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.

Fluctuations in heroin purity and the incidence of fatal heroin overdose

In order to determine the role played by heroin purity in fatal heroin overdoses, time series analyses were conducted on the purity of street heroin seizures in south western Sydney and overdose fatalities in that region. A total of 322 heroin samples were analysed in fortnightly periods between February 1993 to January 1995. A total of 61 overdose deaths occurred in the region in the study period. Cross correlation plots revealed a significant correlation of 0.57 at time lag zero between mean purity of heroin samples per fortnight and number of overdose fatalities. Similarly, there was a significant correlation of 0.50 at time lag zero between the highest heroin purity per fortnight and number of overdose fatalities. The correlation between range of heroin purity and number of deaths per fortnight was 0.40. A simultaneous multiple regression on scores adjusted for first order correlation indicated both the mean level of heroin purity and the range of heroin purity were independent predictors of the number of deaths per fortnight. The results indicate that the occurrence of overdose fatalities was moderately associated with both the average heroin purity and the range of heroin purity over the study period. (C) 1999 Elsevier Science Ireland Ltd. All rights reserved.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

Decoherence and fidelity in ion traps with fluctuating trap parameters

We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (wobbling) of the ion relative to the center of the trap, and fluctuations of the spring constant, which an due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived. [S1050-2947(99)06005-9].

Nickel complexes with tris(2-aminoethyl)amine (tren): [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2)center dot 6H(2)O (ox = oxalate), {[Ni-2(tren)(3)][ClO4](4)center dot H2O}(n), and [Ni-2(tren)(2)(aepd)][ClO4](4)center dot 2H(2)O (aepd = N-(2-aminoethyl)pyrrolidi

Reaction of K-3[Cr(ox)(3)] (ox = oxalate) with nickel(II) and tris(2-aminoethyl)amine (tren) in aqueous solution resulted in isolation of the bimetallic assembly [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2). 6H(2)O. The polymeric complex {[Ni-2(tren)(3)][ClO4](4). H2O}(n) has been prepared by reaction of nickel(II) perchlorate and tren in aqueous solution. From the same reaction mixture the complex [Ni-2(tren)(2)(aepd)][ClO4](4). 2H(2)O (aepd = N-(2-aminoethyl)pyrrolidine-3,4-diamine), in which a bridging tren ligand contains a carbon-carbon bond between two arms forming a substituted pyrrolidine, has been isolated. The complexes have been characterized by X-ray crystallography. The magnetic susceptibility (300-4.2 K) and magnetization data (2, 4 K, H = 0-5 T) for {[Ni-2(tren)(3)][ClO4](4). H2O}(n) (300 K , 4.23 mu(B)) exhibit evidence of weak antiferromagnetic coupling and zero field splitting (2J = -1.8 cm(-1); \ D\ = 2 cm(-1)) at low temperature. For [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2). 6H(2)O the susceptibility data at 300 K are indicative of uncoupled nickel(II) and chromium(III) sites with zero-field splitting and intramolecular antiferromagnetic coupling predicted at low temperature.

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

Bounds on integrals of the Wigner function

The integral of the Wigner function over a subregion of the phase space of a quantum system may be less than zero or greater than one. It is shown that for systems with 1 degree of freedom, the problem of determining the best possible upper and lower bounds on such an integral, over an possible states, reduces to the problem of finding the greatest and least eigenvalues of a Hermitian operator corresponding to the subregion. The problem is solved exactly in the case of an arbitrary elliptical region. These bounds provide checks on experimentally measured quasiprobability distributions.

Solute transport by surface runoff from low-angle slopes: theory and application

The removal of chemicals in solution by overland how from agricultural land has the potential to be a significant source of chemical loss where chemicals are applied to the soil surface, as in zero tillage and surface-mulched farming systems. Currently, we lack detailed understanding of the transfer mechanism between the soil solution and overland flow, particularly under field conditions. A model of solute transfer from soil solution to overland flow was developed. The model is based on the hypothesis that a solute is initially distributed uniformly throughout the soil pore space in a thin layer at the soil surface. A fundamental assumption of the model is that at the time runoff commences, any solute at the soil surface that could be transported into the soil with the infiltrating water will already have been convected away from the area of potential exchange. Solute remaining at the soil surface is therefore not subject to further infiltration and may be approximated as a layer of tracer on a plane impermeable surface. The model fitted experimental data very well in all but one trial. The model in its present form focuses on the exchange of solute between the soil solution and surface water after the commencement of runoff. Future model development requires the relationship between the mass transfer parameters of the model and the time to runoff: to be defined. This would enable the model to be used for extrapolation beyond the specific experimental results of this study. The close agreement between experimental results and model simulations shows that the simple transfer equation proposed in this study has promise for estimating solute loss to surface runoff. Copyright (C) 2000 John Wiley & Sons, Ltd.

Experimental examination of solute transport by surface runoff from low-angle slopes

The removal of chemicals in solution, by overland flow from agricultural land has the potential to be a significant source of chemical loss from zero-till and surface mulched farming systems. The objective of this study was to determine the magnitude of solute loss by surface runoff from agricultural systems. Previous experiments have enhanced the understanding of the exchange process, but the initial soil conditions together with the tracer application method in these experiments have meant that in some cases the results have limited applicability to field situations. In this study, two different sets of experiments were carried out to determine the magnitude of solute loss by surface runoff. These experiments entailed the surface application of bromide to (1) field scale plots 18 m long by 2 m wide and (2) repacked soil cores 236 mm in diameter; followed by the application of simulated rainfall in both cases. The most substantial finding of the field experiments was that the quantities of solute in surface runoff varied greatly with soil type and structure (0.07-14.9% of the applied bromide). Also, on some soils, large quantities of tracer were measured in the surface runoff even after several hours of infiltration. The experiments on soil cores showed that soil structure plays an important role in the quantity of chemical that may be transported in the surface runoff. These field results showed that, in certain systems, solute movement by overland flow is an important transport mechanism, which should be considered when budgeting for chemical loss. (C) 2000 Elsevier Science B.V. All rights reserved.

Early diagnosis of lymphedema in postsurgery breast cancer patients

Lymphedema is an accumulation of lymph fluid in the limb resulting from an insufficiency of the lymphatic system. It is commonly associated with surgical or radiotherapy treatment for breast cancer. As with many progressively debilitating disorders, the effectiveness of treatment is significantly improved by earlier intervention. Multiple frequency bioelectrical impedance analysis (MFBIA) previously was shown to provide accurate relative measures of lymphedema in the upper limb in patients after treatment for breast cancer, This presentation reports progress to date on a three-year prospective study to evaluate the efficacy of MFBIA to predict the early onset of lymphedema in breast cancer patients following treatment. Bioelectrical impedance measurements of each upper limb were recorded in a group of healthy control subjects (n = 50) to determine the ratio of extracellular limb-fluid volumes. From this population, the expected normal range of asymmetry (99.7% confidence) between the limbs was determined, Patients undergoing surgery to treat breast cancer were recruited into the study, and MFBIA measurements were recorded presurgery, at one month and three months after surgery, and then at two-month intervals for up to 24 months postsurgery, When patients had an MFBIA measure outside the 99.7% range of the control group, they were referred to their physician for clinical assessment. Results to date: Over 100 patients were recruited into the study over the past two years; at present, 19 have developed lymphedema and, of these, 12 are receiving treatment. In each of these 19 cases, MFBIA predicted the onset of the condition up to four months before it could be clinically diagnosed. The false-negative rate currently is zero, The study will continue to monitor patients over the remaining year to accurately ascertain estimates of specificity and sensitivity of the procedure.

A numerical study of flexural buckling of foliated rock slopes

The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic-perfectly plastic. Condition of slip at the interfaces are determined by a Mohr-Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87-104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright (C) 2001 John Wiley & Sons, Ltd.

Cyanogenic polymorphism in Eucalyptus polyanthemos Schauer subsp vestita L. Johnson and K. Hill (Myrtaceae)

Plant cyanogenesis, the release of cyanide from endogenous cyanide-containing compounds, is an effective herbivore deterrent. This paper characterises cyanogenesis in the Australian tree Eucalyptus polyanthemos Schauer subsp. vestita L. Johnson and K. Hill for the first time. The cyanogenic glucoside prunasin ((R)-mandelonitrile beta-D-glucoside) was determined to be the only cyanogenic compound in E. polyanthemos foliage. Two natural populations of E. polyanthernos showed quantitative variation in foliar prumasin concentration, varying from zero (i.e. acyanogenic) to 2.07 mg CN g(-1) dry weight in one population and from 0.17 to 1.98 mg CN g(-1) dry weight in the other. No significant difference was detected between the populations with respect to the mean prunasin concentration or the degree of variation in foliar prunasin, despite significant differences in foliar nitrogen. Variation between individuals was also observed with respect to the capacity of foliage to catabolise prunasin to form cyanide. Moreover, variation in this capacity generally correlated with the amount of prunasin in the tissue, suggesting genetic linkage between prunasin and beta-glucosidase. (C) 2002 Elsevier Science Ltd. All rights reserved.

Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

The synthetic organic compound λ(BETS)2FeCl4 undergoes successive transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the Fe3+ magnetic ions in these phase transition. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field He due to the magnetic ions. This suggests that the field-induced superconducting state is the same as the zero-field superconducting state which occurs under pressure or when the Fe3+ ions are replaced by non-magnetic Ga3+ ions. We show how Hc can be extracted from the observed splitting of the Shybnikov-de Haas frequencies. Furthermore, we use this method of extracting He to predict the field range for field-induced superconductivity in other materials. We also show that at high fields the spin fluctuations of the localized spins are not important.

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers observed via a hole-burned free induction decay

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers are observed using a single high-turn-angle microwave pulse. The free induction signal that follows the hole-burning pulse exhibits oscillations that are distinct from the oscillatory free induction decay observable in some inhomogeneously broadened systems. It contains frequencies characteristic of the superhyperfine splittings, together with a zero frequency component. Experimental examples of the effect in both orientationally disordered (powdered) and structurally disordered (glassy) systems are presented and compared with the conceptually similar Fourier transform electron paramagnetic resonance detected nuclear magnetic resonance experiment, together with numerical simulations. (C) 2003 American Institute of Physics.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.