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.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Religious Information Poverty in Australian State Schools

This paper introduces the concept of religious information poverty in Australian state schools from an information science perspective. Information scientists have been theorising about the global information society for some time, along with its increased provision of vital information for the good of the world. Australian state schools see themselves as preparing children for effective participation in the information society, yet Australian children are currently suffering a religious illiteracy that undermines this goal. Some reasons and theories are offered to explain the existence of religious information poverty in state schools, and suggestions for professional stakeholders are offered for its alleviation.

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

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.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Twisted parafermions

A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted Z-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra A(2)((2)) is given.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Immunology of multiple sclerosis

Multiple sclerosis (MS) is an autoimmune disease of the central nervous system (CNS) leading to demyelination, axonal damage, and progressive neurologic disability. The development of MS is influenced by environmental factors, particularly the Epstein-Barr virus (EBV), and genetic factors, which include specific HLA types, particularly DRB1*1501-DQA1*0102-DQB1*0602, and a predisposition to autoimmunity in general. MS patients have increased circulating T-cell and antibody reactivity to myelin proteins and gangliosides. It is proposed that the role of EBV is to infect autoreactive B cells that then seed the CNS and promote the survival of autoreactive T cells there. It is also proposed that the clinical attacks of relapsing-remitting MS are orchestrated by myelin-reactive T cells entering the white matter of the CNS from the blood, and that the progressive disability in primary and secondary progressive MS is caused by the action of autoantibodies produced in the CNS by ­meningeal lymphoid follicles with germinal centers.

Experimental Analysis of Froude Number Effect on Air Entrainment in the Hydraulic Jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in rectangular horizontal flume with partially-developed inflow conditions. The vertical distributions of void fraction and air bubbles count rate were recorded for inflow Froude number Fr1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction Cmax increases with the increasing Fr1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was provided.

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves.

Effects of viscous dissipation and boundary conditions on forced convection in a channel occupied by a saturated porous medium

Forced convection with viscous dissipation in a parallel plate channel filled by a saturated porous medium is investigated numerically. Three different viscous dissipation models are examined. Two different sets of wall conditions are considered: isothermal and isoflux. Analytical expressions are also presented for the asymptotic temperature profile and the asymptotic Nusselt number. With isothermal walls, the Brinkman number significantly influences the developing Nusselt number but not the asymptotic one. At constant wall heat flux, both the developing and the asymptotic Nusselt numbers are affected by the value of the Brinkman number. The Nusselt number is sensitive to the porous medium shape factor under all conditions considered.

Perceptions of mental health service delivery among staff and Indigenous consumers: it's still about communication

Objective: A needs analysis was undertaken to determine the quality and effectiveness of mental health services to Indigenous consumers within a health district of Southern Queensland. The study focussed on identifying gaps in the service provision for Indigenous consumers. Tools and methodologies were developed to achieve this. Method: Data were collected through the distribution of questionnaires to the target populations: district health service staff and Indigenous consumers. Questionnaires were developed through consultation with the community and the Steering Committee in order to achieve culturally appropriate wording. Of prime importance was the adaptation of questionnaire language so it would be fully understood by Indigenous consumers. Both questionnaires were designed to provide a balanced perspective of current mental health service needs for Indigenous people within the mental health service. Results: Results suggest that existing mental health services do not adequately meet the needs of Indigenous people. Conclusions: Recommendations arising from this study indicate a need for better communication and genuine partnerships between the mental health service and Indigenous people that reflect respect of cultural heritage and recognises the importance of including Indigenous people in the design and management of mental health services. Attention to the recommendations from this study will help ensure a culturally appropriate and effective mental health service for Indigenous consumers.

The Indotriradites dolianitii Morphon, a distinctive group of miospore species from the Lower Carboniferous of Gondwana

An emended diagnosis and generic reallocation are proposed for the trilete miospore Indotriradites dolianitii (Daemon, 1974) Loboziak et al., comb. nov. A new species, I. daemonii Loboziak et al., sp. nov., from Viséan strata of Western Gondwana, is erected. These two species, together with I. zosteriformis (Playford et Satterthwait) Playford, 1991 from the Viséan of Australia, belong to a cohesive morphological miospore category, here termed the Indotriradites dolianitii Morphon, which is evidently restricted to the Lower Carboniferous of Gondwana.