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.

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.

U-q[(sl(2)over-cap vertical bar 1)] vertex operators, screen currents, and correlation functions at an arbitrary level

Bosonized q-vertex operators related to the four-dimensional evaluation modules of the quantum affine superalgebra U-q[sl((2) over cap\1)] are constructed for arbitrary level k=alpha, where alpha not equal 0,-1 is a complex parameter appearing in the four-dimensional evaluation representations. They are intertwiners among the level-alpha highest weight Fock-Wakimoto modules. Screen currents which commute with the action of U-q[sl((2) over cap/1)] up to total differences are presented. Integral formulas for N-point functions of type I and type II q-vertex operators are proposed. (C) 2000 American Institute of Physics. [S0022-2488(00)00608-3].

Ladder operators for integrable one-dimensional lattice models

A generalised ladder operator is used to construct the conserved operators for any one-dimensional lattice model derived from the Yang-Baxter equation. As an example, the low order conserved operators for the XYh model are calculated explicitly.

The effect of resource aggregation at different scales: Optimal foraging behavior of Cotesia rubecula

Resources can be aggregated both within and between patches. In this article, we examine how aggregation at these different scales influences the behavior and performance of foragers. We developed an optimal foraging model of the foraging behavior of the parasitoid wasp Cotesia rubecula parasitizing the larvae of the cabbage butterfly Pieris rapae. The optimal behavior was found using stochastic dynamic programming. The most interesting and novel result is that the effect of resource aggregation within and between patches depends on the degree of aggregation both within and between patches as well as on the local host density in the occupied patch, but lifetime reproductive success depends only on aggregation within patches. Our findings have profound implications for the way in which we measure heterogeneity at different scales and model the response of organisms to spatial heterogeneity.

Inhibition of rat platelet aggregation by the diazeniumdiolate nitric oxide donor MAHMA NONOate

1 Inhibition of rat platelet aggregation by the nitric oxide (NO) donor MAHMA NONOate (Z-1-{N-methyl-N-[6-(N-methylammoniohexyl)amino]}diazen-l-ium-1,2-diolate) was investigated. The aims were to compare its anti-aggregatory effect with vasorelaxation, to determine the effects of the soluble guanylate cyclase inhibitor, ODQ (1H-[1,2,4]oxadiazolo[4,3-ajquinoxalin-1-one), and to investigate the possible role of activation of sarco-encloplasmic reticulum calcium-ATPase (SERCA), independent of soluble guanylate cyclase, using thapsigargin. 2 MAHMA NONOate concentration-dependently inhibited sub-maximal aggregation responses to collagen (2 - 10 mug ml(-1)) and adenosine diphosphate (ADP; 2 mum) in platelet rich plasma. It was (i) more effective at inhibiting aggregation induced by collagen than by ADP, and (ii) less potent at inhibiting platelet aggregation than relaxing rat pulmonary artery. 3 ODQ (10 mum) caused only a small shift (approximately half a log unit) in the concentration-response curve to MAHMA NONOate irrespective of the aggregating agent. 4 The NO-independent activator of soluble guanylate cyclase, YC-1 (3-(5'-hydroxymethyl-2'-furyl)-1-benzy] indazole; 1 - 100 mum), did not inhibit aggregation. The cGMP analogue, 8-pCPT-cGMP (8-(4-chlorophenylthio)guanosine 3'5' cyclic monophosphate; 0.1 - 1 mm), caused minimal inhibition. 5 On collagen-aggregated platelets responses to MAHMA NONOate (ODQ 10 PM present) were abolished by thapsigargin (200 nm). On ADP-aggregated platelets thapsigargin caused partial inhibition. 6 Results with S-nitrosoglutathione (GSNO) resembled those with MAHMA NONOate. Glyceryl trinitrate and sodium nitroprusside were poor inhibitors of aggregation. 7 Thus inhibition of rat platelet aggregation by MAHMA NONOate (like GSNO) is largely ODQ-resistant and, by implication, independent of soluble guanylate cyclase. A likely mechanism of inhibition is activation of SERCA.

Prolonged retention after aggregation into secretory granules of human R183H-growth hormone (GH), a mutant that causes autosomal dominant GH deficiency type II

Human R183H-GH causes autosomal dominant GH deficiency type II. Because we show here that the mutant hormone is fully bioactive, we have sought to locate an impairment in its progress through the secretory pathway as assessed by pulse chase experiments. Newly synthesized wild-type and R183H-GH were stable when expressed transiently in AtT20 cells, and both formed equivalent amounts of Lubrol-insoluble aggregates within 40 min after synthesis. There was no evidence for intermolecular disulfide bond formation in aggregates of wild-type hormone or the R183H mutant. Both wildtype and R183H-GH were packaged into secretory granules, assessed by the ability of 1 mm BaCl2 to stimulate release and by immunocytochemistry. The mutant differed from wildtype hormone in its retention in the cells after packaging into secretory granules; 50% more R183H-GH than wild-type aggregates were retained in AtT20 cells 120 min after synthesis, and stimulated release of R183H-GH or a mixture of R183H-GH and wild-type that had been retained in the cell was reduced. The longer retention of R183H-GH aggregates indicates that a single point mutation in a protein contained in secretory granules affects the rate of secretory granule release.

Mean anisotropy of homogeneous Gaussian random fields and anisotropic norms of linear translation-invariant operators on multidimensional integer lattices

Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.