Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Business education in operations management

This paper examines trends in the practice of Operations Management and in teaching the field in major Business Schools. Operations Management has been defined as the design and management of transformation processes that create value for society. The operations function is the one function directly involved in that transformation, and hence is directly responsible for the activities that justify the existence of the firm, both economically and as a value-creating organization in society. The top rated schools in Operations Management are the top-rated research-intensive Business Schools in the world. Operations Management is an area that has been undergoing rapid change in response to changes in business practices worldwide. It is at the heart of changes of which the AACSB report Management Education at Risk, August 2002 (p 20), comments of Business Schools in general: ‘With regard to global relevance (of Business Schools), the complex opportunities and challenges that emanate from the world scope of operations, outsourcing, supply chains, partnerships, and financial and consumer markets – all linked in real time through the Internet – are not reflected adequately in curricula and learning approaches.’ Products, and even services, depend increasingly on advanced technology. This is true globally and especially so for countries in South East and East Asia, from which Australian Universities draw a significant number of students. Services operations management has become much more important, while there are both educational and industrial needs in management science or operations research.

Australia's relationship with the United States: The case for greater independence

A number of recent events-especially attempts to negotiate a bilateral trade agreement and Australia's participation in the conflicts in Afghanistan and Iraq(1)-have thrown Australia's relationship with the United States into sharp relief. While this relationship has historically enjoyed strong bilateral endorsement, such uncritical support is beginning to unravel. At the very least, the relationship is being subjected to a renewed, more critical scrutiny. This paper argues that a dispassionate analysis of the relationship is appropriate and overdue. Not only are the benefits that accrue to 'Australia' from the relationship debateable, even when judged within the limited calculus of the 'national interest', but Australia's uncritical support for US foreign policy is also helping to entrench potentially damaging aspects of American foreign policy and somewhat ironically-undermining the legitimacy of its pre-eminent 'hegemonic' position.

Controlled oxidative protein refolding using an ion-exchange column

Column-based refolding of complex and highly disulfide-bonded proteins simplifies protein renaturation at both preparative and process scale by integrating and automating a number of operations commonly used in dilution refolding. Bovine serum albumin (BSA) was used as a model protein for refolding and oxido-shuffling on an ion-exchange column to give a refolding yield of 55 % after 40 Ih incubation. Successful on-column refolding was conducted at protein concentrations of up to 10 mg/ml and refolded protein, purified from misfolded forms, was eluted directly from the column at a concentration of 3 mg/ml. This technique integrates the dithiothreitol removal, refolding, concentration and purification steps, achieving a high level of process simplification and automation, and a significant saving in reagent costs when scaled. Importantly, the current result suggests that it is possible to controllably refold disulfide-bonded proteins using common and inexpensive matrices, and that it is not always necessary to control protein-surface interactions using affinity tags and expensive chromatographic matrices. Moreover, it is possible to strictly control the oxidative refolding environment once denatured protein is bound to the ion-exchange column, thus allowing precisely controlled oxido-shuffling. (c) 2005 Elsevier B.V. All rights reserved.

Gas dispersion measurements in industrial flotation cells

For nearly 100 years, the flotation plant metallurgist has often wondered what is happening 'beneath the froth'. To assist in unravelling this mystery, new technology has been developed as part of the Australian Mineral Industries Research Association (AMIRA) P9 project, to measure gas dispersion characteristics (such as gas hold-up, superficial gas velocity and bubble size) in industrial flotation cells. These measurements have been conducted in a large number of cells of different types and sizes by researchers from the Julius Kruttschnitt Mineral Research Centre (JKMRC) and JKTech. A large database has been developed and the contents of this database are described in this paper. Typical cell characterization measurements show a wide spread in values, even in the same cell types and sizes performing similar duties. In conventional flotation cells, the typical gas hold-up values range from 3% to 20%, bubble sizes range between I and 2 mm, and superficial gas velocity ranges from 1 to 2.5 cm/s. The ranges of cell characterization measurements given in this paper will enable plant personnel to compare their operation to other similar types of operations from around Australia and the rest of the world, giving opportunities for further improvement to flotation plant operations. (C) 2005 Elsevier Ltd. All rights reserved.

Verifying data refinements using a model checker

In this paper, we consider how refinements between state-based specifications (e.g., written in Z) can be checked by use of a model checker. Specifically, we are interested in the verification of downward and upward simulations which are the standard approach to verifying refinements in state-based notations. We show how downward and upward simulations can be checked using existing temporal logic model checkers. In particular, we show how the branching time temporal logic CTL can be used to encode the standard simulation conditions. We do this for both a blocking, or guarded, interpretation of operations (often used when specifying reactive systems) as well as the more common non-blocking interpretation of operations used in many state-based specification languages (for modelling sequential systems). The approach is general enough to use with any state-based specification language, and we illustrate how refinements between Z specifications can be checked using the SAL CTL model checker using a small example.

Gas dispersion measurements in industrial flotation cells

For nearly 100 years, the flotation plant metallurgist has often wondered what is happening ‘beneath the froth’. To assist in unravelling this mystery, new technology has been developed as part of the Australian Mineral Industries Research Association (AMIRA) P9 project, to measure gas dispersion characteristics (such as gas hold-up, superficial gas velocity and bubble size) in industrial flotation cells. These measurements have been conducted in a large number of cells of different types and sizes by researchers from the Julius Kruttschnitt Mineral Research Centre (JKMRC) and JKTech. A large database has been developed and the contents of this database are described in this paper. Typical cell characterisation measurements show a wide spread in values, even in the same cell types and sizes performing similar duties. In conventional flotation cells, the typical gas hold-up values range from 3 - 20 per cent, bubble sizes range between 1 and 2 mm, and superficial gas velocity ranges from 1 to 2.5 cm/s. The ranges of cell characterisation measurements given in this paper will enable plant personnel to compare their operation to other similar types of operations from around Australia and the rest of the world, giving opportunities for further improvement to flotation plant operations.