+][(L - H)(-)] = 10(7 +/- 2) M-1; 95% methanol/5% water, 298.0 K, NEt3/HClO4 buffer 0.04 M) and [ZnLCl](+) (K-ZnCIL = [ZnCIL+]/[Zn2+][Cl-][L] = 10(7.2) (+/-) (0.1) M-2; d(3)-methanol, 301 K).

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Risk management for scuba diving operators on Australia's Great Barrier Reef

Australia's Great Barrier Reef is one of the world's most popular scuba diving destinations. Unfortunately, a series of recent diving injuries and deaths has tarnished the region's safety record. In particular, media attention surrounding the disappearance of American divers Thomas and Eileen Lonergan has focused attention on dive operators' legal responsibilities and the consequences of failing to discharge their duty of care to customers. This paper briefly examines the relevant Australian law for recreational diving operations, and reviews risk management strategies that may reduce or prevent the occurrence of future problems. (C) 2000 Elsevier Science Ltd. All rights reserved.